f[x_]  :=  
      2 Pi h c^2 ( 
          x^-5 /(Exp[h c /(k T x)]  - 1))

Integrate[f[x], {x, 0, Infinity}]

2 c^2 h Pi k^4 Pi^4 /(15 c^4 h^4)  * T^4

h = 6.626176 10^-34

k = 1.380662 10^-23

c = 2.997925 10^8

N[%3, 8]

T  =  360 ;
g0  =  Plot[f[x], {x, 0, 0.0001} ];
T  =  320 ;
g1  =  Plot[f[x], {x, 0, 0.0001}];
T  =  280 ;
g2  =  Plot[f[x], {x, 0, 0.0001}];
T  =  240 ;
g3  =  Plot[f[x], {x, 0, 0.0001}];
T  =  200 ;
g4  =  
        Plot[f[x], {x, 0, 
            0.0001}];

g  =  Show[g1, g2, g3, g4]