Помогите, пожалуйста, найти
int (arcsin x)^2 dx
int (arcsin x)^2 dx = x * (arcsin x)^2 - int x d((arcsin x)^2) =
= x * (arcsin x)^2 - int x * 2 * arcsin x * (arcsin x)' dx =
= x * (arcsin x)^2 - int x * 2 * arcsin x * 1/(1 - x^2)^(1/2) dx =
= x * (arcsin x)^2 - int arcsin x * 1/(1 - x^2)^(1/2) d(x^2) =
= x * (arcsin x)^2 - 2 * int arcsin x d(-(1 - x^2)^(1/2)) =
= x * (arcsin x)^2 + 2 * int arcsin x d((1 - x^2)^(1/2)) =
= x * (arcsin x)^2 + 2 * arcsin x * (1 - x^2)^(1/2) -
- 2 * int (1 - x^2)^(1/2) d(arcsin x) =
= x * (arcsin x)^2 + 2 * arcsin x * (1 - x^2)^(1/2) -
- 2 * int (1 - x^2)^(1/2) * 1/(1 - x^2)^(1/2) dx =
= x * (arcsin x)^2 + 2 * arcsin x * (1 - x^2)^(1/2) - 2 * int dx =
= x * (arcsin x)^2 + 2 * arcsin x * (1 - x^2)^(1/2) - 2 * x + C
Спасибо за помощь!!
Русская версия Invision Power Board (http://www.invisionboard.com)
© Invision Power Services (http://www.invisionpower.com)