anonymous 3 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. anonymous

original integral $\cos ^{3}xsin ^{4}x$ got the solution with some help of $\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c$

2. hartnn

ok, what you get after factoring out sin^5 x ?

3. anonymous

(1-cos2x)/2

4. anonymous

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. anonymous

do u just multiple the sin5x back into it now

8. anonymous

or do i set a common denominator of 70

9. hartnn

set a common denominator of 70

10. anonymous

which makes more sense

11. anonymous

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 ^_^