INTEGRAL of 1/(x^2+d^2)^1/2

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  • #1

Homework Statement

To find the INTEGRAL of 1/(x^2+d^2)^1/2 integrated with respect to dx.
d is a constant

I tried to write it as :

ln (x^2+ d^2)^1/2

but my book gives an answer of

ln { x + (x^2+ d^2)^1/2 }

i don't understand how. Can you please explain it step by step. Clearly please.
  • #2
how about starting with the subtitution x = d.sec(u)?
  • #3
Even better, use the substitution:

x=d\sinh u
Last edited:
  • #4
actually i meant x = d.tan(u), which makes more sense... but i'd still try huntmat's suggestion
  • #5
also d is a bad constant to use when you're differentiating as you may get confused, something like a or s would be better

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