What is the integral of (2-3x)3 ?

The integral of (2-3x)3 is 3(2x-(3x^2)/2)+C

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integral of (2-3x)3

\int (2 - 3 x) 3 d x

3 (2 x - \frac{3 x ^{2}}{2}) + C

Solution steps

\int (2 - 3 x) \cdot 3 d x

Take the constant out:

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

= 3 \cdot \int 2 - 3 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

= 3 (\int 2 d x - \int 3 x d x)

\int 2 d x = 2 x

\int 3 x d x = \frac{3 x ^{2}}{2}

= 3 (2 x - \frac{3 x ^{2}}{2})

Add a constant to the solution

= 3 (2 x - \frac{3 x ^{2}}{2}) + C