EXERCISE SET $5\mathrm{.}3$

$1-12$ Evaluate the integrals using the indicated substitutions.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}2x(x^2+1{)}^{23}dx$;$u=x^2+1$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}co{s}^{3}xsinxdx$;$u=cosx$

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos2xdx$;$u=2x$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xse{c}^2{x}^{2}dx$;$u=x^2$

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x\sqrt[\phantom{2}]{9x^2-1}}$;$u=3x$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{\sqrt[\phantom{2}]{x}(1+x)}$;$u=\sqrt[\phantom{2}]{x}$