What is the integral of 1/2 (5-x) ?

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

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integral of 1/2 (5-x)

\int \frac{1}{2} (5 - x) d x

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

Solution steps

\int \frac{1}{2} (5 - x) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 5 - 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}{2} (\int 5 d x - \int x d x)

\int 5 d x = 5 x

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

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

Add a constant to the solution

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

\int x^{2} + 1 \cdot x d x

\int x e^{3 x^{2} - 1} d x

\int \frac{2}{5 x} d x

\int \frac{1 + sin ^{2} ( x )}{sin ( x ) cos ( x )} d x

\int (1 + u + u^{2} + u^{5}) d u

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