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 CosIntegral

 http://functions.wolfram.com/06.38.21.0025.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29