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 Cosh

 http://functions.wolfram.com/01.20.21.0324.01

 Input Form

 Integrate[z^3 E^(b z + e) Cosh[c z], z] == (1/((b - c)^4 (b + c)^4)) (E^(e + b z) ((-3 b^6 z^2 + b^7 z^3 + 3 b^2 c^2 (-12 + c^2 z^2) + 3 b^4 (-2 + c^2 z^2) - 3 c^4 (2 + c^2 z^2) + 3 b^3 c^2 z (4 + c^2 z^2) - b c^4 z (18 + c^2 z^2) + b^5 (6 z - 3 c^2 z^3)) Cosh[c z] + c (6 b^5 z^2 - b^6 z^3 + 3 b^4 z (-6 + c^2 z^2) - 3 b^2 c^2 z (-4 + c^2 z^2) - 12 b^3 (-2 + c^2 z^2) + 6 b c^2 (4 + c^2 z^2) + c^4 z (6 + c^2 z^2)) Sinh[c z]))

 Standard Form

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 MathML Form

 z 3 e + b z cosh ( c z ) z 1 ( b - c ) 4 ( b + c ) 4 ( e + b z ( ( z 3 b 7 - 3 z 2 b 6 + ( 6 z - 3 c 2 z 3 ) b 5 + 3 ( c 2 z 2 - 2 ) b 4 + 3 c 2 z ( c 2 z 2 + 4 ) b 3 + 3 c 2 ( c 2 z 2 - 12 ) b 2 - c 4 z ( c 2 z 2 + 18 ) b - 3 c 4 ( c 2 z 2 + 2 ) ) cosh ( c z ) + c ( - z 3 b 6 + 6 z 2 b 5 + 3 z ( c 2 z 2 - 6 ) b 4 - 12 ( c 2 z 2 - 2 ) b 3 - 3 c 2 z ( c 2 z 2 - 4 ) b 2 + 6 c 2 ( c 2 z 2 + 4 ) b + c 4 z ( c 2 z 2 + 6 ) ) sinh ( c z ) ) ) z z 3 e b z c z 1 b -1 c 4 b c 4 -1 e b z z 3 b 7 -1 3 z 2 b 6 6 z -1 3 c 2 z 3 b 5 3 c 2 z 2 -2 b 4 3 c 2 z c 2 z 2 4 b 3 3 c 2 c 2 z 2 -12 b 2 -1 c 4 z c 2 z 2 18 b -1 3 c 4 c 2 z 2 2 c z c -1 z 3 b 6 6 z 2 b 5 3 z c 2 z 2 -6 b 4 -1 12 c 2 z 2 -2 b 3 -1 3 c 2 z c 2 z 2 -4 b 2 6 c 2 c 2 z 2 4 b c 4 z c 2 z 2 6 c z [/itex]

 Rule Form

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

 2002-12-18