00:01
Okay, we want to solve the indefinite integral of e to the x over 4 minus e to the 2x.
00:08
And in order to do this, we will be using an integral table, which is found in the back of textbooks or on the internet.
00:16
But something we want to use here is u substitution in order to manipulate our integral to get it something that can be easily solved by our table of integrals.
00:27
In this case, we'll be using entry 19 from the selected textbook, but first we have to identify what our u is and what our a is, and we're going to plug in to this integral table solution.
00:40
So as we can see, we have e to x in numerator, e the 2x in the denominator.
00:44
So let's just say u is equal to e to the x, and this means that du is just equal to itself ethx dx.
01:08
So that's why e to x is very nice in these u subsituations, because it's derivative e to equals its original function.
01:15
So this means we already have our u squared for our a square minus u squared because we're saying our u is e of x here.
01:24
So this means our u squared is just e of the 2x.
01:28
And our a squared is just four.
01:31
So a is equal to two...