(x+5)/(x²-6x+13)的不定积分
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∫(x+5)/(x^2-6x+13) dx
=(1/2)∫(2x-6)/(x^2-6x+13) dx +8∫dx/(x^2-6x+13)
=(1/2)ln|x^2-6x+13| +2∫dx/{ (x-3)/2]^2+1}
=(1/2)ln|x^2-6x+13| +4∫d[(x-3)/2]/{ (x-3)/2]^2+1}
=(1/2)ln|x^2-6x+13| +4arctan[(x-3)/2] +C
=(1/2)∫(2x-6)/(x^2-6x+13) dx +8∫dx/(x^2-6x+13)
=(1/2)ln|x^2-6x+13| +2∫dx/{ (x-3)/2]^2+1}
=(1/2)ln|x^2-6x+13| +4∫d[(x-3)/2]/{ (x-3)/2]^2+1}
=(1/2)ln|x^2-6x+13| +4arctan[(x-3)/2] +C
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∫x+5/x²-6x+13 dx
=∫(x-3+8)/(x²-6x+13) dx
=∫(x-3)/(x²-6x+13)dx+8∫1/[(x-3)²+2²]dx
=1/2ln(x²-6x+13)+8/2 arctan(x-3)/2+c
=1/2ln(x²-6x+13)+4 arctan(x-3)/2+c
=∫(x-3+8)/(x²-6x+13) dx
=∫(x-3)/(x²-6x+13)dx+8∫1/[(x-3)²+2²]dx
=1/2ln(x²-6x+13)+8/2 arctan(x-3)/2+c
=1/2ln(x²-6x+13)+4 arctan(x-3)/2+c
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∫(X+5)/(X²-6X+13)dX
=∫(X-3+8)/(X²-6X+13)dX
=∫(X-3)/(X²-6X+13)dX+∫8/(X²-6X+13)dX
=(1/2)∫(2X-6)/(X²-6X+13)dX+∫8/(X²-6X+13)dX
=(1/2)∫[d(X²-6X+13)]/(X²-6X+13)+
8∫[d(X-3)]/[(X-3)²+2²]
=(1/2)㏑(X²-6X+13)+4arctan[(X-3)/2]+C
=∫(X-3+8)/(X²-6X+13)dX
=∫(X-3)/(X²-6X+13)dX+∫8/(X²-6X+13)dX
=(1/2)∫(2X-6)/(X²-6X+13)dX+∫8/(X²-6X+13)dX
=(1/2)∫[d(X²-6X+13)]/(X²-6X+13)+
8∫[d(X-3)]/[(X-3)²+2²]
=(1/2)㏑(X²-6X+13)+4arctan[(X-3)/2]+C
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