en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 2(x+y)

Solution

\int 2 (x + y) d x

Solution

2 y x + x^{2} + C

Solution steps

\int 2 (x + y) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int y + x 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

= 2 (\int y d x + \int x d x)

\int y d x = y x

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

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

Simplify

2 (y x + \frac{x ^{2}}{2}) : 2 y x + x^{2}

= 2 y x + x^{2}

Add a constant to the solution

= 2 y x + x^{2} + C

Graph

Popular Examples

(d^2)/(dx^2)(xsin(x))

(\partial)/(\partial x)(cos(y^2-2x))

derivative of (x+1)/(x-1)

(\partial)/(\partial x)(log_{10}(xy))

area y=x^2-2x,y=-x^2+4x

Frequently Asked Questions (FAQ)

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