anonymous
  • anonymous
integrate (x)(cos^3 x) dx
Mathematics
katieb
  • katieb
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sirm3d
  • sirm3d
do you know the reduction formula for \[\int \cos^n x \,\mathrm dx\]
anonymous
  • anonymous
reduction?? nope...
anonymous
  • anonymous
first simplify cos^3 x in terms of cosine of 3x and x and then integrate by parts

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anonymous
  • anonymous
i don't think here u should use reduction formula
anonymous
  • anonymous
its \[\cos ^3 x\] .. where did u get 3x and x @matricked
anonymous
  • anonymous
use cos3x =4 cos^3 (x) - 3cos x
sirm3d
  • sirm3d
why not? it solves the problem too, but the solution may not be attractive to @bii17
anonymous
  • anonymous
i mean use cos^3 (x) =1/4 *(cos3x +3cosx)
anonymous
  • anonymous
oh okay.. then what will happen next ? @matricked
anonymous
  • anonymous
and then use by parts
anonymous
  • anonymous
\[1/4 [x(\cos 3x + 3\cos x)]dx\] is this correct? @matricked
anonymous
  • anonymous
yup
anonymous
  • anonymous
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 ???
anonymous
  • anonymous
for both integration of 1/4 *xcos3x take x as the first function
anonymous
  • anonymous
i get it.. thanks a lot :) @matricked

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