Integrate 2x/(x^2+3) using the substitution u=x^2+3

u=x² + 3

du/dx=2x

dx=du/2x

2x/(x²+3) dx becomes (2x/u) * (du/2x)

the 2x terms cancel out giving 1/u du

this integrates to ln(u)+c becoming ln(x²+3)+c