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Question
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
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Solution
Let I = `int(cos3x - cos4x)/(sin3x + sin4x).dx`
= `int(-2sin((3x + 4x)/2)sin((3x - 4x)/2))/(2sin((3x + 4x)/2)cos((3x - 4x)/2)).dx`
= `int - sin(-x/2)/cos(-x/2).dx`
= `int sin(x/2)/cos(x/2).dx`
= `int tan(x/2).dx`
= `log|sec (x/2)|/((1/2)) + c`
= `2log|sec (x/2)| + c`.
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