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Homework Help: Proving that the integral of (a^x)dx = a^x/(lna)+c ?

  1. Feb 17, 2012 #1
    Proving that the integral of (a^x)dx = a^x/(lna)+c ???

    Hi, I know that:

    ∫ax dx = ax / ln(a) + C

    Could someone give me a step by step that proves this? thanks a lot!
     
  2. jcsd
  3. Feb 17, 2012 #2
    Re: Proving that the integral of (a^x)dx = a^x/(lna)+c ???

    Here's a trick:

    Re-write your integral as:

    [tex]

    \int e^{lna*x}dx
    [/tex]

    Then use a substitution:

    u = ln(a) * x
     
  4. Feb 17, 2012 #3
    Re: Proving that the integral of (a^x)dx = a^x/(lna)+c ???

    Beautiful! Thank you :D
     
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