Positive part function

The positive part function, also known as the ramp function, is similar to the identity function, except that for all negative numbers the number 0 is returned instead of the original value.

Integral
The indefinite integral of the positive part function is the positive part of halved square function, plus an arbitrary constant of integration.

$$\int x^+ \text{d}x$$ = $$ \left( \frac{1}{2} x^2 \right)^+ + c$$