Question

what is integral of 1/xln(x)

Answer 1

\[1/xln(x)\]

Answer 2

substitute \[u = \ln x\]\[du = \frac{1}{x}dx\]

Answer 3

\[\int\limits \frac{1}{xlnx}dx= \int\limits \left(\frac{1}{lnx}\right)\left(\frac{1}{x}\right) dx\]\[u = \ln x\]\[du = \frac{1}{x}dx\]\[= \int\limits \frac{1}{u}du=\ln \left| u \right|+C = \ln \left| lnx \right|+ C\]