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Math Help - Intergration with 6^x

  1. #1
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    Intergration with 6^x

    Its a definate intergral upper limit is e lower is 1 (8^x-4^x)dx
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  2. #2
    Super Member wingless's Avatar
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    \int^{e}_{1} 8^x - 4^x dx

    Do you know that \int a^x dx = \frac{a^x}{\ln a} ?
    We can get that rule by seeing that \frac{d}{dx}a^x = a^x \ln a and its inverse is \frac{a^x}{\ln a}.

    So,
    \int^{e}_{1} 8^x - 4^x dx

    \int^{e}_{1} 8^x dx - \int^{e}_{1} 4^x dx

    \frac{8^x}{\ln 8} - \frac{4^x}{\ln 4} ~|^{e}_{1}

    (\frac{8^e}{\ln 8}-\frac{8}{\ln 8}) - (\frac{4^e}{\ln 4} - \frac{4}{\ln 4})

    \boxed{~\frac{8^e-8}{\ln 8}-\frac{4^e-4}{\ln 4}~}
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