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jennychan12Best ResponseYou've already chosen the best response.0
\[\int\limits_{0}^{1} [e^x \cos (e^x)]dx\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Do a usubstitution with \(u=\sin(e^x)\), and your solution should pop right out.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
but if you do that, then du = e^xcos(e^x) and there's no cos (e^x) in the question.
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
that'd just be ucosu
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.2
\(u=\sin(e^x)\implies du=e^x\cos(e^x)dx\). So your integral becomes\[\int du=u\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Substitute back for \(u\), and you get \[\int_0^1 e^x\cos(e^x)dx=\sin(e^x)_0^1\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
u =e^x du = e^x dx \(\int cos udu\) ohh..now i could say that u =sin e^x is a better substitution..
 one year ago

jennychan12Best ResponseYou've already chosen the best response.0
oh wait. my bad. i thought u said u = sin u ok i see now
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Yup, I like to call my method "guessing the solution and proving you're right"
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Although if you really had no clue of the solution, \(u=e^x\) would be a fine substitution. You would just have to integrate by parts.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
whenever i see a nonstandard angle with sin/cos/.. i'll call that as 'bad angle' and put u= bad angle.... example : sin x^2 , cos log x ....
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
how do we need integration by parts ?? O.o u= e^x du=e^xdx
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Oh. Right. You don't. Ignore my ramblings.
 one year ago
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