∫(1/(sinx+cosx))dx,積分區間為0到PAI/2,最好用萬能公式和sin(x+PAI/4)兩種方法

∫(1/(sinx+cosx))dx,積分區間為0到PAI/2,最好用萬能公式和sin(x+PAI/4)兩種方法

∫dx/(sinx+cosx)
=∫dx/[√2sin(x+π/4)]
=(-1/√2)∫dcos(x+π/4)/[(1-cos(x+π/4))(1+cos(x+π/4))]
=(-1/√2)ln1+cos(x+π/4)/sin(x+π/4 +C