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Finding Indefinite Integral of a combination of hyperbolic functions

  • Thread starter tainted
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  • #1
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Homework Statement



Compute the following:

[itex] \int \frac{cosh(x)}{cosh^2(x) - 1}\,dx [/itex]


Homework Equations


[itex] \int cosh(x)\,dx = sinh(x) + C [/itex]


The Attempt at a Solution


I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made [itex] u = tanh(\frac{x}{2}) [/itex] and I had no clue how I am supposed to know to do that.

Any advice on where to start is greatly appreciated.
 

Answers and Replies

  • #2
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I solved this problem after realizing that [itex] cosh^2(x) - 1 = sinh^2(x) [/itex]. This allowe me to split make it [itex] \int coth(x)csch(x)\,dx [/itex], and then I could use another identity to set that equal to [itex] -csch(x) + c [/itex]
 

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