CPM Homework Help : CALC Problem 7-199

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.

$\int _ { - 1 } ^ { 3 } \frac { d x } { x }$
Hint (a):
Rewrite properly (with limits) before evaluating.

$\int \operatorname { tan } ^ { - 1 } x d x$
Hint (b):
Use integration by parts after you rewrite the integrand as $\operatorname{arctan}(x)$ .
Let $f(x) =\operatorname{arctan}(x)$ and $dg = dx$ .
Then $df =$ _______ and $g(x) =$ _______.
Warning: You will have to use $U$ -substitution to evaluate the integral.

$\int \frac { \operatorname { sin } \sqrt { x } d x } { \sqrt { x } }$

$\int _ { \pi / 3 } ^ { \pi / 2 } \operatorname { csc } ^ { 2 } x d x$