What is the integral of (1/(x-1))^{(-1)/2} ?

The integral of (1/(x-1))^{(-1)/2} is 2/3 (x-1)^{3/2}+C

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integral of (1/(x-1))^{(-1)/2}

integral

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

\frac{2}{3} (x - 1)^{\frac{3}{2}} + C

Solution steps

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

Simplify

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

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

Apply u-substitution

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

Apply the Power Rule

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x - 1

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

Add a constant to the solution

= \frac{2}{3} (x - 1)^{\frac{3}{2}} + C

What is the integral of (1/(x-1))^{(-1)/2} ?
The integral of (1/(x-1))^{(-1)/2} is 2/3 (x-1)^{3/2}+C