求x^2/(x^6+x^3+1)的不定积分

题目详情

▼优质解答

答案和解析

∫x^2/(x^6+x^3+1)dx
=(1/3)∫1/(x^3+1/2)^2+3/4)dx^3
=(1/3)(2/√3)arctan((x^3+1/2)/(√3/2))+C
=(2/(3√3))arctan((2x^3+1)/(√3))+C

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