lim(a趋于0)∫(a到a+1)dx/(1+x^2+a^2)
问题描述：
lim(a趋于0)∫(a到a+1)dx/(1+x^2+a^2)
答
=lim(a趋于0) (1/(1+a^2))·∫(a到a+1) dx/(1+(x/√(1+a^2))²)=lim(a趋于0) (1/√(1+a^2))·∫(a到a+1) d(x/√(1+a^2)) /(1+(x/√(1+a^2))²)=lim(a趋于0) (1/√(1+a^2))·arctan(x/√(1+a^2)) |(a到a+1) =...