That should be a MINUS Ei(x), my mistake, mixed up some things! :)
Here's the explanation of how to do the final problem, since I messed up in the video, sorry again! I just started learning this! I need to look into special integrals more. : )
int(e^xln(x)dx)
u = ln(x)
du = 1/x dx
dv = e^x dx
v = e^x
ln(x)e^x - int(e^x/x dx)
Ei(x) = int((e^t)/t dt) with bounds -infinity and positive x
FINAL ANSWER: [ln(x)e^x - Ei(x) + C]
