Evaluate: `int_(-pi//4)^(pi//4)log(sinx+cosx)dx`

Explanation

Let `I=int_(-pi//4)^(pi//4)log{sqrt(2)sin(x+(pi)/4)}dx`
Putting `x+(pi)/4=theta, dx=d theta`, we get
`I=int_(0)^(pi//2)log(sqrt(2)sin theta)d theta`
`=1/2int_(0)^(pi//2)log 2 d theta +int_(0)^(pi//2) log sin theta d theta`
`=(1/4 pi log 2)-1/2 pi log 2`
`-1/4 pi log 2`