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Math Help - Integral problem

  1. #1
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    Integral problem

    PLEASE HELP ME TO SOLVE THIS PROBLEM

    <br />
\int\sin x\,sin2x\,sin3x\,dx<br /> <br />
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  2. #2
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    Quote Originally Posted by cron1003 View Post
    PLEASE HELP ME TO SOLVE THIS PROBLEM

    <br />
\int\sin x\,sin2x\,sin3x\,dx<br /> <br />
    Dear cron1003,

    Try using sin2x=2sinxcosx~and~sin3x=3sinx-4sin^{3}x
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  3. #3
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    Quote Originally Posted by cron1003 View Post
    PLEASE HELP ME TO SOLVE THIS PROBLEM

    <br />
\int\sin x\,sin2x\,sin3x\,dx<br /> <br />
    .quote=cron1003;494214]PLEASE HELP ME TO SOLVE THIS PROBLEM

    <br />
\int\sin x\,sin2x\,sin3x\,dx<br /> <br />
[/quote]
    Try this
    Using the formula
    sinCsinD = 1/2[cos(C-D) -cos(C+D)]
    cosCsinD = 1/2[sin(C+D) - sin(C-D)]
    You get
    sinx*sin2x*sin3x = 1/2*sin2x(cos2x - cos4x)
    = 1/2[ sin2x*cos2x -sin2x*cos4x]
    = 1/4[sin4x + sin2x - sin6x]
    Now find the integration of each term.
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