What is the integral of \sqrt[3]{x}log_{4}(x) ?

The integral of \sqrt[3]{x}log_{4}(x) is 3/4 x^{4/3}log_{4}(x)-(9x^{4/3})/(32ln(2))+C

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integral of \sqrt[3]{x}log_{4}(x)

\frac{3}{4} x^{\frac{4}{3}} lo g_{4} (x) - \frac{9 x ^{\frac{4}{3}}}{32 ln ( 2 )} + C

Solution steps

Apply Integration By Parts

= \frac{3}{4} x^{\frac{4}{3}} lo g_{4} (x) - \int \frac{3 x ^{\frac{1}{3}}}{8 ln ( 2 )} d x

\int \frac{3 x ^{\frac{1}{3}}}{8 ln ( 2 )} d x = \frac{9 x ^{\frac{4}{3}}}{32 ln ( 2 )}

= \frac{3}{4} x^{\frac{4}{3}} lo g_{4} (x) - \frac{9 x ^{\frac{4}{3}}}{32 ln ( 2 )}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} lo g_{4} (x) - \frac{9 x ^{\frac{4}{3}}}{32 ln ( 2 )} + C

What is the integral of \sqrt[3]{x}log_{4}(x) ?
The integral of \sqrt[3]{x}log_{4}(x) is 3/4 x^{4/3}log_{4}(x)-(9x^{4/3})/(32ln(2))+C