91Ó°ÊÓ

Finding an Indefinite Integral In Exercises \(15-46\) , find the indefinite integral. $$ \int \frac{2}{7 e^{x}+4} d x $$

Differential Equation In Exercises \(33-36,\) solve the differential equation. $$ \frac{d s}{d \alpha}=\sin ^{2} \frac{\alpha}{2} \cos ^{2} \frac{\alpha}{2} $$

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

Evaluating an Improper Integral In Exercises \(33-48\) determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$\int_{0}^{5} \frac{10}{x} d x$$

Use integration tables to find the indefinite integral. \(\int \sqrt{\frac{5-x}{5+x}} d x\)

Finding an Indefinite Integral In Exercises \(27-34,\) use substitution and partial fractions to find the indefinite integral. $$ \int \frac{1}{\sqrt{x}-\sqrt[3]{x}} d x $$

Use integration tables to find the indefinite integral. \(\int \frac{x}{\sqrt{x^{4}-6 x^{2}+5}} d x\)

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

Evaluating an Improper Integral In Exercises \(33-48\) determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$ \int_{0}^{2} \frac{1}{\sqrt[3]{x-1}} d x $$

Differential Equation In Exercises \(33-36,\) solve the differential equation. $$ y^{\prime}=\tan ^{3} 3 x \sec 3 x $$