I am currently facing a difficult trigonometric integral that I want to solve using a solver. However, no solver I found could give me a solution. This could be either due to limited solver capabilities, or due to the integral not having a solution.
Here is the integral:
$$F(t) = \int(\cos(at+(b+c)t^2+dt^3)\cdot(ct+d)) dt$$
I think there should be a solution to this integral, as a parabola in the cosine leads to fresnel integrals. A third order polynomial like this should lead to an Incomplete Gamma Function.
My question is: Is this integral solvable by using Gamma Functions? If not, is there an approximation that might be helpful? Do you know of any solver that might be able to solve this problem?
Thank you very much for reading.
shs