------------------------------ if the input is: RAint(6^(2*n)*x^n*(1-x)^n/(1+6*x)^(n+1),x,n,N,0,1,log(6+1),10); the output is [-36*n-36+(16*n+24)*N+(-n-2)*N^2, -36*n/(n+1)+N, [1, 1, 1, 1], [8+2*7^(1/2), 13\ .29150262], 36, [2*(ln(8+2*7^(1/2))-ln(6))/(ln(8+2*7^(1/2))+1), .4434556792], [ 2*(ln(8+2*7^(1/2))-ln(6))/(ln(8+2*7^(1/2))-2*ln(6)-1), -.796802092]] -------------------- ------------------------------ if the input is: RAint(2^(3*n)*x^(2*n)*(1-x)^(2*n)/(x^2+1)^(2*n+1),x,n,N,0,1,Pi,10); the output is [-4*(n+1)*(2*n+1)*(4*n+7)+4*(4*n+5)*(6*n^2+15*n+8)*N-(4*n+3)*(2*n+3)*(n+2)*N^2, -4*n*(4*n+3)*(2*n-1)/(4*n-1)/(2*n+1)/(n+1)+N, [2, 1, 1, 1], [6+4*2^(1/2), 11.65\ 685425], 4, [2*(ln(6+4*2^(1/2))-ln(2))/(ln(6+4*2^(1/2))+2), .7911979207], [2*( ln(6+4*2^(1/2))-ln(2))/(ln(6+4*2^(1/2))-2*ln(2)-2), -3.789224338]] -------------------- ------------------------------ if the input is: RAint(ArcT(5,n,x),x,n,N,0,1,arctan(1/5),10); the output is [-4*(n+1)*(2*n+1)*(4*n+7)+4*(4*n+5)*(102*n^2+255*n+134)*N-(4*n+3)*(2*n+3)*(n+2) *N^2, -4*n*(4*n+3)*(2*n-1)/(4*n-1)/(2*n+1)/(n+1)+N, [2, 1, 1, 1], [102+20*26^(1 /2), 203.9803903], 4, [2*(ln(102+20*26^(1/2))-ln(2))/(ln(102+20*26^(1/2))+2), 1\ .263968735], [2*(ln(102+20*26^(1/2))-ln(2))/(ln(102+20*26^(1/2))-2*ln(2)-2), 4.\ 788327432]] -------------------- the whole thing took, 1.966, seconds.