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# Integration by parts watch

1. So the rule is, ∫f'g dx=f.g - ∫fg' dx
And this was an example question written on the board: ∫sinxcosx dx
=-cosxcosx-∫-cosx(-sinx) dx
=-cosxcosx-∫cosxsinx dx
Now, I'm confused about the next step:
2∫sinxcosx dx = -cos^2 x + c
Where did the 2 before the integral sign come from?
2. (Original post by Airess3)
So the rule is, ∫f'g dx=f.g - ∫fg' dx
And this was an example question written on the board: ∫sinxcosx dx
=-cosxcosx-∫-cosx(-sinx) dx
=-cosxcosx-∫cosxsinx dx
Now, I'm confused about the next step:
2∫sinxcosx dx = -cos^2 x + c
Where did the 2 before the integral sign come from?
You have:

∫sinxcosx dx = -cosxcosx-∫sinxcosx dx

By adding ∫sinxcosx dx to both sides, you get the 2 before the integral sign.
3. (Original post by Airess3)
And this was an example question written on the board: ∫sinxcosx dx
This is a poor example.

You would be better advised to spot or make a substitution or .

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Updated: January 28, 2015
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