What is the integral of (x+2)/(\sqrt[3]{x-3)} ?

The integral of (x+2)/(\sqrt[3]{x-3)} is 3/2 x(x-3)^{2/3}+3(x-3)^{2/3}-9/10 (x-3)^{5/3}+C

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integral of (x+2)/(\sqrt[3]{x-3)}

\frac{3}{2} x (x - 3)^{\frac{2}{3}} + 3 (x - 3)^{\frac{2}{3}} - \frac{9}{10} (x - 3)^{\frac{5}{3}} + C

Solution steps

Apply Integration By Parts

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

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

\int \frac{3}{2} (x - 3)^{\frac{2}{3}} d x = \frac{9}{10} (x - 3)^{\frac{5}{3}}

= \frac{3}{2} x (x - 3)^{\frac{2}{3}} + 3 (x - 3)^{\frac{2}{3}} - \frac{9}{10} (x - 3)^{\frac{5}{3}}

Add a constant to the solution

= \frac{3}{2} x (x - 3)^{\frac{2}{3}} + 3 (x - 3)^{\frac{2}{3}} - \frac{9}{10} (x - 3)^{\frac{5}{3}} + C

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What is the integral of (x+2)/(\sqrt[3]{x-3)} ?
The integral of (x+2)/(\sqrt[3]{x-3)} is 3/2 x(x-3)^{2/3}+3(x-3)^{2/3}-9/10 (x-3)^{5/3}+C