(1加x的和)乘以[1+(x的平方)]的和分之d(x)的积分?
问题描述：
(1加x的和)乘以[1+(x的平方)]的和分之d(x)的积分?
答
∫dx/[(1+x)(1+x^2)] = (1/2)∫[1/(1+x)+(1-x)/(1+x^2)]dx
= (1/2) [∫dx/(1+x) -∫xdx/(1+x^2)+∫dx/(1+x^2)dx ]
= (1/2) [ln|1+x|-(1/2)ln(1+x^2)+arctanx]+C
= (1/4)ln[(1+x)^2/(1+x^2)]+(1/2)arctanx+C