bii17
integrate (x)(cos^3 x) dx



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sirm3d
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do you know the reduction formula for \[\int \cos^n x \,\mathrm dx\]

bii17
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reduction?? nope...

matricked
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first simplify cos^3 x in terms of cosine of 3x and x
and then integrate by parts

matricked
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i don't think here u should use reduction formula

bii17
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its \[\cos ^3 x\] .. where did u get 3x and x @matricked

matricked
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use
cos3x =4 cos^3 (x)  3cos x

sirm3d
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why not? it solves the problem too, but the solution may not be attractive to @bii17

matricked
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i mean use cos^3 (x) =1/4 *(cos3x +3cosx)

bii17
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oh okay.. then what will happen next ? @matricked

matricked
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and then use by parts

bii17
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\[1/4 [x(\cos 3x + 3\cos x)]dx\] is this correct? @matricked

matricked
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yup

bii17
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so there will be u and du den dv and v... i used Dv as cos 3x dx the V will be 1/3 sin 3x ???

matricked
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for both integration of 1/4 *xcos3x take x as the first function

bii17
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i get it.. thanks a lot :) @matricked