Problem $1$: Evaluate each integral. For definite integrals be sure to use the change of variables formula to create new bounds.

a$.{\displaystyle \underset{0}{\overset{1}{}}}{t}^2{e}^{t}dt$

f$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dt}{(16-t^2{)}^{\frac{3}{2}}}$

b$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x(lnx{)}^{2}dx$

g$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{x\sqrt[\phantom{2}]{x^{2}16}}dx$

c$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{5}^{x}dx$

h$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dz}{z^3\sqrt[\phantom{2}]{z^2-4}}$

d$.{\displaystyle \underset{0}{\overset{}{}}}{e}^{x}sinxdx$

i$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3}{(4x^2-25{)}^{\frac{1}{2}}}dx$

e$.{\displaystyle \underset{1}{\overset{e}{}}}{x}^{3}ln(x)dx$

j$.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2(x^{3}9{)}^{15}dx$