Integrate[ArcCsc[a z + b]/z, z] == (1/8) (I (Pi - 2 ArcCsc[b + a z])^2 + 32 I ArcSin[Sqrt[1 - 1/b]/Sqrt[2]] ArcTan[((1 + b) Tan[(1/4) (Pi - 2 ArcCsc[b + a z])])/Sqrt[1 - b^2]] - 4 (Pi - 2 ArcCsc[b + a z] - 4 ArcSin[Sqrt[1 - 1/b]/Sqrt[2]]) Log[1 + (I (-1 + Sqrt[1 - b^2]))/(b E^(I ArcCsc[b + a z]))] - 4 (Pi - 2 ArcCsc[b + a z] + 4 ArcSin[Sqrt[1 - 1/b]/Sqrt[2]]) Log[1 - (I (1 + Sqrt[1 - b^2]))/(b E^(I ArcCsc[b + a z]))] - 8 ArcCsc[b + a z] Log[1 - E^(2 I ArcCsc[b + a z])] + 4 (Pi - 2 ArcCsc[b + a z]) Log[-((a z)/(b + a z))] + 8 ArcCsc[b + a z] Log[-((a z)/(b + a z))] + 8 I (PolyLog[2, -((I (-1 + Sqrt[1 - b^2]))/(b E^(I ArcCsc[b + a z])))] + PolyLog[2, (I (1 + Sqrt[1 - b^2]))/(b E^(I ArcCsc[b + a z]))]) + 4 I (ArcCsc[b + a z]^2 + PolyLog[2, E^(2 I ArcCsc[b + a z])]))

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2001-10-29