What is the integral of 1/(sqrt(4s)) ?

The integral of 1/(sqrt(4s)) is 1/2 sqrt(s)+1/2 sqrt(s)+C

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integral of 1/(sqrt(4s))

\int \frac{1}{4 s} d s

\frac{1}{2} s + \frac{1}{2} s + C

Solution steps

\int \frac{1}{4 s} d s

Apply Integration By Parts

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

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

= \frac{1}{2} s - (- \frac{1}{2} s^{\frac{1}{2}})

Simplify

\frac{1}{2} s - (- \frac{1}{2} s^{\frac{1}{2}}) : \frac{1}{2} s + \frac{1}{2} s

= \frac{1}{2} s + \frac{1}{2} s

Add a constant to the solution

= \frac{1}{2} s + \frac{1}{2} s + C

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