1-2x方分之x方的积分
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∫x^2/(1-2x^2) dx
=∫[-1/2+(1/2)/(1-2x^2)]dx
=-1/2∫dx+1/2*∫1/(1-2x^2)dx
=-1/2*x+1/2*∫1/(1+√2x)(1-√2x)dx
=-1/2*x+1/4*∫[1/(1+√2x)+1/(1-√2x)]dx
=-1/2*x+1/4*[∫1/(1+√2x)dx-1/(√2x-1)dx]
=-1/2*x+√2/8*[∫1/(1+√2x)d(√2x)-1/(√2x-1)d(√2x)]
=-1/2*x+√2/8*[∫1/(1+√2x)d(1+√2x)-1/(√2x-1)d(√2x-1)]
=-1/2*x+√2/8*[ln(1+√2x)-ln(√2x-1)]+C
=∫[-1/2+(1/2)/(1-2x^2)]dx
=-1/2∫dx+1/2*∫1/(1-2x^2)dx
=-1/2*x+1/2*∫1/(1+√2x)(1-√2x)dx
=-1/2*x+1/4*∫[1/(1+√2x)+1/(1-√2x)]dx
=-1/2*x+1/4*[∫1/(1+√2x)dx-1/(√2x-1)dx]
=-1/2*x+√2/8*[∫1/(1+√2x)d(√2x)-1/(√2x-1)d(√2x)]
=-1/2*x+√2/8*[∫1/(1+√2x)d(1+√2x)-1/(√2x-1)d(√2x-1)]
=-1/2*x+√2/8*[ln(1+√2x)-ln(√2x-1)]+C
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