What is the integral of (x^2)/(sqrt(x^3)) ?

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

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integral of (x^2)/(sqrt(x^3))

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

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

Solution steps

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

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

assuming

x \geq 0

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

Simplify

\frac{x ^{2}}{x ^{\frac{3}{2}}} : x^{\frac{1}{2}}

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

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{d y}{( 6 + y ) ^{2}} = \frac{d x}{( 10 + 9 x ) ^{4}}

\frac{df}{d θ} = sin (θ) + csc (θ)

\int (2 x^{3} - 5 x + 7) d x

\frac{d}{d v} (u \cdot v)

f (θ) = 4 sin (θ) - θ

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