Exam 8: Basic Integration Rules

$\text { Determine whether the improper integral } \int _ { 0 } ^ { \infty } \frac { 10 } { \sqrt { x } ( x + 81 ) } d x \text { diverges or converges. }$ Evaluate the integral if it converges.

$\text { Determine whether the improper integral } \int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt [ 3 ] { 1 - x } } d x \text { diverges or converges. }$ Evaluate the integral if it converges.

Use a table of integrals to find the integral. $\int \frac { \sqrt { 49 - x ^ { 4 } } } { x } d x$

$\text { Determine whether the improper integral } \int _ { 4 } ^ { \infty } \frac { 2 } { x ^ { 3 } } d x \text { diverges or converges. Evaluate }$ the integral if it converges.

$\text { Use partial fractions to find the integral } \int \frac { 12 x ^ { 2 } + 5 x + 225 } { x ^ { 3 } + 25 x } d x$

$\text { Find } \int \frac { \sqrt { 16 x ^ { 2 } + 9 } } { x ^ { 4 } } d x \text {. }$

$\text { Use partial fractions to find the integral } \int \frac { 3 x ^ { 3 } - 28 x ^ { 2 } + 39 x + 82 } { x ^ { 2 } - 10 x + 21 } d x \text {. }$

$\text { Evaluate the limit } \lim _ { x \rightarrow \infty } \frac { 56 - 7 x + 8 x ^ { 2 } } { 5 x ^ { 2 } - 7 } \text { first by using techniques from Chapter } 3 \text { then }$ by using L'Hopital's Rule.

$\text { Solve } \frac { d y } { d x } = x ^ { 2 } \sqrt { x - 32 }$

Find the indefinite integral. $\int \tan ^ { 5 } \left( \frac { x } { 5 } \right) d x$

$\text { Use partial fractions to find the integral } \int \frac { 16 x - 136 } { x ^ { 2 } - 16 x + 60 } d x \text {. }$

Find the indefinite integral. $\int \frac { 3 } { ( w - 4 ) ^ { 7 } } d w$

$\text { Use integration tables to evaluate the integral } \int _ { 0 } ^ { 1 } \sqrt { 63 + x ^ { 2 } } d x \text {. }$

Use a table of integrals with forms involving the trigonometric functions to find the integral. $\int \frac { 1 } { 1 + e ^ { 5 x } } d x$

Find the indefinite integral. $\int 6 ( x - 12 ) ^ { 5 } d x$

Find the indefinite integral. $\int \sin ^ { 3 } 2 x \cos ^ { 4 } 2 x d x$

Find the indefinite integral. $\int \frac { 1 } { x \sqrt { 9 + 49 x ^ { 2 } } } d x$

$\text { Use integration tables to evaluate the integral } \int _ { 0 } ^ { 1 } x ^ { 9 } e ^ { x ^ { 10 } } d x \text {. }$

$\text { Evaluate the } \lim _ { x \rightarrow \infty } \frac { 5 x ^ { 2 } + 4 x - 8 } { 9 x ^ { 2 } + 9 } \text { using L'Hôpital's Rule if necessary. }$