Is the 1/(2π) really only multiplying the first integral?
Note that 'π' is pi. It may or may not look much like it on your machine. On mine, it's really easy to mistake it for 'n'.
If so, I get that the answer given should be multiplied by (4 + 1/π). If it is multiplying both integrals, then I get that it should be multiplied by (2/π). But I did the integrals really quickly, so I could have a mistake somewhere.