00:01
Okay, so we have the integral of the x over x2 or 4 minus 10 x squared plus 9.
00:08
We can factor this into the integral of the x over x plus 3, x minus 3, x plus 1, and x minus 1.
00:21
Okay, so i'm going to have to do partial fraction decomposition on this.
00:25
This is this 1 over x plus 3, x minus 3, x plus 1, and x minus 1, this is equal to a over x plus 3, plus b over x minus 3, plus c over x plus 1, plus d over x minus 1.
00:46
Now let's take the lcd or multiply by our lcd, we get that this is equal to 1 is equal to a, x minus 3, x plus 1, and x plus or x minus 1, yeah, x minus 1, plus plus b, which is x plus 3, x plus 1, x minus 1, plus c which is x minus 3, x plus 3, x minus 1, plus d, which is x minus 3, x plus 3, x plus 3, and x plus 1.
01:27
Okay, so let's solve for days.
01:29
Well, if you look back here, now a has a solution, x is equal to negative 3.
01:34
So if we let x is equal to negative 3, we can see that 1 is equal to a negative 3 minus 3, that's negative 6, negative 3 plus 1, that's negative 2, and negative 3 minus 1, that's negative 4.
01:52
So i get that a, or 6 times 2 times 4, that gives me negative 48a is equal to 1, so i know that a is equal to negative 1 over 4.
02:07
Solving for b, i know b solution, or one of the x factors is x is equal to 3.
02:15
So we get 1 is equal to b, which is 3 plus 3, so that's 6, 3 plus 1, which is 4 and 3 minus 1, which is 2.
02:33
So i get 48b is equal to 1, so b is equal to 1 over 48...