What is the integral of 8sqrt(x)-5\sqrt[3]{x} ?

The integral of 8sqrt(x)-5\sqrt[3]{x} is 16/3 x^{3/2}-15/4 x^{4/3}+C

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integral of 8sqrt(x)-5\sqrt[3]{x}

\int 8 x - 5 3 x d x

\frac{16}{3} x^{\frac{3}{2}} - \frac{15}{4} x^{\frac{4}{3}} + C

Solution steps

\int 8 x - 5 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 8 x d x - \int 5 3 x d x

\int 8 x d x = \frac{16}{3} x^{\frac{3}{2}}

\int 5 3 x d x = \frac{15}{4} x^{\frac{4}{3}}

= \frac{16}{3} x^{\frac{3}{2}} - \frac{15}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{16}{3} x^{\frac{3}{2}} - \frac{15}{4} x^{\frac{4}{3}} + C

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What is the integral of 8sqrt(x)-5\sqrt[3]{x} ?
The integral of 8sqrt(x)-5\sqrt[3]{x} is 16/3 x^{3/2}-15/4 x^{4/3}+C