# Science:Math Exam Resources/Courses/MATH105/April 2017/Question 01 (g)/Solution 1

Note that the derivative of ${\displaystyle e^{x^{4}+1}=4x^{3}e^{x^{4}+1}.}$ Thus ${\displaystyle \int _{-2}^{1}x^{3}e^{x^{4}+1}dx={\frac {1}{4}}\int _{-2}^{1}de^{x^{4}+1}={\frac {1}{4}}[e^{x^{4}+1}]_{-2}^{1}=}$ ${\displaystyle \color {blue}{\frac {1}{4}}(e^{2}-e^{17}).}$