integration

**arsenal12345** · September 18th 2012, 04:32 AM

how do i do this ? please show me with proper working

y= ln(ln(tan x))

also i did the one below , is it right ?

∫ sin y/cos^2 y= - cos y /cos^2 y= 1/cosy= sec y +c

thank you

**Soroban** · September 18th 2012, 07:21 AM

Hello, arsenal12345!

How do I do this? . $y\:=\: \ln\left[\ln(\tan x)\right]$ . Do what?

I see no way to integrate it.
Do you want its derivative?

Also I did the one below ... is it right ?

. . $\int\frac{\sin y}{\cos^2\!y}\,dy \:=\:\underbrace{-\frac{\cos y}{\cos^2\!y}}_{{\color{red}??}} \:=\:\frac{1}{\cos y} \:=\:\sec y + C$

$\int\frac{\sin y}{\cos^2\!y}\,dy \;=\;\int\frac{1}{\cos y}\cdot\frac{\sin y}{\cos y}\,dy \;=\;\int\sec y\tan y\,dy \;=\;\sec y + C$

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