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Math Help - Integration

  1. #1
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    Integration

    Find the following integrals:

    a) integral from -1 to 0 of 1/(sqrt of 1-x) dx
    b) indefinite integral of x(ln(x))^2 dx
    c) indefinite integral of (x+7)/((x-3)(x+2)) dx

    My final exam is almost here. I need help!
    This is a practice question and for part a, I got -2+2sqrt2
    Part b: (ln(x))^2 * x^2/2 - lnx * x^2/2 - x^2/4 + C
    Part C: ln of absolute value of (x-3)^2/(x+2) +C
    Are my answers correct? Thanks!!!
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by Mathbo View Post
    Find the following integrals:

    a) integral from -1 to 0 of 1/(sqrt of 1-x) dx
    b) indefinite integral of x(ln(x))^2 dx
    c) indefinite integral of (x+7)/((x-3)(x+2)) dx

    My final exam is almost here. I need help!
    This is a practice question and for part a, I got -2+2sqrt2
    Part b: (ln(x))^2 * x^2/2 - lnx * x^2/2 - x^2/4 + C
    Part C: ln of absolute value of (x-3)^2/(x+2) +C
    Are my answers correct? Thanks!!!
    Yes all fine.
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  3. #3
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    Quote Originally Posted by Deadstar View Post
    Yes all fine.
    Seriously?
    What method am I supposed to use for part C?
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by Mathbo View Post
    Seriously?
    What method am I supposed to use for part C?
    In your post you said you solved it so whatever method you used is fine. Probably partial fractions or something like that. It's 3am so I can't give it tooo much thought...
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  5. #5
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    Quote Originally Posted by Deadstar View Post
    In your post you said you solved it so whatever method you used is fine. Probably partial fractions or something like that. It's 3am so I can't give it tooo much thought...
    Did you do the actual integration and actually get the same answers as I did? I'm worried that I have problems with integration. And my final is tomorrow!
    Thanks!
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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Mathbo View Post
    Did you do the actual integration and actually get the same answers as I did? I'm worried that I have problems with integration. And my final is tomorrow!
    Thanks!
    use partial fractions to get:

    \int \frac{x+7}{x-3)(x+2)} dx = \int [\frac{2}{x-3} -\frac{1}{x+2}] dx

    and integrate
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  7. #7
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    Well i too solve it. Your answer is right. But the calculations to shown on the post is so difficult so i suggest you to just be relax that you are right in your calculation. Also i would suggest you to don't delete this post because it could be helpful you to ask and take solutions in your any other difficulties.
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  8. #8
    Super Member Deadstar's Avatar
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    Quote Originally Posted by Mathbo View Post
    Did you do the actual integration and actually get the same answers as I did? I'm worried that I have problems with integration. And my final is tomorrow!
    Thanks!
    I did it with Maple. I'd say you'll be fine.
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  9. #9
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    Smile

    By partial integration

    ∫{(x+7)/(x-3)(x+2)}dx=∫{A/(x-3)+B/(x+2)}dx

    A(x+2)+B(x-3)=x+7

    Let x=3

    5A=10

    A=10/5
    A=2

    Let x=-2

    -5B=5

    B=-1

    ∫{(x+7)/(x-3)(x+2)}dx=∫{2/(x-3)-1/(x+2)}dx

    =∫{2/(x-3)dx- ∫1/(x+2)}dx


    =2ln(|x-3|)-ln(|x+2|)+C
    Last edited by edison; April 28th 2010 at 06:04 AM.
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