What is the integral of (5x-sqrt(x)) ?

The integral of (5x-sqrt(x)) is (5x^2)/2-2/3 x^{3/2}+C

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integral of (5x-sqrt(x))

\int (5 x - x) d x

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

Solution steps

\int 5 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 5 x d x - \int x d x

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

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

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

Add a constant to the solution

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

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