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 SinIntegral

 http://functions.wolfram.com/06.37.21.0058.01

 Input Form

 Integrate[z^2 SinIntegral[a z] SinIntegral[b z], z] == (1/3) ((1/b^3) (((-2 + b^2 z^2) Cos[b z] - 2 b z Sin[b z]) SinIntegral[a z]) + (1/a^3) (((-2 + a^2 z^2) Cos[a z] - 2 a z Sin[a z] + a^3 z^3 SinIntegral[a z]) SinIntegral[b z]) + (a b (b (a^2 + 2 b^2) Cos[b z] Sin[a z] + a Cos[a z] (b (a^2 - b^2) z Cos[b z] - (2 a^2 + b^2) Sin[b z])) + (a^5 - a^3 b^2 - a^2 b^3 + b^5) SinIntegral[(a - b) z] + (a^5 - a^3 b^2 + a^2 b^3 - b^5) SinIntegral[(a + b) z])/ (a^3 (a - b) b^3 (a + b)))

 Standard Form

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 MathML Form

 z 2 Si ( a z ) Si ( b z ) z 1 3 ( ( ( b 2 z 2 - 2 ) cos ( b z ) - 2 b z sin ( b z ) ) Si ( a z ) b 3 + 1 a 3 ( ( a 3 Si ( a z ) z 3 - 2 a sin ( a z ) z + ( a 2 z 2 - 2 ) cos ( a z ) ) Si ( b z ) ) + 1 a 3 ( a - b ) b 3 ( a + b ) ( a b ( b ( a 2 + 2 b 2 ) cos ( b z ) sin ( a z ) + a cos ( a z ) ( b ( a 2 - b 2 ) z cos ( b z ) - ( 2 a 2 + b 2 ) sin ( b z ) ) ) + ( a 5 - b 2 a 3 - b 3 a 2 + b 5 ) Si ( ( a - b ) z ) + ( a 5 - b 2 a 3 + b 3 a 2 - b 5 ) Si ( ( a + b ) z ) ) ) z z 2 SinIntegral a z SinIntegral b z 1 3 b 2 z 2 -2 b z -1 2 b z b z SinIntegral a z b 3 -1 1 a 3 -1 a 3 SinIntegral a z z 3 -1 2 a a z z a 2 z 2 -2 a z SinIntegral b z 1 a 3 a -1 b b 3 a b -1 a b b a 2 2 b 2 b z a z a a z b a 2 -1 b 2 z b z -1 2 a 2 b 2 b z a 5 -1 b 2 a 3 -1 b 3 a 2 b 5 SinIntegral a -1 b z a 5 -1 b 2 a 3 b 3 a 2 -1 b 5 SinIntegral a b z [/itex]

 Rule Form

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

 2001-10-29