∫xln⁡aax/23a5x/2b3x+ln⁡bbx2a2xb4xdx where a,b∈R+is equal to

I=∫xln⁡aax/23a5x/2b3x+ln⁡bbx2a2xb4xdx=∫ln⁡a2xb3x6a2xb3xdx  Let a2xb3x=t. Then tln⁡a2b3dx=dt. Therefore, I=∫16ln⁡a2b3ln⁡tt2dt=16ln⁡a2b3−ln⁡tt−∫−1t2dt=−16ln⁡a2b3ln⁡ett+k=−16ln⁡a2b3ln⁡a2xb3xea2xb3x+k