What is the integral of \sqrt[3]{x}ln(x^5) ?

The integral of \sqrt[3]{x}ln(x^5) is 15/4 x^{4/3}ln(x)-45/16 x^{4/3}+C

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integral of \sqrt[3]{x}ln(x^5)

\frac{15}{4} x^{\frac{4}{3}} ln (x) - \frac{45}{16} x^{\frac{4}{3}} + C

Solution steps

Apply Integration By Parts

: \frac{3}{4} x^{\frac{4}{3}} ln (x^{5}) - \int \frac{15}{4} x^{\frac{1}{3}} d x

= \frac{3}{4} x^{\frac{4}{3}} ln (x^{5}) - \int \frac{15}{4} x^{\frac{1}{3}} d x

\int \frac{15}{4} x^{\frac{1}{3}} d x = \frac{45}{16} x^{\frac{4}{3}}

= \frac{3}{4} x^{\frac{4}{3}} ln (x^{5}) - \frac{45}{16} x^{\frac{4}{3}}

\frac{3}{4} x^{\frac{4}{3}} ln (x^{5}) = \frac{15}{4} x^{\frac{4}{3}} ln (x)

= \frac{15}{4} x^{\frac{4}{3}} ln (x) - \frac{45}{16} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{15}{4} x^{\frac{4}{3}} ln (x) - \frac{45}{16} x^{\frac{4}{3}} + C

x \to - \infty lim (x + 1)

3 x^{3} - x^{2} - 10 x, - x^{2} + 2 x

\frac{d}{d x} (3 x^{4} + 2 x^{\frac{1}{3}} - \frac{1}{x ^{2}})

\int \frac{- 11 x - 24}{125 ( x ^{2} + 4 x + 5 )} d x

n = 1 \sum \infty \frac{2}{5 ^{n + 2}}

What is the integral of \sqrt[3]{x}ln(x^5) ?
The integral of \sqrt[3]{x}ln(x^5) is 15/4 x^{4/3}ln(x)-45/16 x^{4/3}+C