91Ó°ÊÓ

Evaluate the integrals. $$\int \cos x \cos 2 x \, d x$$

In exercises find the partial fractions decomposition and an antiderivative. If you have a CAS available, use it to check your answer. $$\frac{x-1}{x^{3}+4 x^{2}+4 x}$$

Evaluate the integrals. $$\int_{0}^{\pi / 4} \tan ^{4} x \sec ^{4} x d x$$

Use the Table of Integrals at the back of the book to find an antiderivative. Note: When checking the back of the book or a CAS for answers, beware of functions that look very different but that are equivalent (through a trig identity, for instance). $$\int \frac{\sqrt{6 x-x^{2}}}{(x-3)^{2}} d x$$

Evaluate the integral. $$\int_{0}^{\pi} \cos x e^{\sin x} d x$$

Use the Table of Integrals at the back of the book to find an antiderivative. Note: When checking the back of the book or a CAS for answers, beware of functions that look very different but that are equivalent (through a trig identity, for instance). $$\int \frac{\sec ^{2} x}{\tan x \sqrt{8 \tan x-\tan ^{2} x}} d x$$

Determine whether the integral converges or diverges. Find the value of the integral if it converges. $$\int_{1}^{5} \frac{2}{\sqrt{5-x}} d x$$

In exercises find the partial fractions decomposition and an antiderivative. If you have a CAS available, use it to check your answer. $$\frac{4 x-5}{x^{3}-3 x^{2}}$$

Evaluate the integrals. $$\int \sin x \sin 2 x \, d x$$

Evaluate the integral. $$\int_{0}^{\pi / 4} \sec ^{2} x e^{\tan x} d x$$