00:01
In this question, we are asked to explain why this integral is an improper integral, and then to calculate this integral.
00:09
This integral is improper because one of the limits of iteration is infinite.
00:16
Therefore, we can write this integral as the limit of the integral from e to the fifth to b, where b goes to infinity of d x over x times lnx squared.
00:34
Now we can use u substitution.
00:37
We will take u to be equal to lnx, then du equals to 1 over x d x.
00:47
We also need to change the limits of iteration.
00:50
To get the new upper limit of iteration, we need to take the old upper limit of iteration and plug in for x in the expression for you to get lnb.
01:03
To get the new lower limit of iteration, we need to take the old upper lower limit and plug in for x in the expression for u.
01:13
We are going to get ln of e to the fifth, and this will be equal to 5...