What is the integral of 2sqrt(3x) ?

The integral of 2sqrt(3x) is 4/(sqrt(3))x^{3/2}+C

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integral of 2sqrt(3x)

\int 2 3 x d x

\frac{4}{3} x^{\frac{3}{2}} + C

Solution steps

\int 2 3 x d x

Take the constant out:

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

= 2 \cdot \int 3 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 2 \cdot \int 3 x d x

Take the constant out:

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

= 23 \cdot \int x d x

Apply the Power Rule

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

= 23 \frac{2}{3} x^{\frac{3}{2}}

Simplify

23 \frac{2}{3} x^{\frac{3}{2}} : \frac{4}{3} x^{\frac{3}{2}}

= \frac{4}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} + C

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What is the integral of 2sqrt(3x) ?
The integral of 2sqrt(3x) is 4/(sqrt(3))x^{3/2}+C