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Integrate[1/(-1 + x^7), x] ==
(-2*ArcTan[Sec[Pi/14]*(x + Sin[Pi/14])]*Cos[Pi/14])/
7 - (2*ArcTan[Sec[(3*Pi)/14]*(x - Sin[(3*Pi)/14])]*
Cos[(3*Pi)/14])/7 + Log[-1 + x]/7 -
(Cos[Pi/7]*Log[1 + x^2 + 2*x*Cos[Pi/7]])/7 -
(Log[1 + x^2 + 2*x*Sin[Pi/14]]*Sin[Pi/14])/7 -
(2*ArcTan[(x + Cos[Pi/7])*Csc[Pi/7]]*Sin[Pi/7])/7 +
(Log[1 + x^2 - 2*x*Sin[(3*Pi)/14]]*Sin[(3*Pi)/14])/7
1
Integrate[-------, x] ==
7
-1 + x Pi Pi Pi
-2 ArcTan[Sec[--] (x + Sin[--])] Cos[--]
14 14 14
---------------------------------------- -
7
3 Pi 3 Pi 3 Pi
2 ArcTan[Sec[----] (x - Sin[----])] Cos[----]
14 14 14
--------------------------------------------- +
7
Pi 2 Pi
Cos[--] Log[1 + x + 2 x Cos[--]]
Log[-1 + x] 7 7
----------- - --------------------------------- -
7 7
2 Pi Pi
Log[1 + x + 2 x Sin[--]] Sin[--]
14 14
--------------------------------- -
7
Pi Pi Pi
2 ArcTan[(x + Cos[--]) Csc[--]] Sin[--]
7 7 7
--------------------------------------- +
7
2 3 Pi 3 Pi
Log[1 + x - 2 x Sin[----]] Sin[----]
14 14
-------------------------------------
7
Time to compute: 0.01 second
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