What is the integral of 5/(\sqrt[3]{x)}-4\sqrt[3]{x} ?

The integral of 5/(\sqrt[3]{x)}-4\sqrt[3]{x} is 15/2 x^{2/3}-3x^{4/3}+C

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integral of 5/(\sqrt[3]{x)}-4\sqrt[3]{x}

\int \frac{5}{3 x} - 4 3 x d x

\frac{15}{2} x^{\frac{2}{3}} - 3 x^{\frac{4}{3}} + C

Solution steps

\int \frac{5}{3 x} - 4 3 x d x

Apply the Sum Rule:

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

= \int \frac{5}{3 x} d x - \int 4 3 x d x

\int \frac{5}{3 x} d x = \frac{15}{2} x^{\frac{2}{3}}

\int 4 3 x d x = 3 x^{\frac{4}{3}}

= \frac{15}{2} x^{\frac{2}{3}} - 3 x^{\frac{4}{3}}

Add a constant to the solution

= \frac{15}{2} x^{\frac{2}{3}} - 3 x^{\frac{4}{3}} + C

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What is the integral of 5/(\sqrt[3]{x)}-4\sqrt[3]{x} ?
The integral of 5/(\sqrt[3]{x)}-4\sqrt[3]{x} is 15/2 x^{2/3}-3x^{4/3}+C