∫ pxp+2q-1-qxq-1x2p+2q+2xp+q+1dx=

∫pxp+2q−1−qxq−1xp+q+12dx​Dividing numerator and denominator by x2q=​∫pxp−1−qx−q−1xp+x−q2dx​put  xp+x−q =t⇒​pxp−1−qx−q−1dx=dt=​∫dtt2​=−1t+c​=−1xp+x−q+c​=−xqxp+q+1+c