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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
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.
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