HELP! on integration

[wonderrrgirl]

Hello, can someone explain to me how to integrate: x(2x) / (1+x^2) ?

It'll be great if you can show the full steps, thanks!

 

[Deleted member 4993]

Hello, can someone explain to me how to integrate: x(2x) / (1+x^2) ?

It'll be great if you can show the full steps, thanks!

I assume your problem is:

\(\displaystyle \int \frac{x\cdot (2x)}{1+x^2} dx\)

\(\displaystyle = \, \int \frac{2x^2}{1+x^2} dx\)

\(\displaystyle = \, \int \frac{2x^2 \, + \, 2 \, - \, 2}{1+x^2} dx\)

\(\displaystyle = \, \int 2 dx \, - \, 2 \int \frac{1}{1+x^2}\)

\(\displaystyle = \, 2x \, - \, 2 \tan^{-1}(x) \, + \, C\)