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

The integral of (sqrt(x)-\sqrt[3]{x}) is 2/3 x^{3/2}-3/4 x^{4/3}+C

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

\frac{2}{3} x^{\frac{3}{2}} - \frac{3}{4} x^{\frac{4}{3}} + 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 x d x = \frac{2}{3} x^{\frac{3}{2}}

= \frac{2}{3} x^{\frac{3}{2}} - \frac{3}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - \frac{3}{4} x^{\frac{4}{3}} + C

What is the integral of (sqrt(x)-\sqrt[3]{x}) ?
The integral of (sqrt(x)-\sqrt[3]{x}) is 2/3 x^{3/2}-3/4 x^{4/3}+C