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1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
3 -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi
4 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 15 E Sin[-- - k x]
5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
6 Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}.
7 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2
8 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x
9 Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]