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Math Help - choosing what method of integration to use?

  1. #1
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    choosing what method of integration to use?

     \int sin3x \\\ cosx \\\ dx

    I have been stuck on this question for some time, I initially used integration by parts, but this became very messy and confusing, I had to keep using integration by parts more than twice.

    What is the correct method to use? Also I cant really think of any trig manipulation that I can do, to re-write sin3x.

    Any help appreciated.

    Thank you.
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  2. #2
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by Tweety View Post
     \int sin3x \\\ cosx \\\ dx

    I have been stuck on this question for some time, I initially used integration by parts, but this became very messy and confusing, I had to keep using integration by parts more than twice.

    What is the correct method to use? Also I cant really think of any trig manipulation that I can do, to re-write sin3x.

    Any help appreciated.

    Thank you.
    \sin (a+b) = \sin a \cos b + \sin b \cos a

    \sin (a-b) = \sin a \cos b - \sin b \cos a add them

    \sin (a+b) + \sin (a-b) = 2 \sin a \cos b

    \sin a \cos b = \left(\frac{1}{2}\right) \left(\sin (a+b) + \sin (a-b) \right)

    use this
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