Question

Решите интеграл!
Срочно​

Answer 1

Ответ:

$arcsin(arcsin(x))$

Пошаговое объяснение:

$\int \frac{dx}{\sqrt{1-x^2}\cdot \sqrt{1-arcsin^2(x)}} = \begin{vmatrix}t = arcsin(x)\\ dt = \frac{dx}{\sqrt{1-x^2}}\end{vmatrix} =$

$\int \frac{dt}{ \sqrt{1-t^2}} = \begin{vmatrix}u = arcsin(t)\\ du = \frac{dt}{\sqrt{1-t^2}}\end{vmatrix} = \int du = u = \begin{vmatrix}\\\end{vmatrix} = arcsin(t) = \begin{vmatrix}\\\end{vmatrix} =arcsin(arcsin(x))$