intergral x((2x)/(x^2+1))dx
Somebody mentioned a sub u= x^2+1 so it is then ln (x^2+1) but what about the x in front of the problem
If it's really $\displaystyle \int \frac{2x^2}{x^2 + 1}~dx$,
$\displaystyle 2\int \frac{x^2}{x^2 + 1}~dx$
$\displaystyle \frac{x^2}{x^2 + 1} = 1-\frac{1}{x^2 + 1}$
So it becomes, $\displaystyle 2 \left ( \int 1~dx - \int \frac{1}{x^2+1}~dx \right )$
$\displaystyle 2 \left ( x - \text{Arctan}x \right )$
$\displaystyle 2x - 2\text{Arctan}x$