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anonymous

  • 5 years ago

how to find the integration int (sinh^-1x)dx

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  1. amistre64
    • 5 years ago
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    it equals ln(x+sqrt(x^2+1))

  2. amistre64
    • 5 years ago
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    thats the derivative...lol

  3. anonymous
    • 5 years ago
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    i need the procedure.......whatever be the ans...

  4. anonymous
    • 5 years ago
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    i have books where the ans is given but not the procedure......

  5. amistre64
    • 5 years ago
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    ack!!...sinh^-1x = ln(x+sqrt(x^2+1))

  6. amistre64
    • 5 years ago
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    integrate the ln function; is that possible?

  7. nowhereman
    • 5 years ago
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    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.

  8. nowhereman
    • 5 years ago
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    I get \[z\cosh z - \sinh z = \sqrt{1+x^2}\sinh^{-1} x - x\] can that be correct?

  9. nowhereman
    • 5 years ago
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    oh wait, you have to exchange sinh and cosh there ;-) but then it's correct. Yeah that substitution works :-)

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