∫(x2+1)/(x4+1)dx

题目详情

∫(x2+1)/(x4+1)dx

▼优质解答

答案和解析

∫(x2+1)/(x4+1)dx=∫(1+1/x2)/(x2+1/x2)dx=∫1/[(x-(1/x))^2+2]d(x-(1/x))=[(√2)/2]arctan{[x-(1/x)]/√2}+C

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