Question

solve the integration (dx/xlogx)

Answer 1

Hi Please find the attachment.
It is solved using substitution.
Hope this helps.

Answer 2

$\int \dfrac{1}{x\log x} \, dx=\log [\log x]+C$

Step-by-step explanation:

We have,

$I=\int \dfrac{1}{x\log x} \, dx$       ....... (1)

To find, $\int \dfrac{1}{x\log x} \, dx=?$

Let $t=\log x$

∴$dt=\dfrac{1}{x} dx$

Now, equation (1) becomes, we get

$I=\int \,\dfrac{dt}{t}$

$I=\log [t]+C$, C is called integration constant.

[ ∵$\int}\dfrac{1}{x} \,dx =\log x$]

Put $t=\log x$, we get

$I=\log [\log x]+C$

Hence, $\int \dfrac{1}{x\log x} \, dx=\log [\log x]+C$