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

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

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integral of 1/(sqrt(3x))

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

\frac{x}{3} + \frac{1}{3} x + C

Solution steps

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

Apply Integration By Parts

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

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

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

= \frac{x}{3} - (- \frac{1}{3} x)

Simplify

= \frac{x}{3} + \frac{1}{3} x

Add a constant to the solution

= \frac{x}{3} + \frac{1}{3} x + C

\frac{d}{d x} (cos (x^{s i n (x)}))

\frac{d}{d x} (x^{4} - 50 x^{2})

\frac{\partial}{\partial x} (2 x^{2} + 2 y - 8)

f (x) = 5 x + 6, (2, 4)

t \cdot sin (t)

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