Question

∫(sec(lnx)tan(lnx)) /x

Answer 1

Substitute $y=\ln x\implies\mathrm dy=\dfrac{\mathrm dx}x$, then the integral becomes


$\displaystyle\int\frac{\sec(\ln x)\tan(\ln x)}x\,\mathrm dx=\int\sec y\tan y\,\mathrm dy$
$=\sec y+C$

$=\sec(\ln x)+C$