$7\mathrm{.}15.$ Use a change $of$ variables $to$ evaluate the following integrals.

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

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

$(c){\displaystyle \underset{0}{\overset{1}{}}}\frac{1}{(t^2+1{)}^2}dt$ Hint: let $t=tanu.$

$(d){\displaystyle \underset{-1}{\overset{1}{}}}{x}^2{e}^{x^3}dx$

$(e){\displaystyle \underset{-1}{\overset{1}{}}}\frac{2t+3}{t^2+9}dt$