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Integral - u substitution with arctan

  • #1

Homework Statement


integral of 1/(x^2 + z^2)^(3/2) dx,
where z is a constant

Homework Equations



The Attempt at a Solution


I set u = arctan(x/z) so du = z/(x^2 + z^2) dx but now I'm honestly stuck.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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You've got the correct substitution but you are thinking of this in a kind of convoluted way. Just put x=z*tan(u), so dx=z*sec(u)^2*du. Factor out a power of z and do the trig integral in u.
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
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540
[tex] x=z\sinh t [/tex]

is also a valid substitution.
 

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