∫cos2=12𝑥+14sin(2𝑥)+𝐶 验证 ′=12+12cos(2𝑥)=12(1+𝑐2−𝑠2)=𝑐2 ∫𝑒−𝑥2=√𝜋∫𝑒−𝑥2𝑥2=√𝜋2 ref: https://math.stackexchange.com/questions/66084/integral-int-infty-infty-x2-e-x2-mathrm-dx