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How to do these integrals?

  1. Jan 27, 2009 #1
    a. [itex]
    \int x*ln(2x) dx
    b. [itex]
    \int \frac{x^2}{x^2-4} dx

    My Attempt:
    a. I have abs. no clue how to start it off. Do you start it off using integration by parts?
    b. Same with this. I don't know how to start it off.

    "Random" Questions:
    1) What does "converge" and "diverge" mean? i.e. Another question asks "Determine if each integral converges or diverges". I can do the integrals, but I'm not sure what its asking. One results in the answer being pi/3, the other results in infinity.
    2) When the question tells you to setup an integral for a volume of a solid generated when the region is rotated about the line x=-2 using cylindrical shells, you just do:
    [itex]\pi *
    \int (f(x)+2)^2 dx


    P.S. I'm not asking for answers, but rather how to start them off. Maybe 1 or 2 beginning steps in integrating these? =D
    Last edited: Jan 27, 2009
  2. jcsd
  3. Jan 27, 2009 #2


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    Gold Member

    Hi lastdayx52, welcome to PF:smile:

    Let's start with a) and b).... For a) try integration by parts....For b), hint: [itex]x^2=(x^2-4)+4[/itex]:wink:

    Give it a shot and post your attempt if you require further assistance.
  4. Jan 27, 2009 #3
    Got a:
    [itex]\frac{x^2*(2*ln(2)-1)}{4}+\frac{x^2*ln(x)}{2} + C[/itex]
    Checked on calculator, and was correct. Thank you!

    Now for b, that doesn't help me at all... >.>
  5. Jan 27, 2009 #4


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    Why not?

    [tex]\int \frac{x^2}{x^2-4} dx=\int \frac{(x^2-4)+4}{x^2-4} dx=\int \frac{x^2-4}{x^2-4} dx +\int \frac{4}{x^2-4} dx[/tex]
  6. Jan 27, 2009 #5
    LOL haha... See I did that, but stupidly thought the integral of 1 = 1, and when checked against the calculator, it was obviously not correct. haha... Thanks! =P
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