91Ó°ÊÓ

How would you evaluate \(\int \tan ^{10} x \sec ^{2} x d x ?\)

Set up the appropriate form of the partial fraction decomposition for the following expressions. Do not find the values of the unknown constants. $$\frac{x+3}{(x-5)^{2}}$$

Evaluate the following integrals or state that they diverge. $$\int_{3}^{\infty} \frac{d x}{x^{2}}$$

Evaluate the following integrals. $$\int_{0}^{\pi / 2} \frac{\sin \theta}{1+\cos ^{2} \theta} d \theta$$

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. $$\int \cos ^{-1} x d x$$

Set up the appropriate form of the partial fraction decomposition for the following expressions. Do not find the values of the unknown constants. $$\frac{2}{x^{3}-2 x^{2}+x}$$

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table. $$\int \sin 3 x \cos 2 x \, d x$$

Use a substitution to reduce the following integrals to \(\int \ln u\) du. Then evaluate the resulting integral using the formula for \(\int \ln x \, d x\). $$\int(\cos x) \ln (\sin x) d x$$

Evaluate the following integrals or state that they diverge. $$\int_{2}^{\infty} \frac{d x}{x}$$

Evaluate the following integrals. $$\int \cos ^{2} 10 x d x$$