What is the integral of-(x+37)/4 ?

The integral of-(x+37)/4 is -1/4 ((x^2)/2+37x)+C

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integral of-(x+37)/4

\int - \frac{x + 37}{4} d x

- \frac{1}{4} (\frac{x ^{2}}{2} + 37 x) + C

Solution steps

\int - \frac{x + 37}{4} d x

Take the constant out:

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

= - \frac{1}{4} \cdot \int x + 37 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}{4} (\int x d x + \int 37 d x)

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

\int 37 d x = 37 x

= - \frac{1}{4} (\frac{x ^{2}}{2} + 37 x)

Add a constant to the solution

= - \frac{1}{4} (\frac{x ^{2}}{2} + 37 x) + C

What is the integral of-(x+37)/4 ?
The integral of-(x+37)/4 is -1/4 ((x^2)/2+37x)+C