en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1+x)^2

Solution

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

Solution

x + x^{2} + \frac{x ^{3}}{3} + C

Solution steps

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

Expand

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

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

Apply the Sum Rule:

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

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

\int 1 d x = x

\int 2 x d x = x^{2}

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

= x + x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= x + x^{2} + \frac{x ^{3}}{3} + C

Popular Examples

integral of 11tan^2(x)sec^3(x)

\int 11 tan^{2} (x) sec^{3} (x) d x

integral of sqrt(1+2sin(3x))cos(3x)

\int 1 + 2 sin (3 x) cos (3 x) d x

limit as x approaches 1 of 8

x \to 1 lim (8)

limit as x approaches 0 of (2sin(3x))/x

x \to 0 lim (\frac{2 sin ( 3 x )}{x})

integral of 1/(4pit)e^{-(r^2)/(4t)}r

\int \frac{1}{4 π t} e^{- \frac{r ^{2}}{4 t}} r d r

Frequently Asked Questions (FAQ)

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