∫1/(2-(sin2x)²)dx
分子分母同除以(cos²2x),得
=∫sec²2x/(2sec²2x-tan²2x)dx
=1/2∫sec²2x/(2sec²2x-tan²2x)d(2x)
=1/2∫1/(2sec²2x-tan²2x)d(tan2x)
=1/2∫1/(2(1+tan²2x)-tan²2x)d(tan2x)
=1/2∫1/(2+tan²2x)d(tan2x)
=(1/2)*(1/√2)arctan((tan2x)/√2)+C
=(√2/4)arctan((tan2x)/√2)+C
代入上下限結(jié)果為：√2π/8