CPM Homework Help : CALC Problem 9-135

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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.

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

$\int\operatorname{sen}m\operatorname{tan}m\operatorname{ln}(\operatorname{se}m)dm$
Hint (b):
Use substitution. Let $u =\operatorname{sec}(m)$ .
More Help (b):
$du =\operatorname{sec}(m)\operatorname{tan}(m)dm$

$\int \frac { 3 } { x ^ { 2 } + 4 x + 3 } d x$
Hint (c):
Use partial fraction decomposition to rewrite the integrand.
$\frac{3}{x^2+4x+3}=\frac{a}{x+3}+\frac{b}{x+1}$

$\int _ { 1 } ^ { \infty } \frac { 1 } { x ^ { 2 } } d x$
Hint (d):
This is an improper integral. Use a limit to properly evaluate this integral.

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