Need help integrating

[dmsjr12]

I ran across this problem on my homework, and I am stumped.

[definite integral from "e" to "1"] 9x^2ln(x)dx

I'm pretty sure I need to use integration by parts. However, usually I would do

u= ln(x)
du=1/x dx
v=3x^3
dv=9x^2dx

from what I can see, this results in 3x^3ln(x)-x^3, but then to solve for the definite integral I am lost when replacing x with e and then 1. Can anyone help me please?

 

[pka]

\(\displaystyle \L\left[ {3x^3 \ln (x) - x^3 } \right]_1^e = \left( {3e^3 \ln (e) - e^3 } \right) - \left( {3\ln (1) - 1} \right)]\)

 

[dmsjr12]

thanks, i was thinking ln(1)=1. I thought something sounded funny.

 

[pka]

\(\displaystyle \L \ln (e) = 1\quad \& \quad \ln (1) = 0\)