What is the integral of x^2sqrt(x^3)+1 ?

The integral of x^2sqrt(x^3)+1 is 2/9 x^{9/2}+x+C

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integral of x^2sqrt(x^3)+1

\int x^{2} x^{3} + 1 d x

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

Solution steps

\int x^{2} x^{3} + 1 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^{3} d x + \int 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

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What is the integral of x^2sqrt(x^3)+1 ?
The integral of x^2sqrt(x^3)+1 is 2/9 x^{9/2}+x+C