IIT JEE , AIEEE Forum - Mathematics , Integral Calculus - Evaluate...It is a cbse sample paper question

faizameer

Evalute....

^{e^tan-1(x) dx/(1+x^2)^2}

Hey......it is possible to substitute t= ^{e^tan-1(x)....if yes how................i have some doubt....pls do this problem}

^{Replay fast......................}

faizameer

Anyone plssss replay.................................

dream

substitute tan^-1x=t
( 1/1+x^2)dx = dt

also tant=x
1+x^2= sec^2x

solve using uv rule

e^t cos^2tdt

hsbhatt

let tan^-1x = t

Then x = tant and dx = sec²t dt

Also 1+x² = sec²t

Hence we get

e^tdt = e^t+C

= e^arctant + C

dream

@hsbhatt

the denominator is (1+x^2)^2

vaibhav_manu

take tan^-1x = t.

use one 1+x²in dt... and write the other one as sec²t... integrate by parts...

faizameer

hi vaibhav....
dream explained the same thing

faizameer

thanx dream...
wat is the final ans......lemme check