What is the integral of (u-1)sqrt(u) ?

The integral of (u-1)sqrt(u) is 2/5 u^{5/2}-2/3 u^{3/2}+C

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integral of (u-1)sqrt(u)

\int (u - 1) u d u

\frac{2}{5} u^{\frac{5}{2}} - \frac{2}{3} u^{\frac{3}{2}} + C

Solution steps

\int (u - 1) u d u

Expand

(u - 1) u : u^{\frac{3}{2}} - u

= \int u^{\frac{3}{2}} - u d u

Apply the Sum Rule:

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

= \int u^{\frac{3}{2}} d u - \int u d u

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int u d u = \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} - \frac{2}{3} u^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{5} u^{\frac{5}{2}} - \frac{2}{3} u^{\frac{3}{2}} + C

\int x^{\frac{4}{3}} d x

f (x) = \frac{ln ( x )}{x + 2}

\frac{\partial}{\partial x} (1 - x y cos (π y))

\int \frac{1}{x ^{2} 64 - x ^{2}} d x

y^{^{''}} - 2 y^{^{'}} = e^{x}

What is the integral of (u-1)sqrt(u) ?
The integral of (u-1)sqrt(u) is 2/5 u^{5/2}-2/3 u^{3/2}+C