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 Cosh

 http://functions.wolfram.com/01.20.21.0882.01

 Input Form

 Integrate[(Sin[c z] Cosh[a z])/z^n, z] == (I (((-1)^n E^(2 a z) ((-(-a - I c)^n) (a - I c) ExpIntegralEi[ (a + I c) z] + (a - I c)^n (a + I c) ExpIntegralEi[ (-a) z + I c z]) + (-a - I c)^n (a - I c) E^(3 a z + I c z) (-1 + n)! Sum[((-a - I c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}] - (a - I c)^n (a + I c) E^((a + I c) z) (-1 + n)! Sum[((a - I c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}])/E^(2 a z) + ((-1)^n E^((a + I c) z) ((-a + I c)^n (a + I c) ExpIntegralEi[ (a - I c) z] - (a - I c) (a + I c)^n ExpIntegralEi[ (-(a + I c)) z]) - (-a + I c)^n (a + I c) E^(2 a z) (-1 + n)! Sum[((-a + I c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}] + (a - I c) (a + I c)^n (-1 + n)! Sum[((a + I c)^(k - n) z^(k - n))/Pochhammer[1 - n, k], {k, 1, -1 + n}])/E^((a + I c) z)))/(4 (a^2 + c^2) (-1 + n)!) /; Element[n, Integers] && n > 0

 Standard Form

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 MathML Form

 z - n sin ( c z ) cosh ( a z ) z 4 ( a 2 + c 2 ) ( n - 1 ) ! ( - ( a + c ) z ( - ( a + c ) 2 a z ( n - 1 ) ! ( k = 1 n - 1 ( c - a ) k - n z k - n ( 1 - n ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], "k"], Pochhammer] ) ( c - a ) n + ( - 1 ) n ( a + c ) z ( ( c - a ) n ( a + c ) Ei ( ( a - c ) z ) - ( a - c ) ( a + c ) n Ei ( - ( a + c ) z ) ) + ( a + c ) n ( a - c ) ( n - 1 ) ! k = 1 n - 1 ( a + c ) k - n z k - n ( 1 - n ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], "k"], Pochhammer] ) + - 2 a z ( ( a - c ) 3 a z + c z ( n - 1 ) ! ( k = 1 n - 1 ( - a - c ) k - n z k - n ( 1 - n ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], "k"], Pochhammer] ) ( - a - c ) n + ( - 1 ) n 2 a z ( ( a - c ) n ( a + c ) Ei ( c z - a z ) - ( - a - c ) n ( a - c ) Ei ( ( a + c ) z ) ) - ( a - c ) n ( a + c ) ( a + c ) z ( n - 1 ) ! k = 1 n - 1 ( a - c ) k - n z k - n ( 1 - n ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], "k"], Pochhammer] ) ) /; n + Condition z z -1 n c z a z 4 a 2 c 2 n -1 -1 -1 a c z -1 a c 2 a z n -1 k 1 n -1 c -1 a k -1 n z k -1 n Pochhammer 1 -1 n k -1 c -1 a n -1 n a c z c -1 a n a c ExpIntegralEi a -1 c z -1 a -1 c a c n ExpIntegralEi -1 a c z a c n a -1 c n -1 k 1 n -1 a c k -1 n z k -1 n Pochhammer 1 -1 n k -1 -2 a z a -1 c 3 a z c z n -1 k 1 n -1 -1 a -1 c k -1 n z k -1 n Pochhammer 1 -1 n k -1 -1 a -1 c n -1 n 2 a z a -1 c n a c ExpIntegralEi c z -1 a z -1 -1 a -1 c n a -1 c ExpIntegralEi a c z -1 a -1 c n a c a c z n -1 k 1 n -1 a -1 c k -1 n z k -1 n Pochhammer 1 -1 n k -1 n SuperPlus [/itex]

 Rule Form

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

 2002-12-18