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Popular >

integral of 2(x+1)

Solution

\int 2 (x + 1) d x

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

Popular Examples

y^{''}+4y^'+5y=0,y(0)=-1,y^'(0)=-3

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = - 1, y^{^{'}} (0) = - 3

integral of sin(x)cos(nx)

\int sin (x) cos (n x) d x

\frac{d y}{d x} y = 8 x

limit as x approaches 0+of x/(x-3)

x \to 0 + lim (\frac{x}{x - 3})

y^{''}+2y^'+5y=t^3

y^{^{''}} + 2 y^{^{'}} + 5 y = t^{3}

Frequently Asked Questions (FAQ)

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