Question

∫(sec(lnx)tan(lnx)) /x

Answer 1

Substitute
`y=\ln x\implies\mathrm dy=\frac{\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`