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

The integral of sqrt(x)(1+2/(\sqrt[3]{x)}) is 2/3 x^{3/2}+12/7 x^{7/6}+C

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integral of sqrt(x)(1+2/(\sqrt[3]{x)})

\frac{2}{3} x^{\frac{3}{2}} + \frac{12}{7} x^{\frac{7}{6}} + 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 d x = \frac{2}{3} x^{\frac{3}{2}}

= \frac{2}{3} x^{\frac{3}{2}} + \frac{12}{7} x^{\frac{7}{6}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{12}{7} x^{\frac{7}{6}} + C

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What is the integral of sqrt(x)(1+2/(\sqrt[3]{x)}) ?
The integral of sqrt(x)(1+2/(\sqrt[3]{x)}) is 2/3 x^{3/2}+12/7 x^{7/6}+C