bbbbaa01
幼苗
共回答了23个问题采纳率:87% 举报
∫ x³/(x⁴-x²+2) dx
=(1/2)∫ x²/(x⁴-x²+2) d(x²)
令x²=u
=(1/2)∫ u/(u²-u+2) du
=(1/2)∫ (u-1/2+1/2)/(u²-u+2) du
=(1/4)∫ (2u-1)/(u²-u+2) du + (1/4)∫ 1/(u²-u+2) du
=(1/4)∫ 1/(u²-u+2) d(u²-u) + (1/4)∫ 1/[(u-1/2)²+7/4] du
=(1/4)ln(u²-u+2) + (√7/14)arctan[2(u-1/2)/√7] + C
=(1/4)ln(x⁴-x²+2) + (√7/14)arctan[(2x²-1)/√7] + C
希望可以帮到你,如果解决了问题,请点下面的"选为满意回答"按钮.
1年前
3