(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex] \int_{1}^{2} x^2 e^{x} dx [/itex]

2. Relevant equations

Integrating by parts. Writing out chain rule, integrating both sides and rearranging gives ∫f(x)g'(x) dx = f(x)g(x) - ∫f'(x)g(x) dx

3. The attempt at a solution

[itex] \int_{1}^{2} x^2 e^{x} dx = \left[x^2 e^x\right]_{1}^{2} - \int_{1}^{2} 2x e^{x} dx[/itex]

Applying again gives:

[itex] \int_{1}^{2} x^2 e^{x} dx = \left[x^2 e^x\right]_{1}^{2} - \left(\left[2x e^x\right]_{1}^{2} - \int_{1}^{2} 2 e^{x} dx\right)[/itex]

Integrating last term gives:

[itex] \int_{1}^{2} x^2 e^{x} dx = \left[x^2 e^x\right]_{1}^{2} - \left(\left[2x e^x\right]_{1}^{2} - \left[2e^x\right]_{1}^{2}\right)[/itex]

When I simplify this I get -2e^{2}+ 3e, however I know the answer should be 2e^{2}-e.

Can someone please point out where my mistake is?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration by parts, where am I going wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**