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}

\int x - 3 x d x

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

Solution steps

\int x - 3 x d x

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 - \int 3 x d x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

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

= \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

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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