arctanx²/2的导数

∫ x/(4 + x²) dx = (1/2)∫ 1/(4 + x²) d(x² + 4) = (1/2)ln(x² + 4) + C

∫ x/(4 + x⁴) dx = (1/2)∫ 1/(4 + x⁴) d(x²) = (1/2)∫ 1/[4 + (x²)²] d(x²) = (1/2)(1/2)arctan(x²/2) = (1/4)arctan(x²/2) + C 或用第一个结果： [arctan(x²/2)]' = 4x/(4 + x⁴) ==> arctan(x²/2) = ∫ 4x/(4 + x⁴) dx ==> (1/4)arctan(x²/2) = ∫ x/(4 + x⁴) dx ==> ∫ x/(4 + x⁴) dx = (1/4)arctan(x²/2) + C