Define: $g(z) = \frac{1}{2}+\frac{1}{2}\sin(\frac{1}{z})$
Define: $f(x) = \int_1^x \Big(\int_1^y g(z)~\, dz\Big) dy~:~ \forall x > 0$
I just want to plot $f$ on the Cartesian plane to see what it looks like. Unfortunately Desmos crashes when I input $f$ and Wolfram Alpha doesn't like it either. This does not come from any textbook question or anything, I just made it up. My motivation for $f$ is that it should be strictly convex on its domain, but something strange that I can't even really describe yet should happen as $x \rightarrow 0^+$ (I think). I want to see what happens.
Does anyone have a tool/program powerful enough to graph this function near 0?