Math Is Fun Forum

Garth

Guest

Help with integration by parts please

How do you do the following using integration by parts?  Note that p and x are variables below.  Thanks to anyone who can help!!!:

1) ∫ x² * e^(px) dx

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help with integration by parts please

Make x² the bit you differentiate and e^(px) the bit you integrate.

Then, using integration by parts, ∫ x² e^(px) dx = x²/p * e^(px) - ∫ 2x/p e^(px) dx.

By parts again, ∫ 2x/p e^(px) dx= 2x/p² * e^(px) - ∫ 2/p² e^(px). You can evaluate that last integral directly.

Substituting everything in, then, your answer is (x²/p - 2x/p² + 2/p³)e^(px) +C.

---

Why did the vector cross the road?
It wanted to be normal.