14题怎么做
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14.
∫[(3x-2)/(x²-4x+5)]dx
=∫[(3x-6+4)/(x²-4x+5)]dx
=(3/2)∫[(2x-4)/(x²-4x+5)]dx + 4∫[1/(x²-4x+5)]dx
=(3/2)∫[(2x-4)/(x²-4x+5)]d(x²-4x+5) + 4∫[1/[1+(x-2)²]d(x-2)
=(3/2)ln(x²-4x+5) +4arctan(x-2) +C
∫[(3x-2)/(x²-4x+5)]dx
=∫[(3x-6+4)/(x²-4x+5)]dx
=(3/2)∫[(2x-4)/(x²-4x+5)]dx + 4∫[1/(x²-4x+5)]dx
=(3/2)∫[(2x-4)/(x²-4x+5)]d(x²-4x+5) + 4∫[1/[1+(x-2)²]d(x-2)
=(3/2)ln(x²-4x+5) +4arctan(x-2) +C
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