Question

Tìm:

a) \(\int x^{\dfrac{3}{5}}dx;\)                  b) \(\int\dfrac{1}{\sqrt[4]{x^3}}dx.\)

Answer 1

a) \(\int {{x^{\frac{3}{5}}}dx} = \frac{{{x^{\frac{3}{5} + 1}}}}{{\frac{3}{5} + 1}} + C = \frac{5}{8}{x^{\frac{8}{5}}} + C\).

b) \(\int {\frac{1}{{\sqrt[4]{{{x^3}}}}}dx} = \int {\frac{1}{{{x^{\frac{3}{4}}}}}dx} = \int {{x^{ - \frac{3}{4}}}dx} = \frac{{{x^{ - \frac{3}{4} + 1}}}}{{^{ - \frac{3}{4} + 1}}} + C = 4{x^{\frac{1}{4}}} + C = 4\sqrt[4]{x} + C\).