What is the integral of 6/5 (2-x) ?

The integral of 6/5 (2-x) is 6/5 (2x-(x^2)/2)+C

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integral of 6/5 (2-x)

\int \frac{6}{5} (2 - x) d x

\frac{6}{5} (2 x - \frac{x ^{2}}{2}) + C

Solution steps

\int \frac{6}{5} (2 - x) d x

Take the constant out:

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

= \frac{6}{5} \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{6}{5} (\int 2 d x - \int x d x)

\int 2 d x = 2 x

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

= \frac{6}{5} (2 x - \frac{x ^{2}}{2})

Add a constant to the solution

= \frac{6}{5} (2 x - \frac{x ^{2}}{2}) + C

What is the integral of 6/5 (2-x) ?
The integral of 6/5 (2-x) is 6/5 (2x-(x^2)/2)+C