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    From the Edexcel c4 2013 paper.

    How do you do it? I seen people say you can do it through reverse chain rule or substitution or the ln^e(ln2)x

    I learnt how do it through reverse chain rule but how do you do it the other 2 ways??
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    Couldn't it also be done by parts?


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    \displaystyle 2^t=e^{\ln(2^t)}=e^{t \ln 2}
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    (Original post by Mr M)
    \displaystyle 2^t=e^{\ln(2^t)}=e^{t \ln 2}
    Is that equivalent to 2^t/ln2?
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    (Original post by cera ess six)
    Is that equivalent to 2^t/ln2?
    Once integrated yes (plus a constant of integration).
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    (Original post by cera ess six)
    Is that equivalent to 2^t/ln2?
    \displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{ax} + C

    right?

    Why? a is just a number!!!
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    (Original post by Mr M)
    Once integrated yes (plus a constant of integration).
    Oh ok how do you integrate further? this was one of the methods which confused me completely when I saw it.
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    (Original post by Indeterminate)
    \displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{2x} + C

    right?

    Why? a is just a number!!!
    I don't much like the look of this!
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    (Original post by cera ess six)
    Oh ok how do you integrate further? this was one of the methods which confused me completely when I saw it.
    If you don't know how to tackle \int e^{kx} \, dx then you need to make sure you are confident about the basics before trying to extend your understanding further.
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    (Original post by Indeterminate)
    \displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{2x} + C

    right?

    Why? a is just a number!!!
    I dont understand that approach sorry
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    (Original post by cera ess six)
    I dont understand that approach sorry
    It is wrong so I'm not surprised you don't understand it.
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    (Original post by Indeterminate)
    \displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{ax} + C

    right?

    Why? a is just a number!!!
    Suspect that was a typo
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    (Original post by Mr M)
    It is wrong so I'm not surprised you don't understand it.
    (Original post by cera ess six)
    I dont understand that approach sorry
    A typo. I thought I should give one example but then decided to generalise. I forgot to change the 2 to an a
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    (Original post by Indeterminate)
    A typo. I thought I should give one example but then decided to generalise. I forgot to change the 2 to an a
    I assumed it probably was.
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    (Original post by Mr M)
    If you don't know how to tackle \int e^{kx} \, dx then you need to make sure you are confident about the basics before trying to extend your understanding further.

    Im sure integrating e^ax = 1/a e^ax just dont how it fits in X_X
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    I would write

    Since

    \dfrac{d}{dt}(2^t) = 2^t \ln 2


    \displaystyle \int 2^t \ dt =...
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    (Original post by cera ess six)
    Im sure integrating e^ax = 1/a e^ax just dont how it fits in X_X
    Try differentiating the result and see what you get.
    Spoiler:
    Show
    Reverse chain rule
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    (Original post by joostan)
    Try differentiating the result and see what you get.
    Spoiler:
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    Reverse chain rule
    I know how to differentiate/integrate it reverse chain rule way.

    F'(t) = 2^t ln2

    Then using reverse chain rule you get 2^t/ln2

    Its just the other methods of doing it I dont understand
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    (Original post by cera ess six)
    Im sure integrating e^ax = 1/a e^ax just dont how it fits in X_X
    Use the substitution u = t\ln 2
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    (Original post by cera ess six)
    Im sure integrating e^ax = 1/a e^ax just dont how it fits in X_X
    Well this is exactly the same. ln 2 is just the constant a.
 
 
 
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