Question

\[\int\limits {1 \over x \ln x}dx----->x=e^u\]

Answer 1

Step by step pleasee

Answer 2

let ln x = u

Answer 3

Put u = ln x and du = 1/x dx

Answer 4

du = dx/x

Answer 5

You have to use x= e^u

Answer 6

that is in the later part ... for now do above

Answer 7

But it says you have to substitute first, with x.

Answer 8

find the value of integration in u,
and put the value of u=e^x and you will have your answer.

Answer 9

I don't know what e^u ln e^u becomes

Answer 10

ln e^u = u assuming uis +

Answer 11

\[Isn't~\it~~ \int\limits {1 \over xlnx}dx ---- > \int\limits {1 \over e^u \ln e^u}dx?\]

Answer 12

no

Answer 13

But I have to substitute the x's as e^u

Answer 14

You should get:
\[\int\limits 1/\ln e^{u} du\]

Answer 15

@order x = e^u implies that dx= e^u du.So the e^u in the denominator cancels out.

Answer 16

I don't think it means dx =e^u. I think it implies x=e^u

Answer 17

If x= e^u then dx/du = e^u implies dx =e^u du

Answer 18

So, can you start from the beginning beginning?

Answer 19

Yup!

Answer 20

\[\int\limits {1 \over xlnx}dx---> becomes??\]

Answer 21

\[\int\limits 1/\ln e^{u} du\]

Answer 22

\[So,~ what~happens~with~the~first~x?\]