anonymous
  • anonymous
((sin^(5)x)/5)-((Sin^(7)x)/7)+c need to make it come out to this solution. (1/70)sin5(x)(5cos(2x)+9)+c
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
original integral \[\cos ^{3}xsin ^{4}x\] got the solution with some help of \[\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c\]
hartnn
  • hartnn
ok, what you get after factoring out sin^5 x ?
anonymous
  • anonymous
(1-cos2x)/2

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anonymous
  • anonymous
thats about where I get lost
hartnn
  • hartnn
that is just sin^2 x \(\large \frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } = \sin^5 x[\frac{ 1 }{ 5 }-\frac{ \sin ^{2}x }{ 7 }] \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\frac{ \dfrac{1-\cos 2x}{2} }{ 7 }] \\ \huge \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\dfrac{1-\cos 2x}{14} ] \)
hartnn
  • hartnn
can you proceed ?
anonymous
  • anonymous
do u just multiple the sin5x back into it now
anonymous
  • anonymous
or do i set a common denominator of 70
hartnn
  • hartnn
set a common denominator of 70
anonymous
  • anonymous
which makes more sense
anonymous
  • anonymous
awesome. I see it now. was just over analysis of it. thank you
hartnn
  • hartnn
i hope you'll get exactly what you want, welcome ^_^

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