What is the integral of 3/(sqrt(5x)) ?

The integral of 3/(sqrt(5x)) is 3(sqrt(x/5)+1/(sqrt(5))sqrt(x))+C

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integral of 3/(sqrt(5x))

\int \frac{3}{5 x} d x

3 (\frac{x}{5} + \frac{1}{5} x) + C

Solution steps

\int \frac{3}{5 x} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{5 x} d x

Apply Integration By Parts

= 3 (\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

= 3 (\frac{x}{5} - (- \frac{1}{5} x))

Simplify

= 3 (\frac{x}{5} + \frac{1}{5} x)

Add a constant to the solution

= 3 (\frac{x}{5} + \frac{1}{5} x) + C

What is the integral of 3/(sqrt(5x)) ?
The integral of 3/(sqrt(5x)) is 3(sqrt(x/5)+1/(sqrt(5))sqrt(x))+C