Fixed-Fixed Beam with two UDL

[reiiling]

I'm looking for the max bending moment and max deflection of the beam shown in the problem statement. I tried using the double integration method to find the deflection, but it does not look right. I did the model in ANSYS to evaluate the solution, and the result does not match with my calculations.
If anyone could provide with a exact sample question with a detailed solution that would be great. Thanks a lot.
Sorry just could not get my head around for this question.

Homework Statement

2. The attempt at a solution

 

[Joppy]

I would recommend using the singularity function method for something like this, otherwise it's quite arduous (as I'm sure you've noticed).