Question

Cum se rezolva integrala din f(x)* f`(x) ? Nu inteleg rezolvarea prin care se ajunge la f^2(x)/2

Answer 1

$\displaystyle\it\\ \boxed{\bigg(f^2(x)\bigg)'=2f(x)f'(x)}\\-------------\\\int f(x)\cdot f'(x)dx=\frac{1}{2}\int 2f(x)\cdot f'(x)dx=\frac{1}{2}\int (f^2(x))'dx=\\\frac{1}{2}\bigg(f^2(x)\bigg)+\mathcal{C}=\boxed{\it \frac{f^2(x)}{2}+\mathcal{C}}.$