91Ó°ÊÓ

Finding an Indefinite Integral In Exercises \(15-46\) , find the indefinite integral. $$ \int \frac{3 x}{x+4} d x $$

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

Finding an Indefinite Integral Involving Secant and Tangent In Exercises \(19-32,\) find the indefinite integral. $$ \int \tan ^{3} \frac{\pi x}{2} \sec ^{2} \frac{\pi x}{2} d x $$

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

Use integration tables to find the indefinite integral. \(\int \frac{e^{x}}{1-\tan e^{x}} d x\)

Evaluating a Limit In Exercises \(11-42,\) evaluate the limit, using L'Hopital's Rule if necessary. $$ \lim _{x \rightarrow \infty} \frac{5 x+3}{x^{3}-6 x+2} $$

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

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

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

Finding an Indefinite Integral Involving Secant and Tangent In Exercises \(19-32,\) find the indefinite integral. $$ \int \tan ^{3} 2 t \sec ^{3} 2 t d t $$