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[TEX]\int (\frac{1}{x}+lnx)e^x dx[/TEX]
[TEX]= \int \frac{1}{x}.e^x dx + \int lnx.e^x dx[/TEX]

[TEX]\int lnx.e^x dx[/TEX]

[TEX]u=lnx \Rightarrow du=\frac{1}{x}dx[/TEX]
[TEX]dv=e^x dx \Rightarrow v=e^x[/TEX]

[TEX]\int lnx.e^x dx = lnx.e^x - \int \frac{1}{x}.e^x dx[/TEX]

[TEX]\int (\frac{1}{x}+lnx)e^x dx = \int \frac{1}{x}.e^x dx + lnx.e^x - \int \frac{1}{x}.e^x dx [/TEX]

[TEX]= lnx.e^x[/TEX]
 
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