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Integrate the follwing functions: cosx/((1-sinx)(2-sinx)) |
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Answer» Solution :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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