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Popular >

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

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Frequently Asked Questions (FAQ)

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