可惜,楼上解繁了,也解错了.
利用待定系数法：
∫dx/(x²+1)x⁴
=∫[A/x + B/x² + C/x³ + D/x⁴+ (Ex + F)/(x² + 1)]dx
=∫[-1/x² + 1/x⁴+ 1/(x² + 1)]dx
= 1/x - 1/3x³ + arctanx + C
可惜,楼上解繁了,也解错了.
利用待定系数法：
∫dx/(x²+1)x⁴
=∫[A/x + B/x² + C/x³ + D/x⁴+ (Ex + F)/(x² + 1)]dx
=∫[-1/x² + 1/x⁴+ 1/(x² + 1)]dx
= 1/x - 1/3x³ + arctanx + C