### Home > APCALC > Chapter 11 > Lesson 11.3.2 > Problem11-97

11-97.

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

1. $\int _ { - 1 } ^ { 1 } x ^ { - 1 / 3 } d x$

The Reverse Chain Rule can be used here, but this is an improper integral, so be sure to use limits (for $x = 0$).

1. $\int \cos(x) · e^{\sin(x)}dx$

Let $u = \sin(x)$.

1. $\int _ { - 6 } ^ { 6 } \operatorname { sin } ( x ^ { 3 } ) d x$

Use the fact that the integrand is odd.

1. $\int \frac { \operatorname { cos } ( x ) } { \operatorname { sin } ( x ) } d x$

Let $u = \sin(x)$.