obviously one can use integration by parts to attempt to solve any integral not just those with funky products in the intergrand so with that in mind i was trying to solve the integral,

using integration by parts after i had already noticed that direct substituion of u=ln(x) would do the trick.

But with the following choices this is what I'm getting:

Let f(x) =

, g(x) =

Then

=

=

As you can see, this is nonsensical.

Mr F says: No it's not. All it says is that the difference between the two integrals is a constant.
Would someone please tell me where I'm erring.

Thanks

The correct result is