Question

Cat face integrala din x/x patrat +1?

Answer 1

$\it \int\dfrac{x}{x^2+1} dx$

Notăm x² +1 = t ⇒ 2x dx =dt ⇒ x dx =(1/2) dt

Integrala devine:

$\it \dfrac{1}{2} \int\dfrac{dt}{t} =\dfrac{1}{2} ln t +C =\dfrac{1}{2} ln(x^2+1) + C$