∫3sin⁡x+2cos⁡x3cos⁡x+2sin⁡xdx is equal to

Let I=∫3sin⁡x+2cos⁡x3cos⁡x+2sin⁡xdx3sin⁡x+2cos⁡x=Addx(3cos⁡x+2sin⁡x)+B(3cos⁡x+2sin⁡x)⇒3sin⁡x+2cos⁡x=A(−3sin⁡x+2cos⁡x)+B(3cos⁡x+2sin⁡x)On comparing the coefficients of sin x and cos x of both sides, we get−3A+2B=3 and 2A+3B=2⇒  B=1213 and A=−513∴ I=∫B(−3sin⁡x+2cos⁡x)+A(3cos⁡x+2sin⁡x)3cos⁡x+2sin⁡xdx⇒ I=A∫1dx+B∫−3sin⁡x+2cos⁡x3cos⁡x+2sin⁡xdx=Ax+B∫dtt, where t=3cos⁡x+2sin⁡x=Ax+Bln⁡|t|+C=−513x+1213ln⁡|3cos⁡x+2sin⁡x|+C