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

  • #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 plz explain it step by step. Clearly plz.
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
how about starting with the subtitution x = d.sec(u)?
 
  • #3
hunt_mat
Homework Helper
1,724
16
Even better, use the substitution:

[tex]
x=d\sinh u
[/tex]
 
Last edited:
  • #4
lanedance
Homework Helper
3,304
2
actually i meant x = d.tan(u), which makes more sense... but i'd still try huntmat's suggestion
 
  • #5
lanedance
Homework Helper
3,304
2
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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