00:01
We're given the integral of sine of 2x over the square root of 1 minus cosine of 2x dx.
00:15
So what you would want to do in this problem, and there's nothing wrong with guessing and checking and guessing wrong and then checking something else.
00:24
But the reason why this is what you want to do is because the derivative of negative cosine is a positive sign.
00:30
You leave that 2x alone, but then you have to multiply by the derivative of 2x, which would be 2dx.
00:40
And this thing is really close to what we have in the numerator, and you can actually put it 2 in there as long as you also multiply that problem by 1⁄2.
00:48
So you're not changing the value of anything.
00:51
And the reason why that works then is it's still one half, still the integral, but everything that i have in that numerator from here to, to here is equal to du.
01:03
And then the denominator, 1 minus cosine of 2x, i let equal to you.
01:09
And because it's in the denominator, it'd be a negative exponent, and the square root would make it the 1 1 half power...