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Question
Find the integrals of the function:
sin4 x
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Solution
Let `I = int sin^4 x dx`
`= int ((1 - cos 2x)/2)^2 dx`
`= 1/4 int (1 + cos^2 2x - 2 cos 2x) dx`
`= 1/4 int [1 + (1 + cos 4x)/2 - 2 cos 2x] dx`
`= 1/4 int 1 dx + 1/8 int (1 + cos 4 x) dx - 2/4 int cos 2x dx`
`= 3/8 int 1 dx + 1/8 int cos 4x dx - 1/2 int cos 2x dx`
`= 3/8 x + 1/32 sin 4x - 1/4 sin 2x + C`
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