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Question
Integrate the following with respect to x.
sin3x
Solution
sin3x = 3 sin x – 4sin3x
4sin3x = 3 sin x – sin3x
⇒ sin3x = `1/4 [3 sin x - sin^3x]`
`int sin^3x "d"x = 1/4 int (3 sin x - sin^3x) "d"x`
= `1/4 [3(- cos x) - ((- cos 3x)/2)] + "c"`
= `(-3)/4 [cos x] + 1/12 [cos 3x] + "c"`
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