maxima:
(%i1) 4*%pi^2*f^2*fn^4*(fn^2+9*f^2)/(fn^2+f^2)^3;
(%o1) (4*%pi^2*f^2*fn^4*(fn^2+9*f^2))/(fn^2+f^2)^3
(%i2) integrate(%, f, minf, inf);
Is fn positive, negative, or zero? positive;
(%o2) 14*%pi^3*fn^3
sympy:
fn=Symbol('fn', positive=True)
4*pi**2*f**2*fn**4*(fn**2+9*f**2)/(fn**2+f**2)**3
Out[27]: 4*pi**2*f**2*fn**4*(fn**2 + 9*f**2)/(f**2 + fn**2)**3
In [28]: integrate(_,(f,-oo,oo))
Out[28]: 0
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