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Integrate the following functions: 1/(si...

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

Text Solution

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`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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