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Math Help - Need help integrating improper integral

  1. #1
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    Need help integrating improper integral

    Hello,

    Can someone please help me with integrating this problem?

    Thanks,
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  2. #2
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    Re: Need help integrating improper integral

    Quote Originally Posted by l flipboi l View Post
    Hello,

    Can someone please help me with integrating this problem?

    Thanks,
    Are you meant to be integrating wrt n? If so, reverse the order of the summation and the integral, using an appropriate theorem to justify this, and then integrate. There is an obvious substitution to make.
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  3. #3
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    Re: Need help integrating improper integral

    Quote Originally Posted by l flipboi l View Post
    Hello,

    Can someone please help me with integrating this problem?

    Thanks,
    I don't see an integral...
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  4. #4
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    Re: Need help integrating improper integral

    Oops sorry, it should be [1,t) e^(1/x^7)/x^8

    Not sure how to do this...
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    Re: Need help integrating improper integral

    Quote Originally Posted by l flipboi l View Post
    Oops sorry, it should be [1,t) e^(1/x^7)/x^8

    Not sure how to do this...
    Assuming you mean \displaystyle \int_1^t{\frac{e^{\frac{1}{x^7}}}{x^8}\,dx} = -\frac{1}{7}\int_1^t{e^{\frac{1}{x^7}}\left(-\frac{7}{x^8}\right)\,dx}, make the substitution \displaystyle u = \frac{1}{x^7} \implies du = -\frac{7}{x^8}\,dx and make note that \displaystyle u(1) = 1 and \displaystyle u(t) = \frac{1}{t^7}.
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