What is the integral of (xsqrt(x))/3 ?

The integral of (xsqrt(x))/3 is 2/15 x^{5/2}+C

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integral of (xsqrt(x))/3

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

\frac{2}{15} x^{\frac{5}{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

Simplify

x x : x^{\frac{3}{2}}

= \frac{1}{3} \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= \frac{1}{3} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{2}{15} x^{\frac{5}{2}}

= \frac{2}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{15} x^{\frac{5}{2}} + C

\frac{d y}{d x} + 10 y = 12

\frac{d}{d x} (\frac{e ^{2 x} + e ^{4 x}}{3})

f (q) = \frac{500}{q ^{2}}

x \to 4 lim (\frac{x + 1}{x - 3})

\int (x^{2} - 3 x) d x

What is the integral of (xsqrt(x))/3 ?
The integral of (xsqrt(x))/3 is 2/15 x^{5/2}+C