What is the integral of (6-3\sqrt[3]{x}+6sqrt(x)) ?

The integral of (6-3\sqrt[3]{x}+6sqrt(x)) is 6x-9/4 x^{4/3}+4x^{3/2}+C

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integral of (6-3\sqrt[3]{x}+6sqrt(x))

6 x - \frac{9}{4} x^{\frac{4}{3}} + 4 x^{\frac{3}{2}} + 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 6 d x = 6 x

\int 6 x d x = 4 x^{\frac{3}{2}}

= 6 x - \frac{9}{4} x^{\frac{4}{3}} + 4 x^{\frac{3}{2}}

Add a constant to the solution

= 6 x - \frac{9}{4} x^{\frac{4}{3}} + 4 x^{\frac{3}{2}} + C

y = x^{\frac{4}{7}} + 6 x

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What is the integral of (6-3\sqrt[3]{x}+6sqrt(x)) ?
The integral of (6-3\sqrt[3]{x}+6sqrt(x)) is 6x-9/4 x^{4/3}+4x^{3/2}+C