What is the integral of 2x-0.25x^2 ?

The integral of 2x-0.25x^2 is x^2-0.08333…x^3+C

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integral of 2x-0.25x^2

\int 2 x - 0.25 x^{2} d x

x^{2} - 0.08333 \dots x^{3} + C

Solution steps

\int 2 x - 0.25 x^{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 2 x d x - \int 0.25 x^{2} d x

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

\int 0.25 x^{2} d x = 0.08333 \dots x^{3}

= x^{2} - 0.08333 \dots x^{3}

Add a constant to the solution

= x^{2} - 0.08333 \dots x^{3} + C

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What is the integral of 2x-0.25x^2 ?
The integral of 2x-0.25x^2 is x^2-0.08333…x^3+C