Solving integrals of functions of Jacobi elliptic amplitudes

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I have an integral on the form $\int \operatorname{dn}(\frac{x}{k},k^2)^2 + \sin({N\pi/2} + \operatorname{am}(\frac{x}{k}, k^2))^2dx$, anyone know of any good sources or solution methods for suchs an integral?