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Integrate the following functions: 1/(sinx cos^3x)

Answer»

Solution :`1/(sinx cos^3x) = COSX/(sinx cos^4x) = sec^4x/tanx`
=`(sec^2x(1+tan^2x))/tanx`
Put tan X =t. Then dt = `sec^2x dx` ,
therefore` int dx/(sinx cos^3x) = int(1+t^2)/t dt`
=`int(1/t+t)dt = log|t|+t^2/2+c`
`log|tanx|+tan^2x/2+c`


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