Use integration by parts

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}4x{e}^{4x}dx$

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

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

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

Do multiple variable integration

$5.{\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{x}{\overset{1}{}}}xydydx$

$6.{\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{x}{}}}(x+y^2)dydx$

$7.{\displaystyle \underset{-1}{\overset{1}{}}}{\displaystyle \underset{x}{\overset{2}{}}}{x}^2+ydydx$