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

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

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

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

Solution steps

\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}{5} + \frac{x ^{2} - 100 x + 6100}{1.1}

\int sin (y) cosh (x) d y

x \to 0 lim (1)

\int \frac{- ( x ^{2} - 1 ) ( 6 x ^{2} + 6 )}{x ^{2} + 1} d x

\int \frac{1}{0.15 x + 20} d x

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