Question

Integrala din x /x^2 +4

Answer 1

$\int\limits { \frac{x}{ x^{2} +4}} \ dx = \frac{1}{2} \int\limits { \frac{2x}{ x^{2} +4} } \, dx =ln( x^{2} +4)+C.$

Answer 2

$\it\int{\dfrac{x}{x^2+4}}\ dx$

Notăm :

$\it x^2+4 = u \Rightarrow 2x dx =du \Rightarrow x dx = \dfrac{1}{2} du$

Integrala devine:

$\it\dfrac{1}{2}\int\dfrac{du}{u} =\dfrac{1}{2}\ln |u| + C = \dfrac{1}{2}\ln |x^2+4| + C = \dfrac{1}{2}\ln (x^2+4) + C \ .$