Question

Решите интеграл!
Срочно​

Answer 1

Ответ:

$arcsin(arcsin(x))$

Пошаговое объяснение:

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

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