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Integration of sec(x)sec(x)tan(x)



I know the integration of sec(x)tan(x) is sec(x) but I don't see how they got the above?
Reply 1
Avatar for Hasufel
Hasufel
16
the derivative of sec2x=2secx(secxtanx)sec^{2}x=2secx(secxtanx)
Reply 2
Avatar for davros
davros
16
Original post by GPODT


I know the integration of sec(x)tan(x) is sec(x) but I don't see how they got the above?



Original post by Hasufel
the derivative of sec2x=2secx(secxtanx)sec^{2}x=2secx(secxtanx)


If you didn't know the result quoted by Hasufel, then an integration by substitution will work because you're integrating sec2xtanxsec^2x tanx so you can put u=tanxu = tan x and du=sec2xdxdu = sec^2x dx
Reply 3
Avatar for GPODT
GPODT
OP
16
Original post by davros
If you didn't know the result quoted by Hasufel, then an integration by substitution will work because you're integrating sec2xtanxsec^2x tanx so you can put u=tanxu = tan x and du=sec2xdxdu = sec^2x dx


This was in the integration by parts section so I was wondering if there was a way to do it via that method. THanks though
Original post by GPODT
This was in the integration by parts section so I was wondering if there was a way to do it via that method. THanks though


Let du=sec⁡xtan⁡x,    v=sec⁡xdu=\sec x\tan x,\;\;v=\sec x

(perform the integration without the "2" - it will appear automatically) :wink:

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