int x * (2 * x + 5)^10 dx Опции

[sit]

Помогите, пожалуйста, найти интеграл
int x * (2 * x + 5)^10 dx

[tig81]

int x * (2 * x + 5)^10 dx = | 2 * x + 5 = t, x = (t - 5)/2, dx = 1/2 dt | =
= 1/2 * int ((t - 5)/2) * t^10 dt = 1/4 * int (t^11 - 5 * t^10) dt =
= 1/4 * (1/12 * t^12 - 5 * 1/11 * t^11) + C = 1/48 * t^12 - 5/44 * t^11 + C =
= | t = 2 * x + 5 | = 1/48 * (2 * x + 5)^12 - 5/44 * (2 * x + 5)^11 + C