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Thread: improper integral: converges/diverges before evaluation?

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    improper integral: converges/diverges before evaluation?

    Hi. I'm a little confused about an issue in my homework problems involving improper integrals. I have problems like so:

    Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

    \int_{1}^{\infty}{\frac{ln\,x}{x}\,dx}
    How do I determine whether it converges or diverges before actually evaluating it?
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    Re: improper integral: converges/diverges before evaluation?

    Quote Originally Posted by infraRed View Post
    Hi. I'm a little confused about an issue in my homework problems involving improper integrals. I have problems like so:
    How do I determine whether it converges or diverges before actually evaluating it?
    What is the derivative of \frac{(\ln(x))^2}{2}~?
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    Re: improper integral: converges/diverges before evaluation?

    ln(x)/x

    ...?
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    Re: improper integral: converges/diverges before evaluation?

    Obviously diverges.
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    Re: improper integral: converges/diverges before evaluation?

    Quote Originally Posted by infraRed View Post
    ln(x)/x...?

    So what that tell you about the integral and why?
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    Re: improper integral: converges/diverges before evaluation?

    \frac{\ln(x)}{x} > \frac{1}{x}. But the integral of 1/x diverges, so the integral of the original function does too.
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