∫ (3 + x)/(x² + 2x + 5) dx，注意d/dx (x² + 2x + 5) = 2x + 2
= ∫ [(1/2)(2x + 2) + 2]/(x² + 2x+ 5) dx
= (1/2)∫ (2x + 2)/(x² + 2x + 5) dx + 2∫ dx/(x² + 2x + 5)
= (1/2)∫ d(x² + 2x + 5)/(x² + 2x + 5) + 2∫ dx/[(x + 1)² + 4]，这里可换元x + 1 = 2tanz
= (1/2)ln|x² + 2x + 5| + 2(1/2)arctan[(x + 1)/2] + C
= (1/2)ln|x² + 2x + 5| + arctan[(x + 1)/2] + C
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024