Originally Posted by

**Sudharaka** Dear temaire,

I think you have substituted wrong.

Substitute, $\displaystyle \theta=tan^{-1}(lny)$

$\displaystyle ln y = tan\theta$

$\displaystyle \frac{1}{y}\frac{dy}{d\theta}=sec^{2}\theta$

$\displaystyle \frac{dy}{y}=sec^{2}{\theta}~d{\theta}$

Also, you have to change the limits...

When, $\displaystyle y=1\Rightarrow{\theta=0}$

When, $\displaystyle y=e\Rightarrow{\theta=\frac{\pi}{4}}$

Then your integration would be, $\displaystyle \int_{0}^{\frac{\pi}{4}}{\frac{sec^{2}\theta~d\the ta}{\sqrt{1+tan^{2}\theta}}}$

Can you do it form here???