Integral dx/((x+sqrt(1+x^2))^2) u substitution

[dubbrock]

Hello,
I'm very stuck on this problem:
dx/((x+sqrt(1+x^2))^2)

I tried u subtitution for 1+x^2, or sqrt(1+x^2) and I seem to run into a much more bigger problem.

here's an attempt, I'm wondering if I'm going in the right direction, and where I left off at, can I substitute the x in du/x? Thank you for your help!

 

[Deleted member 4993]

Hello,
I'm having trouble with this integral. I have tried u-substitution in a few ways and the problem seems to get worse. Here is my attempt. One of the questions I do have is if I can also substitute the x in du/x with sqrt(u-x). Does it look like I'm taking the right approach? Thank You!

Have you considered trigonometric substitution - e.g.

x = tan(Θ)