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Math Help - How to integrate 2^(4-x

  1. #1
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    How to integrate 2^(4-x

    How do you integrate 2^(4-x) and 2^x
    thanks.
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  2. #2
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    Quote Originally Posted by Johnt447 View Post
    How do you integrate 2^(4-x) and 2^x
    thanks.
     \int 2^{(4-x)}dx = \int e^{ln|2^{(4-x)}|} dx

     = \int e^{(4-x)ln|2|} dx

     = \int e^{(4ln|2|-xln|2|)} dx

     = \int e^{(4ln|2|})e^{(-xln|2|)} dx

    Now the first e part is a constant, and the second is of the form  e^Cx , where C is just some constant. You can integrate those, right?

     \int 2^{x}dx = \int e^{ln|2^{x}|} dx

     = \int e^{xln|2|} dx

    See?
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  3. #3
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    First, {{2}^{4-x}}=16\cdot {{2}^{-x}}, then {{2}^{-x}}={{e}^{-x\ln 2}} and perform a substitution from there to integrate an exponencial function.

    (This is what Mush did, just little algebra first after integrating.)
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