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

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

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integral of x-sqrt(x)

\int x - x d x

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

Solution steps

\int 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 x d x - \int x d x

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

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

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

Add a constant to the solution

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

\int \frac{5 x}{cos ^{2} ( x ^{2} )} d x

\int 21 d x

\frac{d ^{2} y}{d x ^{2}} = - 49 y

ln (tan (x^{3}))

\frac{d x}{d t} = - \frac{t}{x}

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