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

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

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integral of x^2sqrt(x)

\int x^{2} 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 e^{3 x} \cdot sin (2 x) d x

\frac{d y}{d t} = k y^{2}

\int_{0}^{64} \frac{3}{x ^{\frac{2}{3}}} d x

x \to - 1 lim (- x + 2)

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 sin (t), y (0) = 0, y^{^{'}} (0) = 1

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