# Does the integral $\int \frac{1}{(ax+b)(cx+d)} dx$ converge?

Let $$a, b, c, d \in \mathbb{R}$$. I was wondering does the integreal $$\int_A^{\infty} \frac{1}{(ax+b)(cx+d)} dx$$ converge? where the integrand is well defined for $$x\geq A$$?

I think it should because $$1/x^2$$ does... but I wasn't sure. Any info would be appreciated!

• As long as the domain over which you integrate does not include the roots to $(ax+b)(cx+d)=0$ – Henry Lee May 12 at 19:03

Yes, it converges, since$$\left\lvert\frac1{(ax+b)(cx+d)}\right\rvert\leqslant\frac2{\lvert ac\rvert x^2}$$if $$x$$ is large enough and because $$\int_A^\infty\frac{\mathrm dx}{x^2}$$ converges.