what is the integral e^x/1+e^2x dx

Question

anonymous · Answer

$$\int\limits_{?}^{?} e^x/e^2x$$

lgbasallote · Answer

i have a feeling this has trigonometric substitution yes?

anonymous · Answer

i think so but i dont know how to do it, sorry its $$\int\limits_{?}^{?} e^{x}/1+e^{2x}$$

lgbasallote · Answer

hmmm i think i can solve the first few parts....

anonymous · Answer

its a multiple choice, so there are possible solution presented should I type them for you?

lgbasallote · Answer

let e^x = u
u^2 = e^2x
du = e^xdx

du/(1+u^2)

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tan^2 (theta) = 1 + u^2

sin (theta) = u
du = cos (theta) d(theta)

cos (theta)/tan^2 (theta)

hmm..any  ideas?

anonymous · Answer

$$ \arctan (e^x)$$

anonymous · Answer

The derivative of $$ \arctan (u)$$ with respect ot $$ u$$ is $$ \frac 1 {1+u^2}$$

anonymous · Answer

the antiderivative is 
$$e^x+(1/2)e^{2x}+c$$
that is if you mean
$$\int\limits_{}^{}(e^x/1)+e^{2x}dx$$

anonymous · Answer

@ 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