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 Cosh

 http://functions.wolfram.com/01.20.21.0291.01

 Input Form

 Integrate[(E^(b z) Cosh[c z])/z^n, z] == (-E^((-b + c) z)) (((-1)^n E^((b - c) z) ((-b - c) (-b + c)^n ExpIntegralEi[(b - c) z] - (-b - c)^n (b - c) ExpIntegralEi[(b + c) z]) + (-b - c)^n (b - c) E^(2 b z) (-1 + n)! Sum[((-b - c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}] - (-b - c) (-b + c)^n E^(2 (b - c) z) (-1 + n)! Sum[((-b + c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}])/ (2 (b^2 - c^2) (-1 + n)!)) /; Element[n, Integers] && n > 0

 Standard Form

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 MathML Form

 z - n b z cosh ( c z ) z - 1 2 ( b 2 - c 2 ) ( n - 1 ) ! ( ( c - b ) z ( ( b - c ) 2 b z ( n - 1 ) ! ( k = 1 n - 1 ( - b - c ) k - n z k - n ( 1 - n ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], "k"], Pochhammer] ) ( - b - c ) n - ( c - b ) n 2 ( b - c ) z ( n - 1 ) ! ( k = 1 n - 1 ( c - b ) k - n z k - n ( 1 - n ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], "k"], Pochhammer] ) ( - b - c ) + ( - 1 ) n ( b - c ) z ( ( - b - c ) ( c - b ) n Ei ( ( b - c ) z ) - ( - b - c ) n ( b - c ) Ei ( ( b + c ) z ) ) ) ) /; n + Condition z z -1 n b z c z -1 1 2 b 2 -1 c 2 n -1 -1 c -1 b z b -1 c 2 b z n -1 k 1 n -1 -1 b -1 c k -1 n z k -1 n Pochhammer 1 -1 n k -1 -1 b -1 c n -1 c -1 b n 2 b -1 c z n -1 k 1 n -1 c -1 b k -1 n z k -1 n Pochhammer 1 -1 n k -1 -1 b -1 c -1 n b -1 c z -1 b -1 c c -1 b n ExpIntegralEi b -1 c z -1 -1 b -1 c n b -1 c ExpIntegralEi b c z n SuperPlus [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18