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

The integral of 6sqrt(x)-\sqrt[6]{x} is 4x^{3/2}-6/7 x^{7/6}+C

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

\int 6 x - 6 x d x

4 x^{\frac{3}{2}} - \frac{6}{7} x^{\frac{7}{6}} + C

Solution steps

\int 6 x - 6 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 6 x d x - \int 6 x d x

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

\int 6 x d x = \frac{6}{7} x^{\frac{7}{6}}

= 4 x^{\frac{3}{2}} - \frac{6}{7} x^{\frac{7}{6}}

Add a constant to the solution

= 4 x^{\frac{3}{2}} - \frac{6}{7} x^{\frac{7}{6}} + C

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What is the integral of 6sqrt(x)-\sqrt[6]{x} ?
The integral of 6sqrt(x)-\sqrt[6]{x} is 4x^{3/2}-6/7 x^{7/6}+C