91Ó°ÊÓ

Finding an Indefinite Integral In Exercises \(15-46\) , find the indefinite integral. $$ \int \frac{x+1}{\sqrt{3 x^{2}+6 x}} d x $$

Finding an Indefinite Integral In Exercises \(15-46\) , find the indefinite integral. $$ \int \frac{x^{2}}{x-1} d x $$

In Exercises 11–30, find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts.) $$ \int x \cos x d x $$

Finding an Indefinite Integral In Exercises \(21-36,\) find the indefinite integral. $$ \int \sqrt{16-4 x^{2}} d x $$

Evaluating a Definite Integral In Exercises \(23-26\) , evaluate the definite integral. Use a graphing utility to verify your result. $$ \int_{0}^{2} \frac{3}{4 x^{2}+5 x+1} d x $$

Evaluating an Improper Integral In Exercises \(17-32\) , determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{0}^{\infty} x^{2} e^{-x} d x $$

Evaluating a Limit In Exercises \(11-42,\) evaluate the limit, using L'Hopital's Rule if necessary. $$ \lim _{x \rightarrow \infty} \frac{5 x^{2}+3 x-1}{4 x^{2}+5} $$

Finding an Indefinite Integral Involving Secant and Tangent In Exercises \(19-32,\) find the indefinite integral. $$ \int \tan ^{5} \frac{x}{2} d x $$

Use integration tables to find the indefinite integral. \(\int e^{x} \arccos e^{x} d x\)

Finding an Indefinite Integral In Exercises \(21-36,\) find the indefinite integral. $$ \int \frac{1}{\sqrt{x^{2}-4}} d x $$