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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Apply the Power Rule

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

= \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

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

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

(1 - x)^{2}

\frac{x ^{2}}{( x + 2 ) ^{3}}

x^{2} e^{- x^{2}}

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