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Integrate the functions1/(cos^2x(1-tanx)...

Integrate the functions`1/(cos^2x(1-tanx)^2)`

Text Solution

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`int (1)/(cos^(2) x(1-tanx)^(2)) dx``" Let 1- tan x=t`
`rArr -sec^(2) x dx =dt`
` rArr sec^(2) x dx =-dt`
`= int (sec^(2) x)/((1- tan x)^(2))dx= int (dt)/(t^(2))`
` =(1)/(t) +c= (1)/(1- tan x)+c`
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