Homework Help: Integral Action

1. Nov 26, 2005

PowerWill

Left my integral table at home, could someone tell me the value of these integrals?
$$\int_0^{\infty} \frac{dx}{(x^2+b^2)^2}$$

$$\int_0^{\infty} \frac{x^2}{(x^2+b^2)^2} dx$$
and the same as the latter but with the denominator raised to the power 4. Thanks!

Last edited: Nov 26, 2005
2. Nov 26, 2005

johnw188

Just solve them yourself, they're both pretty standard trig substitutions. You should always solve the integral forms from the table yourself, at least once, before you use them. They're a nice tool for saving yourself time and effort, not a crutch to avoid learning your integration techniques properly.

3. Nov 27, 2005

benorin

4. Nov 27, 2005

PowerWill

What do I do with the arctan at infinity? Do I just use $$\frac{\pi}{2}$$ or do I have to be saucy about it?

Last edited: Nov 27, 2005
5. Nov 27, 2005

HallsofIvy

Well, I wouldn't recommend be "saucy" about homework! Technically, you should take the limit of arctan t as t goes to $\infty$ but that is, of course, $\frac{\pi}{2}$.

6. Nov 27, 2005

benorin

EDIT: I was going to post the below, but I just realized the it doesn't matter what $\mbox{sgn}(b)$ is, assuming $b\neq 0$, take it to be positive since b is only given by b2, we may assume it is positive.

For $$\int_0^{\infty} \frac{dx}{(x^2+b^2)^2}=\lim_{M\rightarrow\infty} \frac{1}{2b^3} \left(\frac{bM}{b^2+M^2} + \tan^{-1}\left( \frac{M}{b}\right) -0\right)$$
$$=0+\lim_{M\rightarrow\infty} \frac{1}{2b^3} \tan^{-1}\left( \frac{M}{b}\right)=\mbox{sgn}(b) \frac{\pi}{4b^3}$$

Last edited: Nov 27, 2005