00:01
Okay, we're told that this integral converges and we want to evaluate it, okay? so i'm going to realize something here that if i take x to minus x in the integrand, i get the same thing back because it's an even function.
00:27
So this integral is the same as this integral.
00:37
And that just makes life a little easier.
00:39
We could do it the other way, but this way makes it a little easier to see.
00:44
So the next step, i'm going to reduce this by partial fractions.
00:52
And let me note that there are other ways to do this.
00:55
You could do a trigonometric substitution as well that would do the job, but i'm going to do it by partial fractions.
01:05
So four over x squared minus one, i'm going to say that that's a over x minus one plus b over x plus one, because that denominator factors that one, okay? and so i get a plus b equals zero and a minus b equals four.
01:42
There's a one there.
01:44
And that tells me that a is two and b is minus two.
01:51
So this integral is now two to infinity...