smallpig888
幼苗
共回答了16个问题采纳率:100% 举报
∫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/√2*arctan(tanx/√2)+C
1年前
11