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Math Help - What kind of integral, and how do i start?

  1. #1
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    What kind of integral, and how do i start?

    ∫5/x(x+2x+5)dx

    Is this integration by parts?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by hlpplz View Post
    ∫5/x(x+2x+5)dx

    Is this integration by parts?
    This will be a partial fractions problem.

    Note that x^2+2x+5 is an irreducible quadratic.

    Thus, \frac{5}{x(x^2+2x+5)}=\frac{A}{x}+\frac{Bx+C}{x^2+  2x+5}

    Thus, we see that 5=A(x^2+2x+5)+Bx^2+Cx\implies 5=(A+B)x^2+(2A+C)x+5A

    Comparing coefficients, we have A+B=0, 2A+C=0 and 5A=5\implies A=1

    Now, we see that C=-2A=-2(1)=-2 and B=-A=-1

    So \frac{5}{x(x^2+2x+5)}=\frac{1}{x}-\frac{x+2}{x^2+2x+5}

    Therefore, \frac{5\,dx}{x(x^2+2x+5)}=\int\frac{\,dx}{x}-\int\frac{x+2}{x^2+2x+5}\,dx

    Can you take it from here?
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  3. #3
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    i don't know what to do with the second integral.
    I know the first one is simply ln⎮x⎮. Do i have to integrate by partial fractions the second integral again?
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  4. #4
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by hlpplz View Post
    i don't know what to do with the second integral.
    I know the first one is simply ln⎮x⎮. Do i have to integrate by partial fractions the second integral again?

    Yes.
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  5. #5
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    is the final answer

    ln⎮x⎮- 1/2ln⎮x+2x+5⎮- 1/x+1tan-2/x+1 + C ?
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  6. #6
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by hlpplz View Post
    ∫5/(x(x+4x+5))dx

    I got an answer of: ln⎮x⎮- 1/2ln⎮x+4x+5⎮- 1/(x+1) tan-2/(x+1) + C
    Is this correct?
    Differentiate your answer you should get the question if its correct
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  7. #7
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    i havent done integrals in a long time but i just took a shot at this and i think you made a mistake
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  8. #8
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    how would i solve it?
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  9. #9
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    Quote Originally Posted by hlpplz View Post
    ∫5/(x(x+4x+5))dx

    I got an answer of: ln⎮x⎮- 1/2ln⎮x+4x+5⎮- 1/(x+1) tan-2/(x+1) + C
    Is this correct?
    It doesn't look right. If you post all your working it will be easier to find your mistake(s).
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  10. #10
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    Here is the work i did
    Attached Thumbnails Attached Thumbnails What kind of integral, and how do i start?-integral.jpg  
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  11. #11
    Like a stone-audioslave ADARSH's Avatar
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    error in this step
     \int {\frac{da}{a^2 +4}}

    = \frac{1}{2}tan^{-1}(\frac{2}{a}) ~+c
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  12. #12
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    other than that all is well?
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  13. #13
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by hlpplz View Post
    other than that all is well?
    Yes My dear , you are absolutely corrrrecttt... Cool Job buddy

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