Evaluate the integral ∫0^2 π ( d ϕ)/([1+k^2-2 k cos(ϕ-ϕ0)]^2[1+k1^2-2 k1 cos(ϕ-ψ)]), for k<1 and

Question

Evaluate the integral $\int_0^{2 \pi} \frac{\mathrm{~d} \phi}{\left[1+k^2-2 k \cos \left(\phi-\phi_0\right)\right]^2\left[1+k_1^2-2 k_1 \cos (\phi-\psi)\right]}$, for $k<1$ and $k_1<1$.

   Evaluate the integral
$\int_0^{2 \pi} \frac{\mathrm{~d} \phi}{\left[1+k^2-2 k \cos \left(\phi-\phi_0\right)\right]^2\left[1+k_1^2-2 k_1 \cos (\phi-\psi)\right]}$, for $k<1$ and $k_1<1$.

Mixed Boundary Value Problems of Potential Theory and their Applications in Engineering

V.I. Fabrikant 1st Edition

Chapter 1, Problem 3

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Evaluate the integral $\int_0^{2 \pi} \frac{\mathrm{~d} \phi}{\left[1+k^2-2 k \cos \left(\phi-\phi_0\right)\right]^2\left[1+k_1^2-2 k_1 \cos (\phi-\psi)\right]}$, for $k<1$ and $k_1<1$.

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