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∫dx/(1+x^4) = (1/2)∫[(x^2+1)-(x^2-1)]dx/(x^4+1)
= (1/2) [∫(1+1/x^2)dx/(x^2+1/x^2) - ∫(1-1/x^2)dx/(x^2+1/x^2)]
= (1/2) {∫d(x-1/x)/[x-1/x)^2+2] - ∫d(x+1/x)/[x+1/x)^2-2]}
= (√2/4)arctan[(x^2-1)/(√2x)] - (√2/8)ln|(x^2+1-√2x)/(x^2+1+√2x)| + C
= (1/2) [∫(1+1/x^2)dx/(x^2+1/x^2) - ∫(1-1/x^2)dx/(x^2+1/x^2)]
= (1/2) {∫d(x-1/x)/[x-1/x)^2+2] - ∫d(x+1/x)/[x+1/x)^2-2]}
= (√2/4)arctan[(x^2-1)/(√2x)] - (√2/8)ln|(x^2+1-√2x)/(x^2+1+√2x)| + C
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