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

The integral of 1/(sqrt(1-u)) is -2sqrt(1-u)+C

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

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

- 2 1 - u + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{v} d v

= \int - \frac{1}{v} d v

Take the constant out:

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

= - \int \frac{1}{v} d v

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= - 2 v^{\frac{1}{2}}

Substitute back

v = 1 - u

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= - 2 1 - u

Add a constant to the solution

= - 2 1 - u + C

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What is the integral of 1/(sqrt(1-u)) ?
The integral of 1/(sqrt(1-u)) is -2sqrt(1-u)+C