00:01
Here we have the integral of tangent cubed x, and then i'm going to write this as secant to the negative 1 half x dx.
00:14
So we want to manipulate this a bit, and the first thing i'm going to say is that tangent squared x equals secant squared x minus 1, and also the derivative of secant x is tangent x secant x.
00:43
Okay, so keeping that in mind, let's manipulate this a bit so we could get this tangent x secant x out of what we have here.
00:50
So this is going to be the same as integral tangent squared x times tangent x times secant to the negative 1 half x dx.
01:04
So this can be written as secant squared x minus 1 tangent x secant negative 1 over 2 x dx.
01:19
Okay, so we have the tangent x.
01:22
Now let's try to get a secant x out of this.
01:25
So i'm going to distribute the secant here.
01:30
So this is going to be secant to the negative 1 half times secant squared is secant to the 3 over 2 x minus secant to the negative 1 half x tangent x dx.
01:49
So now what we want is we want to take out a secant x from this.
01:57
So let's factor out secant x...