Question

Ajutor:
$\int\limits\frac{1}{\sqrt{1-x^{2} }(arcsin^{2}x-4) } \, dx =$

Answer 1

Răspuns:

Explicație pas cu pas:

$\displastyle \int\dfrac{1}{\sqrt{1-x^2}(\arcsin^2x-4)}dx\\\arcsin x=t\\\dfrac{1}{\sqrt{1-x^2}}dx=dt\\\\=\int\dfrac{1}{t^2-4}dt=\dfrac{1}{4}\ln\left|\dfrac{t-2}{t+2}\right|+C=\dfrac{1}{4}\ln\left|\dfrac{\arcsin x-2}{\arcsin x+2}\right|+C$