求解微积分方程X^2-X+1分之X+1dx

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求解微积分方程X^2-X+1分之X+1dx

求解微积分方程X^2-X+1分之X+1dx
求解微积分方程
X^2-X+1分之X+1dx

求解微积分方程X^2-X+1分之X+1dx
X^2-X+1分之X+1dx
=1/2*S(1/(X^2-X+1))d(X^2-X+1)
+3/2*S(1/[(x-1/2)^2+3/4]d(x-1/2)
=1/2*ln(X^2-X+1)+
(根号3)*arctan[2(x-1/2)/(根号3))]+C

原式=1/2积分号(1/(x^2-x+1))d(x^2-x+1)+(3/2)积分号(1/[(x-1/2)^2+3/4]
=1/2ln(x^2-x+1)+(3/2)*(4/3)积分号1/[4/3*(x-1/2)^2+1]dx+c
=1/2ln(x^2-x+1)+根号(3)tan(2/(根号(3)(x-1/2)))