Question

Să se calculeze :

$\int \frac{1}{x} {ln}^{4} x \: dx \: ,x>0$

(Schimbarea de variabilă)

Answer 1

$\ln x\stackrel{not}{=} t\Rightarrow \dfrac{dx}{x}=dt\\\displaystyle\int \dfrac{1}{x}\ln^4 xdx = \int t^4 dt= \dfrac{t^5}{5}+C=\dfrac{\ln^5 x}{5}+C$