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Currently I am puzzling on a real-world problem, involving some maths which I cannot solve using my limited calculus knowledge. The problem ultimately boils down to finding an expression for the function [itex]\phi(t)[/itex] which satisfies the following equation for any x within limits [itex]0 < x < 1 - x_s[/itex]:

[itex]1 - x - x_{s} = \int_{x_s/\phi_{max}}^{1/\phi_{2} - 1/\phi_{1}\cdot x} \phi(t) dt[/itex]

Constants: [itex]x_{s}, \phi_{1}, \phi_{2}, \phi_{max}[/itex] with [itex]0 < x_s < 1[/itex] and [itex]0 < \phi_{1} < \phi_{2} < \phi_{max}[/itex].

Has anybody got a clue on how to do this? An general approach would be much appreciated! Just gessing functions and trying them out somehow doesn't feel very intelligent...

.edit: I'll put you as co-author ;)

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# Not able to solve this integral problem

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