${\displaystyle \underset{a}{\overset{b}{}}}f(g(x))g^{\text{'}}(x)dx={\displaystyle \underset{g(a)}{\overset{(B)}{}}}f(u)du$

Example $3$ Evaluate the definite integrals.

$($a$){\displaystyle \underset{0}{\overset{4}{}}}\frac{x^2}{x^{3}1}dx$

$($b$){\displaystyle \underset{4}{\overset{25}{}}}\frac{1}{\sqrt[\phantom{2}]{x{e}^{-\sqrt[\phantom{2}]{x}}}}dx$

$($c$){\displaystyle \underset{e^3}{\overset{e^5}{}}}\frac{1}{x(lnx{)}^3}dx$

$($d$){\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^{4}xsinxdx$