Find an integral ∫ d x ( x + 1 ) 2 ( x 2 + 1 ) To solve this indefinite integral, I use fraction expansion and I get a wrong system of equations: { B = 0 A + 2 B + C = 0 A + B + C = 1 What is the problem with my fraction expansion?

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Find an integral   ∫                    d        x                    (        x        +        1                  )          2                (                  x          2                +        1        )            To solve this indefinite integral, I use fraction expansion and I get a wrong system of equations:      {                            B          =          0                                      A          +          2          B          +          C          =          0                                      A          +          B          +          C          =          1                        What is the problem with my fraction expansion?

vyhlodatis · Accepted Answer

Hint. The polynomial at the denominator is of degree 4 and you have three parameters. Try with is the following partial fraction decomposition (with four parameters):      1          (      x      +      1              )        2            (              x        2            +      1      )        =            A      x      +      B                      x        2            +      1        +      C          x      +      1        +      D          (      x      +      1              )        2              .

Find an integral int(dx)/((x+1)^2(x^2+1)) To solve this indefinite integral, I use fraction expansion and I get a wrong system of equations: {(B=0),(A+2B+C=0),(A+B+C=1):} What is the problem with my fraction expansion?

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