Question

Cat este $\int\limits^._. { \frac{x}{ x^{2} +1} } \, dx$ ?

Answer 1

x²+1=t
2xdx=dt
[tex]1/2 \int\ { \frac{2xdx}{ x^{2} +1} } \, dx = \frac{1}{2} \int\ { \frac{dt}{t} } \,= [/tex]=
=1/2lnItI+c=1/2ln(x²+1)+c