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

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

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

\frac{3}{4} x^{\frac{4}{3}} + \frac{4}{5} x^{\frac{5}{4}} + 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

= \frac{3}{4} x^{\frac{4}{3}} + \frac{4}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} + \frac{4}{5} x^{\frac{5}{4}} + C

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