What is the integral of ((x-2))/((1-v)) ?

The integral of ((x-2))/((1-v)) is 1/(1-v)(-2x+(x^2)/2)+C

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integral of ((x-2))/((1-v))

integral

\frac{( x - 2 )}{( 1 - v )}

\frac{1}{1 - v} (- 2 x + \frac{x ^{2}}{2}) + C

Solution steps

\int \frac{x - 2}{1 - v} d x

Take the constant out:

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

= \frac{1}{1 - v} \cdot \int - 2 + 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

= \frac{1}{1 - v} (- \int 2 d x + \int x d x)

\int 2 d x = 2 x

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

= \frac{1}{1 - v} (- 2 x + \frac{x ^{2}}{2})

Add a constant to the solution

= \frac{1}{1 - v} (- 2 x + \frac{x ^{2}}{2}) + C

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