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I solved an equation and now I have this solution but I want to have everything more simple or at least just on Arc or Log! but I can't make them more simple!

FullSimplify[-((2 m ArcTanh[(m x)/Sqrt[-f+(b+m^2) x^2]]+m Log[f-b x^2]-2 Sqrt[b+m^2] Log[b x+m^2 x+Sqrt[b+m^2] Sqrt[-f+(b+m^2) x^2]])/(2 b)),Assumptions->{m>0,b>0,f>0,x>0}]

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  • $\begingroup$ expr = -((2 m ArcTanh[(m x)/Sqrt[-f + (b + m^2) x^2]] + m Log[f - b x^2] - 2 Sqrt[b + m^2] Log[ b x + m^2 x + Sqrt[b + m^2] Sqrt[-f + (b + m^2) x^2]])/(2 b)); and Simplify[TrigToExp[expr], Assumptions -> {m > 0, b > 0, f > 0, x > 0}] ? $\endgroup$
    – Syed
    Oct 28, 2021 at 20:09
  • $\begingroup$ Exactly I wanted this but the problem is now there is a lot of Log[] how to make them joint together? $\endgroup$
    – Mathecis
    Oct 28, 2021 at 20:39
  • $\begingroup$ This term "-f + (b + m^2) x^2 " is everywhere how to one change of the variable I can make them more simple? $\endgroup$
    – Mathecis
    Oct 28, 2021 at 20:43
  • $\begingroup$ I used this but it is not showing anything 1/(2 b) (-m Log[f - b x^2] + m Log[1 - (m x)/Sqrt[-f + (b + m^2) x^2]] - m Log[1 + (m x)/Sqrt[-f + (b + m^2) x^2]] + 2 Sqrt[b + m^2] Log[(b + m^2) x + Sqrt[(b + m^2) (-f + (b + m^2) x^2)]]) /. -f + (b + m^2) x -> Sin[[Theta]] $\endgroup$
    – Mathecis
    Oct 28, 2021 at 20:53
  • $\begingroup$ Try Simplify[1/(2 b)(-m Log[f-b x^2]+m Log[1-(m x)/Sqrt[-f+(b+m^2)x^2]]-m Log[1+(m x)/Sqrt[-f+(b+m^2)x^2]]+2 Sqrt[b+m^2]Log[(b+m^2)x+Sqrt[(b+m^2)(-f+(b+m^2)x^2)]]),-f+(b+m^2)x==st] If that mostly works then you can substitute Sin[Theta] for st. $\endgroup$
    – Bill
    Oct 28, 2021 at 21:44

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