∫[0,π/2]ln(cosx)dx
=xln(cosx)[0,π/2]-∫[0,π/2]xdln(cosx)
=-∫[0,π/2]xdln(cosx)
=∫[0,π/2]xsinx/cosxdx
=∫[0,π/2]xtanxdx
不过这个积分值等于∞