What is the integral of (2x-1)/3 ?

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

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integral of (2x-1)/3

\int \frac{2 x - 1}{3} d x

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

Solution steps

\int \frac{2 x - 1}{3} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int 2 x - 1 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}{3} (\int 2 x d x - \int 1 d x)

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

\int 1 d x = x

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

Add a constant to the solution

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