Im,n=∫10xm(logx)ndx, then Im,n is equal to
nn+1Im,n−1
-mn+1Im,n−1
-nm+1Im,n−1
mn+1Im,n−1
Im,n=∫10xm(logx)ndx=∣∣(logx)n.xm+1m+1∣∣10−∫10n(logx)n−1.1x.xm+1m+1dx=0−nm+1∫10xm(logx)n−1dx=−nm+1Im,n−1