Integration of exponential function (problem below):

Question

I have tried u substitution, but I'm not really sure what to do.

This is what I tried:

$u = x^3 - 2x^2 + x + 7\\ du = (3x^2-4x+1)dx$

But I'm not sure what to do now.

I also tried:

$u = 2x-1\\ du = 2dx$

Answer 1

Two things to help:

Get $e^{-1}$ from the integral, so you just have $e^{-2x}$.

Use IBP to get $\int x^{n+1}e^{-x}$ in terms of $\int x^{n}e^{-x}$ and $x^{n+1}e^{-x}$. And, of course, $\int e^{-x} dx = -e^{-x} $.