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Question
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
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Solution
Let I = `int (2 cos x - 3 sin x)/(6 cos x + 4 sin x)` dx
`= 1/2 int (2 cos x - 3 sin x)/(3 cos x + 2 sin x)` dx
Put 3 cos x + 2 sin x = t
(- 3 sin x + 2 cos x) dx = dt
Hence, `I = 1/2 int 1/t` dt
`= 1/2 log abs t + C`
`= 1/2 log abs (3 cos x + 2 sin x) + C`
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