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Math Help - How can I evaluate this integral?

  1. #1
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    How can I evaluate this integral?

    How can I evaluate this integral?

    Integral sin(ln(x)) dx

    If possible, can anyone show me step by step?

    Thank you
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  2. #2
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    Quote Originally Posted by noppawit View Post
    How can I evaluate this integral?

    Integral sin(ln(x)) dx
    \int \sin (\ln x) dx = \int e^{\ln x}\sin (\ln x)(\ln x)'dx
    By substitution you need to compute,
    \int e^t \sin t dt
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by noppawit View Post
    How can I evaluate this integral?

    Integral sin(ln(x)) dx

    If possible, can anyone show me step by step?

    Thank you
    one way:

    write as \int \frac xx \sin ( \ln x) ~dx

    then make the substitution t = \ln x

    you will get the integral \int e^t \sin t~dt which you would then do using integration by parts, with u = \sin t (the part you differentiate) and dv = e^t~dt (the part you integrate)
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