(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Integrating with Change of variables -method

1. The problem statement, all variables and given/known data

Solve by "Change of variables"-method ∫(dx)/(eˆx + eˆ(-x))

2. Relevant equations

∫f(x)dx=∫f(x(t))*x'(t)dt

3. The attempt at a solution

∫(dx)/(eˆx + eˆ(-x))=∫(eˆx)/(1 + eˆ2x) t=eˆx x=ln (t) (dt)/(dx)=t => dx=1/t dt

∫t/(tˆ2 + 1) * 1/t => ∫1/(tˆ2 + 1) = WRONG!

Where am I making a mistake? How do I know which term I should take as "t"? I have tried to read more in internet of this subject but couldn't find anything helpful. I read one topic here about this subject. The helper had used chain-method to solve this sort of problem but I couldn't understand it. Could someone help me to understand it? I'm just started my studies at university and my knowledge is very very limited. (Sorry my english, I'm finnish...)

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# Homework Help: Integrating with Change of variables -method

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