What is the integral of (5-3x)/9 ?

The integral of (5-3x)/9 is 1/9 (5x-(3x^2)/2)+C

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integral of (5-3x)/9

\int \frac{5 - 3 x}{9} d x

\frac{1}{9} (5 x - \frac{3 x ^{2}}{2}) + C

Solution steps

\int \frac{5 - 3 x}{9} d x

Take the constant out:

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

= \frac{1}{9} \cdot \int 5 - 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

= \frac{1}{9} (\int 5 d x - \int 3 x d x)

\int 5 d x = 5 x

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

= \frac{1}{9} (5 x - \frac{3 x ^{2}}{2})

Add a constant to the solution

= \frac{1}{9} (5 x - \frac{3 x ^{2}}{2}) + C

What is the integral of (5-3x)/9 ?
The integral of (5-3x)/9 is 1/9 (5x-(3x^2)/2)+C