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lands91

((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

  • one year ago
  • one year ago

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  1. lands91
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    original integral \[\cos ^{3}xsin ^{4}x\] got the solution with some help of \[\frac{ \sin ^{5}x }{ 5 }-\frac{ \sin ^{7}x }{ 7 } +c\]

    • one year ago
  2. hartnn
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    ok, what you get after factoring out sin^5 x ?

    • one year ago
  3. lands91
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    (1-cos2x)/2

    • one year ago
  4. lands91
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    thats about where I get lost

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

    • one year ago
  6. hartnn
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    can you proceed ?

    • one year ago
  7. lands91
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    do u just multiple the sin5x back into it now

    • one year ago
  8. lands91
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    or do i set a common denominator of 70

    • one year ago
  9. hartnn
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    set a common denominator of 70

    • one year ago
  10. lands91
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    which makes more sense

    • one year ago
  11. lands91
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    awesome. I see it now. was just over analysis of it. thank you

    • one year ago
  12. hartnn
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    i hope you'll get exactly what you want, welcome ^_^

    • one year ago
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