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((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

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original integral \[\cos ^{3}xsin ^{4}x\] got the solution with some help of \[\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c\]
ok, what you get after factoring out sin^5 x ?

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

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