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 Cosh

 http://functions.wolfram.com/01.20.21.0349.01

 Input Form

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

 Standard Form

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 MathML Form

 z n b z cosh ( d + c z ) z - 1 2 d ( ( ( - 1 ) n Ei ( ( b + c ) z ) ( - n - 1 ) ! + ( b + c ) z k = 0 n ( ( - b - c ) z ) k ( n + 1 ) k - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["k", "-", "n"]]], Pochhammer] - ( b + c ) z k = n + 1 - 1 ( ( - b - c ) z ) k ( n + 1 ) k - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["k", "-", "n"]]], Pochhammer] ) ( - b - c ) - n - 1 + ( c - b ) - n - 1 - 2 d ( ( - 1 ) n Ei ( ( b - c ) z ) ( - n - 1 ) ! + ( b - c ) z k = 0 n ( ( c - b ) z ) k ( n + 1 ) k - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["k", "-", "n"]]], Pochhammer] - ( b - c ) z k = n + 1 - 1 ( ( c - b ) z ) k ( n + 1 ) k - n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], RowBox[List["k", "-", "n"]]], Pochhammer] ) ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z n b z d c z -1 1 2 d -1 n ExpIntegralEi b c z -1 n -1 -1 b c z k 0 n -1 b -1 c z k Pochhammer n 1 k -1 n -1 -1 b c z k n 1 -1 -1 b -1 c z k Pochhammer n 1 k -1 n -1 -1 b -1 c -1 n -1 c -1 b -1 n -1 -2 d -1 n ExpIntegralEi b -1 c z -1 n -1 -1 b -1 c z k 0 n c -1 b z k Pochhammer n 1 k -1 n -1 -1 b -1 c z k n 1 -1 c -1 b z k Pochhammer n 1 k -1 n -1 n [/itex]

 Rule Form

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

 2002-12-18