- #1

mbrmbrg

- 496

- 2

I thought I had a quick way to integrate by parts but it turned out that I had accidentally evaluated [tex]\int{x\ln{x}dx}[/tex] instead.

Revisiting [tex]\int{x(\ln{x})^3dx}[/tex], I wanted to start by making a strange substitution, wherein u=ln(x), du=1/x dx, and x=e^u. This meant that when I rewrote the integral, instead of multiplying dx by a constant to get it to be du, I multiplied it by x (which in this case was e^u). Is that allowed? Because I got a very different, much uglier answer than the book's.

I'd appreciate any comments, whether on my weird "method" or on a more standard approach to evaluating [tex]\int{x(\ln{x})^3dx}[/tex]