Intergation of xlnx by Parts

If you find integral of a function which contains lnx, you have to use the method integration by parts. And you have to consider lnx as u and the other part and dx together to be considered as dv.

Consider the following integral.

∫xlnxdx

The above integral can be written as

∫(lnx)(xdx)

Here, u = lnx and dv = xdx.

∫(lnx)(xdx) = uv - ∫vdu 

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