91Ó°ÊÓ

In exercises find the partial fractions decomposition and an antiderivative. If you have a CAS available, use it to check your answer. $$\frac{x^{3}+x+2}{x^{2}+2 x-8}$$

Determine whether the integral converges or diverges. Find the value of the integral if it converges. $$\int_{0}^{1} x^{-4 / 3} d x$$

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). $$\int_{0}^{\ln 4} \sqrt{16-e^{2 x}} d x$$

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

Evaluate the integrals. $$\int \sin ^{4} x d x$$

Evaluate the integrals. $$\int x^{2} e^{x^{3}} d x$$

In exercises find the partial fractions decomposition and an antiderivative. If you have a CAS available, use it to check your answer. $$\begin{aligned} &\frac{x^{2}+1}{x^{2}-5 x-6}\\\ &2 \end{aligned}$$

In exercises find the partial fractions decomposition and an antiderivative. If you have a CAS available, use it to check your answer. $$\frac{5 x-23}{6 x^{2}-11 x-7}$$

Determine whether the integral converges or diverges. Find the value of the integral if it converges. $$\int_{1}^{\infty} x^{-4 / 5} d x$$

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). $$\int_{0}^{\ln 2} \frac{e^{x}}{\sqrt{e^{2 x}+4}} d x$$