CPM Homework Help : CALC Problem 7-157

Integrate. Show your steps—if you use u-substitution be sure to change the bounds of integration. Homework Help ✎

Step 1(a):

U = sinx
dU = cosx dx

Step 2(a):

$U\left ( \frac{\pi }{4} \right )=\text{ lower bound}$

U(0) = upper bound

Step 3(a):

Assemble the integral and then solve.

Hint (b):

U = sinx
dU = cosx dx

Hint (c):

Before you integrate, rewrite the integrand.

$= \int 3x^{2}-4-\frac{11}{x}+\frac{6}{x^{2}}dx=$

Answer (d):

sec⁻¹x + C (this is a special case)

Hint (e):

$\frac{d}{dx}\left ( \frac{1}{x} \right )=\text{ln}x$

Hint (f):

You could use U-Substitution.
Or you could expand the integrand and evaluate.