Note that the derivative of e x 4 + 1 = 4 x 3 e x 4 + 1 . {\displaystyle e^{x^{4}+1}=4x^{3}e^{x^{4}+1}.} Thus ∫ − 2 1 x 3 e x 4 + 1 d x = 1 4 ∫ − 2 1 d e x 4 + 1 = 1 4 [ e x 4 + 1 ] − 2 1 = {\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}=} 1 4 ( e 2 − e 17 ) . {\displaystyle \color {blue}{\frac {1}{4}}(e^{2}-e^{17}).}
![{\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}=}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/84e394641e46d80ddf6f7dd1ca177a9e4c8e12e1)
