3.1 Integration by Parts

[STARTS AT 9:18]

Professor: Next we have xlnx. And again, it is very easy to differentiate lnx. I'm going to choose that. 

It's easy enough to differentiate or to integrate x. So the integral of x is 1/2x squared and the derivative of lnx is 1 over x. So this will become uv-- so lnx-- and we have a 1/2 times x squared. Let's try that differently. 

1/2x squared lnx minus the integral of vdu. So that would be 1/2x squared times 1 over x, which is going to be 1 over 1/2x. The x terms cancel out of there, our factors cancel out there. And we can integrate that easily. That's going to be x squared over 4 plus c. And we'll bring down our 1/2x squared lnx. 

[ENDS AT 10:47]