# Q. `int log_ex dx` A) `log_e(|x| - 1) + c` B) `(log_e|x|)/x - 1 + c` C) ` ` `x(log_e(|x| - 1)) + c` D) `1/x + log_e|x| + c`

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### 1 Answer

Find `int lnx dx` **lnx is the natural logarithm or `log_e x` **

Use integration by parts:

`int udv=uv-intvdu`

Let `u=lnx, du=1/x dx,v=x,dv=dx`

`int lnx dx=xlnx-int x(1/x dx)`

`=xlnx-int dx`

`=xlnx-x+C` where C is an arbitrary constant.

(Alternative representation x(lnx-1)+C )

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Of the answers provided, C would be correct. Is there a typo in the answer? (Should not be x(ln(|x|-1)); should be x(ln|x|-1) )