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 CosIntegral

 http://functions.wolfram.com/06.38.21.0067.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29