What is the integral of (1-xsqrt(x)) ?

The integral of (1-xsqrt(x)) is x-2/5 x^{5/2}+C

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integral of (1-xsqrt(x))

\int (1 - x x) d x

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

Solution steps

\int 1 - 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 1 d x - \int x x d x

\int 1 d x = x

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

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

Add a constant to the solution

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

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What is the integral of (1-xsqrt(x)) ?
The integral of (1-xsqrt(x)) is x-2/5 x^{5/2}+C