Question

find the answer for the integral question
∫dx/xlogx

Answer 1

hich is a special function known as the integral logarithm.

It can also be represented as -

∫1log(x)dx=∫1log(x)dx=

Let t=log(x)t=log(x) which can also be written as et=xet=x

Therefore on differentiating t=log(x)t=log(x)on both sides we get,

dt=1xdxdt=1xdx

or, dx=xdt→dx=etdtdx=xdt→dx=etdt

∫1log(x)dx=∫ettdt∫1log(x)dx=∫ettdt

which gives Ei(t)+cEi(t)+c

i.e Ei(log(x))+cEi(log(x))+c

Here EiEi is an exponential integral.

Answer 2

Answer is log(log x) + c