00:01
So this integral is actually easier than you might think at first glance.
00:05
Basically, first thing you might notice is we're always trying to look out for when you can do substitution.
00:10
And right here, we have this t here, and the rest of it is written in terms of t squared.
00:18
Well, 2t is the derivative of t squared.
00:21
So we were easily able to do substitution.
00:25
What we can do is just we can, if we want a 2t, we can just put that 2 there.
00:31
Of course you can't just multiply that you also have to make up for that by say multiplying by half and now basically we can do you substitution we're going to let u equal t squared so d u would be 2 t d t and basically that 2 t we can just move all that over because the order for multiplication doesn't matter.
01:09
So basically, this is equal to, you're going to have half of the integral of secant squared.
01:22
And i'm also going to change this order...