What is the integral of (4x-3)/(\sqrt[3]{2x+7)} ?

The integral of (4x-3)/(\sqrt[3]{2x+7)} is 3/5 (2x+7)^{5/3}-51/4 (2x+7)^{2/3}+C

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integral of (4x-3)/(\sqrt[3]{2x+7)}

\frac{3}{5} (2 x + 7)^{\frac{5}{3}} - \frac{51}{4} (2 x + 7)^{\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} (2 x + 7)^{\frac{5}{3}} - \frac{21}{2} (2 x + 7)^{\frac{2}{3}} - \frac{9}{4} (2 x + 7)^{\frac{2}{3}}

Add similar elements:

- \frac{21}{2} (2 x + 7)^{\frac{2}{3}} - \frac{9}{4} (2 x + 7)^{\frac{2}{3}} = - \frac{51}{4} (2 x + 7)^{\frac{2}{3}}

= \frac{3}{5} (2 x + 7)^{\frac{5}{3}} - \frac{51}{4} (2 x + 7)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{5} (2 x + 7)^{\frac{5}{3}} - \frac{51}{4} (2 x + 7)^{\frac{2}{3}} + C

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What is the integral of (4x-3)/(\sqrt[3]{2x+7)} ?
The integral of (4x-3)/(\sqrt[3]{2x+7)} is 3/5 (2x+7)^{5/3}-51/4 (2x+7)^{2/3}+C