1,1,96,0,1.355186," ","integrate((b*x^2+a)*(d*x^2+c)^4,x, algorithm=""maxima"")","\frac{1}{11} \, b d^{4} x^{11} + \frac{1}{9} \, {\left(4 \, b c d^{3} + a d^{4}\right)} x^{9} + \frac{2}{7} \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} x^{7} + a c^{4} x + \frac{2}{5} \, {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} x^{5} + \frac{1}{3} \, {\left(b c^{4} + 4 \, a c^{3} d\right)} x^{3}"," ",0,"1/11*b*d^4*x^11 + 1/9*(4*b*c*d^3 + a*d^4)*x^9 + 2/7*(3*b*c^2*d^2 + 2*a*c*d^3)*x^7 + a*c^4*x + 2/5*(2*b*c^3*d + 3*a*c^2*d^2)*x^5 + 1/3*(b*c^4 + 4*a*c^3*d)*x^3","A",0
2,1,70,0,1.371872," ","integrate((b*x^2+a)*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{9} \, b d^{3} x^{9} + \frac{1}{7} \, {\left(3 \, b c d^{2} + a d^{3}\right)} x^{7} + \frac{3}{5} \, {\left(b c^{2} d + a c d^{2}\right)} x^{5} + a c^{3} x + \frac{1}{3} \, {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{3}"," ",0,"1/9*b*d^3*x^9 + 1/7*(3*b*c*d^2 + a*d^3)*x^7 + 3/5*(b*c^2*d + a*c*d^2)*x^5 + a*c^3*x + 1/3*(b*c^3 + 3*a*c^2*d)*x^3","A",0
3,1,48,0,1.351670," ","integrate((b*x^2+a)*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{7} \, b d^{2} x^{7} + \frac{1}{5} \, {\left(2 \, b c d + a d^{2}\right)} x^{5} + a c^{2} x + \frac{1}{3} \, {\left(b c^{2} + 2 \, a c d\right)} x^{3}"," ",0,"1/7*b*d^2*x^7 + 1/5*(2*b*c*d + a*d^2)*x^5 + a*c^2*x + 1/3*(b*c^2 + 2*a*c*d)*x^3","A",0
4,1,24,0,1.348847," ","integrate((b*x^2+a)*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{5} \, b d x^{5} + \frac{1}{3} \, {\left(b c + a d\right)} x^{3} + a c x"," ",0,"1/5*b*d*x^5 + 1/3*(b*c + a*d)*x^3 + a*c*x","A",0
5,1,34,0,2.997547," ","integrate((b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b x}{d} - \frac{{\left(b c - a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d}"," ",0,"b*x/d - (b*c - a*d)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d)","A",0
6,1,57,0,3.114548," ","integrate((b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b c - a d\right)} x}{2 \, {\left(c d^{2} x^{2} + c^{2} d\right)}} + \frac{{\left(b c + a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d}"," ",0,"-1/2*(b*c - a*d)*x/(c*d^2*x^2 + c^2*d) + 1/2*(b*c + a*d)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d)","A",0
7,1,92,0,2.962927," ","integrate((b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b c d + 3 \, a d^{2}\right)} x^{3} - {\left(b c^{2} - 5 \, a c d\right)} x}{8 \, {\left(c^{2} d^{3} x^{4} + 2 \, c^{3} d^{2} x^{2} + c^{4} d\right)}} + \frac{{\left(b c + 3 \, a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d}"," ",0,"1/8*((b*c*d + 3*a*d^2)*x^3 - (b*c^2 - 5*a*c*d)*x)/(c^2*d^3*x^4 + 2*c^3*d^2*x^2 + c^4*d) + 1/8*(b*c + 3*a*d)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d)","A",0
8,1,124,0,1.394863," ","integrate((b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{11} \, b^{2} d^{3} x^{11} + \frac{1}{9} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{9} + \frac{1}{7} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{7} + a^{2} c^{3} x + \frac{1}{5} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{5} + \frac{1}{3} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{3}"," ",0,"1/11*b^2*d^3*x^11 + 1/9*(3*b^2*c*d^2 + 2*a*b*d^3)*x^9 + 1/7*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^7 + a^2*c^3*x + 1/5*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^5 + 1/3*(2*a*b*c^3 + 3*a^2*c^2*d)*x^3","A",0
9,1,82,0,1.327231," ","integrate((b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} d^{2} x^{9} + \frac{2}{7} \, {\left(b^{2} c d + a b d^{2}\right)} x^{7} + \frac{1}{5} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{5} + a^{2} c^{2} x + \frac{2}{3} \, {\left(a b c^{2} + a^{2} c d\right)} x^{3}"," ",0,"1/9*b^2*d^2*x^9 + 2/7*(b^2*c*d + a*b*d^2)*x^7 + 1/5*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^5 + a^2*c^2*x + 2/3*(a*b*c^2 + a^2*c*d)*x^3","A",0
10,1,48,0,1.320314," ","integrate((b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} d x^{7} + \frac{1}{5} \, {\left(b^{2} c + 2 \, a b d\right)} x^{5} + a^{2} c x + \frac{1}{3} \, {\left(2 \, a b c + a^{2} d\right)} x^{3}"," ",0,"1/7*b^2*d*x^7 + 1/5*(b^2*c + 2*a*b*d)*x^5 + a^2*c*x + 1/3*(2*a*b*c + a^2*d)*x^3","A",0
11,1,68,0,2.886011," ","integrate((b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{2}} + \frac{b^{2} d x^{3} - 3 \, {\left(b^{2} c - 2 \, a b d\right)} x}{3 \, d^{2}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^2) + 1/3*(b^2*d*x^3 - 3*(b^2*c - 2*a*b*d)*x)/d^2","A",0
12,1,96,0,2.840216," ","integrate((b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{2 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}} + \frac{b^{2} x}{d^{2}} - \frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d^{2}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(c*d^3*x^2 + c^2*d^2) + b^2*x/d^2 - 1/2*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d^2)","A",0
13,1,138,0,3.084171," ","integrate((b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(3 \, b^{2} c^{3} + 2 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} x}{8 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}} + \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d^{2}}"," ",0,"-1/8*((5*b^2*c^2*d - 2*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (3*b^2*c^3 + 2*a*b*c^2*d - 5*a^2*c*d^2)*x)/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2) + 1/8*(3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d^2)","A",0
14,1,167,0,1.377811," ","integrate((b*x^2+a)^3*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{13} \, b^{3} d^{3} x^{13} + \frac{3}{11} \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{11} + \frac{1}{3} \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{9} + \frac{1}{7} \, {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{7} + a^{3} c^{3} x + \frac{3}{5} \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} x^{5} + {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x^{3}"," ",0,"1/13*b^3*d^3*x^13 + 3/11*(b^3*c*d^2 + a*b^2*d^3)*x^11 + 1/3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*x^9 + 1/7*(b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*x^7 + a^3*c^3*x + 3/5*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*x^5 + (a^2*b*c^3 + a^3*c^2*d)*x^3","A",0
15,1,124,0,1.362486," ","integrate((b*x^2+a)^3*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{11} \, b^{3} d^{2} x^{11} + \frac{1}{9} \, {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} x^{9} + \frac{1}{7} \, {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x^{7} + a^{3} c^{2} x + \frac{1}{5} \, {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{5} + \frac{1}{3} \, {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} x^{3}"," ",0,"1/11*b^3*d^2*x^11 + 1/9*(2*b^3*c*d + 3*a*b^2*d^2)*x^9 + 1/7*(b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*x^7 + a^3*c^2*x + 1/5*(3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*x^5 + 1/3*(3*a^2*b*c^2 + 2*a^3*c*d)*x^3","A",0
16,1,70,0,1.294384," ","integrate((b*x^2+a)^3*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{9} \, b^{3} d x^{9} + \frac{1}{7} \, {\left(b^{3} c + 3 \, a b^{2} d\right)} x^{7} + \frac{3}{5} \, {\left(a b^{2} c + a^{2} b d\right)} x^{5} + a^{3} c x + \frac{1}{3} \, {\left(3 \, a^{2} b c + a^{3} d\right)} x^{3}"," ",0,"1/9*b^3*d*x^9 + 1/7*(b^3*c + 3*a*b^2*d)*x^7 + 3/5*(a*b^2*c + a^2*b*d)*x^5 + a^3*c*x + 1/3*(3*a^2*b*c + a^3*d)*x^3","A",0
17,1,122,0,3.024819," ","integrate((b*x^2+a)^3/(d*x^2+c),x, algorithm=""maxima"")","-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{3}} + \frac{3 \, b^{3} d^{2} x^{5} - 5 \, {\left(b^{3} c d - 3 \, a b^{2} d^{2}\right)} x^{3} + 15 \, {\left(b^{3} c^{2} - 3 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x}{15 \, d^{3}}"," ",0,"-(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^3) + 1/15*(3*b^3*d^2*x^5 - 5*(b^3*c*d - 3*a*b^2*d^2)*x^3 + 15*(b^3*c^2 - 3*a*b^2*c*d + 3*a^2*b*d^2)*x)/d^3","A",0
18,1,147,0,2.991425," ","integrate((b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{2 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}} + \frac{b^{3} d x^{3} - 3 \, {\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} x}{3 \, d^{3}} + \frac{{\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d^{3}}"," ",0,"-1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x/(c*d^4*x^2 + c^2*d^3) + 1/3*(b^3*d*x^3 - 3*(2*b^3*c - 3*a*b^2*d)*x)/d^3 + 1/2*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d^3)","A",0
19,1,187,0,2.979192," ","integrate((b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{3} x}{d^{3}} + \frac{3 \, {\left(3 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{3} + {\left(7 \, b^{3} c^{4} - 9 \, a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + 5 \, a^{3} c d^{3}\right)} x}{8 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}} - \frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d^{3}}"," ",0,"b^3*x/d^3 + 1/8*(3*(3*b^3*c^3*d - 5*a*b^2*c^2*d^2 + a^2*b*c*d^3 + a^3*d^4)*x^3 + (7*b^3*c^4 - 9*a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + 5*a^3*c*d^3)*x)/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3) - 3/8*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d^3)","A",0
20,1,187,0,3.032914," ","integrate((d*x^2+c)^4/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, b^{3} d^{4} x^{7} + 21 \, {\left(4 \, b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{5} + 35 \, {\left(6 \, b^{3} c^{2} d^{2} - 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3} + 105 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x}{105 \, b^{4}}"," ",0,"(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*b^3*d^4*x^7 + 21*(4*b^3*c*d^3 - a*b^2*d^4)*x^5 + 35*(6*b^3*c^2*d^2 - 4*a*b^2*c*d^3 + a^2*b*d^4)*x^3 + 105*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*x)/b^4","A",0
21,1,122,0,2.911313," ","integrate((d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{2} d^{3} x^{5} + 5 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{3} + 15 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x}{15 \, b^{3}}"," ",0,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^2*d^3*x^5 + 5*(3*b^2*c*d^2 - a*b*d^3)*x^3 + 15*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x)/b^3","A",0
22,1,69,0,2.933612," ","integrate((d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b d^{2} x^{3} + 3 \, {\left(2 \, b c d - a d^{2}\right)} x}{3 \, b^{2}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b*d^2*x^3 + 3*(2*b*c*d - a*d^2)*x)/b^2","A",0
23,1,33,0,2.991377," ","integrate((d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{d x}{b} + \frac{{\left(b c - a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b}"," ",0,"d*x/b + (b*c - a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
24,1,54,0,2.984751," ","integrate(1/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(b c - a d\right)}} - \frac{d \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c - a d\right)} \sqrt{c d}}"," ",0,"b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*(b*c - a*d)) - d*arctan(d*x/sqrt(c*d))/((b*c - a*d)*sqrt(c*d))","A",0
25,1,133,0,3.044708," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b}} - \frac{d x}{2 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}} - \frac{{\left(3 \, b c d - a d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{c d}}"," ",0,"b^2*arctan(b*x/sqrt(a*b))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)) - 1/2*d*x/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2) - 1/2*(3*b*c*d - a*d^2)*arctan(d*x/sqrt(c*d))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(c*d))","A",0
26,1,277,0,3.075140," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b}} - \frac{{\left(15 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \sqrt{c d}} - \frac{{\left(7 \, b c d^{2} - 3 \, a d^{3}\right)} x^{3} + {\left(9 \, b c^{2} d - 5 \, a c d^{2}\right)} x}{8 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"b^3*arctan(b*x/sqrt(a*b))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b)) - 1/8*(15*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*arctan(d*x/sqrt(c*d))/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*sqrt(c*d)) - 1/8*((7*b*c*d^2 - 3*a*d^3)*x^3 + (9*b*c^2*d - 5*a*c*d^2)*x)/(b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*x^4 + 2*(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*x^2)","B",0
27,1,294,0,3.026153," ","integrate((d*x^2+c)^5/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} x}{2 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}} + \frac{15 \, b^{3} d^{5} x^{7} + 21 \, {\left(5 \, b^{3} c d^{4} - 2 \, a b^{2} d^{5}\right)} x^{5} + 35 \, {\left(10 \, b^{3} c^{2} d^{3} - 10 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} x^{3} + 105 \, {\left(10 \, b^{3} c^{3} d^{2} - 20 \, a b^{2} c^{2} d^{3} + 15 \, a^{2} b c d^{4} - 4 \, a^{3} d^{5}\right)} x}{105 \, b^{5}} + \frac{{\left(b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 30 \, a^{2} b^{3} c^{3} d^{2} + 50 \, a^{3} b^{2} c^{2} d^{3} - 35 \, a^{4} b c d^{4} + 9 \, a^{5} d^{5}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{5}}"," ",0,"1/2*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*x/(a*b^6*x^2 + a^2*b^5) + 1/105*(15*b^3*d^5*x^7 + 21*(5*b^3*c*d^4 - 2*a*b^2*d^5)*x^5 + 35*(10*b^3*c^2*d^3 - 10*a*b^2*c*d^4 + 3*a^2*b*d^5)*x^3 + 105*(10*b^3*c^3*d^2 - 20*a*b^2*c^2*d^3 + 15*a^2*b*c*d^4 - 4*a^3*d^5)*x)/b^5 + 1/2*(b^5*c^5 + 5*a*b^4*c^4*d - 30*a^2*b^3*c^3*d^2 + 50*a^3*b^2*c^2*d^3 - 35*a^4*b*c*d^4 + 9*a^5*d^5)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^5)","A",0
28,1,213,0,2.996741," ","integrate((d*x^2+c)^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x}{2 \, {\left(a b^{5} x^{2} + a^{2} b^{4}\right)}} + \frac{3 \, b^{2} d^{4} x^{5} + 10 \, {\left(2 \, b^{2} c d^{3} - a b d^{4}\right)} x^{3} + 15 \, {\left(6 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x}{15 \, b^{4}} + \frac{{\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{4}}"," ",0,"1/2*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x/(a*b^5*x^2 + a^2*b^4) + 1/15*(3*b^2*d^4*x^5 + 10*(2*b^2*c*d^3 - a*b*d^4)*x^3 + 15*(6*b^2*c^2*d^2 - 8*a*b*c*d^3 + 3*a^2*d^4)*x)/b^4 + 1/2*(b^4*c^4 + 4*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 7*a^4*d^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^4)","A",0
29,1,147,0,2.990215," ","integrate((d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{b d^{3} x^{3} + 3 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} x}{3 \, b^{3}} + \frac{{\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{3}}"," ",0,"1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x/(a*b^4*x^2 + a^2*b^3) + 1/3*(b*d^3*x^3 + 3*(3*b*c*d^2 - 2*a*d^3)*x)/b^3 + 1/2*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^3)","A",0
30,1,95,0,2.839097," ","integrate((d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}} + \frac{d^{2} x}{b^{2}} + \frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{2}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(a*b^3*x^2 + a^2*b^2) + d^2*x/b^2 + 1/2*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
31,1,57,0,3.113704," ","integrate((d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c - a d\right)} x}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} + \frac{{\left(b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b}"," ",0,"1/2*(b*c - a*d)*x/(a*b^2*x^2 + a^2*b) + 1/2*(b*c + a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
32,1,132,0,2.915301," ","integrate(1/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{d^{2} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d}} + \frac{b x}{2 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)}} + \frac{{\left(b^{2} c - 3 \, a b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{a b}}"," ",0,"d^2*arctan(d*x/sqrt(c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)) + 1/2*b*x/(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2) + 1/2*(b^2*c - 3*a*b*d)*arctan(b*x/sqrt(a*b))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a*b))","A",0
33,1,294,0,3.139701," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c - 5 \, a b^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \sqrt{a b}} + \frac{{\left(5 \, b c d^{2} - a d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \sqrt{c d}} + \frac{{\left(b^{2} c d + a b d^{2}\right)} x^{3} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} x}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{4} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}\right)}}"," ",0,"1/2*(b^3*c - 5*a*b^2*d)*arctan(b*x/sqrt(a*b))/((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*sqrt(a*b)) + 1/2*(5*b*c*d^2 - a*d^3)*arctan(d*x/sqrt(c*d))/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*sqrt(c*d)) + 1/2*((b^2*c*d + a*b*d^2)*x^3 + (b^2*c^2 + a^2*d^2)*x)/(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^4 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2)","B",0
34,1,529,0,3.409399," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}\right)} \sqrt{a b}} + \frac{{\left(35 \, b^{2} c^{2} d^{2} - 14 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} \sqrt{c d}} + \frac{{\left(4 \, b^{3} c^{2} d^{2} + 11 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} x^{5} + {\left(8 \, b^{3} c^{3} d + 13 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3} - 3 \, a^{3} d^{4}\right)} x^{3} + {\left(4 \, b^{3} c^{4} + 13 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x}{8 \, {\left(a^{2} b^{3} c^{7} - 3 \, a^{3} b^{2} c^{6} d + 3 \, a^{4} b c^{5} d^{2} - a^{5} c^{4} d^{3} + {\left(a b^{4} c^{5} d^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} + 3 \, a^{3} b^{2} c^{3} d^{4} - a^{4} b c^{2} d^{5}\right)} x^{6} + {\left(2 \, a b^{4} c^{6} d - 5 \, a^{2} b^{3} c^{5} d^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} + a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} x^{4} + {\left(a b^{4} c^{7} - a^{2} b^{3} c^{6} d - 3 \, a^{3} b^{2} c^{5} d^{2} + 5 \, a^{4} b c^{4} d^{3} - 2 \, a^{5} c^{3} d^{4}\right)} x^{2}\right)}}"," ",0,"1/2*(b^4*c - 7*a*b^3*d)*arctan(b*x/sqrt(a*b))/((a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4)*sqrt(a*b)) + 1/8*(35*b^2*c^2*d^2 - 14*a*b*c*d^3 + 3*a^2*d^4)*arctan(d*x/sqrt(c*d))/((b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*sqrt(c*d)) + 1/8*((4*b^3*c^2*d^2 + 11*a*b^2*c*d^3 - 3*a^2*b*d^4)*x^5 + (8*b^3*c^3*d + 13*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3 - 3*a^3*d^4)*x^3 + (4*b^3*c^4 + 13*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x)/(a^2*b^3*c^7 - 3*a^3*b^2*c^6*d + 3*a^4*b*c^5*d^2 - a^5*c^4*d^3 + (a*b^4*c^5*d^2 - 3*a^2*b^3*c^4*d^3 + 3*a^3*b^2*c^3*d^4 - a^4*b*c^2*d^5)*x^6 + (2*a*b^4*c^6*d - 5*a^2*b^3*c^5*d^2 + 3*a^3*b^2*c^4*d^3 + a^4*b*c^3*d^4 - a^5*c^2*d^5)*x^4 + (a*b^4*c^7 - a^2*b^3*c^6*d - 3*a^3*b^2*c^5*d^2 + 5*a^4*b*c^4*d^3 - 2*a^5*c^3*d^4)*x^2)","B",0
35,1,334,0,3.037280," ","integrate((d*x^2+c)^5/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{6} c^{5} + 5 \, a b^{5} c^{4} d - 50 \, a^{2} b^{4} c^{3} d^{2} + 90 \, a^{3} b^{3} c^{2} d^{3} - 65 \, a^{4} b^{2} c d^{4} + 17 \, a^{5} b d^{5}\right)} x^{3} + 5 \, {\left(a b^{5} c^{5} - a^{2} b^{4} c^{4} d - 6 \, a^{3} b^{3} c^{3} d^{2} + 14 \, a^{4} b^{2} c^{2} d^{3} - 11 \, a^{5} b c d^{4} + 3 \, a^{6} d^{5}\right)} x}{8 \, {\left(a^{2} b^{7} x^{4} + 2 \, a^{3} b^{6} x^{2} + a^{4} b^{5}\right)}} + \frac{3 \, b^{2} d^{5} x^{5} + 5 \, {\left(5 \, b^{2} c d^{4} - 3 \, a b d^{5}\right)} x^{3} + 15 \, {\left(10 \, b^{2} c^{2} d^{3} - 15 \, a b c d^{4} + 6 \, a^{2} d^{5}\right)} x}{15 \, b^{5}} + \frac{{\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 150 \, a^{3} b^{2} c^{2} d^{3} + 175 \, a^{4} b c d^{4} - 63 \, a^{5} d^{5}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{5}}"," ",0,"1/8*((3*b^6*c^5 + 5*a*b^5*c^4*d - 50*a^2*b^4*c^3*d^2 + 90*a^3*b^3*c^2*d^3 - 65*a^4*b^2*c*d^4 + 17*a^5*b*d^5)*x^3 + 5*(a*b^5*c^5 - a^2*b^4*c^4*d - 6*a^3*b^3*c^3*d^2 + 14*a^4*b^2*c^2*d^3 - 11*a^5*b*c*d^4 + 3*a^6*d^5)*x)/(a^2*b^7*x^4 + 2*a^3*b^6*x^2 + a^4*b^5) + 1/15*(3*b^2*d^5*x^5 + 5*(5*b^2*c*d^4 - 3*a*b*d^5)*x^3 + 15*(10*b^2*c^2*d^3 - 15*a*b*c*d^4 + 6*a^2*d^5)*x)/b^5 + 1/8*(3*b^5*c^5 + 5*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 150*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 - 63*a^5*d^5)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^5)","A",0
36,1,253,0,3.073288," ","integrate((d*x^2+c)^4/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{5} c^{4} + 4 \, a b^{4} c^{3} d - 30 \, a^{2} b^{3} c^{2} d^{2} + 36 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x^{3} + {\left(5 \, a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d - 18 \, a^{3} b^{2} c^{2} d^{2} + 28 \, a^{4} b c d^{3} - 11 \, a^{5} d^{4}\right)} x}{8 \, {\left(a^{2} b^{6} x^{4} + 2 \, a^{3} b^{5} x^{2} + a^{4} b^{4}\right)}} + \frac{b d^{4} x^{3} + 3 \, {\left(4 \, b c d^{3} - 3 \, a d^{4}\right)} x}{3 \, b^{4}} + \frac{{\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 60 \, a^{3} b c d^{3} + 35 \, a^{4} d^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{4}}"," ",0,"1/8*((3*b^5*c^4 + 4*a*b^4*c^3*d - 30*a^2*b^3*c^2*d^2 + 36*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x^3 + (5*a*b^4*c^4 - 4*a^2*b^3*c^3*d - 18*a^3*b^2*c^2*d^2 + 28*a^4*b*c*d^3 - 11*a^5*d^4)*x)/(a^2*b^6*x^4 + 2*a^3*b^5*x^2 + a^4*b^4) + 1/3*(b*d^4*x^3 + 3*(4*b*c*d^3 - 3*a*d^4)*x)/b^4 + 1/8*(3*b^4*c^4 + 4*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 35*a^4*d^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^4)","A",0
37,1,185,0,2.938360," ","integrate((d*x^2+c)^3/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{d^{3} x}{b^{3}} + \frac{3 \, {\left(b^{4} c^{3} + a b^{3} c^{2} d - 5 \, a^{2} b^{2} c d^{2} + 3 \, a^{3} b d^{3}\right)} x^{3} + {\left(5 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d - 9 \, a^{3} b c d^{2} + 7 \, a^{4} d^{3}\right)} x}{8 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}} + \frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{3}}"," ",0,"d^3*x/b^3 + 1/8*(3*(b^4*c^3 + a*b^3*c^2*d - 5*a^2*b^2*c*d^2 + 3*a^3*b*d^3)*x^3 + (5*a*b^3*c^3 - 3*a^2*b^2*c^2*d - 9*a^3*b*c*d^2 + 7*a^4*d^3)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3) + 3/8*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^3)","A",0
38,1,138,0,3.010343," ","integrate((d*x^2+c)^2/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{3} c^{2} + 2 \, a b^{2} c d - 5 \, a^{2} b d^{2}\right)} x^{3} + {\left(5 \, a b^{2} c^{2} - 2 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} x}{8 \, {\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}} + \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{2}}"," ",0,"1/8*((3*b^3*c^2 + 2*a*b^2*c*d - 5*a^2*b*d^2)*x^3 + (5*a*b^2*c^2 - 2*a^2*b*c*d - 3*a^3*d^2)*x)/(a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2) + 1/8*(3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^2)","A",0
39,1,92,0,3.002300," ","integrate((d*x^2+c)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{2} c + a b d\right)} x^{3} + {\left(5 \, a b c - a^{2} d\right)} x}{8 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}} + \frac{{\left(3 \, b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b}"," ",0,"1/8*((3*b^2*c + a*b*d)*x^3 + (5*a*b*c - a^2*d)*x)/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b) + 1/8*(3*b*c + a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b)","A",0
40,1,278,0,3.160549," ","integrate(1/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""maxima"")","-\frac{d^{3} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{c d}} + \frac{{\left(3 \, b^{3} c^{2} - 10 \, a b^{2} c d + 15 \, a^{2} b d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \sqrt{a b}} + \frac{{\left(3 \, b^{3} c - 7 \, a b^{2} d\right)} x^{3} + {\left(5 \, a b^{2} c - 9 \, a^{2} b d\right)} x}{8 \, {\left(a^{4} b^{2} c^{2} - 2 \, a^{5} b c d + a^{6} d^{2} + {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} x^{2}\right)}}"," ",0,"-d^3*arctan(d*x/sqrt(c*d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d)) + 1/8*(3*b^3*c^2 - 10*a*b^2*c*d + 15*a^2*b*d^2)*arctan(b*x/sqrt(a*b))/((a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*sqrt(a*b)) + 1/8*((3*b^3*c - 7*a*b^2*d)*x^3 + (5*a*b^2*c - 9*a^2*b*d)*x)/(a^4*b^2*c^2 - 2*a^5*b*c*d + a^6*d^2 + (a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x^4 + 2*(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*x^2)","A",0
41,1,530,0,3.176665," ","integrate(1/(b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{4} c^{2} - 14 \, a b^{3} c d + 35 \, a^{2} b^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, {\left(a^{2} b^{4} c^{4} - 4 \, a^{3} b^{3} c^{3} d + 6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4}\right)} \sqrt{a b}} - \frac{{\left(7 \, b c d^{3} - a d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}\right)} \sqrt{c d}} + \frac{{\left(3 \, b^{4} c^{2} d - 11 \, a b^{3} c d^{2} - 4 \, a^{2} b^{2} d^{3}\right)} x^{5} + {\left(3 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d - 13 \, a^{2} b^{2} c d^{2} - 8 \, a^{3} b d^{3}\right)} x^{3} + {\left(5 \, a b^{3} c^{3} - 13 \, a^{2} b^{2} c^{2} d - 4 \, a^{4} d^{3}\right)} x}{8 \, {\left(a^{4} b^{3} c^{5} - 3 \, a^{5} b^{2} c^{4} d + 3 \, a^{6} b c^{3} d^{2} - a^{7} c^{2} d^{3} + {\left(a^{2} b^{5} c^{4} d - 3 \, a^{3} b^{4} c^{3} d^{2} + 3 \, a^{4} b^{3} c^{2} d^{3} - a^{5} b^{2} c d^{4}\right)} x^{6} + {\left(a^{2} b^{5} c^{5} - a^{3} b^{4} c^{4} d - 3 \, a^{4} b^{3} c^{3} d^{2} + 5 \, a^{5} b^{2} c^{2} d^{3} - 2 \, a^{6} b c d^{4}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{5} - 5 \, a^{4} b^{3} c^{4} d + 3 \, a^{5} b^{2} c^{3} d^{2} + a^{6} b c^{2} d^{3} - a^{7} c d^{4}\right)} x^{2}\right)}}"," ",0,"1/8*(3*b^4*c^2 - 14*a*b^3*c*d + 35*a^2*b^2*d^2)*arctan(b*x/sqrt(a*b))/((a^2*b^4*c^4 - 4*a^3*b^3*c^3*d + 6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4)*sqrt(a*b)) - 1/2*(7*b*c*d^3 - a*d^4)*arctan(d*x/sqrt(c*d))/((b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4)*sqrt(c*d)) + 1/8*((3*b^4*c^2*d - 11*a*b^3*c*d^2 - 4*a^2*b^2*d^3)*x^5 + (3*b^4*c^3 - 6*a*b^3*c^2*d - 13*a^2*b^2*c*d^2 - 8*a^3*b*d^3)*x^3 + (5*a*b^3*c^3 - 13*a^2*b^2*c^2*d - 4*a^4*d^3)*x)/(a^4*b^3*c^5 - 3*a^5*b^2*c^4*d + 3*a^6*b*c^3*d^2 - a^7*c^2*d^3 + (a^2*b^5*c^4*d - 3*a^3*b^4*c^3*d^2 + 3*a^4*b^3*c^2*d^3 - a^5*b^2*c*d^4)*x^6 + (a^2*b^5*c^5 - a^3*b^4*c^4*d - 3*a^4*b^3*c^3*d^2 + 5*a^5*b^2*c^2*d^3 - 2*a^6*b*c*d^4)*x^4 + (2*a^3*b^4*c^5 - 5*a^4*b^3*c^4*d + 3*a^5*b^2*c^3*d^2 + a^6*b*c^2*d^3 - a^7*c*d^4)*x^2)","B",0
42,1,820,0,3.394947," ","integrate(1/(b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{5} c^{2} - 6 \, a b^{4} c d + 21 \, a^{2} b^{3} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, {\left(a^{2} b^{5} c^{5} - 5 \, a^{3} b^{4} c^{4} d + 10 \, a^{4} b^{3} c^{3} d^{2} - 10 \, a^{5} b^{2} c^{2} d^{3} + 5 \, a^{6} b c d^{4} - a^{7} d^{5}\right)} \sqrt{a b}} - \frac{3 \, {\left(21 \, b^{2} c^{2} d^{3} - 6 \, a b c d^{4} + a^{2} d^{5}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{5} c^{7} - 5 \, a b^{4} c^{6} d + 10 \, a^{2} b^{3} c^{5} d^{2} - 10 \, a^{3} b^{2} c^{4} d^{3} + 5 \, a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} \sqrt{c d}} + \frac{3 \, {\left(b^{5} c^{3} d^{2} - 5 \, a b^{4} c^{2} d^{3} - 5 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{7} + {\left(6 \, b^{5} c^{4} d - 25 \, a b^{4} c^{3} d^{2} - 34 \, a^{2} b^{3} c^{2} d^{3} - 25 \, a^{3} b^{2} c d^{4} + 6 \, a^{4} b d^{5}\right)} x^{5} + {\left(3 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 34 \, a^{2} b^{3} c^{3} d^{2} - 34 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} x^{3} + {\left(5 \, a b^{4} c^{5} - 17 \, a^{2} b^{3} c^{4} d - 17 \, a^{4} b c^{2} d^{3} + 5 \, a^{5} c d^{4}\right)} x}{8 \, {\left(a^{4} b^{4} c^{8} - 4 \, a^{5} b^{3} c^{7} d + 6 \, a^{6} b^{2} c^{6} d^{2} - 4 \, a^{7} b c^{5} d^{3} + a^{8} c^{4} d^{4} + {\left(a^{2} b^{6} c^{6} d^{2} - 4 \, a^{3} b^{5} c^{5} d^{3} + 6 \, a^{4} b^{4} c^{4} d^{4} - 4 \, a^{5} b^{3} c^{3} d^{5} + a^{6} b^{2} c^{2} d^{6}\right)} x^{8} + 2 \, {\left(a^{2} b^{6} c^{7} d - 3 \, a^{3} b^{5} c^{6} d^{2} + 2 \, a^{4} b^{4} c^{5} d^{3} + 2 \, a^{5} b^{3} c^{4} d^{4} - 3 \, a^{6} b^{2} c^{3} d^{5} + a^{7} b c^{2} d^{6}\right)} x^{6} + {\left(a^{2} b^{6} c^{8} - 9 \, a^{4} b^{4} c^{6} d^{2} + 16 \, a^{5} b^{3} c^{5} d^{3} - 9 \, a^{6} b^{2} c^{4} d^{4} + a^{8} c^{2} d^{6}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} c^{8} - 3 \, a^{4} b^{4} c^{7} d + 2 \, a^{5} b^{3} c^{6} d^{2} + 2 \, a^{6} b^{2} c^{5} d^{3} - 3 \, a^{7} b c^{4} d^{4} + a^{8} c^{3} d^{5}\right)} x^{2}\right)}}"," ",0,"3/8*(b^5*c^2 - 6*a*b^4*c*d + 21*a^2*b^3*d^2)*arctan(b*x/sqrt(a*b))/((a^2*b^5*c^5 - 5*a^3*b^4*c^4*d + 10*a^4*b^3*c^3*d^2 - 10*a^5*b^2*c^2*d^3 + 5*a^6*b*c*d^4 - a^7*d^5)*sqrt(a*b)) - 3/8*(21*b^2*c^2*d^3 - 6*a*b*c*d^4 + a^2*d^5)*arctan(d*x/sqrt(c*d))/((b^5*c^7 - 5*a*b^4*c^6*d + 10*a^2*b^3*c^5*d^2 - 10*a^3*b^2*c^4*d^3 + 5*a^4*b*c^3*d^4 - a^5*c^2*d^5)*sqrt(c*d)) + 1/8*(3*(b^5*c^3*d^2 - 5*a*b^4*c^2*d^3 - 5*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^7 + (6*b^5*c^4*d - 25*a*b^4*c^3*d^2 - 34*a^2*b^3*c^2*d^3 - 25*a^3*b^2*c*d^4 + 6*a^4*b*d^5)*x^5 + (3*b^5*c^5 - 5*a*b^4*c^4*d - 34*a^2*b^3*c^3*d^2 - 34*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 3*a^5*d^5)*x^3 + (5*a*b^4*c^5 - 17*a^2*b^3*c^4*d - 17*a^4*b*c^2*d^3 + 5*a^5*c*d^4)*x)/(a^4*b^4*c^8 - 4*a^5*b^3*c^7*d + 6*a^6*b^2*c^6*d^2 - 4*a^7*b*c^5*d^3 + a^8*c^4*d^4 + (a^2*b^6*c^6*d^2 - 4*a^3*b^5*c^5*d^3 + 6*a^4*b^4*c^4*d^4 - 4*a^5*b^3*c^3*d^5 + a^6*b^2*c^2*d^6)*x^8 + 2*(a^2*b^6*c^7*d - 3*a^3*b^5*c^6*d^2 + 2*a^4*b^4*c^5*d^3 + 2*a^5*b^3*c^4*d^4 - 3*a^6*b^2*c^3*d^5 + a^7*b*c^2*d^6)*x^6 + (a^2*b^6*c^8 - 9*a^4*b^4*c^6*d^2 + 16*a^5*b^3*c^5*d^3 - 9*a^6*b^2*c^4*d^4 + a^8*c^2*d^6)*x^4 + 2*(a^3*b^5*c^8 - 3*a^4*b^4*c^7*d + 2*a^5*b^3*c^6*d^2 + 2*a^6*b^2*c^5*d^3 - 3*a^7*b*c^4*d^4 + a^8*c^3*d^5)*x^2)","B",0
43,1,33,0,1.323298," ","integrate((x^2-1)^3/(x^2+1)^4,x, algorithm=""maxima"")","-\frac{3 \, x^{5} + 2 \, x^{3} + 3 \, x}{3 \, {\left(x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1\right)}}"," ",0,"-1/3*(3*x^5 + 2*x^3 + 3*x)/(x^6 + 3*x^4 + 3*x^2 + 1)","A",0
44,1,48,0,2.993655," ","integrate((x^2-1)^4/(x^2+1)^5,x, algorithm=""maxima"")","-\frac{5 \, x^{7} - 3 \, x^{5} + 3 \, x^{3} - 5 \, x}{8 \, {\left(x^{8} + 4 \, x^{6} + 6 \, x^{4} + 4 \, x^{2} + 1\right)}} + \frac{3}{8} \, \arctan\left(x\right)"," ",0,"-1/8*(5*x^7 - 3*x^5 + 3*x^3 - 5*x)/(x^8 + 4*x^6 + 6*x^4 + 4*x^2 + 1) + 3/8*arctan(x)","A",0
45,1,281,0,1.394963," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} d^{3} x^{5}}{8 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} c d^{2} x^{3}}{2 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a d^{3} x^{3}}{48 \, b^{2}} + \frac{1}{2} \, \sqrt{b x^{2} + a} c^{3} x + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} c^{2} d x}{4 \, b} - \frac{3 \, \sqrt{b x^{2} + a} a c^{2} d x}{8 \, b} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a c d^{2} x}{8 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} a^{2} c d^{2} x}{16 \, b^{2}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} d^{3} x}{64 \, b^{3}} - \frac{5 \, \sqrt{b x^{2} + a} a^{3} d^{3} x}{128 \, b^{3}} + \frac{a c^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}} - \frac{3 \, a^{2} c^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}} + \frac{3 \, a^{3} c d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{5}{2}}} - \frac{5 \, a^{4} d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{7}{2}}}"," ",0,"1/8*(b*x^2 + a)^(3/2)*d^3*x^5/b + 1/2*(b*x^2 + a)^(3/2)*c*d^2*x^3/b - 5/48*(b*x^2 + a)^(3/2)*a*d^3*x^3/b^2 + 1/2*sqrt(b*x^2 + a)*c^3*x + 3/4*(b*x^2 + a)^(3/2)*c^2*d*x/b - 3/8*sqrt(b*x^2 + a)*a*c^2*d*x/b - 3/8*(b*x^2 + a)^(3/2)*a*c*d^2*x/b^2 + 3/16*sqrt(b*x^2 + a)*a^2*c*d^2*x/b^2 + 5/64*(b*x^2 + a)^(3/2)*a^2*d^3*x/b^3 - 5/128*sqrt(b*x^2 + a)*a^3*d^3*x/b^3 + 1/2*a*c^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 3/8*a^2*c^2*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/16*a^3*c*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/128*a^4*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
46,1,168,0,1.347088," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} d^{2} x^{3}}{6 \, b} + \frac{1}{2} \, \sqrt{b x^{2} + a} c^{2} x + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} c d x}{2 \, b} - \frac{\sqrt{b x^{2} + a} a c d x}{4 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a d^{2} x}{8 \, b^{2}} + \frac{\sqrt{b x^{2} + a} a^{2} d^{2} x}{16 \, b^{2}} + \frac{a c^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}} - \frac{a^{2} c d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{4 \, b^{\frac{3}{2}}} + \frac{a^{3} d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{5}{2}}}"," ",0,"1/6*(b*x^2 + a)^(3/2)*d^2*x^3/b + 1/2*sqrt(b*x^2 + a)*c^2*x + 1/2*(b*x^2 + a)^(3/2)*c*d*x/b - 1/4*sqrt(b*x^2 + a)*a*c*d*x/b - 1/8*(b*x^2 + a)^(3/2)*a*d^2*x/b^2 + 1/16*sqrt(b*x^2 + a)*a^2*d^2*x/b^2 + 1/2*a*c^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/4*a^2*c*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 1/16*a^3*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
47,1,81,0,1.349516," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{b x^{2} + a} c x + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} d x}{4 \, b} - \frac{\sqrt{b x^{2} + a} a d x}{8 \, b} + \frac{a c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}} - \frac{a^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*c*x + 1/4*(b*x^2 + a)^(3/2)*d*x/b - 1/8*sqrt(b*x^2 + a)*a*d*x/b + 1/2*a*c*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/8*a^2*d*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
48,1,28,0,1.364021," ","integrate((b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{b x^{2} + a} x + \frac{a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}}"," ",0,"1/2*sqrt(b*x^2 + a)*x + 1/2*a*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
49,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{d x^{2} + c}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(d*x^2 + c), x)","F",0
50,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(d*x^2 + c)^2, x)","F",0
51,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(d*x^2 + c)^3, x)","F",0
52,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{{\left(d x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(d*x^2 + c)^4, x)","F",0
53,1,364,0,1.496302," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} d^{3} x^{5}}{10 \, b} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} c d^{2} x^{3}}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a d^{3} x^{3}}{16 \, b^{2}} + \frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} c^{3} x + \frac{3}{8} \, \sqrt{b x^{2} + a} a c^{3} x + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} c^{2} d x}{2 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a c^{2} d x}{8 \, b} - \frac{3 \, \sqrt{b x^{2} + a} a^{2} c^{2} d x}{16 \, b} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a c d^{2} x}{16 \, b^{2}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} c d^{2} x}{64 \, b^{2}} + \frac{9 \, \sqrt{b x^{2} + a} a^{3} c d^{2} x}{128 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} d^{3} x}{32 \, b^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} d^{3} x}{128 \, b^{3}} - \frac{3 \, \sqrt{b x^{2} + a} a^{4} d^{3} x}{256 \, b^{3}} + \frac{3 \, a^{2} c^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}} - \frac{3 \, a^{3} c^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{3}{2}}} + \frac{9 \, a^{4} c d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{5}{2}}} - \frac{3 \, a^{5} d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{7}{2}}}"," ",0,"1/10*(b*x^2 + a)^(5/2)*d^3*x^5/b + 3/8*(b*x^2 + a)^(5/2)*c*d^2*x^3/b - 1/16*(b*x^2 + a)^(5/2)*a*d^3*x^3/b^2 + 1/4*(b*x^2 + a)^(3/2)*c^3*x + 3/8*sqrt(b*x^2 + a)*a*c^3*x + 1/2*(b*x^2 + a)^(5/2)*c^2*d*x/b - 1/8*(b*x^2 + a)^(3/2)*a*c^2*d*x/b - 3/16*sqrt(b*x^2 + a)*a^2*c^2*d*x/b - 3/16*(b*x^2 + a)^(5/2)*a*c*d^2*x/b^2 + 3/64*(b*x^2 + a)^(3/2)*a^2*c*d^2*x/b^2 + 9/128*sqrt(b*x^2 + a)*a^3*c*d^2*x/b^2 + 1/32*(b*x^2 + a)^(5/2)*a^2*d^3*x/b^3 - 1/128*(b*x^2 + a)^(3/2)*a^3*d^3*x/b^3 - 3/256*sqrt(b*x^2 + a)*a^4*d^3*x/b^3 + 3/8*a^2*c^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 3/16*a^3*c^2*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 9/128*a^4*c*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 3/256*a^5*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
54,1,227,0,1.424389," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} d^{2} x^{3}}{8 \, b} + \frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} c^{2} x + \frac{3}{8} \, \sqrt{b x^{2} + a} a c^{2} x + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} c d x}{3 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a c d x}{12 \, b} - \frac{\sqrt{b x^{2} + a} a^{2} c d x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a d^{2} x}{16 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} d^{2} x}{64 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} a^{3} d^{2} x}{128 \, b^{2}} + \frac{3 \, a^{2} c^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}} - \frac{a^{3} c d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}} + \frac{3 \, a^{4} d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{5}{2}}}"," ",0,"1/8*(b*x^2 + a)^(5/2)*d^2*x^3/b + 1/4*(b*x^2 + a)^(3/2)*c^2*x + 3/8*sqrt(b*x^2 + a)*a*c^2*x + 1/3*(b*x^2 + a)^(5/2)*c*d*x/b - 1/12*(b*x^2 + a)^(3/2)*a*c*d*x/b - 1/8*sqrt(b*x^2 + a)*a^2*c*d*x/b - 1/16*(b*x^2 + a)^(5/2)*a*d^2*x/b^2 + 1/64*(b*x^2 + a)^(3/2)*a^2*d^2*x/b^2 + 3/128*sqrt(b*x^2 + a)*a^3*d^2*x/b^2 + 3/8*a^2*c^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/8*a^3*c*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/128*a^4*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
55,1,116,0,1.371900," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} c x + \frac{3}{8} \, \sqrt{b x^{2} + a} a c x + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} d x}{6 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a d x}{24 \, b} - \frac{\sqrt{b x^{2} + a} a^{2} d x}{16 \, b} + \frac{3 \, a^{2} c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}} - \frac{a^{3} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{3}{2}}}"," ",0,"1/4*(b*x^2 + a)^(3/2)*c*x + 3/8*sqrt(b*x^2 + a)*a*c*x + 1/6*(b*x^2 + a)^(5/2)*d*x/b - 1/24*(b*x^2 + a)^(3/2)*a*d*x/b - 1/16*sqrt(b*x^2 + a)*a^2*d*x/b + 3/8*a^2*c*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/16*a^3*d*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
56,1,43,0,1.335647," ","integrate((b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} x + \frac{3}{8} \, \sqrt{b x^{2} + a} a x + \frac{3 \, a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}}"," ",0,"1/4*(b*x^2 + a)^(3/2)*x + 3/8*sqrt(b*x^2 + a)*a*x + 3/8*a^2*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
57,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(d*x^2 + c), x)","F",0
58,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(d*x^2 + c)^2, x)","F",0
59,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(d*x^2 + c)^3, x)","F",0
60,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(d*x^2 + c)^4, x)","F",0
61,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^5,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{5}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(d*x^2 + c)^5, x)","F",0
62,1,447,0,1.472241," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} d^{3} x^{5}}{12 \, b} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} c d^{2} x^{3}}{10 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a d^{3} x^{3}}{24 \, b^{2}} + \frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} c^{3} x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a c^{3} x + \frac{5}{16} \, \sqrt{b x^{2} + a} a^{2} c^{3} x + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} c^{2} d x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a c^{2} d x}{16 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} c^{2} d x}{64 \, b} - \frac{15 \, \sqrt{b x^{2} + a} a^{3} c^{2} d x}{128 \, b} - \frac{9 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a c d^{2} x}{80 \, b^{2}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} c d^{2} x}{160 \, b^{2}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} c d^{2} x}{128 \, b^{2}} + \frac{9 \, \sqrt{b x^{2} + a} a^{4} c d^{2} x}{256 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} a^{2} d^{3} x}{64 \, b^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{3} d^{3} x}{384 \, b^{3}} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4} d^{3} x}{1536 \, b^{3}} - \frac{5 \, \sqrt{b x^{2} + a} a^{5} d^{3} x}{1024 \, b^{3}} + \frac{5 \, a^{3} c^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}} - \frac{15 \, a^{4} c^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{3}{2}}} + \frac{9 \, a^{5} c d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{5}{2}}} - \frac{5 \, a^{6} d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{1024 \, b^{\frac{7}{2}}}"," ",0,"1/12*(b*x^2 + a)^(7/2)*d^3*x^5/b + 3/10*(b*x^2 + a)^(7/2)*c*d^2*x^3/b - 1/24*(b*x^2 + a)^(7/2)*a*d^3*x^3/b^2 + 1/6*(b*x^2 + a)^(5/2)*c^3*x + 5/24*(b*x^2 + a)^(3/2)*a*c^3*x + 5/16*sqrt(b*x^2 + a)*a^2*c^3*x + 3/8*(b*x^2 + a)^(7/2)*c^2*d*x/b - 1/16*(b*x^2 + a)^(5/2)*a*c^2*d*x/b - 5/64*(b*x^2 + a)^(3/2)*a^2*c^2*d*x/b - 15/128*sqrt(b*x^2 + a)*a^3*c^2*d*x/b - 9/80*(b*x^2 + a)^(7/2)*a*c*d^2*x/b^2 + 3/160*(b*x^2 + a)^(5/2)*a^2*c*d^2*x/b^2 + 3/128*(b*x^2 + a)^(3/2)*a^3*c*d^2*x/b^2 + 9/256*sqrt(b*x^2 + a)*a^4*c*d^2*x/b^2 + 1/64*(b*x^2 + a)^(7/2)*a^2*d^3*x/b^3 - 1/384*(b*x^2 + a)^(5/2)*a^3*d^3*x/b^3 - 5/1536*(b*x^2 + a)^(3/2)*a^4*d^3*x/b^3 - 5/1024*sqrt(b*x^2 + a)*a^5*d^3*x/b^3 + 5/16*a^3*c^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 15/128*a^4*c^2*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 9/256*a^5*c*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/1024*a^6*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
63,1,286,0,1.388045," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} d^{2} x^{3}}{10 \, b} + \frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} c^{2} x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a c^{2} x + \frac{5}{16} \, \sqrt{b x^{2} + a} a^{2} c^{2} x + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} c d x}{4 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a c d x}{24 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} c d x}{96 \, b} - \frac{5 \, \sqrt{b x^{2} + a} a^{3} c d x}{64 \, b} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} a d^{2} x}{80 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a^{2} d^{2} x}{160 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} d^{2} x}{128 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} a^{4} d^{2} x}{256 \, b^{2}} + \frac{5 \, a^{3} c^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}} - \frac{5 \, a^{4} c d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{64 \, b^{\frac{3}{2}}} + \frac{3 \, a^{5} d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{5}{2}}}"," ",0,"1/10*(b*x^2 + a)^(7/2)*d^2*x^3/b + 1/6*(b*x^2 + a)^(5/2)*c^2*x + 5/24*(b*x^2 + a)^(3/2)*a*c^2*x + 5/16*sqrt(b*x^2 + a)*a^2*c^2*x + 1/4*(b*x^2 + a)^(7/2)*c*d*x/b - 1/24*(b*x^2 + a)^(5/2)*a*c*d*x/b - 5/96*(b*x^2 + a)^(3/2)*a^2*c*d*x/b - 5/64*sqrt(b*x^2 + a)*a^3*c*d*x/b - 3/80*(b*x^2 + a)^(7/2)*a*d^2*x/b^2 + 1/160*(b*x^2 + a)^(5/2)*a^2*d^2*x/b^2 + 1/128*(b*x^2 + a)^(3/2)*a^3*d^2*x/b^2 + 3/256*sqrt(b*x^2 + a)*a^4*d^2*x/b^2 + 5/16*a^3*c^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 5/64*a^4*c*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/256*a^5*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
64,1,151,0,1.400970," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} c x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a c x + \frac{5}{16} \, \sqrt{b x^{2} + a} a^{2} c x + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} d x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} a d x}{48 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} d x}{192 \, b} - \frac{5 \, \sqrt{b x^{2} + a} a^{3} d x}{128 \, b} + \frac{5 \, a^{3} c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}} - \frac{5 \, a^{4} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{3}{2}}}"," ",0,"1/6*(b*x^2 + a)^(5/2)*c*x + 5/24*(b*x^2 + a)^(3/2)*a*c*x + 5/16*sqrt(b*x^2 + a)*a^2*c*x + 1/8*(b*x^2 + a)^(7/2)*d*x/b - 1/48*(b*x^2 + a)^(5/2)*a*d*x/b - 5/192*(b*x^2 + a)^(3/2)*a^2*d*x/b - 5/128*sqrt(b*x^2 + a)*a^3*d*x/b + 5/16*a^3*c*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 5/128*a^4*d*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
65,1,58,0,1.328027," ","integrate((b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x + \frac{5}{16} \, \sqrt{b x^{2} + a} a^{2} x + \frac{5 \, a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}}"," ",0,"1/6*(b*x^2 + a)^(5/2)*x + 5/24*(b*x^2 + a)^(3/2)*a*x + 5/16*sqrt(b*x^2 + a)*a^2*x + 5/16*a^3*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
66,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(d*x^2 + c), x)","F",0
67,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(d*x^2 + c)^2, x)","F",0
68,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(d*x^2 + c)^3, x)","F",0
69,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^4,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{4}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(d*x^2 + c)^4, x)","F",0
70,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^5,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{5}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(d*x^2 + c)^5, x)","F",0
71,0,0,0,0.000000," ","integrate((-x^2+1)^(1/2)/(x^2+1),x, algorithm=""maxima"")","\int \frac{\sqrt{-x^{2} + 1}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 1)/(x^2 + 1), x)","F",0
72,1,59,0,2.978114," ","integrate((x^2+1)^(1/2)/(x^2-1),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \operatorname{arsinh}\left(\frac{2 \, x}{{\left| 2 \, x + 2 \right|}} - \frac{2}{{\left| 2 \, x + 2 \right|}}\right) - \frac{1}{2} \, \sqrt{2} \operatorname{arsinh}\left(\frac{2 \, x}{{\left| 2 \, x - 2 \right|}} + \frac{2}{{\left| 2 \, x - 2 \right|}}\right) + \operatorname{arsinh}\left(x\right)"," ",0,"-1/2*sqrt(2)*arcsinh(2*x/abs(2*x + 2) - 2/abs(2*x + 2)) - 1/2*sqrt(2)*arcsinh(2*x/abs(2*x - 2) + 2/abs(2*x - 2)) + arcsinh(x)","B",0
73,1,110,0,3.073628," ","integrate((-x^2+1)^(1/2)/(2*x^2-1),x, algorithm=""maxima"")","-\frac{1}{8} \, \sqrt{2} {\left(2 \, \sqrt{2} \arcsin\left(x\right) - \sqrt{2} \log\left(\frac{1}{4} \, \sqrt{2} + \frac{\sqrt{2} \sqrt{-x^{2} + 1}}{{\left| 4 \, x + 2 \, \sqrt{2} \right|}} + \frac{1}{{\left| 4 \, x + 2 \, \sqrt{2} \right|}}\right) + \sqrt{2} \log\left(-\frac{1}{4} \, \sqrt{2} + \frac{\sqrt{2} \sqrt{-x^{2} + 1}}{{\left| 4 \, x - 2 \, \sqrt{2} \right|}} + \frac{1}{{\left| 4 \, x - 2 \, \sqrt{2} \right|}}\right)\right)}"," ",0,"-1/8*sqrt(2)*(2*sqrt(2)*arcsin(x) - sqrt(2)*log(1/4*sqrt(2) + sqrt(2)*sqrt(-x^2 + 1)/abs(4*x + 2*sqrt(2)) + 1/abs(4*x + 2*sqrt(2))) + sqrt(2)*log(-1/4*sqrt(2) + sqrt(2)*sqrt(-x^2 + 1)/abs(4*x - 2*sqrt(2)) + 1/abs(4*x - 2*sqrt(2))))","B",0
74,1,199,0,1.360163," ","integrate((d*x^2+c)^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} d^{3} x^{5}}{6 \, b} + \frac{3 \, \sqrt{b x^{2} + a} c d^{2} x^{3}}{4 \, b} - \frac{5 \, \sqrt{b x^{2} + a} a d^{3} x^{3}}{24 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} c^{2} d x}{2 \, b} - \frac{9 \, \sqrt{b x^{2} + a} a c d^{2} x}{8 \, b^{2}} + \frac{5 \, \sqrt{b x^{2} + a} a^{2} d^{3} x}{16 \, b^{3}} + \frac{c^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{3 \, a c^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{9 \, a^{2} c d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{5 \, a^{3} d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{7}{2}}}"," ",0,"1/6*sqrt(b*x^2 + a)*d^3*x^5/b + 3/4*sqrt(b*x^2 + a)*c*d^2*x^3/b - 5/24*sqrt(b*x^2 + a)*a*d^3*x^3/b^2 + 3/2*sqrt(b*x^2 + a)*c^2*d*x/b - 9/8*sqrt(b*x^2 + a)*a*c*d^2*x/b^2 + 5/16*sqrt(b*x^2 + a)*a^2*d^3*x/b^3 + c^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 3/2*a*c^2*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 9/8*a^2*c*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/16*a^3*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
75,1,109,0,1.469156," ","integrate((d*x^2+c)^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} d^{2} x^{3}}{4 \, b} + \frac{\sqrt{b x^{2} + a} c d x}{b} - \frac{3 \, \sqrt{b x^{2} + a} a d^{2} x}{8 \, b^{2}} + \frac{c^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{a c d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} + \frac{3 \, a^{2} d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/4*sqrt(b*x^2 + a)*d^2*x^3/b + sqrt(b*x^2 + a)*c*d*x/b - 3/8*sqrt(b*x^2 + a)*a*d^2*x/b^2 + c^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) - a*c*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/8*a^2*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
76,1,47,0,1.328889," ","integrate((d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} d x}{2 \, b} + \frac{c \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{a d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*d*x/b + c*arcsinh(b*x/sqrt(a*b))/sqrt(b) - 1/2*a*d*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
77,1,13,0,1.284286," ","integrate(1/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}}"," ",0,"arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
78,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*(d*x^2 + c)), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*(d*x^2 + c)^2), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*(d*x^2 + c)^3), x)","F",0
81,1,311,0,1.382377," ","integrate((d*x^2+c)^4/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{d^{4} x^{7}}{6 \, \sqrt{b x^{2} + a} b} + \frac{c d^{3} x^{5}}{\sqrt{b x^{2} + a} b} - \frac{7 \, a d^{4} x^{5}}{24 \, \sqrt{b x^{2} + a} b^{2}} + \frac{3 \, c^{2} d^{2} x^{3}}{\sqrt{b x^{2} + a} b} - \frac{5 \, a c d^{3} x^{3}}{2 \, \sqrt{b x^{2} + a} b^{2}} + \frac{35 \, a^{2} d^{4} x^{3}}{48 \, \sqrt{b x^{2} + a} b^{3}} + \frac{c^{4} x}{\sqrt{b x^{2} + a} a} - \frac{4 \, c^{3} d x}{\sqrt{b x^{2} + a} b} + \frac{9 \, a c^{2} d^{2} x}{\sqrt{b x^{2} + a} b^{2}} - \frac{15 \, a^{2} c d^{3} x}{2 \, \sqrt{b x^{2} + a} b^{3}} + \frac{35 \, a^{3} d^{4} x}{16 \, \sqrt{b x^{2} + a} b^{4}} + \frac{4 \, c^{3} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} - \frac{9 \, a c^{2} d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}} + \frac{15 \, a^{2} c d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{7}{2}}} - \frac{35 \, a^{3} d^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{9}{2}}}"," ",0,"1/6*d^4*x^7/(sqrt(b*x^2 + a)*b) + c*d^3*x^5/(sqrt(b*x^2 + a)*b) - 7/24*a*d^4*x^5/(sqrt(b*x^2 + a)*b^2) + 3*c^2*d^2*x^3/(sqrt(b*x^2 + a)*b) - 5/2*a*c*d^3*x^3/(sqrt(b*x^2 + a)*b^2) + 35/48*a^2*d^4*x^3/(sqrt(b*x^2 + a)*b^3) + c^4*x/(sqrt(b*x^2 + a)*a) - 4*c^3*d*x/(sqrt(b*x^2 + a)*b) + 9*a*c^2*d^2*x/(sqrt(b*x^2 + a)*b^2) - 15/2*a^2*c*d^3*x/(sqrt(b*x^2 + a)*b^3) + 35/16*a^3*d^4*x/(sqrt(b*x^2 + a)*b^4) + 4*c^3*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 9*a*c^2*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) + 15/2*a^2*c*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2) - 35/16*a^3*d^4*arcsinh(b*x/sqrt(a*b))/b^(9/2)","A",0
82,1,197,0,1.397459," ","integrate((d*x^2+c)^3/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{d^{3} x^{5}}{4 \, \sqrt{b x^{2} + a} b} + \frac{3 \, c d^{2} x^{3}}{2 \, \sqrt{b x^{2} + a} b} - \frac{5 \, a d^{3} x^{3}}{8 \, \sqrt{b x^{2} + a} b^{2}} + \frac{c^{3} x}{\sqrt{b x^{2} + a} a} - \frac{3 \, c^{2} d x}{\sqrt{b x^{2} + a} b} + \frac{9 \, a c d^{2} x}{2 \, \sqrt{b x^{2} + a} b^{2}} - \frac{15 \, a^{2} d^{3} x}{8 \, \sqrt{b x^{2} + a} b^{3}} + \frac{3 \, c^{2} d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} - \frac{9 \, a c d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{5}{2}}} + \frac{15 \, a^{2} d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{7}{2}}}"," ",0,"1/4*d^3*x^5/(sqrt(b*x^2 + a)*b) + 3/2*c*d^2*x^3/(sqrt(b*x^2 + a)*b) - 5/8*a*d^3*x^3/(sqrt(b*x^2 + a)*b^2) + c^3*x/(sqrt(b*x^2 + a)*a) - 3*c^2*d*x/(sqrt(b*x^2 + a)*b) + 9/2*a*c*d^2*x/(sqrt(b*x^2 + a)*b^2) - 15/8*a^2*d^3*x/(sqrt(b*x^2 + a)*b^3) + 3*c^2*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 9/2*a*c*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) + 15/8*a^2*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
83,1,108,0,1.376891," ","integrate((d*x^2+c)^2/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{d^{2} x^{3}}{2 \, \sqrt{b x^{2} + a} b} + \frac{c^{2} x}{\sqrt{b x^{2} + a} a} - \frac{2 \, c d x}{\sqrt{b x^{2} + a} b} + \frac{3 \, a d^{2} x}{2 \, \sqrt{b x^{2} + a} b^{2}} + \frac{2 \, c d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}} - \frac{3 \, a d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{5}{2}}}"," ",0,"1/2*d^2*x^3/(sqrt(b*x^2 + a)*b) + c^2*x/(sqrt(b*x^2 + a)*a) - 2*c*d*x/(sqrt(b*x^2 + a)*b) + 3/2*a*d^2*x/(sqrt(b*x^2 + a)*b^2) + 2*c*d*arcsinh(b*x/sqrt(a*b))/b^(3/2) - 3/2*a*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
84,1,46,0,1.302436," ","integrate((d*x^2+c)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{c x}{\sqrt{b x^{2} + a} a} - \frac{d x}{\sqrt{b x^{2} + a} b} + \frac{d \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}}"," ",0,"c*x/(sqrt(b*x^2 + a)*a) - d*x/(sqrt(b*x^2 + a)*b) + d*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
85,1,14,0,1.323564," ","integrate(1/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{x}{\sqrt{b x^{2} + a} a}"," ",0,"x/(sqrt(b*x^2 + a)*a)","A",0
86,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/2)*(d*x^2 + c)), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/2)*(d*x^2 + c)^2), x)","F",0
88,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} {\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/2)*(d*x^2 + c)^3), x)","F",0
89,1,392,0,1.441875," ","integrate((d*x^2+c)^4/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{d^{4} x^{7}}{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, c d^{3} x^{5}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{7 \, a d^{4} x^{5}}{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} - 2 \, c^{2} d^{2} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} + \frac{10 \, a c d^{3} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b} - \frac{35 \, a^{2} d^{4} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{24 \, b^{2}} + \frac{2 \, c^{4} x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{c^{4} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{4 \, c^{3} d x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{4 \, c^{3} d x}{3 \, \sqrt{b x^{2} + a} a b} - \frac{2 \, c^{2} d^{2} x}{\sqrt{b x^{2} + a} b^{2}} + \frac{10 \, a c d^{3} x}{3 \, \sqrt{b x^{2} + a} b^{3}} - \frac{35 \, a^{2} d^{4} x}{24 \, \sqrt{b x^{2} + a} b^{4}} + \frac{6 \, c^{2} d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}} - \frac{10 \, a c d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{7}{2}}} + \frac{35 \, a^{2} d^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{9}{2}}}"," ",0,"1/4*d^4*x^7/((b*x^2 + a)^(3/2)*b) + 2*c*d^3*x^5/((b*x^2 + a)^(3/2)*b) - 7/8*a*d^4*x^5/((b*x^2 + a)^(3/2)*b^2) - 2*c^2*d^2*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2)) + 10/3*a*c*d^3*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b - 35/24*a^2*d^4*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 + 2/3*c^4*x/(sqrt(b*x^2 + a)*a^2) + 1/3*c^4*x/((b*x^2 + a)^(3/2)*a) - 4/3*c^3*d*x/((b*x^2 + a)^(3/2)*b) + 4/3*c^3*d*x/(sqrt(b*x^2 + a)*a*b) - 2*c^2*d^2*x/(sqrt(b*x^2 + a)*b^2) + 10/3*a*c*d^3*x/(sqrt(b*x^2 + a)*b^3) - 35/24*a^2*d^4*x/(sqrt(b*x^2 + a)*b^4) + 6*c^2*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 10*a*c*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 35/8*a^2*d^4*arcsinh(b*x/sqrt(a*b))/b^(9/2)","A",0
90,1,254,0,1.493182," ","integrate((d*x^2+c)^3/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{d^{3} x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - c d^{2} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} + \frac{5 \, a d^{3} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{6 \, b} + \frac{2 \, c^{3} x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{c^{3} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{c^{2} d x}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{c^{2} d x}{\sqrt{b x^{2} + a} a b} - \frac{c d^{2} x}{\sqrt{b x^{2} + a} b^{2}} + \frac{5 \, a d^{3} x}{6 \, \sqrt{b x^{2} + a} b^{3}} + \frac{3 \, c d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}} - \frac{5 \, a d^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{7}{2}}}"," ",0,"1/2*d^3*x^5/((b*x^2 + a)^(3/2)*b) - c*d^2*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2)) + 5/6*a*d^3*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b + 2/3*c^3*x/(sqrt(b*x^2 + a)*a^2) + 1/3*c^3*x/((b*x^2 + a)^(3/2)*a) - c^2*d*x/((b*x^2 + a)^(3/2)*b) + c^2*d*x/(sqrt(b*x^2 + a)*a*b) - c*d^2*x/(sqrt(b*x^2 + a)*b^2) + 5/6*a*d^3*x/(sqrt(b*x^2 + a)*b^3) + 3*c*d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/2*a*d^3*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
91,1,147,0,1.389132," ","integrate((d*x^2+c)^2/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, d^{2} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} + \frac{2 \, c^{2} x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{c^{2} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{2 \, c d x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, c d x}{3 \, \sqrt{b x^{2} + a} a b} - \frac{d^{2} x}{3 \, \sqrt{b x^{2} + a} b^{2}} + \frac{d^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}}"," ",0,"-1/3*d^2*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2)) + 2/3*c^2*x/(sqrt(b*x^2 + a)*a^2) + 1/3*c^2*x/((b*x^2 + a)^(3/2)*a) - 2/3*c*d*x/((b*x^2 + a)^(3/2)*b) + 2/3*c*d*x/(sqrt(b*x^2 + a)*a*b) - 1/3*d^2*x/(sqrt(b*x^2 + a)*b^2) + d^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
92,1,68,0,1.366250," ","integrate((d*x^2+c)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, c x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{c x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{d x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{d x}{3 \, \sqrt{b x^{2} + a} a b}"," ",0,"2/3*c*x/(sqrt(b*x^2 + a)*a^2) + 1/3*c*x/((b*x^2 + a)^(3/2)*a) - 1/3*d*x/((b*x^2 + a)^(3/2)*b) + 1/3*d*x/(sqrt(b*x^2 + a)*a*b)","A",0
93,1,31,0,1.331929," ","integrate(1/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a}"," ",0,"2/3*x/(sqrt(b*x^2 + a)*a^2) + 1/3*x/((b*x^2 + a)^(3/2)*a)","A",0
94,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/2)*(d*x^2 + c)), x)","F",0
95,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/2)*(d*x^2 + c)^2), x)","F",0
96,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} {\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/2)*(d*x^2 + c)^3), x)","F",0
97,1,465,0,1.512567," ","integrate((b*x^2+a)^3/(d*x^2+c)^(11/2),x, algorithm=""maxima"")","-\frac{b^{3} x^{5}}{4 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} d} - \frac{5 \, b^{3} c x^{3}}{24 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} d^{2}} - \frac{a b^{2} x^{3}}{2 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} d} + \frac{128 \, a^{3} x}{315 \, \sqrt{d x^{2} + c} c^{5}} + \frac{64 \, a^{3} x}{315 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{4}} + \frac{16 \, a^{3} x}{105 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} c^{3}} + \frac{8 \, a^{3} x}{63 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} c^{2}} + \frac{a^{3} x}{9 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} c} + \frac{b^{3} x}{84 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} d^{3}} + \frac{2 \, b^{3} x}{63 \, \sqrt{d x^{2} + c} c^{2} d^{3}} + \frac{b^{3} x}{63 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c d^{3}} + \frac{5 \, b^{3} c x}{504 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} d^{3}} - \frac{5 \, b^{3} c^{2} x}{72 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} d^{3}} + \frac{a b^{2} x}{42 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} d^{2}} + \frac{8 \, a b^{2} x}{105 \, \sqrt{d x^{2} + c} c^{3} d^{2}} + \frac{4 \, a b^{2} x}{105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} d^{2}} + \frac{a b^{2} x}{35 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} c d^{2}} - \frac{a b^{2} c x}{6 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} d^{2}} - \frac{a^{2} b x}{3 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} d} + \frac{16 \, a^{2} b x}{105 \, \sqrt{d x^{2} + c} c^{4} d} + \frac{8 \, a^{2} b x}{105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3} d} + \frac{2 \, a^{2} b x}{35 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} c^{2} d} + \frac{a^{2} b x}{21 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} c d}"," ",0,"-1/4*b^3*x^5/((d*x^2 + c)^(9/2)*d) - 5/24*b^3*c*x^3/((d*x^2 + c)^(9/2)*d^2) - 1/2*a*b^2*x^3/((d*x^2 + c)^(9/2)*d) + 128/315*a^3*x/(sqrt(d*x^2 + c)*c^5) + 64/315*a^3*x/((d*x^2 + c)^(3/2)*c^4) + 16/105*a^3*x/((d*x^2 + c)^(5/2)*c^3) + 8/63*a^3*x/((d*x^2 + c)^(7/2)*c^2) + 1/9*a^3*x/((d*x^2 + c)^(9/2)*c) + 1/84*b^3*x/((d*x^2 + c)^(5/2)*d^3) + 2/63*b^3*x/(sqrt(d*x^2 + c)*c^2*d^3) + 1/63*b^3*x/((d*x^2 + c)^(3/2)*c*d^3) + 5/504*b^3*c*x/((d*x^2 + c)^(7/2)*d^3) - 5/72*b^3*c^2*x/((d*x^2 + c)^(9/2)*d^3) + 1/42*a*b^2*x/((d*x^2 + c)^(7/2)*d^2) + 8/105*a*b^2*x/(sqrt(d*x^2 + c)*c^3*d^2) + 4/105*a*b^2*x/((d*x^2 + c)^(3/2)*c^2*d^2) + 1/35*a*b^2*x/((d*x^2 + c)^(5/2)*c*d^2) - 1/6*a*b^2*c*x/((d*x^2 + c)^(9/2)*d^2) - 1/3*a^2*b*x/((d*x^2 + c)^(9/2)*d) + 16/105*a^2*b*x/(sqrt(d*x^2 + c)*c^4*d) + 8/105*a^2*b*x/((d*x^2 + c)^(3/2)*c^3*d) + 2/35*a^2*b*x/((d*x^2 + c)^(5/2)*c^2*d) + 1/21*a^2*b*x/((d*x^2 + c)^(7/2)*c*d)","B",0
98,1,249,0,1.499583," ","integrate((b*x^2+a)^2/(d*x^2+c)^(9/2),x, algorithm=""maxima"")","-\frac{b^{2} x^{3}}{4 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} d} + \frac{16 \, a^{2} x}{35 \, \sqrt{d x^{2} + c} c^{4}} + \frac{8 \, a^{2} x}{35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3}} + \frac{6 \, a^{2} x}{35 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} c^{2}} + \frac{a^{2} x}{7 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} c} + \frac{3 \, b^{2} x}{140 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} d^{2}} + \frac{2 \, b^{2} x}{35 \, \sqrt{d x^{2} + c} c^{2} d^{2}} + \frac{b^{2} x}{35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c d^{2}} - \frac{3 \, b^{2} c x}{28 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} d^{2}} - \frac{2 \, a b x}{7 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} d} + \frac{16 \, a b x}{105 \, \sqrt{d x^{2} + c} c^{3} d} + \frac{8 \, a b x}{105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} d} + \frac{2 \, a b x}{35 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} c d}"," ",0,"-1/4*b^2*x^3/((d*x^2 + c)^(7/2)*d) + 16/35*a^2*x/(sqrt(d*x^2 + c)*c^4) + 8/35*a^2*x/((d*x^2 + c)^(3/2)*c^3) + 6/35*a^2*x/((d*x^2 + c)^(5/2)*c^2) + 1/7*a^2*x/((d*x^2 + c)^(7/2)*c) + 3/140*b^2*x/((d*x^2 + c)^(5/2)*d^2) + 2/35*b^2*x/(sqrt(d*x^2 + c)*c^2*d^2) + 1/35*b^2*x/((d*x^2 + c)^(3/2)*c*d^2) - 3/28*b^2*c*x/((d*x^2 + c)^(7/2)*d^2) - 2/7*a*b*x/((d*x^2 + c)^(7/2)*d) + 16/105*a*b*x/(sqrt(d*x^2 + c)*c^3*d) + 8/105*a*b*x/((d*x^2 + c)^(3/2)*c^2*d) + 2/35*a*b*x/((d*x^2 + c)^(5/2)*c*d)","A",0
99,1,103,0,1.452958," ","integrate((b*x^2+a)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{8 \, a x}{15 \, \sqrt{d x^{2} + c} c^{3}} + \frac{4 \, a x}{15 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{a x}{5 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} c} - \frac{b x}{5 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} d} + \frac{2 \, b x}{15 \, \sqrt{d x^{2} + c} c^{2} d} + \frac{b x}{15 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c d}"," ",0,"8/15*a*x/(sqrt(d*x^2 + c)*c^3) + 4/15*a*x/((d*x^2 + c)^(3/2)*c^2) + 1/5*a*x/((d*x^2 + c)^(5/2)*c) - 1/5*b*x/((d*x^2 + c)^(5/2)*d) + 2/15*b*x/(sqrt(d*x^2 + c)*c^2*d) + 1/15*b*x/((d*x^2 + c)^(3/2)*c*d)","A",0
100,1,31,0,1.337844," ","integrate(1/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, x}{3 \, \sqrt{d x^{2} + c} c^{2}} + \frac{x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c}"," ",0,"2/3*x/(sqrt(d*x^2 + c)*c^2) + 1/3*x/((d*x^2 + c)^(3/2)*c)","A",0
101,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(3/2)), x)","F",0
102,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*sqrt(d*x^2 + c)), x)","F",0
103,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^3, x)","F",0
104,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^4,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{4}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^4, x)","F",0
105,0,0,0,0.000000," ","integrate(1/(b*c/d+b*x^2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + \frac{b c}{d}\right)} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + b*c/d)*sqrt(d*x^2 + c)), x)","F",0
106,0,0,0,0.000000," ","integrate(1/(x^2+1)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 1\right)} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/((x^2 + 1)*sqrt(-x^2 + 1)), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
108,1,13,0,2.782371," ","integrate((x^2-1)/(x^2+1)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, x}{\sqrt{x^{2} + 1}} + \operatorname{arsinh}\left(x\right)"," ",0,"-2*x/sqrt(x^2 + 1) + arcsinh(x)","A",0
109,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a)^3,x, algorithm=""maxima"")","\int {\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3*(-b*x^2 + a)^(2/3), x)","F",0
110,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int {\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2*(-b*x^2 + a)^(2/3), x)","F",0
111,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a),x, algorithm=""maxima"")","\int {\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)*(-b*x^2 + a)^(2/3), x)","F",0
112,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a),x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b x^{2} + 3 \, a}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a), x)","F",0
113,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a)^2, x)","F",0
114,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^3,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{3}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a)^3, x)","F",0
115,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^4,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{4}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a)^4, x)","F",0
116,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a)^3,x, algorithm=""maxima"")","\int {\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3*(-b*x^2 + a)^(5/3), x)","F",0
117,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int {\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2*(-b*x^2 + a)^(5/3), x)","F",0
118,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a),x, algorithm=""maxima"")","\int {\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)*(-b*x^2 + a)^(5/3), x)","F",0
119,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a),x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{3}}}{b x^{2} + 3 \, a}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/3)/(b*x^2 + 3*a), x)","F",0
120,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/3)/(b*x^2 + 3*a)^2, x)","F",0
121,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a)^3,x, algorithm=""maxima"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{3}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/3)/(b*x^2 + 3*a)^3, x)","F",0
122,0,0,0,0.000000," ","integrate((b*x^2+3*a)^4/(-b*x^2+a)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{4}}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^4/(-b*x^2 + a)^(1/3), x)","F",0
123,0,0,0,0.000000," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{3}}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3/(-b*x^2 + a)^(1/3), x)","F",0
124,0,0,0,0.000000," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{2}}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(1/3), x)","F",0
125,0,0,0,0.000000," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(1/3),x, algorithm=""maxima"")","\int \frac{b x^{2} + 3 \, a}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)/(-b*x^2 + a)^(1/3), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(1/3)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^2*(-b*x^2 + a)^(1/3)), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^3*(-b*x^2 + a)^(1/3)), x)","F",0
129,0,0,0,0.000000," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{3}}{{\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3/(-b*x^2 + a)^(4/3), x)","F",0
130,0,0,0,0.000000," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{2}}{{\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(4/3), x)","F",0
131,0,0,0,0.000000," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(4/3),x, algorithm=""maxima"")","\int \frac{b x^{2} + 3 \, a}{{\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)/(-b*x^2 + a)^(4/3), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(4/3)), x)","F",0
133,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^2*(-b*x^2 + a)^(4/3)), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^3*(-b*x^2 + a)^(4/3)), x)","F",0
135,0,0,0,0.000000," ","integrate((b*x^2+3*a)^4/(-b*x^2+a)^(7/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{4}}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^4/(-b*x^2 + a)^(7/3), x)","F",0
136,0,0,0,0.000000," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(7/3),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{3}}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3/(-b*x^2 + a)^(7/3), x)","F",0
137,1,33,0,1.889647," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(7/3),x, algorithm=""maxima"")","\frac{3 \, {\left(b x^{3} - 3 \, a x\right)}}{{\left(b x^{2} - a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}"," ",0,"3*(b*x^3 - 3*a*x)/((b*x^2 - a)*(-b*x^2 + a)^(1/3))","A",0
138,0,0,0,0.000000," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(7/3),x, algorithm=""maxima"")","\int \frac{b x^{2} + 3 \, a}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)/(-b*x^2 + a)^(7/3), x)","F",0
139,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(7/3)), x)","F",0
140,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^2*(-b*x^2 + a)^(7/3)), x)","F",0
141,0,0,0,0.000000," ","integrate(1/(-b*x^2-3*a)/(b*x^2-a)^(1/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(b x^{2} - a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"-integrate(1/((b*x^2 + 3*a)*(b*x^2 - a)^(1/3)), x)","F",0
142,0,0,0,0.000000," ","integrate(1/(-b*x^2+3*a)/(b*x^2+a)^(1/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{3}} {\left(b x^{2} - 3 \, a\right)}}\,{d x}"," ",0,"-integrate(1/((b*x^2 + a)^(1/3)*(b*x^2 - 3*a)), x)","F",0
143,0,0,0,0.000000," ","integrate(1/(-d*x^2+c)/(3*d*x^2+c)^(1/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, d x^{2} + c\right)}^{\frac{1}{3}} {\left(d x^{2} - c\right)}}\,{d x}"," ",0,"-integrate(1/((3*d*x^2 + c)^(1/3)*(d*x^2 - c)), x)","F",0
144,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(1/3)), x)","F",0
145,0,0,0,0.000000," ","integrate(1/(-3*d*x^2+c)^(1/3)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x^{2} + c\right)} {\left(-3 \, d x^{2} + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 + c)*(-3*d*x^2 + c)^(1/3)), x)","F",0
146,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
147,0,0,0,0.000000," ","integrate(1/(-x^2+3)/(x^2+1)^(1/3),x, algorithm=""maxima"")","-\int \frac{1}{{\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(x^{2} - 3\right)}}\,{d x}"," ",0,"-integrate(1/((x^2 + 1)^(1/3)*(x^2 - 3)), x)","F",0
148,0,0,0,0.000000," ","integrate((3-x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","-\int \frac{x - 3}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"-integrate((x - 3)/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
149,0,0,0,0.000000," ","integrate((3+x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\int \frac{x + 3}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x + 3)/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
150,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/3)/(9*a*d/b+d*x^2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{3}} {\left(d x^{2} + \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(1/3)*(d*x^2 + 9*a*d/b)), x)","F",0
151,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(-9*a*d/b+d*x^2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}} {\left(d x^{2} - \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((-b*x^2 + a)^(1/3)*(d*x^2 - 9*a*d/b)), x)","F",0
152,0,0,0,0.000000," ","integrate(1/(b*x^2-a)^(1/3)/(-9*a*d/b+d*x^2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{\frac{1}{3}} {\left(d x^{2} - \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^(1/3)*(d*x^2 - 9*a*d/b)), x)","F",0
153,0,0,0,0.000000," ","integrate(1/(-b*x^2-a)^(1/3)/(9*a*d/b+d*x^2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-b x^{2} - a\right)}^{\frac{1}{3}} {\left(d x^{2} + \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((-b*x^2 - a)^(1/3)*(d*x^2 + 9*a*d/b)), x)","F",0
154,0,0,0,0.000000," ","integrate(1/(b*x^2+2)^(1/3)/(18*d/b+d*x^2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 2\right)}^{\frac{1}{3}} {\left(d x^{2} + \frac{18 \, d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 2)^(1/3)*(d*x^2 + 18*d/b)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/(b*x^2-2)^(1/3)/(-18*d/b+d*x^2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} - 2\right)}^{\frac{1}{3}} {\left(d x^{2} - \frac{18 \, d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - 2)^(1/3)*(d*x^2 - 18*d/b)), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(3*x^2+2)^(1/3)/(d*x^2+6*d),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x^{2} + 6 \, d\right)} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 + 6*d)*(3*x^2 + 2)^(1/3)), x)","F",0
157,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/3)/(d*x^2-6*d),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x^{2} - 6 \, d\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 - 6*d)*(-3*x^2 + 2)^(1/3)), x)","F",0
158,0,0,0,0.000000," ","integrate(1/(3*x^2-2)^(1/3)/(d*x^2-6*d),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x^{2} - 6 \, d\right)} {\left(3 \, x^{2} - 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 - 6*d)*(3*x^2 - 2)^(1/3)), x)","F",0
159,0,0,0,0.000000," ","integrate(1/(-3*x^2-2)^(1/3)/(d*x^2+6*d),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x^{2} + 6 \, d\right)} {\left(-3 \, x^{2} - 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 + 6*d)*(-3*x^2 - 2)^(1/3)), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/3)/(x^2+9),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 9\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 9)*(x^2 + 1)^(1/3)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(b*x^2+1)^(1/3)/(b*x^2+9),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 9\right)} {\left(b x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 9)*(b*x^2 + 1)^(1/3)), x)","F",0
162,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/3)/(-x^2+9),x, algorithm=""maxima"")","-\int \frac{1}{{\left(x^{2} - 9\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"-integrate(1/((x^2 - 9)*(-x^2 + 1)^(1/3)), x)","F",0
163,1,70,0,1.493379," ","integrate((c^2*x^2-1)^(1/2)/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{x}{2 \, {\left(c^{2} \sqrt{-d} d^{2} x^{2} - \sqrt{-d} d^{2}\right)}} - \frac{\sqrt{-d} \log\left(c x + 1\right)}{4 \, c d^{3}} + \frac{\sqrt{-d} \log\left(c x - 1\right)}{4 \, c d^{3}}"," ",0,"-1/2*x/(c^2*sqrt(-d)*d^2*x^2 - sqrt(-d)*d^2) - 1/4*sqrt(-d)*log(c*x + 1)/(c*d^3) + 1/4*sqrt(-d)*log(c*x - 1)/(c*d^3)","A",0
164,0,0,0,0.000000," ","integrate(1/(c^2*x^2-1)^(3/2)/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-c^{2} d x^{2} + d} {\left(c^{2} x^{2} - 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*d*x^2 + d)*(c^2*x^2 - 1)^(3/2)), x)","F",0
165,0,0,0,0.000000," ","integrate(1/(c^2*x^2-1)^(1/2)/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \sqrt{c^{2} x^{2} - 1}}\,{d x}"," ",0,"integrate(1/((-c^2*d*x^2 + d)^(3/2)*sqrt(c^2*x^2 - 1)), x)","F",0
166,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c), x)","F",0
167,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)*sqrt(d*x^2 + c), x)","F",0
168,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
169,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^(3/2), x)","F",0
170,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^(7/2), x)","F",0
172,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int {\left(b x^{2} + a\right)}^{\frac{3}{2}} {\left(d x^{2} + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)*(d*x^2 + c)^(3/2), x)","F",0
173,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)*(d*x^2 + c)^(3/2), x)","F",0
174,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/sqrt(b*x^2 + a), x)","F",0
175,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^(3/2), x)","F",0
176,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^(5/2), x)","F",0
177,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^(7/2), x)","F",0
178,0,0,0,0.000000," ","integrate((b*x^2+2)^(1/2)*(d*x^2+3)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3), x)","F",0
179,0,0,0,0.000000," ","integrate((-6*x^2+3)^(1/2)*(4*x^2+2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, x^{2} + 2} \sqrt{-6 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(4*x^2 + 2)*sqrt(-6*x^2 + 3), x)","F",0
180,0,0,0,0.000000," ","integrate((4*x^2+2)^(1/2)*(6*x^2+3)^(1/2),x, algorithm=""maxima"")","\int \sqrt{6 \, x^{2} + 3} \sqrt{4 \, x^{2} + 2}\,{d x}"," ",0,"integrate(sqrt(6*x^2 + 3)*sqrt(4*x^2 + 2), x)","F",0
181,0,0,0,0.000000," ","integrate((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + 2)/sqrt(d*x^2 + 3), x)","F",0
182,0,0,0,0.000000," ","integrate((-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-x^{2} + 4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 4)/sqrt(d*x^2 + c), x)","F",0
183,0,0,0,0.000000," ","integrate((x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{x^{2} + 4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 4)/sqrt(d*x^2 + c), x)","F",0
184,0,0,0,0.000000," ","integrate((-x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
185,0,0,0,0.000000," ","integrate((-x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-x^{2} + 4}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 4)/sqrt(-3*x^2 + 2), x)","F",0
186,0,0,0,0.000000," ","integrate((-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-4 \, x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-4*x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
187,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(-x^2 + 1), x)","F",0
188,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
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254,0,0,0,0.000000," ","integrate(1/(-2*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-2*x^2 + 2)), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-3*x^2 + 2)), x)","F",0
256,0,0,0,0.000000," ","integrate(1/(-4*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-4*x^2 + 2)), x)","F",0
257,0,0,0,0.000000," ","integrate(1/(-5*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-5*x^2 + 2)), x)","F",0
258,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(-d*x^2 + c), x)","F",0
259,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(-d*x^2 + c), x)","F",0
260,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(d*x^2 - c), x)","F",0
261,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(d*x^2 - c), x)","F",0
262,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(-d*x^2 + c), x)","F",0
263,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(-d*x^2 + c), x)","F",0
264,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(d*x^2 - c), x)","F",0
265,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(d*x^2 - c), x)","F",0
266,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
267,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(d*x^2 + c), x)","F",0
268,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(-d*x^2 - c), x)","F",0
269,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(-d*x^2 - c), x)","F",0
270,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
271,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(d*x^2 + c), x)","F",0
272,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(-d*x^2 - c), x)","F",0
273,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(-d*x^2 - c), x)","F",0
274,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(-b*x^2 + a), x)","F",0
275,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(-b*x^2 + a), x)","F",0
276,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(b*x^2 - a), x)","F",0
277,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(b*x^2 - a), x)","F",0
278,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(-b*x^2 + a), x)","F",0
279,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(-b*x^2 + a), x)","F",0
280,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(b*x^2 - a), x)","F",0
281,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(b*x^2 - a), x)","F",0
282,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
283,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(b*x^2 + a), x)","F",0
284,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(-b*x^2 - a), x)","F",0
285,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(-b*x^2 - a), x)","F",0
286,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
287,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(b*x^2 + a), x)","F",0
288,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(-b*x^2 - a), x)","F",0
289,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(-b*x^2 - a), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3)), x)","F",0
291,0,0,0,0.000000," ","integrate(1/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{d x^{2} + c} \sqrt{-x^{2} + 4}}\,{d x}"," ",0,"integrate(1/(sqrt(d*x^2 + c)*sqrt(-x^2 + 4)), x)","F",0
292,0,0,0,0.000000," ","integrate(1/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{d x^{2} + c} \sqrt{x^{2} + 4}}\,{d x}"," ",0,"integrate(1/(sqrt(d*x^2 + c)*sqrt(x^2 + 4)), x)","F",0
293,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{2 \, x^{2} - 1} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^2 - 1)*sqrt(-x^2 + 1)), x)","F",0
294,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/sqrt(c^2*x^2 + 1), x)","F",0
295,0,0,0,0.000000," ","integrate((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + 2)/sqrt(d*x^2 + 3), x)","F",0
296,0,0,0,0.000000," ","integrate((3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{3 \, x^{2} - 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(3*x^2 - 1)/sqrt(-3*x^2 + 2), x)","F",0
297,0,0,0,0.000000," ","integrate((1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1-2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{2 \, c x^{2}}{b - \sqrt{b^{2} - 4 \, a c}} + 1}}{\sqrt{-\frac{2 \, c x^{2}}{b + \sqrt{b^{2} - 4 \, a c}} + 1}}\,{d x}"," ",0,"integrate(sqrt(2*c*x^2/(b - sqrt(b^2 - 4*a*c)) + 1)/sqrt(-2*c*x^2/(b + sqrt(b^2 - 4*a*c)) + 1), x)","F",0
298,0,0,0,0.000000," ","integrate((1-2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1-2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\frac{2 \, c x^{2}}{b - \sqrt{b^{2} - 4 \, a c}} + 1}}{\sqrt{-\frac{2 \, c x^{2}}{b + \sqrt{b^{2} - 4 \, a c}} + 1}}\,{d x}"," ",0,"integrate(sqrt(-2*c*x^2/(b - sqrt(b^2 - 4*a*c)) + 1)/sqrt(-2*c*x^2/(b + sqrt(b^2 - 4*a*c)) + 1), x)","F",0
299,0,0,0,0.000000," ","integrate((1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\frac{2 \, c x^{2}}{b - \sqrt{b^{2} - 4 \, a c}} + 1}}{\sqrt{\frac{2 \, c x^{2}}{b + \sqrt{b^{2} - 4 \, a c}} + 1}}\,{d x}"," ",0,"integrate(sqrt(2*c*x^2/(b - sqrt(b^2 - 4*a*c)) + 1)/sqrt(2*c*x^2/(b + sqrt(b^2 - 4*a*c)) + 1), x)","F",0
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301,0,0,0,0.000000," ","integrate((-2*x^2+1)^m/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-2 \, x^{2} + 1\right)}^{m}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate((-2*x^2 + 1)^m/sqrt(-x^2 + 1), x)","F",0
302,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/2)/(7+x^2-4*3^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{x^{2} - 4 \, \sqrt{3} + 7} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 4*sqrt(3) + 7)*sqrt(x^2 - 1)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(3+x^2*(-3+3^(1/2)))^(1/2)/(3-3*3^(1/2)+2*3^(1/2)*x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{x^{2} {\left(\sqrt{3} - 3\right)} + 3} \sqrt{2 \, \sqrt{3} x^{2} - 3 \, \sqrt{3} + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2*(sqrt(3) - 3) + 3)*sqrt(2*sqrt(3)*x^2 - 3*sqrt(3) + 3)), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(3*x^2+2)^(1/4)/(3*x^2+4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} + 4\right)} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^2 + 4)*(3*x^2 + 2)^(1/4)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)), x)","F",0
306,0,0,0,0.000000," ","integrate(1/(b*x^2+2)^(1/4)/(b*x^2+4),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 4\right)} {\left(b x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 4)*(b*x^2 + 2)^(1/4)), x)","F",0
307,0,0,0,0.000000," ","integrate(1/(-b*x^2+2)^(1/4)/(-b*x^2+4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{2} - 4\right)} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((b*x^2 - 4)*(-b*x^2 + 2)^(1/4)), x)","F",0
308,0,0,0,0.000000," ","integrate(1/(3*x^2+a)^(1/4)/(3*x^2+2*a),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} + 2 \, a\right)} {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^2 + 2*a)*(3*x^2 + a)^(1/4)), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(-3*x^2+a)^(1/4)/(-3*x^2+2*a),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} - 2 \, a\right)} {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((3*x^2 - 2*a)*(-3*x^2 + a)^(1/4)), x)","F",0
310,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(b*x^2+2*a),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + 2 \, a\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 2*a)*(b*x^2 + a)^(1/4)), x)","F",0
311,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/4)/(-b*x^2+2*a),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{2} - 2 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((b*x^2 - 2*a)*(-b*x^2 + a)^(1/4)), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F",0
313,0,0,0,0.000000," ","integrate(1/(-3*x^2-2)/(-3*x^2-1)^(1/4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} + 2\right)} {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((3*x^2 + 2)*(-3*x^2 - 1)^(1/4)), x)","F",0
314,0,0,0,0.000000," ","integrate(1/(b*x^2-2)/(b*x^2-1)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} - 1\right)}^{\frac{1}{4}} {\left(b x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - 1)^(1/4)*(b*x^2 - 2)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(-b*x^2-2)/(-b*x^2-1)^(1/4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{2} + 2\right)} {\left(-b x^{2} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((b*x^2 + 2)*(-b*x^2 - 1)^(1/4)), x)","F",0
316,0,0,0,0.000000," ","integrate(1/(3*x^2-2*a)/(3*x^2-a)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} - a\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2 \, a\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 - a)^(1/4)*(3*x^2 - 2*a)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/(-3*x^2-2*a)/(-3*x^2-a)^(1/4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} + 2 \, a\right)} {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((3*x^2 + 2*a)*(-3*x^2 - a)^(1/4)), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(b*x^2-2*a)/(b*x^2-a)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{\frac{1}{4}} {\left(b x^{2} - 2 \, a\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^(1/4)*(b*x^2 - 2*a)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(-b*x^2-2*a)/(-b*x^2-a)^(1/4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(b x^{2} + 2 \, a\right)} {\left(-b x^{2} - a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"-integrate(1/((b*x^2 + 2*a)*(-b*x^2 - a)^(1/4)), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(-x^2+2)/(x^2-1)^(1/4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(x^{2} - 1\right)}^{\frac{1}{4}} {\left(x^{2} - 2\right)}}\,{d x}"," ",0,"-integrate(1/((x^2 - 1)^(1/4)*(x^2 - 2)), x)","F",0
321,0,0,0,0.000000," ","integrate((b*x^2+a)^(7/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(7/4)/(d*x^2 + c), x)","F",0
322,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/4)/(d*x^2 + c), x)","F",0
323,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/4)/(d*x^2 + c), x)","F",0
324,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(1/4)/(d*x^2 + c), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(1/4)*(d*x^2 + c)), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/4)*(d*x^2 + c)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/4)*(d*x^2 + c)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(7/4)*(d*x^2 + c)), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(9/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(9/4)*(d*x^2 + c)), x)","F",0
330,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(11/4)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{11}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(11/4)*(d*x^2 + c)), x)","F",0
331,0,0,0,0.000000," ","integrate((b*x^2+a)^(7/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(7/4)/(d*x^2 + c)^2, x)","F",0
332,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/4)/(d*x^2 + c)^2, x)","F",0
333,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/4)/(d*x^2 + c)^2, x)","F",0
334,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(1/4)/(d*x^2 + c)^2, x)","F",0
335,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(1/4)*(d*x^2 + c)^2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/4)*(d*x^2 + c)^2), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/4)*(d*x^2 + c)^2), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(7/4)*(d*x^2 + c)^2), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(9/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(9/4)*(d*x^2 + c)^2), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(11/4)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{11}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(11/4)*(d*x^2 + c)^2), x)","F",0
341,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""maxima"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
342,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^3,x, algorithm=""maxima"")","\int {\left(d x^{2} + c\right)}^{3} {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^2 + c)^3*(b*x^2 + a)^p, x)","F",0
343,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^2,x, algorithm=""maxima"")","\int {\left(d x^{2} + c\right)}^{2} {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^2 + c)^2*(b*x^2 + a)^p, x)","F",0
344,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c),x, algorithm=""maxima"")","\int {\left(d x^{2} + c\right)} {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^2 + c)*(b*x^2 + a)^p, x)","F",0
345,0,0,0,0.000000," ","integrate((b*x^2+a)^p,x, algorithm=""maxima"")","\int {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^2 + a)^p, x)","F",0
346,0,0,0,0.000000," ","integrate((b*x^2+a)^p/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{p}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^p/(d*x^2 + c), x)","F",0
347,0,0,0,0.000000," ","integrate((b*x^2+a)^p/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{p}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p/(d*x^2 + c)^2, x)","F",0
348,0,0,0,0.000000," ","integrate((b*x^2+a)^p/(d*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{{\left(b x^{2} + a\right)}^{p}}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p/(d*x^2 + c)^3, x)","F",0
349,0,0,0,0.000000," ","integrate((b*x^2+a)^(-1-b*c/(-2*a*d+2*b*c))*(d*x^2+c)^(-1+a*d/(-2*a*d+2*b*c)),x, algorithm=""maxima"")","\int {\left(b x^{2} + a\right)}^{-\frac{b c}{2 \, {\left(b c - a d\right)}} - 1} {\left(d x^{2} + c\right)}^{\frac{a d}{2 \, {\left(b c - a d\right)}} - 1}\,{d x}"," ",0,"integrate((b*x^2 + a)^(-1/2*b*c/(b*c - a*d) - 1)*(d*x^2 + c)^(1/2*a*d/(b*c - a*d) - 1), x)","F",0
