(1-x)/(9-4x^2)=a/(3+2x)+b/(3-2x)
=[a(3-2x)+b(3+2x)]/(9-4x^2)
所以3a-2ax+3b+2bx=1-x
3a+3b=1
2b-2a=-1
a=5/12,b=-1/12
(1-x)/(9-4x^2)
=(5/12)*1/(3+2x)-(1/12)*1/(3-2x)
所以∫(1-x)/(9-4x^2) dx
=(5/12)∫1/(3+2x)dx-(1/12)∫1/(3-2x)dx
=(5/24)∫1/(3+2x)d(3+2x)+(1/24)∫1/(3-2x)d(3-2x)
=(5/24)*ln|3+2x|+(1/24)*ln|3-2x|+C
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