CPM Homework Help : CALC Problem 10-12

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.

$\int _ { 1 } ^ { 4 } \sqrt { 1 + \frac { 9 } { 4 } x } d x$
Hint (a):
$\int\Big(1+w\Big)^{1/2}dw=\frac{2}{3}\Big(1+w\Big)^{3/2}$

$\int 2 x \operatorname { csc } ( x ^ { 2 } ) \operatorname { cot } ( x ^ { 2 } ) d x$
Hint (b):
$\frac{d}{dx}\csc(x)=-\csc(x)\cot(x)$
More Help (b):
Use substitution. Let $u = x^2$

$\int \frac { e ^ { 1 / x } } { 2 x ^ { 2 } } d x$
Hint (c):
Use substitution. Let $u =\frac{1}{x}$ .

$\int _ { - 10 } ^ { 10 } \operatorname { cos } 0 d x$
Hint (d):
What is the value of $\operatorname{cos}(0)$ ?