不定积分(x^2/x^4-1)dx
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∫ x²/(x⁴ - 1) dx
= (1/2)∫ 2x²/[(x² - 1)(x² + 1)] dx
= (1/2)∫ [(x² - 1) + (x² + 1)]/[(x² - 1)(x² + 1)] dx
= (1/2)∫ dx/(x² + 1) + (1/2)∫ dx/(x² - 1)
= (1/2)arctan(x) + (1/4)ln|(x - 1)/(x + 1)| + C
= (1/2)∫ 2x²/[(x² - 1)(x² + 1)] dx
= (1/2)∫ [(x² - 1) + (x² + 1)]/[(x² - 1)(x² + 1)] dx
= (1/2)∫ dx/(x² + 1) + (1/2)∫ dx/(x² - 1)
= (1/2)arctan(x) + (1/4)ln|(x - 1)/(x + 1)| + C
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