00:02
For problem 41, we're given an integral that we need to solve, but we can't solve it in its current form.
00:06
So let's go ahead and try and figure out how we can use u substitution to our advantage.
00:11
If we make u equal to sign, the derivative of that will become a cosine, which will help us replace this segment, but we'll also have to use the chain rule, which will create a derivative that will look awfully similar to this.
00:23
So let's use u equals sign of 1 over theta and take the derivative of that.
00:30
So du is going to equal cosine of 1 over theta, d theta, and then we need to multiply it by the chain rule.
00:38
So the derivative of this inside here, the derivative of theta to the negative 1 is going to become, right, bring that down.
00:46
So negative theta to negative 2.
00:48
So out front, negative theta to negative 2.
00:51
Let's rewrite this one more time.
00:53
D .u is going to equal negative 1 over theta squared times the cosine of 1 of 1.
01:01
Over theta, d theta, which we can notice pretty much perfectly replaces what we have left here.
01:08
With the only exception, meaning this negative, that we can just go ahead and flip to the other side so that we can write it out front...