It's so handy to have functions that evaluate to either the derivative or the integral for a particular (version of a) shaping function like smoothstep. Analyt

It's so handy to have functions that evaluate to either the derivative or the integral for a particular (version of a) shaping function like smoothstep. Analytic integration has yielded some of the most stunning optimizations in graphics rendering! Replacing sample-the-hell-out-of-signal-and-integrate-the-samples with instead direct evaluation of an integral (or good-enough-standin-integral) function (where that itself can be known or derived) can yield many speedups and cool tricks!