### Home > CALC > Chapter 10 > Lesson 10.1.8 > Problem10-80

10-80.

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy. After evaluating each integral, write a short description of your method.

1. $\int \frac { \operatorname { sec } ^ { 2 } t } { 1 + \operatorname { tan } t } d t$

Use substitution. Let $u =\operatorname{tan}(t)$.

1. $\int _ { 0 } ^ { 2 } \frac { 1 } { ( x - 2 ) ( x + 1 ) } d x$

Use partial fraction decomposition.

$1/(x – 2)$ is undefined when $x = 2$, so a limit needs to be used to evaluate this integral.

1. $\int \frac { d y } { d x } ( e ^ { \sqrt { 2 x } } ) d x$

Since this is the integral of a derivative, your answer should have $a^{\prime\prime}+ C^{\prime\prime}$.

1. $\int \frac { 1 } { x \sqrt { \operatorname { ln } x } } d x$

Use substitution. Let $u =\operatorname{ln}(x)$.