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Integrate the following functions 1/(cos...

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

Text Solution

Verified by Experts

`1/(cos^2x(1-tanx)^2) = sec^x/(1-tanx)^2`
Let 1-tanx = t
Then `dt = -sec^2xdx`
`gt sec^2x dx = -dt`
therefore` int 1/(cos^2x(1-tanx)^2 dx`
=`int -(dt)/t^2 = 1/t+c = 1/(1-tanx)+c`
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