integrales de funciones trigonometricas hiperbolicas
04-22-2019, 06:43 AM
Post: #7
 Wes Loewer Member Posts: 195 Joined: Jan 2014
RE: integrales de funciones trigonometricas hiperbolicas

The Prime gives
∫(tanh(x),x) --> ln((e^x)^2+1)-x
which is correct.

By hand I would have done the following:

∫tanh(x) dx = ∫sinh(x)/cosh(x) dx = ln(cosh(x))+C

but this can be rewritten as

= ln((e^x+e^-x)/2) + C
= ln((e^(2x)+1)/(2e^x)) + C
= ln(e^2x)+1) - ln(2e^x) + C
= ln(e^2x)+1) - ln(2) - ln(e^x) + C
= ln(e^2x)+1) - x + (C-ln(2))
= ln(e^2x)+1) - x + D

Once again, the correct answers can be rewritten such that they differ by only a constant.

I've learned over the years that whenever a CAS's antiderivative looks different than mine, it's usually that they differ by a constant, or my antiderivative is wrong. :-)
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 Messages In This Thread integrales de funciones trigonometricas hiperbolicas - eduardo_MO0@hotmail.com - 04-16-2019, 09:13 PM RE: integrales de funciones trigonometricas hiperbolicas - Wes Loewer - 04-17-2019, 04:18 AM RE: integrales de funciones trigonometricas hiperbolicas - Tim Wessman - 04-17-2019, 04:28 AM RE: integrales de funciones trigonometricas hiperbolicas - Aries - 04-17-2019, 06:17 AM RE: integrales de funciones trigonometricas hiperbolicas - Carlos295pz - 04-20-2019, 02:02 AM RE: integrales de funciones trigonometricas hiperbolicas - Wes Loewer - 04-20-2019, 04:21 AM RE: integrales de funciones trigonometricas hiperbolicas - Wes Loewer - 04-22-2019 06:43 AM

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