What is the integral of (sqrt(3x)) ?

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

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integral of (sqrt(3x))

\int (3 x) d x

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

Solution steps

\int 3 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int 3 x d x

Take the constant out:

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

= 3 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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