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 Exp

 http://functions.wolfram.com/01.03.21.0147.01

 Input Form

 Integrate[(z E^(d z))/(a z^2 + b z + c)^2, z] == ((b (b - Sqrt[b^2 - 4 a c]) d + 2 a (b - 2 c d)) E^(((-b + Sqrt[b^2 - 4 a c]) d)/(2 a)) ExpIntegralEi[ (d (b - Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)] + (1/(c + z (b + a z))) ((2 a Sqrt[b^2 - 4 a c] E^((d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)) (2 c + b z) - (b (b + Sqrt[b^2 - 4 a c]) d + 2 a (b - 2 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))))/ (2 a (b^2 - 4 a c)^(3/2))

 Standard Form

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 MathML Form

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

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