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Question
Integrate the following with respect to x.
`1/(sin^2x cos^2x) ["Hint:" sin^2x + cos^2x = 1]`
Solution
`int 1/(sin^2x cos^2x) "d"x = int ((sin^2x + cos^2x))/(sin^2x cos^2x) "d"x`
= `int (sin^2x)/(sin^2x cos^2x) "d"x + int (cos^2x)/(sin^2x cos^2x) "d"x`
= `int 1/(cos^2x) "d"x + int 1/(sin^2x) "d"x`
= `int sec^2 x "d"x + int 1/(sin^2x) "d"x`
= `int sec^2 x "d"x + int "cosec"^2 x "d"x`
= tan x – cot x + c
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