∫[x^2/(1+4x^2)]dx

题目详情

∫[x^2/(1+4x^2)]dx

▼优质解答

答案和解析

∫ x²/(1+4x²) dx
=(1/4)∫ (4x²+1-1)/(1+4x²) dx
=(1/4)∫ 1 dx - (1/4)∫1/(1+4x²) dx
=(1/4)x - (1/8)∫1/[1+(2x)²] d(2x)
=(1/4)x - (1/8)arctan(2x) + C
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