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Evaluate int(dx)/(cot^(2)x-1)...

Evaluate `int(dx)/(cot^(2)x-1)`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(4)log_(e)|sec 2x+tan 2x|-(x)/(2)+C`
`int(dx)/(cot^(2)x-1)=int(sin^(2)x dx)/(cos 2x)`
`=(1)/(2)int((1-cos2x)dx)/(cos2x)`
`=(1)/(2)[int sec 2x dx-int dx]`
`=(1)/(2)[(1)/(2)log_(e)|sec 2x +tan 2x| -x]+C`
`=(1)/(4)log_(e)|sec 2x+tan 2x|-(x)/(2)+C`
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