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Integrate: dx/(2x^2 + 4x + 7)

  • calculus -

    messy, are you sure you typed correctly?
    I was hoping the bottom would factor so I could use partial fractions.

    the way it stands I ran it through an integration program to get

    (√10/10)[tan -1 [√10(x+1)/5]

    are you working at that sophisticated level of integration??
    Is this highschool level ??

  • calculus -

    You can just write the denominator as:

    2x^2 + 4x + 7 =

    2 (x^2 + 2 x + 7/2) =

    2 [(x + 1)^2 + 5/2]

    Then you use the fact that the integral of dx/(x^2 + a^2) = 1/a arctan (x/a)

    So, the integral is:

    1/2 1/sqrt(5/2) arctan[(x+1)/sqrt(5/2)]=

    Answer given by Reiny above.

  • calculus -

    Thanks Reiny + Iblis!

    This is from Wiley textbook "Calculus: Early Transcendentals Combined, 8th Edition", section 8.4. I think problem #41 (from memory).

    I typed it right. The answer you two wrote matches the book, however I couldn't figure out how to do it. Makes sense now. Thanks

    Reiny, thanks for writing that. I feel like an idiot getting stuck on these textbook problems sometimes.

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