integrate; 1/(x+1)x^2

Question

amistre64 · Answer

x^-2 -x^-1 + 1 ....
               ---------------
x^2+x^3 ) 1
               (1+x)
              ------
                   -x
                 (-x-x^2)
                 ---------
                        x^2

$$\int   x^{-2} -x^{-1} + 1 -x+x^2-x^3....\ dx$$

anonymous · Answer

i did it by partial fraction decomposition

amistre64 · Answer

i think the ideal thing to do tho is to decompose it into separate fraction

amistre64 · Answer

1             a          b            c
-------  = ---- + ---- + -------
x^2(x+1)      x         x^2        x+1


 1 =  ax(x+1) + b(x+1) +  cx^2

 1 =  ax(x+1) + b(x+1) +  cx^2
                         1             1

 1 =  ax(x+1) + (x+1) +  x^2

 1 =  a2(3) + (3) +  9

 1 =  a6 + 12

a = -11/6  if I did that right

amistre64 · Answer

missed it somples; but a=-1 according to the wolf

anonymous · Answer

help

anonymous · Answer

http://openstudy.com/updates/4f8882a5e4b02251ecc96da9

anonymous · Answer

yeaah i got -1 for a and 1 for both B and C