00:01
Consider this given integral here.
00:02
Now to evaluate this integral, first thing we have to do is to rewrite the integrand as a sum of its partial fractions.
00:09
To do that, we need to factor out first the denominator.
00:13
So if we have y squared over y to the fourth minus one, note that we can factor out the denominator into y minus one times y plus one times y squared plus one.
00:25
So this becomes y over those factors.
00:30
And we can rewrite this as a sum of partial fractions with denominators y minus one, y plus one, and then y squared plus one.
00:42
So those with linear denominators will have constant numerators.
00:47
Let's call them a and b.
00:50
But for the quadratic denominator, it will have a linear numerator.
00:54
So let's call that c y plus d.
00:57
And then from here, we should multiply both sides of the equation by the lcd so we can find the values of a, b, c, and d.
01:08
So this will be times y minus one times y plus one times y squared plus one.
01:15
So then the equation becomes y squared equal to a times y plus one times y squared plus one plus you have b times y minus one times y squared plus one plus we have c y plus d times y minus one times y plus one.
01:37
And then for an easier way of solving for a, b, c, and d, we just fix values for y.
01:44
So let's say y minus one equals zero.
01:50
That means y equals one...