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Math Help - This integral brings me somewhat back to where I started after Integration by parts!

  1. #1
    s3a
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    This integral brings me somewhat back to where I started after Integration by parts!

    After having attempted integration by parts, it only seems to make this problem harder! I tried having u = e^(2x), and as the work shows, u = sin(3x) and neither way brings me anywhere. (In the problem x = theta)

    (I attached my work.)

    Someone please help me!
    Thanks!

    P.S.
    Wolfram Alpha shows something beyond my understanding: http://www.wolframalpha.com/input/?i=integral+e^(2x)+*+sin(3x)

    P.P.S
    I am getting really scared because I tried to advance in my homework but the following problem seems to be similar to this one and if I can't do this one then I can't advance! I will still attempt it however, while someone answers this question here.
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  2. #2
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    Quote Originally Posted by s3a View Post
    After having attempted integration by parts, it only seems to make this problem harder! I tried having u = e^(2x), and as the work shows, u = sin(3x) and neither way brings me anywhere. (In the problem x = theta)

    (I attached my work.)

    Someone please help me!
    Thanks!

    P.S.
    Wolfram Alpha shows something beyond my understanding: http://www.wolframalpha.com/input/?i=integral+e^(2x)+*+sin(3x)

    P.P.S
    I am getting really scared because I tried to advance in my homework but the following problem seems to be similar to this one and if I can't do this one then I can't advance! I will still attempt it however, while someone answers this question here.
    If you use integration by parts again on your new integral, you will end up with an equation in \int{e^{2\theta}\sin{3\theta}\,d\theta}.

    Then by moving all of the integrals to one side, you can solve for the integral.
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  3. #3
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    Keep going until you get your original integral back on the right side. Subtract that integral from both sides and divide.
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    Quote Originally Posted by s3a View Post
    After having attempted integration by parts, it only seems to make this problem harder! I tried having u = e^(2x), and as the work shows, u = sin(3x) and neither way brings me anywhere. (In the problem x = theta)

    (I attached my work.)

    Someone please help me!
    Thanks!

    P.S.
    Wolfram Alpha shows something beyond my understanding: http://www.wolframalpha.com/input/?i=integral+e^(2x)+*+sin(3x)

    P.P.S
    I am getting really scared because I tried to advance in my homework but the following problem seems to be similar to this one and if I can't do this one then I can't advance! I will still attempt it however, while someone answers this question here.
    Use integration by parts again to intgrate \int{e^{2\theta}\cos{3\theta}\,d\theta}
    You will get \int{e^{2\theta}\sin{3\theta}\,d\theta} appearing again.
    Bring it over to the left side of the equation.
    Go for it
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