What is the integral of sqrt(u^3) ?

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

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integral of sqrt(u^3)

\int u^{3} d u

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

Solution steps

\int u^{3} d u

u^{3} = u^{\frac{3}{2}},

assuming

u \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

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