If polynomials P and Q satisfies∫((3x−1)cos⁡x+(1−2x)sin⁡x)dx=Pcos⁡x+Qsin⁡x (ignoring the constant of integration) then

Integrating by parts, the given integral is equal to(3x−1)sin⁡x−3∫sin⁡xdx−(1−2x)cos⁡x−2∫cos⁡xdx=(3x−1)sin⁡x+3cos⁡x−(1−2x)cos⁡x−2sin⁡x=(3x−3)sin⁡x+(2+2x)cos⁡xHence Q=3(x−1) and P=2(1+x)