Deck 8: Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

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Question
Evaluate the definite integral <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Question
Write the form of the partial fraction decomposition for the following rational expression. <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use substitution to find the integral <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Write the form of the partial fraction decomposition for the following rational expression. <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Write the form of the partial fraction decomposition for the following rational expression. <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> (1/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> )arctan(x/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> ) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> (1/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> )arcsin(x/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> )+C
D) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> arctan(x/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px> ) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   <div style=padding-top: 35px>
Question
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use partial fractions to find <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
Question
Use substitution to find the integral <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 8: Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals
1
Evaluate the definite integral <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the definite integral   .</strong> A)   B)   C)   D)   E)
2
Write the form of the partial fraction decomposition for the following rational expression. <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)

A) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
B) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
C) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
D) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
E) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
3
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
4
Use partial fractions to find <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
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5
Use substitution to find the integral <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
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6
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
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7
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
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8
Write the form of the partial fraction decomposition for the following rational expression. <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)

A) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
B) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
C) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
D) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
E) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
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9
Write the form of the partial fraction decomposition for the following rational expression. <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)

A) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
B) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
C) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
D) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
E) <strong>Write the form of the partial fraction decomposition for the following rational expression.  </strong> A)   B)   C)   D)   E)
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10
Use partial fractions to find <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   .

A) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   (1/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   )arctan(x/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   ) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )
B) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )
C) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   (1/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   )arcsin(x/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   )+C
D) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )
E) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   arctan(x/ <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )   ) <strong>Use partial fractions to find   .</strong> A)   (1/   )arctan(x/   )   B)   C)   (1/   )arcsin(x/   )+C D)   E)   arctan(x/   )
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11
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
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12
Use partial fractions to find the integral <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find the integral   .</strong> A)   B)   C)   D)   E)
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13
Use partial fractions to find <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
B) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
C) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
D) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
E) <strong>Use partial fractions to find   .</strong> A)   B)   C)   D)   E)
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14
Use substitution to find the integral <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)   .

A) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
B) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
C) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
D) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
E) <strong>Use substitution to find the integral   .</strong> A)   B)   C)   D)   E)
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Unlock for access to all 14 flashcards in this deck.