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

The integral of (2\sqrt[3]{x^4}-x^{-3}) is 6/7 x^{7/3}+1/(2x^2)+C

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integral of (2\sqrt[3]{x^4}-x^{-3})

\int (2 3 x^{4} - x^{- 3}) d x

\frac{6}{7} x^{\frac{7}{3}} + \frac{1}{2 x ^{2}} + C

Solution steps

\int 2 3 x^{4} - x^{- 3} 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 2 3 x^{4} d x - \int x^{- 3} d x

\int 2 3 x^{4} d x = \frac{6}{7} x^{\frac{7}{3}}

\int x^{- 3} d x = - \frac{1}{2 x ^{2}}

= \frac{6}{7} x^{\frac{7}{3}} - (- \frac{1}{2 x ^{2}})

Simplify

= \frac{6}{7} x^{\frac{7}{3}} + \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{3}} + \frac{1}{2 x ^{2}} + C

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What is the integral of (2\sqrt[3]{x^4}-x^{-3}) ?
The integral of (2\sqrt[3]{x^4}-x^{-3}) is 6/7 x^{7/3}+1/(2x^2)+C