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 CosIntegral

 http://functions.wolfram.com/06.38.21.0069.01

 Input Form

 Integrate[z^2 SinIntegral[b z] CosIntegral[a z], z] == (1/6) ((1/b^3) (ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] + ExpIntegralEi[(-I) (a + b) z] + ExpIntegralEi[I (a + b) z]) - (1/(2 b^2)) ((1/(a^2 - b^2)) (-8 b Cos[a z] Cos[b z] + b (-a^2 + b^2) z^2 (ExpIntegralE[-1, (-I) (a - b) z] + ExpIntegralE[-1, I (a - b) z] + ExpIntegralE[-1, (-I) (a + b) z] + ExpIntegralE[-1, I (a + b) z]) - 8 a Sin[a z] Sin[b z])) - (1/b^3) (CosIntegral[a z] (Gamma[3, (-I) b z] + Gamma[3, I b z])) + 2 z^3 CosIntegral[a z] SinIntegral[b z] - (1/a^3) (((a^2 - b^2)^2 (ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] - ExpIntegralEi[(-I) (a + b) z] - ExpIntegralEi[I (a + b) z]) + 2 a b Cos[b z] (2 (-2 a^2 + b^2) Cos[a z] + a (-a^2 + b^2) z Sin[a z]) + 2 a^2 (a (a - b) (a + b) z Cos[a z] + (-3 a^2 + b^2) Sin[a z]) Sin[b z])/(a^2 - b^2)^2 + I (Gamma[3, (-I) a z] - Gamma[3, I a z]) SinIntegral[b z]))

 Standard Form

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 MathML Form

 z 2 Si ( b z ) Ci ( a z ) z 1 6 ( 2 Ci ( a z ) Si ( b z ) z 3 + 1 b 3 ( Ei ( - ( a - b ) z ) + Ei ( ( a - b ) z ) + Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) ) - 1 ( 2 b 2 ) ( a 2 - b 2 ) ( b ( b 2 - a 2 ) ( E TagBox["E", ExpIntegralE] - 1 ( - ( a - b ) z ) + E TagBox["E", ExpIntegralE] - 1 ( ( a - b ) z ) + E TagBox["E", ExpIntegralE] - 1 ( - ( a + b ) z ) + E TagBox["E", ExpIntegralE] - 1 ( ( a + b ) z ) ) z 2 - 8 b cos ( a z ) cos ( b z ) - 8 a sin ( a z ) sin ( b z ) ) - 1 a 3 ( 1 ( a 2 - b 2 ) 2 ( 2 ( a ( a - b ) ( a + b ) z cos ( a z ) + ( b 2 - 3 a 2 ) sin ( a z ) ) sin ( b z ) a 2 + 2 b cos ( b z ) ( 2 ( b 2 - 2 a 2 ) cos ( a z ) + a ( b 2 - a 2 ) z sin ( a z ) ) a + ( a 2 - b 2 ) 2 ( Ei ( - ( a - b ) z ) + Ei ( ( a - b ) z ) - Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) ) ) + ( Γ ( 3 , - a z ) - Γ ( 3 , a z ) ) Si ( b z ) ) ) - Ci ( a z ) ( Γ ( 3 , - b z ) + Γ ( 3 , b z ) ) b 3 z z 2 SinIntegral b z CosIntegral a z 1 6 2 CosIntegral a z SinIntegral b z z 3 1 b 3 -1 ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z ExpIntegralEi -1 a b z ExpIntegralEi a b z -1 1 2 b 2 a 2 -1 b 2 -1 b b 2 -1 a 2 ExpIntegralE -1 -1 a -1 b z ExpIntegralE -1 a -1 b z ExpIntegralE -1 -1 a b z ExpIntegralE -1 a b z z 2 -1 8 b a z b z -1 8 a a z b z -1 1 a 3 -1 1 a 2 -1 b 2 2 -1 2 a a -1 b a b z a z b 2 -1 3 a 2 a z b z a 2 2 b b z 2 b 2 -1 2 a 2 a z a b 2 -1 a 2 z a z a a 2 -1 b 2 2 ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z -1 ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z Gamma 3 -1 a z -1 Gamma 3 a z SinIntegral b z -1 CosIntegral a z Gamma 3 -1 b z Gamma 3 b z b 3 -1 [/itex]

 Rule Form

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

 2001-10-29