Problem $18.$ Use integration by parts to evaluate the integrals.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}cosxdx$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^2-5x)e^{x}dx$

$($b$){\displaystyle \underset{1}{\overset{e}{}}}{x}^{3}lnxdx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xse{c}^{2}xdx$

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{-x}cosxdx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{3}4e^{-x}dx$

$($g$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sin(lnx)dx$

Problem $19.$ Evaluate the integrals.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^3\sqrt[\phantom{2}]{x^2+1}dx$

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{x}{e}^{\sqrt[\phantom{2}]{x}}dx$

$($k$){\displaystyle \underset{0}{\overset{1}{}}}x\sqrt[\phantom{2}]{1-x}dx$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{x}lnxdx$

$($g$){\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}{x}^{3}cos2xdx$

$($l$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ln(x+x^2)dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos\sqrt[\phantom{2}]{x}dx$

$($h$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}se{c}^{3}xdx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}sin{x}^{3}dx$

$($i$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}secxta{n}^{2}xdx$

$($m$){\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}xta{n}^{2}xdx$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^5{e}^{x^3}dx$

$($j$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xco{s}^{3}xdx$

$($n$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2dx}{x\sqrt[\phantom{2}]{1-4(lnx{)}^2}}$

Problem $20.$ Use integration by trigonometric substitution to evaluate the integrals.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{\sqrt[\phantom{2}]{9+x^2}}$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{xdx}{\sqrt[\phantom{2}]{1+x^4}}$

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

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{1-(lnx{)}^2}}{xlnx}dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{25-t^2}dt$

$($g$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{x-2}}{\sqrt[\phantom{2}]{x-1}}$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{\sqrt[\phantom{2}]{4x^2-49}},x>\frac{7}{2}$

$($h$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{4+x^2}dx$

Problem $21.$ Use integration by partial fraction decomposition to evaluate the integrals.

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

$($g$)\frac{dx}{((x^2-1){)}^2}$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+4}{x^2+5x-6}dx$

$($h$){\displaystyle \underset{0}{\overset{1}{}}}\frac{dx}{(x+1)(x^2+1)}$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^2+2x}$

$($i$){\displaystyle \underset{1}{\overset{\sqrt[\phantom{2}]{3}}{}}}\frac{3x^2+x+4}{x^3+x}dx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x+1}{x^2-7x+12}dx$

$($j$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{t^2+2t+1}{(t^2+1{)}^2}dt$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+3}{2x^3-8x}dx$

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

$($f$){\displaystyle \underset{0}{\overset{1}{}}}\frac{x^3}{x^2+2x+1}dx$

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