Question

Integrate 1/(xlogx) dx.

Answer 1

put t=ln x

Answer 2

then dt would be dt=(1/x)dx
and your integral will reduce to
integral of 1/t dt
ok?

Answer 3

integration by parts is fun too...

Answer 4

complicated..but fun

Answer 5

\[\int\limits\limits\limits\limits_{}^{}\frac{ 1 }{ t }dt = \int\limits\limits\limits\limits_{}^{}\frac{ 1 }{ xlnx } dx \neq \int\limits_{}^{} \frac{ 1 }{ xlogx }\] What am I missing?

Answer 6

in ur question it's ln x or log x?

Answer 7

logx

Answer 8

then change into natural log 1st
ln x = 2.303 log x

Answer 9

then do the substitution t=lnx

Answer 10

does it make sense?

Answer 11

or log x= log e * ln x

Answer 12

so u can substitute t = log x also
then dt = log e /x dx

Answer 13

I'm getting \[\log x = \frac{ 1 }{ \ln10} lnx\]

Answer 14

yes

Answer 15

Ok here's what I have, would you mind just double checking it for me?

\[\int\limits_{}^{}\frac{ 1 }{ xlogx } dx\]

\[t=logx, dt=\frac{ 1 }{ xln10}\]\[\ln10\int\limits_{}^{}1/t dt = \ln10\ln \left| u \right|+c= \ln10\ln \left| logx \right|+c\]

look good?