Question 1

Find $\int \frac { 5 x } { 2 x ^ { 2 } + 1 } d x$

Accepted Answer

A)  $\frac { 5 } { 2 } \ln \left( 2 x ^ { 2 } + 1 \right) + C$ 
B)  $\frac { 5 } { 4 } \ln \left( 2 x ^ { 2 } + 1 \right) + C$ 
C)  $\frac { 5 } { 2 } \ln \left( 2 x ^ { 2 } - 1 \right) + C$ 
D)  $\frac { 5 } { 4 } \ln \left( 2 x ^ { 2 } - 1 \right) + C$ 
A)  $\frac { 5 } { 2 } \ln \left( 2 x ^ { 2 } + 1 \right) + C$ 
B)  $\frac { 5 } { 4 } \ln \left( 2 x ^ { 2 } + 1 \right) + C$ 
C)  $\frac { 5 } { 2 } \ln \left( 2 x ^ { 2 } - 1 \right) + C$ 
D)  $\frac { 5 } { 4 } \ln \left( 2 x ^ { 2 } - 1 \right) + C$

Question 2

Find $\int \cos ^ { 5 } ( x ) \sin ^ { 4 } ( x ) d x$

Accepted Answer

The answer of Find \(\int \cos ^ { 5 }...

Question 3

Find $\int \frac { \csc ^ { 2 } ( x ) } { 1 + 2 \cot ( x ) } d x$

Accepted Answer

A)  $\ln | 1 + 2 \cot x | + C$ 
B)  $\frac { 1 } { 2 } \ln | 1 + 2 \cot x | + C$ 
C)  $\frac { - 1 } { 2 } \ln | 1 + 2 \cot x | + C$ 
D)  $- \ln | 1 + 2 \cot x | + C$ 
A)  $\ln | 1 + 2 \cot x | + C$ 
B)  $\frac { 1 } { 2 } \ln | 1 + 2 \cot x | + C$ 
C)  $\frac { - 1 } { 2 } \ln | 1 + 2 \cot x | + C$ 
D)  $- \ln | 1 + 2 \cot x | + C$

Question 4

Find $\int \frac { 1 } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$

Accepted Answer

The answer of Find \(\int \frac { 1 } {...

Find $\int \frac { 5 x } { 2 x ^ { 2 } + 1 } d x$

Find $\int \cos ^ { 5 } ( x ) \sin ^ { 4 } ( x ) d x$

Find $\int \frac { \csc ^ { 2 } ( x ) } { 1 + 2 \cot ( x ) } d x$

Find $\int \frac { 1 } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$

Limits

Derivatives

Applications of the Derivative

Definite Integrals

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Functions and Precalculus

Filters

Exam 5: Techniques of Integration

Find ∫5x2x2+1dx\int \frac { 5 x } { 2 x ^ { 2 } + 1 } d x∫2x2+15x​dx

Find ∫cos⁡5(x)sin⁡4(x)dx\int \cos ^ { 5 } ( x ) \sin ^ { 4 } ( x ) d x∫cos5(x)sin4(x)dx

Find ∫csc⁡2(x)1+2cot⁡(x)dx\int \frac { \csc ^ { 2 } ( x ) } { 1 + 2 \cot ( x ) } d x∫1+2cot(x)csc2(x)​dx

Find ∫1(x2+4)2dx\int \frac { 1 } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x∫(x2+4)21​dx

Limits

Derivatives

Applications of the Derivative

Definite Integrals

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Functions and Precalculus

Filters

Find $\int \frac { 5 x } { 2 x ^ { 2 } + 1 } d x$

Find $\int \cos ^ { 5 } ( x ) \sin ^ { 4 } ( x ) d x$

Find $\int \frac { \csc ^ { 2 } ( x ) } { 1 + 2 \cot ( x ) } d x$

Find $\int \frac { 1 } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$