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Question
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Solution
`int (3 + 4cosx)/(sin^2x) "d"x = int(3/(sin^2x) + (4cosx)/(sin^2x)) "d"x`
= `int 3/(sin^2x) "d"x + int (4cosx)/sinx * 1/sinx * "d"x`
= `3 int "cosec"^2 x "d"x + 4 int cotx "cosec" x * "d"x`
= `3 int "cosec"^2x "d"x + 4 int "cosec" x cotx "d"x`
= 3 × – cot x + 4 × – cosec x + c
= – 3 cot x – 4 cosec x + c
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