I have seen the wikipedia's proof which can be found here: https://proofwiki.org/wiki/Integration_by_Substitution(adsbygoogle = window.adsbygoogle || []).push({});

However sometimes, we have problems where you have a ##d(x)## times ## f(g(x))## times g prime of x where we use substitution and it works but the proof didn't prove this condition..

I was wondering if you can prove why it works through infinite sums like for example

##( f(g(x)) g^{'}(x) dx + f(g(x+dx)) g^{'}(x+dx) dx + ..... ) ##

If I can change that to this

##( f(y) dy + f(y+dy) dy + .... ## where you set y = g(x)

It would statisfy me.. But is it possible to prove it using this?

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# B Integration by substitution

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