∫pxp+2q−1−qxq−1x2p+2q+2xp+q+1dx is equal to

∫pxp+2q−1−qxq−1xp+q+12dx (Dividing Nr and Dr by x2q ) =∫pxp−1−qx−q−1xp+x−q2dxt=xp+x−q,   dt= pxp-1-qx-q-1dx=∫dtt2=1t+C =−1xp+x−q+C=−xqxp+q+1+C