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Evaluate int(1)/(1-sinx)dx....

Evaluate `int(1)/(1-sinx)dx`.

Text Solution

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`int(1)/(1+sinx)dx=int(1)/((1+sinx))*((1-sinx))/((1-sinx))dx`
`=int(1-sinx)/(1-sin^(2)x)dx`
`=int(1-sinx)/(cos^(2)x)dx`
`=int(1)/(cos^(2)x)dx-int(sinx)/(cos^(2)x)dx`
`=int sec^(2)x dx-int tan x sec x dx`
`=tan x- sec x +C`
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