Why don't we add a constant of integration when integrating the second function while applying integration by parts?
I'm searching for a perfectly logical answer

Ofcourse you cannot take different constants. You are integrating only one function, no matter twice. It should be the same general constt., or no constant at all.

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TopNewestWhat is "the second function"? On \(\int u \, dv = uv - \int v \, du\), is the second function \(v\) or \(v \, du\)?

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The second function is 'dv', the function whose integral is 'v'

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It will not affect the final answer. You can try it out yourself. The extra part, if you think there will be any, will get cancelled out at the end.

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What if I took different constants while integrating

P.S. You have to integrate g(x) twice while applying by parts

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Ofcourse you cannot take different constants. You are integrating only one function, no matter twice. It should be the same general constt., or no constant at all.

P.s. refer to the derivation of the formula once

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Thanks for asking this question, I had the same one in my mind!

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Well I've reasoned something out... I'm waiting for some other replies

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Comment deleted Jul 07, 2015

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