91Ó°ÊÓ

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

Evaluate the integral using integration by parts and substitution. (As we recommended in the text, "Try something!") $$\int \cos ^{-1} x d x$$

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). $$\int e^{x} \tan ^{-1}\left(e^{x}\right) d x$$

Determine whether the integral converges or diverges. Find the value of the integral if it converges. $$\int_{0}^{2} \frac{x}{x^{2}-1} d x$$

Evaluate the integral. $$\int\left(x^{2}+4\right)^{2} d x$$

Evaluate the integral using integration by parts and substitution. (As we recommended in the text, "Try something!") $$\int \tan ^{-1} x d x$$

Evaluate the integrals. $$\int \frac{1}{\sqrt{x^{2}+4}} d x$$

Evaluate the integral. $$\int x\left(x^{2}+4\right)^{2} d x$$

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). $$\int(\ln 4 x)^{3} d x$$

Determine whether the integral converges or diverges. Find the value of the integral if it converges. $$\int_{0}^{\infty} \frac{1}{(x-2)^{2}} d x$$