int (arctan(e^x))/(1+e^2x)dx

Question

hartnn · Answer

did you try the substitution 
u = e^x ?

can you also verify your question ? because the funtion you posted is not integrable in terms of standard math functions.

hartnn · Answer

i mean, try e^x = tan y

anonymous · Answer

i did try letting u=e^x. it did not get me anywhere .
The limits on te question are really from 0 too 2
and the question is asking for the numerical value 
$$\int\limits_{0}^{?}$$

anonymous · Answer

$$\int\limits_{0}^{2}(\arctan(e^x))/(1+e^2x)dx$$

hartnn · Answer

$\large \int\limits_{0}^{2}\dfrac {(\arctan(e^x))}{(1+e^{2x})}dx$

with e^x = tan y 
e^x dx = sec^2 y dy 
dx = sec^2 y/ tan y dy

anonymous · Answer

how is e^x dx = sec^2 y dy

hartnn · Answer

took derivative on both sides
derivative of e^x is e^x dx
derivative of tan y is sec^2 y dy

anonymous · Answer

ohh i see

anonymous · Answer

$$\frac{ \tan y }{-\ln \cos y }$$

Am i on the right track ?

hartnn · Answer

don't you just get y/tan y ?

|dw:1386696538289:dw|