X^3/4+x^2/3+x^1/2/x dx

Для вычисления выражения (x^ (3/4) + x^ (2/3) + x^ (1/2) + x) dx, нужно вычислить производную функции.

Производная функции равна:

(x^ (3/4) + x^ (2/3) + x^ (1/2) + x) dx = (x^ (3/4) + x^ (2/3) + x^ (1/2) + x) ' = 3/4 * x^ (3/4 - 1) + 2/3 * x^ (2/3 - 1) + 1/2 * x^ (1/2 - 1) + 1 = 3/4 * x^ (3/4 - 4/4) + 2/3 * x^ (2/3 - 3/3) + 1/2 * x^ (1/2 - 2/2) + 1 = 3/4 * x^ (-1/4) + 2/3 * x^ (-1/3) + 1/2 * x^ (-1/2) + 1;

Значит, (x^ (3/4) + x^ (2/3) + x^ (1/2) + x) dx = 3/4 * x^ (-1/4) + 2/3 * x^ (-1/3) + 1/2 * x^ (-1/2) + 1.