一题不定积分题求解
2个回答
2017-10-08
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∫(x+3)/(x^2-5x+6)dx
=∫(x+3)/[(x-2)(x-3)]dx
=∫(x-3+6)/[(x-2)(x-3)]dx
=∫{1/(x-2)+6*[(x-2)-(x-3)]/[(x-2)(x-3)]}dx
=∫[1/(x-2)+6/(x-3)-6/[(x-2)]dx
=∫[6/(x-3)-5/[(x-2)]dx
=6ln|x-3|-5ln|x-2|+C
=∫(x+3)/[(x-2)(x-3)]dx
=∫(x-3+6)/[(x-2)(x-3)]dx
=∫{1/(x-2)+6*[(x-2)-(x-3)]/[(x-2)(x-3)]}dx
=∫[1/(x-2)+6/(x-3)-6/[(x-2)]dx
=∫[6/(x-3)-5/[(x-2)]dx
=6ln|x-3|-5ln|x-2|+C
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