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 CosIntegral

 http://functions.wolfram.com/06.38.21.0024.01

 Input Form

 Integrate[z^n Sin[b z] CosIntegral[a z], z] == (-(I/4)) (I b)^(-1 - n) n! ((-(-1)^n) ExpIntegralEi[(-I) (a - b) z] - ExpIntegralEi[I (a - b) z] - ExpIntegralEi[(-I) (a + b) z] - (-1)^n ExpIntegralEi[I (a + b) z] + (1/Gamma[2 + n]) (2 (1 + n) CosIntegral[a z] ((-1)^n Gamma[1 + n, (-I) b z] + Gamma[1 + n, I b z])) + (-1)^n E^(I (a + b) z) Sum[((b/(b + a))^m Sum[(((-I) a - I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] + ((-1)^n Sum[((b/(b - a))^m Sum[((I a - I b)^k z^k)/k!, {k, 0, -1 + m}])/ m, {m, 1, n}])/E^(I (a - b) z) + E^(I (a - b) z) Sum[((b/(b - a))^m Sum[(((-I) a + I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] + Sum[((b/(b + a))^m Sum[((I a + I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}]/E^(I (a + b) z)) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n sin ( b z ) Ci ( a z ) z - 4 ( b ) - n - 1 n ! ( - ( - 1 ) n Ei ( - ( a - b ) z ) - Ei ( ( a - b ) z ) - Ei ( - ( a + b ) z ) - ( - 1 ) n Ei ( ( a + b ) z ) + 1 Γ ( n + 2 ) ( 2 ( n + 1 ) Ci ( a z ) ( ( - 1 ) n Γ ( n + 1 , - b z ) + Γ ( n + 1 , b z ) ) ) + ( a - b ) z m = 1 n 1 m ( b b - a ) m k = 0 m - 1 ( - a + b ) k z k k ! + - ( a + b ) z m = 1 n 1 m ( b a + b ) m k = 0 m - 1 ( a + b ) k z k k ! + ( - 1 ) n ( a + b ) z m = 1 n 1 m ( b a + b ) m k = 0 m - 1 ( - a - b ) k z k k ! + ( - 1 ) n - ( a - b ) z m = 1 n 1 m ( b b - a ) m k = 0 m - 1 ( a - b ) k z k k ! ) /; n Condition z z n b z CosIntegral a z -1 4 -1 b -1 n -1 n -1 -1 n ExpIntegralEi -1 a -1 b z -1 ExpIntegralEi a -1 b z -1 ExpIntegralEi -1 a b z -1 -1 n ExpIntegralEi a b z 1 Gamma n 2 -1 2 n 1 CosIntegral a z -1 n Gamma n 1 -1 b z Gamma n 1 b z a -1 b z m 1 n 1 m -1 b b -1 a -1 m k 0 m -1 -1 a b k z k k -1 -1 a b z m 1 n 1 m -1 b a b -1 m k 0 m -1 a b k z k k -1 -1 n a b z m 1 n 1 m -1 b a b -1 m k 0 m -1 -1 a -1 b k z k k -1 -1 n -1 a -1 b z m 1 n 1 m -1 b b -1 a -1 m k 0 m -1 a -1 b k z k k -1 n [/itex]

 Rule Form

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

 2001-10-29