Помогите, пожалуйста, найти интеграл
int (1 + x^(4/5))^(1/2)/x^(11/5) dx

int (1 + x^(4/5))^(1/2)/x^(11/5) dx = int (x^(4/5) * (1 + x^(-4/5)))^(1/2)/x^(11/5) dx =
= int x^(2/5) * (1 + x^(-4/5))^(1/2)/x^(11/5) dx = int (1 + x^(-4/5))^(1/2)/x^(9/5) dx =
= | z = (1 + x^(-4/5))^(1/2), z^2 = 1 + x^(-4/5), 2 * z dz = -4/5 * x^(-9/5) dx =>
=> 1/x^(9/5) dx = -5/2 * z dz | =
= int z * (-5/2 * z) dz = -5/2 * int z^2 dx = -5/2 * (1/3 * z^3) + C =
= -5/6 * z^3 + C = | z = (1 + x^(-4/5))^(1/2) | =
= -5/6 * (1 + x^(-4/5))^(3/2) + C = -5/6 * (1 + x^(4/5))^(3/2)/x^(6/5) + C