- #1
Lancelot59
- 646
- 1
I'm attempting to solve the following problem:
[tex]\int_{0}^{\infty} {\frac{x arctan(x)}{(1+x^{2})^{2}}dx}[/tex]
I started with a substitution:
[tex]u=arctan(x), du=\frac{1}{(1+x^{2})}dx[/tex]
This seemed like the right thing to do, but after trying to put it together in several different ways I got nowhere. I looked at what WolframAlpha had to say. It got this after doing the same substitution:
[tex]\int_{}^{} {u sin(u)cos(u)du}[/tex]
I've gone at this for over half an hour now and I've gotten nowhere. Some insight into how this step was made would be appreciated.
[tex]\int_{0}^{\infty} {\frac{x arctan(x)}{(1+x^{2})^{2}}dx}[/tex]
I started with a substitution:
[tex]u=arctan(x), du=\frac{1}{(1+x^{2})}dx[/tex]
This seemed like the right thing to do, but after trying to put it together in several different ways I got nowhere. I looked at what WolframAlpha had to say. It got this after doing the same substitution:
[tex]\int_{}^{} {u sin(u)cos(u)du}[/tex]
I've gone at this for over half an hour now and I've gotten nowhere. Some insight into how this step was made would be appreciated.