What is the integral of (x-7)/(\sqrt[3]{x-3)} ?

The integral of (x-7)/(\sqrt[3]{x-3)} is 3/5 (x-3)^{5/3}-6(x-3)^{2/3}+C

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integral of (x-7)/(\sqrt[3]{x-3)}

\frac{3}{5} (x - 3)^{\frac{5}{3}} - 6 (x - 3)^{\frac{2}{3}} + C

Solution steps

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{3}{5} (x - 3)^{\frac{5}{3}} + \frac{9}{2} (x - 3)^{\frac{2}{3}} - \frac{21}{2} (x - 3)^{\frac{2}{3}}

Add similar elements:

\frac{9}{2} (x - 3)^{\frac{2}{3}} - \frac{21}{2} (x - 3)^{\frac{2}{3}} = - 6 (x - 3)^{\frac{2}{3}}

= \frac{3}{5} (x - 3)^{\frac{5}{3}} - 6 (x - 3)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{5} (x - 3)^{\frac{5}{3}} - 6 (x - 3)^{\frac{2}{3}} + C

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What is the integral of (x-7)/(\sqrt[3]{x-3)} ?
The integral of (x-7)/(\sqrt[3]{x-3)} is 3/5 (x-3)^{5/3}-6(x-3)^{2/3}+C