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 Cosh

 http://functions.wolfram.com/01.20.21.1422.01

 Input Form

 Integrate[z^n E^(b z^2 + e) Cos[a z^2 + q] Cosh[c z^2 + g], z] == (-(1/8)) z^(1 + n) (E^(e + g + I q) (((-I) a - b - c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, ((-I) a - b - c) z^2] + E^(e + g - I q) ((I a - b - c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (I a - b - c) z^2] + E^(e - g + I q) (((-I) a - b + c) z^2)^ ((1/2) (-1 - n)) Gamma[(1 + n)/2, ((-I) a - b + c) z^2] + E^(e - g - I q) ((I a - b + c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (I a - b + c) z^2]) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n b z 2 + e cos ( a z 2 + q ) cosh ( c z 2 + g ) z - 1 8 z n + 1 ( e + g + q Γ ( n + 1 2 , ( - b - c - a ) z 2 ) ( ( - b - c - a ) z 2 ) 1 2 ( - n - 1 ) + e + g - q ( ( - b - c + a ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b - c + a ) z 2 ) + e - g + q ( ( - b + c - a ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + c - a ) z 2 ) + e - g - q ( ( - b + c + a ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + c + a ) z 2 ) ) /; n Condition z z n b z 2 e a z 2 q c z 2 g -1 1 8 z n 1 e g q Gamma n 1 2 -1 -1 b -1 c -1 a z 2 -1 b -1 c -1 a z 2 1 2 -1 n -1 e g -1 q -1 b -1 c a z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b -1 c a z 2 e -1 g q -1 b c -1 a z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b c -1 a z 2 e -1 g -1 q -1 b c a z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b c a z 2 n [/itex]

 Rule Form

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

 2002-12-18