Fraction of integrals with different variables

[huey910]

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

 

[CompuChip]

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.

 

[Char. Limit]

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?

 

[micromass]

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

Or rather atan(x)+C...

 

[Char. Limit]

Or rather atan(x)+C...

Touche.

 

[CompuChip]

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