What is the integral of xsqrt(u) ?

The integral of xsqrt(u) is x 2/3 u^{3/2}+C

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integral of xsqrt(u)

\int x u d u

x \frac{2}{3} u^{\frac{3}{2}} + C

Solution steps

\int x u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

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

Add a constant to the solution

= x \frac{2}{3} u^{\frac{3}{2}} + C

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