00:01
All right.
00:03
So what we need to do is find the antiderivative of the secant of 4x.
00:12
And the approach we're going to take is we first hand notice this looks very similar to just secant of x, and we know the integral or the anti -derivative of sequin of x, and that's given to us right here.
00:24
So what we want to do is try and make a variable substitution such that we can, this expression here looks like some factor times the secant of x, which we already know.
00:39
So let's try making the following u substitution.
00:43
So we can say u equals 4x.
00:48
If we take the differential of both sides of that equation, we get d u equals 4 d x.
00:57
So now all we need to do is use these two equations here to replace 4.
01:02
4x and dx with you and then rearrange things so that we can make it look like the integral we know.
01:13
So to that end, here we'll call this i, i equals the integral secant...