1,0,-1,127,0.000000,"\text{Not used}","int(x^3*(a + b*x^2)^(1/2)*(A + B*x),x)","\int x^3\,\sqrt{b\,x^2+a}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x^3*(a + b*x^2)^(1/2)*(A + B*x), x)","F"
2,0,-1,104,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^(1/2)*(A + B*x),x)","\int x^2\,\sqrt{b\,x^2+a}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x^2*(a + b*x^2)^(1/2)*(A + B*x), x)","F"
3,0,-1,80,0.000000,"\text{Not used}","int(x*(a + b*x^2)^(1/2)*(A + B*x),x)","\int x\,\sqrt{b\,x^2+a}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x*(a + b*x^2)^(1/2)*(A + B*x), x)","F"
4,1,52,67,1.161768,"\text{Not used}","int((a + b*x^2)^(1/2)*(A + B*x),x)","\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{3\,b}+\frac{A\,x\,\sqrt{b\,x^2+a}}{2}+\frac{A\,a\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{2\,\sqrt{b}}","Not used",1,"(B*(a + b*x^2)^(3/2))/(3*b) + (A*x*(a + b*x^2)^(1/2))/2 + (A*a*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/(2*b^(1/2))","B"
5,1,68,79,1.235658,"\text{Not used}","int(((a + b*x^2)^(1/2)*(A + B*x))/x,x)","A\,\sqrt{b\,x^2+a}-A\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)+\frac{B\,x\,\sqrt{b\,x^2+a}}{2}+\frac{B\,a\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{2\,\sqrt{b}}","Not used",1,"A*(a + b*x^2)^(1/2) - A*a^(1/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) + (B*x*(a + b*x^2)^(1/2))/2 + (B*a*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/(2*b^(1/2))","B"
6,1,89,75,1.687905,"\text{Not used}","int(((a + b*x^2)^(1/2)*(A + B*x))/x^2,x)","B\,\sqrt{b\,x^2+a}-\frac{A\,\sqrt{b\,x^2+a}}{x}-B\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)-\frac{A\,\sqrt{b}\,\mathrm{asin}\left(\frac{\sqrt{b}\,x\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}\,\sqrt{\frac{b\,x^2}{a}+1}}","Not used",1,"B*(a + b*x^2)^(1/2) - (A*(a + b*x^2)^(1/2))/x - B*a^(1/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) - (A*b^(1/2)*asin((b^(1/2)*x*1i)/a^(1/2))*(a + b*x^2)^(1/2)*1i)/(a^(1/2)*((b*x^2)/a + 1)^(1/2))","B"
7,1,94,80,1.794704,"\text{Not used}","int(((a + b*x^2)^(1/2)*(A + B*x))/x^3,x)","-\frac{A\,\sqrt{b\,x^2+a}}{2\,x^2}-\frac{B\,\sqrt{b\,x^2+a}}{x}-\frac{A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,\sqrt{a}}-\frac{B\,\sqrt{b}\,\mathrm{asin}\left(\frac{\sqrt{b}\,x\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}\,\sqrt{\frac{b\,x^2}{a}+1}}","Not used",1,"- (A*(a + b*x^2)^(1/2))/(2*x^2) - (B*(a + b*x^2)^(1/2))/x - (A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(1/2)) - (B*b^(1/2)*asin((b^(1/2)*x*1i)/a^(1/2))*(a + b*x^2)^(1/2)*1i)/(a^(1/2)*((b*x^2)/a + 1)^(1/2))","B"
8,0,-1,150,0.000000,"\text{Not used}","int(x^3*(a + b*x^2)^(3/2)*(A + B*x),x)","\int x^3\,{\left(b\,x^2+a\right)}^{3/2}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x^3*(a + b*x^2)^(3/2)*(A + B*x), x)","F"
9,0,-1,127,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^(3/2)*(A + B*x),x)","\int x^2\,{\left(b\,x^2+a\right)}^{3/2}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x^2*(a + b*x^2)^(3/2)*(A + B*x), x)","F"
10,0,-1,103,0.000000,"\text{Not used}","int(x*(a + b*x^2)^(3/2)*(A + B*x),x)","\int x\,{\left(b\,x^2+a\right)}^{3/2}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x*(a + b*x^2)^(3/2)*(A + B*x), x)","F"
11,1,54,87,1.181854,"\text{Not used}","int((a + b*x^2)^(3/2)*(A + B*x),x)","\frac{B\,{\left(b\,x^2+a\right)}^{5/2}}{5\,b}+\frac{A\,x\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"(B*(a + b*x^2)^(5/2))/(5*b) + (A*x*(a + b*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(3/2)","B"
12,1,83,106,1.312374,"\text{Not used}","int(((a + b*x^2)^(3/2)*(A + B*x))/x,x)","\frac{A\,{\left(b\,x^2+a\right)}^{3/2}}{3}-A\,a^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)+A\,a\,\sqrt{b\,x^2+a}+\frac{B\,x\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"(A*(a + b*x^2)^(3/2))/3 - A*a^(3/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) + A*a*(a + b*x^2)^(1/2) + (B*x*(a + b*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(3/2)","B"
13,1,86,108,1.877406,"\text{Not used}","int(((a + b*x^2)^(3/2)*(A + B*x))/x^2,x)","\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{3}-B\,a^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)+B\,a\,\sqrt{b\,x^2+a}-\frac{A\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{b\,x^2}{a}\right)}{x\,{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"(B*(a + b*x^2)^(3/2))/3 - B*a^(3/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) + B*a*(a + b*x^2)^(1/2) - (A*(a + b*x^2)^(3/2)*hypergeom([-3/2, -1/2], 1/2, -(b*x^2)/a))/(x*((b*x^2)/a + 1)^(3/2))","B"
14,1,91,111,2.120247,"\text{Not used}","int(((a + b*x^2)^(3/2)*(A + B*x))/x^3,x)","A\,b\,\sqrt{b\,x^2+a}-\frac{A\,a\,\sqrt{b\,x^2+a}}{2\,x^2}-\frac{3\,A\,\sqrt{a}\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2}-\frac{B\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{b\,x^2}{a}\right)}{x\,{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"A*b*(a + b*x^2)^(1/2) - (A*a*(a + b*x^2)^(1/2))/(2*x^2) - (3*A*a^(1/2)*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/2 - (B*(a + b*x^2)^(3/2)*hypergeom([-3/2, -1/2], 1/2, -(b*x^2)/a))/(x*((b*x^2)/a + 1)^(3/2))","B"
15,0,-1,173,0.000000,"\text{Not used}","int(x^3*(a + b*x^2)^(5/2)*(A + B*x),x)","\int x^3\,{\left(b\,x^2+a\right)}^{5/2}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x^3*(a + b*x^2)^(5/2)*(A + B*x), x)","F"
16,0,-1,150,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^(5/2)*(A + B*x),x)","\int x^2\,{\left(b\,x^2+a\right)}^{5/2}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x^2*(a + b*x^2)^(5/2)*(A + B*x), x)","F"
17,0,-1,126,0.000000,"\text{Not used}","int(x*(a + b*x^2)^(5/2)*(A + B*x),x)","\int x\,{\left(b\,x^2+a\right)}^{5/2}\,\left(A+B\,x\right) \,d x","Not used",1,"int(x*(a + b*x^2)^(5/2)*(A + B*x), x)","F"
18,1,54,107,1.163449,"\text{Not used}","int((a + b*x^2)^(5/2)*(A + B*x),x)","\frac{B\,{\left(b\,x^2+a\right)}^{7/2}}{7\,b}+\frac{A\,x\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}","Not used",1,"(B*(a + b*x^2)^(7/2))/(7*b) + (A*x*(a + b*x^2)^(5/2)*hypergeom([-5/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(5/2)","B"
19,1,101,132,1.246907,"\text{Not used}","int(((a + b*x^2)^(5/2)*(A + B*x))/x,x)","\frac{A\,{\left(b\,x^2+a\right)}^{5/2}}{5}+A\,a^2\,\sqrt{b\,x^2+a}+\frac{A\,a\,{\left(b\,x^2+a\right)}^{3/2}}{3}+\frac{B\,x\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}+A\,a^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}","Not used",1,"(A*(a + b*x^2)^(5/2))/5 + A*a^2*(a + b*x^2)^(1/2) + A*a^(5/2)*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i + (A*a*(a + b*x^2)^(3/2))/3 + (B*x*(a + b*x^2)^(5/2)*hypergeom([-5/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(5/2)","B"
20,1,104,136,2.163500,"\text{Not used}","int(((a + b*x^2)^(5/2)*(A + B*x))/x^2,x)","\frac{B\,{\left(b\,x^2+a\right)}^{5/2}}{5}+B\,a^2\,\sqrt{b\,x^2+a}+\frac{B\,a\,{\left(b\,x^2+a\right)}^{3/2}}{3}-\frac{A\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{b\,x^2}{a}\right)}{x\,{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}+B\,a^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}","Not used",1,"(B*(a + b*x^2)^(5/2))/5 + B*a^2*(a + b*x^2)^(1/2) + B*a^(5/2)*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i + (B*a*(a + b*x^2)^(3/2))/3 - (A*(a + b*x^2)^(5/2)*hypergeom([-5/2, -1/2], 1/2, -(b*x^2)/a))/(x*((b*x^2)/a + 1)^(5/2))","B"
21,1,111,141,2.590505,"\text{Not used}","int(((a + b*x^2)^(5/2)*(A + B*x))/x^3,x)","\frac{A\,b\,{\left(b\,x^2+a\right)}^{3/2}}{3}+2\,A\,a\,b\,\sqrt{b\,x^2+a}-\frac{A\,a^2\,\sqrt{b\,x^2+a}}{2\,x^2}-\frac{B\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{b\,x^2}{a}\right)}{x\,{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}+\frac{A\,a^{3/2}\,b\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{2}","Not used",1,"(A*b*(a + b*x^2)^(3/2))/3 + 2*A*a*b*(a + b*x^2)^(1/2) - (A*a^2*(a + b*x^2)^(1/2))/(2*x^2) + (A*a^(3/2)*b*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/2 - (B*(a + b*x^2)^(5/2)*hypergeom([-5/2, -1/2], 1/2, -(b*x^2)/a))/(x*((b*x^2)/a + 1)^(5/2))","B"
22,0,-1,104,0.000000,"\text{Not used}","int((x^3*(A + B*x))/(a + b*x^2)^(1/2),x)","\int \frac{x^3\,\left(A+B\,x\right)}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((x^3*(A + B*x))/(a + b*x^2)^(1/2), x)","F"
23,1,93,81,1.467222,"\text{Not used}","int((x^2*(A + B*x))/(a + b*x^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{3\,B\,x^4+4\,A\,x^3}{12\,\sqrt{a}} & \text{\ if\ \ }b=0\\ \frac{A\,x\,\sqrt{b\,x^2+a}}{2\,b}-\frac{A\,a\,\ln\left(2\,\sqrt{b}\,x+2\,\sqrt{b\,x^2+a}\right)}{2\,b^{3/2}}-\frac{B\,\sqrt{b\,x^2+a}\,\left(2\,a-b\,x^2\right)}{3\,b^2} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, (4*A*x^3 + 3*B*x^4)/(12*a^(1/2)), b ~= 0, - (A*a*log(2*b^(1/2)*x + 2*(a + b*x^2)^(1/2)))/(2*b^(3/2)) + (A*x*(a + b*x^2)^(1/2))/(2*b) - (B*(a + b*x^2)^(1/2)*(2*a - b*x^2))/(3*b^2))","B"
24,1,82,56,1.237465,"\text{Not used}","int((x*(A + B*x))/(a + b*x^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{2\,B\,x^3+3\,A\,x^2}{6\,\sqrt{a}} & \text{\ if\ \ }b=0\\ \frac{A\,\sqrt{b\,x^2+a}}{b}-\frac{B\,a\,\ln\left(2\,\sqrt{b}\,x+2\,\sqrt{b\,x^2+a}\right)}{2\,b^{3/2}}+\frac{B\,x\,\sqrt{b\,x^2+a}}{2\,b} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, (3*A*x^2 + 2*B*x^3)/(6*a^(1/2)), b ~= 0, (A*(a + b*x^2)^(1/2))/b - (B*a*log(2*b^(1/2)*x + 2*(a + b*x^2)^(1/2)))/(2*b^(3/2)) + (B*x*(a + b*x^2)^(1/2))/(2*b))","B"
25,1,36,43,1.143755,"\text{Not used}","int((A + B*x)/(a + b*x^2)^(1/2),x)","\frac{B\,\sqrt{b\,x^2+a}}{b}+\frac{A\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}","Not used",1,"(B*(a + b*x^2)^(1/2))/b + (A*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2)","B"
26,1,42,53,1.299124,"\text{Not used}","int((A + B*x)/(x*(a + b*x^2)^(1/2)),x)","\frac{B\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"(B*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2) - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2)","B"
27,1,39,47,1.201308,"\text{Not used}","int((A + B*x)/(x^2*(a + b*x^2)^(1/2)),x)","-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{A\,\sqrt{b\,x^2+a}}{a\,x}","Not used",1,"- (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2) - (A*(a + b*x^2)^(1/2))/(a*x)","B"
28,1,58,72,1.349717,"\text{Not used}","int((A + B*x)/(x^3*(a + b*x^2)^(1/2)),x)","\frac{A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{B\,\sqrt{b\,x^2+a}}{a\,x}-\frac{A\,\sqrt{b\,x^2+a}}{2\,a\,x^2}","Not used",1,"(A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2)) - (B*(a + b*x^2)^(1/2))/(a*x) - (A*(a + b*x^2)^(1/2))/(2*a*x^2)","B"
29,0,-1,81,0.000000,"\text{Not used}","int((x^3*(A + B*x))/(a + b*x^2)^(3/2),x)","\int \frac{x^3\,\left(A+B\,x\right)}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((x^3*(A + B*x))/(a + b*x^2)^(3/2), x)","F"
30,1,61,66,1.342285,"\text{Not used}","int((x^2*(A + B*x))/(a + b*x^2)^(3/2),x)","\frac{A\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{b^{3/2}}-\frac{A\,x}{b\,\sqrt{b\,x^2+a}}+\frac{B\,\left(b\,x^2+2\,a\right)}{b^2\,\sqrt{b\,x^2+a}}","Not used",1,"(A*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(3/2) - (A*x)/(b*(a + b*x^2)^(1/2)) + (B*(2*a + b*x^2))/(b^2*(a + b*x^2)^(1/2))","B"
31,1,53,48,1.055183,"\text{Not used}","int((x*(A + B*x))/(a + b*x^2)^(3/2),x)","\frac{B\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{b^{3/2}}-\frac{A}{b\,\sqrt{b\,x^2+a}}-\frac{B\,x}{b\,\sqrt{b\,x^2+a}}","Not used",1,"(B*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(3/2) - A/(b*(a + b*x^2)^(1/2)) - (B*x)/(b*(a + b*x^2)^(1/2))","B"
32,1,24,28,0.909229,"\text{Not used}","int((A + B*x)/(a + b*x^2)^(3/2),x)","-\frac{\frac{B}{b}-\frac{A\,x}{a}}{\sqrt{b\,x^2+a}}","Not used",1,"-(B/b - (A*x)/a)/(a + b*x^2)^(1/2)","B"
33,1,50,47,1.291116,"\text{Not used}","int((A + B*x)/(x*(a + b*x^2)^(3/2)),x)","\frac{A}{a\,\sqrt{b\,x^2+a}}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{B\,x}{a\,\sqrt{b\,x^2+a}}","Not used",1,"A/(a*(a + b*x^2)^(1/2)) - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(3/2) + (B*x)/(a*(a + b*x^2)^(1/2))","B"
34,1,70,70,1.447672,"\text{Not used}","int((A + B*x)/(x^2*(a + b*x^2)^(3/2)),x)","\frac{B}{a\,\sqrt{b\,x^2+a}}-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{A}{a\,x\,\sqrt{b\,x^2+a}}-\frac{2\,A\,b\,x}{a^2\,\sqrt{b\,x^2+a}}","Not used",1,"B/(a*(a + b*x^2)^(1/2)) - (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(3/2) - A/(a*x*(a + b*x^2)^(1/2)) - (2*A*b*x)/(a^2*(a + b*x^2)^(1/2))","B"
35,1,94,95,1.591792,"\text{Not used}","int((A + B*x)/(x^3*(a + b*x^2)^(3/2)),x)","\frac{3\,A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{5/2}}-\frac{3\,A\,b}{2\,a^2\,\sqrt{b\,x^2+a}}-\frac{A}{2\,a\,x^2\,\sqrt{b\,x^2+a}}-\frac{\sqrt{b\,x^2+a}\,\left(\frac{B}{a}+\frac{2\,B\,b\,x^2}{a^2}\right)}{b\,x^3+a\,x}","Not used",1,"(3*A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(5/2)) - (3*A*b)/(2*a^2*(a + b*x^2)^(1/2)) - A/(2*a*x^2*(a + b*x^2)^(1/2)) - ((a + b*x^2)^(1/2)*(B/a + (2*B*b*x^2)/a^2))/(a*x + b*x^3)","B"
36,0,-1,79,0.000000,"\text{Not used}","int((x^3*(A + B*x))/(a + b*x^2)^(5/2),x)","\int \frac{x^3\,\left(A+B\,x\right)}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((x^3*(A + B*x))/(a + b*x^2)^(5/2), x)","F"
37,1,51,53,0.967216,"\text{Not used}","int((x^2*(A + B*x))/(a + b*x^2)^(5/2),x)","\frac{B\,a^2-3\,B\,a\,\left(b\,x^2+a\right)+A\,b\,x\,\left(b\,x^2+a\right)-A\,a\,b\,x}{3\,a\,b^2\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(B*a^2 - 3*B*a*(a + b*x^2) + A*b*x*(a + b*x^2) - A*a*b*x)/(3*a*b^2*(a + b*x^2)^(3/2))","B"
38,1,34,50,0.924396,"\text{Not used}","int((x*(A + B*x))/(a + b*x^2)^(5/2),x)","\frac{B\,x^3}{3\,a\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{A}{3\,b\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(B*x^3)/(3*a*(a + b*x^2)^(3/2)) - A/(3*b*(a + b*x^2)^(3/2))","B"
39,1,41,51,0.929024,"\text{Not used}","int((A + B*x)/(a + b*x^2)^(5/2),x)","\frac{2\,A\,b\,x\,\left(b\,x^2+a\right)-B\,a^2+A\,a\,b\,x}{3\,a^2\,b\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(2*A*b*x*(a + b*x^2) - B*a^2 + A*a*b*x)/(3*a^2*b*(a + b*x^2)^(3/2))","B"
40,1,80,76,1.375008,"\text{Not used}","int((A + B*x)/(x*(a + b*x^2)^(5/2)),x)","\frac{\frac{A}{3\,a}+\frac{A\,\left(b\,x^2+a\right)}{a^2}}{{\left(b\,x^2+a\right)}^{3/2}}+\frac{2\,B\,x\,\left(b\,x^2+a\right)+B\,a\,x}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{5/2}}","Not used",1,"(A/(3*a) + (A*(a + b*x^2))/a^2)/(a + b*x^2)^(3/2) + (2*B*x*(a + b*x^2) + B*a*x)/(3*a^2*(a + b*x^2)^(3/2)) - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(5/2)","B"
41,1,96,104,1.578588,"\text{Not used}","int((A + B*x)/(x^2*(a + b*x^2)^(5/2)),x)","\frac{\frac{B}{3\,a}+\frac{B\,\left(b\,x^2+a\right)}{a^2}}{{\left(b\,x^2+a\right)}^{3/2}}-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A\,a^2-8\,A\,{\left(b\,x^2+a\right)}^2+4\,A\,a\,\left(b\,x^2+a\right)}{3\,a^3\,x\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(B/(3*a) + (B*(a + b*x^2))/a^2)/(a + b*x^2)^(3/2) - (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(5/2) + (A*a^2 - 8*A*(a + b*x^2)^2 + 4*A*a*(a + b*x^2))/(3*a^3*x*(a + b*x^2)^(3/2))","B"
42,1,123,129,1.621212,"\text{Not used}","int((A + B*x)/(x^3*(a + b*x^2)^(5/2)),x)","\frac{B\,a^2-8\,B\,{\left(b\,x^2+a\right)}^2+4\,B\,a\,\left(b\,x^2+a\right)}{3\,a^3\,x\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{10\,A\,b}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{A}{2\,a\,x^2\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{5\,A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{7/2}}-\frac{5\,A\,b^2\,x^2}{2\,a^3\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(B*a^2 - 8*B*(a + b*x^2)^2 + 4*B*a*(a + b*x^2))/(3*a^3*x*(a + b*x^2)^(3/2)) - (10*A*b)/(3*a^2*(a + b*x^2)^(3/2)) - A/(2*a*x^2*(a + b*x^2)^(3/2)) + (5*A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(7/2)) - (5*A*b^2*x^2)/(2*a^3*(a + b*x^2)^(3/2))","B"
43,1,20,27,0.040070,"\text{Not used}","int(-(x*(x - 1))/(1 - x^2)^(1/2),x)","\left(\frac{x}{2}-1\right)\,\sqrt{1-x^2}-\frac{\mathrm{asin}\left(x\right)}{2}","Not used",1,"(x/2 - 1)*(1 - x^2)^(1/2) - asin(x)/2","B"
44,1,20,27,0.033059,"\text{Not used}","int((x - x^2)/(1 - x^2)^(1/2),x)","\left(\frac{x}{2}-1\right)\,\sqrt{1-x^2}-\frac{\mathrm{asin}\left(x\right)}{2}","Not used",1,"(x/2 - 1)*(1 - x^2)^(1/2) - asin(x)/2","B"
45,1,14,17,0.918787,"\text{Not used}","int((x^2 + 3)/(x^2 - 3),x)","x-2\,\sqrt{3}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,x}{3}\right)","Not used",1,"x - 2*3^(1/2)*atanh((3^(1/2)*x)/3)","B"
46,1,6,6,0.039374,"\text{Not used}","int((x^2 - 1)/(x^2 + 1),x)","x-2\,\mathrm{atan}\left(x\right)","Not used",1,"x - 2*atan(x)","B"
47,0,-1,213,0.000000,"\text{Not used}","int((x^7*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\int \frac{x^7\,\left(C\,x^2+B\,x+A\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^7*(A + B*x + C*x^2))/(a + b*x^2)^(9/2), x)","F"
48,0,-1,150,0.000000,"\text{Not used}","int((x^6*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\int \frac{x^6\,\left(C\,x^2+B\,x+A\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^6*(A + B*x + C*x^2))/(a + b*x^2)^(9/2), x)","F"
49,1,196,132,1.273696,"\text{Not used}","int((x^5*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\frac{\frac{a\,\left(\frac{C}{3\,b^3}-\frac{7\,A\,b-14\,C\,a}{21\,a\,b^3}\right)}{b}-\frac{3\,B\,x}{7\,b^3}}{{\left(b\,x^2+a\right)}^{3/2}}-\frac{\frac{a^2\,\left(\frac{A}{7\,b}-\frac{C\,a}{7\,b^2}\right)}{b^2}+\frac{B\,a^2\,x}{7\,b^3}}{{\left(b\,x^2+a\right)}^{7/2}}-\frac{\frac{C}{b^4}-\frac{B\,x}{7\,a\,b^3}}{\sqrt{b\,x^2+a}}-\frac{\frac{a\,\left(\frac{7\,C\,a^2-7\,A\,a\,b}{35\,a\,b^3}+\frac{a\,\left(\frac{C}{5\,b^2}-\frac{7\,A\,b^2-7\,C\,a\,b}{35\,a\,b^3}\right)}{b}\right)}{b}-\frac{3\,B\,a\,x}{7\,b^3}}{{\left(b\,x^2+a\right)}^{5/2}}","Not used",1,"((a*(C/(3*b^3) - (7*A*b - 14*C*a)/(21*a*b^3)))/b - (3*B*x)/(7*b^3))/(a + b*x^2)^(3/2) - ((a^2*(A/(7*b) - (C*a)/(7*b^2)))/b^2 + (B*a^2*x)/(7*b^3))/(a + b*x^2)^(7/2) - (C/b^4 - (B*x)/(7*a*b^3))/(a + b*x^2)^(1/2) - ((a*((7*C*a^2 - 7*A*a*b)/(35*a*b^3) + (a*(C/(5*b^2) - (7*A*b^2 - 7*C*a*b)/(35*a*b^3)))/b))/b - (3*B*a*x)/(7*b^3))/(a + b*x^2)^(5/2)","B"
50,1,186,149,1.192266,"\text{Not used}","int((x^4*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\frac{x\,\left(\frac{C\,a^2-A\,a\,b}{35\,a\,b^3}+\frac{a\,\left(\frac{C}{5\,b^2}-\frac{7\,A\,b^2-7\,C\,a\,b}{35\,a\,b^3}\right)}{b}\right)+\frac{2\,B\,a}{5\,b^3}}{{\left(b\,x^2+a\right)}^{5/2}}-\frac{\frac{B}{3\,b^3}+x\,\left(\frac{C}{3\,b^3}-\frac{3\,A\,b-10\,C\,a}{105\,a\,b^3}\right)}{{\left(b\,x^2+a\right)}^{3/2}}-\frac{\frac{B\,a^2}{7\,b^3}-\frac{a\,x\,\left(\frac{A}{7\,b}-\frac{C\,a}{7\,b^2}\right)}{b}}{{\left(b\,x^2+a\right)}^{7/2}}+\frac{x\,\left(2\,A\,b+5\,C\,a\right)}{35\,a^2\,b^3\,\sqrt{b\,x^2+a}}","Not used",1,"(x*((C*a^2 - A*a*b)/(35*a*b^3) + (a*(C/(5*b^2) - (7*A*b^2 - 7*C*a*b)/(35*a*b^3)))/b) + (2*B*a)/(5*b^3))/(a + b*x^2)^(5/2) - (B/(3*b^3) + x*(C/(3*b^3) - (3*A*b - 10*C*a)/(105*a*b^3)))/(a + b*x^2)^(3/2) - ((B*a^2)/(7*b^3) - (a*x*(A/(7*b) - (C*a)/(7*b^2)))/b)/(a + b*x^2)^(7/2) + (x*(2*A*b + 5*C*a))/(35*a^2*b^3*(a + b*x^2)^(1/2))","B"
51,1,133,139,1.138133,"\text{Not used}","int((x^3*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\frac{\frac{a\,\left(\frac{A}{7\,b}-\frac{C\,a}{7\,b^2}\right)}{b}+\frac{B\,a\,x}{7\,b^2}}{{\left(b\,x^2+a\right)}^{7/2}}-\frac{\frac{C}{3\,b^3}-\frac{B\,x}{35\,a\,b^2}}{{\left(b\,x^2+a\right)}^{3/2}}+\frac{\frac{a\,\left(\frac{C}{5\,b^2}-\frac{7\,A\,b-7\,C\,a}{35\,a\,b^2}\right)}{b}-\frac{8\,B\,x}{35\,b^2}}{{\left(b\,x^2+a\right)}^{5/2}}+\frac{2\,B\,x}{35\,a^2\,b^2\,\sqrt{b\,x^2+a}}","Not used",1,"((a*(A/(7*b) - (C*a)/(7*b^2)))/b + (B*a*x)/(7*b^2))/(a + b*x^2)^(7/2) - (C/(3*b^3) - (B*x)/(35*a*b^2))/(a + b*x^2)^(3/2) + ((a*(C/(5*b^2) - (7*A*b - 7*C*a)/(35*a*b^2)))/b - (8*B*x)/(35*b^2))/(a + b*x^2)^(5/2) + (2*B*x)/(35*a^2*b^2*(a + b*x^2)^(1/2))","B"
52,1,133,139,1.093995,"\text{Not used}","int((x^2*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\frac{x\,\left(4\,A\,b+3\,C\,a\right)}{105\,a^2\,b^2\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{\frac{B}{5\,b^2}+x\,\left(\frac{C}{5\,b^2}-\frac{A\,b-C\,a}{35\,a\,b^2}\right)}{{\left(b\,x^2+a\right)}^{5/2}}-\frac{x\,\left(\frac{A}{7\,b}-\frac{C\,a}{7\,b^2}\right)-\frac{B\,a}{7\,b^2}}{{\left(b\,x^2+a\right)}^{7/2}}+\frac{x\,\left(8\,A\,b+6\,C\,a\right)}{105\,a^3\,b^2\,\sqrt{b\,x^2+a}}","Not used",1,"(x*(4*A*b + 3*C*a))/(105*a^2*b^2*(a + b*x^2)^(3/2)) - (B/(5*b^2) + x*(C/(5*b^2) - (A*b - C*a)/(35*a*b^2)))/(a + b*x^2)^(5/2) - (x*(A/(7*b) - (C*a)/(7*b^2)) - (B*a)/(7*b^2))/(a + b*x^2)^(7/2) + (x*(8*A*b + 6*C*a))/(105*a^3*b^2*(a + b*x^2)^(1/2))","B"
53,1,99,119,1.048936,"\text{Not used}","int((x*(A + B*x + C*x^2))/(a + b*x^2)^(9/2),x)","\frac{8\,B\,x}{105\,a^3\,b\,\sqrt{b\,x^2+a}}-\frac{\frac{A}{7\,b}-\frac{C\,a}{7\,b^2}+\frac{B\,x}{7\,b}}{{\left(b\,x^2+a\right)}^{7/2}}-\frac{\frac{C}{5\,b^2}-\frac{B\,x}{35\,a\,b}}{{\left(b\,x^2+a\right)}^{5/2}}+\frac{4\,B\,x}{105\,a^2\,b\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(8*B*x)/(105*a^3*b*(a + b*x^2)^(1/2)) - (A/(7*b) - (C*a)/(7*b^2) + (B*x)/(7*b))/(a + b*x^2)^(7/2) - (C/(5*b^2) - (B*x)/(35*a*b))/(a + b*x^2)^(5/2) + (4*B*x)/(105*a^2*b*(a + b*x^2)^(3/2))","B"
54,1,115,127,1.033020,"\text{Not used}","int((A + B*x + C*x^2)/(a + b*x^2)^(9/2),x)","\frac{x\,\left(6\,A\,b+C\,a\right)}{35\,a^2\,b\,{\left(b\,x^2+a\right)}^{5/2}}-\frac{\frac{B}{7\,b}-x\,\left(\frac{A}{7\,a}-\frac{C}{7\,b}\right)}{{\left(b\,x^2+a\right)}^{7/2}}+\frac{x\,\left(24\,A\,b+4\,C\,a\right)}{105\,a^3\,b\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{x\,\left(48\,A\,b+8\,C\,a\right)}{105\,a^4\,b\,\sqrt{b\,x^2+a}}","Not used",1,"(x*(6*A*b + C*a))/(35*a^2*b*(a + b*x^2)^(5/2)) - (B/(7*b) - x*(A/(7*a) - C/(7*b)))/(a + b*x^2)^(7/2) + (x*(24*A*b + 4*C*a))/(105*a^3*b*(a + b*x^2)^(3/2)) + (x*(48*A*b + 8*C*a))/(105*a^4*b*(a + b*x^2)^(1/2))","B"
55,1,159,138,1.620222,"\text{Not used}","int((A + B*x + C*x^2)/(x*(a + b*x^2)^(9/2)),x)","\frac{\frac{A}{7\,a}+\frac{A\,{\left(b\,x^2+a\right)}^2}{3\,a^3}+\frac{A\,{\left(b\,x^2+a\right)}^3}{a^4}+\frac{A\,\left(b\,x^2+a\right)}{5\,a^2}}{{\left(b\,x^2+a\right)}^{7/2}}-\frac{C}{7\,b\,{\left(b\,x^2+a\right)}^{7/2}}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{16\,B\,x}{35\,a^4\,\sqrt{b\,x^2+a}}+\frac{8\,B\,x}{35\,a^3\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{6\,B\,x}{35\,a^2\,{\left(b\,x^2+a\right)}^{5/2}}+\frac{B\,x}{7\,a\,{\left(b\,x^2+a\right)}^{7/2}}","Not used",1,"(A/(7*a) + (A*(a + b*x^2)^2)/(3*a^3) + (A*(a + b*x^2)^3)/a^4 + (A*(a + b*x^2))/(5*a^2))/(a + b*x^2)^(7/2) - C/(7*b*(a + b*x^2)^(7/2)) - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(9/2) + (16*B*x)/(35*a^4*(a + b*x^2)^(1/2)) + (8*B*x)/(35*a^3*(a + b*x^2)^(3/2)) + (6*B*x)/(35*a^2*(a + b*x^2)^(5/2)) + (B*x)/(7*a*(a + b*x^2)^(7/2))","B"
56,1,225,188,2.095496,"\text{Not used}","int((A + B*x + C*x^2)/(x^2*(a + b*x^2)^(9/2)),x)","\frac{\frac{B}{7\,a}+\frac{B\,{\left(b\,x^2+a\right)}^2}{3\,a^3}+\frac{B\,{\left(b\,x^2+a\right)}^3}{a^4}+\frac{B\,\left(b\,x^2+a\right)}{5\,a^2}}{{\left(b\,x^2+a\right)}^{7/2}}-\frac{\frac{A}{a^4}+\frac{128\,A\,b\,x^2}{35\,a^5}}{x\,\sqrt{b\,x^2+a}}-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{16\,C\,x}{35\,a^4\,\sqrt{b\,x^2+a}}+\frac{8\,C\,x}{35\,a^3\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{6\,C\,x}{35\,a^2\,{\left(b\,x^2+a\right)}^{5/2}}+\frac{C\,x}{7\,a\,{\left(b\,x^2+a\right)}^{7/2}}-\frac{29\,A\,b\,x}{35\,a^4\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{13\,A\,b\,x}{35\,a^3\,{\left(b\,x^2+a\right)}^{5/2}}-\frac{A\,b\,x}{7\,a^2\,{\left(b\,x^2+a\right)}^{7/2}}","Not used",1,"(B/(7*a) + (B*(a + b*x^2)^2)/(3*a^3) + (B*(a + b*x^2)^3)/a^4 + (B*(a + b*x^2))/(5*a^2))/(a + b*x^2)^(7/2) - (A/a^4 + (128*A*b*x^2)/(35*a^5))/(x*(a + b*x^2)^(1/2)) - (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(9/2) + (16*C*x)/(35*a^4*(a + b*x^2)^(1/2)) + (8*C*x)/(35*a^3*(a + b*x^2)^(3/2)) + (6*C*x)/(35*a^2*(a + b*x^2)^(5/2)) + (C*x)/(7*a*(a + b*x^2)^(7/2)) - (29*A*b*x)/(35*a^4*(a + b*x^2)^(3/2)) - (13*A*b*x)/(35*a^3*(a + b*x^2)^(5/2)) - (A*b*x)/(7*a^2*(a + b*x^2)^(7/2))","B"
57,1,279,219,2.517781,"\text{Not used}","int((A + B*x + C*x^2)/(x^3*(a + b*x^2)^(9/2)),x)","\frac{\frac{C}{7\,a}+\frac{C\,{\left(b\,x^2+a\right)}^2}{3\,a^3}+\frac{C\,{\left(b\,x^2+a\right)}^3}{a^4}+\frac{C\,\left(b\,x^2+a\right)}{5\,a^2}}{{\left(b\,x^2+a\right)}^{7/2}}-\frac{\frac{A\,b}{7\,a}+\frac{9\,A\,b\,\left(b\,x^2+a\right)}{35\,a^2}+\frac{3\,A\,b\,{\left(b\,x^2+a\right)}^2}{5\,a^3}+\frac{3\,A\,b\,{\left(b\,x^2+a\right)}^3}{a^4}-\frac{9\,A\,b\,{\left(b\,x^2+a\right)}^4}{2\,a^5}}{a\,{\left(b\,x^2+a\right)}^{7/2}-{\left(b\,x^2+a\right)}^{9/2}}-\frac{\frac{B}{a^4}+\frac{128\,B\,b\,x^2}{35\,a^5}}{x\,\sqrt{b\,x^2+a}}-\frac{C\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{9\,A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{11/2}}-\frac{29\,B\,b\,x}{35\,a^4\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{13\,B\,b\,x}{35\,a^3\,{\left(b\,x^2+a\right)}^{5/2}}-\frac{B\,b\,x}{7\,a^2\,{\left(b\,x^2+a\right)}^{7/2}}","Not used",1,"(C/(7*a) + (C*(a + b*x^2)^2)/(3*a^3) + (C*(a + b*x^2)^3)/a^4 + (C*(a + b*x^2))/(5*a^2))/(a + b*x^2)^(7/2) - ((A*b)/(7*a) + (9*A*b*(a + b*x^2))/(35*a^2) + (3*A*b*(a + b*x^2)^2)/(5*a^3) + (3*A*b*(a + b*x^2)^3)/a^4 - (9*A*b*(a + b*x^2)^4)/(2*a^5))/(a*(a + b*x^2)^(7/2) - (a + b*x^2)^(9/2)) - (B/a^4 + (128*B*b*x^2)/(35*a^5))/(x*(a + b*x^2)^(1/2)) - (C*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(9/2) + (9*A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(11/2)) - (29*B*b*x)/(35*a^4*(a + b*x^2)^(3/2)) - (13*B*b*x)/(35*a^3*(a + b*x^2)^(5/2)) - (B*b*x)/(7*a^2*(a + b*x^2)^(7/2))","B"
58,0,-1,45,0.000000,"\text{Not used}","int((A*(c*x)^m)/(a + b*x^2),x)","\int \frac{A\,{\left(c\,x\right)}^m}{b\,x^2+a} \,d x","Not used",1,"int((A*(c*x)^m)/(a + b*x^2), x)","F"
59,0,-1,91,0.000000,"\text{Not used}","int(((c*x)^m*(A + B*x))/(a + b*x^2),x)","\int \frac{{\left(c\,x\right)}^m\,\left(A+B\,x\right)}{b\,x^2+a} \,d x","Not used",1,"int(((c*x)^m*(A + B*x))/(a + b*x^2), x)","F"
60,0,-1,76,0.000000,"\text{Not used}","int(((A + C*x^2)*(c*x)^m)/(a + b*x^2),x)","\int \frac{\left(C\,x^2+A\right)\,{\left(c\,x\right)}^m}{b\,x^2+a} \,d x","Not used",1,"int(((A + C*x^2)*(c*x)^m)/(a + b*x^2), x)","F"
61,0,-1,121,0.000000,"\text{Not used}","int(((c*x)^m*(A + B*x + C*x^2))/(a + b*x^2),x)","\int \frac{{\left(c\,x\right)}^m\,\left(C\,x^2+B\,x+A\right)}{b\,x^2+a} \,d x","Not used",1,"int(((c*x)^m*(A + B*x + C*x^2))/(a + b*x^2), x)","F"
62,1,57,65,1.204765,"\text{Not used}","int(x^3*(a + b*x^2)*(A + B*x + C*x^2 + x^3*D),x)","\frac{a\,x^7\,D}{7}+\frac{b\,x^9\,D}{9}+\frac{A\,a\,x^4}{4}+\frac{B\,a\,x^5}{5}+\frac{A\,b\,x^6}{6}+\frac{C\,a\,x^6}{6}+\frac{B\,b\,x^7}{7}+\frac{C\,b\,x^8}{8}","Not used",1,"(a*x^7*D)/7 + (b*x^9*D)/9 + (A*a*x^4)/4 + (B*a*x^5)/5 + (A*b*x^6)/6 + (C*a*x^6)/6 + (B*b*x^7)/7 + (C*b*x^8)/8","B"
63,1,57,65,1.184453,"\text{Not used}","int(x^2*(a + b*x^2)*(A + B*x + C*x^2 + x^3*D),x)","\frac{a\,x^6\,D}{6}+\frac{b\,x^8\,D}{8}+\frac{A\,a\,x^3}{3}+\frac{B\,a\,x^4}{4}+\frac{A\,b\,x^5}{5}+\frac{C\,a\,x^5}{5}+\frac{B\,b\,x^6}{6}+\frac{C\,b\,x^7}{7}","Not used",1,"(a*x^6*D)/6 + (b*x^8*D)/8 + (A*a*x^3)/3 + (B*a*x^4)/4 + (A*b*x^5)/5 + (C*a*x^5)/5 + (B*b*x^6)/6 + (C*b*x^7)/7","B"
64,1,57,65,1.185139,"\text{Not used}","int(x*(a + b*x^2)*(A + B*x + C*x^2 + x^3*D),x)","\frac{a\,x^5\,D}{5}+\frac{b\,x^7\,D}{7}+\frac{A\,a\,x^2}{2}+\frac{B\,a\,x^3}{3}+\frac{A\,b\,x^4}{4}+\frac{C\,a\,x^4}{4}+\frac{B\,b\,x^5}{5}+\frac{C\,b\,x^6}{6}","Not used",1,"(a*x^5*D)/5 + (b*x^7*D)/7 + (A*a*x^2)/2 + (B*a*x^3)/3 + (A*b*x^4)/4 + (C*a*x^4)/4 + (B*b*x^5)/5 + (C*b*x^6)/6","B"
65,1,54,60,1.164405,"\text{Not used}","int((a + b*x^2)*(A + B*x + C*x^2 + x^3*D),x)","\frac{a\,x^4\,D}{4}+\frac{b\,x^6\,D}{6}+A\,a\,x+\frac{B\,a\,x^2}{2}+\frac{A\,b\,x^3}{3}+\frac{C\,a\,x^3}{3}+\frac{B\,b\,x^4}{4}+\frac{C\,b\,x^5}{5}","Not used",1,"(a*x^4*D)/4 + (b*x^6*D)/6 + A*a*x + (B*a*x^2)/2 + (A*b*x^3)/3 + (C*a*x^3)/3 + (B*b*x^4)/4 + (C*b*x^5)/5","B"
66,1,52,56,1.169909,"\text{Not used}","int(((a + b*x^2)*(A + B*x + C*x^2 + x^3*D))/x,x)","\frac{a\,x^3\,D}{3}+\frac{b\,x^5\,D}{5}+B\,a\,x+\frac{A\,b\,x^2}{2}+\frac{C\,a\,x^2}{2}+\frac{B\,b\,x^3}{3}+\frac{C\,b\,x^4}{4}+A\,a\,\ln\left(x\right)","Not used",1,"(a*x^3*D)/3 + (b*x^5*D)/5 + B*a*x + (A*b*x^2)/2 + (C*a*x^2)/2 + (B*b*x^3)/3 + (C*b*x^4)/4 + A*a*log(x)","B"
67,1,49,54,1.144839,"\text{Not used}","int(((a + b*x^2)*(A + B*x + C*x^2 + x^3*D))/x^2,x)","\frac{a\,x^2\,D}{2}+\frac{b\,x^4\,D}{4}+A\,b\,x+C\,a\,x-\frac{A\,a}{x}+\frac{B\,b\,x^2}{2}+\frac{C\,b\,x^3}{3}+B\,a\,\ln\left(x\right)","Not used",1,"(a*x^2*D)/2 + (b*x^4*D)/4 + A*b*x + C*a*x - (A*a)/x + (B*b*x^2)/2 + (C*b*x^3)/3 + B*a*log(x)","B"
68,1,47,54,1.138005,"\text{Not used}","int(((a + b*x^2)*(A + B*x + C*x^2 + x^3*D))/x^3,x)","\frac{b\,x^3\,D}{3}+B\,b\,x-\frac{A\,a}{2\,x^2}-\frac{B\,a}{x}+\frac{C\,b\,x^2}{2}+A\,b\,\ln\left(x\right)+C\,a\,\ln\left(x\right)+a\,x\,D","Not used",1,"(b*x^3*D)/3 + B*b*x - (A*a)/(2*x^2) - (B*a)/x + (C*b*x^2)/2 + A*b*log(x) + C*a*log(x) + a*x*D","B"
69,1,50,54,1.148086,"\text{Not used}","int(((a + b*x^2)*(A + B*x + C*x^2 + x^3*D))/x^4,x)","\frac{b\,x^2\,D}{2}+a\,\ln\left(x\right)\,D+C\,b\,x-\frac{A\,a}{3\,x^3}-\frac{A\,b}{x}-\frac{B\,a}{2\,x^2}-\frac{C\,a}{x}+B\,b\,\ln\left(x\right)","Not used",1,"(b*x^2*D)/2 + a*log(x)*D + C*b*x - (A*a)/(3*x^3) - (A*b)/x - (B*a)/(2*x^2) - (C*a)/x + B*b*log(x)","B"
70,1,108,109,1.130409,"\text{Not used}","int(x^3*(a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D),x)","\frac{a^2\,x^7\,D}{7}+\frac{b^2\,x^{11}\,D}{11}+\frac{A\,x^4\,\left(6\,a^2+8\,a\,b\,x^2+3\,b^2\,x^4\right)}{24}+\frac{B\,x^5\,\left(63\,a^2+90\,a\,b\,x^2+35\,b^2\,x^4\right)}{315}+\frac{C\,x^6\,\left(10\,a^2+15\,a\,b\,x^2+6\,b^2\,x^4\right)}{60}+\frac{2\,a\,b\,x^9\,D}{9}","Not used",1,"(a^2*x^7*D)/7 + (b^2*x^11*D)/11 + (A*x^4*(6*a^2 + 3*b^2*x^4 + 8*a*b*x^2))/24 + (B*x^5*(63*a^2 + 35*b^2*x^4 + 90*a*b*x^2))/315 + (C*x^6*(10*a^2 + 6*b^2*x^4 + 15*a*b*x^2))/60 + (2*a*b*x^9*D)/9","B"
71,1,108,109,1.110586,"\text{Not used}","int(x^2*(a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D),x)","\frac{a^2\,x^6\,D}{6}+\frac{b^2\,x^{10}\,D}{10}+\frac{A\,x^3\,\left(35\,a^2+42\,a\,b\,x^2+15\,b^2\,x^4\right)}{105}+\frac{B\,x^4\,\left(6\,a^2+8\,a\,b\,x^2+3\,b^2\,x^4\right)}{24}+\frac{C\,x^5\,\left(63\,a^2+90\,a\,b\,x^2+35\,b^2\,x^4\right)}{315}+\frac{a\,b\,x^8\,D}{4}","Not used",1,"(a^2*x^6*D)/6 + (b^2*x^10*D)/10 + (A*x^3*(35*a^2 + 15*b^2*x^4 + 42*a*b*x^2))/105 + (B*x^4*(6*a^2 + 3*b^2*x^4 + 8*a*b*x^2))/24 + (C*x^5*(63*a^2 + 35*b^2*x^4 + 90*a*b*x^2))/315 + (a*b*x^8*D)/4","B"
72,1,107,104,1.110747,"\text{Not used}","int(x*(a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D),x)","\frac{a^2\,x^5\,D}{5}+\frac{b^2\,x^9\,D}{9}+\frac{A\,x^2\,\left(3\,a^2+3\,a\,b\,x^2+b^2\,x^4\right)}{6}+\frac{B\,x^3\,\left(35\,a^2+42\,a\,b\,x^2+15\,b^2\,x^4\right)}{105}+\frac{C\,x^4\,\left(6\,a^2+8\,a\,b\,x^2+3\,b^2\,x^4\right)}{24}+\frac{2\,a\,b\,x^7\,D}{7}","Not used",1,"(a^2*x^5*D)/5 + (b^2*x^9*D)/9 + (A*x^2*(3*a^2 + b^2*x^4 + 3*a*b*x^2))/6 + (B*x^3*(35*a^2 + 15*b^2*x^4 + 42*a*b*x^2))/105 + (C*x^4*(6*a^2 + 3*b^2*x^4 + 8*a*b*x^2))/24 + (2*a*b*x^7*D)/7","B"
73,1,105,99,1.105884,"\text{Not used}","int((a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D),x)","\frac{A\,x\,\left(15\,a^2+10\,a\,b\,x^2+3\,b^2\,x^4\right)}{15}+\frac{a^2\,x^4\,D}{4}+\frac{b^2\,x^8\,D}{8}+\frac{B\,x^2\,\left(3\,a^2+3\,a\,b\,x^2+b^2\,x^4\right)}{6}+\frac{C\,x^3\,\left(35\,a^2+42\,a\,b\,x^2+15\,b^2\,x^4\right)}{105}+\frac{a\,b\,x^6\,D}{3}","Not used",1,"(A*x*(15*a^2 + 3*b^2*x^4 + 10*a*b*x^2))/15 + (a^2*x^4*D)/4 + (b^2*x^8*D)/8 + (B*x^2*(3*a^2 + b^2*x^4 + 3*a*b*x^2))/6 + (C*x^3*(35*a^2 + 15*b^2*x^4 + 42*a*b*x^2))/105 + (a*b*x^6*D)/3","B"
74,1,103,92,1.105924,"\text{Not used}","int(((a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D))/x,x)","\frac{A\,\left(4\,a^2\,\ln\left(x\right)+b^2\,x^4+4\,a\,b\,x^2\right)}{4}+\frac{B\,x\,\left(15\,a^2+10\,a\,b\,x^2+3\,b^2\,x^4\right)}{15}+\frac{a^2\,x^3\,D}{3}+\frac{b^2\,x^7\,D}{7}+\frac{C\,x^2\,\left(3\,a^2+3\,a\,b\,x^2+b^2\,x^4\right)}{6}+\frac{2\,a\,b\,x^5\,D}{5}","Not used",1,"(A*(4*a^2*log(x) + b^2*x^4 + 4*a*b*x^2))/4 + (B*x*(15*a^2 + 3*b^2*x^4 + 10*a*b*x^2))/15 + (a^2*x^3*D)/3 + (b^2*x^7*D)/7 + (C*x^2*(3*a^2 + b^2*x^4 + 3*a*b*x^2))/6 + (2*a*b*x^5*D)/5","B"
75,1,92,90,1.106512,"\text{Not used}","int(((a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D))/x^2,x)","\frac{B\,\left(4\,a^2\,\ln\left(x\right)+b^2\,x^4+4\,a\,b\,x^2\right)}{4}+\frac{{\left(b\,x^2+a\right)}^3\,D}{6\,b}+\frac{C\,x\,\left(15\,a^2+10\,a\,b\,x^2+3\,b^2\,x^4\right)}{15}+\frac{A\,\left(-3\,a^2+6\,a\,b\,x^2+b^2\,x^4\right)}{3\,x}","Not used",1,"(B*(4*a^2*log(x) + b^2*x^4 + 4*a*b*x^2))/4 + ((a + b*x^2)^3*D)/(6*b) + (C*x*(15*a^2 + 3*b^2*x^4 + 10*a*b*x^2))/15 + (A*(b^2*x^4 - 3*a^2 + 6*a*b*x^2))/(3*x)","B"
76,1,103,98,1.105779,"\text{Not used}","int(((a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D))/x^3,x)","\frac{C\,\left(4\,a^2\,\ln\left(x\right)+b^2\,x^4+4\,a\,b\,x^2\right)}{4}+a^2\,x\,D+\frac{b^2\,x^5\,D}{5}+\frac{A\,\left(b^2\,x^4-a^2+4\,a\,b\,x^2\,\ln\left(x\right)\right)}{2\,x^2}+\frac{B\,\left(-3\,a^2+6\,a\,b\,x^2+b^2\,x^4\right)}{3\,x}+\frac{2\,a\,b\,x^3\,D}{3}","Not used",1,"(C*(4*a^2*log(x) + b^2*x^4 + 4*a*b*x^2))/4 + a^2*x*D + (b^2*x^5*D)/5 + (A*(b^2*x^4 - a^2 + 4*a*b*x^2*log(x)))/(2*x^2) + (B*(b^2*x^4 - 3*a^2 + 6*a*b*x^2))/(3*x) + (2*a*b*x^3*D)/3","B"
77,1,106,98,1.275111,"\text{Not used}","int(((a + b*x^2)^2*(A + B*x + C*x^2 + x^3*D))/x^4,x)","\frac{b^2\,x^4\,D}{4}+\frac{a^2\,\ln\left(x^2\right)\,D}{2}-\frac{A\,\left(a^2+6\,a\,b\,x^2-3\,b^2\,x^4\right)}{3\,x^3}+\frac{B\,\left(b^2\,x^4-a^2+4\,a\,b\,x^2\,\ln\left(x\right)\right)}{2\,x^2}+\frac{C\,\left(-3\,a^2+6\,a\,b\,x^2+b^2\,x^4\right)}{3\,x}+a\,b\,x^2\,D","Not used",1,"(b^2*x^4*D)/4 + (a^2*log(x^2)*D)/2 - (A*(a^2 - 3*b^2*x^4 + 6*a*b*x^2))/(3*x^3) + (B*(b^2*x^4 - a^2 + 4*a*b*x^2*log(x)))/(2*x^2) + (C*(b^2*x^4 - 3*a^2 + 6*a*b*x^2))/(3*x) + a*b*x^2*D","B"
78,1,153,149,1.299459,"\text{Not used}","int(x^3*(a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D),x)","\frac{A\,a^3\,x^4}{4}+\frac{B\,a^3\,x^5}{5}+\frac{A\,b^3\,x^{10}}{10}+\frac{C\,a^3\,x^6}{6}+\frac{B\,b^3\,x^{11}}{11}+\frac{C\,b^3\,x^{12}}{12}+\frac{a^3\,x^7\,D}{7}+\frac{b^3\,x^{13}\,D}{13}+\frac{a^2\,b\,x^9\,D}{3}+\frac{3\,a\,b^2\,x^{11}\,D}{11}+\frac{A\,a^2\,b\,x^6}{2}+\frac{3\,A\,a\,b^2\,x^8}{8}+\frac{3\,B\,a^2\,b\,x^7}{7}+\frac{B\,a\,b^2\,x^9}{3}+\frac{3\,C\,a^2\,b\,x^8}{8}+\frac{3\,C\,a\,b^2\,x^{10}}{10}","Not used",1,"(A*a^3*x^4)/4 + (B*a^3*x^5)/5 + (A*b^3*x^10)/10 + (C*a^3*x^6)/6 + (B*b^3*x^11)/11 + (C*b^3*x^12)/12 + (a^3*x^7*D)/7 + (b^3*x^13*D)/13 + (a^2*b*x^9*D)/3 + (3*a*b^2*x^11*D)/11 + (A*a^2*b*x^6)/2 + (3*A*a*b^2*x^8)/8 + (3*B*a^2*b*x^7)/7 + (B*a*b^2*x^9)/3 + (3*C*a^2*b*x^8)/8 + (3*C*a*b^2*x^10)/10","B"
79,1,153,149,1.275280,"\text{Not used}","int(x^2*(a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D),x)","\frac{A\,a^3\,x^3}{3}+\frac{B\,a^3\,x^4}{4}+\frac{A\,b^3\,x^9}{9}+\frac{C\,a^3\,x^5}{5}+\frac{B\,b^3\,x^{10}}{10}+\frac{C\,b^3\,x^{11}}{11}+\frac{a^3\,x^6\,D}{6}+\frac{b^3\,x^{12}\,D}{12}+\frac{3\,a^2\,b\,x^8\,D}{8}+\frac{3\,a\,b^2\,x^{10}\,D}{10}+\frac{3\,A\,a^2\,b\,x^5}{5}+\frac{3\,A\,a\,b^2\,x^7}{7}+\frac{B\,a^2\,b\,x^6}{2}+\frac{3\,B\,a\,b^2\,x^8}{8}+\frac{3\,C\,a^2\,b\,x^7}{7}+\frac{C\,a\,b^2\,x^9}{3}","Not used",1,"(A*a^3*x^3)/3 + (B*a^3*x^4)/4 + (A*b^3*x^9)/9 + (C*a^3*x^5)/5 + (B*b^3*x^10)/10 + (C*b^3*x^11)/11 + (a^3*x^6*D)/6 + (b^3*x^12*D)/12 + (3*a^2*b*x^8*D)/8 + (3*a*b^2*x^10*D)/10 + (3*A*a^2*b*x^5)/5 + (3*A*a*b^2*x^7)/7 + (B*a^2*b*x^6)/2 + (3*B*a*b^2*x^8)/8 + (3*C*a^2*b*x^7)/7 + (C*a*b^2*x^9)/3","B"
80,1,153,138,1.278326,"\text{Not used}","int(x*(a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D),x)","\frac{A\,a^3\,x^2}{2}+\frac{B\,a^3\,x^3}{3}+\frac{A\,b^3\,x^8}{8}+\frac{C\,a^3\,x^4}{4}+\frac{B\,b^3\,x^9}{9}+\frac{C\,b^3\,x^{10}}{10}+\frac{a^3\,x^5\,D}{5}+\frac{b^3\,x^{11}\,D}{11}+\frac{3\,a^2\,b\,x^7\,D}{7}+\frac{a\,b^2\,x^9\,D}{3}+\frac{3\,A\,a^2\,b\,x^4}{4}+\frac{A\,a\,b^2\,x^6}{2}+\frac{3\,B\,a^2\,b\,x^5}{5}+\frac{3\,B\,a\,b^2\,x^7}{7}+\frac{C\,a^2\,b\,x^6}{2}+\frac{3\,C\,a\,b^2\,x^8}{8}","Not used",1,"(A*a^3*x^2)/2 + (B*a^3*x^3)/3 + (A*b^3*x^8)/8 + (C*a^3*x^4)/4 + (B*b^3*x^9)/9 + (C*b^3*x^10)/10 + (a^3*x^5*D)/5 + (b^3*x^11*D)/11 + (3*a^2*b*x^7*D)/7 + (a*b^2*x^9*D)/3 + (3*A*a^2*b*x^4)/4 + (A*a*b^2*x^6)/2 + (3*B*a^2*b*x^5)/5 + (3*B*a*b^2*x^7)/7 + (C*a^2*b*x^6)/2 + (3*C*a*b^2*x^8)/8","B"
81,1,149,133,1.258884,"\text{Not used}","int((a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D),x)","\frac{B\,a^3\,x^2}{2}+\frac{A\,b^3\,x^7}{7}+\frac{C\,a^3\,x^3}{3}+\frac{B\,b^3\,x^8}{8}+\frac{C\,b^3\,x^9}{9}+\frac{a^3\,x^4\,D}{4}+\frac{b^3\,x^{10}\,D}{10}+A\,a^3\,x+\frac{a^2\,b\,x^6\,D}{2}+\frac{3\,a\,b^2\,x^8\,D}{8}+A\,a^2\,b\,x^3+\frac{3\,A\,a\,b^2\,x^5}{5}+\frac{3\,B\,a^2\,b\,x^4}{4}+\frac{B\,a\,b^2\,x^6}{2}+\frac{3\,C\,a^2\,b\,x^5}{5}+\frac{3\,C\,a\,b^2\,x^7}{7}","Not used",1,"(B*a^3*x^2)/2 + (A*b^3*x^7)/7 + (C*a^3*x^3)/3 + (B*b^3*x^8)/8 + (C*b^3*x^9)/9 + (a^3*x^4*D)/4 + (b^3*x^10*D)/10 + A*a^3*x + (a^2*b*x^6*D)/2 + (3*a*b^2*x^8*D)/8 + A*a^2*b*x^3 + (3*A*a*b^2*x^5)/5 + (3*B*a^2*b*x^4)/4 + (B*a*b^2*x^6)/2 + (3*C*a^2*b*x^5)/5 + (3*C*a*b^2*x^7)/7","B"
82,1,147,129,1.263837,"\text{Not used}","int(((a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D))/x,x)","\frac{A\,b^3\,x^6}{6}+\frac{C\,a^3\,x^2}{2}+\frac{B\,b^3\,x^7}{7}+\frac{C\,b^3\,x^8}{8}+A\,a^3\,\ln\left(x\right)+\frac{a^3\,x^3\,D}{3}+\frac{b^3\,x^9\,D}{9}+B\,a^3\,x+\frac{3\,a^2\,b\,x^5\,D}{5}+\frac{3\,a\,b^2\,x^7\,D}{7}+\frac{3\,A\,a^2\,b\,x^2}{2}+\frac{3\,A\,a\,b^2\,x^4}{4}+B\,a^2\,b\,x^3+\frac{3\,B\,a\,b^2\,x^5}{5}+\frac{3\,C\,a^2\,b\,x^4}{4}+\frac{C\,a\,b^2\,x^6}{2}","Not used",1,"(A*b^3*x^6)/6 + (C*a^3*x^2)/2 + (B*b^3*x^7)/7 + (C*b^3*x^8)/8 + A*a^3*log(x) + (a^3*x^3*D)/3 + (b^3*x^9*D)/9 + B*a^3*x + (3*a^2*b*x^5*D)/5 + (3*a*b^2*x^7*D)/7 + (3*A*a^2*b*x^2)/2 + (3*A*a*b^2*x^4)/4 + B*a^2*b*x^3 + (3*B*a*b^2*x^5)/5 + (3*C*a^2*b*x^4)/4 + (C*a*b^2*x^6)/2","B"
83,1,121,124,1.184135,"\text{Not used}","int(((a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D))/x^2,x)","\frac{{\left(b\,x^2+a\right)}^4\,D}{8\,b}-\frac{A\,a^3}{x}+\frac{A\,b^3\,x^5}{5}+\frac{B\,b^3\,x^6}{6}+\frac{C\,b^3\,x^7}{7}+B\,a^3\,\ln\left(x\right)+C\,a^3\,x+3\,A\,a^2\,b\,x+A\,a\,b^2\,x^3+\frac{3\,B\,a^2\,b\,x^2}{2}+\frac{3\,B\,a\,b^2\,x^4}{4}+C\,a^2\,b\,x^3+\frac{3\,C\,a\,b^2\,x^5}{5}","Not used",1,"((a + b*x^2)^4*D)/(8*b) - (A*a^3)/x + (A*b^3*x^5)/5 + (B*b^3*x^6)/6 + (C*b^3*x^7)/7 + B*a^3*log(x) + C*a^3*x + 3*A*a^2*b*x + A*a*b^2*x^3 + (3*B*a^2*b*x^2)/2 + (3*B*a*b^2*x^4)/4 + C*a^2*b*x^3 + (3*C*a*b^2*x^5)/5","B"
84,1,143,135,1.257074,"\text{Not used}","int(((a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D))/x^3,x)","\frac{A\,b^3\,x^4}{4}-\frac{B\,a^3}{x}-\frac{A\,a^3}{2\,x^2}+\frac{B\,b^3\,x^5}{5}+\frac{C\,b^3\,x^6}{6}+C\,a^3\,\ln\left(x\right)+a^3\,x\,D+\frac{b^3\,x^7\,D}{7}+a^2\,b\,x^3\,D+\frac{3\,a\,b^2\,x^5\,D}{5}+3\,B\,a^2\,b\,x+\frac{3\,A\,a\,b^2\,x^2}{2}+B\,a\,b^2\,x^3+\frac{3\,C\,a^2\,b\,x^2}{2}+\frac{3\,C\,a\,b^2\,x^4}{4}+3\,A\,a^2\,b\,\ln\left(x\right)","Not used",1,"(A*b^3*x^4)/4 - (B*a^3)/x - (A*a^3)/(2*x^2) + (B*b^3*x^5)/5 + (C*b^3*x^6)/6 + C*a^3*log(x) + a^3*x*D + (b^3*x^7*D)/7 + a^2*b*x^3*D + (3*a*b^2*x^5*D)/5 + 3*B*a^2*b*x + (3*A*a*b^2*x^2)/2 + B*a*b^2*x^3 + (3*C*a^2*b*x^2)/2 + (3*C*a*b^2*x^4)/4 + 3*A*a^2*b*log(x)","B"
85,1,148,139,1.367939,"\text{Not used}","int(((a + b*x^2)^3*(A + B*x + C*x^2 + x^3*D))/x^4,x)","\frac{B\,b^3\,x^4}{4}-\frac{C\,a^3}{x}-\frac{B\,a^3}{2\,x^2}+\frac{C\,b^3\,x^5}{5}+\frac{b^3\,x^6\,D}{6}-\frac{A\,\left(a^3+9\,a^2\,b\,x^2-9\,a\,b^2\,x^4-b^3\,x^6\right)}{3\,x^3}+\frac{a^3\,\ln\left(x^2\right)\,D}{2}+\frac{3\,a^2\,b\,x^2\,D}{2}+3\,C\,a^2\,b\,x+\frac{3\,a\,b^2\,x^4\,D}{4}+\frac{3\,B\,a\,b^2\,x^2}{2}+C\,a\,b^2\,x^3+3\,B\,a^2\,b\,\ln\left(x\right)","Not used",1,"(B*b^3*x^4)/4 - (C*a^3)/x - (B*a^3)/(2*x^2) + (C*b^3*x^5)/5 + (b^3*x^6*D)/6 - (A*(a^3 - b^3*x^6 + 9*a^2*b*x^2 - 9*a*b^2*x^4))/(3*x^3) + (a^3*log(x^2)*D)/2 + (3*a^2*b*x^2*D)/2 + 3*C*a^2*b*x + (3*a*b^2*x^4*D)/4 + (3*B*a*b^2*x^2)/2 + C*a*b^2*x^3 + 3*B*a^2*b*log(x)","B"
86,0,-1,151,0.000000,"\text{Not used}","int((x^4*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2),x)","\int \frac{x^4\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{b\,x^2+a} \,d x","Not used",1,"int((x^4*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2), x)","F"
87,0,-1,130,0.000000,"\text{Not used}","int((x^3*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2),x)","\int \frac{x^3\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{b\,x^2+a} \,d x","Not used",1,"int((x^3*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2), x)","F"
88,0,-1,111,0.000000,"\text{Not used}","int((x^2*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2),x)","\int \frac{x^2\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{b\,x^2+a} \,d x","Not used",1,"int((x^2*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2), x)","F"
89,0,-1,92,0.000000,"\text{Not used}","int((x*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2),x)","\int \frac{x\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{b\,x^2+a} \,d x","Not used",1,"int((x*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2), x)","F"
90,1,79,73,1.424760,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(a + b*x^2),x)","\frac{B\,\ln\left(b\,x^2+a\right)}{2\,b}-\frac{\left(a\,\ln\left(b\,x^2+a\right)-b\,x^2\right)\,D}{2\,b^2}+\frac{C\,x}{b}+\frac{A\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}-\frac{C\,\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{b^{3/2}}","Not used",1,"(B*log(a + b*x^2))/(2*b) - ((a*log(a + b*x^2) - b*x^2)*D)/(2*b^2) + (C*x)/b + (A*atan((b^(1/2)*x)/a^(1/2)))/(a^(1/2)*b^(1/2)) - (C*a^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/b^(3/2)","B"
91,0,-1,72,0.000000,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x*(a + b*x^2)),x)","\int \frac{A+B\,x+C\,x^2+x^3\,D}{x\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((A + B*x + C*x^2 + x^3*D)/(x*(a + b*x^2)), x)","F"
92,1,78,76,1.212118,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x^2*(a + b*x^2)),x)","\frac{\ln\left(b\,x^2+a\right)\,D}{2\,b}-\frac{A}{a\,x}-\frac{B\,\left(\ln\left(b\,x^2+a\right)-2\,\ln\left(x\right)\right)}{2\,a}-\frac{A\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{a^{3/2}}+\frac{C\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}","Not used",1,"(log(a + b*x^2)*D)/(2*b) - A/(a*x) - (B*(log(a + b*x^2) - 2*log(x)))/(2*a) - (A*b^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/a^(3/2) + (C*atan((b^(1/2)*x)/a^(1/2)))/(a^(1/2)*b^(1/2))","B"
93,1,97,92,1.303675,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x^3*(a + b*x^2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,D}{\sqrt{a}\,\sqrt{b}}-\frac{B}{a\,x}-\frac{C\,\left(\ln\left(b\,x^2+a\right)-2\,\ln\left(x\right)\right)}{2\,a}-\frac{A}{2\,a\,x^2}+\frac{A\,b\,\ln\left(b\,x^2+a\right)}{2\,a^2}-\frac{A\,b\,\ln\left(x\right)}{a^2}-\frac{B\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{a^{3/2}}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*D)/(a^(1/2)*b^(1/2)) - B/(a*x) - (C*(log(a + b*x^2) - 2*log(x)))/(2*a) - A/(2*a*x^2) + (A*b*log(a + b*x^2))/(2*a^2) - (A*b*log(x))/a^2 - (B*b^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/a^(3/2)","B"
94,0,-1,176,0.000000,"\text{Not used}","int((x^4*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2,x)","\int \frac{x^4\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^4*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2, x)","F"
95,0,-1,154,0.000000,"\text{Not used}","int((x^3*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2,x)","\int \frac{x^3\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^3*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2, x)","F"
96,1,152,134,1.291861,"\text{Not used}","int((x^2*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2,x)","\frac{B\,\ln\left(b\,x^2+a\right)}{2\,b^2}+\frac{x^2\,D}{2\,b^2}+\frac{C\,x}{b^2}-\frac{a^2\,D}{2\,b^3\,\left(b\,x^2+a\right)}+\frac{B\,a}{2\,b^2\,\left(b\,x^2+a\right)}-\frac{A\,x}{2\,b\,\left(b\,x^2+a\right)}+\frac{C\,a\,x}{2\,\left(b^3\,x^2+a\,b^2\right)}+\frac{A\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,\sqrt{a}\,b^{3/2}}-\frac{3\,C\,\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,b^{5/2}}-\frac{a\,\ln\left(b\,x^2+a\right)\,D}{b^3}","Not used",1,"(B*log(a + b*x^2))/(2*b^2) + (x^2*D)/(2*b^2) + (C*x)/b^2 - (a^2*D)/(2*b^3*(a + b*x^2)) + (B*a)/(2*b^2*(a + b*x^2)) - (A*x)/(2*b*(a + b*x^2)) + (C*a*x)/(2*(a*b^2 + b^3*x^2)) + (A*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(1/2)*b^(3/2)) - (3*C*a^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/(2*b^(5/2)) - (a*log(a + b*x^2)*D)/b^3","B"
97,0,-1,101,0.000000,"\text{Not used}","int((x*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2,x)","\int \frac{x\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^2, x)","F"
98,1,110,93,1.315506,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(a + b*x^2)^2,x)","\frac{\left(\ln\left(b\,x^2+a\right)+\frac{a}{b\,x^2+a}\right)\,D}{2\,b^2}-\frac{B}{2\,b\,\left(b\,x^2+a\right)}+\frac{A\,x}{2\,a\,\left(b\,x^2+a\right)}-\frac{C\,x}{2\,b\,\left(b\,x^2+a\right)}+\frac{A\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,a^{3/2}\,\sqrt{b}}+\frac{C\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,\sqrt{a}\,b^{3/2}}","Not used",1,"((log(a + b*x^2) + a/(a + b*x^2))*D)/(2*b^2) - B/(2*b*(a + b*x^2)) + (A*x)/(2*a*(a + b*x^2)) - (C*x)/(2*b*(a + b*x^2)) + (A*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(3/2)*b^(1/2)) + (C*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(1/2)*b^(3/2))","B"
99,0,-1,95,0.000000,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x*(a + b*x^2)^2),x)","\int \frac{A+B\,x+C\,x^2+x^3\,D}{x\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((A + B*x + C*x^2 + x^3*D)/(x*(a + b*x^2)^2), x)","F"
100,1,133,110,1.409733,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x^2*(a + b*x^2)^2),x)","\frac{B}{2\,a\,\left(b\,x^2+a\right)}-\frac{\frac{A}{a}+\frac{3\,A\,b\,x^2}{2\,a^2}}{b\,x^3+a\,x}-\frac{B\,\ln\left(b\,x^2+a\right)}{2\,a^2}+\frac{B\,\ln\left(x\right)}{a^2}-\frac{D}{2\,b\,\left(b\,x^2+a\right)}+\frac{C\,x}{2\,a\,\left(b\,x^2+a\right)}-\frac{3\,A\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,a^{5/2}}+\frac{C\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,a^{3/2}\,\sqrt{b}}","Not used",1,"B/(2*a*(a + b*x^2)) - (A/a + (3*A*b*x^2)/(2*a^2))/(a*x + b*x^3) - (B*log(a + b*x^2))/(2*a^2) + (B*log(x))/a^2 - D/(2*b*(a + b*x^2)) + (C*x)/(2*a*(a + b*x^2)) - (3*A*b^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(5/2)) + (C*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(3/2)*b^(1/2))","B"
101,1,158,135,1.348359,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x^3*(a + b*x^2)^2),x)","\frac{C}{2\,a\,\left(b\,x^2+a\right)}-\frac{\frac{A}{2\,a}+\frac{A\,b\,x^2}{a^2}}{b\,x^4+a\,x^2}-\frac{\frac{B}{a}+\frac{3\,B\,b\,x^2}{2\,a^2}}{b\,x^3+a\,x}-\frac{C\,\ln\left(b\,x^2+a\right)}{2\,a^2}+\frac{C\,\ln\left(x\right)}{a^2}+\frac{A\,b\,\ln\left(b\,x^2+a\right)}{a^3}-\frac{2\,A\,b\,\ln\left(x\right)}{a^3}+\frac{x\,D\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},2;\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{a^2}-\frac{3\,B\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,a^{5/2}}","Not used",1,"C/(2*a*(a + b*x^2)) - (A/(2*a) + (A*b*x^2)/a^2)/(a*x^2 + b*x^4) - (B/a + (3*B*b*x^2)/(2*a^2))/(a*x + b*x^3) - (C*log(a + b*x^2))/(2*a^2) + (C*log(x))/a^2 + (A*b*log(a + b*x^2))/a^3 - (2*A*b*log(x))/a^3 + (x*D*hypergeom([1/2, 2], 3/2, -(b*x^2)/a))/a^2 - (3*B*b^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(5/2))","B"
102,1,232,185,1.556058,"\text{Not used}","int((x^4*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^3,x)","\frac{\frac{7\,C\,a^2\,x}{8}+\frac{9\,C\,b\,a\,x^3}{8}}{a^2\,b^3+2\,a\,b^4\,x^2+b^5\,x^4}-\frac{\frac{5\,A\,x^3}{8\,b}+\frac{3\,A\,a\,x}{8\,b^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\frac{3\,B\,a^2}{4\,b^3}+\frac{B\,a\,x^2}{b^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{D\,\left(3\,a\,\ln\left(b\,x^2+a\right)-b\,x^2+\frac{3\,a^2}{b\,x^2+a}-\frac{a^3}{2\,{\left(b\,x^2+a\right)}^2}\right)}{2\,b^4}+\frac{B\,\ln\left(b\,x^2+a\right)}{2\,b^3}+\frac{C\,x}{b^3}+\frac{3\,A\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,\sqrt{a}\,b^{5/2}}-\frac{15\,C\,\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,b^{7/2}}","Not used",1,"((7*C*a^2*x)/8 + (9*C*a*b*x^3)/8)/(a^2*b^3 + b^5*x^4 + 2*a*b^4*x^2) - ((5*A*x^3)/(8*b) + (3*A*a*x)/(8*b^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) + ((3*B*a^2)/(4*b^3) + (B*a*x^2)/b^2)/(a^2 + b^2*x^4 + 2*a*b*x^2) - (D*(3*a*log(a + b*x^2) - b*x^2 + (3*a^2)/(a + b*x^2) - a^3/(2*(a + b*x^2)^2)))/(2*b^4) + (B*log(a + b*x^2))/(2*b^3) + (C*x)/b^3 + (3*A*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(1/2)*b^(5/2)) - (15*C*a^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/(8*b^(7/2))","B"
103,0,-1,155,0.000000,"\text{Not used}","int((x^3*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^3,x)","\int \frac{x^3\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{{\left(b\,x^2+a\right)}^3} \,d x","Not used",1,"int((x^3*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^3, x)","F"
104,1,195,136,1.391440,"\text{Not used}","int((x^2*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^3,x)","\frac{\frac{A\,x^3}{8\,a}-\frac{A\,x}{8\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{\frac{B\,x^2}{2\,b}+\frac{B\,a}{4\,b^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{\frac{5\,C\,x^3}{8\,b}+\frac{3\,C\,a\,x}{8\,b^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{D\,\left(\ln\left(b\,x^2+a\right)+\frac{2\,a}{b\,x^2+a}-\frac{a^2}{2\,{\left(b\,x^2+a\right)}^2}\right)}{2\,b^3}+\frac{A\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,a^{3/2}\,b^{3/2}}+\frac{3\,C\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,\sqrt{a}\,b^{5/2}}","Not used",1,"((A*x^3)/(8*a) - (A*x)/(8*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) - ((B*x^2)/(2*b) + (B*a)/(4*b^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) - ((5*C*x^3)/(8*b) + (3*C*a*x)/(8*b^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (D*(log(a + b*x^2) + (2*a)/(a + b*x^2) - a^2/(2*(a + b*x^2)^2)))/(2*b^3) + (A*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(3/2)*b^(3/2)) + (3*C*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(1/2)*b^(5/2))","B"
105,0,-1,119,0.000000,"\text{Not used}","int((x*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^3,x)","\int \frac{x\,\left(A+B\,x+C\,x^2+x^3\,D\right)}{{\left(b\,x^2+a\right)}^3} \,d x","Not used",1,"int((x*(A + B*x + C*x^2 + x^3*D))/(a + b*x^2)^3, x)","F"
106,1,163,116,1.327154,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(a + b*x^2)^3,x)","\frac{\frac{C\,x^3}{8\,a}-\frac{C\,x}{8\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\frac{5\,A\,x}{8\,a}+\frac{3\,A\,b\,x^3}{8\,a^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{B}{4\,b\,\left(a^2+2\,a\,b\,x^2+b^2\,x^4\right)}-\frac{\left(2\,b\,x^2+a\right)\,D}{4\,b^2\,{\left(b\,x^2+a\right)}^2}+\frac{3\,A\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,a^{5/2}\,\sqrt{b}}+\frac{C\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,a^{3/2}\,b^{3/2}}","Not used",1,"((C*x^3)/(8*a) - (C*x)/(8*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) + ((5*A*x)/(8*a) + (3*A*b*x^3)/(8*a^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) - B/(4*b*(a^2 + b^2*x^4 + 2*a*b*x^2)) - ((a + 2*b*x^2)*D)/(4*b^2*(a + b*x^2)^2) + (3*A*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(5/2)*b^(1/2)) + (C*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(3/2)*b^(3/2))","B"
107,0,-1,130,0.000000,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x*(a + b*x^2)^3),x)","\int \frac{A+B\,x+C\,x^2+x^3\,D}{x\,{\left(b\,x^2+a\right)}^3} \,d x","Not used",1,"int((A + B*x + C*x^2 + x^3*D)/(x*(a + b*x^2)^3), x)","F"
108,1,202,144,1.400047,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x^2*(a + b*x^2)^3),x)","\frac{\frac{3\,B}{4\,a}+\frac{B\,b\,x^2}{2\,a^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\frac{5\,C\,x}{8\,a}+\frac{3\,C\,b\,x^3}{8\,a^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{\frac{A}{a}+\frac{25\,A\,b\,x^2}{8\,a^2}+\frac{15\,A\,b^2\,x^4}{8\,a^3}}{a^2\,x+2\,a\,b\,x^3+b^2\,x^5}-\frac{D}{4\,b\,{\left(b\,x^2+a\right)}^2}-\frac{B\,\ln\left(b\,x^2+a\right)}{2\,a^3}+\frac{B\,\ln\left(x\right)}{a^3}-\frac{15\,A\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,a^{7/2}}+\frac{3\,C\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,a^{5/2}\,\sqrt{b}}","Not used",1,"((3*B)/(4*a) + (B*b*x^2)/(2*a^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) + ((5*C*x)/(8*a) + (3*C*b*x^3)/(8*a^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) - (A/a + (25*A*b*x^2)/(8*a^2) + (15*A*b^2*x^4)/(8*a^3))/(a^2*x + b^2*x^5 + 2*a*b*x^3) - D/(4*b*(a + b*x^2)^2) - (B*log(a + b*x^2))/(2*a^3) + (B*log(x))/a^3 - (15*A*b^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(7/2)) + (3*C*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(5/2)*b^(1/2))","B"
109,1,229,174,1.455702,"\text{Not used}","int((A + B*x + C*x^2 + x^3*D)/(x^3*(a + b*x^2)^3),x)","\frac{\frac{3\,C}{4\,a}+\frac{C\,b\,x^2}{2\,a^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{\frac{A}{2\,a}+\frac{9\,A\,b\,x^2}{4\,a^2}+\frac{3\,A\,b^2\,x^4}{2\,a^3}}{a^2\,x^2+2\,a\,b\,x^4+b^2\,x^6}-\frac{\frac{B}{a}+\frac{25\,B\,b\,x^2}{8\,a^2}+\frac{15\,B\,b^2\,x^4}{8\,a^3}}{a^2\,x+2\,a\,b\,x^3+b^2\,x^5}-\frac{C\,\ln\left(b\,x^2+a\right)}{2\,a^3}+\frac{C\,\ln\left(x\right)}{a^3}+\frac{3\,A\,b\,\ln\left(b\,x^2+a\right)}{2\,a^4}-\frac{3\,A\,b\,\ln\left(x\right)}{a^4}+\frac{x\,D\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},3;\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{a^3}-\frac{15\,B\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{8\,a^{7/2}}","Not used",1,"((3*C)/(4*a) + (C*b*x^2)/(2*a^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) - (A/(2*a) + (9*A*b*x^2)/(4*a^2) + (3*A*b^2*x^4)/(2*a^3))/(a^2*x^2 + b^2*x^6 + 2*a*b*x^4) - (B/a + (25*B*b*x^2)/(8*a^2) + (15*B*b^2*x^4)/(8*a^3))/(a^2*x + b^2*x^5 + 2*a*b*x^3) - (C*log(a + b*x^2))/(2*a^3) + (C*log(x))/a^3 + (3*A*b*log(a + b*x^2))/(2*a^4) - (3*A*b*log(x))/a^4 + (x*D*hypergeom([1/2, 3], 3/2, -(b*x^2)/a))/a^3 - (15*B*b^(1/2)*atan((b^(1/2)*x)/a^(1/2)))/(8*a^(7/2))","B"
110,1,20,20,0.911887,"\text{Not used}","int(-(x - 4*x^3)/(x^2 + 5)^2,x)","2\,\ln\left(x^2+5\right)+\frac{21}{2\,\left(x^2+5\right)}","Not used",1,"2*log(x^2 + 5) + 21/(2*(x^2 + 5))","B"
111,1,14,23,0.101513,"\text{Not used}","int(-(x - x^3)/(x^2 - 2)^(1/2),x)","\frac{\left(x^2+1\right)\,\sqrt{x^2-2}}{3}","Not used",1,"((x^2 + 1)*(x^2 - 2)^(1/2))/3","B"
112,1,20,25,0.038495,"\text{Not used}","int(-(x^2 - 2*x^4)/(2*x^2 + 1),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\right)}{2}-x+\frac{x^3}{3}","Not used",1,"(2^(1/2)*atan(2^(1/2)*x))/2 - x + x^3/3","B"
113,1,24,30,0.034952,"\text{Not used}","int((x^3 + x^4)/(x^2 + 1),x)","\mathrm{atan}\left(x\right)-\frac{\ln\left(x^2+1\right)}{2}-x+\frac{x^2}{2}+\frac{x^3}{3}","Not used",1,"atan(x) - log(x^2 + 1)/2 - x + x^2/2 + x^3/3","B"
114,1,289,210,0.928567,"\text{Not used}","int((x^6*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2),x)","x^9\,\left(\frac{e}{9\,b}-\frac{a\,f}{9\,b^2}\right)+x^7\,\left(\frac{d}{7\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{7\,b}\right)+x^5\,\left(\frac{c}{5\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{5\,b}\right)+\frac{f\,x^{11}}{11\,b}+\frac{a^{5/2}\,\mathrm{atan}\left(\frac{a^{5/2}\,\sqrt{b}\,x\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{f\,a^6-e\,a^5\,b+d\,a^4\,b^2-c\,a^3\,b^3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{b^{13/2}}-\frac{a\,x^3\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{3\,b}+\frac{a^2\,x\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{b^2}","Not used",1,"x^9*(e/(9*b) - (a*f)/(9*b^2)) + x^7*(d/(7*b) - (a*(e/b - (a*f)/b^2))/(7*b)) + x^5*(c/(5*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(5*b)) + (f*x^11)/(11*b) + (a^(5/2)*atan((a^(5/2)*b^(1/2)*x*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^6*f - a^3*b^3*c + a^4*b^2*d - a^5*b*e))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/b^(13/2) - (a*x^3*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/(3*b) + (a^2*x*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/b^2","B"
115,1,243,172,0.944050,"\text{Not used}","int((x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2),x)","x^7\,\left(\frac{e}{7\,b}-\frac{a\,f}{7\,b^2}\right)+x^5\,\left(\frac{d}{5\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{5\,b}\right)+x^3\,\left(\frac{c}{3\,b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{3\,b}\right)+\frac{f\,x^9}{9\,b}-\frac{a\,x\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)}{b}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{f\,a^5-e\,a^4\,b+d\,a^3\,b^2-c\,a^2\,b^3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{b^{11/2}}","Not used",1,"x^7*(e/(7*b) - (a*f)/(7*b^2)) + x^5*(d/(5*b) - (a*(e/b - (a*f)/b^2))/(5*b)) + x^3*(c/(3*b) - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/(3*b)) + (f*x^9)/(9*b) - (a*x*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b))/b - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^5*f - a^2*b^3*c + a^3*b^2*d - a^4*b*e))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/b^(11/2)","B"
116,1,193,136,0.911870,"\text{Not used}","int((x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2),x)","x^5\,\left(\frac{e}{5\,b}-\frac{a\,f}{5\,b^2}\right)+x^3\,\left(\frac{d}{3\,b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{3\,b}\right)+x\,\left(\frac{c}{b}-\frac{a\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)}{b}\right)+\frac{f\,x^7}{7\,b}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{f\,a^4-e\,a^3\,b+d\,a^2\,b^2-c\,a\,b^3}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{b^{9/2}}","Not used",1,"x^5*(e/(5*b) - (a*f)/(5*b^2)) + x^3*(d/(3*b) - (a*(e/b - (a*f)/b^2))/(3*b)) + x*(c/b - (a*(d/b - (a*(e/b - (a*f)/b^2))/b))/b) + (f*x^7)/(7*b) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^4*f + a^2*b^2*d - a*b^3*c - a^3*b*e))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/b^(9/2)","B"
117,1,96,100,0.935913,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2),x)","x^3\,\left(\frac{e}{3\,b}-\frac{a\,f}{3\,b^2}\right)+x\,\left(\frac{d}{b}-\frac{a\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)}{b}\right)+\frac{f\,x^5}{5\,b}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{\sqrt{a}\,b^{7/2}}","Not used",1,"x^3*(e/(3*b) - (a*f)/(3*b^2)) + x*(d/b - (a*(e/b - (a*f)/b^2))/b) + (f*x^5)/(5*b) + (atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^(1/2)*b^(7/2))","B"
118,1,76,84,1.067408,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)),x)","x\,\left(\frac{e}{b}-\frac{a\,f}{b^2}\right)-\frac{c}{a\,x}+\frac{f\,x^3}{3\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^{3/2}\,b^{5/2}}","Not used",1,"x*(e/b - (a*f)/b^2) - c/(a*x) + (f*x^3)/(3*b) - (atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^(3/2)*b^(5/2))","B"
119,1,80,82,0.110523,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)),x)","\frac{f\,x}{b}-\frac{\frac{b\,c}{3\,a}+\frac{b\,x^2\,\left(a\,d-b\,c\right)}{a^2}}{b\,x^3}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^{5/2}\,b^{3/2}}","Not used",1,"(f*x)/b - ((b*c)/(3*a) + (b*x^2*(a*d - b*c))/a^2)/(b*x^3) + (atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^(5/2)*b^(3/2))","B"
120,1,94,104,1.203145,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)),x)","-\frac{\frac{c}{5\,a}+\frac{x^2\,\left(a\,d-b\,c\right)}{3\,a^2}+\frac{x^4\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{a^3}}{x^5}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^{7/2}\,\sqrt{b}}","Not used",1,"- (c/(5*a) + (x^2*(a*d - b*c))/(3*a^2) + (x^4*(b^2*c + a^2*e - a*b*d))/a^3)/x^5 - (atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(a^(7/2)*b^(1/2))","B"
121,1,127,137,0.980888,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)),x)","\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^{9/2}}-\frac{\frac{c}{7\,a}-\frac{x^6\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^4}+\frac{x^2\,\left(a\,d-b\,c\right)}{5\,a^2}+\frac{x^4\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{3\,a^3}}{x^7}","Not used",1,"(b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^(9/2) - (c/(7*a) - (x^6*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^4 + (x^2*(a*d - b*c))/(5*a^2) + (x^4*(b^2*c + a^2*e - a*b*d))/(3*a^3))/x^7","B"
122,1,161,175,1.018057,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)),x)","-\frac{\frac{c}{9\,a}-\frac{x^6\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^4}+\frac{x^2\,\left(a\,d-b\,c\right)}{7\,a^2}+\frac{x^4\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{5\,a^3}+\frac{b\,x^8\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^5}}{x^9}-\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^{11/2}}","Not used",1,"- (c/(9*a) - (x^6*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^4) + (x^2*(a*d - b*c))/(7*a^2) + (x^4*(b^2*c + a^2*e - a*b*d))/(5*a^3) + (b*x^8*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^5)/x^9 - (b^(3/2)*atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^(11/2)","B"
123,1,197,211,0.987670,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^12*(a + b*x^2)),x)","\frac{b^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^{13/2}}-\frac{\frac{c}{11\,a}-\frac{x^6\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{5\,a^4}+\frac{x^2\,\left(a\,d-b\,c\right)}{9\,a^2}+\frac{x^4\,\left(e\,a^2-d\,a\,b+c\,b^2\right)}{7\,a^3}+\frac{b\,x^8\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{3\,a^5}-\frac{b^2\,x^{10}\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{a^6}}{x^{11}}","Not used",1,"(b^(5/2)*atan((b^(1/2)*x)/a^(1/2))*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^(13/2) - (c/(11*a) - (x^6*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(5*a^4) + (x^2*(a*d - b*c))/(9*a^2) + (x^4*(b^2*c + a^2*e - a*b*d))/(7*a^3) + (b*x^8*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(3*a^5) - (b^2*x^10*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/a^6)/x^11","B"
124,1,413,240,0.098939,"\text{Not used}","int((x^6*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^2,x)","x^7\,\left(\frac{e}{7\,b^2}-\frac{2\,a\,f}{7\,b^3}\right)-x\,\left(\frac{2\,a\,\left(\frac{c}{b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b}\right)}{b}-\frac{a^2\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b^2}\right)-x^5\,\left(\frac{a^2\,f}{5\,b^4}-\frac{d}{5\,b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{5\,b}\right)+x^3\,\left(\frac{c}{3\,b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{3\,b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{3\,b}\right)+\frac{f\,x^9}{9\,b^2}+\frac{x\,\left(\frac{f\,a^5}{2}-\frac{e\,a^4\,b}{2}+\frac{d\,a^3\,b^2}{2}-\frac{c\,a^2\,b^3}{2}\right)}{b^7\,x^2+a\,b^6}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(-11\,f\,a^3+9\,e\,a^2\,b-7\,d\,a\,b^2+5\,c\,b^3\right)}{11\,f\,a^5-9\,e\,a^4\,b+7\,d\,a^3\,b^2-5\,c\,a^2\,b^3}\right)\,\left(-11\,f\,a^3+9\,e\,a^2\,b-7\,d\,a\,b^2+5\,c\,b^3\right)}{2\,b^{13/2}}","Not used",1,"x^7*(e/(7*b^2) - (2*a*f)/(7*b^3)) - x*((2*a*(c/b^2 - (a^2*(e/b^2 - (2*a*f)/b^3))/b^2 + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b))/b - (a^2*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b^2) - x^5*((a^2*f)/(5*b^4) - d/(5*b^2) + (2*a*(e/b^2 - (2*a*f)/b^3))/(5*b)) + x^3*(c/(3*b^2) - (a^2*(e/b^2 - (2*a*f)/b^3))/(3*b^2) + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/(3*b)) + (f*x^9)/(9*b^2) + (x*((a^5*f)/2 - (a^2*b^3*c)/2 + (a^3*b^2*d)/2 - (a^4*b*e)/2))/(a*b^6 + b^7*x^2) - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(5*b^3*c - 11*a^3*f - 7*a*b^2*d + 9*a^2*b*e))/(11*a^5*f - 5*a^2*b^3*c + 7*a^3*b^2*d - 9*a^4*b*e))*(5*b^3*c - 11*a^3*f - 7*a*b^2*d + 9*a^2*b*e))/(2*b^(13/2))","B"
125,1,288,202,0.965715,"\text{Not used}","int((x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^2,x)","x^5\,\left(\frac{e}{5\,b^2}-\frac{2\,a\,f}{5\,b^3}\right)+x\,\left(\frac{c}{b^2}-\frac{a^2\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b^2}+\frac{2\,a\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)}{b}\right)-x^3\,\left(\frac{a^2\,f}{3\,b^4}-\frac{d}{3\,b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{3\,b}\right)-\frac{x\,\left(\frac{f\,a^4}{2}-\frac{e\,a^3\,b}{2}+\frac{d\,a^2\,b^2}{2}-\frac{c\,a\,b^3}{2}\right)}{b^6\,x^2+a\,b^5}+\frac{f\,x^7}{7\,b^2}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(-9\,f\,a^3+7\,e\,a^2\,b-5\,d\,a\,b^2+3\,c\,b^3\right)}{9\,f\,a^4-7\,e\,a^3\,b+5\,d\,a^2\,b^2-3\,c\,a\,b^3}\right)\,\left(-9\,f\,a^3+7\,e\,a^2\,b-5\,d\,a\,b^2+3\,c\,b^3\right)}{2\,b^{11/2}}","Not used",1,"x^5*(e/(5*b^2) - (2*a*f)/(5*b^3)) + x*(c/b^2 - (a^2*(e/b^2 - (2*a*f)/b^3))/b^2 + (2*a*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b))/b) - x^3*((a^2*f)/(3*b^4) - d/(3*b^2) + (2*a*(e/b^2 - (2*a*f)/b^3))/(3*b)) - (x*((a^4*f)/2 + (a^2*b^2*d)/2 - (a*b^3*c)/2 - (a^3*b*e)/2))/(a*b^5 + b^6*x^2) + (f*x^7)/(7*b^2) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(3*b^3*c - 9*a^3*f - 5*a*b^2*d + 7*a^2*b*e))/(9*a^4*f + 5*a^2*b^2*d - 3*a*b^3*c - 7*a^3*b*e))*(3*b^3*c - 9*a^3*f - 5*a*b^2*d + 7*a^2*b*e))/(2*b^(11/2))","B"
126,1,153,163,1.001596,"\text{Not used}","int((x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^2,x)","x^3\,\left(\frac{e}{3\,b^2}-\frac{2\,a\,f}{3\,b^3}\right)-x\,\left(\frac{a^2\,f}{b^4}-\frac{d}{b^2}+\frac{2\,a\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)}{b}\right)-\frac{x\,\left(-\frac{f\,a^3}{2}+\frac{e\,a^2\,b}{2}-\frac{d\,a\,b^2}{2}+\frac{c\,b^3}{2}\right)}{b^5\,x^2+a\,b^4}+\frac{f\,x^5}{5\,b^2}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-7\,f\,a^3+5\,e\,a^2\,b-3\,d\,a\,b^2+c\,b^3\right)}{2\,\sqrt{a}\,b^{9/2}}","Not used",1,"x^3*(e/(3*b^2) - (2*a*f)/(3*b^3)) - x*((a^2*f)/b^4 - d/b^2 + (2*a*(e/b^2 - (2*a*f)/b^3))/b) - (x*((b^3*c)/2 - (a^3*f)/2 - (a*b^2*d)/2 + (a^2*b*e)/2))/(a*b^4 + b^5*x^2) + (f*x^5)/(5*b^2) + (atan((b^(1/2)*x)/a^(1/2))*(b^3*c - 7*a^3*f - 3*a*b^2*d + 5*a^2*b*e))/(2*a^(1/2)*b^(9/2))","B"
127,1,113,118,0.099992,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2)^2,x)","x\,\left(\frac{e}{b^2}-\frac{2\,a\,f}{b^3}\right)+\frac{f\,x^3}{3\,b^2}+\frac{x\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right)}{2\,a\,\left(b^4\,x^2+a\,b^3\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(5\,f\,a^3-3\,e\,a^2\,b+d\,a\,b^2+c\,b^3\right)}{2\,a^{3/2}\,b^{7/2}}","Not used",1,"x*(e/b^2 - (2*a*f)/b^3) + (f*x^3)/(3*b^2) + (x*(b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(2*a*(a*b^3 + b^4*x^2)) + (atan((b^(1/2)*x)/a^(1/2))*(b^3*c + 5*a^3*f + a*b^2*d - 3*a^2*b*e))/(2*a^(3/2)*b^(7/2))","B"
128,1,112,112,0.995602,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)^2),x)","\frac{f\,x}{b^2}-\frac{\frac{x^2\,\left(-f\,a^3+e\,a^2\,b-d\,a\,b^2+3\,c\,b^3\right)}{2\,a^2}+\frac{b^2\,c}{a}}{b^3\,x^3+a\,b^2\,x}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,f\,a^3-e\,a^2\,b-d\,a\,b^2+3\,c\,b^3\right)}{2\,a^{5/2}\,b^{5/2}}","Not used",1,"(f*x)/b^2 - ((x^2*(3*b^3*c - a^3*f - a*b^2*d + a^2*b*e))/(2*a^2) + (b^2*c)/a)/(b^3*x^3 + a*b^2*x) - (atan((b^(1/2)*x)/a^(1/2))*(3*b^3*c + 3*a^3*f - a*b^2*d - a^2*b*e))/(2*a^(5/2)*b^(5/2))","B"
129,1,119,121,0.131301,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(f\,a^3+e\,a^2\,b-3\,d\,a\,b^2+5\,c\,b^3\right)}{2\,a^{7/2}\,b^{3/2}}-\frac{\frac{c}{3\,a}+\frac{x^2\,\left(3\,a\,d-5\,b\,c\right)}{3\,a^2}-\frac{x^4\,\left(-f\,a^3+e\,a^2\,b-3\,d\,a\,b^2+5\,c\,b^3\right)}{2\,a^3\,b}}{b\,x^5+a\,x^3}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(5*b^3*c + a^3*f - 3*a*b^2*d + a^2*b*e))/(2*a^(7/2)*b^(3/2)) - (c/(3*a) + (x^2*(3*a*d - 5*b*c))/(3*a^2) - (x^4*(5*b^3*c - a^3*f - 3*a*b^2*d + a^2*b*e))/(2*a^3*b))/(a*x^3 + b*x^5)","B"
130,1,145,152,0.998921,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)^2),x)","-\frac{\frac{c}{5\,a}+\frac{x^6\,\left(-f\,a^3+3\,e\,a^2\,b-5\,d\,a\,b^2+7\,c\,b^3\right)}{2\,a^4}+\frac{x^2\,\left(5\,a\,d-7\,b\,c\right)}{15\,a^2}+\frac{x^4\,\left(3\,e\,a^2-5\,d\,a\,b+7\,c\,b^2\right)}{3\,a^3}}{b\,x^7+a\,x^5}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-f\,a^3+3\,e\,a^2\,b-5\,d\,a\,b^2+7\,c\,b^3\right)}{2\,a^{9/2}\,\sqrt{b}}","Not used",1,"- (c/(5*a) + (x^6*(7*b^3*c - a^3*f - 5*a*b^2*d + 3*a^2*b*e))/(2*a^4) + (x^2*(5*a*d - 7*b*c))/(15*a^2) + (x^4*(7*b^2*c + 3*a^2*e - 5*a*b*d))/(3*a^3))/(a*x^5 + b*x^7) - (atan((b^(1/2)*x)/a^(1/2))*(7*b^3*c - a^3*f - 5*a*b^2*d + 3*a^2*b*e))/(2*a^(9/2)*b^(1/2))","B"
131,1,181,189,0.986765,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)^2),x)","\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-3\,f\,a^3+5\,e\,a^2\,b-7\,d\,a\,b^2+9\,c\,b^3\right)}{2\,a^{11/2}}-\frac{\frac{c}{7\,a}-\frac{x^6\,\left(-3\,f\,a^3+5\,e\,a^2\,b-7\,d\,a\,b^2+9\,c\,b^3\right)}{3\,a^4}+\frac{x^2\,\left(7\,a\,d-9\,b\,c\right)}{35\,a^2}+\frac{x^4\,\left(5\,e\,a^2-7\,d\,a\,b+9\,c\,b^2\right)}{15\,a^3}-\frac{b\,x^8\,\left(-3\,f\,a^3+5\,e\,a^2\,b-7\,d\,a\,b^2+9\,c\,b^3\right)}{2\,a^5}}{b\,x^9+a\,x^7}","Not used",1,"(b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(9*b^3*c - 3*a^3*f - 7*a*b^2*d + 5*a^2*b*e))/(2*a^(11/2)) - (c/(7*a) - (x^6*(9*b^3*c - 3*a^3*f - 7*a*b^2*d + 5*a^2*b*e))/(3*a^4) + (x^2*(7*a*d - 9*b*c))/(35*a^2) + (x^4*(9*b^2*c + 5*a^2*e - 7*a*b*d))/(15*a^3) - (b*x^8*(9*b^3*c - 3*a^3*f - 7*a*b^2*d + 5*a^2*b*e))/(2*a^5))/(a*x^7 + b*x^9)","B"
132,1,219,230,1.009851,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)^2),x)","-\frac{\frac{c}{9\,a}-\frac{x^6\,\left(-5\,f\,a^3+7\,e\,a^2\,b-9\,d\,a\,b^2+11\,c\,b^3\right)}{15\,a^4}+\frac{x^2\,\left(9\,a\,d-11\,b\,c\right)}{63\,a^2}+\frac{x^4\,\left(7\,e\,a^2-9\,d\,a\,b+11\,c\,b^2\right)}{35\,a^3}+\frac{b\,x^8\,\left(-5\,f\,a^3+7\,e\,a^2\,b-9\,d\,a\,b^2+11\,c\,b^3\right)}{3\,a^5}+\frac{b^2\,x^{10}\,\left(-5\,f\,a^3+7\,e\,a^2\,b-9\,d\,a\,b^2+11\,c\,b^3\right)}{2\,a^6}}{b\,x^{11}+a\,x^9}-\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-5\,f\,a^3+7\,e\,a^2\,b-9\,d\,a\,b^2+11\,c\,b^3\right)}{2\,a^{13/2}}","Not used",1,"- (c/(9*a) - (x^6*(11*b^3*c - 5*a^3*f - 9*a*b^2*d + 7*a^2*b*e))/(15*a^4) + (x^2*(9*a*d - 11*b*c))/(63*a^2) + (x^4*(11*b^2*c + 7*a^2*e - 9*a*b*d))/(35*a^3) + (b*x^8*(11*b^3*c - 5*a^3*f - 9*a*b^2*d + 7*a^2*b*e))/(3*a^5) + (b^2*x^10*(11*b^3*c - 5*a^3*f - 9*a*b^2*d + 7*a^2*b*e))/(2*a^6))/(a*x^9 + b*x^11) - (b^(3/2)*atan((b^(1/2)*x)/a^(1/2))*(11*b^3*c - 5*a^3*f - 9*a*b^2*d + 7*a^2*b*e))/(2*a^(13/2))","B"
133,1,506,287,0.999408,"\text{Not used}","int((x^8*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x)","x^7\,\left(\frac{e}{7\,b^3}-\frac{3\,a\,f}{7\,b^4}\right)+x^3\,\left(\frac{c}{3\,b^3}-\frac{a^3\,f}{3\,b^6}-\frac{a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)+\frac{x\,\left(\frac{23\,f\,a^6}{8}-\frac{19\,e\,a^5\,b}{8}+\frac{15\,d\,a^4\,b^2}{8}-\frac{11\,c\,a^3\,b^3}{8}\right)-x^3\,\left(-\frac{25\,f\,a^5\,b}{8}+\frac{21\,e\,a^4\,b^2}{8}-\frac{17\,d\,a^3\,b^3}{8}+\frac{13\,c\,a^2\,b^4}{8}\right)}{a^2\,b^7+2\,a\,b^8\,x^2+b^9\,x^4}-x\,\left(\frac{3\,a\,\left(\frac{c}{b^3}-\frac{a^3\,f}{b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)}{b}-\frac{3\,a^2\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b^2}+\frac{a^3\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^3}\right)-x^5\,\left(\frac{3\,a^2\,f}{5\,b^5}-\frac{d}{5\,b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{5\,b}\right)+\frac{f\,x^9}{9\,b^3}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(-143\,f\,a^3+99\,e\,a^2\,b-63\,d\,a\,b^2+35\,c\,b^3\right)}{143\,f\,a^5-99\,e\,a^4\,b+63\,d\,a^3\,b^2-35\,c\,a^2\,b^3}\right)\,\left(-143\,f\,a^3+99\,e\,a^2\,b-63\,d\,a\,b^2+35\,c\,b^3\right)}{8\,b^{15/2}}","Not used",1,"x^7*(e/(7*b^3) - (3*a*f)/(7*b^4)) + x^3*(c/(3*b^3) - (a^3*f)/(3*b^6) - (a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b) + (x*((23*a^6*f)/8 - (11*a^3*b^3*c)/8 + (15*a^4*b^2*d)/8 - (19*a^5*b*e)/8) - x^3*((13*a^2*b^4*c)/8 - (17*a^3*b^3*d)/8 + (21*a^4*b^2*e)/8 - (25*a^5*b*f)/8))/(a^2*b^7 + b^9*x^4 + 2*a*b^8*x^2) - x*((3*a*(c/b^3 - (a^3*f)/b^6 - (3*a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b))/b - (3*a^2*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b^2 + (a^3*(e/b^3 - (3*a*f)/b^4))/b^3) - x^5*((3*a^2*f)/(5*b^5) - d/(5*b^3) + (3*a*(e/b^3 - (3*a*f)/b^4))/(5*b)) + (f*x^9)/(9*b^3) - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(35*b^3*c - 143*a^3*f - 63*a*b^2*d + 99*a^2*b*e))/(143*a^5*f - 35*a^2*b^3*c + 63*a^3*b^2*d - 99*a^4*b*e))*(35*b^3*c - 143*a^3*f - 63*a*b^2*d + 99*a^2*b*e))/(8*b^(15/2))","B"
134,1,348,247,0.106548,"\text{Not used}","int((x^6*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x)","x^5\,\left(\frac{e}{5\,b^3}-\frac{3\,a\,f}{5\,b^4}\right)+x\,\left(\frac{c}{b^3}-\frac{a^3\,f}{b^6}-\frac{3\,a^2\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b^2}+\frac{3\,a\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)}{b}\right)-x^3\,\left(\frac{a^2\,f}{b^5}-\frac{d}{3\,b^3}+\frac{a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)-\frac{\left(\frac{21\,f\,a^4\,b}{8}-\frac{17\,e\,a^3\,b^2}{8}+\frac{13\,d\,a^2\,b^3}{8}-\frac{9\,c\,a\,b^4}{8}\right)\,x^3+\left(\frac{19\,f\,a^5}{8}-\frac{15\,e\,a^4\,b}{8}+\frac{11\,d\,a^3\,b^2}{8}-\frac{7\,c\,a^2\,b^3}{8}\right)\,x}{a^2\,b^6+2\,a\,b^7\,x^2+b^8\,x^4}+\frac{f\,x^7}{7\,b^3}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(-99\,f\,a^3+63\,e\,a^2\,b-35\,d\,a\,b^2+15\,c\,b^3\right)}{99\,f\,a^4-63\,e\,a^3\,b+35\,d\,a^2\,b^2-15\,c\,a\,b^3}\right)\,\left(-99\,f\,a^3+63\,e\,a^2\,b-35\,d\,a\,b^2+15\,c\,b^3\right)}{8\,b^{13/2}}","Not used",1,"x^5*(e/(5*b^3) - (3*a*f)/(5*b^4)) + x*(c/b^3 - (a^3*f)/b^6 - (3*a^2*(e/b^3 - (3*a*f)/b^4))/b^2 + (3*a*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b))/b) - x^3*((a^2*f)/b^5 - d/(3*b^3) + (a*(e/b^3 - (3*a*f)/b^4))/b) - (x*((19*a^5*f)/8 - (7*a^2*b^3*c)/8 + (11*a^3*b^2*d)/8 - (15*a^4*b*e)/8) + x^3*((13*a^2*b^3*d)/8 - (17*a^3*b^2*e)/8 - (9*a*b^4*c)/8 + (21*a^4*b*f)/8))/(a^2*b^6 + b^8*x^4 + 2*a*b^7*x^2) + (f*x^7)/(7*b^3) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(15*b^3*c - 99*a^3*f - 35*a*b^2*d + 63*a^2*b*e))/(99*a^4*f + 35*a^2*b^2*d - 15*a*b^3*c - 63*a^3*b*e))*(15*b^3*c - 99*a^3*f - 35*a*b^2*d + 63*a^2*b*e))/(8*b^(13/2))","B"
135,1,206,207,0.954443,"\text{Not used}","int((x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x)","x^3\,\left(\frac{e}{3\,b^3}-\frac{a\,f}{b^4}\right)-x\,\left(\frac{3\,a^2\,f}{b^5}-\frac{d}{b^3}+\frac{3\,a\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)}{b}\right)-\frac{x^3\,\left(-\frac{17\,f\,a^3\,b}{8}+\frac{13\,e\,a^2\,b^2}{8}-\frac{9\,d\,a\,b^3}{8}+\frac{5\,c\,b^4}{8}\right)-x\,\left(\frac{15\,f\,a^4}{8}-\frac{11\,e\,a^3\,b}{8}+\frac{7\,d\,a^2\,b^2}{8}-\frac{3\,c\,a\,b^3}{8}\right)}{a^2\,b^5+2\,a\,b^6\,x^2+b^7\,x^4}+\frac{f\,x^5}{5\,b^3}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-63\,f\,a^3+35\,e\,a^2\,b-15\,d\,a\,b^2+3\,c\,b^3\right)}{8\,\sqrt{a}\,b^{11/2}}","Not used",1,"x^3*(e/(3*b^3) - (a*f)/b^4) - x*((3*a^2*f)/b^5 - d/b^3 + (3*a*(e/b^3 - (3*a*f)/b^4))/b) - (x^3*((5*b^4*c)/8 + (13*a^2*b^2*e)/8 - (9*a*b^3*d)/8 - (17*a^3*b*f)/8) - x*((15*a^4*f)/8 + (7*a^2*b^2*d)/8 - (3*a*b^3*c)/8 - (11*a^3*b*e)/8))/(a^2*b^5 + b^7*x^4 + 2*a*b^6*x^2) + (f*x^5)/(5*b^3) + (atan((b^(1/2)*x)/a^(1/2))*(3*b^3*c - 63*a^3*f - 15*a*b^2*d + 35*a^2*b*e))/(8*a^(1/2)*b^(11/2))","B"
136,1,163,167,1.018071,"\text{Not used}","int((x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^3,x)","x\,\left(\frac{e}{b^3}-\frac{3\,a\,f}{b^4}\right)-\frac{x\,\left(\frac{11\,f\,a^3}{8}-\frac{7\,e\,a^2\,b}{8}+\frac{3\,d\,a\,b^2}{8}+\frac{c\,b^3}{8}\right)-\frac{x^3\,\left(-13\,f\,a^3\,b+9\,e\,a^2\,b^2-5\,d\,a\,b^3+c\,b^4\right)}{8\,a}}{a^2\,b^4+2\,a\,b^5\,x^2+b^6\,x^4}+\frac{f\,x^3}{3\,b^3}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(35\,f\,a^3-15\,e\,a^2\,b+3\,d\,a\,b^2+c\,b^3\right)}{8\,a^{3/2}\,b^{9/2}}","Not used",1,"x*(e/b^3 - (3*a*f)/b^4) - (x*((b^3*c)/8 + (11*a^3*f)/8 + (3*a*b^2*d)/8 - (7*a^2*b*e)/8) - (x^3*(b^4*c + 9*a^2*b^2*e - 5*a*b^3*d - 13*a^3*b*f))/(8*a))/(a^2*b^4 + b^6*x^4 + 2*a*b^5*x^2) + (f*x^3)/(3*b^3) + (atan((b^(1/2)*x)/a^(1/2))*(b^3*c + 35*a^3*f + 3*a*b^2*d - 15*a^2*b*e))/(8*a^(3/2)*b^(9/2))","B"
137,1,148,147,1.047452,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2)^3,x)","\frac{\frac{x\,\left(7\,f\,a^3-3\,e\,a^2\,b-d\,a\,b^2+5\,c\,b^3\right)}{8\,a}+\frac{x^3\,\left(9\,f\,a^3\,b-5\,e\,a^2\,b^2+d\,a\,b^3+3\,c\,b^4\right)}{8\,a^2}}{a^2\,b^3+2\,a\,b^4\,x^2+b^5\,x^4}+\frac{f\,x}{b^3}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-15\,f\,a^3+3\,e\,a^2\,b+d\,a\,b^2+3\,c\,b^3\right)}{8\,a^{5/2}\,b^{7/2}}","Not used",1,"((x*(5*b^3*c + 7*a^3*f - a*b^2*d - 3*a^2*b*e))/(8*a) + (x^3*(3*b^4*c - 5*a^2*b^2*e + a*b^3*d + 9*a^3*b*f))/(8*a^2))/(a^2*b^3 + b^5*x^4 + 2*a*b^4*x^2) + (f*x)/b^3 + (atan((b^(1/2)*x)/a^(1/2))*(3*b^3*c - 15*a^3*f + a*b^2*d + 3*a^2*b*e))/(8*a^(5/2)*b^(7/2))","B"
138,1,149,153,1.094312,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)^3),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,f\,a^3+e\,a^2\,b+3\,d\,a\,b^2-15\,c\,b^3\right)}{8\,a^{7/2}\,b^{5/2}}-\frac{\frac{c}{a}+\frac{x^4\,\left(5\,f\,a^3-e\,a^2\,b-3\,d\,a\,b^2+15\,c\,b^3\right)}{8\,a^3\,b}+\frac{x^2\,\left(3\,f\,a^3+e\,a^2\,b-5\,d\,a\,b^2+25\,c\,b^3\right)}{8\,a^2\,b^2}}{a^2\,x+2\,a\,b\,x^3+b^2\,x^5}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(3*a^3*f - 15*b^3*c + 3*a*b^2*d + a^2*b*e))/(8*a^(7/2)*b^(5/2)) - (c/a + (x^4*(15*b^3*c + 5*a^3*f - 3*a*b^2*d - a^2*b*e))/(8*a^3*b) + (x^2*(25*b^3*c + 3*a^3*f - 5*a*b^2*d + a^2*b*e))/(8*a^2*b^2))/(a^2*x + b^2*x^5 + 2*a*b*x^3)","B"
139,1,166,168,1.026664,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)^3),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(f\,a^3+3\,e\,a^2\,b-15\,d\,a\,b^2+35\,c\,b^3\right)}{8\,a^{9/2}\,b^{3/2}}-\frac{\frac{c}{3\,a}-\frac{x^6\,\left(f\,a^3+3\,e\,a^2\,b-15\,d\,a\,b^2+35\,c\,b^3\right)}{8\,a^4}+\frac{x^2\,\left(3\,a\,d-7\,b\,c\right)}{3\,a^2}-\frac{x^4\,\left(-3\,f\,a^3+15\,e\,a^2\,b-75\,d\,a\,b^2+175\,c\,b^3\right)}{24\,a^3\,b}}{a^2\,x^3+2\,a\,b\,x^5+b^2\,x^7}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(35*b^3*c + a^3*f - 15*a*b^2*d + 3*a^2*b*e))/(8*a^(9/2)*b^(3/2)) - (c/(3*a) - (x^6*(35*b^3*c + a^3*f - 15*a*b^2*d + 3*a^2*b*e))/(8*a^4) + (x^2*(3*a*d - 7*b*c))/(3*a^2) - (x^4*(175*b^3*c - 3*a^3*f - 75*a*b^2*d + 15*a^2*b*e))/(24*a^3*b))/(a^2*x^3 + b^2*x^7 + 2*a*b*x^5)","B"
140,1,192,196,1.042855,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)^3),x)","-\frac{\frac{c}{5\,a}+\frac{5\,x^6\,\left(-3\,f\,a^3+15\,e\,a^2\,b-35\,d\,a\,b^2+63\,c\,b^3\right)}{24\,a^4}+\frac{x^2\,\left(5\,a\,d-9\,b\,c\right)}{15\,a^2}+\frac{x^4\,\left(15\,e\,a^2-35\,d\,a\,b+63\,c\,b^2\right)}{15\,a^3}+\frac{b\,x^8\,\left(-3\,f\,a^3+15\,e\,a^2\,b-35\,d\,a\,b^2+63\,c\,b^3\right)}{8\,a^5}}{a^2\,x^5+2\,a\,b\,x^7+b^2\,x^9}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-3\,f\,a^3+15\,e\,a^2\,b-35\,d\,a\,b^2+63\,c\,b^3\right)}{8\,a^{11/2}\,\sqrt{b}}","Not used",1,"- (c/(5*a) + (5*x^6*(63*b^3*c - 3*a^3*f - 35*a*b^2*d + 15*a^2*b*e))/(24*a^4) + (x^2*(5*a*d - 9*b*c))/(15*a^2) + (x^4*(63*b^2*c + 15*a^2*e - 35*a*b*d))/(15*a^3) + (b*x^8*(63*b^3*c - 3*a^3*f - 35*a*b^2*d + 15*a^2*b*e))/(8*a^5))/(a^2*x^5 + b^2*x^9 + 2*a*b*x^7) - (atan((b^(1/2)*x)/a^(1/2))*(63*b^3*c - 3*a^3*f - 35*a*b^2*d + 15*a^2*b*e))/(8*a^(11/2)*b^(1/2))","B"
141,1,230,234,1.045938,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)^3),x)","\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-15\,f\,a^3+35\,e\,a^2\,b-63\,d\,a\,b^2+99\,c\,b^3\right)}{8\,a^{13/2}}-\frac{\frac{c}{7\,a}-\frac{x^6\,\left(-15\,f\,a^3+35\,e\,a^2\,b-63\,d\,a\,b^2+99\,c\,b^3\right)}{15\,a^4}+\frac{x^2\,\left(7\,a\,d-11\,b\,c\right)}{35\,a^2}+\frac{x^4\,\left(35\,e\,a^2-63\,d\,a\,b+99\,c\,b^2\right)}{105\,a^3}-\frac{5\,b\,x^8\,\left(-15\,f\,a^3+35\,e\,a^2\,b-63\,d\,a\,b^2+99\,c\,b^3\right)}{24\,a^5}-\frac{b^2\,x^{10}\,\left(-15\,f\,a^3+35\,e\,a^2\,b-63\,d\,a\,b^2+99\,c\,b^3\right)}{8\,a^6}}{a^2\,x^7+2\,a\,b\,x^9+b^2\,x^{11}}","Not used",1,"(b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(99*b^3*c - 15*a^3*f - 63*a*b^2*d + 35*a^2*b*e))/(8*a^(13/2)) - (c/(7*a) - (x^6*(99*b^3*c - 15*a^3*f - 63*a*b^2*d + 35*a^2*b*e))/(15*a^4) + (x^2*(7*a*d - 11*b*c))/(35*a^2) + (x^4*(99*b^2*c + 35*a^2*e - 63*a*b*d))/(105*a^3) - (5*b*x^8*(99*b^3*c - 15*a^3*f - 63*a*b^2*d + 35*a^2*b*e))/(24*a^5) - (b^2*x^10*(99*b^3*c - 15*a^3*f - 63*a*b^2*d + 35*a^2*b*e))/(8*a^6))/(a^2*x^7 + b^2*x^11 + 2*a*b*x^9)","B"
142,1,268,277,1.070297,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)^3),x)","-\frac{\frac{c}{9\,a}-\frac{x^6\,\left(-35\,f\,a^3+63\,e\,a^2\,b-99\,d\,a\,b^2+143\,c\,b^3\right)}{105\,a^4}+\frac{x^2\,\left(9\,a\,d-13\,b\,c\right)}{63\,a^2}+\frac{x^4\,\left(63\,e\,a^2-99\,d\,a\,b+143\,c\,b^2\right)}{315\,a^3}+\frac{b\,x^8\,\left(-35\,f\,a^3+63\,e\,a^2\,b-99\,d\,a\,b^2+143\,c\,b^3\right)}{15\,a^5}+\frac{5\,b^2\,x^{10}\,\left(-35\,f\,a^3+63\,e\,a^2\,b-99\,d\,a\,b^2+143\,c\,b^3\right)}{24\,a^6}+\frac{b^3\,x^{12}\,\left(-35\,f\,a^3+63\,e\,a^2\,b-99\,d\,a\,b^2+143\,c\,b^3\right)}{8\,a^7}}{a^2\,x^9+2\,a\,b\,x^{11}+b^2\,x^{13}}-\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(-35\,f\,a^3+63\,e\,a^2\,b-99\,d\,a\,b^2+143\,c\,b^3\right)}{8\,a^{15/2}}","Not used",1,"- (c/(9*a) - (x^6*(143*b^3*c - 35*a^3*f - 99*a*b^2*d + 63*a^2*b*e))/(105*a^4) + (x^2*(9*a*d - 13*b*c))/(63*a^2) + (x^4*(143*b^2*c + 63*a^2*e - 99*a*b*d))/(315*a^3) + (b*x^8*(143*b^3*c - 35*a^3*f - 99*a*b^2*d + 63*a^2*b*e))/(15*a^5) + (5*b^2*x^10*(143*b^3*c - 35*a^3*f - 99*a*b^2*d + 63*a^2*b*e))/(24*a^6) + (b^3*x^12*(143*b^3*c - 35*a^3*f - 99*a*b^2*d + 63*a^2*b*e))/(8*a^7))/(a^2*x^9 + b^2*x^13 + 2*a*b*x^11) - (b^(3/2)*atan((b^(1/2)*x)/a^(1/2))*(143*b^3*c - 35*a^3*f - 99*a*b^2*d + 63*a^2*b*e))/(8*a^(15/2))","B"
143,1,186,214,1.191469,"\text{Not used}","int((x^5*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{x^6\,\left(400\,f\,a^2\,b^3-440\,e\,a\,b^4+495\,d\,b^5\right)}{3465\,b^6}-\frac{1280\,f\,a^5-1408\,e\,a^4\,b+1584\,d\,a^3\,b^2-1848\,c\,a^2\,b^3}{3465\,b^6}+\frac{x^4\,\left(-480\,f\,a^3\,b^2+528\,e\,a^2\,b^3-594\,d\,a\,b^4+693\,c\,b^5\right)}{3465\,b^6}+\frac{f\,x^{10}}{11\,b}+\frac{x^8\,\left(385\,b^5\,e-350\,a\,b^4\,f\right)}{3465\,b^6}-\frac{4\,a\,x^2\,\left(-160\,f\,a^3+176\,e\,a^2\,b-198\,d\,a\,b^2+231\,c\,b^3\right)}{3465\,b^5}\right)","Not used",1,"(a + b*x^2)^(1/2)*((x^6*(495*b^5*d + 400*a^2*b^3*f - 440*a*b^4*e))/(3465*b^6) - (1280*a^5*f - 1848*a^2*b^3*c + 1584*a^3*b^2*d - 1408*a^4*b*e)/(3465*b^6) + (x^4*(693*b^5*c + 528*a^2*b^3*e - 480*a^3*b^2*f - 594*a*b^4*d))/(3465*b^6) + (f*x^10)/(11*b) + (x^8*(385*b^5*e - 350*a*b^4*f))/(3465*b^6) - (4*a*x^2*(231*b^3*c - 160*a^3*f - 198*a*b^2*d + 176*a^2*b*e))/(3465*b^5))","B"
144,1,146,167,1.107462,"\text{Not used}","int((x^3*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{128\,f\,a^4-144\,e\,a^3\,b+168\,d\,a^2\,b^2-210\,c\,a\,b^3}{315\,b^5}+\frac{x^4\,\left(48\,f\,a^2\,b^2-54\,e\,a\,b^3+63\,d\,b^4\right)}{315\,b^5}+\frac{f\,x^8}{9\,b}+\frac{x^6\,\left(45\,b^4\,e-40\,a\,b^3\,f\right)}{315\,b^5}+\frac{x^2\,\left(-64\,f\,a^3\,b+72\,e\,a^2\,b^2-84\,d\,a\,b^3+105\,c\,b^4\right)}{315\,b^5}\right)","Not used",1,"(a + b*x^2)^(1/2)*((128*a^4*f + 168*a^2*b^2*d - 210*a*b^3*c - 144*a^3*b*e)/(315*b^5) + (x^4*(63*b^4*d + 48*a^2*b^2*f - 54*a*b^3*e))/(315*b^5) + (f*x^8)/(9*b) + (x^6*(45*b^4*e - 40*a*b^3*f))/(315*b^5) + (x^2*(105*b^4*c + 72*a^2*b^2*e - 84*a*b^3*d - 64*a^3*b*f))/(315*b^5))","B"
145,1,103,121,1.063919,"\text{Not used}","int((x*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{-48\,f\,a^3+56\,e\,a^2\,b-70\,d\,a\,b^2+105\,c\,b^3}{105\,b^4}+\frac{f\,x^6}{7\,b}+\frac{x^2\,\left(24\,f\,a^2\,b-28\,e\,a\,b^2+35\,d\,b^3\right)}{105\,b^4}+\frac{x^4\,\left(21\,b^3\,e-18\,a\,b^2\,f\right)}{105\,b^4}\right)","Not used",1,"(a + b*x^2)^(1/2)*((105*b^3*c - 48*a^3*f - 70*a*b^2*d + 56*a^2*b*e)/(105*b^4) + (f*x^6)/(7*b) + (x^2*(35*b^3*d - 28*a*b^2*e + 24*a^2*b*f))/(105*b^4) + (x^4*(21*b^3*e - 18*a*b^2*f))/(105*b^4))","B"
146,1,99,103,1.809711,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x*(a + b*x^2)^(1/2)),x)","\sqrt{b\,x^2+a}\,\left(\frac{8\,a^2\,f}{15\,b^3}+\frac{f\,x^4}{5\,b}-\frac{4\,a\,f\,x^2}{15\,b^2}\right)+\frac{d\,\sqrt{b\,x^2+a}}{b}-\frac{c\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{e\,\sqrt{b\,x^2+a}\,\left(2\,a-b\,x^2\right)}{3\,b^2}","Not used",1,"(a + b*x^2)^(1/2)*((8*a^2*f)/(15*b^3) + (f*x^4)/(5*b) - (4*a*f*x^2)/(15*b^2)) + (d*(a + b*x^2)^(1/2))/b - (c*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2) - (e*(a + b*x^2)^(1/2)*(2*a - b*x^2))/(3*b^2)","B"
147,1,99,100,1.947294,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^3*(a + b*x^2)^(1/2)),x)","\frac{e\,\sqrt{b\,x^2+a}}{b}-\frac{d\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{c\,\sqrt{b\,x^2+a}}{2\,a\,x^2}+\frac{b\,c\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{f\,\sqrt{b\,x^2+a}\,\left(2\,a-b\,x^2\right)}{3\,b^2}","Not used",1,"(e*(a + b*x^2)^(1/2))/b - (d*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2) - (c*(a + b*x^2)^(1/2))/(2*a*x^2) + (b*c*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2)) - (f*(a + b*x^2)^(1/2)*(2*a - b*x^2))/(3*b^2)","B"
148,1,133,114,2.191416,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^5*(a + b*x^2)^(1/2)),x)","\frac{f\,\sqrt{b\,x^2+a}}{b}-\frac{e\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{5\,c\,\sqrt{b\,x^2+a}}{8\,a\,x^4}+\frac{3\,c\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a^2\,x^4}-\frac{d\,\sqrt{b\,x^2+a}}{2\,a\,x^2}+\frac{b\,d\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{3\,b^2\,c\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{5/2}}","Not used",1,"(f*(a + b*x^2)^(1/2))/b - (e*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2) - (5*c*(a + b*x^2)^(1/2))/(8*a*x^4) + (3*c*(a + b*x^2)^(3/2))/(8*a^2*x^4) - (d*(a + b*x^2)^(1/2))/(2*a*x^2) + (b*d*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2)) - (3*b^2*c*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(5/2))","B"
149,1,199,146,2.542891,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^7*(a + b*x^2)^(1/2)),x)","\frac{5\,c\,{\left(b\,x^2+a\right)}^{3/2}}{6\,a^2\,x^6}-\frac{11\,c\,\sqrt{b\,x^2+a}}{16\,a\,x^6}-\frac{f\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{5\,c\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a^3\,x^6}-\frac{5\,d\,\sqrt{b\,x^2+a}}{8\,a\,x^4}+\frac{3\,d\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a^2\,x^4}-\frac{e\,\sqrt{b\,x^2+a}}{2\,a\,x^2}+\frac{b\,e\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{3\,b^2\,d\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{5/2}}-\frac{b^3\,c\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{16\,a^{7/2}}","Not used",1,"(5*c*(a + b*x^2)^(3/2))/(6*a^2*x^6) - (11*c*(a + b*x^2)^(1/2))/(16*a*x^6) - (f*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2) - (5*c*(a + b*x^2)^(5/2))/(16*a^3*x^6) - (5*d*(a + b*x^2)^(1/2))/(8*a*x^4) + (3*d*(a + b*x^2)^(3/2))/(8*a^2*x^4) - (e*(a + b*x^2)^(1/2))/(2*a*x^2) + (b*e*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2)) - (b^3*c*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(16*a^(7/2)) - (3*b^2*d*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(5/2))","B"
150,1,277,195,2.913454,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^9*(a + b*x^2)^(1/2)),x)","\frac{511\,c\,{\left(b\,x^2+a\right)}^{3/2}}{384\,a^2\,x^8}-\frac{93\,c\,\sqrt{b\,x^2+a}}{128\,a\,x^8}-\frac{385\,c\,{\left(b\,x^2+a\right)}^{5/2}}{384\,a^3\,x^8}+\frac{35\,c\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a^4\,x^8}-\frac{11\,d\,\sqrt{b\,x^2+a}}{16\,a\,x^6}+\frac{5\,d\,{\left(b\,x^2+a\right)}^{3/2}}{6\,a^2\,x^6}-\frac{5\,d\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a^3\,x^6}-\frac{5\,e\,\sqrt{b\,x^2+a}}{8\,a\,x^4}+\frac{3\,e\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a^2\,x^4}-\frac{f\,\sqrt{b\,x^2+a}}{2\,a\,x^2}+\frac{b\,f\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{3\,b^2\,e\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{5/2}}+\frac{b^4\,c\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,35{}\mathrm{i}}{128\,a^{9/2}}-\frac{b^3\,d\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{16\,a^{7/2}}","Not used",1,"(511*c*(a + b*x^2)^(3/2))/(384*a^2*x^8) - (93*c*(a + b*x^2)^(1/2))/(128*a*x^8) - (385*c*(a + b*x^2)^(5/2))/(384*a^3*x^8) + (35*c*(a + b*x^2)^(7/2))/(128*a^4*x^8) - (11*d*(a + b*x^2)^(1/2))/(16*a*x^6) + (5*d*(a + b*x^2)^(3/2))/(6*a^2*x^6) - (5*d*(a + b*x^2)^(5/2))/(16*a^3*x^6) - (5*e*(a + b*x^2)^(1/2))/(8*a*x^4) + (3*e*(a + b*x^2)^(3/2))/(8*a^2*x^4) - (f*(a + b*x^2)^(1/2))/(2*a*x^2) + (b*f*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2)) + (b^4*c*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*35i)/(128*a^(9/2)) - (b^3*d*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(16*a^(7/2)) - (3*b^2*e*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(5/2))","B"
151,0,-1,245,0.000000,"\text{Not used}","int((x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2),x)","\int \frac{x^4\,\left(f\,x^6+e\,x^4+d\,x^2+c\right)}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((x^4*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2), x)","F"
152,0,-1,194,0.000000,"\text{Not used}","int((x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2),x)","\int \frac{x^2\,\left(f\,x^6+e\,x^4+d\,x^2+c\right)}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((x^2*(c + d*x^2 + e*x^4 + f*x^6))/(a + b*x^2)^(1/2), x)","F"
153,0,-1,145,0.000000,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2)^(1/2),x)","\int \frac{f\,x^6+e\,x^4+d\,x^2+c}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2 + e*x^4 + f*x^6)/(a + b*x^2)^(1/2), x)","F"
154,0,-1,117,0.000000,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)^(1/2)),x)","\int \frac{f\,x^6+e\,x^4+d\,x^2+c}{x^2\,\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((c + d*x^2 + e*x^4 + f*x^6)/(x^2*(a + b*x^2)^(1/2)), x)","F"
155,1,143,110,2.198988,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^4*(a + b*x^2)^(1/2)),x)","\left\{\begin{array}{cl} -\frac{-f\,x^6-3\,e\,x^4+3\,d\,x^2+c}{3\,\sqrt{a}\,x^3} & \text{\ if\ \ }b=0\\ \frac{e\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}-\frac{d\,\sqrt{b\,x^2+a}}{a\,x}-\frac{a\,f\,\ln\left(2\,\sqrt{b}\,x+2\,\sqrt{b\,x^2+a}\right)}{2\,b^{3/2}}+\frac{f\,x\,\sqrt{b\,x^2+a}}{2\,b}-\frac{c\,\sqrt{b\,x^2+a}\,\left(a-2\,b\,x^2\right)}{3\,a^2\,x^3} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, -(c + 3*d*x^2 - 3*e*x^4 - f*x^6)/(3*a^(1/2)*x^3), b ~= 0, (e*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2) - (d*(a + b*x^2)^(1/2))/(a*x) - (a*f*log(2*b^(1/2)*x + 2*(a + b*x^2)^(1/2)))/(2*b^(3/2)) + (f*x*(a + b*x^2)^(1/2))/(2*b) - (c*(a + b*x^2)^(1/2)*(a - 2*b*x^2))/(3*a^2*x^3))","B"
156,1,105,118,1.723558,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^6*(a + b*x^2)^(1/2)),x)","\frac{f\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}-\frac{e\,\sqrt{b\,x^2+a}}{a\,x}-\frac{d\,\sqrt{b\,x^2+a}\,\left(a-2\,b\,x^2\right)}{3\,a^2\,x^3}-\frac{c\,\sqrt{b\,x^2+a}\,\left(3\,a^2-4\,a\,b\,x^2+8\,b^2\,x^4\right)}{15\,a^3\,x^5}","Not used",1,"(f*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2) - (e*(a + b*x^2)^(1/2))/(a*x) - (d*(a + b*x^2)^(1/2)*(a - 2*b*x^2))/(3*a^2*x^3) - (c*(a + b*x^2)^(1/2)*(3*a^2 + 8*b^2*x^4 - 4*a*b*x^2))/(15*a^3*x^5)","B"
157,1,124,140,1.279663,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^8*(a + b*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(-105\,f\,a^3+70\,e\,a^2\,b-56\,d\,a\,b^2+48\,c\,b^3\right)}{105\,a^4\,x}-\frac{\sqrt{b\,x^2+a}\,\left(7\,a\,d-6\,b\,c\right)}{35\,a^2\,x^5}-\frac{\sqrt{b\,x^2+a}\,\left(35\,e\,a^2-28\,d\,a\,b+24\,c\,b^2\right)}{105\,a^3\,x^3}-\frac{c\,\sqrt{b\,x^2+a}}{7\,a\,x^7}","Not used",1,"((a + b*x^2)^(1/2)*(48*b^3*c - 105*a^3*f - 56*a*b^2*d + 70*a^2*b*e))/(105*a^4*x) - ((a + b*x^2)^(1/2)*(7*a*d - 6*b*c))/(35*a^2*x^5) - ((a + b*x^2)^(1/2)*(24*b^2*c + 35*a^2*e - 28*a*b*d))/(105*a^3*x^3) - (c*(a + b*x^2)^(1/2))/(7*a*x^7)","B"
158,1,171,189,1.282307,"\text{Not used}","int((c + d*x^2 + e*x^4 + f*x^6)/(x^10*(a + b*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(-105\,f\,a^3+84\,e\,a^2\,b-72\,d\,a\,b^2+64\,c\,b^3\right)}{315\,a^4\,x^3}-\frac{\sqrt{b\,x^2+a}\,\left(9\,a\,d-8\,b\,c\right)}{63\,a^2\,x^7}-\frac{\sqrt{b\,x^2+a}\,\left(21\,e\,a^2-18\,d\,a\,b+16\,c\,b^2\right)}{105\,a^3\,x^5}-\frac{\sqrt{b\,x^2+a}\,\left(-210\,f\,a^3\,b+168\,e\,a^2\,b^2-144\,d\,a\,b^3+128\,c\,b^4\right)}{315\,a^5\,x}-\frac{c\,\sqrt{b\,x^2+a}}{9\,a\,x^9}","Not used",1,"((a + b*x^2)^(1/2)*(64*b^3*c - 105*a^3*f - 72*a*b^2*d + 84*a^2*b*e))/(315*a^4*x^3) - ((a + b*x^2)^(1/2)*(9*a*d - 8*b*c))/(63*a^2*x^7) - ((a + b*x^2)^(1/2)*(16*b^2*c + 21*a^2*e - 18*a*b*d))/(105*a^3*x^5) - ((a + b*x^2)^(1/2)*(128*b^4*c + 168*a^2*b^2*e - 144*a*b^3*d - 210*a^3*b*f))/(315*a^5*x) - (c*(a + b*x^2)^(1/2))/(9*a*x^9)","B"
159,0,-1,381,0.000000,"\text{Not used}","int((x^8*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2),x)","\int \frac{x^8\,\left(A+B\,x^2+C\,x^4+x^6\,D\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^8*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2), x)","F"
160,0,-1,279,0.000000,"\text{Not used}","int((x^6*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2),x)","\int \frac{x^6\,\left(A+B\,x^2+C\,x^4+x^6\,D\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^6*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2), x)","F"
161,0,-1,210,0.000000,"\text{Not used}","int((x^4*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2),x)","\int \frac{x^4\,\left(A+B\,x^2+C\,x^4+x^6\,D\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^4*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2), x)","F"
162,0,-1,179,0.000000,"\text{Not used}","int((x^2*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2),x)","\int \frac{x^2\,\left(A+B\,x^2+C\,x^4+x^6\,D\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^2*(A + B*x^2 + C*x^4 + x^6*D))/(a + b*x^2)^(9/2), x)","F"
163,0,-1,134,0.000000,"\text{Not used}","int((A + B*x^2 + C*x^4 + x^6*D)/(a + b*x^2)^(9/2),x)","\int \frac{A+B\,x^2+C\,x^4+x^6\,D}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((A + B*x^2 + C*x^4 + x^6*D)/(a + b*x^2)^(9/2), x)","F"
164,0,-1,185,0.000000,"\text{Not used}","int((A + B*x^2 + C*x^4 + x^6*D)/(x^2*(a + b*x^2)^(9/2)),x)","\int \frac{A+B\,x^2+C\,x^4+x^6\,D}{x^2\,{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((A + B*x^2 + C*x^4 + x^6*D)/(x^2*(a + b*x^2)^(9/2)), x)","F"
165,0,-1,242,0.000000,"\text{Not used}","int((A + B*x^2 + C*x^4 + x^6*D)/(x^4*(a + b*x^2)^(9/2)),x)","\int \frac{A+B\,x^2+C\,x^4+x^6\,D}{x^4\,{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((A + B*x^2 + C*x^4 + x^6*D)/(x^4*(a + b*x^2)^(9/2)), x)","F"
166,1,405,281,2.396955,"\text{Not used}","int((A + B*x^2 + C*x^4 + x^6*D)/(x^6*(a + b*x^2)^(9/2)),x)","\frac{\frac{61\,A\,b}{35\,a^3}+\frac{78\,A\,b^2\,x^2}{35\,a^4}}{x^3\,{\left(b\,x^2+a\right)}^{5/2}}+\frac{\frac{128\,B\,b}{21\,a^5}+\frac{256\,B\,b^2\,x^2}{21\,a^6}}{x\,\sqrt{b\,x^2+a}}+\frac{x\,D}{{\left(b\,x^2+a\right)}^{9/2}}-\frac{\frac{B}{3\,a^2}+\frac{19\,B\,b\,x^2}{21\,a^3}}{x^3\,{\left(b\,x^2+a\right)}^{5/2}}-\frac{\frac{C}{a^4}+\frac{128\,C\,b\,x^2}{35\,a^5}}{x\,\sqrt{b\,x^2+a}}-\frac{\frac{512\,A\,b^2}{35\,a^6}+\frac{1024\,A\,b^3\,x^2}{35\,a^7}}{x\,\sqrt{b\,x^2+a}}-\frac{A\,\sqrt{b\,x^2+a}}{5\,a^5\,x^5}+\frac{18\,b^2\,x^5\,D}{5\,a^2\,{\left(b\,x^2+a\right)}^{9/2}}+\frac{72\,b^3\,x^7\,D}{35\,a^3\,{\left(b\,x^2+a\right)}^{9/2}}+\frac{16\,b^4\,x^9\,D}{35\,a^4\,{\left(b\,x^2+a\right)}^{9/2}}-\frac{A\,b}{7\,a^2\,x^3\,{\left(b\,x^2+a\right)}^{7/2}}-\frac{32\,B\,b}{21\,a^4\,x\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{B\,b^2\,x}{7\,a^3\,{\left(b\,x^2+a\right)}^{7/2}}+\frac{27\,A\,b^2}{7\,a^5\,x\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{3\,b\,x^3\,D}{a\,{\left(b\,x^2+a\right)}^{9/2}}-\frac{29\,C\,b\,x}{35\,a^4\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{13\,C\,b\,x}{35\,a^3\,{\left(b\,x^2+a\right)}^{5/2}}-\frac{C\,b\,x}{7\,a^2\,{\left(b\,x^2+a\right)}^{7/2}}","Not used",1,"((61*A*b)/(35*a^3) + (78*A*b^2*x^2)/(35*a^4))/(x^3*(a + b*x^2)^(5/2)) + ((128*B*b)/(21*a^5) + (256*B*b^2*x^2)/(21*a^6))/(x*(a + b*x^2)^(1/2)) + (x*D)/(a + b*x^2)^(9/2) - (B/(3*a^2) + (19*B*b*x^2)/(21*a^3))/(x^3*(a + b*x^2)^(5/2)) - (C/a^4 + (128*C*b*x^2)/(35*a^5))/(x*(a + b*x^2)^(1/2)) - ((512*A*b^2)/(35*a^6) + (1024*A*b^3*x^2)/(35*a^7))/(x*(a + b*x^2)^(1/2)) - (A*(a + b*x^2)^(1/2))/(5*a^5*x^5) + (18*b^2*x^5*D)/(5*a^2*(a + b*x^2)^(9/2)) + (72*b^3*x^7*D)/(35*a^3*(a + b*x^2)^(9/2)) + (16*b^4*x^9*D)/(35*a^4*(a + b*x^2)^(9/2)) - (A*b)/(7*a^2*x^3*(a + b*x^2)^(7/2)) - (32*B*b)/(21*a^4*x*(a + b*x^2)^(3/2)) + (B*b^2*x)/(7*a^3*(a + b*x^2)^(7/2)) + (27*A*b^2)/(7*a^5*x*(a + b*x^2)^(3/2)) + (3*b*x^3*D)/(a*(a + b*x^2)^(9/2)) - (29*C*b*x)/(35*a^4*(a + b*x^2)^(3/2)) - (13*C*b*x)/(35*a^3*(a + b*x^2)^(5/2)) - (C*b*x)/(7*a^2*(a + b*x^2)^(7/2))","B"
167,1,421,334,2.836149,"\text{Not used}","int((A + B*x^2 + C*x^4 + x^6*D)/(x^8*(a + b*x^2)^(9/2)),x)","\frac{\frac{61\,B\,b}{35\,a^3}+\frac{78\,B\,b^2\,x^2}{35\,a^4}}{x^3\,{\left(b\,x^2+a\right)}^{5/2}}+\frac{\frac{128\,C\,b}{21\,a^5}+\frac{256\,C\,b^2\,x^2}{21\,a^6}}{x\,\sqrt{b\,x^2+a}}-\frac{\frac{C}{3\,a^2}+\frac{19\,C\,b\,x^2}{21\,a^3}}{x^3\,{\left(b\,x^2+a\right)}^{5/2}}-\frac{\frac{167\,A\,b^2}{35\,a^4}+\frac{191\,A\,b^3\,x^2}{35\,a^5}}{x^3\,{\left(b\,x^2+a\right)}^{5/2}}+\frac{\frac{1024\,A\,b^3}{35\,a^7}+\frac{2048\,A\,b^4\,x^2}{35\,a^8}}{x\,\sqrt{b\,x^2+a}}-\frac{\frac{512\,B\,b^2}{35\,a^6}+\frac{1024\,B\,b^3\,x^2}{35\,a^7}}{x\,\sqrt{b\,x^2+a}}-\frac{A\,\sqrt{b\,x^2+a}}{7\,a^5\,x^7}-\frac{B\,\sqrt{b\,x^2+a}}{5\,a^5\,x^5}-\frac{{\left(\frac{a}{b\,x^2}+1\right)}^{9/2}\,D\,{{}}_2{\mathrm{F}}_1\left(\frac{9}{2},5;\ 6;\ -\frac{a}{b\,x^2}\right)}{10\,x\,{\left(b\,x^2+a\right)}^{9/2}}+\frac{34\,A\,b\,\sqrt{b\,x^2+a}}{35\,a^6\,x^5}-\frac{B\,b}{7\,a^2\,x^3\,{\left(b\,x^2+a\right)}^{7/2}}-\frac{32\,C\,b}{21\,a^4\,x\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{C\,b^2\,x}{7\,a^3\,{\left(b\,x^2+a\right)}^{7/2}}-\frac{58\,A\,b^3}{7\,a^6\,x\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{A\,b^2}{7\,a^3\,x^3\,{\left(b\,x^2+a\right)}^{7/2}}+\frac{27\,B\,b^2}{7\,a^5\,x\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"((61*B*b)/(35*a^3) + (78*B*b^2*x^2)/(35*a^4))/(x^3*(a + b*x^2)^(5/2)) + ((128*C*b)/(21*a^5) + (256*C*b^2*x^2)/(21*a^6))/(x*(a + b*x^2)^(1/2)) - (C/(3*a^2) + (19*C*b*x^2)/(21*a^3))/(x^3*(a + b*x^2)^(5/2)) - ((167*A*b^2)/(35*a^4) + (191*A*b^3*x^2)/(35*a^5))/(x^3*(a + b*x^2)^(5/2)) + ((1024*A*b^3)/(35*a^7) + (2048*A*b^4*x^2)/(35*a^8))/(x*(a + b*x^2)^(1/2)) - ((512*B*b^2)/(35*a^6) + (1024*B*b^3*x^2)/(35*a^7))/(x*(a + b*x^2)^(1/2)) - (A*(a + b*x^2)^(1/2))/(7*a^5*x^7) - (B*(a + b*x^2)^(1/2))/(5*a^5*x^5) - ((a/(b*x^2) + 1)^(9/2)*D*hypergeom([9/2, 5], 6, -a/(b*x^2)))/(10*x*(a + b*x^2)^(9/2)) + (34*A*b*(a + b*x^2)^(1/2))/(35*a^6*x^5) - (B*b)/(7*a^2*x^3*(a + b*x^2)^(7/2)) - (32*C*b)/(21*a^4*x*(a + b*x^2)^(3/2)) + (C*b^2*x)/(7*a^3*(a + b*x^2)^(7/2)) - (58*A*b^3)/(7*a^6*x*(a + b*x^2)^(3/2)) + (A*b^2)/(7*a^3*x^3*(a + b*x^2)^(7/2)) + (27*B*b^2)/(7*a^5*x*(a + b*x^2)^(3/2))","B"
168,0,-1,392,0.000000,"\text{Not used}","int((A + B*x^2 + C*x^4 + x^6*D)/(x^10*(a + b*x^2)^(9/2)),x)","\int \frac{A+B\,x^2+C\,x^4+x^6\,D}{x^{10}\,{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((A + B*x^2 + C*x^4 + x^6*D)/(x^10*(a + b*x^2)^(9/2)), x)","F"
169,1,186,214,1.203319,"\text{Not used}","int((c*x^5 + d*x^7 + e*x^9 + f*x^11)/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{x^6\,\left(400\,f\,a^2\,b^3-440\,e\,a\,b^4+495\,d\,b^5\right)}{3465\,b^6}-\frac{1280\,f\,a^5-1408\,e\,a^4\,b+1584\,d\,a^3\,b^2-1848\,c\,a^2\,b^3}{3465\,b^6}+\frac{x^4\,\left(-480\,f\,a^3\,b^2+528\,e\,a^2\,b^3-594\,d\,a\,b^4+693\,c\,b^5\right)}{3465\,b^6}+\frac{f\,x^{10}}{11\,b}+\frac{x^8\,\left(385\,b^5\,e-350\,a\,b^4\,f\right)}{3465\,b^6}-\frac{4\,a\,x^2\,\left(-160\,f\,a^3+176\,e\,a^2\,b-198\,d\,a\,b^2+231\,c\,b^3\right)}{3465\,b^5}\right)","Not used",1,"(a + b*x^2)^(1/2)*((x^6*(495*b^5*d + 400*a^2*b^3*f - 440*a*b^4*e))/(3465*b^6) - (1280*a^5*f - 1848*a^2*b^3*c + 1584*a^3*b^2*d - 1408*a^4*b*e)/(3465*b^6) + (x^4*(693*b^5*c + 528*a^2*b^3*e - 480*a^3*b^2*f - 594*a*b^4*d))/(3465*b^6) + (f*x^10)/(11*b) + (x^8*(385*b^5*e - 350*a*b^4*f))/(3465*b^6) - (4*a*x^2*(231*b^3*c - 160*a^3*f - 198*a*b^2*d + 176*a^2*b*e))/(3465*b^5))","B"
170,1,146,167,1.140328,"\text{Not used}","int((c*x^3 + d*x^5 + e*x^7 + f*x^9)/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{128\,f\,a^4-144\,e\,a^3\,b+168\,d\,a^2\,b^2-210\,c\,a\,b^3}{315\,b^5}+\frac{x^4\,\left(48\,f\,a^2\,b^2-54\,e\,a\,b^3+63\,d\,b^4\right)}{315\,b^5}+\frac{f\,x^8}{9\,b}+\frac{x^6\,\left(45\,b^4\,e-40\,a\,b^3\,f\right)}{315\,b^5}+\frac{x^2\,\left(-64\,f\,a^3\,b+72\,e\,a^2\,b^2-84\,d\,a\,b^3+105\,c\,b^4\right)}{315\,b^5}\right)","Not used",1,"(a + b*x^2)^(1/2)*((128*a^4*f + 168*a^2*b^2*d - 210*a*b^3*c - 144*a^3*b*e)/(315*b^5) + (x^4*(63*b^4*d + 48*a^2*b^2*f - 54*a*b^3*e))/(315*b^5) + (f*x^8)/(9*b) + (x^6*(45*b^4*e - 40*a*b^3*f))/(315*b^5) + (x^2*(105*b^4*c + 72*a^2*b^2*e - 84*a*b^3*d - 64*a^3*b*f))/(315*b^5))","B"
171,1,103,121,1.083765,"\text{Not used}","int((c*x + d*x^3 + e*x^5 + f*x^7)/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{-48\,f\,a^3+56\,e\,a^2\,b-70\,d\,a\,b^2+105\,c\,b^3}{105\,b^4}+\frac{f\,x^6}{7\,b}+\frac{x^2\,\left(24\,f\,a^2\,b-28\,e\,a\,b^2+35\,d\,b^3\right)}{105\,b^4}+\frac{x^4\,\left(21\,b^3\,e-18\,a\,b^2\,f\right)}{105\,b^4}\right)","Not used",1,"(a + b*x^2)^(1/2)*((105*b^3*c - 48*a^3*f - 70*a*b^2*d + 56*a^2*b*e)/(105*b^4) + (f*x^6)/(7*b) + (x^2*(35*b^3*d - 28*a*b^2*e + 24*a^2*b*f))/(105*b^4) + (x^4*(21*b^3*e - 18*a*b^2*f))/(105*b^4))","B"
172,0,-1,261,0.000000,"\text{Not used}","int((x^2*(A + B*x^2 + C*x^4 + F*x^8 + x^6*D))/(a + b*x^2)^(9/2),x)","\int \frac{x^2\,\left(A+B\,x^2+C\,x^4+F\,x^8+x^6\,D\right)}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((x^2*(A + B*x^2 + C*x^4 + F*x^8 + x^6*D))/(a + b*x^2)^(9/2), x)","F"
173,0,-1,214,0.000000,"\text{Not used}","int((A + B*x^2 + C*x^4 + F*x^8 + x^6*D)/(a + b*x^2)^(9/2),x)","\int \frac{A+B\,x^2+C\,x^4+F\,x^8+x^6\,D}{{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((A + B*x^2 + C*x^4 + F*x^8 + x^6*D)/(a + b*x^2)^(9/2), x)","F"
174,0,-1,193,0.000000,"\text{Not used}","int((A + B*x^2 + C*x^4 + F*x^8 + x^6*D)/(x^2*(a + b*x^2)^(9/2)),x)","\int \frac{A+B\,x^2+C\,x^4+F\,x^8+x^6\,D}{x^2\,{\left(b\,x^2+a\right)}^{9/2}} \,d x","Not used",1,"int((A + B*x^2 + C*x^4 + F*x^8 + x^6*D)/(x^2*(a + b*x^2)^(9/2)), x)","F"