The integral in question looks like this: \begin{aligned} \large \ \int x^3 \cdot e^{8-7x^4} dx \end{aligned} I tried using u-substitution on all the part before dx and it eliminated e (with all its degrees) but left a huge mess: \begin{aligned} \ \int \frac {x^3}{3x^2-28x^6} du \end{aligned} I must have made a some simple mistake...
2026-05-05 11:49:04.1777981744
How to deal with multilevel degree inside of an indefinite integral?
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Remember that the chain rule says $(e^{f(x)})'=f'(x)e^{f(x)}$. In your case, $f(x)=8-7x^4$, $f'(x)=-28x^3$; from here you should be able to construct any anti-derivative explicitly.