What is the integral of (4x)/(sqrt(3x)) ?

The integral of (4x)/(sqrt(3x)) is 4(sqrt(x/3)x-1/(3sqrt(3))x^{3/2})+C

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integral of (4x)/(sqrt(3x))

\int \frac{4 x}{3 x} d x

4 (\frac{x}{3} x - \frac{1}{3 3} x^{\frac{3}{2}}) + C

Solution steps

\int \frac{4 x}{3 x} d x

Take the constant out:

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

= 4 \cdot \int \frac{x}{3 x} d x

Apply Integration By Parts

: \frac{x}{3} x - \int \frac{1}{2 3} x d x

= 4 (\frac{x}{3} x - \int \frac{1}{2 3} x d x)

\int \frac{1}{2 3} x d x = \frac{1}{3 3} x^{\frac{3}{2}}

= 4 (\frac{x}{3} x - \frac{1}{3 3} x^{\frac{3}{2}})

Add a constant to the solution

= 4 (\frac{x}{3} x - \frac{1}{3 3} x^{\frac{3}{2}}) + C

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What is the integral of (4x)/(sqrt(3x)) ?
The integral of (4x)/(sqrt(3x)) is 4(sqrt(x/3)x-1/(3sqrt(3))x^{3/2})+C