What is the integral of sqrt(ax) ?

The integral of sqrt(ax) is sqrt(a) 2/3 x^{3/2}+C

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integral of sqrt(ax)

\int a x d x

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

Solution steps

\int a x d x

a x = a x

= \int a x d x

Take the constant out:

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

= a \cdot \int x d x

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{d}{d x} (sec (x^{3}))

\int x \cdot e^{- a \cdot x} d x

\int_{1}^{4} π (x - 1)^{2} d x

\frac{d y}{d x} = - \frac{6 x}{y}

What is the integral of sqrt(ax) ?
The integral of sqrt(ax) is sqrt(a) 2/3 x^{3/2}+C