I have a certain integration result which Sage is currently unaware of. I
need a way to make sage aware of it in some fashion, via substitution or
anything else.
For example, sage currently cannot perform the following integral
sage: var(' k t')
sage: integrate(sqrt(1-k^2*sin(t)^2),t,0,pi/2)
integrate(sqrt(-k^2*sin(t)^2+1),t,0,pi/2)
In fact, the integral defines the elliptice function E(k).
Is there any way of substituting the unknown integral above for a function
like E(k) in sage? Can sage be programmed to recognise such substitutions
automatically?
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