What is the integral of 1/(sqrt(5x)) ?

The integral of 1/(sqrt(5x)) is sqrt(x/5)+1/(sqrt(5))sqrt(x)+C

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integral of 1/(sqrt(5x))

\int \frac{1}{5 x} d x

\frac{x}{5} + \frac{1}{5} x + C

Solution steps

\int \frac{1}{5 x} d x

Apply Integration By Parts

: \frac{x}{5} - \int - \frac{1}{2 5 x ^{\frac{1}{2}}} d x

= \frac{x}{5} - \int - \frac{1}{2 5 x ^{\frac{1}{2}}} d x

\int - \frac{1}{2 5 x ^{\frac{1}{2}}} d x = - \frac{1}{5} x

= \frac{x}{5} - (- \frac{1}{5} x)

Simplify

= \frac{x}{5} + \frac{1}{5} x

Add a constant to the solution

= \frac{x}{5} + \frac{1}{5} x + C

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What is the integral of 1/(sqrt(5x)) ?
The integral of 1/(sqrt(5x)) is sqrt(x/5)+1/(sqrt(5))sqrt(x)+C