text: ## lands91 2 years ago ((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
  
  1. lands91
  
  original integral $\cos ^{3}xsin ^{4}x$ got the solution with some help of $\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c$
  
  2. hartnn
  
  ok, what you get after factoring out sin^5 x ?
  
  3. lands91
  
  (1-cos2x)/2
  
  4. lands91
  
  thats about where I get lost
  
  5. hartnn
  
  that is just sin^2 x $$\large \frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } = \sin^5 x[\frac{ 1 }{ 5 }-\frac{ \sin ^{2}x }{ 7 }] \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\frac{ \dfrac{1-\cos 2x}{2} }{ 7 }] \\ \huge \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\dfrac{1-\cos 2x}{14} ]$$
  
  6. hartnn
  
  can you proceed ?
  
  7. lands91
  
  do u just multiple the sin5x back into it now
  
  8. lands91
  
  or do i set a common denominator of 70
  
  9. hartnn
  
  set a common denominator of 70
  
  10. lands91
  
  which makes more sense
  
  11. lands91
  
  awesome. I see it now. was just over analysis of it. thank you
  
  12. hartnn
  
  i hope you'll get exactly what you want, welcome ^_^