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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0079.01

 Input Form

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

 Standard Form

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 MathML Form

 z n Shi ( a z ) Chi ( a z ) z z n + 1 Shi ( a z ) Chi ( a z ) n + 1 - a - n - 1 Chi ( a z ) ( ( - 1 ) n Γ ( n + 1 , - a z ) + Γ ( n + 1 , a z ) ) 2 ( n + 1 ) + a - n - 1 n ! 4 ( n + 1 ) ( Ei ( - 2 a z ) + log ( z ) + ( - 1 ) n ( Ei ( 2 a z ) + log ( z ) ) ) - ( - a ) - n 4 a ( n + 1 ) ( 2 ( Γ ( n + 1 , - a z ) - ( - 1 ) n Γ ( n + 1 , a z ) ) Shi ( a z ) - n ! ( ( - 1 ) n Ei ( - 2 a z ) + Ei ( 2 a z ) - ( 1 + ( - 1 ) n ) log ( z ) - 2 k = 1 n 1 k ! ( ( - a z ) k 2 k + 2 - k - 1 Γ ( k , - 2 a z ) ) - 2 ( - 1 ) n k = 1 n 1 k ! ( ( a z ) k 2 k + 2 - k - 1 Γ ( k , 2 a z ) ) ) ) + a - n - 1 n ! 2 ( n + 1 ) ( ( - 1 ) n k = 1 n 1 k ! ( ( - a z ) k 2 k - 2 - k - 1 Γ ( k , - 2 a z ) ) + k = 1 n 1 k ! ( ( a z ) k 2 k - 2 - k - 1 Γ ( k , 2 a z ) ) ) /; n Condition z z n SinhIntegral a z CoshIntegral a z z n 1 SinhIntegral a z CoshIntegral a z n 1 -1 -1 a -1 n -1 CoshIntegral a z -1 n Gamma n 1 -1 a z Gamma n 1 a z 2 n 1 -1 a -1 n -1 n 4 n 1 -1 ExpIntegralEi -2 a z z -1 n ExpIntegralEi 2 a z z -1 -1 a -1 n 4 a n 1 -1 2 Gamma n 1 -1 a z -1 -1 n Gamma n 1 a z SinhIntegral a z -1 n -1 n ExpIntegralEi -2 a z ExpIntegralEi 2 a z -1 1 -1 n z -1 2 k 1 n 1 k -1 -1 a z k 2 k -1 2 -1 k -1 Gamma k -2 a z -1 2 -1 n k 1 n 1 k -1 a z k 2 k -1 2 -1 k -1 Gamma k 2 a z a -1 n -1 n 2 n 1 -1 -1 n k 1 n 1 k -1 -1 a z k 2 k -1 -1 2 -1 k -1 Gamma k -2 a z k 1 n 1 k -1 a z k 2 k -1 -1 2 -1 k -1 Gamma k 2 a z n [/itex]

 Rule Form

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

 2001-10-29