Question

integral 1/x raiz 1-ln^2

Answer 1

$∫ \frac{1}{x \sqrt{1 - ln(x) {}^{2} } } dx$

$∫ \frac{1}{x \sqrt{1 - ln(x) {}^{2} } } dx = ∫ \frac{du}{ \sqrt{1 - {u}^{2} } }$

$∫ \frac{du}{ \sqrt{1 - {u}^{2} } } = arc \sin(u) + c$

$∫ \frac{1}{x \sqrt{1 - ln(x) {}^{2} } } dx \\ = arc \sin( ln (x) ) + c$

u=lnx

du=1/x dx