What is the integral of (\sqrt[3]{x^5}+1/(3sqrt(x))) ?

The integral of (\sqrt[3]{x^5}+1/(3sqrt(x))) is 3/8 x^{8/3}+2/3 sqrt(x)+C

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integral of (\sqrt[3]{x^5}+1/(3sqrt(x)))

\frac{3}{8} x^{\frac{8}{3}} + \frac{2}{3} x + 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 \frac{1}{3 x} d x = \frac{2}{3} x

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

Add a constant to the solution

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

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800 x - 0.1 x^{2}

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What is the integral of (\sqrt[3]{x^5}+1/(3sqrt(x))) ?
The integral of (\sqrt[3]{x^5}+1/(3sqrt(x))) is 3/8 x^{8/3}+2/3 sqrt(x)+C