integrate

∫1 ⁄ x(1+x²)^1/2dx

Dear Jithu Prasad

∫1 ⁄ x(1+x²)^1/2dx

∫x ⁄ x²(1+x²)^1/2dx

let (1+x²) =t²

xdx =tdt

so intigral become

∫1/t² -1  dt 

1/2 ln|t-1|/|t+1|  + C

1/2 ln|(1+x²)^1/2-1|/|(1+x²)^1/2+1|  + C

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin