What is the antiderivative of # 1/(xlnx)#?

1 Answer
Sep 26, 2015

Answer:

#ln(lnx)#

Explanation:

antiderivative of #1/(xlnx)# could be written as #int(1/(xlnx)dx)#

Or as #int1/(lnx)*1/xdx#

Recall that : the derivative of #lnx# is #1/x#
This means that : #(d(lnx))/(dx)=1/x#

Implying : #d(lnx)=1/x(dx)#

Hence, #int1/lnx*1/xdx=int1/lnx*d(lnx)#

we are left with the antiderivative of #1/lnx# with respect to #lnx#

This case is simlar to finding the antiderivative of say, #1/u# wrt #u#
The answer would be #lnu#

Similarly, the antiderivative of #1/lnx# with respect to #lnx# is #color(blue)(ln(lnx))#