∫1/1+(cos^2x)dx=∫(sin^2x+cos^2x)/(sin^2x+cos^2x+cos^2x)dx=∫(sin^2x+cos^2x)/(sin^2x+2cos^2x)dx (被积函数上下同除以cos^2x)=∫(tan^2x+1)/(tan^2x+2)dx =∫(sec^2x)/(tan^2x+2)dx = ∫1/(tan^2x+2)dtanx =1/...