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

The integral of x^2sqrt(x^3) is 2/9 x^{9/2}+C

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integral of x^2sqrt(x^3)

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

\frac{2}{9} x^{\frac{9}{2}} + C

Solution steps

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

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

assuming

x \geq 0

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

Simplify

x^{2} x^{\frac{3}{2}} : x^{\frac{7}{2}}

= \int x^{\frac{7}{2}} d x

Apply the Power Rule

: \frac{2}{9} x^{\frac{9}{2}}

= \frac{2}{9} x^{\frac{9}{2}}

Add a constant to the solution

= \frac{2}{9} x^{\frac{9}{2}} + C

\frac{\partial}{\partial x} (sin (7 y - x))

5 ln (x^{2}), 1

\frac{d}{d x} (5 tan (x) sec (x))

f (x) = x^{2} - x, (1, 0)

x \to 9 lim (\frac{( x ^{2} - 4 x - 45 )}{x ^{2} - 81})

What is the integral of x^2sqrt(x^3) ?
The integral of x^2sqrt(x^3) is 2/9 x^{9/2}+C