Home > APCALC > Chapter 10 > Lesson 10.1.8 > Problem10-98

10-98.

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy for each part. Evaluate each integral and briefly describe your method.

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

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

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 "$+ C$".

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

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