Question

根号下(x^4+x^-4+2)/x^3，分子在根号下。请问这道题的不定积分怎么求呢？急

Answer 1

∫√[(x⁴+x⁻⁴+2)/x³]dx =∫√[(x²+x⁻²)²/x³]dx =∫[(x²+x⁻²)/x³]dx =∫(x⁻¹+x⁻⁵)dx =ln|x| -¼x⁻⁴ +C