1,1,1089,210,5.644363,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^3*(c + d*x^n),x)","\frac{A\,a^3\,c\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{b^2\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+3\,B\,a\,d+B\,b\,c\right)\,\left(m^4+11\,m^3\,n+4\,m^3+41\,m^2\,n^2+33\,m^2\,n+6\,m^2+61\,m\,n^3+82\,m\,n^2+33\,m\,n+4\,m+30\,n^4+61\,n^3+41\,n^2+11\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{a\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(3\,A\,b^2\,c+B\,a^2\,d+3\,A\,a\,b\,d+3\,B\,a\,b\,c\right)\,\left(m^4+13\,m^3\,n+4\,m^3+59\,m^2\,n^2+39\,m^2\,n+6\,m^2+107\,m\,n^3+118\,m\,n^2+39\,m\,n+4\,m+60\,n^4+107\,n^3+59\,n^2+13\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{b\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(A\,b^2\,c+3\,B\,a^2\,d+3\,A\,a\,b\,d+3\,B\,a\,b\,c\right)\,\left(m^4+12\,m^3\,n+4\,m^3+49\,m^2\,n^2+36\,m^2\,n+6\,m^2+78\,m\,n^3+98\,m\,n^2+36\,m\,n+4\,m+40\,n^4+78\,n^3+49\,n^2+12\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{a^2\,x\,x^n\,{\left(e\,x\right)}^m\,\left(A\,a\,d+3\,A\,b\,c+B\,a\,c\right)\,\left(m^4+14\,m^3\,n+4\,m^3+71\,m^2\,n^2+42\,m^2\,n+6\,m^2+154\,m\,n^3+142\,m\,n^2+42\,m\,n+4\,m+120\,n^4+154\,n^3+71\,n^2+14\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{B\,b^3\,d\,x\,x^{5\,n}\,{\left(e\,x\right)}^m\,\left(m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}","Not used",1,"(A*a^3*c*x*(e*x)^m)/(m + 1) + (b^2*x*x^(4*n)*(e*x)^m*(A*b*d + 3*B*a*d + B*b*c)*(4*m + 11*n + 33*m*n + 82*m*n^2 + 33*m^2*n + 61*m*n^3 + 11*m^3*n + 6*m^2 + 4*m^3 + m^4 + 41*n^2 + 61*n^3 + 30*n^4 + 41*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (a*x*x^(2*n)*(e*x)^m*(3*A*b^2*c + B*a^2*d + 3*A*a*b*d + 3*B*a*b*c)*(4*m + 13*n + 39*m*n + 118*m*n^2 + 39*m^2*n + 107*m*n^3 + 13*m^3*n + 6*m^2 + 4*m^3 + m^4 + 59*n^2 + 107*n^3 + 60*n^4 + 59*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (b*x*x^(3*n)*(e*x)^m*(A*b^2*c + 3*B*a^2*d + 3*A*a*b*d + 3*B*a*b*c)*(4*m + 12*n + 36*m*n + 98*m*n^2 + 36*m^2*n + 78*m*n^3 + 12*m^3*n + 6*m^2 + 4*m^3 + m^4 + 49*n^2 + 78*n^3 + 40*n^4 + 49*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (a^2*x*x^n*(e*x)^m*(A*a*d + 3*A*b*c + B*a*c)*(4*m + 14*n + 42*m*n + 142*m*n^2 + 42*m^2*n + 154*m*n^3 + 14*m^3*n + 6*m^2 + 4*m^3 + m^4 + 71*n^2 + 154*n^3 + 120*n^4 + 71*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (B*b^3*d*x*x^(5*n)*(e*x)^m*(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1)","B"
2,1,588,160,5.230942,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^2*(c + d*x^n),x)","\frac{x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(A\,b^2\,c+B\,a^2\,d+2\,A\,a\,b\,d+2\,B\,a\,b\,c\right)\,\left(m^3+8\,m^2\,n+3\,m^2+19\,m\,n^2+16\,m\,n+3\,m+12\,n^3+19\,n^2+8\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{A\,a^2\,c\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{a\,x\,x^n\,{\left(e\,x\right)}^m\,\left(A\,a\,d+2\,A\,b\,c+B\,a\,c\right)\,\left(m^3+9\,m^2\,n+3\,m^2+26\,m\,n^2+18\,m\,n+3\,m+24\,n^3+26\,n^2+9\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{b\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+2\,B\,a\,d+B\,b\,c\right)\,\left(m^3+7\,m^2\,n+3\,m^2+14\,m\,n^2+14\,m\,n+3\,m+8\,n^3+14\,n^2+7\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{B\,b^2\,d\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}","Not used",1,"(x*x^(2*n)*(e*x)^m*(A*b^2*c + B*a^2*d + 2*A*a*b*d + 2*B*a*b*c)*(3*m + 8*n + 16*m*n + 19*m*n^2 + 8*m^2*n + 3*m^2 + m^3 + 19*n^2 + 12*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (A*a^2*c*x*(e*x)^m)/(m + 1) + (a*x*x^n*(e*x)^m*(A*a*d + 2*A*b*c + B*a*c)*(3*m + 9*n + 18*m*n + 26*m*n^2 + 9*m^2*n + 3*m^2 + m^3 + 26*n^2 + 24*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (b*x*x^(3*n)*(e*x)^m*(A*b*d + 2*B*a*d + B*b*c)*(3*m + 7*n + 14*m*n + 14*m*n^2 + 7*m^2*n + 3*m^2 + m^3 + 14*n^2 + 8*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (B*b^2*d*x*x^(4*n)*(e*x)^m*(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1)","B"
3,1,271,108,4.957754,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)*(c + d*x^n),x)","\frac{A\,a\,c\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+B\,a\,d+B\,b\,c\right)\,\left(m^2+4\,m\,n+2\,m+3\,n^2+4\,n+1\right)}{m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1}+\frac{x\,x^n\,{\left(e\,x\right)}^m\,\left(A\,a\,d+A\,b\,c+B\,a\,c\right)\,\left(m^2+5\,m\,n+2\,m+6\,n^2+5\,n+1\right)}{m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1}+\frac{B\,b\,d\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(m^2+3\,m\,n+2\,m+2\,n^2+3\,n+1\right)}{m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1}","Not used",1,"(A*a*c*x*(e*x)^m)/(m + 1) + (x*x^(2*n)*(e*x)^m*(A*b*d + B*a*d + B*b*c)*(2*m + 4*n + 4*m*n + m^2 + 3*n^2 + 1))/(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1) + (x*x^n*(e*x)^m*(A*a*d + A*b*c + B*a*c)*(2*m + 5*n + 5*m*n + m^2 + 6*n^2 + 1))/(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1) + (B*b*d*x*x^(3*n)*(e*x)^m*(2*m + 3*n + 3*m*n + m^2 + 2*n^2 + 1))/(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1)","B"
4,1,91,66,4.830001,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(c + d*x^n),x)","{\left(e\,x\right)}^m\,\left(\frac{A\,c\,x}{m+1}+\frac{x\,x^n\,\left(A\,d+B\,c\right)\,\left(m+2\,n+1\right)}{m^2+3\,m\,n+2\,m+2\,n^2+3\,n+1}+\frac{B\,d\,x\,x^{2\,n}\,\left(m+n+1\right)}{m^2+3\,m\,n+2\,m+2\,n^2+3\,n+1}\right)","Not used",1,"(e*x)^m*((A*c*x)/(m + 1) + (x*x^n*(A*d + B*c)*(m + 2*n + 1))/(2*m + 3*n + 3*m*n + m^2 + 2*n^2 + 1) + (B*d*x*x^(2*n)*(m + n + 1))/(2*m + 3*n + 3*m*n + m^2 + 2*n^2 + 1))","B"
5,0,-1,120,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,\left(c+d\,x^n\right)}{a+b\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n), x)","F"
6,0,-1,177,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,\left(c+d\,x^n\right)}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n)^2, x)","F"
7,0,-1,228,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n)^3,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,\left(c+d\,x^n\right)}{{\left(a+b\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n))/(a + b*x^n)^3, x)","F"
8,1,1882,318,6.347546,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^3*(c + d*x^n)^2,x)","\frac{x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(B\,a^3\,d^2+6\,B\,a^2\,b\,c\,d+3\,A\,a^2\,b\,d^2+3\,B\,a\,b^2\,c^2+6\,A\,a\,b^2\,c\,d+A\,b^3\,c^2\right)\,\left(m^5+18\,m^4\,n+5\,m^4+121\,m^3\,n^2+72\,m^3\,n+10\,m^3+372\,m^2\,n^3+363\,m^2\,n^2+108\,m^2\,n+10\,m^2+508\,m\,n^4+744\,m\,n^3+363\,m\,n^2+72\,m\,n+5\,m+240\,n^5+508\,n^4+372\,n^3+121\,n^2+18\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{A\,a^3\,c^2\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{a\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(2\,B\,a^2\,c\,d+A\,a^2\,d^2+3\,B\,a\,b\,c^2+6\,A\,a\,b\,c\,d+3\,A\,b^2\,c^2\right)\,\left(m^5+19\,m^4\,n+5\,m^4+137\,m^3\,n^2+76\,m^3\,n+10\,m^3+461\,m^2\,n^3+411\,m^2\,n^2+114\,m^2\,n+10\,m^2+702\,m\,n^4+922\,m\,n^3+411\,m\,n^2+76\,m\,n+5\,m+360\,n^5+702\,n^4+461\,n^3+137\,n^2+19\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{b\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(3\,B\,a^2\,d^2+6\,B\,a\,b\,c\,d+3\,A\,a\,b\,d^2+B\,b^2\,c^2+2\,A\,b^2\,c\,d\right)\,\left(m^5+17\,m^4\,n+5\,m^4+107\,m^3\,n^2+68\,m^3\,n+10\,m^3+307\,m^2\,n^3+321\,m^2\,n^2+102\,m^2\,n+10\,m^2+396\,m\,n^4+614\,m\,n^3+321\,m\,n^2+68\,m\,n+5\,m+180\,n^5+396\,n^4+307\,n^3+107\,n^2+17\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{a^2\,c\,x\,x^n\,{\left(e\,x\right)}^m\,\left(2\,A\,a\,d+3\,A\,b\,c+B\,a\,c\right)\,\left(m^5+20\,m^4\,n+5\,m^4+155\,m^3\,n^2+80\,m^3\,n+10\,m^3+580\,m^2\,n^3+465\,m^2\,n^2+120\,m^2\,n+10\,m^2+1044\,m\,n^4+1160\,m\,n^3+465\,m\,n^2+80\,m\,n+5\,m+720\,n^5+1044\,n^4+580\,n^3+155\,n^2+20\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{b^2\,d\,x\,x^{5\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+3\,B\,a\,d+2\,B\,b\,c\right)\,\left(m^5+16\,m^4\,n+5\,m^4+95\,m^3\,n^2+64\,m^3\,n+10\,m^3+260\,m^2\,n^3+285\,m^2\,n^2+96\,m^2\,n+10\,m^2+324\,m\,n^4+520\,m\,n^3+285\,m\,n^2+64\,m\,n+5\,m+144\,n^5+324\,n^4+260\,n^3+95\,n^2+16\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{B\,b^3\,d^2\,x\,x^{6\,n}\,{\left(e\,x\right)}^m\,\left(m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}","Not used",1,"(x*x^(3*n)*(e*x)^m*(A*b^3*c^2 + B*a^3*d^2 + 3*A*a^2*b*d^2 + 3*B*a*b^2*c^2 + 6*A*a*b^2*c*d + 6*B*a^2*b*c*d)*(5*m + 18*n + 72*m*n + 363*m*n^2 + 108*m^2*n + 744*m*n^3 + 72*m^3*n + 508*m*n^4 + 18*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 121*n^2 + 372*n^3 + 508*n^4 + 240*n^5 + 363*m^2*n^2 + 372*m^2*n^3 + 121*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (A*a^3*c^2*x*(e*x)^m)/(m + 1) + (a*x*x^(2*n)*(e*x)^m*(A*a^2*d^2 + 3*A*b^2*c^2 + 3*B*a*b*c^2 + 2*B*a^2*c*d + 6*A*a*b*c*d)*(5*m + 19*n + 76*m*n + 411*m*n^2 + 114*m^2*n + 922*m*n^3 + 76*m^3*n + 702*m*n^4 + 19*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 137*n^2 + 461*n^3 + 702*n^4 + 360*n^5 + 411*m^2*n^2 + 461*m^2*n^3 + 137*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (b*x*x^(4*n)*(e*x)^m*(3*B*a^2*d^2 + B*b^2*c^2 + 3*A*a*b*d^2 + 2*A*b^2*c*d + 6*B*a*b*c*d)*(5*m + 17*n + 68*m*n + 321*m*n^2 + 102*m^2*n + 614*m*n^3 + 68*m^3*n + 396*m*n^4 + 17*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 107*n^2 + 307*n^3 + 396*n^4 + 180*n^5 + 321*m^2*n^2 + 307*m^2*n^3 + 107*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (a^2*c*x*x^n*(e*x)^m*(2*A*a*d + 3*A*b*c + B*a*c)*(5*m + 20*n + 80*m*n + 465*m*n^2 + 120*m^2*n + 1160*m*n^3 + 80*m^3*n + 1044*m*n^4 + 20*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 155*n^2 + 580*n^3 + 1044*n^4 + 720*n^5 + 465*m^2*n^2 + 580*m^2*n^3 + 155*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (b^2*d*x*x^(5*n)*(e*x)^m*(A*b*d + 3*B*a*d + 2*B*b*c)*(5*m + 16*n + 64*m*n + 285*m*n^2 + 96*m^2*n + 520*m*n^3 + 64*m^3*n + 324*m*n^4 + 16*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 95*n^2 + 260*n^3 + 324*n^4 + 144*n^5 + 285*m^2*n^2 + 260*m^2*n^3 + 95*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (B*b^3*d^2*x*x^(6*n)*(e*x)^m*(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1)","B"
9,1,1119,237,5.591072,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^2*(c + d*x^n)^2,x)","\frac{x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(2\,B\,a^2\,c\,d+A\,a^2\,d^2+2\,B\,a\,b\,c^2+4\,A\,a\,b\,c\,d+A\,b^2\,c^2\right)\,\left(m^4+13\,m^3\,n+4\,m^3+59\,m^2\,n^2+39\,m^2\,n+6\,m^2+107\,m\,n^3+118\,m\,n^2+39\,m\,n+4\,m+60\,n^4+107\,n^3+59\,n^2+13\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(B\,a^2\,d^2+4\,B\,a\,b\,c\,d+2\,A\,a\,b\,d^2+B\,b^2\,c^2+2\,A\,b^2\,c\,d\right)\,\left(m^4+12\,m^3\,n+4\,m^3+49\,m^2\,n^2+36\,m^2\,n+6\,m^2+78\,m\,n^3+98\,m\,n^2+36\,m\,n+4\,m+40\,n^4+78\,n^3+49\,n^2+12\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{A\,a^2\,c^2\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{b\,d\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+2\,B\,a\,d+2\,B\,b\,c\right)\,\left(m^4+11\,m^3\,n+4\,m^3+41\,m^2\,n^2+33\,m^2\,n+6\,m^2+61\,m\,n^3+82\,m\,n^2+33\,m\,n+4\,m+30\,n^4+61\,n^3+41\,n^2+11\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{B\,b^2\,d^2\,x\,x^{5\,n}\,{\left(e\,x\right)}^m\,\left(m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{a\,c\,x\,x^n\,{\left(e\,x\right)}^m\,\left(2\,A\,a\,d+2\,A\,b\,c+B\,a\,c\right)\,\left(m^4+14\,m^3\,n+4\,m^3+71\,m^2\,n^2+42\,m^2\,n+6\,m^2+154\,m\,n^3+142\,m\,n^2+42\,m\,n+4\,m+120\,n^4+154\,n^3+71\,n^2+14\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}","Not used",1,"(x*x^(2*n)*(e*x)^m*(A*a^2*d^2 + A*b^2*c^2 + 2*B*a*b*c^2 + 2*B*a^2*c*d + 4*A*a*b*c*d)*(4*m + 13*n + 39*m*n + 118*m*n^2 + 39*m^2*n + 107*m*n^3 + 13*m^3*n + 6*m^2 + 4*m^3 + m^4 + 59*n^2 + 107*n^3 + 60*n^4 + 59*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (x*x^(3*n)*(e*x)^m*(B*a^2*d^2 + B*b^2*c^2 + 2*A*a*b*d^2 + 2*A*b^2*c*d + 4*B*a*b*c*d)*(4*m + 12*n + 36*m*n + 98*m*n^2 + 36*m^2*n + 78*m*n^3 + 12*m^3*n + 6*m^2 + 4*m^3 + m^4 + 49*n^2 + 78*n^3 + 40*n^4 + 49*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (A*a^2*c^2*x*(e*x)^m)/(m + 1) + (b*d*x*x^(4*n)*(e*x)^m*(A*b*d + 2*B*a*d + 2*B*b*c)*(4*m + 11*n + 33*m*n + 82*m*n^2 + 33*m^2*n + 61*m*n^3 + 11*m^3*n + 6*m^2 + 4*m^3 + m^4 + 41*n^2 + 61*n^3 + 30*n^4 + 41*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (B*b^2*d^2*x*x^(5*n)*(e*x)^m*(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (a*c*x*x^n*(e*x)^m*(2*A*a*d + 2*A*b*c + B*a*c)*(4*m + 14*n + 42*m*n + 142*m*n^2 + 42*m^2*n + 154*m*n^3 + 14*m^3*n + 6*m^2 + 4*m^3 + m^4 + 71*n^2 + 154*n^3 + 120*n^4 + 71*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1)","B"
10,1,588,160,5.195844,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)*(c + d*x^n)^2,x)","\frac{x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(A\,a\,d^2+B\,b\,c^2+2\,A\,b\,c\,d+2\,B\,a\,c\,d\right)\,\left(m^3+8\,m^2\,n+3\,m^2+19\,m\,n^2+16\,m\,n+3\,m+12\,n^3+19\,n^2+8\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{A\,a\,c^2\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{c\,x\,x^n\,{\left(e\,x\right)}^m\,\left(2\,A\,a\,d+A\,b\,c+B\,a\,c\right)\,\left(m^3+9\,m^2\,n+3\,m^2+26\,m\,n^2+18\,m\,n+3\,m+24\,n^3+26\,n^2+9\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{d\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+B\,a\,d+2\,B\,b\,c\right)\,\left(m^3+7\,m^2\,n+3\,m^2+14\,m\,n^2+14\,m\,n+3\,m+8\,n^3+14\,n^2+7\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{B\,b\,d^2\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}","Not used",1,"(x*x^(2*n)*(e*x)^m*(A*a*d^2 + B*b*c^2 + 2*A*b*c*d + 2*B*a*c*d)*(3*m + 8*n + 16*m*n + 19*m*n^2 + 8*m^2*n + 3*m^2 + m^3 + 19*n^2 + 12*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (A*a*c^2*x*(e*x)^m)/(m + 1) + (c*x*x^n*(e*x)^m*(2*A*a*d + A*b*c + B*a*c)*(3*m + 9*n + 18*m*n + 26*m*n^2 + 9*m^2*n + 3*m^2 + m^3 + 26*n^2 + 24*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (d*x*x^(3*n)*(e*x)^m*(A*b*d + B*a*d + 2*B*b*c)*(3*m + 7*n + 14*m*n + 14*m*n^2 + 7*m^2*n + 3*m^2 + m^3 + 14*n^2 + 8*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (B*b*d^2*x*x^(4*n)*(e*x)^m*(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1)","B"
11,1,265,102,5.112921,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(c + d*x^n)^2,x)","\frac{A\,c^2\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{c\,x\,x^n\,{\left(e\,x\right)}^m\,\left(2\,A\,d+B\,c\right)\,\left(m^2+5\,m\,n+2\,m+6\,n^2+5\,n+1\right)}{m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1}+\frac{d\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(A\,d+2\,B\,c\right)\,\left(m^2+4\,m\,n+2\,m+3\,n^2+4\,n+1\right)}{m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1}+\frac{B\,d^2\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(m^2+3\,m\,n+2\,m+2\,n^2+3\,n+1\right)}{m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1}","Not used",1,"(A*c^2*x*(e*x)^m)/(m + 1) + (c*x*x^n*(e*x)^m*(2*A*d + B*c)*(2*m + 5*n + 5*m*n + m^2 + 6*n^2 + 1))/(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1) + (d*x*x^(2*n)*(e*x)^m*(A*d + 2*B*c)*(2*m + 4*n + 4*m*n + m^2 + 3*n^2 + 1))/(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1) + (B*d^2*x*x^(3*n)*(e*x)^m*(2*m + 3*n + 3*m*n + m^2 + 2*n^2 + 1))/(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1)","B"
12,0,-1,185,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(c+d\,x^n\right)}^2}{a+b\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n), x)","F"
13,0,-1,268,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(c+d\,x^n\right)}^2}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n)^2, x)","F"
14,0,-1,322,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n)^3,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(c+d\,x^n\right)}^2}{{\left(a+b\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^2)/(a + b*x^n)^3, x)","F"
15,1,2949,410,7.494625,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^3*(c + d*x^n)^3,x)","\frac{x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(3\,B\,a^3\,c\,d^2+A\,a^3\,d^3+9\,B\,a^2\,b\,c^2\,d+9\,A\,a^2\,b\,c\,d^2+3\,B\,a\,b^2\,c^3+9\,A\,a\,b^2\,c^2\,d+A\,b^3\,c^3\right)\,\left(m^6+25\,m^5\,n+6\,m^5+247\,m^4\,n^2+125\,m^4\,n+15\,m^4+1219\,m^3\,n^3+988\,m^3\,n^2+250\,m^3\,n+20\,m^3+3112\,m^2\,n^4+3657\,m^2\,n^3+1482\,m^2\,n^2+250\,m^2\,n+15\,m^2+3796\,m\,n^5+6224\,m\,n^4+3657\,m\,n^3+988\,m\,n^2+125\,m\,n+6\,m+1680\,n^6+3796\,n^5+3112\,n^4+1219\,n^3+247\,n^2+25\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}+\frac{x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(B\,a^3\,d^3+9\,B\,a^2\,b\,c\,d^2+3\,A\,a^2\,b\,d^3+9\,B\,a\,b^2\,c^2\,d+9\,A\,a\,b^2\,c\,d^2+B\,b^3\,c^3+3\,A\,b^3\,c^2\,d\right)\,\left(m^6+24\,m^5\,n+6\,m^5+226\,m^4\,n^2+120\,m^4\,n+15\,m^4+1056\,m^3\,n^3+904\,m^3\,n^2+240\,m^3\,n+20\,m^3+2545\,m^2\,n^4+3168\,m^2\,n^3+1356\,m^2\,n^2+240\,m^2\,n+15\,m^2+2952\,m\,n^5+5090\,m\,n^4+3168\,m\,n^3+904\,m\,n^2+120\,m\,n+6\,m+1260\,n^6+2952\,n^5+2545\,n^4+1056\,n^3+226\,n^2+24\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}+\frac{A\,a^3\,c^3\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{a^2\,c^2\,x\,x^n\,{\left(e\,x\right)}^m\,\left(3\,A\,a\,d+3\,A\,b\,c+B\,a\,c\right)\,\left(m^6+27\,m^5\,n+6\,m^5+295\,m^4\,n^2+135\,m^4\,n+15\,m^4+1665\,m^3\,n^3+1180\,m^3\,n^2+270\,m^3\,n+20\,m^3+5104\,m^2\,n^4+4995\,m^2\,n^3+1770\,m^2\,n^2+270\,m^2\,n+15\,m^2+8028\,m\,n^5+10208\,m\,n^4+4995\,m\,n^3+1180\,m\,n^2+135\,m\,n+6\,m+5040\,n^6+8028\,n^5+5104\,n^4+1665\,n^3+295\,n^2+27\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}+\frac{B\,b^3\,d^3\,x\,x^{7\,n}\,{\left(e\,x\right)}^m\,\left(m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}+\frac{3\,a\,c\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(B\,a^2\,c\,d+A\,a^2\,d^2+B\,a\,b\,c^2+3\,A\,a\,b\,c\,d+A\,b^2\,c^2\right)\,\left(m^6+26\,m^5\,n+6\,m^5+270\,m^4\,n^2+130\,m^4\,n+15\,m^4+1420\,m^3\,n^3+1080\,m^3\,n^2+260\,m^3\,n+20\,m^3+3929\,m^2\,n^4+4260\,m^2\,n^3+1620\,m^2\,n^2+260\,m^2\,n+15\,m^2+5274\,m\,n^5+7858\,m\,n^4+4260\,m\,n^3+1080\,m\,n^2+130\,m\,n+6\,m+2520\,n^6+5274\,n^5+3929\,n^4+1420\,n^3+270\,n^2+26\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}+\frac{3\,b\,d\,x\,x^{5\,n}\,{\left(e\,x\right)}^m\,\left(B\,a^2\,d^2+3\,B\,a\,b\,c\,d+A\,a\,b\,d^2+B\,b^2\,c^2+A\,b^2\,c\,d\right)\,\left(m^6+23\,m^5\,n+6\,m^5+207\,m^4\,n^2+115\,m^4\,n+15\,m^4+925\,m^3\,n^3+828\,m^3\,n^2+230\,m^3\,n+20\,m^3+2144\,m^2\,n^4+2775\,m^2\,n^3+1242\,m^2\,n^2+230\,m^2\,n+15\,m^2+2412\,m\,n^5+4288\,m\,n^4+2775\,m\,n^3+828\,m\,n^2+115\,m\,n+6\,m+1008\,n^6+2412\,n^5+2144\,n^4+925\,n^3+207\,n^2+23\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}+\frac{b^2\,d^2\,x\,x^{6\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+3\,B\,a\,d+3\,B\,b\,c\right)\,\left(m^6+22\,m^5\,n+6\,m^5+190\,m^4\,n^2+110\,m^4\,n+15\,m^4+820\,m^3\,n^3+760\,m^3\,n^2+220\,m^3\,n+20\,m^3+1849\,m^2\,n^4+2460\,m^2\,n^3+1140\,m^2\,n^2+220\,m^2\,n+15\,m^2+2038\,m\,n^5+3698\,m\,n^4+2460\,m\,n^3+760\,m\,n^2+110\,m\,n+6\,m+840\,n^6+2038\,n^5+1849\,n^4+820\,n^3+190\,n^2+22\,n+1\right)}{m^7+28\,m^6\,n+7\,m^6+322\,m^5\,n^2+168\,m^5\,n+21\,m^5+1960\,m^4\,n^3+1610\,m^4\,n^2+420\,m^4\,n+35\,m^4+6769\,m^3\,n^4+7840\,m^3\,n^3+3220\,m^3\,n^2+560\,m^3\,n+35\,m^3+13132\,m^2\,n^5+20307\,m^2\,n^4+11760\,m^2\,n^3+3220\,m^2\,n^2+420\,m^2\,n+21\,m^2+13068\,m\,n^6+26264\,m\,n^5+20307\,m\,n^4+7840\,m\,n^3+1610\,m\,n^2+168\,m\,n+7\,m+5040\,n^7+13068\,n^6+13132\,n^5+6769\,n^4+1960\,n^3+322\,n^2+28\,n+1}","Not used",1,"(x*x^(3*n)*(e*x)^m*(A*a^3*d^3 + A*b^3*c^3 + 3*B*a*b^2*c^3 + 3*B*a^3*c*d^2 + 9*A*a*b^2*c^2*d + 9*A*a^2*b*c*d^2 + 9*B*a^2*b*c^2*d)*(6*m + 25*n + 125*m*n + 988*m*n^2 + 250*m^2*n + 3657*m*n^3 + 250*m^3*n + 6224*m*n^4 + 125*m^4*n + 3796*m*n^5 + 25*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 247*n^2 + 1219*n^3 + 3112*n^4 + 3796*n^5 + 1680*n^6 + 1482*m^2*n^2 + 3657*m^2*n^3 + 988*m^3*n^2 + 3112*m^2*n^4 + 1219*m^3*n^3 + 247*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1) + (x*x^(4*n)*(e*x)^m*(B*a^3*d^3 + B*b^3*c^3 + 3*A*a^2*b*d^3 + 3*A*b^3*c^2*d + 9*A*a*b^2*c*d^2 + 9*B*a*b^2*c^2*d + 9*B*a^2*b*c*d^2)*(6*m + 24*n + 120*m*n + 904*m*n^2 + 240*m^2*n + 3168*m*n^3 + 240*m^3*n + 5090*m*n^4 + 120*m^4*n + 2952*m*n^5 + 24*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 226*n^2 + 1056*n^3 + 2545*n^4 + 2952*n^5 + 1260*n^6 + 1356*m^2*n^2 + 3168*m^2*n^3 + 904*m^3*n^2 + 2545*m^2*n^4 + 1056*m^3*n^3 + 226*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1) + (A*a^3*c^3*x*(e*x)^m)/(m + 1) + (a^2*c^2*x*x^n*(e*x)^m*(3*A*a*d + 3*A*b*c + B*a*c)*(6*m + 27*n + 135*m*n + 1180*m*n^2 + 270*m^2*n + 4995*m*n^3 + 270*m^3*n + 10208*m*n^4 + 135*m^4*n + 8028*m*n^5 + 27*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 295*n^2 + 1665*n^3 + 5104*n^4 + 8028*n^5 + 5040*n^6 + 1770*m^2*n^2 + 4995*m^2*n^3 + 1180*m^3*n^2 + 5104*m^2*n^4 + 1665*m^3*n^3 + 295*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1) + (B*b^3*d^3*x*x^(7*n)*(e*x)^m*(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1) + (3*a*c*x*x^(2*n)*(e*x)^m*(A*a^2*d^2 + A*b^2*c^2 + B*a*b*c^2 + B*a^2*c*d + 3*A*a*b*c*d)*(6*m + 26*n + 130*m*n + 1080*m*n^2 + 260*m^2*n + 4260*m*n^3 + 260*m^3*n + 7858*m*n^4 + 130*m^4*n + 5274*m*n^5 + 26*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 270*n^2 + 1420*n^3 + 3929*n^4 + 5274*n^5 + 2520*n^6 + 1620*m^2*n^2 + 4260*m^2*n^3 + 1080*m^3*n^2 + 3929*m^2*n^4 + 1420*m^3*n^3 + 270*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1) + (3*b*d*x*x^(5*n)*(e*x)^m*(B*a^2*d^2 + B*b^2*c^2 + A*a*b*d^2 + A*b^2*c*d + 3*B*a*b*c*d)*(6*m + 23*n + 115*m*n + 828*m*n^2 + 230*m^2*n + 2775*m*n^3 + 230*m^3*n + 4288*m*n^4 + 115*m^4*n + 2412*m*n^5 + 23*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 207*n^2 + 925*n^3 + 2144*n^4 + 2412*n^5 + 1008*n^6 + 1242*m^2*n^2 + 2775*m^2*n^3 + 828*m^3*n^2 + 2144*m^2*n^4 + 925*m^3*n^3 + 207*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1) + (b^2*d^2*x*x^(6*n)*(e*x)^m*(A*b*d + 3*B*a*d + 3*B*b*c)*(6*m + 22*n + 110*m*n + 760*m*n^2 + 220*m^2*n + 2460*m*n^3 + 220*m^3*n + 3698*m*n^4 + 110*m^4*n + 2038*m*n^5 + 22*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 190*n^2 + 820*n^3 + 1849*n^4 + 2038*n^5 + 840*n^6 + 1140*m^2*n^2 + 2460*m^2*n^3 + 760*m^3*n^2 + 1849*m^2*n^4 + 820*m^3*n^3 + 190*m^4*n^2 + 1))/(7*m + 28*n + 168*m*n + 1610*m*n^2 + 420*m^2*n + 7840*m*n^3 + 560*m^3*n + 20307*m*n^4 + 420*m^4*n + 26264*m*n^5 + 168*m^5*n + 13068*m*n^6 + 28*m^6*n + 21*m^2 + 35*m^3 + 35*m^4 + 21*m^5 + 7*m^6 + m^7 + 322*n^2 + 1960*n^3 + 6769*n^4 + 13132*n^5 + 13068*n^6 + 5040*n^7 + 3220*m^2*n^2 + 11760*m^2*n^3 + 3220*m^3*n^2 + 20307*m^2*n^4 + 7840*m^3*n^3 + 1610*m^4*n^2 + 13132*m^2*n^5 + 6769*m^3*n^4 + 1960*m^4*n^3 + 322*m^5*n^2 + 1)","B"
16,1,1882,310,6.414369,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^2*(c + d*x^n)^3,x)","\frac{x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(3\,B\,a^2\,c\,d^2+A\,a^2\,d^3+6\,B\,a\,b\,c^2\,d+6\,A\,a\,b\,c\,d^2+B\,b^2\,c^3+3\,A\,b^2\,c^2\,d\right)\,\left(m^5+18\,m^4\,n+5\,m^4+121\,m^3\,n^2+72\,m^3\,n+10\,m^3+372\,m^2\,n^3+363\,m^2\,n^2+108\,m^2\,n+10\,m^2+508\,m\,n^4+744\,m\,n^3+363\,m\,n^2+72\,m\,n+5\,m+240\,n^5+508\,n^4+372\,n^3+121\,n^2+18\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{A\,a^2\,c^3\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{c\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(3\,B\,a^2\,c\,d+3\,A\,a^2\,d^2+2\,B\,a\,b\,c^2+6\,A\,a\,b\,c\,d+A\,b^2\,c^2\right)\,\left(m^5+19\,m^4\,n+5\,m^4+137\,m^3\,n^2+76\,m^3\,n+10\,m^3+461\,m^2\,n^3+411\,m^2\,n^2+114\,m^2\,n+10\,m^2+702\,m\,n^4+922\,m\,n^3+411\,m\,n^2+76\,m\,n+5\,m+360\,n^5+702\,n^4+461\,n^3+137\,n^2+19\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{d\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(B\,a^2\,d^2+6\,B\,a\,b\,c\,d+2\,A\,a\,b\,d^2+3\,B\,b^2\,c^2+3\,A\,b^2\,c\,d\right)\,\left(m^5+17\,m^4\,n+5\,m^4+107\,m^3\,n^2+68\,m^3\,n+10\,m^3+307\,m^2\,n^3+321\,m^2\,n^2+102\,m^2\,n+10\,m^2+396\,m\,n^4+614\,m\,n^3+321\,m\,n^2+68\,m\,n+5\,m+180\,n^5+396\,n^4+307\,n^3+107\,n^2+17\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{a\,c^2\,x\,x^n\,{\left(e\,x\right)}^m\,\left(3\,A\,a\,d+2\,A\,b\,c+B\,a\,c\right)\,\left(m^5+20\,m^4\,n+5\,m^4+155\,m^3\,n^2+80\,m^3\,n+10\,m^3+580\,m^2\,n^3+465\,m^2\,n^2+120\,m^2\,n+10\,m^2+1044\,m\,n^4+1160\,m\,n^3+465\,m\,n^2+80\,m\,n+5\,m+720\,n^5+1044\,n^4+580\,n^3+155\,n^2+20\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{b\,d^2\,x\,x^{5\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+2\,B\,a\,d+3\,B\,b\,c\right)\,\left(m^5+16\,m^4\,n+5\,m^4+95\,m^3\,n^2+64\,m^3\,n+10\,m^3+260\,m^2\,n^3+285\,m^2\,n^2+96\,m^2\,n+10\,m^2+324\,m\,n^4+520\,m\,n^3+285\,m\,n^2+64\,m\,n+5\,m+144\,n^5+324\,n^4+260\,n^3+95\,n^2+16\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}+\frac{B\,b^2\,d^3\,x\,x^{6\,n}\,{\left(e\,x\right)}^m\,\left(m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1\right)}{m^6+21\,m^5\,n+6\,m^5+175\,m^4\,n^2+105\,m^4\,n+15\,m^4+735\,m^3\,n^3+700\,m^3\,n^2+210\,m^3\,n+20\,m^3+1624\,m^2\,n^4+2205\,m^2\,n^3+1050\,m^2\,n^2+210\,m^2\,n+15\,m^2+1764\,m\,n^5+3248\,m\,n^4+2205\,m\,n^3+700\,m\,n^2+105\,m\,n+6\,m+720\,n^6+1764\,n^5+1624\,n^4+735\,n^3+175\,n^2+21\,n+1}","Not used",1,"(x*x^(3*n)*(e*x)^m*(A*a^2*d^3 + B*b^2*c^3 + 3*A*b^2*c^2*d + 3*B*a^2*c*d^2 + 6*A*a*b*c*d^2 + 6*B*a*b*c^2*d)*(5*m + 18*n + 72*m*n + 363*m*n^2 + 108*m^2*n + 744*m*n^3 + 72*m^3*n + 508*m*n^4 + 18*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 121*n^2 + 372*n^3 + 508*n^4 + 240*n^5 + 363*m^2*n^2 + 372*m^2*n^3 + 121*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (A*a^2*c^3*x*(e*x)^m)/(m + 1) + (c*x*x^(2*n)*(e*x)^m*(3*A*a^2*d^2 + A*b^2*c^2 + 2*B*a*b*c^2 + 3*B*a^2*c*d + 6*A*a*b*c*d)*(5*m + 19*n + 76*m*n + 411*m*n^2 + 114*m^2*n + 922*m*n^3 + 76*m^3*n + 702*m*n^4 + 19*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 137*n^2 + 461*n^3 + 702*n^4 + 360*n^5 + 411*m^2*n^2 + 461*m^2*n^3 + 137*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (d*x*x^(4*n)*(e*x)^m*(B*a^2*d^2 + 3*B*b^2*c^2 + 2*A*a*b*d^2 + 3*A*b^2*c*d + 6*B*a*b*c*d)*(5*m + 17*n + 68*m*n + 321*m*n^2 + 102*m^2*n + 614*m*n^3 + 68*m^3*n + 396*m*n^4 + 17*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 107*n^2 + 307*n^3 + 396*n^4 + 180*n^5 + 321*m^2*n^2 + 307*m^2*n^3 + 107*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (a*c^2*x*x^n*(e*x)^m*(3*A*a*d + 2*A*b*c + B*a*c)*(5*m + 20*n + 80*m*n + 465*m*n^2 + 120*m^2*n + 1160*m*n^3 + 80*m^3*n + 1044*m*n^4 + 20*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 155*n^2 + 580*n^3 + 1044*n^4 + 720*n^5 + 465*m^2*n^2 + 580*m^2*n^3 + 155*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (b*d^2*x*x^(5*n)*(e*x)^m*(A*b*d + 2*B*a*d + 3*B*b*c)*(5*m + 16*n + 64*m*n + 285*m*n^2 + 96*m^2*n + 520*m*n^3 + 64*m^3*n + 324*m*n^4 + 16*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 95*n^2 + 260*n^3 + 324*n^4 + 144*n^5 + 285*m^2*n^2 + 260*m^2*n^3 + 95*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1) + (B*b^2*d^3*x*x^(6*n)*(e*x)^m*(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1))/(6*m + 21*n + 105*m*n + 700*m*n^2 + 210*m^2*n + 2205*m*n^3 + 210*m^3*n + 3248*m*n^4 + 105*m^4*n + 1764*m*n^5 + 21*m^5*n + 15*m^2 + 20*m^3 + 15*m^4 + 6*m^5 + m^6 + 175*n^2 + 735*n^3 + 1624*n^4 + 1764*n^5 + 720*n^6 + 1050*m^2*n^2 + 2205*m^2*n^3 + 700*m^3*n^2 + 1624*m^2*n^4 + 735*m^3*n^3 + 175*m^4*n^2 + 1)","B"
17,1,1089,210,5.652932,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)*(c + d*x^n)^3,x)","\frac{A\,a\,c^3\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{d^2\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(A\,b\,d+B\,a\,d+3\,B\,b\,c\right)\,\left(m^4+11\,m^3\,n+4\,m^3+41\,m^2\,n^2+33\,m^2\,n+6\,m^2+61\,m\,n^3+82\,m\,n^2+33\,m\,n+4\,m+30\,n^4+61\,n^3+41\,n^2+11\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{c\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(3\,A\,a\,d^2+B\,b\,c^2+3\,A\,b\,c\,d+3\,B\,a\,c\,d\right)\,\left(m^4+13\,m^3\,n+4\,m^3+59\,m^2\,n^2+39\,m^2\,n+6\,m^2+107\,m\,n^3+118\,m\,n^2+39\,m\,n+4\,m+60\,n^4+107\,n^3+59\,n^2+13\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{d\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(A\,a\,d^2+3\,B\,b\,c^2+3\,A\,b\,c\,d+3\,B\,a\,c\,d\right)\,\left(m^4+12\,m^3\,n+4\,m^3+49\,m^2\,n^2+36\,m^2\,n+6\,m^2+78\,m\,n^3+98\,m\,n^2+36\,m\,n+4\,m+40\,n^4+78\,n^3+49\,n^2+12\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{c^2\,x\,x^n\,{\left(e\,x\right)}^m\,\left(3\,A\,a\,d+A\,b\,c+B\,a\,c\right)\,\left(m^4+14\,m^3\,n+4\,m^3+71\,m^2\,n^2+42\,m^2\,n+6\,m^2+154\,m\,n^3+142\,m\,n^2+42\,m\,n+4\,m+120\,n^4+154\,n^3+71\,n^2+14\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}+\frac{B\,b\,d^3\,x\,x^{5\,n}\,{\left(e\,x\right)}^m\,\left(m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1\right)}{m^5+15\,m^4\,n+5\,m^4+85\,m^3\,n^2+60\,m^3\,n+10\,m^3+225\,m^2\,n^3+255\,m^2\,n^2+90\,m^2\,n+10\,m^2+274\,m\,n^4+450\,m\,n^3+255\,m\,n^2+60\,m\,n+5\,m+120\,n^5+274\,n^4+225\,n^3+85\,n^2+15\,n+1}","Not used",1,"(A*a*c^3*x*(e*x)^m)/(m + 1) + (d^2*x*x^(4*n)*(e*x)^m*(A*b*d + B*a*d + 3*B*b*c)*(4*m + 11*n + 33*m*n + 82*m*n^2 + 33*m^2*n + 61*m*n^3 + 11*m^3*n + 6*m^2 + 4*m^3 + m^4 + 41*n^2 + 61*n^3 + 30*n^4 + 41*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (c*x*x^(2*n)*(e*x)^m*(3*A*a*d^2 + B*b*c^2 + 3*A*b*c*d + 3*B*a*c*d)*(4*m + 13*n + 39*m*n + 118*m*n^2 + 39*m^2*n + 107*m*n^3 + 13*m^3*n + 6*m^2 + 4*m^3 + m^4 + 59*n^2 + 107*n^3 + 60*n^4 + 59*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (d*x*x^(3*n)*(e*x)^m*(A*a*d^2 + 3*B*b*c^2 + 3*A*b*c*d + 3*B*a*c*d)*(4*m + 12*n + 36*m*n + 98*m*n^2 + 36*m^2*n + 78*m*n^3 + 12*m^3*n + 6*m^2 + 4*m^3 + m^4 + 49*n^2 + 78*n^3 + 40*n^4 + 49*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (c^2*x*x^n*(e*x)^m*(3*A*a*d + A*b*c + B*a*c)*(4*m + 14*n + 42*m*n + 142*m*n^2 + 42*m^2*n + 154*m*n^3 + 14*m^3*n + 6*m^2 + 4*m^3 + m^4 + 71*n^2 + 154*n^3 + 120*n^4 + 71*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1) + (B*b*d^3*x*x^(5*n)*(e*x)^m*(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1))/(5*m + 15*n + 60*m*n + 255*m*n^2 + 90*m^2*n + 450*m*n^3 + 60*m^3*n + 274*m*n^4 + 15*m^4*n + 10*m^2 + 10*m^3 + 5*m^4 + m^5 + 85*n^2 + 225*n^3 + 274*n^4 + 120*n^5 + 255*m^2*n^2 + 225*m^2*n^3 + 85*m^3*n^2 + 1)","B"
18,1,563,137,5.306824,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(c + d*x^n)^3,x)","\frac{A\,c^3\,x\,{\left(e\,x\right)}^m}{m+1}+\frac{d^2\,x\,x^{3\,n}\,{\left(e\,x\right)}^m\,\left(A\,d+3\,B\,c\right)\,\left(m^3+7\,m^2\,n+3\,m^2+14\,m\,n^2+14\,m\,n+3\,m+8\,n^3+14\,n^2+7\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{c^2\,x\,x^n\,{\left(e\,x\right)}^m\,\left(3\,A\,d+B\,c\right)\,\left(m^3+9\,m^2\,n+3\,m^2+26\,m\,n^2+18\,m\,n+3\,m+24\,n^3+26\,n^2+9\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{B\,d^3\,x\,x^{4\,n}\,{\left(e\,x\right)}^m\,\left(m^3+6\,m^2\,n+3\,m^2+11\,m\,n^2+12\,m\,n+3\,m+6\,n^3+11\,n^2+6\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}+\frac{3\,c\,d\,x\,x^{2\,n}\,{\left(e\,x\right)}^m\,\left(A\,d+B\,c\right)\,\left(m^3+8\,m^2\,n+3\,m^2+19\,m\,n^2+16\,m\,n+3\,m+12\,n^3+19\,n^2+8\,n+1\right)}{m^4+10\,m^3\,n+4\,m^3+35\,m^2\,n^2+30\,m^2\,n+6\,m^2+50\,m\,n^3+70\,m\,n^2+30\,m\,n+4\,m+24\,n^4+50\,n^3+35\,n^2+10\,n+1}","Not used",1,"(A*c^3*x*(e*x)^m)/(m + 1) + (d^2*x*x^(3*n)*(e*x)^m*(A*d + 3*B*c)*(3*m + 7*n + 14*m*n + 14*m*n^2 + 7*m^2*n + 3*m^2 + m^3 + 14*n^2 + 8*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (c^2*x*x^n*(e*x)^m*(3*A*d + B*c)*(3*m + 9*n + 18*m*n + 26*m*n^2 + 9*m^2*n + 3*m^2 + m^3 + 26*n^2 + 24*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (B*d^3*x*x^(4*n)*(e*x)^m*(3*m + 6*n + 12*m*n + 11*m*n^2 + 6*m^2*n + 3*m^2 + m^3 + 11*n^2 + 6*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1) + (3*c*d*x*x^(2*n)*(e*x)^m*(A*d + B*c)*(3*m + 8*n + 16*m*n + 19*m*n^2 + 8*m^2*n + 3*m^2 + m^3 + 19*n^2 + 12*n^3 + 1))/(4*m + 10*n + 30*m*n + 70*m*n^2 + 30*m^2*n + 50*m*n^3 + 10*m^3*n + 6*m^2 + 4*m^3 + m^4 + 35*n^2 + 50*n^3 + 24*n^4 + 35*m^2*n^2 + 1)","B"
19,0,-1,270,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^3)/(a + b*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(c+d\,x^n\right)}^3}{a+b\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^3)/(a + b*x^n), x)","F"
20,0,-1,394,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^3)/(a + b*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(c+d\,x^n\right)}^3}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(c + d*x^n)^3)/(a + b*x^n)^2, x)","F"
21,0,-1,380,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^4)/(c + d*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^4}{c+d\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^4)/(c + d*x^n), x)","F"
22,0,-1,272,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^3)/(c + d*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^3}{c+d\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^3)/(c + d*x^n), x)","F"
23,0,-1,187,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^2)/(c + d*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^2}{c+d\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^2)/(c + d*x^n), x)","F"
24,0,-1,122,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n))/(c + d*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,\left(a+b\,x^n\right)}{c+d\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n))/(c + d*x^n), x)","F"
25,0,-1,78,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/(c + d*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{c+d\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/(c + d*x^n), x)","F"
26,0,-1,127,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)), x)","F"
27,0,-1,212,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)), x)","F"
28,0,-1,407,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^3*(c + d*x^n)),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(a+b\,x^n\right)}^3\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^3*(c + d*x^n)), x)","F"
29,0,-1,386,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^3)/(c + d*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^3}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^3)/(c + d*x^n)^2, x)","F"
30,0,-1,267,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^2)/(c + d*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^2}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^2)/(c + d*x^n)^2, x)","F"
31,0,-1,178,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n))/(c + d*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,\left(a+b\,x^n\right)}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n))/(c + d*x^n)^2, x)","F"
32,0,-1,107,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/(c + d*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/(c + d*x^n)^2, x)","F"
33,0,-1,211,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)^2),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{\left(a+b\,x^n\right)\,{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)^2), x)","F"
34,0,-1,315,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)^2),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(a+b\,x^n\right)}^2\,{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)^2), x)","F"
35,0,-1,567,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^3*(c + d*x^n)^2),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(a+b\,x^n\right)}^3\,{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^3*(c + d*x^n)^2), x)","F"
36,0,-1,322,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^2)/(c + d*x^n)^3,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^2}{{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^2)/(c + d*x^n)^3, x)","F"
37,0,-1,228,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n))/(c + d*x^n)^3,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,\left(a+b\,x^n\right)}{{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n))/(c + d*x^n)^3, x)","F"
38,0,-1,112,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/(c + d*x^n)^3,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/(c + d*x^n)^3, x)","F"
39,0,-1,366,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)^3),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{\left(a+b\,x^n\right)\,{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)*(c + d*x^n)^3), x)","F"
40,0,-1,482,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)^3),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)}{{\left(a+b\,x^n\right)}^2\,{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n))/((a + b*x^n)^2*(c + d*x^n)^3), x)","F"
41,0,-1,211,0.000000,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^p*(c + d*x^n)^q,x)","\int {\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^p\,{\left(c+d\,x^n\right)}^q \,d x","Not used",1,"int((e*x)^m*(A + B*x^n)*(a + b*x^n)^p*(c + d*x^n)^q, x)","F"
42,0,-1,271,0.000000,"\text{Not used}","int((e*x)^m*(A + B*x^n)*(a + b*x^n)^p*(c + d*x^n),x)","\int {\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^p\,\left(c+d\,x^n\right) \,d x","Not used",1,"int((e*x)^m*(A + B*x^n)*(a + b*x^n)^p*(c + d*x^n), x)","F"
43,0,-1,164,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^p)/(c + d*x^n),x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^p}{c+d\,x^n} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^p)/(c + d*x^n), x)","F"
44,0,-1,304,0.000000,"\text{Not used}","int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^p)/(c + d*x^n)^2,x)","\int \frac{{\left(e\,x\right)}^m\,\left(A+B\,x^n\right)\,{\left(a+b\,x^n\right)}^p}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(((e*x)^m*(A + B*x^n)*(a + b*x^n)^p)/(c + d*x^n)^2, x)","F"
45,0,-1,139,0.000000,"\text{Not used}","int(((a + b*x^(n/2))^(1/n - 1)*(b*x^(n/2) - a)^(1/n - 1)*(c + d*x^n))/x^2,x)","\int \frac{{\left(a+b\,x^{n/2}\right)}^{\frac{1}{n}-1}\,{\left(b\,x^{n/2}-a\right)}^{\frac{1}{n}-1}\,\left(c+d\,x^n\right)}{x^2} \,d x","Not used",1,"int(((a + b*x^(n/2))^(1/n - 1)*(b*x^(n/2) - a)^(1/n - 1)*(c + d*x^n))/x^2, x)","F"
46,0,-1,139,0.000000,"\text{Not used}","int((c + d*x^n)/(x^2*(a + b*x^(n/2))^((n - 1)/n)*(b*x^(n/2) - a)^((n - 1)/n)),x)","\int \frac{c+d\,x^n}{x^2\,{\left(a+b\,x^{n/2}\right)}^{\frac{n-1}{n}}\,{\left(b\,x^{n/2}-a\right)}^{\frac{n-1}{n}}} \,d x","Not used",1,"int((c + d*x^n)/(x^2*(a + b*x^(n/2))^((n - 1)/n)*(b*x^(n/2) - a)^((n - 1)/n)), x)","F"