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I am working on deriving expression for deflection of a tapered beam with an elliptic cross-section. Hence, area moment of inertia is a linear function of the beam length. The beam is fixed at one end, and a concentrated force F is applied on its tip at the free end. I am using the known relation between second derivative of deflection and moment. To verify my solution of the first integral (yielding the slope), I compare the result with the expression for the slope of tapered beam with circular cross-section under the same boundary conditions, by equating the minor and major semi-axes of the elliptic cross-section. The problem is: by equating the minor and major axes of the elliptic cross section, the solution diverges (resulting in 0/0). I tried integration manually and with mathematica, but the solution always diverges. Attached is my solution.

I would appreciate hints about what is wrong with this solution.

Thanks!

I would appreciate hints about what is wrong with this solution.

Thanks!