What is the integral of (x-4\sqrt[5]{x}+7) ?

The integral of (x-4\sqrt[5]{x}+7) is (x^2)/2-10/3 x^{6/5}+7x+C

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integral of (x-4\sqrt[5]{x}+7)

\int (x - 4 5 x + 7) d x

\frac{x ^{2}}{2} - \frac{10}{3} x^{\frac{6}{5}} + 7 x + C

Solution steps

\int x - 4 5 x + 7 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 4 5 x d x + \int 7 d x

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

\int 4 5 x d x = \frac{10}{3} x^{\frac{6}{5}}

\int 7 d x = 7 x

= \frac{x ^{2}}{2} - \frac{10}{3} x^{\frac{6}{5}} + 7 x

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{10}{3} x^{\frac{6}{5}} + 7 x + C

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What is the integral of (x-4\sqrt[5]{x}+7) ?
The integral of (x-4\sqrt[5]{x}+7) is (x^2)/2-10/3 x^{6/5}+7x+C