What is the integral of x^2sqrt(x^3)+4 ?

The integral of x^2sqrt(x^3)+4 is 2/9 x^{9/2}+4x+C

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integral of x^2sqrt(x^3)+4

\int x^{2} x^{3} + 4 d x

\frac{2}{9} x^{\frac{9}{2}} + 4 x + C

Solution steps

\int x^{2} x^{3} + 4 d x

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

assuming

x \geq 0

= \int x^{2} x^{\frac{3}{2}} + 4 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} x^{\frac{3}{2}} d x + \int 4 d x

\int x^{2} x^{\frac{3}{2}} d x = \frac{2}{9} x^{\frac{9}{2}}

\int 4 d x = 4 x

= \frac{2}{9} x^{\frac{9}{2}} + 4 x

Add a constant to the solution

= \frac{2}{9} x^{\frac{9}{2}} + 4 x + C

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What is the integral of x^2sqrt(x^3)+4 ?
The integral of x^2sqrt(x^3)+4 is 2/9 x^{9/2}+4x+C