00:01
Okay, for this integral, we want to take the indefinite integral of cosine x over sine squared x minus 9.
00:09
And for this, we're going to use substitution and the fact that we can use an integral table from a reference section in textbook or an integral table from online.
00:20
So we'll be using entry 20.
00:22
In order to utilize this integral table equation, we first have to use some use substitution to ensure that our function in black here.
00:32
In black ink can be applied to what's in blue to simplify the integral for us.
00:38
So let's say that you is going to just be sine of x.
00:45
And this means if we do our normal du, so the derivative of sine x is cosine x, then we have the dx.
00:56
Okay, so based on this, what we just found, does this plug into our blue equation here? and it actually does, because if we say, that our u is sine x we square that we get sine squared x which is right there in the denominator then also say that a is equal to three so three squared is nine covered and this means our d u what is our d u so our d u is just our cosine x d x and that is what matches in our numerator and that is what matches in our numerator our cosine x and our d x so this is a suitable integral formally we can use because our u substitution makes it so that this works...