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Integrate the following functions sqrt(t...

Integrate the following functions `sqrt(tanx)/(sinx cosx)`

Text Solution

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`sqrt(tanx)/(sinx cosx) = sqrt(tanx)/(cos^2x (sinx/cosx))`
=`sqrt(tanx)/(cos^2x tanx) = sec^2x/sqrt(tanx)`
= Let t = tanx.
Then dt = `sec^2x dx `
therefore `int sqrt(tanx)/(sinx cosx)`
=`int dt/sqrtt = 2sqrtt +c = 2sqrt(tanx) +c`
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