Question 1

Find the general solution of the differential equation below and check the result by differentiation. $$\frac { d T } { d x } = 28 x ^ { 6 }$$

Accepted Answer

A)  $T ( x ) = 168 x ^ { 5 }$ 
B)  $T ( x ) = 4 x ^ { 2 } + C$ 
C)  $T ( x ) = 168 x ^ { 5 } + C$ 
D)  $T ( x ) = 4 x ^ { 7 } + 1$ 
E)  $T ( x ) = 4 x ^ { 2 }$ 
A)  $T ( x ) = 168 x ^ { 5 }$ 
B)  $T ( x ) = 4 x ^ { 2 } + C$ 
C)  $T ( x ) = 168 x ^ { 5 } + C$ 
D)  $T ( x ) = 4 x ^ { 7 } + 1$ 
E)  $T ( x ) = 4 x ^ { 2 }$

Question 2

Find the indefinite integral. $\int e ^ { - 2 x } d x$

Accepted Answer

A)  $- \frac { 1 } { 2 } e ^ { - 2 x } + C$ 
B)  $- \frac { 1 } { 2 x } e ^ { - 2 x } + C$ 
C)  $\frac { 1 } { 2 } e ^ { - 2 x } + C$ 
D)  $- 2 e ^ { - 2 x } + C$ 
E)  $e ^ { - 2 x } + C$ 
A)  $- \frac { 1 } { 2 } e ^ { - 2 x } + C$ 
B)  $- \frac { 1 } { 2 x } e ^ { - 2 x } + C$ 
C)  $\frac { 1 } { 2 } e ^ { - 2 x } + C$ 
D)  $- 2 e ^ { - 2 x } + C$ 
E)  $e ^ { - 2 x } + C$

Question 3

$\text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. }$

Accepted Answer

A) $\frac { ( 1 + 4 z ) ^ { 6 } } { 20 } + C$ 
B)  $\frac { ( 1 + 4 z ) ^ { 6 } } { 6 } + C$ 
C)  $\frac { ( 1 + 4 z ) ^ { 6 } } { 24 } + C$ 
D)  $6 ( 1 + 4 z ) ^ { 6 } + C$ 
E)  $\frac { ( 1 + 4 z ) ^ { 6 } } { 5 } + C$ 
A) $\frac { ( 1 + 4 z ) ^ { 6 } } { 20 } + C$ 
B)  $\frac { ( 1 + 4 z ) ^ { 6 } } { 6 } + C$ 
C)  $\frac { ( 1 + 4 z ) ^ { 6 } } { 24 } + C$ 
D)  $6 ( 1 + 4 z ) ^ { 6 } + C$ 
E)  $\frac { ( 1 + 4 z ) ^ { 6 } } { 5 } + C$

Question 4

Evaluate the integral. $\int _ { 5 } ^ { 6 } \left( - 12 u ^ { 3 } - 2 u \right) d u$
given,
$\int x ^ { 3 } d x = \frac { 671 } { 4 }$
$\int x ^ { 2 } d x = \frac { 91 } { 3 }$
$\int x d x = \frac { 11 } { 2 }$
$\int _ { 5 } ^ { 6 } d x = 1$

Accepted Answer

A)  $- 65$ 
B)  $- 2377$ 
C)  $- 66$ 
D)  $- 2024$ 
E)  $- 2025$ 
A)  $- 65$ 
B)  $- 2377$ 
C)  $- 66$ 
D)  $- 2024$ 
E)  $- 2025$

Question 5

Find the smallest n such that the error estimate from the error formula in the approximation of the definite integral $\int _ { 0 } ^ { 2 } \sqrt { x + 7 } d x$ is less than $0.00001$ using the Trapezoidal Rule.

Accepted Answer

A)  49 
B)  26 
C)  73 
D)  30 
E)  15 
A)  49 
B)  26 
C)  73 
D)  30 
E)  15

Question 6

Use the properties of summation and Theorem 5.2 to evaluate the sum. $$\sum _ { i = 1 } ^ { 22 } \left( 2 i ^ { 2 } + 3 \right)$$

Accepted Answer

A)  239 
B)  7,656 
C)  7,612 
D)  3,861 
E)  7,590 
A)  239 
B)  7,656 
C)  7,612 
D)  3,861 
E)  7,590

Question 7

$\text { Find the solution of the differential equation } \frac { d y } { d x } = \frac { 2 } { 5 - x } \text { which passes through the }$ point $( 4,0 )$.

Accepted Answer

A)  $y = \frac { 1 } { 2 } \ln | 5 - x |$ 
B)  $y = - \frac { 1 } { 2 } \ln | 5 - x |$ 
C)  $y = - \frac { 1 } { 5 } \ln | 2 - x |$ 
D)  $y = - 2 \ln | 5 - x |$ 
E)  $y = 2 \ln | 5 - x |$ 
A)  $y = \frac { 1 } { 2 } \ln | 5 - x |$ 
B)  $y = - \frac { 1 } { 2 } \ln | 5 - x |$ 
C)  $y = - \frac { 1 } { 5 } \ln | 2 - x |$ 
D)  $y = - 2 \ln | 5 - x |$ 
E)  $y = 2 \ln | 5 - x |$

Question 8

Find table lists several measurements gathered in an experiment to approximate an unknown continuous function $y = f ( x )$. Approximate the integral $\int _ { 0 } ^ { 2 } f ( x ) d x$ using the Simpson's Rule. Round your answer to three decimal places.
$\begin{array}{|l|l|l|l|l|l|l|l|l|l|}
\hline x & 0.00 & 0.25 & 0.50 & 0.75 & 1.00 & 1.25 & 1.50 & 1.75 & 2.00 \
\hline y & 4.72 & 4.77 & 4.82 & 6.17 & 6.52 & 7.17 & 7.32 & 7.97 & 8.02 \
\hline
\end{array}$

Accepted Answer

A)  $12.197$ 
B)  $8.518$ 
C)  $15.975$ 
D)  $12.865$ 
E)  $11.628$ 
A)  $12.197$ 
B)  $8.518$ 
C)  $15.975$ 
D)  $12.865$ 
E)  $11.628$

Question 9

Evaluate the following definite integral by the limit definition. $$\int _ { 5 } ^ { 10 } 15 u ^ { 2 } d u$$

Accepted Answer

A)  4375 
B)  $\frac { 12328 } { 3 }$ 
C)  4372 
D)  1125 
E)  $\frac { 4375 } { 3 }$ 
A)  4375 
B)  $\frac { 12328 } { 3 }$ 
C)  4372 
D)  1125 
E)  $\frac { 4375 } { 3 }$

Question 10

Evaluate the definite integral of a function $\int _ { 0 } ^ { 1 } u ^ { \frac { 3 } { 2 } } d u \text {. Use a graphing utility to verify }$ your results.

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 9 } { 7 }$ 
C)  $\frac { 7 } { 8 }$ 
D)  $\frac { 2 } { 5 }$ 
E)  $\frac { 5 } { 6 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 9 } { 7 }$ 
C)  $\frac { 7 } { 8 }$ 
D)  $\frac { 2 } { 5 }$ 
E)  $\frac { 5 } { 6 }$

Question 11

Suppose that the probability that a person will remember between $100 a \% \text { and } 100 b \%$ of material learned in an experiment is $P _ { a , b } = \int _ { a } ^ { b } \frac { 15 } { 4 } x \sqrt { 1 - x } d x$ where $x$ represents the proportion
remembered. Determine from the figure below, the probability that a randomly chosen individual will recall between $50 \%$ and $75 \%$ of the material? Express your answer as a percent rounded to three decimal places.

Accepted Answer

A)  $19.900 \%$ 
B)  $12.500 \%$ 
C)  $11.000 \%$ 
D)  $35.300 \%$ 
E)  $106.600 \%$ 
A)  $19.900 \%$ 
B)  $12.500 \%$ 
C)  $11.000 \%$ 
D)  $35.300 \%$ 
E)  $106.600 \%$

Question 12

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 8 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.
$\int _ { 4 } ^ { 5 } \sqrt { 4 + t ^ { 5 } } d t$

Accepted Answer

A)  The Trapezoidal rule gives $43.377044$ and Simpson's rule gives $45.513198$. 
B)  The Trapezoidal rule gives $43.345903$ and Simpson's rule gives $43.335523$. 
C)  The Trapezoidal rule gives 43.377044 and Simpson's rule gives 43.335523. 
D)  The Trapezoidal rule gives $43.345903$ and Simpson's rule gives $45.513198$. 
E)  The Trapezoidal rule gives $- 43.345903$ and Simpson's rule gives $- 43.335523$. 
A)  The Trapezoidal rule gives $43.377044$ and Simpson's rule gives $45.513198$. 
B)  The Trapezoidal rule gives $43.345903$ and Simpson's rule gives $43.335523$. 
C)  The Trapezoidal rule gives 43.377044 and Simpson's rule gives 43.335523. 
D)  The Trapezoidal rule gives $43.345903$ and Simpson's rule gives $45.513198$. 
E)  The Trapezoidal rule gives $- 43.345903$ and Simpson's rule gives $- 43.335523$.

Question 13

Evaluate the following definite integral by the limit definition. $$\int _ { - 2 } ^ { 1 } 5 s ^ { 3 } d s$$

Accepted Answer

A)  $\frac { 49 } { 4 }$ 
B)  $- \frac { 75 } { 4 }$ 
C)  $\frac { 45 } { 4 }$ 
D)  $- \frac { 71 } { 4 }$ 
E)  $- 15$ 
A)  $\frac { 49 } { 4 }$ 
B)  $- \frac { 75 } { 4 }$ 
C)  $\frac { 45 } { 4 }$ 
D)  $- \frac { 71 } { 4 }$ 
E)  $- 15$

Question 14

$\text { The rate of disbursement } d Q / d t \text { of a } 2 \text { million dollar federal grant is proportional to }$ the square of $100 - t$. Time $t$ is measured in days $( 0 \leq t \leq 100 )$ and $Q$ is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 30 days. Assume that all the money will be disbursed in 100 days.

Accepted Answer

A)  $\$ 686,000$ 
B)  $\$ 50,700$ 
C)  $\$ 101,400$ 
D)  $\$ 33,800$ 
E)  $\$ 1,029,000$ 
A)  $\$ 686,000$ 
B)  $\$ 50,700$ 
C)  $\$ 101,400$ 
D)  $\$ 33,800$ 
E)  $\$ 1,029,000$

Question 15

Find the general solution of the differential equation below and check the result by differentiation. $$\frac { d Y } { d u } = \frac { 9 } { 4 } u ^ { \frac { 5 } { 4 } }$$

Accepted Answer

A) 
$$Y ( u ) = \frac { 45 } { 16 } u ^ { \frac { 9 } { 4 } } + C$$ 
B) 
$$Y ( u ) = u ^ { \frac { 9 } { 4 } } + C$$ 
C) 
$$Y ( u ) = \frac { 45 } { 16 } u ^ { \frac { 1 } { 4 } } + C ^ { 4 }$$ 
D) 
$$Y ( u ) = \frac { 9 } { 4 } u ^ { \frac { 9 } { 4 } } + C$$ 
E) 
$$Y ( u ) = u ^ { \frac { 9 } { 4 } }$$ 
A) 
$$Y ( u ) = \frac { 45 } { 16 } u ^ { \frac { 9 } { 4 } } + C$$ 
B) 
$$Y ( u ) = u ^ { \frac { 9 } { 4 } } + C$$ 
C) 
$$Y ( u ) = \frac { 45 } { 16 } u ^ { \frac { 1 } { 4 } } + C ^ { 4 }$$ 
D) 
$$Y ( u ) = \frac { 9 } { 4 } u ^ { \frac { 9 } { 4 } } + C$$ 
E) 
$$Y ( u ) = u ^ { \frac { 9 } { 4 } }$$

Question 16

$\text { Find the average value of } f ( x ) = \frac { 5 \left( x ^ { 2 } + 5 \right) } { x ^ { 2 } } \text { on the interval } [ 1,3 ] \text {. }$

Accepted Answer

A)  $\frac { 40 } { 3 }$ 
B)  35 
C)  $\frac { 25 } { 3 }$ 
D)  $\frac { 80 } { 3 }$ 
E)  40 
A)  $\frac { 40 } { 3 }$ 
B)  35 
C)  $\frac { 25 } { 3 }$ 
D)  $\frac { 80 } { 3 }$ 
E)  40

Question 17

$\text { Use Simpson's Rule to approximate the value of the definite integral } \int _ { 0 } ^ { 8 } 2 \sqrt [ 4 ] { x } d x \text { with }$ $n = 8$. Round your answer to four decimal places

Accepted Answer

A)  $16.9283$ 
B)  $22.3017$ 
C)  $21.1805$ 
D)  $24.5441$ 
E)  $18.5139$ 
A)  $16.9283$ 
B)  $22.3017$ 
C)  $21.1805$ 
D)  $24.5441$ 
E)  $18.5139$

Question 18

Write the limit $\lim _ { | \Delta | \rightarrow 0 } \sum _ { i = 1 } ^ { n } \left( \frac { 6 } { c _ { i } ^ { 2 } } \right) \Delta x _ { i } , \text { as a definite integral on the interval } [ 8,10 ]$ where ci is any point in the $i ^ { t h }$ subinterval.

Accepted Answer

A)  $\int _ { 10 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$ 
B)  $\int _ { 0 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$ 
C)  $\int _ { 0 } ^ { 2 } \frac { 6 } { x ^ { 2 } } d x$ 
D)  $\int _ { 0 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$ 
E) $\int _ { 8 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$ 
A)  $\int _ { 10 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$ 
B)  $\int _ { 0 } ^ { 8 } \frac { 6 } { x ^ { 2 } } d x$ 
C)  $\int _ { 0 } ^ { 2 } \frac { 6 } { x ^ { 2 } } d x$ 
D)  $\int _ { 0 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$ 
E) $\int _ { 8 } ^ { 10 } \frac { 6 } { x ^ { 2 } } d x$

Question 19

Find the indefinite integral. $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$

Accepted Answer

A)  $\frac { \ln \left| - 4 x ^ { 2 } + 9 \right| } { - 4 x ^ { 2 } + 9 } + C$ 
B)  $\frac { - 1 } { 8 } \ln \left| - 4 x ^ { 2 } + 9 \right| + C$ 
C)  $\ln \left| - 4 x ^ { 2 } + 9 \right| + C$ 
D)  $\ln \left| - 4 x ^ { 2 } - 9 \right| + C$ 
E)  $\frac { 1 } { - 8 x } + C$ 
A)  $\frac { \ln \left| - 4 x ^ { 2 } + 9 \right| } { - 4 x ^ { 2 } + 9 } + C$ 
B)  $\frac { - 1 } { 8 } \ln \left| - 4 x ^ { 2 } + 9 \right| + C$ 
C)  $\ln \left| - 4 x ^ { 2 } + 9 \right| + C$ 
D)  $\ln \left| - 4 x ^ { 2 } - 9 \right| + C$ 
E)  $\frac { 1 } { - 8 x } + C$

Question 20

Find the indefinite integral $$\int \left( - 9 t ^ { 2 } + 14 t - 2 \right) d t$$

Accepted Answer

A)  $- 9 t ^ { 3 } + 14 t ^ { 2 } - 2 t + C$ 
B)  $- 3 t ^ { 3 } + 14 t ^ { 2 } - 2 t + C$ 
C)  $- 3 t ^ { 3 } + 7 t ^ { 2 } - 2 t + C$ 
D)  $- 18 t ^ { 2 } + 14 t + C$ 
E)  $- 9 t ^ { 3 } + 14 t ^ { 2 } - 2 + C$ 
A)  $- 9 t ^ { 3 } + 14 t ^ { 2 } - 2 t + C$ 
B)  $- 3 t ^ { 3 } + 14 t ^ { 2 } - 2 t + C$ 
C)  $- 3 t ^ { 3 } + 7 t ^ { 2 } - 2 t + C$ 
D)  $- 18 t ^ { 2 } + 14 t + C$ 
E)  $- 9 t ^ { 3 } + 14 t ^ { 2 } - 2 + C$

Find the general solution of the differential equation below and check the result by differentiation. $\frac { d T } { d x } = 28 x ^ { 6 }$

Find the indefinite integral. $\int e ^ { - 2 x } d x$

$\text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. }$

Evaluate the integral. $\int _ { 5 } ^ { 6 } \left( - 12 u ^ { 3 } - 2 u \right) d u$ given, $\int x ^ { 3 } d x = \frac { 671 } { 4 }$ $\int x ^ { 2 } d x = \frac { 91 } { 3 }$ $\int x d x = \frac { 11 } { 2 }$ $\int _ { 5 } ^ { 6 } d x = 1$

Find the smallest n such that the error estimate from the error formula in the approximation of the definite integral $\int _ { 0 } ^ { 2 } \sqrt { x + 7 } d x$ is less than $0.00001$ using the Trapezoidal Rule.

Use the properties of summation and Theorem 5.2 to evaluate the sum. $\sum _ { i = 1 } ^ { 22 } \left( 2 i ^ { 2 } + 3 \right)$

$\text { Find the solution of the differential equation } \frac { d y } { d x } = \frac { 2 } { 5 - x } \text { which passes through the }$ point $( 4,0 )$ .

Evaluate the following definite integral by the limit definition. $\int _ { 5 } ^ { 10 } 15 u ^ { 2 } d u$

Evaluate the definite integral of a function $\int _ { 0 } ^ { 1 } u ^ { \frac { 3 } { 2 } } d u \text {. Use a graphing utility to verify }$ your results.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 8 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. $\int _ { 4 } ^ { 5 } \sqrt { 4 + t ^ { 5 } } d t$

Evaluate the following definite integral by the limit definition. $\int _ { - 2 } ^ { 1 } 5 s ^ { 3 } d s$

Find the general solution of the differential equation below and check the result by differentiation. $\frac { d Y } { d u } = \frac { 9 } { 4 } u ^ { \frac { 5 } { 4 } }$

$\text { Find the average value of } f ( x ) = \frac { 5 \left( x ^ { 2 } + 5 \right) } { x ^ { 2 } } \text { on the interval } [ 1,3 ] \text {. }$

$\text { Use Simpson's Rule to approximate the value of the definite integral } \int _ { 0 } ^ { 8 } 2 \sqrt [ 4 ] { x } d x \text { with }$ $n = 8$ . Round your answer to four decimal places

Write the limit $\lim _ { | \Delta | \rightarrow 0 } \sum _ { i = 1 } ^ { n } \left( \frac { 6 } { c _ { i } ^ { 2 } } \right) \Delta x _ { i } , \text { as a definite integral on the interval } [ 8,10 ]$ where ci is any point in the $i ^ { t h }$ subinterval.

Find the indefinite integral. $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$

Find the indefinite integral $\int \left( - 9 t ^ { 2 } + 14 t - 2 \right) d t$

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 5: Antiderivatives and Indefinite Integration

Find the general solution of the differential equation below and check the result by differentiation. dTdx=28x6\frac { d T } { d x } = 28 x ^ { 6 }dxdT​=28x6

Find the indefinite integral. ∫e−2xdx\int e ^ { - 2 x } d x∫e−2xdx

Find the indefinite integral ∫(1+4z)5dz. \text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. } Find the indefinite integral ∫(1+4z)5dz.

Find the smallest n such that the error estimate from the error formula in the approximation of the definite integral ∫02x+7dx\int _ { 0 } ^ { 2 } \sqrt { x + 7 } d x∫02​x+7​dx is less than 0.000010.000010.00001 using the Trapezoidal Rule.

Use the properties of summation and Theorem 5.2 to evaluate the sum. ∑i=122(2i2+3)\sum _ { i = 1 } ^ { 22 } \left( 2 i ^ { 2 } + 3 \right)∑i=122​(2i2+3)

Evaluate the following definite integral by the limit definition. ∫51015u2du\int _ { 5 } ^ { 10 } 15 u ^ { 2 } d u∫510​15u2du

Evaluate the definite integral of a function ∫01u32du. Use a graphing utility to verify \int _ { 0 } ^ { 1 } u ^ { \frac { 3 } { 2 } } d u \text {. Use a graphing utility to verify }∫01​u23​du. Use a graphing utility to verify your results.

Evaluate the following definite integral by the limit definition. ∫−215s3ds\int _ { - 2 } ^ { 1 } 5 s ^ { 3 } d s∫−21​5s3ds

Find the general solution of the differential equation below and check the result by differentiation. dYdu=94u54\frac { d Y } { d u } = \frac { 9 } { 4 } u ^ { \frac { 5 } { 4 } }dudY​=49​u45​

Find the average value of f(x)=5(x2+5)x2 on the interval [1,3]. \text { Find the average value of } f ( x ) = \frac { 5 \left( x ^ { 2 } + 5 \right) } { x ^ { 2 } } \text { on the interval } [ 1,3 ] \text {. } Find the average value of f(x)=x25(x2+5)​ on the interval [1,3].

Find the indefinite integral. ∫x−4x2+9dx\int \frac { x } { - 4 x ^ { 2 } + 9 } d x∫−4x2+9x​dx

Find the indefinite integral ∫(−9t2+14t−2)dt\int \left( - 9 t ^ { 2 } + 14 t - 2 \right) d t∫(−9t2+14t−2)dt

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Find the general solution of the differential equation below and check the result by differentiation. $\frac { d T } { d x } = 28 x ^ { 6 }$

Find the indefinite integral. $\int e ^ { - 2 x } d x$

$\text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. }$

Find the smallest n such that the error estimate from the error formula in the approximation of the definite integral $\int _ { 0 } ^ { 2 } \sqrt { x + 7 } d x$ is less than $0.00001$ using the Trapezoidal Rule.

Use the properties of summation and Theorem 5.2 to evaluate the sum. $\sum _ { i = 1 } ^ { 22 } \left( 2 i ^ { 2 } + 3 \right)$

Evaluate the following definite integral by the limit definition. $\int _ { 5 } ^ { 10 } 15 u ^ { 2 } d u$

Evaluate the definite integral of a function $\int _ { 0 } ^ { 1 } u ^ { \frac { 3 } { 2 } } d u \text {. Use a graphing utility to verify }$ your results.

Evaluate the following definite integral by the limit definition. $\int _ { - 2 } ^ { 1 } 5 s ^ { 3 } d s$

Find the general solution of the differential equation below and check the result by differentiation. $\frac { d Y } { d u } = \frac { 9 } { 4 } u ^ { \frac { 5 } { 4 } }$

$\text { Find the average value of } f ( x ) = \frac { 5 \left( x ^ { 2 } + 5 \right) } { x ^ { 2 } } \text { on the interval } [ 1,3 ] \text {. }$

Find the indefinite integral. $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$

Find the indefinite integral $\int \left( - 9 t ^ { 2 } + 14 t - 2 \right) d t$