anonymous
  • anonymous
what is the integral e^x/1+e^2x dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{?}^{?} e^x/e^2x\]
lgbasallote
  • lgbasallote
i have a feeling this has trigonometric substitution yes?
anonymous
  • anonymous
i think so but i dont know how to do it, sorry its \[\int\limits_{?}^{?} e^{x}/1+e^{2x}\]

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lgbasallote
  • lgbasallote
hmmm i think i can solve the first few parts....
anonymous
  • anonymous
its a multiple choice, so there are possible solution presented should I type them for you?
lgbasallote
  • lgbasallote
let e^x = u u^2 = e^2x du = e^xdx du/(1+u^2) |dw:1333533519536:dw| tan^2 (theta) = 1 + u^2 sin (theta) = u du = cos (theta) d(theta) cos (theta)/tan^2 (theta) hmm..any ideas?
anonymous
  • anonymous
\[ \arctan (e^x)\]
anonymous
  • anonymous
The derivative of \[ \arctan (u)\] with respect ot \[ u\] is \[ \frac 1 {1+u^2}\]
anonymous
  • anonymous
the antiderivative is \[e^x+(1/2)e^{2x}+c\] that is if you mean \[\int\limits_{}^{}(e^x/1)+e^{2x}dx\]
anonymous
  • anonymous
@ anonymoustwo: no thats not what I mean but eliassaab answered me thank you. I didnt know that the derivatite of 1/1_u^2 is arctan u thank you guys for the help all of you

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