# Thread: Antiderivitive of natural log of xe^2x/x dx

1. ## Antiderivitive of natural log of xe^2x/x dx

This one has me all kinds of confused. I am the weakest at natural log and its base e. I was trying to use u substitution, but the /x is throwing me for a loop. Help please??

the numerator is ln(xe^2x), denominator is x, I'm trying to find the indefinite integral

2. Originally Posted by ceb0196
This one has me all kinds of confused. I am the weakest at natural log and its base e. I was trying to use u substitution, but the /x is throwing me for a loop. Help please??

the numerator is ln(xe^2x), denominator is x, I'm trying to find the indefinite integral
First simplify:

$\displaystyle \frac{\ln\!\left(xe^{2x}\right)}{x}=\frac{\ln x+\ln\!\left(e^{2x}\right)}{x}=\frac{\ln x}{x}+2$

So $\displaystyle \int\frac{\ln\!\left(xe^{2x}\right)}{x}\,dx=\int\f rac{\ln x}{x}+2\,dx$

Can you continue from here?

3. AH, yes I can finish. I just could not figure out how to split any of it up. THANKS!!