Integrating e^x(x+1)lnx Using Integration by Parts

[BrownianMan]

$$\[\int e^x(x+1)\ln x \ dx \]$$

Not sure how to approach this. Would I have to multiply it out first?

 

[Mark44]

$$\[\int e^x(x+1)\ln x \ dx \]$$

Not sure how to approach this. Would I have to multiply it out first?

For starters, I would split it into two integrals and see if integration by parts works on each one.

$$\[\int e^x(x+1)\ln x dx = \int xe^x~lnx~dx + \int e^x~lnx~dx$$

 

[BrownianMan]

Thanks! I got it.