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

The integral of x/(\sqrt[3]{4-3x)} is -1/2 x(4-3x)^{2/3}-1/10 (4-3x)^{5/3}+C

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

- \frac{1}{2} x (4 - 3 x)^{\frac{2}{3}} - \frac{1}{10} (4 - 3 x)^{\frac{5}{3}} + C

Solution steps

Apply Integration By Parts

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

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

\int - \frac{1}{2} (4 - 3 x)^{\frac{2}{3}} d x = \frac{1}{10} (4 - 3 x)^{\frac{5}{3}}

= - \frac{1}{2} x (4 - 3 x)^{\frac{2}{3}} - \frac{1}{10} (4 - 3 x)^{\frac{5}{3}}

Add a constant to the solution

= - \frac{1}{2} x (4 - 3 x)^{\frac{2}{3}} - \frac{1}{10} (4 - 3 x)^{\frac{5}{3}} + C

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What is the integral of x/(\sqrt[3]{4-3x)} ?
The integral of x/(\sqrt[3]{4-3x)} is -1/2 x(4-3x)^{2/3}-1/10 (4-3x)^{5/3}+C