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#### renyikouniao

##### Member

- Jun 1, 2013

- 41

2) integral (upper bound:1, lower bound:0) (x^4+x^2+1)/(x^3+x^2+x-3) dx

Now I know how to use Partial Fractions,My question is:

1) For the first part ln(x) is not defined at 0

¼ʃ1/x dx + ¼ʃ(3x-1)/(x²+x+4) dx

= ¼ ln|x| + ¼ʃ(3x-1)/(x²+x+4) dx

2) ln(x-1) is not defined at 1 for this part

ʃ1/[2(x-1)] + (x+7) / [2(x²+2x+3)] dx

= ½ʃ1/(x-1) +½ ʃ(x+7)/(x²+2x+3) dx

= ½ ln |x-1| +½ ʃ(x+7)/(x²+2x+3) dx

So If I want to evaluate this definite integral, what I should do next?