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

The integral of 3sqrt(x)-\sqrt[3]{x^5} is 2x^{3/2}-3/8 x^{8/3}+C

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

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

Solution steps

Apply the Sum Rule:

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

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

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

Add a constant to the solution

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

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What is the integral of 3sqrt(x)-\sqrt[3]{x^5} ?
The integral of 3sqrt(x)-\sqrt[3]{x^5} is 2x^{3/2}-3/8 x^{8/3}+C