这个定积分过程是?
1个回答
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解:1/(x^2-3x+2)
=1/[(x-2)(x-1)]
=-[1/(x-1)-1/(x-2)]
=[(x-2)-(x-1)]/[(x-1)(x-2)]=(x-2-x+1)/[(x-1)(x-2)]=-1/[(x-1)(x-2)]
原式=积分-[1/(x-1)-1/(x-2)]dx
=积分[1/(x-2)-1/(x-1)]dx
=积分1/(x-2)dx-积分1/(x-1)dx
=ln/x-2/-ln/x-1/
=ln/(x-2)/(x-1)/
原式=ln/3/4/-ln/1/2/=ln3/4/1/2=ln3/2
答:答案是ln3/2.
=1/[(x-2)(x-1)]
=-[1/(x-1)-1/(x-2)]
=[(x-2)-(x-1)]/[(x-1)(x-2)]=(x-2-x+1)/[(x-1)(x-2)]=-1/[(x-1)(x-2)]
原式=积分-[1/(x-1)-1/(x-2)]dx
=积分[1/(x-2)-1/(x-1)]dx
=积分1/(x-2)dx-积分1/(x-1)dx
=ln/x-2/-ln/x-1/
=ln/(x-2)/(x-1)/
原式=ln/3/4/-ln/1/2/=ln3/4/1/2=ln3/2
答:答案是ln3/2.
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