anonymous
  • anonymous
how to find the integration int (sinh^-1x)dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
it equals ln(x+sqrt(x^2+1))
amistre64
  • amistre64
thats the derivative...lol
anonymous
  • anonymous
i need the procedure.......whatever be the ans...

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anonymous
  • anonymous
i have books where the ans is given but not the procedure......
amistre64
  • amistre64
ack!!...sinh^-1x = ln(x+sqrt(x^2+1))
amistre64
  • amistre64
integrate the ln function; is that possible?
nowhereman
  • nowhereman
There is a better way, substitute x = sinh(z). Then you can integrate by hand, because only terms of the form exp(z) and z exp(z) remain.
nowhereman
  • nowhereman
I get \[z\cosh z - \sinh z = \sqrt{1+x^2}\sinh^{-1} x - x\] can that be correct?
nowhereman
  • nowhereman
oh wait, you have to exchange sinh and cosh there ;-) but then it's correct. Yeah that substitution works :-)

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