00:01
Hi there, so for this problem, we are asked to solve the following integral, that is x to the 3 divided by x square, 1 minus x square.
00:15
This integrated over x.
00:20
So what we are going to do now is to first solve this division here of polynomics.
00:28
So that will be 1 minus x square.
00:36
So what we can try in here is minus adds, because if we do the multiplication in here, we need to subtract in here.
00:53
X minus, oh, well, should be x.
00:59
Sorry, it should be s because, oh no, it should be minus because this minus cancel with this minus in here.
01:09
And we will obtain positive.
01:12
So we will have this in here.
01:17
So you can see that this cancel with this.
01:20
And then we will obtain just simply x.
01:23
So with that said, is that we can write that x to the 3 can be written as minus x times 1 minus x squared.
01:34
And this plus x.
01:39
So with that said, we can divide both sides by this in here, and then we will obtain just simply minus x plus x divided by 1 minus x square.
01:57
So now we can do just simply because this is equal to this, we can substitute this latest expression in the integral.
02:07
The integral that we are doing, this one in here, now becomes the following...