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Math Help - logarithm integration!

  1. #1
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    logarithm integration!

    if  s=t^u find \frac{ds}{du}

    pls help not sure of my answer, thanks
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  2. #2
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    Re: logarithm integration!

    t^u=e^{\ln t^u}=e^{u \ln t}
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  3. #3
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    Re: logarithm integration!

    Quote Originally Posted by lawochekel View Post
    if  s=t^u find \frac{ds}{du}

    pls help not sure of my answer, thanks
    \left(a^x\right)'=a^x \cdot \ln a
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  4. #4
    Member sbhatnagar's Avatar
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    Re: logarithm integration!

    \begin{aligned} s=t^u \quad \Rightarrow \quad \ln(s) &=u\ln(t) \\ \frac{1}{s}\frac{ds}{du} &=\ln(t) \\ \frac{ds}{du}&=t^u \ln(t)\end{aligned}
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