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

\int e^{x} 9 + e^{x} d x

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\frac{d}{d x} (x sin (e^{x}))

\frac{d y}{d x} + 2 y = 3, y (0) = 1

f (x) = x^{4} + 8 x

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