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jennychan12
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} [e^x \cos (e^x)]dx\]

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

jennychan12
 one year ago
Best ResponseYou've already chosen the best response.0but if you do that, then du = e^xcos(e^x) and there's no cos (e^x) in the question.

jennychan12
 one year ago
Best ResponseYou've already chosen the best response.0that'd just be ucosu

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

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

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

jennychan12
 one year ago
Best ResponseYou've already chosen the best response.0oh wait. my bad. i thought u said u = sin u ok i see now

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

KingGeorge
 one year ago
Best ResponseYou've already chosen the best response.2Although 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.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1whenever 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 ....

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

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