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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Complete the square

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

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = x + 1

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

Add a constant to the solution

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

\frac{d y}{d x} = (\frac{x y + 5 x - y - 5}{x y - 2 x + 6 y - 12})

x y^{3} d x + e^{x^{2}} d y = 0

(5 x^{2} + 2 x^{- 1} y + 2 x^{- 1} y^{2}) d x + (1 + 2 y) d y = 0

e^{θ} sin (5 θ)

x + 4

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