dx\(1+cos^2x)从0到派\2的定积分

dx\(1+cos^2x)从0到派\2的定积分
dx\(1+cos^2x)从0到派\2的定积分

dx\(1+cos^2x)从0到派\2的定积分
∫(0→π/2) dx/(1 + cos^2x)
= ∫(0→π/2) dx/[(sin^2x + cos^2x) + cos^2x]
= ∫(0→π/2) dx/(sin^2x + 2cos^2x)
= ∫(0→π/2) dx/[cos^2x(2 + tan^2x)]
= ∫(0→π/2) d(tanx)/(2 + tan^2x)
= (1/√2)arctan[(tanx)/√2] |(0→π/2)
= (1/√2)(π/2 - 0)
= π/(2√2)

原函数1/2*tan(x)，定积分不收敛。