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Math Help - Integrating a^x wrt x

  1. #1
    Newbie emterics90's Avatar
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    Integrating a^x wrt x

    I have y=7^x and originally I wanted to derive this, but now I want to integrate it. How do I find \int 7^x dx?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by emterics90 View Post
    I have y=7^x and originally I wanted to derive this, but now I want to integrate it. How do I find \int 7^x dx?
    \int a^x~dx = \frac {1}{\ln a} a^x + C
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  3. #3
    Math Engineering Student
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    \int7^x\,dx=\int e^{x\ln7}\,dx

    Let's set u=x\ln7\implies du=\ln7\,dx, this yields

    \int7^x\,dx=\frac1{\ln7}\int e^u\,du=\frac1{\ln7}e^{x\ln7}+k=\frac{7^x}{\ln7}+k  ,\,k\in\mathbb R
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