Compute the given integral. Use exact values.

01(4x3+9x2)ex4+3x3dx=\displaystyle {\int_{{0}}^{{1}}}{\left({4}{x}^{{3}}+{9}{x}^{{2}}\right)}{e}^{{{x}^{{4}}+{3}{x}^{{3}}}}{\left.{d}{x}\right.}=