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

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

\int \frac{x - 1}{x + 1} d x

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

Solution steps

\int \frac{x - 1}{x + 1} d x

Apply u-substitution

: \int 2 (u^{2} - 2) d u

= \int 2 (u^{2} - 2) d u

Take the constant out:

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

= 2 \cdot \int u^{2} - 2 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int u^{2} d u - \int 2 d u)

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

\int 2 d u = 2 u

= 2 (\frac{u ^{3}}{3} - 2 u)

Substitute back

u = x + 1

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

Simplify

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

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

Add a constant to the solution

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

\int (sin (3 x))^{3} d x

\int x 4 x - 3 d x

\int \frac{3}{u} d u

\int \frac{- 8}{x} d x

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