Tính nguyên hàm √x√x√x.dx

10/32

Tính ∫xxxdx

\(\frac{4}{{15}}x\sqrt[{15}]{{{x^7}}} + C\).

\(\frac{8}{{15}}x\sqrt[{15}]{{{x^7}}} + C\).

\(\frac{8}{{15}}x\sqrt[{15}]{x} + C\).

\(\frac{4}{{15}}x\sqrt[{15}]{x} + C\).

Giải thích

Chọn B

\(\int {\sqrt {x\sqrt {x\sqrt x } } dx} = \int {\sqrt {x\sqrt {x.{x^{\frac{1}{2}}}} } dx} = \int {\sqrt {x.{x^{\frac{3}{4}}}} dx} = \int {{x^{\frac{7}{8}}}dx} = \frac{{{x^{\frac{7}{8} + 1}}}}{{\frac{7}{8} + 1}} + C = \frac{8}{{15}}x\sqrt[{15}]{{{x^7}}} + C\)