What is the integral of x^2+2xy+y^2 ?

The integral of x^2+2xy+y^2 is y^2x+(x^3)/3+yx^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2+2xy+y^2

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

\frac{d y}{d x} = \frac{1}{1 - x ^{2}} - \frac{1}{x}

x^{2} + 4 x + 6

\int x^{2} ln (x^{2}) d x

2 t^{2} - t + 1

\int (5 x + 4)^{2} d x

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