00:01
Let's evaluate the integral.
00:03
First thing we should do is to see if this denominator will factor.
00:08
We see that in the bottom, we can pull out of x squared, and you're left over with x squared plus 6.
00:18
So for the first term in the denominator, we see that this is a repeated linear factor, x times x.
00:29
Now for this other quadratic, x squared plus 6, we'd like to see if that factors.
00:35
So to do so, we check the discriminant.
00:37
Which is b squared minus 4 ac here b is the coefficient in front of the x there's no x here so that's a 0 minus 4 times 1 in front of the x squared and then times c which is 6 and that is definitely less than 0 this tells us that the denominator x squared plus 6 term will not factor.
01:06
So for the first term x squared, we can use what the book calls case 2, repeated linear factor.
01:18
And then for the last term, x squared plus 6, we'll use what the book calls case 3.
01:24
Cx plus d over x squared plus 6.
01:31
Now let's take this equation up here and multiply both sides by that denominator in the left.
01:39
When we do so, we should get x cubed, 6x minus 2...