What is the integral from 2 to x of ((2x-3))/6 ?

The integral from 2 to x of ((2x-3))/6 is 1/6 (x^2-3x+2)

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integral from 2 to x of ((2x-3))/6

\int_{2}^{x} \frac{( 2 x - 3 )}{6} d x

\frac{1}{6} (x^{2} - 3 x + 2)

Solution steps

\int_{2}^{x} \frac{2 x - 3}{6} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int_{2}^{x} 2 x - 3 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}{6} (\int_{2}^{x} 2 x d x - \int_{2}^{x} 3 d x)

\int_{2}^{x} 2 x d x = x^{2} - 4

\int_{2}^{x} 3 d x = 3 x - 6

= \frac{1}{6} (x^{2} - 4 - (3 x - 6))

Simplify

\frac{1}{6} (x^{2} - 4 - (3 x - 6)) : \frac{1}{6} (x^{2} - 3 x + 2)

= \frac{1}{6} (x^{2} - 3 x + 2)

x \to - 5 lim (sin (x \cdot π))

\frac{\partial}{\partial x} ((14 + 17 x) y^{t a n (x)})

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

\frac{d}{d x} (ln (sin (e^{x})))

g (x) = ln (3 x)

What is the integral from 2 to x of ((2x-3))/6 ?
The integral from 2 to x of ((2x-3))/6 is 1/6 (x^2-3x+2)