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 Exp

 http://functions.wolfram.com/01.03.21.0778.01

 Input Form

 Integrate[z^4/(a + b c^(d z))^2, z] == (1/(5 a^2)) (z^5 - (5 z^4)/(d Log[c]) + (5 a z^4)/(a d Log[c] + b c^(d z) d Log[c]) + (20 z^3 Log[1 + (b c^(d z))/a])/(d^2 Log[c]^2) - (5 z^4 Log[1 + (b c^(d z))/a])/(d Log[c]) - (20 z^2 (-3 + d z Log[c]) PolyLog[2, -((b c^(d z))/a)])/(d^3 Log[c]^3) + (60 z (-2 + d z Log[c]) PolyLog[3, -((b c^(d z))/a)])/(d^4 Log[c]^4) + (120 PolyLog[4, -((b c^(d z))/a)])/(d^5 Log[c]^5) - (120 z PolyLog[4, -((b c^(d z))/a)])/(d^4 Log[c]^4) + (120 PolyLog[5, -((b c^(d z))/a)])/(d^5 Log[c]^5))

 Standard Form

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 MathML Form

 z 4 ( a + b c d z ) 2 z 1 5 a 2 ( z 5 - 5 log ( b c d z a + 1 ) z 4 d log ( c ) - 5 z 4 d log ( c ) + 5 a z 4 b d log ( c ) c d z + a d log ( c ) + 20 log ( b c d z a + 1 ) z 3 d 2 log 2 ( c ) - 20 ( d z log ( c ) - 3 ) Li PolyLog 2 ( - b c d z a ) z 2 d 3 log 3 ( c ) + 60 ( d z log ( c ) - 2 ) Li PolyLog 3 ( - b c d z a ) z d 4 log 4 ( c ) - 120 Li PolyLog 4 ( - b c d z a ) z d 4 log 4 ( c ) + 120 Li PolyLog 4 ( - b c d z a ) d 5 log 5 ( c ) + 120 Li PolyLog 5 ( - b c d z a ) d 5 log 5 ( c ) ) z z 4 a b c d z 2 -1 1 5 a 2 -1 z 5 -1 5 b c d z a -1 1 z 4 d c -1 -1 5 z 4 d c -1 5 a z 4 b d c c d z a d c -1 20 b c d z a -1 1 z 3 d 2 c 2 -1 -1 20 d z c -3 PolyLog 2 -1 b c d z a -1 z 2 d 3 c 3 -1 60 d z c -2 PolyLog 3 -1 b c d z a -1 z d 4 c 4 -1 -1 120 PolyLog 4 -1 b c d z a -1 z d 4 c 4 -1 120 PolyLog 4 -1 b c d z a -1 d 5 c 5 -1 120 PolyLog 5 -1 b c d z a -1 d 5 c 5 -1 [/itex]

 Rule Form

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

 2002-12-18