Помогите, пожалуйста, найти интеграл:
int x^3 * 2^(-x^2) dx

int x^3 * 2^(-x^2) dx = int x^2 * 2^(-x^2) * x dx =
= int x^2 * 2^(-x^2) d(1/2 * x^2) = 1/2 * int x^2 * 2^(-x^2) d(x^2) = | t = x^2 | =
= 1/2 * int t * 2^(-t) dt = 1/2 * int t d(2^(-t)/(-ln 2)) = -1/2 * 1/ln 2 * int t d(2^(-t)) =
= -1/2 * 1/ln 2 * t * 2^(-t) + 1/2 * 1/ln 2 * int 2^(-t) dt =
= -1/(2 * ln 2) * t * 2^(-t) + 1/(2 * ln 2) * 2^(-t)/(-ln 2) + C =
= -1/(2 * ln 2) * t * 2^(-t) - 1/(2 * ln^2 2) * 2^(-t) + C =
= -1/(2 * ln^2 2) * 2^(-t) * (t * ln 2 + 1) + C = | t = x^2 | =
= -1/(2 * ln^2 2) * 2^(-x^2) * (x^2 * ln 2 + 1) + C