00:02
Evaluate the following integral.
00:05
The integral of the exponential of x over the exponential 2x plus 11 times the exponential of x plus 18.
00:12
To solve this integral, let's pose the following, the function of variable.
00:16
Let's pose that u is equal to the exponential of x such that the u is equal to the exponential of x tx.
00:23
So we now obtain the integral of 1 over u squared plus 11 u plus 18 dx.
00:43
From here, let's complete the square in a denominator here, and we find, or actually, it this backers out quite nicely, as u plus 9 times times u plus 2 the x.
01:20
Oh, i apologize, i wrote the x here right into you.
01:31
And from here, what we can do is we can apply the partial fractions technique.
01:38
We call this the partial fraction of decomposition, and so we want to write this single fraction as a sum of two fractions...