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

The integral of x^2*sqrt(x) is 2/7 x^{7/2}+C

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integral of x^2*sqrt(x)

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

\frac{2}{7} x^{\frac{7}{2}} + C

Solution steps

\int x^{2} x d x

Simplify

x^{2} x : x^{\frac{5}{2}}

= \int x^{\frac{5}{2}} d x

Apply the Power Rule

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

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

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} + C

\int \frac{x}{( x + 1 ) ( x + 2 ) ( x + 3 ) ^{2}} d x

y^{^{'}} + 2 y = e^{t}

f (x) = - 6 x^{2} - 3 x - 5 x^{3}

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

What is the integral of x^2*sqrt(x) ?
The integral of x^2*sqrt(x) is 2/7 x^{7/2}+C