91Ó°ÊÓ

Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. $$\int \frac{9 x^{3}-3 x+1}{x^{3}-x^{2}} d x$$

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. $$\int \frac{d y}{y \sqrt{3+(\ln y)^{2}}}$$

Use any method to evaluate the integrals in Exercises \(15-38 .\) Most will require trigonometric substitutions, but some can be evaluated by other methods. $$\int \frac{x d x}{25+4 x^{2}}$$

Evaluate the integrals $$\int \sec ^{3} x \tan ^{3} x d x$$

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. $$\int \tan ^{-1} \sqrt{y} d y$$

Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. $$\int \frac{16 x^{3}}{4 x^{2}-4 x+1} d x$$

When solving Exercises \(33-40\), you may need to use a calculator or a computer. Find, to two decimal places, the areas of the surfaces generated by revolving the curves in Exercises 35 and 36 about the \(x\) -axis. $$y=x^{2} / 4, \quad 0 \leq x \leq 2$$

Evaluate the integrals. Some integrals do not require integration by parts. $$\int \frac{(\ln x)^{3}}{x} d x$$

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. $$\int \frac{1}{\sqrt{x^{2}+2 x+5}} d x$$ (Hint: Complete the square.)

Evaluate the integrals $$\int \sec ^{2} x \tan ^{2} x d x$$