∫x^3dx/(x^4-x^2+2)

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∫x^3dx/(x^4-x^2+2)
∫x^3dx/(x^4-x^2+2)

∫x^3dx/(x^4-x^2+2)
∫ x³/(x⁴-x²+2) dx
=(1/2)∫ x²/(x⁴-x²+2) d(x²)
令x²=u
=(1/2)∫ u/(u²-u+2) du
=(1/2)∫ (u-1/2+1/2)/(u²-u+2) du
=(1/4)∫ (2u-1)/(u²-u+2) du + (1/4)∫ 1/(u²-u+2) du
=(1/4)∫ 1/(u²-u+2) d(u²-u) + (1/4)∫ 1/[(u-1/2)²+7/4] du
=(1/4)ln(u²-u+2) + (√7/14)arctan[2(u-1/2)/√7] + C
=(1/4)ln(x⁴-x²+2) + (√7/14)arctan[(2x²-1)/√7] + C
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∫(x^3-x^2+x+1)/(x^2+1) dx∫(x+4)/(x^2-x-2) dx ∫(3x^4+x^2)/(x^2+1)dx ∫x^3dx/(x^4-x^2+2) ∫x/(3+4x+x^2)^1/2dx ∫{√（x^4+x^-4+2)}/x^3dx ∫(x^11)/(x^8+3x^4+2)dx ∫[(x^2-x+6)/(x^3+3x)]dx ∫dx/x(2x+3)^2 ∫（x^2+1/x^4)dx ∫dx/根号(4x-x^2) ∫1/(x^4-x^2)dx ∫x/(4+9x^2)dx ∫(2^x+3^x)²dx ∫x^3/9+X^2 dx. ∫X^2 e^-X^3 dx. ∫（x-3x+2）dx ∫x^3/1+x^2 dx ∫(x-1)^2/x^3 dx