CPM Homework Help : CALC Problem 11-112

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.

$\int _ { - 1 } ^ { 1 } x ^ { - 1 / 3 } d x$
Hint (a):
The Reverse Chain Rule can be used here, but this is an improper integral, so be sure to use limits (for $x = 0$ ).

$\int \operatorname { cos } x \cdot e ^ { \operatorname { sin } x } d x$
Hint (b):
Let $u =\operatorname{sin}(x)$ .

$\int _ { - 6 } ^ { 6 } \operatorname { sin } ( x ^ { 3 } ) d x$
Hint (c):
Use the fact that the integrand is odd.

$\int \frac { \operatorname { cos } x } { \operatorname { sin } x } d x$
Hint (d):
Let $u =\operatorname{sin}(x)$ .