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

The integral of x^2sqrt(u) is (sqrt(u)x^3)/3+C

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integral of x^2sqrt(u)

\int x^{2} u

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

Solution steps

\int x^{2} u d x

Take the constant out:

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

= u \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

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What is the integral of x^2sqrt(u) ?
The integral of x^2sqrt(u) is (sqrt(u)x^3)/3+C