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Math Help - Substitution Rule

  1. #1
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    Substitution Rule

    I'm been working problems to help learn the substitution rule for integrals. Is this correct?

    \int\frac{{\sin{\ln{x}}}}{x}dx

    Let u=\ln{x} and du = \frac{1}{x}dx.

    = \int{\sin{u}du}
    = -\cos{u} + c
    = -\cos{\ln{x}} + c

    Thanks,
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by centenial View Post
    I'm been working problems to help learn the substitution rule for integrals. Is this correct?

    \int\frac{{\sin{\ln{x}}}}{x}dx

    Let u=\ln{x} and du = \frac{1}{x}dx.

    = \int{\sin{u}du}
    = -\cos{u} + c
    = -\cos{\ln{x}} + c

    Thanks,
    Yes, that's correct.
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