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

The integral of \sqrt[3]{x}ln(x) is 3/4 x^{4/3}ln(x)-9/16 x^{4/3}+C

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

\frac{3}{4} x^{\frac{4}{3}} ln (x) - \frac{9}{16} x^{\frac{4}{3}} + C

Solution steps

Apply Integration By Parts

: \frac{3}{4} x^{\frac{4}{3}} ln (x) - \int \frac{3}{4} x^{\frac{1}{3}} d x

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

\int \frac{3}{4} x^{\frac{1}{3}} d x = \frac{9}{16} x^{\frac{4}{3}}

= \frac{3}{4} x^{\frac{4}{3}} ln (x) - \frac{9}{16} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} ln (x) - \frac{9}{16} x^{\frac{4}{3}} + C

f (x) = x 3^{x}

(sin^{2} (3 x))^{^{'}}

\int \frac{5 - 50 x}{9 - 25 x ^{2}} d x

\frac{d}{d x} (3 x sin (x^{2}))

f (x) = 2 - 3 x

What is the integral of \sqrt[3]{x}ln(x) ?
The integral of \sqrt[3]{x}ln(x) is 3/4 x^{4/3}ln(x)-9/16 x^{4/3}+C