Exam 8: Techniques of Integration

The integral $\int \frac { x - 1 } { x ^ { 2 } + 2 x + 10 } d x$ is

The integral $\int \frac { 1 } { \left( \sqrt { 4 x - x ^ { 2 } } \right) ^ { 3 } } d x$ is

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

The improper integral $\int _ { - \infty } ^ { 0 } \frac { 5 } { ( x - 4 ) ^ { 2 } } d x$ is

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

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

The integral $\int \tan ^ { 4 } x d x$ is

Using the Trapezoidal Rule with n = 3, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { x ^ { 2 } } d x$ to three decimal places, is

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

The integral $\int x ^ { 3 } ( \ln x ) ^ { 2 } d x$ is

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

The integral $\int \tan ^ { 5 } x \sec ^ { 2 } x d x$ is

The integral $\int \sin ( 2 x ) \sin ( 3 x ) d x$ is

The integral $\int \frac { x } { x ^ { 2 } - 2 x - 3 } d x$ is

The integral $\int \frac { 1 } { 9 x ^ { 2 } - 4 } d x$ is

The number of subintervals needed to guarantee that the Simpson's Rule approximates $\int _ { \pi } ^ { 2 \pi } \frac { \sin x } { x } d x$ to within 0.0001 is

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

The integral $\int x \sin x d x$ is

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

Using the Trapezoidal Rule with n = 6, the approximated value of $\int _ { \frac { \pi } { 2 } } ^ { \frac { 3 \pi } { 2 } } \frac { \sin x } { x } d x,$ to three decimal places, is