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  1. #1
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    Thumbs up please trying to solve

    6. INT (2X^2 + 1)/[(X^6 + 2X^4 + 2X^2 + 1)]^(1/2)dx????



    7. INT [(2X^6 + 1)]/(X^6)[(1 + X^2)] dx????




    8. INT [(2x^2 - 5)]/[(x^4 - 5x^2 + 6)]dx ?????
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  2. #2
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    Quote Originally Posted by berkanatci View Post
    INT [(2x^2 - 5)]/[(x^4 - 5x^2 + 6)]dx
    You post many integrals every day.

    If you really wanna learn, take it easy, it's much better.

    Notice that x^4 - 5x + 6 = (x - 3)(x - 2), and (x - 3) + (x - 2) = 2x - 5; then split the integral in two.
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  3. #3
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    you are right but my exam ll be very soon and I am afraid
    this weekend ,my friend and I ll try to understand your solving problems
    bec of not enough time,I cant solve questions.

    please help me
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  4. #4
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    Create a post which says something about your exam, pick up all the integrals you can't solve and all we're gonna help ya.
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  5. #5
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    ok
    thank u for everything... this weekend ,I ll study a lot.I promise u

    monday or tuesday,I ll send a new mail which I cant solve new problems
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  6. #6
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    Quote Originally Posted by berkanatci View Post
    7. INT [(2X^6 + 1)]/(X^6)[(1 + X^2)] dx????
    As you have written now, you don't even have an integral.

    Careful with parentheses:

    int([(2x^6 + 1)/(x^6)]*(1 + x^2)dx)

    Is that what you're trying to compute?

    If so:

    Expand (x^2 + 1)*(2x^6 + 1) = 2x^8 + 2x^6 + x^2 + 1

    And thus, (2x^8 + 2x^6 + x^2 + 1)/x^6

    Simplify: 2x^2 + 1/x^4 + 1/x^6 + 2

    Integrate: (2x^3)/3 - 1/(3x^3) - 1/(5x^5) + 2x + C
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  7. #7
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    Quote Originally Posted by AfterShock View Post
    As you have written now, you don't even have an integral.

    Careful with parentheses:

    int([(2x^6 + 1)/(x^6)]*(1 + x^2)dx)

    Is that what you're trying to compute?

    If so:

    Expand (x^2 + 1)*(2x^6 + 1) = 2x^8 + 2x^6 + x^2 + 1

    And thus, (2x^8 + 2x^6 + x^2 + 1)/x^6

    Simplify: 2x^2 + 1/x^4 + 1/x^6 + 2

    Integrate: (2x^3)/3 - 1/(3x^3) - 1/(5x^5) + 2x + C
    I think he's actually trying to integrate:

    INT (2x^6 + 1)/[(x^6)(1 + x^2)] dx ... the x^6 and 1 + x^2 both being on the denominator.

    Most of the problems I have helped him on so far are actually very long and complicated. He has yet to integrate something as simple as some product of polynomials divided by x^6. So you are very correct in that he needs to be careful with parenthesis.
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  8. #8
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    [INT (2x^6 + 1)/[(x^6)(1 + x^2)] dx ... this is correct one.

    can u solve it
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  9. #9
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by berkanatci View Post
    6. INT (2X^2 + 1)/[(X^6 + 2X^4 + 2X^2 + 1)]^(1/2)dx????



    7. INT [(2X^6 + 1)]/(X^6)[(1 + X^2)] dx????




    8. INT [(2x^2 - 5)]/[(x^4 - 5x^2 + 6)]dx ?????
    7. INT (2X^6 + 1)/[(x^6)(1 + x^2)] dx

    This one is pretty interesting. I won't go through the entire process of solving it, but I will set up the final integration:

    First, add and subtract 1 from the numerator
    INT (2x^6 + 2 - 1)/[(x^6)(1 + x^2)] dx
    INT 2(x^6 + 1)/[(x^6)(1 + x^2)] dx - INT 1/[(x^6)(1 + x^2)] dx

    This numerator is a sum of cubes, which can be factored:
    2*INT [(x^2 + 1)(x^4 - x^2 + 1)]/[(x^6)(1 + x^2)] dx
    2*INT (x^4 - x^2 + 1)/x^6 dx
    2*INT (1/x^2 - 1/x^4 + 1/x^6) dx

    Add and subtract x^2 from this integration:
    INT (1 + x^2 - x^2)/
    [(x^6)(1 + x^2)] dx
    INT (1 + x^2)/[(x^6)(1 + x^2)] dx - INT x^2/[(x^6)(1 + x^2)] dx
    INT 1/x^6 - INT 1/[(x^4)(1 + x^2)] dx

    Add and subtract x^2 from this integration:
    INT (1 + x^2 - x^2)/[(x^4)(1 + x^2)] dx
    INT (1 + x^2)/[(x^4)(1 + x^2)] dx - INT x^2/[(x^4)(1 + x^2)] dx
    INT 1/x^4 dx - INT 1/[(x^2)(1 + x^2)] dx

    Add and subtract x^2 from this integration:
    INT (1 + x^2 - x^2)/[(x^2)(1 + x^2)] dx
    INT (1 + x^2)/[(x^2)(1 + x^2)] dx - INT x^2/[(x^2)(1 + x^2)] dx
    INT 1/x^2 dx - INT 1/(1 + x^2) dx

    Combine the entire integration into one (be careful with negative signs) and integrate. It will be much easier to do at this point.


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  10. #10
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    Quote Originally Posted by berkanatci View Post
    [INT (2x^6 + 1)/[(x^6)(1 + x)] dx ... this is correct one.

    can u solve it
    Split the integral in two, you'll get one with 2x^6/(x^6(x + 1)), which is easy to solve, and 1/(x^6(x + 1)) = (x^4 - x + 1)/x^6 - 1/(x + 1) (see why)

    Then the second one it's easy to solve and the problem it's done.
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