What is the integral of (x-sqrt(x))/3 ?

The integral of (x-sqrt(x))/3 is 1/3 ((x^2)/2-2/3 x^{3/2})+C

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integral of (x-sqrt(x))/3

\int \frac{x - x}{3} d x

\frac{1}{3} (\frac{x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}}) + C

Solution steps

\int \frac{x - x}{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \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

= \frac{1}{3} (\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{1}{3} (\frac{x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}})

Add a constant to the solution

= \frac{1}{3} (\frac{x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}}) + C

x \to 0 lim (\frac{( x )}{x})

\int \frac{3 x + 1}{3 x - 1} d x

(x + 2 x) e^{x}

\int - \frac{1}{3 x} d x

What is the integral of (x-sqrt(x))/3 ?
The integral of (x-sqrt(x))/3 is 1/3 ((x^2)/2-2/3 x^{3/2})+C