Solving ∫ ( 5 x 2 + 3 x − 2 x 3 + 2 x 2 ) via partial fractionsSo, first of all, we must factorize the denominator: x 3 + 2 x 2 = ( x + 2 ) ⋅ x 2 Great. So now we write three fractions: A x 2 + B x + C x + 2 Eventually we conclude that A ( x + 2 ) + B ( x + 2 ) ( x ) + C ( x 2 ) = 5 x 2 + 3 x − 2So now we look at what happens when x=−2:C=12When x=0:A=−1And now we are missing B, but we can just pick an arbitrary number for x like... 1:B=−1

Question

Solving   ∫      (                  5                  x          2                +        3        x        −        2                              x          3                +        2                  x          2                      )   via partial fractionsSo, first of all, we must factorize the denominator:      x    3    +  2      x    2    =  (  x  +  2  )  ⋅      x    2  Great. So now we write three fractions:      A          x      2        +      B    x    +      C          x      +      2      Eventually we conclude that  A  (  x  +  2  )  +  B  (  x  +  2  )  (  x  )  +  C  (      x    2    )  =  5      x    2    +  3  x  −  2So now we look at what happens when x=−2:C=12When x=0:A=−1And now we are missing B, but we can just pick an arbitrary number for x like... 1:B=−1

Zachery Conway · Accepted Answer

You have an algebra error. When you put x=−2, the constraint equation collapses to 4C=12, so C=3.Your method for determining B is correct – the constraining identity must hold for any x. Putting x=1 is a fine choice as the arithmetic is easier. However the incorrect value for C will affect the value you determine for B.

Jamison Rios · Accepted Answer

I think this is the easiest way.  (  B  +  C  )      x    2    +  (  A  +  2  B  )  x  +  2  A  =  5      x    2    +  3  x  −  2                    2        A                            =        −        2                    →        A                            =        −        1                            A        +        2        B                            =        −        1        +        2        B        =        3                    →        B                            =        2                            B        +        C                            =        2        +        C        =        5                    →        C                            =        3

Solving ∫ ( 5 x 2

Answered question

Answer & Explanation

New Questions in Electric current