00:01
Okay, so we have the integral of the x over 1 plus x squared to the power of 2.
00:09
Okay, let's write out our triangle.
00:12
Well, this is 1 squared plus x squared, so let this be 1, just be x, and then we have square roots of 1 plus x squared.
00:19
Now we can let x equal to tangents of theta, and then if we do so, our derivative dx is going to equal to sequence squared theta, d theta.
00:34
Secant is 1 over cosine that's one over if cosine is 1 over square roots of 1 plus x squared then sequence squared of data would be let's see sequence of theta would equal to the reciprocal of this so that's square root of 1 plus x squared okay okay so let's work with this let's rewrite our integral so we have the integral of d x which is secant square of theta d theta and then we have that over 1 plus x squared.
01:14
Let's see, we can actually rewrite that, so we can have the square root of 1 plus x squared to the power of 4, right? so if we do that, this would turn into secanths to the power 4, so that's 2c2 .4 theta.
01:32
Okay, this implies to this the integral of sequence squared data, d theta.
01:38
Wait, no is that, no, that's just 1 over c2 squared theta, which is equal to just the integral of cosine squared theta, d -data.
01:53
Now we can rewrite cosine square theta using our power -reducing rules.
01:57
So we get the integral of 1 plus cosine 2 -data over 2 d -data...