Nevermind. I did it now.
It was a simple mistake on my part.
The integral should look like:
\int_0^1{\frac{2u}{1+u}du}
after substitution
and then it should be calculated with integration by parts from there.
I'm having trouble calculating an integral:
\int_0^1{\frac{1}{1+\sqrt{x}}dx}
I decided to do a substitution:
u=\sqrt{x}
du=\frac{1}{2\sqrt{x}}dx=\frac{1}{2u}dx
thus making the integral look like this:
\int_0^1{\frac{1}{2u}\cdot\frac{1}{1+u}du}
I transformed this integral to...