∫xdx/(1-2x-x^2)RT
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![∫xdx/(1-2x-x^2)RT](/uploads/image/z/5909168-56-8.jpg?t=%E2%88%ABxdx%2F%281-2x-x%5E2%29RT)
∫xdx/(1-2x-x^2)RT
∫xdx/(1-2x-x^2)
RT
∫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