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Math Help - Integral

  1. #1
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    Integral

    Hello! How would you integrate 2^x / ln2? Thanks already!
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  2. #2
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    Re: Integral

    \displaystyle 2^x=e^{\ln 2^x}=e^{x \ln 2}
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  3. #3
    MHF Contributor

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    Re: Integral

    note that:

    \frac{1}{\ln(2)} = \frac{\ln(2)}{(\ln(2))^2}

    you can take the denominator (which is just a constant) outside the integral, so:

    \int \frac{2^x}{\ln(2)}\ dx = \frac{1}{(\ln(2))^2}\int \ln(2)2^x\ dx = \frac{1}{(\ln(2))^2} \int e^{\ln(2)x} \ln(2)\ dx

    if you use the substitution u = \ln(2)x what would du be?
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