91Ó°ÊÓ

Evaluate the following integrals using integration by parts. $$\int \frac{\ln x}{x^{10}} d x$$

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. $$\int \frac{e^{x}}{\sqrt{e^{2 x}+4}} d x$$

Evaluate the following integrals or state that they diverge. $$\int_{1}^{\infty} \frac{3 x^{2}+1}{x^{3}+x} d x$$

Give the partial fraction decomposition for the following expressions. $$\frac{6}{x^{2}-2 x-8}$$

Trapezoid Rule approximations Find the indicated Trapezoid Rule approximations to the following integrals. $$\int_{2}^{10} 2 x^{2} d x \text { using } n=2,4, \text { and } 8 \text { sub-intervals }$$

Evaluate the following integrals or state that they diverge. $$\int_{1}^{\infty} 2^{-x} d x$$

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. $$\int \frac{\sqrt{\ln ^{2} x+4}}{x} d x$$

Evaluate the following integrals. $$\int e^{x}\left(1+e^{x}\right)^{9}\left(1-e^{x}\right) d x$$

Trapezoid Rule approximations Find the indicated Trapezoid Rule approximations to the following integrals. \(\int_{1}^{9} x^{3} d x\) using \(n=2,4,\) and 8 sub-intervals

Give the partial fraction decomposition for the following expressions. $$\frac{x^{2}-4 x+11}{(x-3)(x-1)(x+1)}$$