fX(x)=∫【-∞,+∞】f(x,y)dy
=∫【-∞,+∞】2/[π^2(1+x^2)(1+4y^2)]dy
=1/[π^2(1+x^2)]*∫【-∞,+∞】1/(1+4y^2)d(2y)
=1/[π^2(1+x^2)]*arctan2y|【-∞,+∞】
=1/[π^2(1+x^2)]*π
=1/[π(1+x^2)]
fY(y)=∫【-∞,+∞】f(x,y)dx
=∫【-∞,+∞】2/[π^2(1+x^2)(1+4y^2)]dx
=2/[π^2(1+4y^2)]*∫【-∞,+∞】1/(1+x^2)dx
=2/[π^2(1+4y^2)]*arctanx|【-∞,+∞】
=2/[π^2(1+4y^2)]*π
=2/[π(1+4y^2)]
解毕