Fraction of integrals with different variables

huey910
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how would one evaluate this without using trig substitution? Is it possible to make one integral out of this?

{int[(y^2 + a1^2)^-1]dy +c1}/{int[(x^2 + a2^2)^-1]dx +c2} +c3

the numbers behind the 'a's and 'c's are supposed to be subscripts.

Also, how would one deal with this:

{int[(y^2 + a1^2)^-1]dy +c1}/(a tan{int[(x^2 + a2^2)^-1]dx +c2}) +c3


Please advise
 
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You can use the standard integral
\int \frac{1}{1 + x^2} \, dx = \tanh(x)
and a "normal" (non-trig) substitution, and then you can do them separately.
 
CompuChip said:
You can use the standard integral
\int \frac{1}{1 + x^2} \, dx = \tanh(x)
and a "normal" (non-trig) substitution, and then you can do them separately.

That doesn't seem right. Isn't that integral tan(x)+C, and not tanh(x)+C?
 
Char. Limit said:
That doesn't seem right. Isn't that integral tan(x)+C, and not tanh(x)+C?

Or rather atan(x)+C...
 
micromass said:
Or rather atan(x)+C...

Touche.
 
Heh, double fail :-)
I knew it was something with tan and an extra letter! Thanks micromass :)
 
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