What is the integral of (x^2)/(sqrt(x)) ?

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

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integral of (x^2)/(sqrt(x))

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

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

Solution steps

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

Simplify

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

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

Apply the Power Rule

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

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

Add a constant to the solution

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

f (x) = - 5 x^{2} - 3 x, at x = - 3

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

\int e^{\frac{- 1}{x}} d x

10 \cdot 2^{- 0.274 x}

\frac{2 x}{7 - tan ( x )}

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