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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0050.01

 Input Form

 Integrate[z^n SinhIntegral[a z]^2, z] == (z^(n + 1)/(n + 1)) SinhIntegral[a z]^2 - (1/((-a)^n (2 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 ) 2 z z n + 1 Shi ( a z ) 2 n + 1 - 1 2 a ( n + 1 ) ( ( - a ) - n ( 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 ) ) ) ) ) /; n Condition z z n SinhIntegral a z 2 z n 1 SinhIntegral a z 2 n 1 -1 -1 1 2 a n 1 -1 -1 a -1 n 2 Gamma n 1 -1 a z -1 n Gamma n 1 a z SinhIntegral a z n -1 n ExpIntegralEi -2 a z -1 ExpIntegralEi 2 a z 1 -1 -1 n z 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 n [/itex]

 Rule Form

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

 2001-10-29