# Invoking deep thoughts: Integration

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

Note by Mayank Singh
2 years, 11 months ago

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What is "the second function"? On $$\int u \, dv = uv - \int v \, du$$, is the second function $$v$$ or $$v \, du$$?

- 2 years, 11 months ago

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

- 2 years, 11 months ago

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.

- 2 years, 11 months ago

What if I took different constants while integrating

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

- 2 years, 11 months ago

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

- 2 years, 11 months ago

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

- 2 years, 11 months ago

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

- 2 years, 11 months ago

Comment deleted Jul 07, 2015

Just last year

- 2 years, 11 months ago