计算∫π/40[x/(1+cos2x)]dx.
【正确答案】：∫π/40[x/(1+cos2x)]dx=∫π/40
(x/cos2x)]dx=(1/2) ∫π/40xsec2 xdx
=(1/2)∫π/40xd(tan x)
=(1/2)(xtanx∣π04-∫π/4
0tan xdx)
=(1/2)(π/4+ln(cos x)∣π/40xd(tan x)
=π/8-(1/4)ln 2
计算∫π/40[x/(1+cos2x)]dx.
- 2024-11-07 09:12:45
- 高等数学（经管类）(13125)