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

The integral of (sqrt(x^3)+x)\sqrt[3]{x} is 6/17 x^{17/6}+3/7 x^{7/3}+C

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

\frac{6}{17} x^{\frac{17}{6}} + \frac{3}{7} x^{\frac{7}{3}} + C

Solution steps

Expand

Apply the Sum Rule:

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

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

= \frac{6}{17} x^{\frac{17}{6}} + \frac{3}{7} x^{\frac{7}{3}}

Add a constant to the solution

= \frac{6}{17} x^{\frac{17}{6}} + \frac{3}{7} x^{\frac{7}{3}} + C

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What is the integral of (sqrt(x^3)+x)\sqrt[3]{x} ?
The integral of (sqrt(x^3)+x)\sqrt[3]{x} is 6/17 x^{17/6}+3/7 x^{7/3}+C