∫xdx/(1-2x-x^2)RT

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∫xdx/(1-2x-x^2)
RT

有理函数积分
∫xdx/(1-2x-x^2)
=∫xdx/[2-（x+1）^2]
=(1/2)∫(2x+2-2)dx/(1-2x-x^2)
=-(1/2)∫d(1-2x-x^2)/(1-2x-x^2)-∫dx/[2-（x+1）^2]
=-(1/2)ln│1-2x-x^2│+∫d（x+1)/[（x+1）^2-2]
=-(1/2)ln│1-2x-x^2│+√2/4ln│（x+1-√2)/（x+1+√2）│+C

∫xdx/(1-2x-x^2)RT ∫((x^2-1)^(1/2))/xdx, ∫xdx/(√(1+x^(2/3))) ∫ (x^2+1)e^xdx ∫xe^-xdx/(1-x)^2 ∫(x^2+1)e^xdx ∫ln（1+x^2）*xdx ∫(1-x)^2/xdx=? ∫e^xdx/[e^(2x)-1] ∫x^2/e^xdx ∫ e^(-x^2)xdx ∫e^x^2*xdx ∫x/sin^2xdx ∫x^2e^xdx ∫(x^2+x-2)e^xdx ∫(x+2)(x-3)/xdx ∫(1,2)(x∧2-2x-3)/xdx ∫(1-1/x^2)√x^3√xdx