00:01
Okay, so for this integral, we're going to want to multiply the two factors together before we do the integral.
00:06
So, x squared minus 1 times x squared, or sorry, the square root of x minus 1 times the square root of x minus 1.
00:12
It's going to be x, and then it's going to be minus 2 times the square root of x and plus 1, and then times dx.
00:22
And so how we're going to do this integral is i'm just going to split it up into three different integrals and take them all separately.
00:35
And that's the whole reason why i multiplied the two factors together first, was so that we could just get three separate terms, that we could then just take the integral of each separately.
00:48
And so the integral of x, it's a power rule, integral, anti -derivative.
00:52
And so whenever we have x raises some power, all we do when we're taking the integral is we add one to the power.
00:58
So we're going to have x squared, and then we divide by that power.
01:02
Here, it doesn't matter if the power is a fraction...