1. The problem statement, all variables and given/known data Find ∫ In(ζ) dθ , where ζ= cosθ and In(ζ) is the gegenbauer function of the first kind. The original problem is to find find ∫ sinθ *I//n(ζ) dθ where I//n= 2nd differential of In(ζ) with respect to ζ. 2. Relevant equations d/dζ In(ζ)=-Pn-1(ζ), where Pn(ζ) is the legendre function of the first kind. In(ζ)= [Pn-2(ζ)-Pn(ζ)]/(2n-1) 3. The attempt at a solution I know d/dθ= d/dζ * dζ/dθ = -sinθ*d/dζ by the chain rule since ζ=cosθ, but how to apply that to integration of the gegenbauer with respect to theta? I came across that problem as I used integration via parts to solve the original problem.