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

The integral of (-3)/(\sqrt[3]{x)}-4sqrt(x) is -9/2 x^{2/3}-8/3 x^{3/2}+C

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

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

- \frac{9}{2} x^{\frac{2}{3}} - \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

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

\int \frac{- 3}{3 x} d x = - \frac{9}{2} x^{\frac{2}{3}}

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= - \frac{9}{2} x^{\frac{2}{3}} - \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{9}{2} x^{\frac{2}{3}} - \frac{8}{3} x^{\frac{3}{2}} + C

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What is the integral of (-3)/(\sqrt[3]{x)}-4sqrt(x) ?
The integral of (-3)/(\sqrt[3]{x)}-4sqrt(x) is -9/2 x^{2/3}-8/3 x^{3/2}+C