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Question
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Solution
Let I = `int(2sinx cosx)/(3cos^2x + 4sin^2x).dx`
Put 3cos2x + 4sin2x = t
∴ `[3(2cosx)d/dx(cosx) + 4(2sinx)d/dx(sinx)]dx` = dt
∴ [–6 cosx sinx + 8 sinx cosx]dx = dt
∴ 2 sinx cosx dx = dt
Then I = `int dt/t` = log|t| + c
= log|3cos2x + 4sin2x| + c
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