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Integrate the functions1/(sinxcos^3x)...

Integrate the functions`1/(sinxcos^3x)`

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` int (1)/(sin x. cos^(3) x)dx`
` = int(1)/((sinx)/(cosx).cos^(4) x) dx= int (sec^(4))/(tanx) dx`
`= int ((1+tan^(2)x))/(tanx) .sec^(2) x dx " " underset(rArr sec^(2) x dc =dt)(" Let " tan x=t)`
` = int (1+t^(2))/(l) dt = int ((1)/(l)+t)dt`
`= log |t| +(t^(2))/(2)+c`
`=log |tan x|+(1)/(2) tan^(2) x+c`
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