How to integrate functions involving logrithm

Question

I have functions

   f= 1/8 E^(-I \[Phi]) (2 E^(
    I \[Phi]) (1 + x^2 + \[Lambda]^2 + 
      2 x \[Lambda] Cos[\[Theta]] Sin[t]^2) + 
   2 x \[Lambda] Cos[t] Sin[\[Theta]] + 
   2 E^(2 I \[Phi])
     x \[Lambda] Cos[
     t] Sin[\[Theta]] - \[Sqrt](E^(
      2 I \[Phi]) (-(x^4 - 
            2 x^2 (-1 + \[Lambda]^2) + (1 + \[Lambda]^2)^2) Sin[
          2 t]^2 + 
        4 (1 + x^2 + \[Lambda]^2 + 
           2 x \[Lambda] (Cos[\[Theta]] Sin[t]^2 + 
          Cos[t] Cos[\[Phi]] Sin[\[Theta]]))^2)))

and

 g=1/8 E^(-I \[Phi]) (2 E^(
    I \[Phi]) (1 + x^2 + \[Lambda]^2 + 
      2 x \[Lambda] Cos[\[Theta]] Sin[t]^2) + 
   2 x \[Lambda] Cos[t] Sin[\[Theta]] + 
   2 E^(2 I \[Phi])
     x \[Lambda] Cos[
     t] Sin[\[Theta]] + \[Sqrt](E^(
      2 I \[Phi]) (-(x^4 - 
            2 x^2 (-1 + \[Lambda]^2) + (1 + \[Lambda]^2)^2) Sin[
          2 t]^2 + 
        4 (1 + x^2 + \[Lambda]^2 + 
           2 x \[Lambda] (Cos[\[Theta]] Sin[t]^2 + 
              Cos[t] Cos[\[Phi]] Sin[\[Theta]]))^2)))

I tried to integrate $-fLog[2,f]-gLog[2,g]$, with respect to $\theta$ and $\phi$ such that $0 \le \theta \le \pi$ and $0 \le \phi \le 2 \pi$. However, it does not show the answer, rather it gives the expressions back with integral signs $\int_\theta \int_\phi$.

Kindly help to resolve the issue. Thanks.

Answer 1

Maybe this will get you started:

f[x_] := Sin[x];
Integrate[f[x] Log[2, f[x]], x]

If you want the definite integral:

Integrate[f[x] Log[2, f[x]], {x, 0, 2 Pi}]

I would suggest starting here and slowly making your function more complicated/realistic. At some point the integration may fail and then you will know where the problem lies.