Calculus AB

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Please help me integrate this equation using partial fractions:

Integrate [(x^2+5)/(x^3-x^2+x+3)]dx.

Thank you very much.

  • Calculus AB -

    x^3-x^2+x+3=(x+1)(x^2-2x+3)

    (x^2+5)/(x^3-x^2+x+3)=
    =A/(x+1)+(Bx+C)/(x^2-2x+3)

    A(x^2-2x+3)+(Bx+C)(x+1)=x^2+5

    A+B=1
    -2A+B+C=0
    3A+C=5
    Find A,B,C

  • Calculus AB -

    In google type:
    wolfram alpha

    When you see list of results click on:
    Wolfram Alpha:Computational Knoweledge Engine

    When page be open in rectangle type:
    (x^2+5)/(x^3-x^2+x+3) and click option =

    After few secons you will see all about that function.

    Now click option:
    Partial fraction expansion: Show steps


    Now in wolfram alpha rectangle type:
    2/(x^2-2x+3)+1/(x+1)
    and click option =

    When you see results clic option:
    Indefinite integral: Show steps

  • Calculus AB -

    Thank you very much.

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