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Question

What is the integration of lnx?


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Solution

Find integration of lnx.

From integration by parts:

uvdx=uvdx-(vdx)dudxdx

Let u=lnx,v=1

To findlnxdx, Put u=lnx,v=1 in uvdx=uvdx-vdxdudxdx:

lnxdx=lnxx-x1xdxddxlnx=1xlnxdx=xlnx-dxlnxdx=xlnx-x+Cdx=x.

Hence, the required integral is lnxdx=xlnx-x+C where C is a constant of integration .


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