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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

Popular Examples

y^{''}+2y^'+36y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

integral from 1 to 3 of (x-1)

\int_{1}^{3} (x - 1) d x

derivative of 2tan(xsec^2(x))

\frac{d}{d x} (2 tan (x) sec^{2} (x))

derivative of ln(tan(x))derivative of

ln (tan (x))

(\partial)/(\partial x)(((-x+y))/(x*y+3*x))

\frac{\partial}{\partial x} (\frac{( - x + y )}{x \cdot y + 3 \cdot x})

Frequently Asked Questions (FAQ)

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