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Question
`int cos^3x dx` = ______.
Options
`1/12 sin 3x + 3/4 sin x + c`
`1/12 sin 3x + 1/4 sin x + c`
`1/12 sin 3x - 3/4 sin x + c`
`1/12 sin 3x - 1/4 sin x + c`
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Solution
`int cos^3x dx` = `underlinebb(1/12 sin 3x + 3/4 sin x + c)`.
Explanation:
`int cos^3x . dx`
cos 3A = 4 cos3 A – 3 cos A
I = `int 1/4 (cos 3x + 3 cos x) . dx`
= `1/4 (sin 3x . 1/3 + 3 . sin x) + c`
= `1/12 sin 3x + 3/4 sin x + c`
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