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1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
3 -7 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 -7 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 -7 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 -7 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 -7 c x + I k0 x 2 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 -7 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 -7 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 -7 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 -7 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 -7 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 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] 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 4 4 4 4 Pi 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 4 4 4 4 4
6 Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}.
7 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2
8 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 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 Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 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)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]