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Integrate the follwing functions: cosx/(...

Integrate the follwing functions: `cosx/((1-sinx)(2-sinx))`

Text Solution

Verified by Experts

Put sinx = t. Then dt = cosx dx
therefore `int cosx/((1-sinx)(2-sinx)) dx`
`int dt/((1-t)(2-t))` (by partial fraction)
=`int[1/(1-t)-1/(2-t)]dt`
`log|1-t|/-1 -log|2-t|/-1 +c`
=`log|2-t|-log|1-t|+c`
=`log|(2-t)/(1-t)|+c`
=`log|(2-sinx)/(1-sinx)|+c`
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