令x=(1/2)tgy,则4x^2+1 = (tgy)^2 +1 = (secy)^2 取y属于(0, arctg3),则secy >0 所以原来积分等于 = secy d(1/2) tgy = 0.5 secy (secy)^2 dy = 0.5 cosy/(cosy)^4 dy = 0.5 /(1-sin^2y)^2 d siny 然后积分就简单了
=x*(-e^(-y/2))=x(1-e^(-x²/2))
像傅叶级数吧