Frankly, this is not just a good introduction to the Weierstrass substitution, but to integral transformations in general. This was a far clearer demonstration than anything I had seen on Wikipedia for that topic. Thank you.
hope to request, derive lagrangian multiplier, and the relation between polar coor and rectangular coor without making discontinuity, example how can r be negative? when r(theta) = cos(theta) when r is "defined" all positive. finding theta for (x,y)=(2/1) and (x,y) =(-2/-1) different in rectangular coor, but they are the same in polar coor