Evaluate the integral. You may need to complete the square or change variables to put the integral into a form with recognizable antiderivative. Hint: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{u^{2}1}dx=ta{n}^{-1}(u)c$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^{2}2x26}$

Evaluate the integral

${\displaystyle \underset{2}{\overset{4}{}}}\frac{1}{(x-3{)}^2}dx$

Evaluate the integral

${\displaystyle \underset{1}{\overset{}{}}}x{e}^{-x}dx$

Without integrating determine whether the integral

${\displaystyle \underset{1}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{x^{3}1}}dx$

converges or diverges. Explain. Hint: Compare the integrand to $g(x)=\frac{1}{\sqrt[\phantom{2}]{x^3}}.$

$32.$ Determine whether the integral converges or diverges. If it converges, evaluate it$.$

${\displaystyle \underset{0}{\overset{}{}}}{e}^{-x}cosxdx$

Determine whether the integral converges or diverges. If it converges, evaluate it$.$

${\displaystyle \underset{-}{\overset{}{}}}\frac{1}{x^{2}1}dx$