CPM Homework Help : CALC Problem 5-117

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

$\int _ { - 2 } ^ { 1 } ( 3 x + 1 ) ^ { 2 } d x$
Hint (a):
Before integrating, expand the integrand.

$\int \operatorname { csc } ^ { 2 } ( x ) d x$
Hint (b):
Think about the derivatives of common trig functions. Be mindful about the sign of your antiderivative.

$\int _ { x } ^ { 0 } \operatorname { sin } ( t ) d t$
Hint (c):
Refer to hint in part (b).

$\int _ { 0 } ^ { \pi } \operatorname { cot } ( x ) \operatorname { tan } ( x ) d x$
Hint (d):
Refer to hint in part (b).