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 CosIntegral

 http://functions.wolfram.com/06.38.21.0028.01

 Input Form

 Integrate[z^3 Sin[b z] CosIntegral[a z], z] == (1/(2 b^4)) (3 I (-ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] + ExpIntegralEi[(-I) (a + b) z] - ExpIntegralEi[I (a + b) z]) + (1/((a - b)^3 (a + b)^3)) (2 a b Sin[a z] ((b^4 (-18 + b^2 z^2) - 2 a^2 b^2 (-8 + b^2 z^2) + a^4 (-6 + b^2 z^2)) Cos[b z] + b (-3 a^4 + 10 a^2 b^2 - 7 b^4) z Sin[b z])) - 2 CosIntegral[a z] (b z (-6 + b^2 z^2) Cos[b z] - 3 (-2 + b^2 z^2) Sin[b z]) + (1/((-a + b)^3 (a + b)^3)) (2 b^2 Cos[a z] (b (a^4 - 6 a^2 b^2 + 5 b^4) z Cos[b z] + (b^4 (-11 + b^2 z^2) + a^4 (-3 + b^2 z^2) + a^2 (6 b^2 - 2 b^4 z^2)) Sin[b z])))

 Standard Form

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 MathML Form

 z 3 sin ( b z ) Ci ( a z ) z 1 2 b 4 ( 3 ( - Ei ( - ( a - b ) z ) + Ei ( ( a - b ) z ) + Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) ) + 1 ( a - b ) 3 ( a + b ) 3 ( 2 a b sin ( a z ) ( ( ( b 2 z 2 - 6 ) a 4 - 2 b 2 ( b 2 z 2 - 8 ) a 2 + b 4 ( b 2 z 2 - 18 ) ) cos ( b z ) + b ( - 3 a 4 + 10 b 2 a 2 - 7 b 4 ) z sin ( b z ) ) ) + 1 ( b - a ) 3 ( a + b ) 3 ( 2 b 2 cos ( a z ) ( b ( a 4 - 6 b 2 a 2 + 5 b 4 ) z cos ( b z ) + ( ( b 2 z 2 - 3 ) a 4 + ( 6 b 2 - 2 b 4 z 2 ) a 2 + b 4 ( b 2 z 2 - 11 ) ) sin ( b z ) ) ) - 2 Ci ( a z ) ( b z ( b 2 z 2 - 6 ) cos ( b z ) - 3 ( b 2 z 2 - 2 ) sin ( b z ) ) ) z z 3 b z CosIntegral a z 1 2 b 4 -1 3 -1 ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z 1 a -1 b 3 a b 3 -1 2 a b a z b 2 z 2 -6 a 4 -1 2 b 2 b 2 z 2 -8 a 2 b 4 b 2 z 2 -18 b z b -3 a 4 10 b 2 a 2 -1 7 b 4 z b z 1 b -1 a 3 a b 3 -1 2 b 2 a z b a 4 -1 6 b 2 a 2 5 b 4 z b z b 2 z 2 -3 a 4 6 b 2 -1 2 b 4 z 2 a 2 b 4 b 2 z 2 -11 b z -1 2 CosIntegral a z b z b 2 z 2 -6 b z -1 3 b 2 z 2 -2 b z [/itex]

 Rule Form

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

 2001-10-29