Use uuu-substitution: ∫xx2+1 dx\int \frac{x}{x^2+1}\,dx∫x2+1xdx.
12ln(x2+1)+C\frac{1}{2}\ln(x^2+1) + C21ln(x2+1)+C
ln(x2+1)+C\ln(x^2+1) + Cln(x2+1)+C
12(x2+1)+C\frac{1}{2(x^2+1)} + C2(x2+1)1+C
arctanx+C\arctan x + Carctanx+C