What is the integral of (sqrt(1-w))/(sqrt(w)) ?

The integral of (sqrt(1-w))/(sqrt(w)) is sqrt((1-w)/w)w+arcsin(sqrt(w))+C

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integral of (sqrt(1-w))/(sqrt(w))

\int \frac{1 - w}{w} d w

\frac{1 - w}{w} w + arcsin (w) + C

Solution steps

\int \frac{1 - w}{w} d w

Apply Integration By Parts

= \frac{1 - w}{w} w - \int - \frac{1}{2 w ^{\frac{1}{2}} - w + 1} d w

\int - \frac{1}{2 w ^{\frac{1}{2}} - w + 1} d w = - arcsin (w)

= \frac{1 - w}{w} w - (- arcsin (w))

Simplify

= \frac{1 - w}{w} w + arcsin (w)

Add a constant to the solution

= \frac{1 - w}{w} w + arcsin (w) + C

What is the integral of (sqrt(1-w))/(sqrt(w)) ?
The integral of (sqrt(1-w))/(sqrt(w)) is sqrt((1-w)/w)w+arcsin(sqrt(w))+C