What is the integral of 1/(sqrt(20x)) ?

The integral of 1/(sqrt(20x)) is 1/(sqrt(5))sqrt(x)+C

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integral of 1/(sqrt(20x))

\int \frac{1}{20 x} d x

\frac{1}{5} x + C

Solution steps

\int \frac{1}{20 x} d x

Apply Integration By Parts

: \frac{1}{2 5} x - \int - \frac{1}{4 5 x ^{\frac{1}{2}}} d x

= \frac{1}{2 5} x - \int - \frac{1}{4 5 x ^{\frac{1}{2}}} d x

\int - \frac{1}{4 5 x ^{\frac{1}{2}}} d x = - \frac{1}{2 5} x

= \frac{1}{2 5} x - (- \frac{1}{2 5} x)

Simplify

\frac{1}{2 5} x - (- \frac{1}{2 5} x) : \frac{1}{5} x

= \frac{1}{5} x

Add a constant to the solution

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

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What is the integral of 1/(sqrt(20x)) ?
The integral of 1/(sqrt(20x)) is 1/(sqrt(5))sqrt(x)+C