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 Exp

 http://functions.wolfram.com/01.03.21.0146.01

 Input Form

 Integrate[E^(d z)/(a z^2 + b z + c)^2, z] == ((-Sqrt[b^2 - 4 a c]) E^((d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)) (b + 2 a z) - (2 a - Sqrt[b^2 - 4 a c] d) E^((Sqrt[b^2 - 4 a c] d)/a) (c + z (b + a z)) ExpIntegralEi[(d (b - Sqrt[b^2 - 4 a c] + 2 a z))/ (2 a)] + (2 a + Sqrt[b^2 - 4 a c] d) (c + z (b + a z)) ExpIntegralEi[(d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)])/ E^(((b + Sqrt[b^2 - 4 a c]) d)/(2 a))/((b^2 - 4 a c)^(3/2) (c + z (b + a z)))

 Standard Form

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 MathML Form

 d z ( a z 2 + b z + c ) 2 z 1 ( b 2 - 4 a c ) 3 / 2 ( c + z ( b + a z ) ) - ( b + b 2 - 4 a c ) d 2 a ( - b 2 - 4 a c d ( b + 2 a z + b 2 - 4 a c ) 2 a ( b + 2 a z ) - ( 2 a - b 2 - 4 a c d ) b 2 - 4 a c d a ( c + z ( b + a z ) ) Ei ( d ( b + 2 a z - b 2 - 4 a c ) 2 a ) + ( 2 a + b 2 - 4 a c d ) ( c + z ( b + a z ) ) Ei ( d ( b + 2 a z + b 2 - 4 a c ) 2 a ) ) z d z a z 2 b z c 2 -1 1 b 2 -1 4 a c 3 2 c z b a z -1 -1 b b 2 -1 4 a c 1 2 d 2 a -1 -1 b 2 -1 4 a c 1 2 d b 2 a z b 2 -1 4 a c 1 2 2 a -1 b 2 a z -1 2 a -1 b 2 -1 4 a c 1 2 d b 2 -1 4 a c 1 2 d a -1 c z b a z ExpIntegralEi d b 2 a z -1 b 2 -1 4 a c 1 2 2 a -1 2 a b 2 -1 4 a c 1 2 d c z b a z ExpIntegralEi d b 2 a z b 2 -1 4 a c 1 2 2 a -1 [/itex]

 Rule Form

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

 2002-12-18