Find the integral of ∫ DX / X (X & # 178; + 1)?

Find the integral of ∫ DX / X (X & # 178; + 1)?

∫dx/x(x²+1)
=∫xdx/ x²(x²+1)
=0.5∫dx²/ x²(x²+1)
=0.5∫1/x² -1/(x²+1) dx²
=0.5lnx & # 178; - 0.5ln (X & # 178; + 1) + C, C is constant