\int\limits^a_b {(1)/(xln(x)) } \, dx

Question

`\int\limits^a_b {(1)/(xln(x)) } \, dx`

Answer 1

Explanation:

Let u = ln x

du = dx/x

`\int {(1)/(x \ln(x)) }\: dx = \int (du)/(u)`

`= \ln |u| + k`

or

`\int_b^a {(1)/(x \ln(x)) }\:dx= \ln |\ln|x|| _b^a`

`=\ln|\ln(a)| - \ln|\ln(b)|`