Mathematics

This is an integration by parts problem where you'll need to apply the technique repeatedly. The key insight is to choose $u = x^3$ (so its derivatives get simpler) and $dv = e^x\,dx$ (since $e^x$ stays manageable). Each application of integration by parts reduces the power of $x$ by one, so you'll repeat the process three times until the polynomial term vanishes and you're left with just $e^x$ to integrate.

This is an integration by parts problem where you'll need to apply the technique repeatedly. The key insight is to choose $u = x^3$ (so its derivatives get simpler) and $dv = e^x\,dx$ (since $e^x$ stays manageable). Each application of integration by parts reduces the power of $x$ by one, so you'll repeat the process three times until the polynomial term vanishes and you're left with just $e^x$ to integrate.