What is the integral of 1/((1-x)^{0.5)} ?

The integral of 1/((1-x)^{0.5)} is -2sqrt(1-x)+C

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integral of 1/((1-x)^{0.5)}

\int \frac{1}{( 1 - x ) ^{0.5}} d x

- 2 1 - x + C

Solution steps

\int \frac{1}{( 1 - x ) ^{0.5}} d x

Apply u-substitution

: \int - \frac{1}{u ^{\frac{1}{2}}} d u

= \int - \frac{1}{u ^{\frac{1}{2}}} d u

Take the constant out:

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

= - \int \frac{1}{u ^{\frac{1}{2}}} d u

Apply the Power Rule

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

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

Substitute back

u = 1 - x

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

Apply radical rule:

= - 2 1 - x

Add a constant to the solution

= - 2 1 - x + C

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\int \frac{1}{( 1 - 3 x ) ^{2}} d x

\int 16 x (3 - 4 x)^{40} d x

What is the integral of 1/((1-x)^{0.5)} ?
The integral of 1/((1-x)^{0.5)} is -2sqrt(1-x)+C