Exam 8: Techniques of Integration

The integral $\int e ^ { 2 x } \sin x d x$ is

The integral $\int \frac { x } { x ^ { 2 } + 2 x + 10 } d x$ is

The integral $\int x ^ { 2 } \ln x d x$ is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { \pi } ^ { 2 \pi } \frac { \sin x } { x } d x,$ to three decimal places, is

The improper integral $\int _ { 0 } ^ { 1 } \frac { \ln x } { x } d x$ is

The integral $\int \frac { 1 } { x \sqrt { 4 x + 5 } } d x$ is

The integral $\int \sec ^ { 2 } x d x$ is

The number C of chipmunks in a small rural township t days after May 1, 2015, follows the logistic model $\frac { d C } { d t } = 1.56 C \left( 1 - \frac { C } { 2,000 } \right)$ . The number of chipmunks recorded on May 1, 2015, was 775. How many chipmunks were initially present in this scenario?

The integral $\int \tan ^ { - 1 } x d x$ is

The integral $\int \cos ( \ln x ) d x$ is

The integral $\int \frac { x ^ { 2 } } { \sqrt { 9 x ^ { 2 } - 4 } } d x$ is

The improper integral $\int _ { 1 } ^ { 2 } \frac { 2 x } { \sqrt { x ^ { 2 } - 1 } } d x$ is

The improper integral $\int _ { 0 } ^ { \infty } \frac { 1 } { e ^ { x } + e ^ { - x } } d x$ is

The integral $\int \frac { 1 } { \sqrt { 16 x ^ { 2 } - 1 } } d x$ is

The integral $\int \frac { 1 } { ( x - 1 ) \sqrt { x ^ { 2 } - 2 x + 2 } } d x$ is

The improper integral $\int _ { 0 } ^ { 1 } \frac { x } { x ^ { 2 } - 4 } d x$ is

The integral $\int \tan ^ { 2 } x d x$ is

The integral $\int \sin ^ { 2 } x d x$ is

The integral $\int \frac { 1 } { x ^ { 2 } \sqrt { x ^ { 2 } - 9 } } d x$ is

The integral $\int \frac { 1 } { ( x - 2 ) \sqrt { x ^ { 2 } - 4 x + 5 } } d x$ is