Is the order important when calculating partial integration? When I for example have an integral $$ \int e^x \sin(2x)$$ and the formula for partial integration is $$ \int u v' = u v- \int u' v$$ So when I solve this problem, is the $$e^x \Rightarrow u$$ or is $$sin(2x) \Rightarrow u$$
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It works both ways. – Wuestenfux May 21 '17 at 16:19
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In this situation, either works, both give the same answer, and both take the same number of steps. – Chappers May 21 '17 at 16:20
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In other cases one way might work, but the other not. It's not that one way is invalid, but that the integrals becomes more difficult. – md2perpe May 21 '17 at 16:34
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Your question is almost equal to this https://math.stackexchange.com/q/408634/752 . – Américo Tavares May 21 '17 at 17:38
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For this kind of integrals, there is absolutely no difference between the two approaches. You will get the same result. Try by yourself to be convinced
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The first function and second function, $u$ and $v$ respectively, are decides by ILATE rule. In $95\%$ it works.
I: Inverse, L:Logarithmic, A: Algebraic, T: Trigonometric and E: Exponential.
We can take Exponential function as the %2nd% function as it is easy to integrate.
In your case, both ways will give the correct answer in equal no of steps.
Dharmaraj Deka
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