problem 5: solution to the slightly harder integral

I must say, this was a bit more challenging, but nothing I can't do.

Using properties of logarithms, I can rewrite the integral like this:

It simplifies to this:

Now I just need a little u-substitution. 

For u-substitution to work, I'll also have to rewrite the integral as follows:

After doing u-substitution, it should look like this:

The integral of ln(x) requires integration by parts. I'm not going to go through the process now because I did it in a different post. It should like this this:

Well, it's simple from here. Just plug back in (x^2+1) in place of u. I'm going to leave it in terms of u because it's long and messy in terms of x.