What is the integral of x^2(1-x)^{3/2} ?

The integral of x^2(1-x)^{3/2} is -2/5 x^2(1-x)^{5/2}-8/315 (7x+2)(-x+1)^{7/2}+C

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integral of x^2(1-x)^{3/2}

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

- \frac{2}{5} x^{2} (1 - x)^{\frac{5}{2}} - \frac{8}{315} (7 x + 2) (- x + 1)^{\frac{7}{2}} + C

Solution steps

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

Apply Integration By Parts

: - \frac{2}{5} x^{2} (1 - x)^{\frac{5}{2}} - \int - \frac{4}{5} x (1 - x)^{\frac{5}{2}} d x

= - \frac{2}{5} x^{2} (1 - x)^{\frac{5}{2}} - \int - \frac{4}{5} x (1 - x)^{\frac{5}{2}} d x

\int - \frac{4}{5} x (1 - x)^{\frac{5}{2}} d x = \frac{8}{315} (7 x + 2) (- x + 1)^{\frac{7}{2}}

= - \frac{2}{5} x^{2} (1 - x)^{\frac{5}{2}} - \frac{8}{315} (7 x + 2) (- x + 1)^{\frac{7}{2}}

Add a constant to the solution

= - \frac{2}{5} x^{2} (1 - x)^{\frac{5}{2}} - \frac{8}{315} (7 x + 2) (- x + 1)^{\frac{7}{2}} + C

t y^{^{'}} = 2 y - 3 t^{2} cos (4 t)

\frac{\partial}{\partial x} (\frac{1}{2} e^{2 x})

f (x) = x^{[2]} + 1, at x = 3

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

n = 1 \sum \infty (\frac{1}{11})^{n}

What is the integral of x^2(1-x)^{3/2} ?
The integral of x^2(1-x)^{3/2} is -2/5 x^2(1-x)^{5/2}-8/315 (7x+2)(-x+1)^{7/2}+C