Exam 5: Techniques of Integration

Evaluate $\int _ { 0 } ^ { \sqrt { \pi / 2 } } x \cos \left( x ^ { 2 } \right) d x$

Find $\int \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 3 } + 2 x ^ { 2 } } d x$

Find $\int \frac { e ^ { 3 x } } { e ^ { 3 x } + 4 } d x$

Find $\int e ^ { - x } \cos ( x ) d x$

Find $\int \frac { 1 } { x ^ { 2 } + 4 } d x$

Evaluate $\int _ { - \pi / 4 } ^ { 0 } \frac { \sin ^ { 2 } ( x ) } { \cos ^ { 4 } ( x ) } d x$

Evaluate $\int _ { 0 } ^ { \pi / 2 } \cos ^ { 3 } ( x ) \sin ^ { 2 } ( x ) d x$

Find $\int \frac { 1 } { \sqrt { x ^ { 2 } - 6 x + 17 } } d x$

Evaluate $\int _ { 0 } ^ { 2 } x \sqrt { 2 - x } d x$

Use reference triangles and unit circle to write the given trigonometric composition as an algebraic function: $\sin \left( \cos ^ { - 1 } ( x ) \right)$

Evaluate $\int _ { 2 } ^ { 4 } \sqrt { x ^ { 2 } - 4 } d x$

Evaluate $\int _ { 1 }^{3} \ln x d x$

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

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

Find $\int \frac { \sqrt { 9 - x ^ { 2 } } } { x ^ { 2 } } d x$

Use reference triangles and unit circle to write the given trigonometric composition as an algebraic function: $\tan \left( \sec ^ { - 1 } ( x ) \right)$

Find $\int \frac { \sin ( \sqrt { x } ) } { \sqrt { x } } d x$

Evaluate $\int _ { - 1 } ^ { 1 } \tan ^ { - 1 } ( x ) d x$

Find $\int \sqrt { x ^ { 2 } + 9 } d x$

Find $\int x ^ { 2 } \ln x d x$