x平方减x加一分之一的不定积分
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x^2-x+1=0
x= (1+√5)/2 or (1-√5)/2
x^2-x+1 = [ x-(1+√5)/2 ]. [ x-(1-√5)/2 ]
∫ dx/(x^2-x+1)
=∫ dx/{ [ x-(1+√5)/2 ]. [ x-(1-√5)/2 ] }
=(1/√5) ∫ { 1/ [ x-(1+√5)/2 ] -1/ [ x-(1-√5)/2 ] } dx
=(1/√5) ln| [ x-(1+√5)/2 ] / [ x-(1-√5)/2 ] | +C
x= (1+√5)/2 or (1-√5)/2
x^2-x+1 = [ x-(1+√5)/2 ]. [ x-(1-√5)/2 ]
∫ dx/(x^2-x+1)
=∫ dx/{ [ x-(1+√5)/2 ]. [ x-(1-√5)/2 ] }
=(1/√5) ∫ { 1/ [ x-(1+√5)/2 ] -1/ [ x-(1-√5)/2 ] } dx
=(1/√5) ln| [ x-(1+√5)/2 ] / [ x-(1-√5)/2 ] | +C
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