What is the integral of 1/(x^2+2x+1) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(x^2+2x+1)

\int \frac{1}{x ^{2} + 2 x + 1} d x

- \frac{1}{x + 1} + C

Solution steps

\int \frac{1}{x ^{2} + 2 x + 1} d x

Complete the square

x^{2} + 2 x + 1 : (x + 1)^{2}

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

Apply u-substitution

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

Apply the Power Rule

= - \frac{1}{u}

Substitute back

u = x + 1

= - \frac{1}{x + 1}

Add a constant to the solution

= - \frac{1}{x + 1} + C

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