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Integration of tanx/x Please give another method. I m unable toUnderstand above one

Integration of tanx/x Please give another method. I m unable toUnderstand above one

Grade:12th pass

1 Answers

Ritika Das
105 Points
4 years ago
Let 1/x=dv
After integrating, log x.dx = v
Also, let tan x = u 
Therefore,sec2x.dx=du 
Integral of u.dv= uv-integral vdu
                      =log x.tan x- integral log x.sec2x.dx 
 Integral of tanx/x dx= log x.tanx- integral logx sec2x.dx.........(1) 
Right hand side 2nd term consideration, we get : –  
Integral log x.sec2x dx,
By integration by parts method, 
Let u= log x 
Therefore du= (1/x).dx integral sec2x dx= dv ,
Putting value we get v= tan x
So thus log x.tan x- integral tan x/x.dx 
Putting value in next part of the right hand side we get..... (1)
Integral tan x/x.dx= log x.tan x + log x.tan -integral tan x/x.dx 
2integral tan x/x.dx= 2log x.tan x 
Thus,
Integral tan x/x =log x.tan x+c
There you go!

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