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

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

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integral of (2\sqrt[3]{x}-7sqrt(x^5))

\int (2 3 x - 7 x^{5}) d x

\frac{3}{2} x^{\frac{4}{3}} - 2 x^{\frac{7}{2}} + C

Solution steps

\int 2 3 x - 7 x^{5} 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 d x - \int 7 x^{5} d x

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

\int 7 x^{5} d x = 2 x^{\frac{7}{2}}

= \frac{3}{2} x^{\frac{4}{3}} - 2 x^{\frac{7}{2}}

Add a constant to the solution

= \frac{3}{2} x^{\frac{4}{3}} - 2 x^{\frac{7}{2}} + C

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