What is the integral of a/2 x+a/2 ?

The integral of a/2 x+a/2 is (ax^2)/4+a/2 x+C

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integral of a/2 x+a/2

\int \frac{a}{2} x + \frac{a}{2} d x

\frac{a x ^{2}}{4} + \frac{a}{2} x + C

Solution steps

\int \frac{a}{2} x + \frac{a}{2} 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

= \int \frac{a}{2} x d x + \int \frac{a}{2} d x

\int \frac{a}{2} x d x = \frac{a x ^{2}}{4}

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

= \frac{a x ^{2}}{4} + \frac{a}{2} x

Add a constant to the solution

= \frac{a x ^{2}}{4} + \frac{a}{2} x + C

x \to 8 lim (2 x - 7 x^{2})

\frac{d}{d x} (\frac{x + y}{x - y})

f (x) = x^{4} - 18 x^{2} + 81, at x = 1

\frac{\partial}{\partial x} (2 y^{3} x)

\frac{d}{d x} (sin (\frac{x}{y}))

What is the integral of a/2 x+a/2 ?
The integral of a/2 x+a/2 is (ax^2)/4+a/2 x+C