What is the integral of 4\sqrt[3]{x}-2xsqrt(x) ?

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

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integral of 4\sqrt[3]{x}-2xsqrt(x)

\int 4 3 x - 2 x x d x

3 x^{\frac{4}{3}} - \frac{4}{5} x^{\frac{5}{2}} + C

Solution steps

\int 4 3 x - 2 x 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 4 3 x d x - \int 2 x x d x

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

\int 2 x x d x = \frac{4}{5} x^{\frac{5}{2}}

= 3 x^{\frac{4}{3}} - \frac{4}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 3 x^{\frac{4}{3}} - \frac{4}{5} x^{\frac{5}{2}} + C

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