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Math Help - Need help with an integral. Thanks in advance!

  1. #1
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    Need help with an integral. Thanks in advance!

    I need help with this integral that was on an AP Calculus BC Practice Test.

    <br />
\int_{1}^{e} \frac{ (x^2+1) } {x} dx<br /> <br />

    This is on the non-calculator section, so it doesn't need to be in decimal format - just simplified would be great.

    Maybe even just give me a prod in the right direction as far as which method to use. I tried integration by parts, but got a different answer than what was provided in the five choices.

    Thanks in advance!
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  2. #2
    Member
    Joined
    Feb 2010
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    integral

    Hello,

    Do as follows:

    \int_{0}^{e} \frac{x^{2}+1}{x}dx=\int_{0}^{e}\left( \frac{x^{2}}{x}+\frac{1}{x} \right)dx=\int_{0}^{e}\left( x+\frac{1}{x} \right) dx=\left[\frac{1}{2}x^{2}+\ln|x|\right]_{0}^{e}

    Form here, simply insert the limits (the upper limit minus the lower limit).
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  3. #3
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    May 2010
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    Wow, that's a lot simpler than I was making it

    Thank you so much!
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