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Math Help - Need helping integrating...

  1. #1
    Junior Member
    Joined
    Mar 2008
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    Need helping integrating...

    Hi all,

    I need help integrating the following:
    <br />
\int \frac {1}{4^x} dx<br />

    I know that d/dx(a) = ln(a)a^x. However i wondering if anyone could show me the steps of integration for the above without recognition.

    Thanks in advance,
    ArTiCk
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  2. #2
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I need help integrating the following:
    <br />
\int \frac {1}{4^x} dx<br />

    I know that d/dx(a) = ln(a)a^x. However i wondering if anyone could show me the steps of integration for the above without recognition.

    Thanks in advance,
    ArTiCk
    let u = 4^{-x} so \ln u = -x \ln 4. Further -\frac{1}{\ln 4} \cdot \frac{du}{u} = dx. Your integral becomes

    \int 4^{-x}\,dx = - \frac{1}{\ln4} \int u \cdot \frac{du}{u} = - \frac{1}{\ln4} \int du .

    I believe you can take it from here.
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