Integration by Substitution

$9\mathrm{.}1.$ Evaluate each integral using substitution.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}3y^2(y^3-4)dy$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos(t)\sqrt[\phantom{2}]{2sin(t)}dt$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos(4x)dx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{t}cos(1+e^t)dt$

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

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ta{n}^2(2t)se{c}^2(2t)dt$

$($g$){\displaystyle \underset{0}{\overset{1}{}}}\frac{sin(\sqrt[\phantom{2}]{x})}{\sqrt[\phantom{2}]{x}}dx$

$($h$){\displaystyle \underset{1}{\overset{3}{}}}\frac{dt}{3t+1}$

$($i$){\displaystyle \underset{0}{\overset{ln(e)}{}}}\frac{e^x}{e^x+1}dx$

$($j$){\displaystyle \underset{0}{\overset{2}{}}}\frac{dt}{1+(\frac{t^2}{4})}$

$($k$){\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}3sin(x)co{s}^4(x)dx$

$(1){\displaystyle \underset{0}{\overset{1}{}}}\frac{t}{\sqrt[\phantom{2}]{1+2t^2}}dt$