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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x+1)^{-3}

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

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

Solution steps

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

Apply u-substitution

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

Substitute back

u = x + 1

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

Add a constant to the solution

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

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