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Find the integral `int cot^2 y dy`

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user7200498 | eNotes Newbie

Posted April 25, 2013 at 11:12 AM via web

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Find the integral `int cot^2 y dy`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 26, 2013 at 4:21 AM (Answer #1)

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The integral `int cot^2 y dy` has to be determined.

`int cot^2 y dy`

= `int (cos^2 y)/(sin^2 y) dy`

= `int (1 - sin^2 y)/(sin^2 y) dy`

= `int 1/(sin^2 y) - 1 dy`

= `int cosec^2 y - 1 dy`

= `int cosec^2 y dy - int 1 dy`

= `-cot y - y + C`

The required integral is `-cot y - y + C`

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