Question

((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

Answer 1

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

Answer 2

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

Answer 3

(1-cos2x)/2

Answer 4

thats about where I get lost

Answer 5

that is just sin^2 x
\(\large \frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } = \sin^5 x[\frac{ 1 }{ 5 }-\frac{ \sin ^{2}x }{ 7 }] \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\frac{ \dfrac{1-\cos 2x}{2} }{ 7 }] \\ \huge \\ \huge =\sin^5 x[\frac{ 1 }{ 5 }-\dfrac{1-\cos 2x}{14} ] \)

Answer 6

can you proceed ?

Answer 7

do u just multiple the sin5x back into it now

Answer 8

or do i set a common denominator of 70

Answer 9

set a common denominator of 70

Answer 10

which makes more sense

Answer 11

awesome. I see it now. was just over analysis of it. thank you

Answer 12

i hope you'll get exactly what you want,
welcome ^_^