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Popular Calculus >

integral of 2(x+1)

Solution

integral

2 (x + 1)

Solution

x^{2} + 2 x + C

Solution steps

\int 2 (x + 1) d x

Take the constant out:

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

= 2 \cdot \int x + 1 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 x d x + \int 1 d x)

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

\int 1 d x = x

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

Simplify

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

= x^{2} + 2 x

Add a constant to the solution

= x^{2} + 2 x + C

Graph

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Frequently Asked Questions (FAQ)

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