I need some help solving this integration problem.

[ParveshD.Singh]

 

[skeeter]

use the substitution [MATH]t=\sqrt{x}[/MATH]

 

[ParveshD.Singh]

I tried that and i got to tan^-1(u).u/u+u^(3), now im stuck.

 

[skeeter]

[MATH]t=\sqrt{x} \implies dt = \dfrac{dx}{2\sqrt{x}}[/MATH]
[MATH]2\int \dfrac{\arctan{\sqrt{x}}}{1+x} \cdot \dfrac{dx}{2\sqrt{x}}[/MATH]
[MATH]2\int \arctan{t} \cdot \dfrac{1}{1+t^2} \, dt[/MATH]
easy integral now ...