What is the integral of 3/4-1/(2sqrt(3x)) ?

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

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integral of 3/4-1/(2sqrt(3x))

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

\frac{3}{4} x - \frac{x}{3} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= \frac{3}{4} x - \frac{x}{3}

Add a constant to the solution

= \frac{3}{4} x - \frac{x}{3} + C

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