### Home > CALC > Chapter 7 > Lesson 7.4.3 > Problem7-199

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.

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

Rewrite properly (with limits) before evaluating.

1. $\int \operatorname { tan } ^ { - 1 } x d x$

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.

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

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