What is the integral of 4\sqrt[3]{x}+3\sqrt[6]{x^5} ?

The integral of 4\sqrt[3]{x}+3\sqrt[6]{x^5} is 3x^{4/3}+18/11 x^{11/6}+C

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integral of 4\sqrt[3]{x}+3\sqrt[6]{x^5}

3 x^{\frac{4}{3}} + \frac{18}{11} x^{\frac{11}{6}} + C

Solution steps

assuming

x \geq 0

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^{\frac{5}{6}} d x = \frac{18}{11} x^{\frac{11}{6}}

= 3 x^{\frac{4}{3}} + \frac{18}{11} x^{\frac{11}{6}}

Add a constant to the solution

= 3 x^{\frac{4}{3}} + \frac{18}{11} x^{\frac{11}{6}} + C

What is the integral of 4\sqrt[3]{x}+3\sqrt[6]{x^5} ?
The integral of 4\sqrt[3]{x}+3\sqrt[6]{x^5} is 3x^{4/3}+18/11 x^{11/6}+C