Помогите, пожалуйста, найти интеграл
int arcsin (x/3) dx

int arcsin (x/3) dx = | t = x/3, x = 3 * t, dx = 3 dt | =
= int arcsin t * 3 dt = 3 * int arcsin t dt =
= 3 * t * arcsin t - 3 * int t d(arcsin t) =
= 3 * t * arcsin t - 3 * int t * 1/(1 - t^2)^(1/2) dt =
= 3 * t * arcsin t - 3 * int 1/(1 - t^2)^(1/2) d(1/2 * t^2) =
= 3 * t * arcsin t - 3 * 1/2 * int 1/(1 - t^2)^(1/2) d(t^2) = | t^2 = u | =
= 3 * t * arcsin t - 3/2 * int 1/(1 - u)^(1/2) du =
= 3 * t * arcsin t - 3/2 * int (1 - u)^(-1/2) du =
= 3 * t * arcsin t - 3/2 * (-1) * 1/(-1/2 + 1) * (1 - u)^(-1/2 + 1) + C =
= 3 * t * arcsin t + 3/2 * 2 * (1 - u)^(1/2) + C = | u = t^2 | =
= 3 * t * arcsin t + 3 * (1 - t^2)^(1/2) + C = | t = x/3 | =
= 3 * x/3 * arcsin (x/3) + 3 * (1 - (x/3)^2)^(1/2) + C =
= x * arcsin (x/3) + 3 * (1 - x^2/9)^(1/2) + C =
= x * arcsin (x/3) + 3 * ((9 - x^2)/9)^(1/2) + C =
= x * arcsin (x/3) + 3 * (9 - x^2)^(1/2)/3 + C =
= x * arcsin (x/3) + (9 - x^2)^(1/2) + C

Большое спасибо!!