# Calculating this integral? $\int \frac{1}{1+x^2\cdot y^2}$dy

So I have this integral $\displaystyle\int \frac{1}{1+x^2\cdot y^2}dy$. Is it possible to rewrite this integral to $\displaystyle\int \frac{1}{1+u^2}du$ using substitution, as I know the value of this integral, that is I want to remove $x^2$ from the denominator somehow. I'm not sure how.

• Btw, the limits on these integrals are $-\infty$ and $\infty$. – seht111 Jan 19 '17 at 17:40
• Since you are only integrating with respect to $y$ you may treat $x^2$ like a constant. When you realize this it is easy to recognize this integral as a standard one. – Vik78 Jan 19 '17 at 17:41
• @seht111, then you should write $\int_{-\infty}^\infty$ instead of just $\int$. You can still edit you post – Yuriy S Jan 19 '17 at 21:24

Setting $$xy=t$$ then we get $$xdy=dt$$ and our integral will be $$\frac{1}{x}\int\frac{1}{1+t^2}dt$$