∫(x+1)/(x^2+x+1)dx怎么算急急急啊帮忙咯在线等谢咯

Question

∫(x+1)/(x^2+x+1)dx 怎么算 急急急啊 帮忙咯 在线等 谢咯

Answer 1

∫ (x + 1)/(x² + x + 1) dx
= (1/2)∫ (2x + 2)/(x² + x + 1) dx
= (1/2)∫ (2x + 1)/(x² + x + 1) dx + (1/2)∫ dx/(x² + x + 1)
= (1/2)∫ d(x² + x + 1)/(x² + x + 1) + (1/2)∫ dx/[(x + 1/2)² + (√3/2)²]
= (1/2)ln(x² + x + 1) + (1/2) • (2/√3)arctan[(x + 1/2)/(√3/2)] + C
= (1/2)ln(x² + x + 1) + (1/√3)arctan[(2x + 1)/√3] + C