Morning distinguished Engineers

Discussion in 'Homework Help' started by Breeze, Sep 25, 2015.

  1. Breeze

    Thread Starter New Member

    Jun 30, 2015
    24
    1
    I need help with simplifying this integral,i have tried a couple of formulae but with no success

    2x+1/3x^2+3x+5 dx...see the uploaded attachment of my attempts at solving it
     
  2. RBR1317

    Active Member

    Nov 13, 2010
    229
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    Attached are the output of two different symbolic math engines. The software does not explain how it does the evaluation.
     
  3. Papabravo

    Expert

    Feb 24, 2006
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    The integral is in the proper form of

    \frac{du}{u}

    I don't see the problem.
     
  4. Russmax

    Member

    Sep 3, 2015
    81
    12
    More accurately, Papa, you do see the problem and the solution.
     
  5. Papabravo

    Expert

    Feb 24, 2006
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    Yes I do. Once the constant factor, k, is removed the numerator is the derivative of the denominator, and the answer follows as:

    k\cdot ln(u)
     
  6. WBahn

    Moderator

    Mar 31, 2012
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    One thing you need to do is to stop being sloppy with your notation. What you have written above is

    <br />
\int \; \( 2x \; + \; \frac{1}{3}x^2 \; + \; 3x \; + \; 5 \) \; dx<br />

    Sloppiness in notation leads to (or results from) sloppiness in thought.
     
  7. Breeze

    Thread Starter New Member

    Jun 30, 2015
    24
    1
    Thank you all for your help have actually found the answer following your leads,i have seen where my mistake was,i had somehow overlooked the concept in my notes,so i actually found it some moments ago of course with the hints from all of you.I want to apologize for my sloppiness as it were,as a newbie in Engineering i certainly have a lot of concepts to learn and master,needless to say i need to quickly master the art of writing in proper notation,i will as a matter of urgency get myself well acquainted wit TEX.I want to express my heartfelt gratitude at your tireless efforts in helping me through my schooling as an aspiring budding engineer.
     
  8. Breeze

    Thread Starter New Member

    Jun 30, 2015
    24
    1
    i am very sorry about my sloppiness,the above expression should actually be,find the integral of: (2x+1)/(3x^2+3x+5) dx
     
  9. shteii01

    AAC Fanatic!

    Feb 19, 2010
    3,387
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    hm...
    <br />
\frac{2x+1}{3x^2+3x+5}=\frac{2x}{3x^2+3x+5}+\frac{1}{3x^2+3x+5}<br />
    then
    <br />
\int\frac{2x+1}{3x^2+3x+5}dx=\int\frac{2x}{3x^2+3x+5}+\frac{1}{3x^2+3x+5}dx=\int\frac{2x}{3x^2+3x+5}dx+\int\frac{1}{3x^2+3x+5}dx=2\int\frac{x}{3x^2+3x+5}dx+\int\frac{1}{3x^2+3x+5}dx<br />
    ^ would finding two simpler integrals and then combining the results help?
     
  10. Papabravo

    Expert

    Feb 24, 2006
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    Conceivably it could also have been:

    ( \; 2x \; +\; \frac{1}{3x^2} \; +\; 3x \; + \; 5 \; )
     
    Last edited: Sep 25, 2015
  11. Papabravo

    Expert

    Feb 24, 2006
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    No it makes it harder. The key insight is that except for a constant the numerator is the derivative of the denominator.
     
  12. WBahn

    Moderator

    Mar 31, 2012
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    Nope. Division and multiplication have equal precedence and are left associative. Thus the division is performed before the multiplication.

    Highest priority -- exponentiation:

    2x+1/3x^2+3x+5 = 2x+1/3(x^2)+3x+5

    Next, multiplication and division, left to right:

    (2x)+((1/3)(x^2))+(3x)+5

    Next, addition and subtraction, left to right:

    ((((2x)+((1/3)(x^2)))+(3x))+5)
     
  13. shteii01

    AAC Fanatic!

    Feb 19, 2010
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    You are right, it would not have helped. My freshman calculus textbook does not have that form in the table of integrals.
     
  14. Papabravo

    Expert

    Feb 24, 2006
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    There are exceptions to the left associative rule: APL for one. But I agree, that it is the most common practice in many programming languages. Maybe we should all learn RPN and dispense with the ambiguity of infix notation.

    2\; x\; *\; 1\; +\; 3\; x\; x\; *\; *\; 3\; x\; *\; +\; 5\; +\; /\;

    or perhaps

    2\; x\; *\; 1\; +\; 3\; x\; 2\; \^\; *\; 3\; x\; *\; +\; 5\; +\; /\;

    On second thought -- maybe not.
     
    Last edited: Sep 25, 2015
  15. WBahn

    Moderator

    Mar 31, 2012
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    Has nothing to do with programming languages (the TS's problem has nothing to do with programs). This is the (as far as I know) universal precedence rules taught in grade school.

    I'm definitely a proponent of RPN, but postfix notation has the real potential to cause confusion when written out because the operands often run together -- that's probably why humans adopted infix notation a few centuries ago.
     
  16. Papabravo

    Expert

    Feb 24, 2006
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    I find it hard to believe that:

    \int \; \frac{1}{x} \; dx \; =\; ln(x) \; + \; C

    is not there. All of mine do!
     
    Last edited: Sep 25, 2015
  17. Breeze

    Thread Starter New Member

    Jun 30, 2015
    24
    1
    i actually have found this particular formula in my text bk,thanks a lot
     
    Papabravo likes this.
  18. Papabravo

    Expert

    Feb 24, 2006
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    It was supposed to be joke son. Kinda like the fantasy that we could adopt the metric system. You didn't think I was serious I hope.
     
  19. joeyd999

    AAC Fanatic!

    Jun 6, 2011
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    In fact, RPN is far more computationally efficient than infix -- especially for low complexity hardware. It is for this reason that I have my own set of stack-based floating point libraries for my PIC work.
     
  20. WBahn

    Moderator

    Mar 31, 2012
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    Definitely no argument there.
     
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