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Question
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Options
tanx + cotx + C
x + cotx)2 + C
tanx – cotx + C
(tanx – cotx)2 + C
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Solution
`int "dx"/(sin^2x cos^2x)` is equal to tanx – cotx + C.
Explanation:
I = `int ("d"x)/(sin^2x cos^2x)`
= `int ((sin^2x + cos^2x)"d"x)/(sin^2xcos^2x)`
= `int sec^2 x"d"x + int "cosec"^2x "d"x`
= tanx – cotx + C
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