### Home > CALC > Chapter 9 > Lesson 9.4.3 > Problem9-135

9-135.

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. $\int \frac { 1 } { y ( 2 - y ) } d y$

Use partial fraction decomposition to rewrite the integrand.
$\frac{1}{y(2-y)}=\frac{a}{y}+\frac{b}{2-y}$

1. $\int\operatorname{sen}m\operatorname{tan}m\operatorname{ln}(\operatorname{se}m)dm$

Use substitution. Let $u =\operatorname{sec}(m)$.

$du =\operatorname{sec}(m)\operatorname{tan}(m)dm$

1. $\int \frac { 3 } { x ^ { 2 } + 4 x + 3 } d x$

Use partial fraction decomposition to rewrite the integrand.
$\frac{3}{x^2+4x+3}=\frac{a}{x+3}+\frac{b}{x+1}$

1. $\int _ { 1 } ^ { \infty } \frac { 1 } { x ^ { 2 } } d x$

This is an improper integral. Use a limit to properly evaluate this integral.