企源知识库

求定积分∫^π/2₀sinxcosx/(1+cos²x)
【正确答案】：∫^π/2₀[sinxcox/(1+cos²x)]dx=-∫^π/2₀[cosx/(1+cos²x)]dcosx=-(1/2)∫^π/2₀d(1+cos²x)/(1+cos²x)=-(1/2)ln(1+cos²x)∣^π/2₀=(1/2)ln2