1,0,-1,145,0.000000,"\text{Not used}","int(1/((x^3 + 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{1}{\sqrt{x^3+1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int(1/((x^3 + 1)^(1/2)*(x + 2^(2/3))), x)","F"
2,0,-1,160,0.000000,"\text{Not used}","int(-1/((1 - x^3)^(1/2)*(x - 2^(2/3))),x)","-\int \frac{1}{\sqrt{1-x^3}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"-int(1/((1 - x^3)^(1/2)*(x - 2^(2/3))), x)","F"
3,0,-1,163,0.000000,"\text{Not used}","int(-1/((x^3 - 1)^(1/2)*(x - 2^(2/3))),x)","-\int \frac{1}{\sqrt{x^3-1}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"-int(1/((x^3 - 1)^(1/2)*(x - 2^(2/3))), x)","F"
4,0,-1,156,0.000000,"\text{Not used}","int(1/((- x^3 - 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{1}{\sqrt{-x^3-1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int(1/((- x^3 - 1)^(1/2)*(x + 2^(2/3))), x)","F"
5,0,-1,280,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\int \frac{1}{\sqrt{b\,x^3+a}\,\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)), x)","F"
6,0,-1,288,0.000000,"\text{Not used}","int(1/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\int \frac{1}{\sqrt{a-b\,x^3}\,\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)} \,d x","Not used",1,"int(1/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)), x)","F"
7,0,-1,297,0.000000,"\text{Not used}","int(1/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\int \frac{1}{\sqrt{b\,x^3-a}\,\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)} \,d x","Not used",1,"int(1/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)), x)","F"
8,0,-1,293,0.000000,"\text{Not used}","int(1/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\int \frac{1}{\sqrt{-b\,x^3-a}\,\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)} \,d x","Not used",1,"int(1/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)), x)","F"
9,0,-1,249,0.000000,"\text{Not used}","int(1/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)),x)","\int \frac{1}{\sqrt{c^3+4\,d^3\,x^3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(1/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)), x)","F"
10,-1,-1,146,0.000000,"\text{Not used}","int(1/((x^3 + 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
11,-1,-1,164,0.000000,"\text{Not used}","int(1/((1 - x^3)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
12,-1,-1,167,0.000000,"\text{Not used}","int(1/((x^3 - 1)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
13,-1,-1,157,0.000000,"\text{Not used}","int(1/((- x^3 - 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
14,1,164,329,0.215941,"\text{Not used}","int(1/((x^3 + 1)^(1/2)*(x + 3)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{3}{4}-\frac{\sqrt{3}\,1{}\mathrm{i}}{4};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{2\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(- (3^(1/2)*1i)/4 - 3/4, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(2*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
15,1,180,380,2.419982,"\text{Not used}","int(1/((1 - x^3)^(1/2)*(x + 3)),x)","-\frac{\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{8}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{2\,\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-(((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/8 + 3/8, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(2*(1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
16,1,164,374,0.049567,"\text{Not used}","int(1/((x^3 - 1)^(1/2)*(x + 3)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{8}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{4\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/8 + 3/8, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(4*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
17,1,179,340,0.046189,"\text{Not used}","int(1/((- x^3 - 1)^(1/2)*(x + 3)),x)","\frac{\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{3}{4}-\frac{\sqrt{3}\,1{}\mathrm{i}}{4};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(- (3^(1/2)*1i)/4 - 3/4, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
18,0,-1,139,0.000000,"\text{Not used}","int(1/((d^3*x^3 - c^3)^(1/3)*(c + d*x)),x)","\int \frac{1}{{\left(d^3\,x^3-c^3\right)}^{1/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(1/((d^3*x^3 - c^3)^(1/3)*(c + d*x)), x)","F"
19,0,-1,186,0.000000,"\text{Not used}","int(1/((2*c^3 + d^3*x^3)^(1/3)*(c + d*x)),x)","\int \frac{1}{{\left(2\,c^3+d^3\,x^3\right)}^{1/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(1/((2*c^3 + d^3*x^3)^(1/3)*(c + d*x)), x)","F"
20,0,-1,187,0.000000,"\text{Not used}","int(1/((2*c^3 + d^3*x^3)^(2/3)*(c + d*x)),x)","\int \frac{1}{{\left(2\,c^3+d^3\,x^3\right)}^{2/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(1/((2*c^3 + d^3*x^3)^(2/3)*(c + d*x)), x)","F"
21,0,-1,147,0.000000,"\text{Not used}","int(1/((x^3 + 1)^(2/3)*(2^(1/3)*x + 1)),x)","\int \frac{1}{{\left(x^3+1\right)}^{2/3}\,\left(2^{1/3}\,x+1\right)} \,d x","Not used",1,"int(1/((x^3 + 1)^(2/3)*(2^(1/3)*x + 1)), x)","F"
22,0,-1,159,0.000000,"\text{Not used}","int(-1/((1 - x^3)^(2/3)*(2^(1/3)*x - 1)),x)","-\int \frac{1}{{\left(1-x^3\right)}^{2/3}\,\left(2^{1/3}\,x-1\right)} \,d x","Not used",1,"-int(1/((1 - x^3)^(2/3)*(2^(1/3)*x - 1)), x)","F"
23,0,-1,387,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(c + d*x)^4,x)","\int {\left(b\,x^3+a\right)}^{1/3}\,{\left(c+d\,x\right)}^4 \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(c + d*x)^4, x)","F"
24,0,-1,242,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(c + d*x)^3,x)","\int {\left(b\,x^3+a\right)}^{1/3}\,{\left(c+d\,x\right)}^3 \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(c + d*x)^3, x)","F"
25,0,-1,192,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(c + d*x)^2,x)","\int {\left(b\,x^3+a\right)}^{1/3}\,{\left(c+d\,x\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(c + d*x)^2, x)","F"
26,0,-1,155,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(c + d*x),x)","\int {\left(b\,x^3+a\right)}^{1/3}\,\left(c+d\,x\right) \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(c + d*x), x)","F"
27,0,-1,435,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(c + d*x),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{c+d\,x} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(c + d*x), x)","F"
28,0,-1,818,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(c + d*x)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{{\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(c + d*x)^2, x)","F"
29,0,-1,310,0.000000,"\text{Not used}","int((c + d*x)^4/(a + b*x^3)^(1/3),x)","\int \frac{{\left(c+d\,x\right)}^4}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((c + d*x)^4/(a + b*x^3)^(1/3), x)","F"
30,0,-1,255,0.000000,"\text{Not used}","int((c + d*x)^3/(a + b*x^3)^(1/3),x)","\int \frac{{\left(c+d\,x\right)}^3}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((c + d*x)^3/(a + b*x^3)^(1/3), x)","F"
31,0,-1,147,0.000000,"\text{Not used}","int((c + d*x)^2/(a + b*x^3)^(1/3),x)","\int \frac{{\left(c+d\,x\right)}^2}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((c + d*x)^2/(a + b*x^3)^(1/3), x)","F"
32,0,-1,124,0.000000,"\text{Not used}","int((c + d*x)/(a + b*x^3)^(1/3),x)","\int \frac{c+d\,x}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((c + d*x)/(a + b*x^3)^(1/3), x)","F"
33,0,-1,333,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x)), x)","F"
34,0,-1,761,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,{\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x)^2), x)","F"
35,0,-1,1513,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,{\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x)^3), x)","F"
36,0,-1,306,0.000000,"\text{Not used}","int((c + d*x)^4/(a + b*x^3)^(2/3),x)","\int \frac{{\left(c+d\,x\right)}^4}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((c + d*x)^4/(a + b*x^3)^(2/3), x)","F"
37,0,-1,187,0.000000,"\text{Not used}","int((c + d*x)^3/(a + b*x^3)^(2/3),x)","\int \frac{{\left(c+d\,x\right)}^3}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((c + d*x)^3/(a + b*x^3)^(2/3), x)","F"
38,0,-1,141,0.000000,"\text{Not used}","int((c + d*x)^2/(a + b*x^3)^(2/3),x)","\int \frac{{\left(c+d\,x\right)}^2}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((c + d*x)^2/(a + b*x^3)^(2/3), x)","F"
39,0,-1,121,0.000000,"\text{Not used}","int((c + d*x)/(a + b*x^3)^(2/3),x)","\int \frac{c+d\,x}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((c + d*x)/(a + b*x^3)^(2/3), x)","F"
40,0,-1,332,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x)), x)","F"
41,0,-1,760,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,{\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x)^2), x)","F"
42,0,-1,1357,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,{\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x)^3), x)","F"
43,1,70,37,3.593050,"\text{Not used}","int(-(2*x - 2^(2/3))/((x^3 + 1)^(1/2)*(x + 2^(2/3))),x)","\frac{2^{2/3}\,\sqrt{3}\,\ln\left(\frac{\left(\sqrt{3}\,1{}\mathrm{i}+\sqrt{x^3+1}+2^{1/3}\,\sqrt{3}\,x\,1{}\mathrm{i}\right)\,{\left(\sqrt{3}\,1{}\mathrm{i}-\sqrt{x^3+1}+2^{1/3}\,\sqrt{3}\,x\,1{}\mathrm{i}\right)}^3}{{\left(x+2^{2/3}\right)}^6}\right)\,1{}\mathrm{i}}{3}","Not used",1,"(2^(2/3)*3^(1/2)*log(((3^(1/2)*1i + (x^3 + 1)^(1/2) + 2^(1/3)*3^(1/2)*x*1i)*(3^(1/2)*1i - (x^3 + 1)^(1/2) + 2^(1/3)*3^(1/2)*x*1i)^3)/(x + 2^(2/3))^6)*1i)/3","B"
44,1,74,40,3.631373,"\text{Not used}","int(-(2*x + 2^(2/3))/((1 - x^3)^(1/2)*(x - 2^(2/3))),x)","\frac{2^{2/3}\,\sqrt{3}\,\ln\left(\frac{\left(\sqrt{1-x^3}-\sqrt{3}\,1{}\mathrm{i}+2^{1/3}\,\sqrt{3}\,x\,1{}\mathrm{i}\right)\,{\left(\sqrt{3}\,1{}\mathrm{i}+\sqrt{1-x^3}-2^{1/3}\,\sqrt{3}\,x\,1{}\mathrm{i}\right)}^3}{{\left(x-2^{2/3}\right)}^6}\right)\,1{}\mathrm{i}}{3}","Not used",1,"(2^(2/3)*3^(1/2)*log((((1 - x^3)^(1/2) - 3^(1/2)*1i + 2^(1/3)*3^(1/2)*x*1i)*(3^(1/2)*1i + (1 - x^3)^(1/2) - 2^(1/3)*3^(1/2)*x*1i)^3)/(x - 2^(2/3))^6)*1i)/3","B"
45,1,62,38,2.860925,"\text{Not used}","int(-(2*x + 2^(2/3))/((x^3 - 1)^(1/2)*(x - 2^(2/3))),x)","\frac{2^{2/3}\,\sqrt{3}\,\ln\left(\frac{{\left(\sqrt{x^3-1}-\sqrt{3}+2^{1/3}\,\sqrt{3}\,x\right)}^3\,\left(\sqrt{3}+\sqrt{x^3-1}-2^{1/3}\,\sqrt{3}\,x\right)}{{\left(x-2^{2/3}\right)}^6}\right)}{3}","Not used",1,"(2^(2/3)*3^(1/2)*log((((x^3 - 1)^(1/2) - 3^(1/2) + 2^(1/3)*3^(1/2)*x)^3*(3^(1/2) + (x^3 - 1)^(1/2) - 2^(1/3)*3^(1/2)*x))/(x - 2^(2/3))^6))/3","B"
46,1,63,39,2.842976,"\text{Not used}","int(-(2*x - 2^(2/3))/((- x^3 - 1)^(1/2)*(x + 2^(2/3))),x)","\frac{2^{2/3}\,\sqrt{3}\,\ln\left(\frac{{\left(\sqrt{3}+\sqrt{-x^3-1}+2^{1/3}\,\sqrt{3}\,x\right)}^3\,\left(\sqrt{3}-\sqrt{-x^3-1}+2^{1/3}\,\sqrt{3}\,x\right)}{{\left(x+2^{2/3}\right)}^6}\right)}{3}","Not used",1,"(2^(2/3)*3^(1/2)*log(((3^(1/2) + (- x^3 - 1)^(1/2) + 2^(1/3)*3^(1/2)*x)^3*(3^(1/2) - (- x^3 - 1)^(1/2) + 2^(1/3)*3^(1/2)*x))/(x + 2^(2/3))^6))/3","B"
47,1,106,63,5.811671,"\text{Not used}","int((2^(2/3)*a^(1/3) - 2*b^(1/3)*x)/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\frac{2^{2/3}\,\sqrt{3}\,\ln\left(\frac{{\left(\sqrt{3}\,\sqrt{a}\,1{}\mathrm{i}-\sqrt{b\,x^3+a}+2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\,1{}\mathrm{i}\right)}^3\,\left(\sqrt{3}\,\sqrt{a}\,1{}\mathrm{i}+\sqrt{b\,x^3+a}+2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\,1{}\mathrm{i}\right)}{{\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)}^6}\right)\,1{}\mathrm{i}}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"(2^(2/3)*3^(1/2)*log(((3^(1/2)*a^(1/2)*1i - (a + b*x^3)^(1/2) + 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x*1i)^3*(3^(1/2)*a^(1/2)*1i + (a + b*x^3)^(1/2) + 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x*1i))/(2^(2/3)*a^(1/3) + b^(1/3)*x)^6)*1i)/(3*a^(1/6)*b^(1/3))","B"
48,1,107,65,5.851410,"\text{Not used}","int((2^(2/3)*a^(1/3) + 2*b^(1/3)*x)/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\frac{2^{2/3}\,\sqrt{3}\,\ln\left(\frac{\left(\sqrt{a-b\,x^3}-\sqrt{3}\,\sqrt{a}\,1{}\mathrm{i}+2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\,1{}\mathrm{i}\right)\,{\left(\sqrt{3}\,\sqrt{a}\,1{}\mathrm{i}+\sqrt{a-b\,x^3}-2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\,1{}\mathrm{i}\right)}^3}{{\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)}^6}\right)\,1{}\mathrm{i}}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"(2^(2/3)*3^(1/2)*log((((a - b*x^3)^(1/2) - 3^(1/2)*a^(1/2)*1i + 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x*1i)*(3^(1/2)*a^(1/2)*1i + (a - b*x^3)^(1/2) - 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x*1i)^3)/(2^(2/3)*a^(1/3) - b^(1/3)*x)^6)*1i)/(3*a^(1/6)*b^(1/3))","B"
49,1,102,66,3.677355,"\text{Not used}","int((2^(2/3)*a^(1/3) + 2*b^(1/3)*x)/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\frac{\sqrt{3}\,4^{1/3}\,\ln\left(\frac{\left(\sqrt{b\,x^3-a}+\sqrt{3}\,\sqrt{a}-2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\right)\,{\left(\sqrt{b\,x^3-a}-\sqrt{3}\,\sqrt{a}+2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\right)}^3}{{\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)}^6}\right)}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"(3^(1/2)*4^(1/3)*log((((b*x^3 - a)^(1/2) + 3^(1/2)*a^(1/2) - 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x)*((b*x^3 - a)^(1/2) - 3^(1/2)*a^(1/2) + 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x)^3)/(2^(2/3)*a^(1/3) - b^(1/3)*x)^6))/(3*a^(1/6)*b^(1/3))","B"
50,1,103,66,3.647275,"\text{Not used}","int((2^(2/3)*a^(1/3) - 2*b^(1/3)*x)/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\frac{\sqrt{3}\,4^{1/3}\,\ln\left(\frac{{\left(\sqrt{-b\,x^3-a}+\sqrt{3}\,\sqrt{a}+2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\right)}^3\,\left(\sqrt{3}\,\sqrt{a}-\sqrt{-b\,x^3-a}+2^{1/3}\,\sqrt{3}\,a^{1/6}\,b^{1/3}\,x\right)}{{\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)}^6}\right)}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"(3^(1/2)*4^(1/3)*log((((- a - b*x^3)^(1/2) + 3^(1/2)*a^(1/2) + 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x)^3*(3^(1/2)*a^(1/2) - (- a - b*x^3)^(1/2) + 2^(1/3)*3^(1/2)*a^(1/6)*b^(1/3)*x))/(2^(2/3)*a^(1/3) + b^(1/3)*x)^6))/(3*a^(1/6)*b^(1/3))","B"
51,1,95,49,4.730678,"\text{Not used}","int((c - 2*d*x)/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)),x)","\frac{\sqrt{3}\,\ln\left(\frac{{\left(-\sqrt{c^3+4\,d^3\,x^3}+\sqrt{3}\,c^{3/2}\,1{}\mathrm{i}+\sqrt{3}\,\sqrt{c}\,d\,x\,2{}\mathrm{i}\right)}^3\,\left(\sqrt{c^3+4\,d^3\,x^3}+\sqrt{3}\,c^{3/2}\,1{}\mathrm{i}+\sqrt{3}\,\sqrt{c}\,d\,x\,2{}\mathrm{i}\right)}{{\left(c+d\,x\right)}^6}\right)\,1{}\mathrm{i}}{3\,\sqrt{c}\,d}","Not used",1,"(3^(1/2)*log(((3^(1/2)*c^(3/2)*1i - (c^3 + 4*d^3*x^3)^(1/2) + 3^(1/2)*c^(1/2)*d*x*2i)^3*((c^3 + 4*d^3*x^3)^(1/2) + 3^(1/2)*c^(3/2)*1i + 3^(1/2)*c^(1/2)*d*x*2i))/(c + d*x)^6)*1i)/(3*c^(1/2)*d)","B"
52,0,-1,158,0.000000,"\text{Not used}","int((3*x + 2)/((x^3 + 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{3\,x+2}{\sqrt{x^3+1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int((3*x + 2)/((x^3 + 1)^(1/2)*(x + 2^(2/3))), x)","F"
53,0,-1,173,0.000000,"\text{Not used}","int(-(3*x + 2)/((1 - x^3)^(1/2)*(x - 2^(2/3))),x)","\int -\frac{3\,x+2}{\sqrt{1-x^3}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"int(-(3*x + 2)/((1 - x^3)^(1/2)*(x - 2^(2/3))), x)","F"
54,0,-1,176,0.000000,"\text{Not used}","int(-(3*x + 2)/((x^3 - 1)^(1/2)*(x - 2^(2/3))),x)","\int -\frac{3\,x+2}{\sqrt{x^3-1}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"int(-(3*x + 2)/((x^3 - 1)^(1/2)*(x - 2^(2/3))), x)","F"
55,0,-1,169,0.000000,"\text{Not used}","int((3*x + 2)/((- x^3 - 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{3\,x+2}{\sqrt{-x^3-1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int((3*x + 2)/((- x^3 - 1)^(1/2)*(x + 2^(2/3))), x)","F"
56,0,-1,159,0.000000,"\text{Not used}","int((e + f*x)/((x^3 + 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{e+f\,x}{\sqrt{x^3+1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int((e + f*x)/((x^3 + 1)^(1/2)*(x + 2^(2/3))), x)","F"
57,0,-1,175,0.000000,"\text{Not used}","int(-(e + f*x)/((1 - x^3)^(1/2)*(x - 2^(2/3))),x)","\int -\frac{e+f\,x}{\sqrt{1-x^3}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"int(-(e + f*x)/((1 - x^3)^(1/2)*(x - 2^(2/3))), x)","F"
58,0,-1,178,0.000000,"\text{Not used}","int(-(e + f*x)/((x^3 - 1)^(1/2)*(x - 2^(2/3))),x)","\int -\frac{e+f\,x}{\sqrt{x^3-1}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"int(-(e + f*x)/((x^3 - 1)^(1/2)*(x - 2^(2/3))), x)","F"
59,0,-1,170,0.000000,"\text{Not used}","int((e + f*x)/((- x^3 - 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{e+f\,x}{\sqrt{-x^3-1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int((e + f*x)/((- x^3 - 1)^(1/2)*(x + 2^(2/3))), x)","F"
60,0,-1,316,0.000000,"\text{Not used}","int((e + f*x)/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\int \frac{e+f\,x}{\sqrt{b\,x^3+a}\,\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)} \,d x","Not used",1,"int((e + f*x)/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)), x)","F"
61,0,-1,324,0.000000,"\text{Not used}","int((e + f*x)/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\int \frac{e+f\,x}{\sqrt{a-b\,x^3}\,\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)} \,d x","Not used",1,"int((e + f*x)/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)), x)","F"
62,0,-1,333,0.000000,"\text{Not used}","int((e + f*x)/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\int \frac{e+f\,x}{\sqrt{b\,x^3-a}\,\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)} \,d x","Not used",1,"int((e + f*x)/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)), x)","F"
63,0,-1,329,0.000000,"\text{Not used}","int((e + f*x)/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\int \frac{e+f\,x}{\sqrt{-b\,x^3-a}\,\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)} \,d x","Not used",1,"int((e + f*x)/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)), x)","F"
64,0,-1,265,0.000000,"\text{Not used}","int((e + f*x)/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)),x)","\int \frac{e+f\,x}{\sqrt{c^3+4\,d^3\,x^3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int((e + f*x)/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)), x)","F"
65,0,-1,145,0.000000,"\text{Not used}","int(x/((x^3 + 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{x}{\sqrt{x^3+1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int(x/((x^3 + 1)^(1/2)*(x + 2^(2/3))), x)","F"
66,0,-1,160,0.000000,"\text{Not used}","int(-x/((1 - x^3)^(1/2)*(x - 2^(2/3))),x)","-\int \frac{x}{\sqrt{1-x^3}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"-int(x/((1 - x^3)^(1/2)*(x - 2^(2/3))), x)","F"
67,0,-1,163,0.000000,"\text{Not used}","int(-x/((x^3 - 1)^(1/2)*(x - 2^(2/3))),x)","-\int \frac{x}{\sqrt{x^3-1}\,\left(x-2^{2/3}\right)} \,d x","Not used",1,"-int(x/((x^3 - 1)^(1/2)*(x - 2^(2/3))), x)","F"
68,0,-1,156,0.000000,"\text{Not used}","int(x/((- x^3 - 1)^(1/2)*(x + 2^(2/3))),x)","\int \frac{x}{\sqrt{-x^3-1}\,\left(x+2^{2/3}\right)} \,d x","Not used",1,"int(x/((- x^3 - 1)^(1/2)*(x + 2^(2/3))), x)","F"
69,0,-1,275,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\int \frac{x}{\sqrt{b\,x^3+a}\,\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)} \,d x","Not used",1,"int(x/((a + b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)), x)","F"
70,0,-1,283,0.000000,"\text{Not used}","int(x/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\int \frac{x}{\sqrt{a-b\,x^3}\,\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)} \,d x","Not used",1,"int(x/((a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)), x)","F"
71,0,-1,292,0.000000,"\text{Not used}","int(x/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)),x)","\int \frac{x}{\sqrt{b\,x^3-a}\,\left(2^{2/3}\,a^{1/3}-b^{1/3}\,x\right)} \,d x","Not used",1,"int(x/((b*x^3 - a)^(1/2)*(2^(2/3)*a^(1/3) - b^(1/3)*x)), x)","F"
72,0,-1,288,0.000000,"\text{Not used}","int(x/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)),x)","\int \frac{x}{\sqrt{-b\,x^3-a}\,\left(2^{2/3}\,a^{1/3}+b^{1/3}\,x\right)} \,d x","Not used",1,"int(x/((- a - b*x^3)^(1/2)*(2^(2/3)*a^(1/3) + b^(1/3)*x)), x)","F"
73,0,-1,246,0.000000,"\text{Not used}","int(x/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)),x)","\int \frac{x}{\sqrt{c^3+4\,d^3\,x^3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(x/((c^3 + 4*d^3*x^3)^(1/2)*(c + d*x)), x)","F"
74,1,205,23,0.225103,"\text{Not used}","int(-(x + 1)/((x^3 + 1)^(1/2)*(x - 2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticPi((3^(1/2)*1i)/6 + 1/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
75,1,221,27,0.184046,"\text{Not used}","int(-(x - 1)/((1 - x^3)^(1/2)*(x + 2)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticPi((3^(1/2)*1i)/6 + 1/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
76,1,205,25,2.551007,"\text{Not used}","int(-(x - 1)/((x^3 - 1)^(1/2)*(x + 2)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticPi((3^(1/2)*1i)/6 + 1/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
77,1,221,25,2.528586,"\text{Not used}","int(-(x + 1)/((- x^3 - 1)^(1/2)*(x - 2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticPi((3^(1/2)*1i)/6 + 1/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
78,1,65,50,3.443971,"\text{Not used}","int(-(b^(1/3)*x + a^(1/3))/((b^(1/3)*x - 2*a^(1/3))*(a + b*x^3)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)\,{\left(\sqrt{b\,x^3+a}-\sqrt{a}+2\,a^{1/6}\,b^{1/3}\,x\right)}^3}{x^3\,{\left(b^{1/3}\,x-2\,a^{1/3}\right)}^3}\right)}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"log((((a + b*x^3)^(1/2) + a^(1/2))*((a + b*x^3)^(1/2) - a^(1/2) + 2*a^(1/6)*b^(1/3)*x)^3)/(x^3*(b^(1/3)*x - 2*a^(1/3))^3))/(3*a^(1/6)*b^(1/3))","B"
79,1,67,52,3.590965,"\text{Not used}","int(-(b^(1/3)*x - a^(1/3))/((b^(1/3)*x + 2*a^(1/3))*(a - b*x^3)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{a-b\,x^3}-\sqrt{a}\right)\,{\left(\sqrt{a-b\,x^3}+\sqrt{a}+2\,a^{1/6}\,b^{1/3}\,x\right)}^3}{x^3\,{\left(b^{1/3}\,x+2\,a^{1/3}\right)}^3}\right)}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"log((((a - b*x^3)^(1/2) - a^(1/2))*((a - b*x^3)^(1/2) + a^(1/2) + 2*a^(1/6)*b^(1/3)*x)^3)/(x^3*(b^(1/3)*x + 2*a^(1/3))^3))/(3*a^(1/6)*b^(1/3))","B"
80,1,74,53,5.453180,"\text{Not used}","int(-(b^(1/3)*x - a^(1/3))/((b^(1/3)*x + 2*a^(1/3))*(b*x^3 - a)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{b\,x^3-a}+\sqrt{a}\,1{}\mathrm{i}\right)\,{\left(\sqrt{a}+2\,a^{1/6}\,b^{1/3}\,x+\sqrt{b\,x^3-a}\,1{}\mathrm{i}\right)}^3}{x^3\,{\left(b^{1/3}\,x+2\,a^{1/3}\right)}^3}\right)\,1{}\mathrm{i}}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"(log((((b*x^3 - a)^(1/2) + a^(1/2)*1i)*((b*x^3 - a)^(1/2)*1i + a^(1/2) + 2*a^(1/6)*b^(1/3)*x)^3)/(x^3*(b^(1/3)*x + 2*a^(1/3))^3))*1i)/(3*a^(1/6)*b^(1/3))","B"
81,1,78,53,5.373188,"\text{Not used}","int(-(b^(1/3)*x + a^(1/3))/((b^(1/3)*x - 2*a^(1/3))*(- a - b*x^3)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{-b\,x^3-a}-\sqrt{a}\,1{}\mathrm{i}\right)\,{\left(2\,a^{1/6}\,b^{1/3}\,x-\sqrt{a}+\sqrt{-b\,x^3-a}\,1{}\mathrm{i}\right)}^3}{x^3\,{\left(b^{1/3}\,x-2\,a^{1/3}\right)}^3}\right)\,1{}\mathrm{i}}{3\,a^{1/6}\,b^{1/3}}","Not used",1,"(log((((- a - b*x^3)^(1/2) - a^(1/2)*1i)*((- a - b*x^3)^(1/2)*1i - a^(1/2) + 2*a^(1/6)*b^(1/3)*x)^3)/(x^3*(b^(1/3)*x - 2*a^(1/3))^3))*1i)/(3*a^(1/6)*b^(1/3))","B"
82,1,67,46,3.126025,"\text{Not used}","int((c - 2*d*x)/((c^3 - 8*d^3*x^3)^(1/2)*(c + d*x)),x)","\frac{\ln\left(\frac{\left(\sqrt{c^3-8\,d^3\,x^3}-c^{3/2}\right)\,{\left(\sqrt{c^3-8\,d^3\,x^3}+c^{3/2}+4\,\sqrt{c}\,d\,x\right)}^3}{x^3\,{\left(c+d\,x\right)}^3}\right)}{3\,\sqrt{c}\,d}","Not used",1,"log((((c^3 - 8*d^3*x^3)^(1/2) - c^(3/2))*((c^3 - 8*d^3*x^3)^(1/2) + c^(3/2) + 4*c^(1/2)*d*x)^3)/(x^3*(c + d*x)^3))/(3*c^(1/2)*d)","B"
83,1,327,139,2.710965,"\text{Not used}","int(-(e + f*x)/((x^3 + 1)^(1/2)*(x - 2)),x)","\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(e+2\,f\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(e + 2*f)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (2*f*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
84,1,359,153,0.189690,"\text{Not used}","int((e + f*x)/((1 - x^3)^(1/2)*(x + 2)),x)","-\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(e-2\,f\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"- (2*f*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(e - 2*f)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*(1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
85,1,327,156,0.119627,"\text{Not used}","int((e + f*x)/((x^3 - 1)^(1/2)*(x + 2)),x)","-\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(e-2\,f\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"- (2*f*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(e - 2*f)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
86,1,359,150,2.543103,"\text{Not used}","int(-(e + f*x)/((- x^3 - 1)^(1/2)*(x - 2)),x)","-\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(e+2\,f\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(e + 2*f)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*(- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (2*f*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
87,0,-1,297,0.000000,"\text{Not used}","int(-(e + f*x)/((b^(1/3)*x - 2*a^(1/3))*(a + b*x^3)^(1/2)),x)","\int -\frac{e+f\,x}{\left(b^{1/3}\,x-2\,a^{1/3}\right)\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int(-(e + f*x)/((b^(1/3)*x - 2*a^(1/3))*(a + b*x^3)^(1/2)), x)","F"
88,0,-1,304,0.000000,"\text{Not used}","int((e + f*x)/((b^(1/3)*x + 2*a^(1/3))*(a - b*x^3)^(1/2)),x)","\int \frac{e+f\,x}{\left(b^{1/3}\,x+2\,a^{1/3}\right)\,\sqrt{a-b\,x^3}} \,d x","Not used",1,"int((e + f*x)/((b^(1/3)*x + 2*a^(1/3))*(a - b*x^3)^(1/2)), x)","F"
89,0,-1,313,0.000000,"\text{Not used}","int((e + f*x)/((b^(1/3)*x + 2*a^(1/3))*(b*x^3 - a)^(1/2)),x)","\int \frac{e+f\,x}{\left(b^{1/3}\,x+2\,a^{1/3}\right)\,\sqrt{b\,x^3-a}} \,d x","Not used",1,"int((e + f*x)/((b^(1/3)*x + 2*a^(1/3))*(b*x^3 - a)^(1/2)), x)","F"
90,0,-1,310,0.000000,"\text{Not used}","int(-(e + f*x)/((b^(1/3)*x - 2*a^(1/3))*(- a - b*x^3)^(1/2)),x)","\int -\frac{e+f\,x}{\left(b^{1/3}\,x-2\,a^{1/3}\right)\,\sqrt{-b\,x^3-a}} \,d x","Not used",1,"int(-(e + f*x)/((b^(1/3)*x - 2*a^(1/3))*(- a - b*x^3)^(1/2)), x)","F"
91,0,-1,221,0.000000,"\text{Not used}","int((e + f*x)/((c^3 - 8*d^3*x^3)^(1/2)*(c + d*x)),x)","\int \frac{e+f\,x}{\sqrt{c^3-8\,d^3\,x^3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int((e + f*x)/((c^3 - 8*d^3*x^3)^(1/2)*(c + d*x)), x)","F"
92,1,207,129,0.056872,"\text{Not used}","int(-x/((x^3 + 1)^(1/2)*(x - 2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(3\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-2\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{3\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(3*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 2*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(3*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
93,1,224,145,0.065641,"\text{Not used}","int(x/((1 - x^3)^(1/2)*(x + 2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(3\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-2\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{3\,\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(3*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 2*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(3*(1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
94,1,208,148,2.534379,"\text{Not used}","int(x/((x^3 - 1)^(1/2)*(x + 2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(3\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-2\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{3\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(3*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 2*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(3*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
95,1,223,140,0.064103,"\text{Not used}","int(-x/((- x^3 - 1)^(1/2)*(x - 2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(3\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-2\,\Pi \left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{3\,\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(3*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 2*ellipticPi((3^(1/2)*1i)/6 + 1/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(3*(- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
96,0,-1,260,0.000000,"\text{Not used}","int(-x/((b^(1/3)*x - 2*a^(1/3))*(a + b*x^3)^(1/2)),x)","-\int \frac{x}{\left(b^{1/3}\,x-2\,a^{1/3}\right)\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"-int(x/((b^(1/3)*x - 2*a^(1/3))*(a + b*x^3)^(1/2)), x)","F"
97,0,-1,268,0.000000,"\text{Not used}","int(x/((b^(1/3)*x + 2*a^(1/3))*(a - b*x^3)^(1/2)),x)","\int \frac{x}{\left(b^{1/3}\,x+2\,a^{1/3}\right)\,\sqrt{a-b\,x^3}} \,d x","Not used",1,"int(x/((b^(1/3)*x + 2*a^(1/3))*(a - b*x^3)^(1/2)), x)","F"
98,0,-1,277,0.000000,"\text{Not used}","int(x/((b^(1/3)*x + 2*a^(1/3))*(b*x^3 - a)^(1/2)),x)","\int \frac{x}{\left(b^{1/3}\,x+2\,a^{1/3}\right)\,\sqrt{b\,x^3-a}} \,d x","Not used",1,"int(x/((b^(1/3)*x + 2*a^(1/3))*(b*x^3 - a)^(1/2)), x)","F"
99,0,-1,273,0.000000,"\text{Not used}","int(-x/((b^(1/3)*x - 2*a^(1/3))*(- a - b*x^3)^(1/2)),x)","-\int \frac{x}{\left(b^{1/3}\,x-2\,a^{1/3}\right)\,\sqrt{-b\,x^3-a}} \,d x","Not used",1,"-int(x/((b^(1/3)*x - 2*a^(1/3))*(- a - b*x^3)^(1/2)), x)","F"
100,0,-1,202,0.000000,"\text{Not used}","int(x/((c^3 - 8*d^3*x^3)^(1/2)*(c + d*x)),x)","\int \frac{x}{\sqrt{c^3-8\,d^3\,x^3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int(x/((c^3 - 8*d^3*x^3)^(1/2)*(c + d*x)), x)","F"
101,-1,-1,42,0.000000,"\text{Not used}","int((x + 3^(1/2) + 1)/((x^3 + 1)^(1/2)*(x - 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
102,-1,-1,46,0.000000,"\text{Not used}","int(-(3^(1/2) - x + 1)/((1 - x^3)^(1/2)*(x + 3^(1/2) - 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
103,-1,-1,44,0.000000,"\text{Not used}","int(-(3^(1/2) - x + 1)/((x^3 - 1)^(1/2)*(x + 3^(1/2) - 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
104,-1,-1,44,0.000000,"\text{Not used}","int((x + 3^(1/2) + 1)/((- x^3 - 1)^(1/2)*(x - 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
105,-1,-1,69,0.000000,"\text{Not used}","int((b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))/((a + b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
106,-1,-1,71,0.000000,"\text{Not used}","int((b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))/((a - b*x^3)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
107,-1,-1,72,0.000000,"\text{Not used}","int((b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))/((b*x^3 - a)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
108,-1,-1,72,0.000000,"\text{Not used}","int((b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))/((- a - b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
109,0,-1,73,0.000000,"\text{Not used}","int((3^(1/2) + x*(b/a)^(1/3) + 1)/((a + b*x^3)^(1/2)*(x*(b/a)^(1/3) - 3^(1/2) + 1)),x)","\int \frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{b\,x^3+a}\,\left(x\,{\left(\frac{b}{a}\right)}^{1/3}-\sqrt{3}+1\right)} \,d x","Not used",1,"int((3^(1/2) + x*(b/a)^(1/3) + 1)/((a + b*x^3)^(1/2)*(x*(b/a)^(1/3) - 3^(1/2) + 1)), x)","F"
110,0,-1,75,0.000000,"\text{Not used}","int(-(3^(1/2) - x*(b/a)^(1/3) + 1)/((a - b*x^3)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) - 1)),x)","\int -\frac{\sqrt{3}-x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{a-b\,x^3}\,\left(\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}-1\right)} \,d x","Not used",1,"int(-(3^(1/2) - x*(b/a)^(1/3) + 1)/((a - b*x^3)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) - 1)), x)","F"
111,0,-1,76,0.000000,"\text{Not used}","int(-(3^(1/2) - x*(b/a)^(1/3) + 1)/((b*x^3 - a)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) - 1)),x)","\int -\frac{\sqrt{3}-x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{b\,x^3-a}\,\left(\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}-1\right)} \,d x","Not used",1,"int(-(3^(1/2) - x*(b/a)^(1/3) + 1)/((b*x^3 - a)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) - 1)), x)","F"
112,0,-1,76,0.000000,"\text{Not used}","int((3^(1/2) + x*(b/a)^(1/3) + 1)/((- a - b*x^3)^(1/2)*(x*(b/a)^(1/3) - 3^(1/2) + 1)),x)","\int \frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}+1}{\sqrt{-b\,x^3-a}\,\left(x\,{\left(\frac{b}{a}\right)}^{1/3}-\sqrt{3}+1\right)} \,d x","Not used",1,"int((3^(1/2) + x*(b/a)^(1/3) + 1)/((- a - b*x^3)^(1/2)*(x*(b/a)^(1/3) - 3^(1/2) + 1)), x)","F"
113,-1,-1,42,0.000000,"\text{Not used}","int((x - 3^(1/2) + 1)/((x^3 + 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
114,-1,-1,46,0.000000,"\text{Not used}","int(-(x + 3^(1/2) - 1)/((1 - x^3)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
115,-1,-1,44,0.000000,"\text{Not used}","int(-(x + 3^(1/2) - 1)/((x^3 - 1)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
116,-1,-1,44,0.000000,"\text{Not used}","int((x - 3^(1/2) + 1)/((- x^3 - 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
117,-1,-1,69,0.000000,"\text{Not used}","int((b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))/((a + b*x^3)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
118,-1,-1,71,0.000000,"\text{Not used}","int((b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))/((a - b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
119,-1,-1,72,0.000000,"\text{Not used}","int((b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))/((b*x^3 - a)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) + 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
120,-1,-1,72,0.000000,"\text{Not used}","int((b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))/((- a - b*x^3)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) + 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
121,0,-1,73,0.000000,"\text{Not used}","int((x*(b/a)^(1/3) - 3^(1/2) + 1)/((a + b*x^3)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) + 1)),x)","\int \frac{x\,{\left(\frac{b}{a}\right)}^{1/3}-\sqrt{3}+1}{\sqrt{b\,x^3+a}\,\left(\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}+1\right)} \,d x","Not used",1,"int((x*(b/a)^(1/3) - 3^(1/2) + 1)/((a + b*x^3)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) + 1)), x)","F"
122,0,-1,75,0.000000,"\text{Not used}","int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/((a - b*x^3)^(1/2)*(3^(1/2) - x*(b/a)^(1/3) + 1)),x)","\int -\frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}-1}{\sqrt{a-b\,x^3}\,\left(\sqrt{3}-x\,{\left(\frac{b}{a}\right)}^{1/3}+1\right)} \,d x","Not used",1,"int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/((a - b*x^3)^(1/2)*(3^(1/2) - x*(b/a)^(1/3) + 1)), x)","F"
123,0,-1,76,0.000000,"\text{Not used}","int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/((b*x^3 - a)^(1/2)*(3^(1/2) - x*(b/a)^(1/3) + 1)),x)","\int -\frac{\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}-1}{\sqrt{b\,x^3-a}\,\left(\sqrt{3}-x\,{\left(\frac{b}{a}\right)}^{1/3}+1\right)} \,d x","Not used",1,"int(-(3^(1/2) + x*(b/a)^(1/3) - 1)/((b*x^3 - a)^(1/2)*(3^(1/2) - x*(b/a)^(1/3) + 1)), x)","F"
124,0,-1,76,0.000000,"\text{Not used}","int((x*(b/a)^(1/3) - 3^(1/2) + 1)/((- a - b*x^3)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) + 1)),x)","\int \frac{x\,{\left(\frac{b}{a}\right)}^{1/3}-\sqrt{3}+1}{\sqrt{-b\,x^3-a}\,\left(\sqrt{3}+x\,{\left(\frac{b}{a}\right)}^{1/3}+1\right)} \,d x","Not used",1,"int((x*(b/a)^(1/3) - 3^(1/2) + 1)/((- a - b*x^3)^(1/2)*(3^(1/2) + x*(b/a)^(1/3) + 1)), x)","F"
125,-1,-1,145,0.000000,"\text{Not used}","int((x + 1)/((x^3 + 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
126,-1,-1,145,0.000000,"\text{Not used}","int((x + 1)/((x^3 + 1)^(1/2)*(x - 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
127,-1,-1,173,0.000000,"\text{Not used}","int((e + f*x)/((x^3 + 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
128,-1,-1,187,0.000000,"\text{Not used}","int((e + f*x)/((1 - x^3)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
129,-1,-1,190,0.000000,"\text{Not used}","int((e + f*x)/((x^3 - 1)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
130,-1,-1,183,0.000000,"\text{Not used}","int((e + f*x)/((- x^3 - 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
131,0,-1,332,0.000000,"\text{Not used}","int((e + f*x)/((a + b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))),x)","\int \frac{e+f\,x}{\sqrt{b\,x^3+a}\,\left(b^{1/3}\,x-a^{1/3}\,\left(\sqrt{3}-1\right)\right)} \,d x","Not used",1,"int((e + f*x)/((a + b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))), x)","F"
132,0,-1,336,0.000000,"\text{Not used}","int(-(e + f*x)/((a - b*x^3)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))),x)","\int -\frac{e+f\,x}{\sqrt{a-b\,x^3}\,\left(b^{1/3}\,x+a^{1/3}\,\left(\sqrt{3}-1\right)\right)} \,d x","Not used",1,"int(-(e + f*x)/((a - b*x^3)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))), x)","F"
133,-1,-1,345,0.000000,"\text{Not used}","int(-(e + f*x)/((b*x^3 - a)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
134,-1,-1,345,0.000000,"\text{Not used}","int((e + f*x)/((- a - b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
135,-1,-1,136,0.000000,"\text{Not used}","int(x/((x^3 + 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
136,-1,-1,152,0.000000,"\text{Not used}","int(x/((1 - x^3)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
137,-1,-1,164,0.000000,"\text{Not used}","int(x/((x^3 - 1)^(1/2)*(3^(1/2) - x + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
138,-1,-1,156,0.000000,"\text{Not used}","int(x/((- x^3 - 1)^(1/2)*(x + 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
139,-1,-1,147,0.000000,"\text{Not used}","int(x/((x^3 + 1)^(1/2)*(x - 3^(1/2) + 1)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
140,-1,-1,278,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
141,-1,-1,286,0.000000,"\text{Not used}","int(-x/((a - b*x^3)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
142,-1,-1,282,0.000000,"\text{Not used}","int(-x/((b*x^3 - a)^(1/2)*(b^(1/3)*x + a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
143,-1,-1,278,0.000000,"\text{Not used}","int(x/((- a - b*x^3)^(1/2)*(b^(1/3)*x - a^(1/3)*(3^(1/2) - 1))),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
144,-1,-1,317,0.000000,"\text{Not used}","int((x + 3^(1/2) + 1)/((x^3 + 1)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
145,-1,-1,329,0.000000,"\text{Not used}","int((3^(1/2) - x + 1)/((1 - x^3)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
146,-1,-1,325,0.000000,"\text{Not used}","int((3^(1/2) - x + 1)/((x^3 - 1)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
147,-1,-1,321,0.000000,"\text{Not used}","int((x + 3^(1/2) + 1)/((- x^3 - 1)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
148,-1,-1,358,0.000000,"\text{Not used}","int((x - 3^(1/2) + 1)/((x^3 + 1)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
149,-1,-1,346,0.000000,"\text{Not used}","int(-(x + 3^(1/2) - 1)/((1 - x^3)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
150,-1,-1,342,0.000000,"\text{Not used}","int(-(x + 3^(1/2) - 1)/((x^3 - 1)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
151,-1,-1,362,0.000000,"\text{Not used}","int((x - 3^(1/2) + 1)/((- x^3 - 1)^(1/2)*(c + d*x)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
152,1,334,125,0.139212,"\text{Not used}","int((x + 3^(1/2) + 1)/(x*(x^3 + 1)^(1/2)),x)","-\frac{2\,\sqrt{3}\,\mathrm{atanh}\left(\sqrt{x^3+1}\right)}{3}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (2*3^(1/2)*atanh((x^3 + 1)^(1/2)))/3 - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
153,1,373,139,3.637122,"\text{Not used}","int((3^(1/2) - x + 1)/(x*(1 - x^3)^(1/2)),x)","\frac{\sqrt{3}\,\ln\left(\frac{{\left(\sqrt{1-x^3}-1\right)}^3\,\left(\sqrt{1-x^3}+1\right)}{x^6}\right)}{3}+\frac{\sqrt{x^3-1}\,\left(\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\right)}{\sqrt{1-x^3}}","Not used",1,"(3^(1/2)*log((((1 - x^3)^(1/2) - 1)^3*((1 - x^3)^(1/2) + 1))/x^6))/3 + ((x^3 - 1)^(1/2)*((2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)))/(1 - x^3)^(1/2)","B"
154,1,334,142,2.715765,"\text{Not used}","int((3^(1/2) - x + 1)/(x*(x^3 - 1)^(1/2)),x)","\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\sqrt{x^3-1}\right)}{3}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*3^(1/2)*atan((x^3 - 1)^(1/2)))/3 + (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
155,1,376,136,4.450776,"\text{Not used}","int((x + 3^(1/2) + 1)/(x*(- x^3 - 1)^(1/2)),x)","\frac{\sqrt{3}\,\ln\left(\frac{\left(\sqrt{-x^3-1}-\mathrm{i}\right)\,{\left(\sqrt{-x^3-1}+1{}\mathrm{i}\right)}^3}{x^6}\right)\,1{}\mathrm{i}}{3}+\frac{\sqrt{x^3+1}\,\left(\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\right)}{\sqrt{-x^3-1}}","Not used",1,"(3^(1/2)*log((((- x^3 - 1)^(1/2) - 1i)*((- x^3 - 1)^(1/2) + 1i)^3)/x^6)*1i)/3 + ((x^3 + 1)^(1/2)*((2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)))/(- x^3 - 1)^(1/2)","B"
156,1,334,127,2.646744,"\text{Not used}","int((x - 3^(1/2) + 1)/(x*(x^3 + 1)^(1/2)),x)","\frac{2\,\sqrt{3}\,\mathrm{atanh}\left(\sqrt{x^3+1}\right)}{3}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*3^(1/2)*atanh((x^3 + 1)^(1/2)))/3 + (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
157,1,373,141,3.242335,"\text{Not used}","int(-(x + 3^(1/2) - 1)/(x*(1 - x^3)^(1/2)),x)","\frac{\sqrt{3}\,\ln\left(\frac{\left(\sqrt{1-x^3}-1\right)\,{\left(\sqrt{1-x^3}+1\right)}^3}{x^6}\right)}{3}+\frac{\sqrt{x^3-1}\,\left(\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\right)}{\sqrt{1-x^3}}","Not used",1,"(3^(1/2)*log((((1 - x^3)^(1/2) - 1)*((1 - x^3)^(1/2) + 1)^3)/x^6))/3 + ((x^3 - 1)^(1/2)*((2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)))/(1 - x^3)^(1/2)","B"
158,1,334,144,2.702447,"\text{Not used}","int(-(x + 3^(1/2) - 1)/(x*(x^3 - 1)^(1/2)),x)","-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\sqrt{x^3-1}\right)}{3}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) - (2*3^(1/2)*atan((x^3 - 1)^(1/2)))/3 - (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
159,1,376,138,4.098875,"\text{Not used}","int((x - 3^(1/2) + 1)/(x*(- x^3 - 1)^(1/2)),x)","\frac{\sqrt{3}\,\ln\left(\frac{{\left(\sqrt{-x^3-1}-\mathrm{i}\right)}^3\,\left(\sqrt{-x^3-1}+1{}\mathrm{i}\right)}{x^6}\right)\,1{}\mathrm{i}}{3}+\frac{\sqrt{x^3+1}\,\left(\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\right)}{\sqrt{-x^3-1}}","Not used",1,"(3^(1/2)*log((((- x^3 - 1)^(1/2) - 1i)^3*((- x^3 - 1)^(1/2) + 1i))/x^6)*1i)/3 + ((x^3 + 1)^(1/2)*((2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)))/(- x^3 - 1)^(1/2)","B"
160,1,207,332,0.225128,"\text{Not used}","int(x/((x^3 + 1)^(1/2)*(x + 3)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(2\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-3\,\Pi \left(-\frac{3}{4}-\frac{\sqrt{3}\,1{}\mathrm{i}}{4};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{2\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(2*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 3*ellipticPi(- (3^(1/2)*1i)/4 - 3/4, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(2*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
161,1,224,377,2.742154,"\text{Not used}","int(x/((1 - x^3)^(1/2)*(x + 3)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(4\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-3\,\Pi \left(\frac{3}{8}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{4\,\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(4*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 3*ellipticPi((3^(1/2)*1i)/8 + 3/8, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(4*(1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
162,1,208,373,2.646970,"\text{Not used}","int(x/((x^3 - 1)^(1/2)*(x + 3)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(4\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-3\,\Pi \left(\frac{3}{8}+\frac{\sqrt{3}\,1{}\mathrm{i}}{8};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{4\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(4*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 3*ellipticPi((3^(1/2)*1i)/8 + 3/8, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(4*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
163,1,223,341,2.610673,"\text{Not used}","int(x/((- x^3 - 1)^(1/2)*(x + 3)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(2\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-3\,\Pi \left(-\frac{3}{4}-\frac{\sqrt{3}\,1{}\mathrm{i}}{4};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{2\,\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(2*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - 3*ellipticPi(- (3^(1/2)*1i)/4 - 3/4, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(2*(- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
164,1,356,450,0.127766,"\text{Not used}","int((e + f*x)/((x^3 + 1)^(1/2)*(c + d*x)),x)","\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(c\,f-d\,e\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{c}{d}-1};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d^2\,\left(\frac{c}{d}-1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*f*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(c*f - d*e)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(c/d - 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d^2*(c/d - 1)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
165,1,387,474,0.092923,"\text{Not used}","int((e + f*x)/((1 - x^3)^(1/2)*(c + d*x)),x)","-\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d\,\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(c\,f-d\,e\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{c}{d}+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d^2\,\sqrt{1-x^3}\,\left(\frac{c}{d}+1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(c*f - d*e)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(c/d + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d^2*(1 - x^3)^(1/2)*(c/d + 1)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (2*f*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d*(1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
166,1,355,475,2.674962,"\text{Not used}","int((e + f*x)/((x^3 - 1)^(1/2)*(c + d*x)),x)","-\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(c\,f-d\,e\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{c}{d}+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d^2\,\left(\frac{c}{d}+1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(c*f - d*e)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(c/d + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d^2*(c/d + 1)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (2*f*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
167,1,388,463,0.097347,"\text{Not used}","int((e + f*x)/((- x^3 - 1)^(1/2)*(c + d*x)),x)","\frac{2\,f\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d\,\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(c\,f-d\,e\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{c}{d}-1};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{d^2\,\sqrt{-x^3-1}\,\left(\frac{c}{d}-1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*f*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d*(- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(c*f - d*e)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(c/d - 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(d^2*(- x^3 - 1)^(1/2)*(c/d - 1)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
168,1,207,120,2.637231,"\text{Not used}","int((e + f*x)/(x*(x^3 + 1)^(1/2)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(f\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-e\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(f*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - e*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
169,1,223,134,0.064537,"\text{Not used}","int((e + f*x)/(x*(1 - x^3)^(1/2)),x)","-\frac{\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(f\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+e\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(\sqrt{3}-3{}\mathrm{i}\right)\,1{}\mathrm{i}}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(f*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) + e*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(3^(1/2) - 3i)*1i)/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
170,1,207,137,2.616660,"\text{Not used}","int((e + f*x)/(x*(x^3 - 1)^(1/2)),x)","-\frac{\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(f\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+e\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(\sqrt{3}-3{}\mathrm{i}\right)\,1{}\mathrm{i}}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(f*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) + e*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(3^(1/2) - 3i)*1i)/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
171,1,223,131,2.656363,"\text{Not used}","int((e + f*x)/(x*(- x^3 - 1)^(1/2)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(f\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)-e\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*(f*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - e*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
172,0,-1,95,0.000000,"\text{Not used}","int((c - d*x)/((2*c^3 + d^3*x^3)^(1/3)*(c + d*x)),x)","\int \frac{c-d\,x}{{\left(2\,c^3+d^3\,x^3\right)}^{1/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int((c - d*x)/((2*c^3 + d^3*x^3)^(1/3)*(c + d*x)), x)","F"
173,0,-1,234,0.000000,"\text{Not used}","int((e + f*x)/((d^3*x^3 - c^3)^(1/3)*(c + d*x)),x)","\int \frac{e+f\,x}{{\left(d^3\,x^3-c^3\right)}^{1/3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int((e + f*x)/((d^3*x^3 - c^3)^(1/3)*(c + d*x)), x)","F"
174,1,495,160,3.203962,"\text{Not used}","int(x^2*(c + d*x^3)*(a + b*x)^n,x)","{\left(a+b\,x\right)}^n\,\left(\frac{d\,x^6\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720}+\frac{2\,a^3\,\left(-60\,d\,a^3+c\,b^3\,n^3+15\,c\,b^3\,n^2+74\,c\,b^3\,n+120\,c\,b^3\right)}{b^6\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}+\frac{x^3\,\left(n^2+3\,n+2\right)\,\left(20\,d\,a^3\,n+c\,b^3\,n^3+15\,c\,b^3\,n^2+74\,c\,b^3\,n+120\,c\,b^3\right)}{b^3\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{2\,a^2\,n\,x\,\left(-60\,d\,a^3+c\,b^3\,n^3+15\,c\,b^3\,n^2+74\,c\,b^3\,n+120\,c\,b^3\right)}{b^5\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}+\frac{a\,d\,n\,x^5\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}{b\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}+\frac{a\,n\,x^2\,\left(n+1\right)\,\left(-60\,d\,a^3+c\,b^3\,n^3+15\,c\,b^3\,n^2+74\,c\,b^3\,n+120\,c\,b^3\right)}{b^4\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}-\frac{5\,a^2\,d\,n\,x^4\,\left(n^3+6\,n^2+11\,n+6\right)}{b^2\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}\right)","Not used",1,"(a + b*x)^n*((d*x^6*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720) + (2*a^3*(120*b^3*c - 60*a^3*d + 15*b^3*c*n^2 + b^3*c*n^3 + 74*b^3*c*n))/(b^6*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) + (x^3*(3*n + n^2 + 2)*(120*b^3*c + 15*b^3*c*n^2 + b^3*c*n^3 + 20*a^3*d*n + 74*b^3*c*n))/(b^3*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (2*a^2*n*x*(120*b^3*c - 60*a^3*d + 15*b^3*c*n^2 + b^3*c*n^3 + 74*b^3*c*n))/(b^5*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) + (a*d*n*x^5*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))/(b*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) + (a*n*x^2*(n + 1)*(120*b^3*c - 60*a^3*d + 15*b^3*c*n^2 + b^3*c*n^3 + 74*b^3*c*n))/(b^4*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)) - (5*a^2*d*n*x^4*(11*n + 6*n^2 + n^3 + 6))/(b^2*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720)))","B"
175,1,363,126,2.949903,"\text{Not used}","int(x*(c + d*x^3)*(a + b*x)^n,x)","{\left(a+b\,x\right)}^n\,\left(\frac{d\,x^5\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}{n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120}-\frac{a^2\,\left(-24\,d\,a^3+c\,b^3\,n^3+12\,c\,b^3\,n^2+47\,c\,b^3\,n+60\,c\,b^3\right)}{b^5\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}+\frac{x^2\,\left(n+1\right)\,\left(12\,d\,a^3\,n+c\,b^3\,n^3+12\,c\,b^3\,n^2+47\,c\,b^3\,n+60\,c\,b^3\right)}{b^3\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}+\frac{a\,n\,x\,\left(-24\,d\,a^3+c\,b^3\,n^3+12\,c\,b^3\,n^2+47\,c\,b^3\,n+60\,c\,b^3\right)}{b^4\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}+\frac{a\,d\,n\,x^4\,\left(n^3+6\,n^2+11\,n+6\right)}{b\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}-\frac{4\,a^2\,d\,n\,x^3\,\left(n^2+3\,n+2\right)}{b^2\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}\right)","Not used",1,"(a + b*x)^n*((d*x^5*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))/(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120) - (a^2*(60*b^3*c - 24*a^3*d + 12*b^3*c*n^2 + b^3*c*n^3 + 47*b^3*c*n))/(b^5*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120)) + (x^2*(n + 1)*(60*b^3*c + 12*b^3*c*n^2 + b^3*c*n^3 + 12*a^3*d*n + 47*b^3*c*n))/(b^3*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120)) + (a*n*x*(60*b^3*c - 24*a^3*d + 12*b^3*c*n^2 + b^3*c*n^3 + 47*b^3*c*n))/(b^4*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120)) + (a*d*n*x^4*(11*n + 6*n^2 + n^3 + 6))/(b*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120)) - (4*a^2*d*n*x^3*(3*n + n^2 + 2))/(b^2*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120)))","B"
176,1,247,94,2.946292,"\text{Not used}","int((c + d*x^3)*(a + b*x)^n,x)","{\left(a+b\,x\right)}^n\,\left(\frac{x\,\left(6\,d\,a^3\,b\,n+c\,b^4\,n^3+9\,c\,b^4\,n^2+26\,c\,b^4\,n+24\,c\,b^4\right)}{b^4\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}+\frac{a\,\left(-6\,d\,a^3+c\,b^3\,n^3+9\,c\,b^3\,n^2+26\,c\,b^3\,n+24\,c\,b^3\right)}{b^4\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}+\frac{d\,x^4\,\left(n^3+6\,n^2+11\,n+6\right)}{n^4+10\,n^3+35\,n^2+50\,n+24}-\frac{3\,a^2\,d\,n\,x^2\,\left(n+1\right)}{b^2\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}+\frac{a\,d\,n\,x^3\,\left(n^2+3\,n+2\right)}{b\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}\right)","Not used",1,"(a + b*x)^n*((x*(24*b^4*c + 9*b^4*c*n^2 + b^4*c*n^3 + 26*b^4*c*n + 6*a^3*b*d*n))/(b^4*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)) + (a*(24*b^3*c - 6*a^3*d + 9*b^3*c*n^2 + b^3*c*n^3 + 26*b^3*c*n))/(b^4*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)) + (d*x^4*(11*n + 6*n^2 + n^3 + 6))/(50*n + 35*n^2 + 10*n^3 + n^4 + 24) - (3*a^2*d*n*x^2*(n + 1))/(b^2*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)) + (a*d*n*x^3*(3*n + n^2 + 2))/(b*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)))","B"
177,0,-1,99,0.000000,"\text{Not used}","int(((c + d*x^3)*(a + b*x)^n)/x,x)","\int \frac{\left(d\,x^3+c\right)\,{\left(a+b\,x\right)}^n}{x} \,d x","Not used",1,"int(((c + d*x^3)*(a + b*x)^n)/x, x)","F"
178,1,1410,294,3.734050,"\text{Not used}","int(x^2*(c + d*x^3)^2*(a + b*x)^n,x)","\frac{d^2\,x^9\,{\left(a+b\,x\right)}^n\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}{n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880}+\frac{2\,a^3\,{\left(a+b\,x\right)}^n\,\left(20160\,a^6\,d^2-120\,a^3\,b^3\,c\,d\,n^3-2880\,a^3\,b^3\,c\,d\,n^2-22920\,a^3\,b^3\,c\,d\,n-60480\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+39\,b^6\,c^2\,n^5+625\,b^6\,c^2\,n^4+5265\,b^6\,c^2\,n^3+24574\,b^6\,c^2\,n^2+60216\,b^6\,c^2\,n+60480\,b^6\,c^2\right)}{b^9\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}+\frac{x^3\,{\left(a+b\,x\right)}^n\,\left(n^2+3\,n+2\right)\,\left(-6720\,a^6\,d^2\,n+40\,a^3\,b^3\,c\,d\,n^4+960\,a^3\,b^3\,c\,d\,n^3+7640\,a^3\,b^3\,c\,d\,n^2+20160\,a^3\,b^3\,c\,d\,n+b^6\,c^2\,n^6+39\,b^6\,c^2\,n^5+625\,b^6\,c^2\,n^4+5265\,b^6\,c^2\,n^3+24574\,b^6\,c^2\,n^2+60216\,b^6\,c^2\,n+60480\,b^6\,c^2\right)}{b^6\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}+\frac{2\,d\,x^6\,{\left(a+b\,x\right)}^n\,\left(28\,d\,a^3\,n+c\,b^3\,n^3+24\,c\,b^3\,n^2+191\,c\,b^3\,n+504\,c\,b^3\right)\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{b^3\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}-\frac{2\,a^2\,n\,x\,{\left(a+b\,x\right)}^n\,\left(20160\,a^6\,d^2-120\,a^3\,b^3\,c\,d\,n^3-2880\,a^3\,b^3\,c\,d\,n^2-22920\,a^3\,b^3\,c\,d\,n-60480\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+39\,b^6\,c^2\,n^5+625\,b^6\,c^2\,n^4+5265\,b^6\,c^2\,n^3+24574\,b^6\,c^2\,n^2+60216\,b^6\,c^2\,n+60480\,b^6\,c^2\right)}{b^8\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}+\frac{a\,n\,x^2\,\left(n+1\right)\,{\left(a+b\,x\right)}^n\,\left(20160\,a^6\,d^2-120\,a^3\,b^3\,c\,d\,n^3-2880\,a^3\,b^3\,c\,d\,n^2-22920\,a^3\,b^3\,c\,d\,n-60480\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+39\,b^6\,c^2\,n^5+625\,b^6\,c^2\,n^4+5265\,b^6\,c^2\,n^3+24574\,b^6\,c^2\,n^2+60216\,b^6\,c^2\,n+60480\,b^6\,c^2\right)}{b^7\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}+\frac{a\,d^2\,n\,x^8\,{\left(a+b\,x\right)}^n\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{b\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}-\frac{8\,a^2\,d^2\,n\,x^7\,{\left(a+b\,x\right)}^n\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}{b^2\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}-\frac{10\,a^2\,d\,n\,x^4\,{\left(a+b\,x\right)}^n\,\left(n^3+6\,n^2+11\,n+6\right)\,\left(-168\,d\,a^3+c\,b^3\,n^3+24\,c\,b^3\,n^2+191\,c\,b^3\,n+504\,c\,b^3\right)}{b^5\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}+\frac{2\,a\,d\,n\,x^5\,{\left(a+b\,x\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)\,\left(-168\,d\,a^3+c\,b^3\,n^3+24\,c\,b^3\,n^2+191\,c\,b^3\,n+504\,c\,b^3\right)}{b^4\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}","Not used",1,"(d^2*x^9*(a + b*x)^n*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))/(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880) + (2*a^3*(a + b*x)^n*(20160*a^6*d^2 + 60480*b^6*c^2 + 60216*b^6*c^2*n + 24574*b^6*c^2*n^2 + 5265*b^6*c^2*n^3 + 625*b^6*c^2*n^4 + 39*b^6*c^2*n^5 + b^6*c^2*n^6 - 60480*a^3*b^3*c*d - 22920*a^3*b^3*c*d*n - 2880*a^3*b^3*c*d*n^2 - 120*a^3*b^3*c*d*n^3))/(b^9*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) + (x^3*(a + b*x)^n*(3*n + n^2 + 2)*(60480*b^6*c^2 - 6720*a^6*d^2*n + 60216*b^6*c^2*n + 24574*b^6*c^2*n^2 + 5265*b^6*c^2*n^3 + 625*b^6*c^2*n^4 + 39*b^6*c^2*n^5 + b^6*c^2*n^6 + 20160*a^3*b^3*c*d*n + 7640*a^3*b^3*c*d*n^2 + 960*a^3*b^3*c*d*n^3 + 40*a^3*b^3*c*d*n^4))/(b^6*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) + (2*d*x^6*(a + b*x)^n*(504*b^3*c + 24*b^3*c*n^2 + b^3*c*n^3 + 28*a^3*d*n + 191*b^3*c*n)*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(b^3*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) - (2*a^2*n*x*(a + b*x)^n*(20160*a^6*d^2 + 60480*b^6*c^2 + 60216*b^6*c^2*n + 24574*b^6*c^2*n^2 + 5265*b^6*c^2*n^3 + 625*b^6*c^2*n^4 + 39*b^6*c^2*n^5 + b^6*c^2*n^6 - 60480*a^3*b^3*c*d - 22920*a^3*b^3*c*d*n - 2880*a^3*b^3*c*d*n^2 - 120*a^3*b^3*c*d*n^3))/(b^8*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) + (a*n*x^2*(n + 1)*(a + b*x)^n*(20160*a^6*d^2 + 60480*b^6*c^2 + 60216*b^6*c^2*n + 24574*b^6*c^2*n^2 + 5265*b^6*c^2*n^3 + 625*b^6*c^2*n^4 + 39*b^6*c^2*n^5 + b^6*c^2*n^6 - 60480*a^3*b^3*c*d - 22920*a^3*b^3*c*d*n - 2880*a^3*b^3*c*d*n^2 - 120*a^3*b^3*c*d*n^3))/(b^7*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) + (a*d^2*n*x^8*(a + b*x)^n*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(b*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) - (8*a^2*d^2*n*x^7*(a + b*x)^n*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))/(b^2*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) - (10*a^2*d*n*x^4*(a + b*x)^n*(11*n + 6*n^2 + n^3 + 6)*(504*b^3*c - 168*a^3*d + 24*b^3*c*n^2 + b^3*c*n^3 + 191*b^3*c*n))/(b^5*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880)) + (2*a*d*n*x^5*(a + b*x)^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)*(504*b^3*c - 168*a^3*d + 24*b^3*c*n^2 + b^3*c*n^3 + 191*b^3*c*n))/(b^4*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880))","B"
179,1,1136,248,3.391691,"\text{Not used}","int(x*(c + d*x^3)^2*(a + b*x)^n,x)","\frac{d^2\,x^8\,{\left(a+b\,x\right)}^n\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320}-\frac{a^2\,{\left(a+b\,x\right)}^n\,\left(5040\,a^6\,d^2-48\,a^3\,b^3\,c\,d\,n^3-1008\,a^3\,b^3\,c\,d\,n^2-7008\,a^3\,b^3\,c\,d\,n-16128\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+33\,b^6\,c^2\,n^5+445\,b^6\,c^2\,n^4+3135\,b^6\,c^2\,n^3+12154\,b^6\,c^2\,n^2+24552\,b^6\,c^2\,n+20160\,b^6\,c^2\right)}{b^8\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{x^2\,\left(n+1\right)\,{\left(a+b\,x\right)}^n\,\left(-2520\,a^6\,d^2\,n+24\,a^3\,b^3\,c\,d\,n^4+504\,a^3\,b^3\,c\,d\,n^3+3504\,a^3\,b^3\,c\,d\,n^2+8064\,a^3\,b^3\,c\,d\,n+b^6\,c^2\,n^6+33\,b^6\,c^2\,n^5+445\,b^6\,c^2\,n^4+3135\,b^6\,c^2\,n^3+12154\,b^6\,c^2\,n^2+24552\,b^6\,c^2\,n+20160\,b^6\,c^2\right)}{b^6\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{a\,n\,x\,{\left(a+b\,x\right)}^n\,\left(5040\,a^6\,d^2-48\,a^3\,b^3\,c\,d\,n^3-1008\,a^3\,b^3\,c\,d\,n^2-7008\,a^3\,b^3\,c\,d\,n-16128\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+33\,b^6\,c^2\,n^5+445\,b^6\,c^2\,n^4+3135\,b^6\,c^2\,n^3+12154\,b^6\,c^2\,n^2+24552\,b^6\,c^2\,n+20160\,b^6\,c^2\right)}{b^7\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{2\,d\,x^5\,{\left(a+b\,x\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)\,\left(21\,d\,a^3\,n+c\,b^3\,n^3+21\,c\,b^3\,n^2+146\,c\,b^3\,n+336\,c\,b^3\right)}{b^3\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{a\,d^2\,n\,x^7\,{\left(a+b\,x\right)}^n\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}{b\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{7\,a^2\,d^2\,n\,x^6\,{\left(a+b\,x\right)}^n\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{b^2\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}+\frac{2\,a\,d\,n\,x^4\,{\left(a+b\,x\right)}^n\,\left(n^3+6\,n^2+11\,n+6\right)\,\left(-105\,d\,a^3+c\,b^3\,n^3+21\,c\,b^3\,n^2+146\,c\,b^3\,n+336\,c\,b^3\right)}{b^4\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}-\frac{8\,a^2\,d\,n\,x^3\,{\left(a+b\,x\right)}^n\,\left(n^2+3\,n+2\right)\,\left(-105\,d\,a^3+c\,b^3\,n^3+21\,c\,b^3\,n^2+146\,c\,b^3\,n+336\,c\,b^3\right)}{b^5\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}","Not used",1,"(d^2*x^8*(a + b*x)^n*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320) - (a^2*(a + b*x)^n*(5040*a^6*d^2 + 20160*b^6*c^2 + 24552*b^6*c^2*n + 12154*b^6*c^2*n^2 + 3135*b^6*c^2*n^3 + 445*b^6*c^2*n^4 + 33*b^6*c^2*n^5 + b^6*c^2*n^6 - 16128*a^3*b^3*c*d - 7008*a^3*b^3*c*d*n - 1008*a^3*b^3*c*d*n^2 - 48*a^3*b^3*c*d*n^3))/(b^8*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (x^2*(n + 1)*(a + b*x)^n*(20160*b^6*c^2 - 2520*a^6*d^2*n + 24552*b^6*c^2*n + 12154*b^6*c^2*n^2 + 3135*b^6*c^2*n^3 + 445*b^6*c^2*n^4 + 33*b^6*c^2*n^5 + b^6*c^2*n^6 + 8064*a^3*b^3*c*d*n + 3504*a^3*b^3*c*d*n^2 + 504*a^3*b^3*c*d*n^3 + 24*a^3*b^3*c*d*n^4))/(b^6*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (a*n*x*(a + b*x)^n*(5040*a^6*d^2 + 20160*b^6*c^2 + 24552*b^6*c^2*n + 12154*b^6*c^2*n^2 + 3135*b^6*c^2*n^3 + 445*b^6*c^2*n^4 + 33*b^6*c^2*n^5 + b^6*c^2*n^6 - 16128*a^3*b^3*c*d - 7008*a^3*b^3*c*d*n - 1008*a^3*b^3*c*d*n^2 - 48*a^3*b^3*c*d*n^3))/(b^7*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (2*d*x^5*(a + b*x)^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)*(336*b^3*c + 21*b^3*c*n^2 + b^3*c*n^3 + 21*a^3*d*n + 146*b^3*c*n))/(b^3*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (a*d^2*n*x^7*(a + b*x)^n*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))/(b*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (7*a^2*d^2*n*x^6*(a + b*x)^n*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(b^2*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) + (2*a*d*n*x^4*(a + b*x)^n*(11*n + 6*n^2 + n^3 + 6)*(336*b^3*c - 105*a^3*d + 21*b^3*c*n^2 + b^3*c*n^3 + 146*b^3*c*n))/(b^4*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320)) - (8*a^2*d*n*x^3*(a + b*x)^n*(3*n + n^2 + 2)*(336*b^3*c - 105*a^3*d + 21*b^3*c*n^2 + b^3*c*n^3 + 146*b^3*c*n))/(b^5*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))","B"
180,1,878,203,3.191533,"\text{Not used}","int((c + d*x^3)^2*(a + b*x)^n,x)","\frac{a\,{\left(a+b\,x\right)}^n\,\left(720\,a^6\,d^2-12\,a^3\,b^3\,c\,d\,n^3-216\,a^3\,b^3\,c\,d\,n^2-1284\,a^3\,b^3\,c\,d\,n-2520\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+27\,b^6\,c^2\,n^5+295\,b^6\,c^2\,n^4+1665\,b^6\,c^2\,n^3+5104\,b^6\,c^2\,n^2+8028\,b^6\,c^2\,n+5040\,b^6\,c^2\right)}{b^7\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}+\frac{d^2\,x^7\,{\left(a+b\,x\right)}^n\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}{n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040}+\frac{x\,{\left(a+b\,x\right)}^n\,\left(-720\,a^6\,b\,d^2\,n+12\,a^3\,b^4\,c\,d\,n^4+216\,a^3\,b^4\,c\,d\,n^3+1284\,a^3\,b^4\,c\,d\,n^2+2520\,a^3\,b^4\,c\,d\,n+b^7\,c^2\,n^6+27\,b^7\,c^2\,n^5+295\,b^7\,c^2\,n^4+1665\,b^7\,c^2\,n^3+5104\,b^7\,c^2\,n^2+8028\,b^7\,c^2\,n+5040\,b^7\,c^2\right)}{b^7\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}+\frac{2\,d\,x^4\,{\left(a+b\,x\right)}^n\,\left(n^3+6\,n^2+11\,n+6\right)\,\left(15\,d\,a^3\,n+c\,b^3\,n^3+18\,c\,b^3\,n^2+107\,c\,b^3\,n+210\,c\,b^3\right)}{b^3\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}+\frac{a\,d^2\,n\,x^6\,{\left(a+b\,x\right)}^n\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{b\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}-\frac{6\,a^2\,d^2\,n\,x^5\,{\left(a+b\,x\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)}{b^2\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}+\frac{2\,a\,d\,n\,x^3\,{\left(a+b\,x\right)}^n\,\left(n^2+3\,n+2\right)\,\left(-60\,d\,a^3+c\,b^3\,n^3+18\,c\,b^3\,n^2+107\,c\,b^3\,n+210\,c\,b^3\right)}{b^4\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}-\frac{6\,a^2\,d\,n\,x^2\,\left(n+1\right)\,{\left(a+b\,x\right)}^n\,\left(-60\,d\,a^3+c\,b^3\,n^3+18\,c\,b^3\,n^2+107\,c\,b^3\,n+210\,c\,b^3\right)}{b^5\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}","Not used",1,"(a*(a + b*x)^n*(720*a^6*d^2 + 5040*b^6*c^2 + 8028*b^6*c^2*n + 5104*b^6*c^2*n^2 + 1665*b^6*c^2*n^3 + 295*b^6*c^2*n^4 + 27*b^6*c^2*n^5 + b^6*c^2*n^6 - 2520*a^3*b^3*c*d - 1284*a^3*b^3*c*d*n - 216*a^3*b^3*c*d*n^2 - 12*a^3*b^3*c*d*n^3))/(b^7*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040)) + (d^2*x^7*(a + b*x)^n*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))/(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040) + (x*(a + b*x)^n*(5040*b^7*c^2 + 8028*b^7*c^2*n + 5104*b^7*c^2*n^2 + 1665*b^7*c^2*n^3 + 295*b^7*c^2*n^4 + 27*b^7*c^2*n^5 + b^7*c^2*n^6 - 720*a^6*b*d^2*n + 2520*a^3*b^4*c*d*n + 1284*a^3*b^4*c*d*n^2 + 216*a^3*b^4*c*d*n^3 + 12*a^3*b^4*c*d*n^4))/(b^7*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040)) + (2*d*x^4*(a + b*x)^n*(11*n + 6*n^2 + n^3 + 6)*(210*b^3*c + 18*b^3*c*n^2 + b^3*c*n^3 + 15*a^3*d*n + 107*b^3*c*n))/(b^3*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040)) + (a*d^2*n*x^6*(a + b*x)^n*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(b*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040)) - (6*a^2*d^2*n*x^5*(a + b*x)^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24))/(b^2*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040)) + (2*a*d*n*x^3*(a + b*x)^n*(3*n + n^2 + 2)*(210*b^3*c - 60*a^3*d + 18*b^3*c*n^2 + b^3*c*n^3 + 107*b^3*c*n))/(b^4*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040)) - (6*a^2*d*n*x^2*(n + 1)*(a + b*x)^n*(210*b^3*c - 60*a^3*d + 18*b^3*c*n^2 + b^3*c*n^3 + 107*b^3*c*n))/(b^5*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))","B"
181,0,-1,209,0.000000,"\text{Not used}","int(((c + d*x^3)^2*(a + b*x)^n)/x,x)","\int \frac{{\left(d\,x^3+c\right)}^2\,{\left(a+b\,x\right)}^n}{x} \,d x","Not used",1,"int(((c + d*x^3)^2*(a + b*x)^n)/x, x)","F"
182,1,2896,459,7.139524,"\text{Not used}","int(x^2*(c + d*x^3)^3*(a + b*x)^n,x)","\frac{2\,a^3\,{\left(a+b\,x\right)}^n\,\left(-19958400\,a^9\,d^3+60480\,a^6\,b^3\,c\,d^2\,n^3+1995840\,a^6\,b^3\,c\,d^2\,n^2+21893760\,a^6\,b^3\,c\,d^2\,n+79833600\,a^6\,b^3\,c\,d^2-180\,a^3\,b^6\,c^2\,d\,n^6-10260\,a^3\,b^6\,c^2\,d\,n^5-242100\,a^3\,b^6\,c^2\,d\,n^4-3026700\,a^3\,b^6\,c^2\,d\,n^3-21141720\,a^3\,b^6\,c^2\,d\,n^2-78222240\,a^3\,b^6\,c^2\,d\,n-119750400\,a^3\,b^6\,c^2\,d+b^9\,c^3\,n^9+72\,b^9\,c^3\,n^8+2274\,b^9\,c^3\,n^7+41328\,b^9\,c^3\,n^6+476049\,b^9\,c^3\,n^5+3602088\,b^9\,c^3\,n^4+17893196\,b^9\,c^3\,n^3+56231712\,b^9\,c^3\,n^2+101378880\,b^9\,c^3\,n+79833600\,b^9\,c^3\right)}{b^{12}\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{d^3\,x^{12}\,{\left(a+b\,x\right)}^n\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}{n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600}+\frac{x^3\,{\left(a+b\,x\right)}^n\,\left(n^2+3\,n+2\right)\,\left(6652800\,a^9\,d^3\,n-20160\,a^6\,b^3\,c\,d^2\,n^4-665280\,a^6\,b^3\,c\,d^2\,n^3-7297920\,a^6\,b^3\,c\,d^2\,n^2-26611200\,a^6\,b^3\,c\,d^2\,n+60\,a^3\,b^6\,c^2\,d\,n^7+3420\,a^3\,b^6\,c^2\,d\,n^6+80700\,a^3\,b^6\,c^2\,d\,n^5+1008900\,a^3\,b^6\,c^2\,d\,n^4+7047240\,a^3\,b^6\,c^2\,d\,n^3+26074080\,a^3\,b^6\,c^2\,d\,n^2+39916800\,a^3\,b^6\,c^2\,d\,n+b^9\,c^3\,n^9+72\,b^9\,c^3\,n^8+2274\,b^9\,c^3\,n^7+41328\,b^9\,c^3\,n^6+476049\,b^9\,c^3\,n^5+3602088\,b^9\,c^3\,n^4+17893196\,b^9\,c^3\,n^3+56231712\,b^9\,c^3\,n^2+101378880\,b^9\,c^3\,n+79833600\,b^9\,c^3\right)}{b^9\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{3\,d\,x^6\,{\left(a+b\,x\right)}^n\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)\,\left(-18480\,a^6\,d^2\,n+56\,a^3\,b^3\,c\,d\,n^4+1848\,a^3\,b^3\,c\,d\,n^3+20272\,a^3\,b^3\,c\,d\,n^2+73920\,a^3\,b^3\,c\,d\,n+b^6\,c^2\,n^6+57\,b^6\,c^2\,n^5+1345\,b^6\,c^2\,n^4+16815\,b^6\,c^2\,n^3+117454\,b^6\,c^2\,n^2+434568\,b^6\,c^2\,n+665280\,b^6\,c^2\right)}{b^6\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}-\frac{2\,a^2\,n\,x\,{\left(a+b\,x\right)}^n\,\left(-19958400\,a^9\,d^3+60480\,a^6\,b^3\,c\,d^2\,n^3+1995840\,a^6\,b^3\,c\,d^2\,n^2+21893760\,a^6\,b^3\,c\,d^2\,n+79833600\,a^6\,b^3\,c\,d^2-180\,a^3\,b^6\,c^2\,d\,n^6-10260\,a^3\,b^6\,c^2\,d\,n^5-242100\,a^3\,b^6\,c^2\,d\,n^4-3026700\,a^3\,b^6\,c^2\,d\,n^3-21141720\,a^3\,b^6\,c^2\,d\,n^2-78222240\,a^3\,b^6\,c^2\,d\,n-119750400\,a^3\,b^6\,c^2\,d+b^9\,c^3\,n^9+72\,b^9\,c^3\,n^8+2274\,b^9\,c^3\,n^7+41328\,b^9\,c^3\,n^6+476049\,b^9\,c^3\,n^5+3602088\,b^9\,c^3\,n^4+17893196\,b^9\,c^3\,n^3+56231712\,b^9\,c^3\,n^2+101378880\,b^9\,c^3\,n+79833600\,b^9\,c^3\right)}{b^{11}\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{d^2\,x^9\,{\left(a+b\,x\right)}^n\,\left(110\,d\,a^3\,n+3\,c\,b^3\,n^3+99\,c\,b^3\,n^2+1086\,c\,b^3\,n+3960\,c\,b^3\right)\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}{b^3\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{a\,d^3\,n\,x^{11}\,{\left(a+b\,x\right)}^n\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}{b\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}-\frac{11\,a^2\,d^3\,n\,x^{10}\,{\left(a+b\,x\right)}^n\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}{b^2\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{a\,n\,x^2\,\left(n+1\right)\,{\left(a+b\,x\right)}^n\,\left(-19958400\,a^9\,d^3+60480\,a^6\,b^3\,c\,d^2\,n^3+1995840\,a^6\,b^3\,c\,d^2\,n^2+21893760\,a^6\,b^3\,c\,d^2\,n+79833600\,a^6\,b^3\,c\,d^2-180\,a^3\,b^6\,c^2\,d\,n^6-10260\,a^3\,b^6\,c^2\,d\,n^5-242100\,a^3\,b^6\,c^2\,d\,n^4-3026700\,a^3\,b^6\,c^2\,d\,n^3-21141720\,a^3\,b^6\,c^2\,d\,n^2-78222240\,a^3\,b^6\,c^2\,d\,n-119750400\,a^3\,b^6\,c^2\,d+b^9\,c^3\,n^9+72\,b^9\,c^3\,n^8+2274\,b^9\,c^3\,n^7+41328\,b^9\,c^3\,n^6+476049\,b^9\,c^3\,n^5+3602088\,b^9\,c^3\,n^4+17893196\,b^9\,c^3\,n^3+56231712\,b^9\,c^3\,n^2+101378880\,b^9\,c^3\,n+79833600\,b^9\,c^3\right)}{b^{10}\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{3\,a\,d\,n\,x^5\,{\left(a+b\,x\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)\,\left(110880\,a^6\,d^2-336\,a^3\,b^3\,c\,d\,n^3-11088\,a^3\,b^3\,c\,d\,n^2-121632\,a^3\,b^3\,c\,d\,n-443520\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+57\,b^6\,c^2\,n^5+1345\,b^6\,c^2\,n^4+16815\,b^6\,c^2\,n^3+117454\,b^6\,c^2\,n^2+434568\,b^6\,c^2\,n+665280\,b^6\,c^2\right)}{b^7\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}-\frac{15\,a^2\,d\,n\,x^4\,{\left(a+b\,x\right)}^n\,\left(n^3+6\,n^2+11\,n+6\right)\,\left(110880\,a^6\,d^2-336\,a^3\,b^3\,c\,d\,n^3-11088\,a^3\,b^3\,c\,d\,n^2-121632\,a^3\,b^3\,c\,d\,n-443520\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+57\,b^6\,c^2\,n^5+1345\,b^6\,c^2\,n^4+16815\,b^6\,c^2\,n^3+117454\,b^6\,c^2\,n^2+434568\,b^6\,c^2\,n+665280\,b^6\,c^2\right)}{b^8\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}+\frac{3\,a\,d^2\,n\,x^8\,{\left(a+b\,x\right)}^n\,\left(-330\,d\,a^3+c\,b^3\,n^3+33\,c\,b^3\,n^2+362\,c\,b^3\,n+1320\,c\,b^3\right)\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{b^4\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}-\frac{24\,a^2\,d^2\,n\,x^7\,{\left(a+b\,x\right)}^n\,\left(-330\,d\,a^3+c\,b^3\,n^3+33\,c\,b^3\,n^2+362\,c\,b^3\,n+1320\,c\,b^3\right)\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}{b^5\,\left(n^{12}+78\,n^{11}+2717\,n^{10}+55770\,n^9+749463\,n^8+6926634\,n^7+44990231\,n^6+206070150\,n^5+657206836\,n^4+1414014888\,n^3+1931559552\,n^2+1486442880\,n+479001600\right)}","Not used",1,"(2*a^3*(a + b*x)^n*(79833600*b^9*c^3 - 19958400*a^9*d^3 + 101378880*b^9*c^3*n + 56231712*b^9*c^3*n^2 + 17893196*b^9*c^3*n^3 + 3602088*b^9*c^3*n^4 + 476049*b^9*c^3*n^5 + 41328*b^9*c^3*n^6 + 2274*b^9*c^3*n^7 + 72*b^9*c^3*n^8 + b^9*c^3*n^9 - 119750400*a^3*b^6*c^2*d + 79833600*a^6*b^3*c*d^2 - 78222240*a^3*b^6*c^2*d*n + 21893760*a^6*b^3*c*d^2*n - 21141720*a^3*b^6*c^2*d*n^2 + 1995840*a^6*b^3*c*d^2*n^2 - 3026700*a^3*b^6*c^2*d*n^3 + 60480*a^6*b^3*c*d^2*n^3 - 242100*a^3*b^6*c^2*d*n^4 - 10260*a^3*b^6*c^2*d*n^5 - 180*a^3*b^6*c^2*d*n^6))/(b^12*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (d^3*x^12*(a + b*x)^n*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800))/(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600) + (x^3*(a + b*x)^n*(3*n + n^2 + 2)*(79833600*b^9*c^3 + 6652800*a^9*d^3*n + 101378880*b^9*c^3*n + 56231712*b^9*c^3*n^2 + 17893196*b^9*c^3*n^3 + 3602088*b^9*c^3*n^4 + 476049*b^9*c^3*n^5 + 41328*b^9*c^3*n^6 + 2274*b^9*c^3*n^7 + 72*b^9*c^3*n^8 + b^9*c^3*n^9 + 39916800*a^3*b^6*c^2*d*n - 26611200*a^6*b^3*c*d^2*n + 26074080*a^3*b^6*c^2*d*n^2 - 7297920*a^6*b^3*c*d^2*n^2 + 7047240*a^3*b^6*c^2*d*n^3 - 665280*a^6*b^3*c*d^2*n^3 + 1008900*a^3*b^6*c^2*d*n^4 - 20160*a^6*b^3*c*d^2*n^4 + 80700*a^3*b^6*c^2*d*n^5 + 3420*a^3*b^6*c^2*d*n^6 + 60*a^3*b^6*c^2*d*n^7))/(b^9*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (3*d*x^6*(a + b*x)^n*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120)*(665280*b^6*c^2 - 18480*a^6*d^2*n + 434568*b^6*c^2*n + 117454*b^6*c^2*n^2 + 16815*b^6*c^2*n^3 + 1345*b^6*c^2*n^4 + 57*b^6*c^2*n^5 + b^6*c^2*n^6 + 73920*a^3*b^3*c*d*n + 20272*a^3*b^3*c*d*n^2 + 1848*a^3*b^3*c*d*n^3 + 56*a^3*b^3*c*d*n^4))/(b^6*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) - (2*a^2*n*x*(a + b*x)^n*(79833600*b^9*c^3 - 19958400*a^9*d^3 + 101378880*b^9*c^3*n + 56231712*b^9*c^3*n^2 + 17893196*b^9*c^3*n^3 + 3602088*b^9*c^3*n^4 + 476049*b^9*c^3*n^5 + 41328*b^9*c^3*n^6 + 2274*b^9*c^3*n^7 + 72*b^9*c^3*n^8 + b^9*c^3*n^9 - 119750400*a^3*b^6*c^2*d + 79833600*a^6*b^3*c*d^2 - 78222240*a^3*b^6*c^2*d*n + 21893760*a^6*b^3*c*d^2*n - 21141720*a^3*b^6*c^2*d*n^2 + 1995840*a^6*b^3*c*d^2*n^2 - 3026700*a^3*b^6*c^2*d*n^3 + 60480*a^6*b^3*c*d^2*n^3 - 242100*a^3*b^6*c^2*d*n^4 - 10260*a^3*b^6*c^2*d*n^5 - 180*a^3*b^6*c^2*d*n^6))/(b^11*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (d^2*x^9*(a + b*x)^n*(3960*b^3*c + 99*b^3*c*n^2 + 3*b^3*c*n^3 + 110*a^3*d*n + 1086*b^3*c*n)*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))/(b^3*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (a*d^3*n*x^11*(a + b*x)^n*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800))/(b*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) - (11*a^2*d^3*n*x^10*(a + b*x)^n*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880))/(b^2*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (a*n*x^2*(n + 1)*(a + b*x)^n*(79833600*b^9*c^3 - 19958400*a^9*d^3 + 101378880*b^9*c^3*n + 56231712*b^9*c^3*n^2 + 17893196*b^9*c^3*n^3 + 3602088*b^9*c^3*n^4 + 476049*b^9*c^3*n^5 + 41328*b^9*c^3*n^6 + 2274*b^9*c^3*n^7 + 72*b^9*c^3*n^8 + b^9*c^3*n^9 - 119750400*a^3*b^6*c^2*d + 79833600*a^6*b^3*c*d^2 - 78222240*a^3*b^6*c^2*d*n + 21893760*a^6*b^3*c*d^2*n - 21141720*a^3*b^6*c^2*d*n^2 + 1995840*a^6*b^3*c*d^2*n^2 - 3026700*a^3*b^6*c^2*d*n^3 + 60480*a^6*b^3*c*d^2*n^3 - 242100*a^3*b^6*c^2*d*n^4 - 10260*a^3*b^6*c^2*d*n^5 - 180*a^3*b^6*c^2*d*n^6))/(b^10*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (3*a*d*n*x^5*(a + b*x)^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)*(110880*a^6*d^2 + 665280*b^6*c^2 + 434568*b^6*c^2*n + 117454*b^6*c^2*n^2 + 16815*b^6*c^2*n^3 + 1345*b^6*c^2*n^4 + 57*b^6*c^2*n^5 + b^6*c^2*n^6 - 443520*a^3*b^3*c*d - 121632*a^3*b^3*c*d*n - 11088*a^3*b^3*c*d*n^2 - 336*a^3*b^3*c*d*n^3))/(b^7*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) - (15*a^2*d*n*x^4*(a + b*x)^n*(11*n + 6*n^2 + n^3 + 6)*(110880*a^6*d^2 + 665280*b^6*c^2 + 434568*b^6*c^2*n + 117454*b^6*c^2*n^2 + 16815*b^6*c^2*n^3 + 1345*b^6*c^2*n^4 + 57*b^6*c^2*n^5 + b^6*c^2*n^6 - 443520*a^3*b^3*c*d - 121632*a^3*b^3*c*d*n - 11088*a^3*b^3*c*d*n^2 - 336*a^3*b^3*c*d*n^3))/(b^8*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) + (3*a*d^2*n*x^8*(a + b*x)^n*(1320*b^3*c - 330*a^3*d + 33*b^3*c*n^2 + b^3*c*n^3 + 362*b^3*c*n)*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(b^4*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600)) - (24*a^2*d^2*n*x^7*(a + b*x)^n*(1320*b^3*c - 330*a^3*d + 33*b^3*c*n^2 + b^3*c*n^3 + 362*b^3*c*n)*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))/(b^5*(1486442880*n + 1931559552*n^2 + 1414014888*n^3 + 657206836*n^4 + 206070150*n^5 + 44990231*n^6 + 6926634*n^7 + 749463*n^8 + 55770*n^9 + 2717*n^10 + 78*n^11 + n^12 + 479001600))","B"
183,1,2436,396,5.597793,"\text{Not used}","int(x*(c + d*x^3)^3*(a + b*x)^n,x)","\frac{d^3\,x^{11}\,{\left(a+b\,x\right)}^n\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}{n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800}-\frac{a^2\,{\left(a+b\,x\right)}^n\,\left(-3628800\,a^9\,d^3+15120\,a^6\,b^3\,c\,d^2\,n^3+453600\,a^6\,b^3\,c\,d^2\,n^2+4520880\,a^6\,b^3\,c\,d^2\,n+14968800\,a^6\,b^3\,c\,d^2-72\,a^3\,b^6\,c^2\,d\,n^6-3672\,a^3\,b^6\,c^2\,d\,n^5-77400\,a^3\,b^6\,c^2\,d\,n^4-862920\,a^3\,b^6\,c^2\,d\,n^3-5365728\,a^3\,b^6\,c^2\,d\,n^2-17640288\,a^3\,b^6\,c^2\,d\,n-23950080\,a^3\,b^6\,c^2\,d+b^9\,c^3\,n^9+63\,b^9\,c^3\,n^8+1734\,b^9\,c^3\,n^7+27342\,b^9\,c^3\,n^6+271929\,b^9\,c^3\,n^5+1767087\,b^9\,c^3\,n^4+7494416\,b^9\,c^3\,n^3+19978308\,b^9\,c^3\,n^2+30334320\,b^9\,c^3\,n+19958400\,b^9\,c^3\right)}{b^{11}\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{x^2\,\left(n+1\right)\,{\left(a+b\,x\right)}^n\,\left(1814400\,a^9\,d^3\,n-7560\,a^6\,b^3\,c\,d^2\,n^4-226800\,a^6\,b^3\,c\,d^2\,n^3-2260440\,a^6\,b^3\,c\,d^2\,n^2-7484400\,a^6\,b^3\,c\,d^2\,n+36\,a^3\,b^6\,c^2\,d\,n^7+1836\,a^3\,b^6\,c^2\,d\,n^6+38700\,a^3\,b^6\,c^2\,d\,n^5+431460\,a^3\,b^6\,c^2\,d\,n^4+2682864\,a^3\,b^6\,c^2\,d\,n^3+8820144\,a^3\,b^6\,c^2\,d\,n^2+11975040\,a^3\,b^6\,c^2\,d\,n+b^9\,c^3\,n^9+63\,b^9\,c^3\,n^8+1734\,b^9\,c^3\,n^7+27342\,b^9\,c^3\,n^6+271929\,b^9\,c^3\,n^5+1767087\,b^9\,c^3\,n^4+7494416\,b^9\,c^3\,n^3+19978308\,b^9\,c^3\,n^2+30334320\,b^9\,c^3\,n+19958400\,b^9\,c^3\right)}{b^9\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{a\,n\,x\,{\left(a+b\,x\right)}^n\,\left(-3628800\,a^9\,d^3+15120\,a^6\,b^3\,c\,d^2\,n^3+453600\,a^6\,b^3\,c\,d^2\,n^2+4520880\,a^6\,b^3\,c\,d^2\,n+14968800\,a^6\,b^3\,c\,d^2-72\,a^3\,b^6\,c^2\,d\,n^6-3672\,a^3\,b^6\,c^2\,d\,n^5-77400\,a^3\,b^6\,c^2\,d\,n^4-862920\,a^3\,b^6\,c^2\,d\,n^3-5365728\,a^3\,b^6\,c^2\,d\,n^2-17640288\,a^3\,b^6\,c^2\,d\,n-23950080\,a^3\,b^6\,c^2\,d+b^9\,c^3\,n^9+63\,b^9\,c^3\,n^8+1734\,b^9\,c^3\,n^7+27342\,b^9\,c^3\,n^6+271929\,b^9\,c^3\,n^5+1767087\,b^9\,c^3\,n^4+7494416\,b^9\,c^3\,n^3+19978308\,b^9\,c^3\,n^2+30334320\,b^9\,c^3\,n+19958400\,b^9\,c^3\right)}{b^{10}\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{3\,d\,x^5\,{\left(a+b\,x\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)\,\left(-10080\,a^6\,d^2\,n+42\,a^3\,b^3\,c\,d\,n^4+1260\,a^3\,b^3\,c\,d\,n^3+12558\,a^3\,b^3\,c\,d\,n^2+41580\,a^3\,b^3\,c\,d\,n+b^6\,c^2\,n^6+51\,b^6\,c^2\,n^5+1075\,b^6\,c^2\,n^4+11985\,b^6\,c^2\,n^3+74524\,b^6\,c^2\,n^2+245004\,b^6\,c^2\,n+332640\,b^6\,c^2\right)}{b^6\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{3\,d^2\,x^8\,{\left(a+b\,x\right)}^n\,\left(30\,d\,a^3\,n+c\,b^3\,n^3+30\,c\,b^3\,n^2+299\,c\,b^3\,n+990\,c\,b^3\right)\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{b^3\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{a\,d^3\,n\,x^{10}\,{\left(a+b\,x\right)}^n\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}{b\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}-\frac{10\,a^2\,d^3\,n\,x^9\,{\left(a+b\,x\right)}^n\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}{b^2\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{3\,a\,d^2\,n\,x^7\,{\left(a+b\,x\right)}^n\,\left(-240\,d\,a^3+c\,b^3\,n^3+30\,c\,b^3\,n^2+299\,c\,b^3\,n+990\,c\,b^3\right)\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}{b^4\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}-\frac{21\,a^2\,d^2\,n\,x^6\,{\left(a+b\,x\right)}^n\,\left(-240\,d\,a^3+c\,b^3\,n^3+30\,c\,b^3\,n^2+299\,c\,b^3\,n+990\,c\,b^3\right)\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{b^5\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}+\frac{3\,a\,d\,n\,x^4\,{\left(a+b\,x\right)}^n\,\left(n^3+6\,n^2+11\,n+6\right)\,\left(50400\,a^6\,d^2-210\,a^3\,b^3\,c\,d\,n^3-6300\,a^3\,b^3\,c\,d\,n^2-62790\,a^3\,b^3\,c\,d\,n-207900\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+51\,b^6\,c^2\,n^5+1075\,b^6\,c^2\,n^4+11985\,b^6\,c^2\,n^3+74524\,b^6\,c^2\,n^2+245004\,b^6\,c^2\,n+332640\,b^6\,c^2\right)}{b^7\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}-\frac{12\,a^2\,d\,n\,x^3\,{\left(a+b\,x\right)}^n\,\left(n^2+3\,n+2\right)\,\left(50400\,a^6\,d^2-210\,a^3\,b^3\,c\,d\,n^3-6300\,a^3\,b^3\,c\,d\,n^2-62790\,a^3\,b^3\,c\,d\,n-207900\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+51\,b^6\,c^2\,n^5+1075\,b^6\,c^2\,n^4+11985\,b^6\,c^2\,n^3+74524\,b^6\,c^2\,n^2+245004\,b^6\,c^2\,n+332640\,b^6\,c^2\right)}{b^8\,\left(n^{11}+66\,n^{10}+1925\,n^9+32670\,n^8+357423\,n^7+2637558\,n^6+13339535\,n^5+45995730\,n^4+105258076\,n^3+150917976\,n^2+120543840\,n+39916800\right)}","Not used",1,"(d^3*x^11*(a + b*x)^n*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800))/(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800) - (a^2*(a + b*x)^n*(19958400*b^9*c^3 - 3628800*a^9*d^3 + 30334320*b^9*c^3*n + 19978308*b^9*c^3*n^2 + 7494416*b^9*c^3*n^3 + 1767087*b^9*c^3*n^4 + 271929*b^9*c^3*n^5 + 27342*b^9*c^3*n^6 + 1734*b^9*c^3*n^7 + 63*b^9*c^3*n^8 + b^9*c^3*n^9 - 23950080*a^3*b^6*c^2*d + 14968800*a^6*b^3*c*d^2 - 17640288*a^3*b^6*c^2*d*n + 4520880*a^6*b^3*c*d^2*n - 5365728*a^3*b^6*c^2*d*n^2 + 453600*a^6*b^3*c*d^2*n^2 - 862920*a^3*b^6*c^2*d*n^3 + 15120*a^6*b^3*c*d^2*n^3 - 77400*a^3*b^6*c^2*d*n^4 - 3672*a^3*b^6*c^2*d*n^5 - 72*a^3*b^6*c^2*d*n^6))/(b^11*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (x^2*(n + 1)*(a + b*x)^n*(19958400*b^9*c^3 + 1814400*a^9*d^3*n + 30334320*b^9*c^3*n + 19978308*b^9*c^3*n^2 + 7494416*b^9*c^3*n^3 + 1767087*b^9*c^3*n^4 + 271929*b^9*c^3*n^5 + 27342*b^9*c^3*n^6 + 1734*b^9*c^3*n^7 + 63*b^9*c^3*n^8 + b^9*c^3*n^9 + 11975040*a^3*b^6*c^2*d*n - 7484400*a^6*b^3*c*d^2*n + 8820144*a^3*b^6*c^2*d*n^2 - 2260440*a^6*b^3*c*d^2*n^2 + 2682864*a^3*b^6*c^2*d*n^3 - 226800*a^6*b^3*c*d^2*n^3 + 431460*a^3*b^6*c^2*d*n^4 - 7560*a^6*b^3*c*d^2*n^4 + 38700*a^3*b^6*c^2*d*n^5 + 1836*a^3*b^6*c^2*d*n^6 + 36*a^3*b^6*c^2*d*n^7))/(b^9*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (a*n*x*(a + b*x)^n*(19958400*b^9*c^3 - 3628800*a^9*d^3 + 30334320*b^9*c^3*n + 19978308*b^9*c^3*n^2 + 7494416*b^9*c^3*n^3 + 1767087*b^9*c^3*n^4 + 271929*b^9*c^3*n^5 + 27342*b^9*c^3*n^6 + 1734*b^9*c^3*n^7 + 63*b^9*c^3*n^8 + b^9*c^3*n^9 - 23950080*a^3*b^6*c^2*d + 14968800*a^6*b^3*c*d^2 - 17640288*a^3*b^6*c^2*d*n + 4520880*a^6*b^3*c*d^2*n - 5365728*a^3*b^6*c^2*d*n^2 + 453600*a^6*b^3*c*d^2*n^2 - 862920*a^3*b^6*c^2*d*n^3 + 15120*a^6*b^3*c*d^2*n^3 - 77400*a^3*b^6*c^2*d*n^4 - 3672*a^3*b^6*c^2*d*n^5 - 72*a^3*b^6*c^2*d*n^6))/(b^10*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (3*d*x^5*(a + b*x)^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)*(332640*b^6*c^2 - 10080*a^6*d^2*n + 245004*b^6*c^2*n + 74524*b^6*c^2*n^2 + 11985*b^6*c^2*n^3 + 1075*b^6*c^2*n^4 + 51*b^6*c^2*n^5 + b^6*c^2*n^6 + 41580*a^3*b^3*c*d*n + 12558*a^3*b^3*c*d*n^2 + 1260*a^3*b^3*c*d*n^3 + 42*a^3*b^3*c*d*n^4))/(b^6*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (3*d^2*x^8*(a + b*x)^n*(990*b^3*c + 30*b^3*c*n^2 + b^3*c*n^3 + 30*a^3*d*n + 299*b^3*c*n)*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(b^3*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (a*d^3*n*x^10*(a + b*x)^n*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880))/(b*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) - (10*a^2*d^3*n*x^9*(a + b*x)^n*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))/(b^2*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (3*a*d^2*n*x^7*(a + b*x)^n*(990*b^3*c - 240*a^3*d + 30*b^3*c*n^2 + b^3*c*n^3 + 299*b^3*c*n)*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))/(b^4*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) - (21*a^2*d^2*n*x^6*(a + b*x)^n*(990*b^3*c - 240*a^3*d + 30*b^3*c*n^2 + b^3*c*n^3 + 299*b^3*c*n)*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(b^5*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) + (3*a*d*n*x^4*(a + b*x)^n*(11*n + 6*n^2 + n^3 + 6)*(50400*a^6*d^2 + 332640*b^6*c^2 + 245004*b^6*c^2*n + 74524*b^6*c^2*n^2 + 11985*b^6*c^2*n^3 + 1075*b^6*c^2*n^4 + 51*b^6*c^2*n^5 + b^6*c^2*n^6 - 207900*a^3*b^3*c*d - 62790*a^3*b^3*c*d*n - 6300*a^3*b^3*c*d*n^2 - 210*a^3*b^3*c*d*n^3))/(b^7*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800)) - (12*a^2*d*n*x^3*(a + b*x)^n*(3*n + n^2 + 2)*(50400*a^6*d^2 + 332640*b^6*c^2 + 245004*b^6*c^2*n + 74524*b^6*c^2*n^2 + 11985*b^6*c^2*n^3 + 1075*b^6*c^2*n^4 + 51*b^6*c^2*n^5 + b^6*c^2*n^6 - 207900*a^3*b^3*c*d - 62790*a^3*b^3*c*d*n - 6300*a^3*b^3*c*d*n^2 - 210*a^3*b^3*c*d*n^3))/(b^8*(120543840*n + 150917976*n^2 + 105258076*n^3 + 45995730*n^4 + 13339535*n^5 + 2637558*n^6 + 357423*n^7 + 32670*n^8 + 1925*n^9 + 66*n^10 + n^11 + 39916800))","B"
184,1,2001,337,4.338431,"\text{Not used}","int((c + d*x^3)^3*(a + b*x)^n,x)","\frac{{\left(a+b\,x\right)}^n\,\left(-362880\,a^{10}\,d^3+2160\,a^7\,b^3\,c\,d^2\,n^3+58320\,a^7\,b^3\,c\,d^2\,n^2+522720\,a^7\,b^3\,c\,d^2\,n+1555200\,a^7\,b^3\,c\,d^2-18\,a^4\,b^6\,c^2\,d\,n^6-810\,a^4\,b^6\,c^2\,d\,n^5-15030\,a^4\,b^6\,c^2\,d\,n^4-147150\,a^4\,b^6\,c^2\,d\,n^3-801432\,a^4\,b^6\,c^2\,d\,n^2-2301480\,a^4\,b^6\,c^2\,d\,n-2721600\,a^4\,b^6\,c^2\,d+a\,b^9\,c^3\,n^9+54\,a\,b^9\,c^3\,n^8+1266\,a\,b^9\,c^3\,n^7+16884\,a\,b^9\,c^3\,n^6+140889\,a\,b^9\,c^3\,n^5+761166\,a\,b^9\,c^3\,n^4+2655764\,a\,b^9\,c^3\,n^3+5753736\,a\,b^9\,c^3\,n^2+6999840\,a\,b^9\,c^3\,n+3628800\,a\,b^9\,c^3\right)}{b^{10}\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}+\frac{x\,{\left(a+b\,x\right)}^n\,\left(362880\,a^9\,b\,d^3\,n-2160\,a^6\,b^4\,c\,d^2\,n^4-58320\,a^6\,b^4\,c\,d^2\,n^3-522720\,a^6\,b^4\,c\,d^2\,n^2-1555200\,a^6\,b^4\,c\,d^2\,n+18\,a^3\,b^7\,c^2\,d\,n^7+810\,a^3\,b^7\,c^2\,d\,n^6+15030\,a^3\,b^7\,c^2\,d\,n^5+147150\,a^3\,b^7\,c^2\,d\,n^4+801432\,a^3\,b^7\,c^2\,d\,n^3+2301480\,a^3\,b^7\,c^2\,d\,n^2+2721600\,a^3\,b^7\,c^2\,d\,n+b^{10}\,c^3\,n^9+54\,b^{10}\,c^3\,n^8+1266\,b^{10}\,c^3\,n^7+16884\,b^{10}\,c^3\,n^6+140889\,b^{10}\,c^3\,n^5+761166\,b^{10}\,c^3\,n^4+2655764\,b^{10}\,c^3\,n^3+5753736\,b^{10}\,c^3\,n^2+6999840\,b^{10}\,c^3\,n+3628800\,b^{10}\,c^3\right)}{b^{10}\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}+\frac{d^3\,x^{10}\,{\left(a+b\,x\right)}^n\,\left(n^9+45\,n^8+870\,n^7+9450\,n^6+63273\,n^5+269325\,n^4+723680\,n^3+1172700\,n^2+1026576\,n+362880\right)}{n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800}+\frac{3\,d^2\,x^7\,{\left(a+b\,x\right)}^n\,\left(24\,d\,a^3\,n+c\,b^3\,n^3+27\,c\,b^3\,n^2+242\,c\,b^3\,n+720\,c\,b^3\right)\,\left(n^6+21\,n^5+175\,n^4+735\,n^3+1624\,n^2+1764\,n+720\right)}{b^3\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}+\frac{3\,d\,x^4\,{\left(a+b\,x\right)}^n\,\left(n^3+6\,n^2+11\,n+6\right)\,\left(-5040\,a^6\,d^2\,n+30\,a^3\,b^3\,c\,d\,n^4+810\,a^3\,b^3\,c\,d\,n^3+7260\,a^3\,b^3\,c\,d\,n^2+21600\,a^3\,b^3\,c\,d\,n+b^6\,c^2\,n^6+45\,b^6\,c^2\,n^5+835\,b^6\,c^2\,n^4+8175\,b^6\,c^2\,n^3+44524\,b^6\,c^2\,n^2+127860\,b^6\,c^2\,n+151200\,b^6\,c^2\right)}{b^6\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}+\frac{a\,d^3\,n\,x^9\,{\left(a+b\,x\right)}^n\,\left(n^8+36\,n^7+546\,n^6+4536\,n^5+22449\,n^4+67284\,n^3+118124\,n^2+109584\,n+40320\right)}{b\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}-\frac{9\,a^2\,d^3\,n\,x^8\,{\left(a+b\,x\right)}^n\,\left(n^7+28\,n^6+322\,n^5+1960\,n^4+6769\,n^3+13132\,n^2+13068\,n+5040\right)}{b^2\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}+\frac{3\,a\,d\,n\,x^3\,{\left(a+b\,x\right)}^n\,\left(n^2+3\,n+2\right)\,\left(20160\,a^6\,d^2-120\,a^3\,b^3\,c\,d\,n^3-3240\,a^3\,b^3\,c\,d\,n^2-29040\,a^3\,b^3\,c\,d\,n-86400\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+45\,b^6\,c^2\,n^5+835\,b^6\,c^2\,n^4+8175\,b^6\,c^2\,n^3+44524\,b^6\,c^2\,n^2+127860\,b^6\,c^2\,n+151200\,b^6\,c^2\right)}{b^7\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}-\frac{9\,a^2\,d\,n\,x^2\,\left(n+1\right)\,{\left(a+b\,x\right)}^n\,\left(20160\,a^6\,d^2-120\,a^3\,b^3\,c\,d\,n^3-3240\,a^3\,b^3\,c\,d\,n^2-29040\,a^3\,b^3\,c\,d\,n-86400\,a^3\,b^3\,c\,d+b^6\,c^2\,n^6+45\,b^6\,c^2\,n^5+835\,b^6\,c^2\,n^4+8175\,b^6\,c^2\,n^3+44524\,b^6\,c^2\,n^2+127860\,b^6\,c^2\,n+151200\,b^6\,c^2\right)}{b^8\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}+\frac{3\,a\,d^2\,n\,x^6\,{\left(a+b\,x\right)}^n\,\left(-168\,d\,a^3+c\,b^3\,n^3+27\,c\,b^3\,n^2+242\,c\,b^3\,n+720\,c\,b^3\right)\,\left(n^5+15\,n^4+85\,n^3+225\,n^2+274\,n+120\right)}{b^4\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}-\frac{18\,a^2\,d^2\,n\,x^5\,{\left(a+b\,x\right)}^n\,\left(n^4+10\,n^3+35\,n^2+50\,n+24\right)\,\left(-168\,d\,a^3+c\,b^3\,n^3+27\,c\,b^3\,n^2+242\,c\,b^3\,n+720\,c\,b^3\right)}{b^5\,\left(n^{10}+55\,n^9+1320\,n^8+18150\,n^7+157773\,n^6+902055\,n^5+3416930\,n^4+8409500\,n^3+12753576\,n^2+10628640\,n+3628800\right)}","Not used",1,"((a + b*x)^n*(3628800*a*b^9*c^3 - 362880*a^10*d^3 - 2721600*a^4*b^6*c^2*d + 1555200*a^7*b^3*c*d^2 + 5753736*a*b^9*c^3*n^2 + 2655764*a*b^9*c^3*n^3 + 761166*a*b^9*c^3*n^4 + 140889*a*b^9*c^3*n^5 + 16884*a*b^9*c^3*n^6 + 1266*a*b^9*c^3*n^7 + 54*a*b^9*c^3*n^8 + a*b^9*c^3*n^9 + 6999840*a*b^9*c^3*n - 2301480*a^4*b^6*c^2*d*n + 522720*a^7*b^3*c*d^2*n - 801432*a^4*b^6*c^2*d*n^2 + 58320*a^7*b^3*c*d^2*n^2 - 147150*a^4*b^6*c^2*d*n^3 + 2160*a^7*b^3*c*d^2*n^3 - 15030*a^4*b^6*c^2*d*n^4 - 810*a^4*b^6*c^2*d*n^5 - 18*a^4*b^6*c^2*d*n^6))/(b^10*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) + (x*(a + b*x)^n*(3628800*b^10*c^3 + 6999840*b^10*c^3*n + 5753736*b^10*c^3*n^2 + 2655764*b^10*c^3*n^3 + 761166*b^10*c^3*n^4 + 140889*b^10*c^3*n^5 + 16884*b^10*c^3*n^6 + 1266*b^10*c^3*n^7 + 54*b^10*c^3*n^8 + b^10*c^3*n^9 + 362880*a^9*b*d^3*n + 2721600*a^3*b^7*c^2*d*n - 1555200*a^6*b^4*c*d^2*n + 2301480*a^3*b^7*c^2*d*n^2 - 522720*a^6*b^4*c*d^2*n^2 + 801432*a^3*b^7*c^2*d*n^3 - 58320*a^6*b^4*c*d^2*n^3 + 147150*a^3*b^7*c^2*d*n^4 - 2160*a^6*b^4*c*d^2*n^4 + 15030*a^3*b^7*c^2*d*n^5 + 810*a^3*b^7*c^2*d*n^6 + 18*a^3*b^7*c^2*d*n^7))/(b^10*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) + (d^3*x^10*(a + b*x)^n*(1026576*n + 1172700*n^2 + 723680*n^3 + 269325*n^4 + 63273*n^5 + 9450*n^6 + 870*n^7 + 45*n^8 + n^9 + 362880))/(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800) + (3*d^2*x^7*(a + b*x)^n*(720*b^3*c + 27*b^3*c*n^2 + b^3*c*n^3 + 24*a^3*d*n + 242*b^3*c*n)*(1764*n + 1624*n^2 + 735*n^3 + 175*n^4 + 21*n^5 + n^6 + 720))/(b^3*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) + (3*d*x^4*(a + b*x)^n*(11*n + 6*n^2 + n^3 + 6)*(151200*b^6*c^2 - 5040*a^6*d^2*n + 127860*b^6*c^2*n + 44524*b^6*c^2*n^2 + 8175*b^6*c^2*n^3 + 835*b^6*c^2*n^4 + 45*b^6*c^2*n^5 + b^6*c^2*n^6 + 21600*a^3*b^3*c*d*n + 7260*a^3*b^3*c*d*n^2 + 810*a^3*b^3*c*d*n^3 + 30*a^3*b^3*c*d*n^4))/(b^6*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) + (a*d^3*n*x^9*(a + b*x)^n*(109584*n + 118124*n^2 + 67284*n^3 + 22449*n^4 + 4536*n^5 + 546*n^6 + 36*n^7 + n^8 + 40320))/(b*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) - (9*a^2*d^3*n*x^8*(a + b*x)^n*(13068*n + 13132*n^2 + 6769*n^3 + 1960*n^4 + 322*n^5 + 28*n^6 + n^7 + 5040))/(b^2*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) + (3*a*d*n*x^3*(a + b*x)^n*(3*n + n^2 + 2)*(20160*a^6*d^2 + 151200*b^6*c^2 + 127860*b^6*c^2*n + 44524*b^6*c^2*n^2 + 8175*b^6*c^2*n^3 + 835*b^6*c^2*n^4 + 45*b^6*c^2*n^5 + b^6*c^2*n^6 - 86400*a^3*b^3*c*d - 29040*a^3*b^3*c*d*n - 3240*a^3*b^3*c*d*n^2 - 120*a^3*b^3*c*d*n^3))/(b^7*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) - (9*a^2*d*n*x^2*(n + 1)*(a + b*x)^n*(20160*a^6*d^2 + 151200*b^6*c^2 + 127860*b^6*c^2*n + 44524*b^6*c^2*n^2 + 8175*b^6*c^2*n^3 + 835*b^6*c^2*n^4 + 45*b^6*c^2*n^5 + b^6*c^2*n^6 - 86400*a^3*b^3*c*d - 29040*a^3*b^3*c*d*n - 3240*a^3*b^3*c*d*n^2 - 120*a^3*b^3*c*d*n^3))/(b^8*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) + (3*a*d^2*n*x^6*(a + b*x)^n*(720*b^3*c - 168*a^3*d + 27*b^3*c*n^2 + b^3*c*n^3 + 242*b^3*c*n)*(274*n + 225*n^2 + 85*n^3 + 15*n^4 + n^5 + 120))/(b^4*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800)) - (18*a^2*d^2*n*x^5*(a + b*x)^n*(50*n + 35*n^2 + 10*n^3 + n^4 + 24)*(720*b^3*c - 168*a^3*d + 27*b^3*c*n^2 + b^3*c*n^3 + 242*b^3*c*n))/(b^5*(10628640*n + 12753576*n^2 + 8409500*n^3 + 3416930*n^4 + 902055*n^5 + 157773*n^6 + 18150*n^7 + 1320*n^8 + 55*n^9 + n^10 + 3628800))","B"
185,0,-1,358,0.000000,"\text{Not used}","int(((c + d*x^3)^3*(a + b*x)^n)/x,x)","\int \frac{{\left(d\,x^3+c\right)}^3\,{\left(a+b\,x\right)}^n}{x} \,d x","Not used",1,"int(((c + d*x^3)^3*(a + b*x)^n)/x, x)","F"
186,0,-1,324,0.000000,"\text{Not used}","int((x^5*(e + f*x)^n)/(a + b*x^3),x)","\int \frac{x^5\,{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((x^5*(e + f*x)^n)/(a + b*x^3), x)","F"
187,0,-1,332,0.000000,"\text{Not used}","int((x^4*(e + f*x)^n)/(a + b*x^3),x)","\int \frac{x^4\,{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((x^4*(e + f*x)^n)/(a + b*x^3), x)","F"
188,0,-1,293,0.000000,"\text{Not used}","int((x^3*(e + f*x)^n)/(a + b*x^3),x)","\int \frac{x^3\,{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((x^3*(e + f*x)^n)/(a + b*x^3), x)","F"
189,0,-1,253,0.000000,"\text{Not used}","int((x^2*(e + f*x)^n)/(a + b*x^3),x)","\int \frac{x^2\,{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((x^2*(e + f*x)^n)/(a + b*x^3), x)","F"
190,0,-1,288,0.000000,"\text{Not used}","int((x*(e + f*x)^n)/(a + b*x^3),x)","\int \frac{x\,{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((x*(e + f*x)^n)/(a + b*x^3), x)","F"
191,0,-1,263,0.000000,"\text{Not used}","int((e + f*x)^n/(a + b*x^3),x)","\int \frac{{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((e + f*x)^n/(a + b*x^3), x)","F"
192,0,-1,300,0.000000,"\text{Not used}","int((e + f*x)^n/(x*(a + b*x^3)),x)","\int \frac{{\left(e+f\,x\right)}^n}{x\,\left(b\,x^3+a\right)} \,d x","Not used",1,"int((e + f*x)^n/(x*(a + b*x^3)), x)","F"
193,0,-1,326,0.000000,"\text{Not used}","int((e + f*x)^n/(x^2*(a + b*x^3)),x)","\int \frac{{\left(e+f\,x\right)}^n}{x^2\,\left(b\,x^3+a\right)} \,d x","Not used",1,"int((e + f*x)^n/(x^2*(a + b*x^3)), x)","F"
194,0,-1,253,0.000000,"\text{Not used}","int((x^2*(c + d*x)^(n + 1))/(a + b*x^3),x)","\int \frac{x^2\,{\left(c+d\,x\right)}^{n+1}}{b\,x^3+a} \,d x","Not used",1,"int((x^2*(c + d*x)^(n + 1))/(a + b*x^3), x)","F"
195,0,-1,211,0.000000,"\text{Not used}","int((x^m*(e + f*x)^n)/(a + b*x^3),x)","\int \frac{x^m\,{\left(e+f\,x\right)}^n}{b\,x^3+a} \,d x","Not used",1,"int((x^m*(e + f*x)^n)/(a + b*x^3), x)","F"
196,0,-1,1480,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(a + b*x),x)","\int \frac{\sqrt{d\,x^3+c}}{a+b\,x} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(a + b*x), x)","F"
197,0,-1,135,0.000000,"\text{Not used}","int((d^3 + e^3*x^3)^p/(d + e*x),x)","\int \frac{{\left(d^3+e^3\,x^3\right)}^p}{d+e\,x} \,d x","Not used",1,"int((d^3 + e^3*x^3)^p/(d + e*x), x)","F"
198,1,273,16,0.200932,"\text{Not used}","int(-(2*x + x^2 - 2)/((x^2 + 2)*(x^3 + 1)^(1/2)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(-\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i + 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) + ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i - 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
199,1,292,20,2.831182,"\text{Not used}","int((2*x - x^2 + 2)/((x^2 + 2)*(1 - x^3)^(1/2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(-\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) + ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i - 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
200,1,276,18,2.771469,"\text{Not used}","int((2*x - x^2 + 2)/((x^2 + 2)*(x^3 - 1)^(1/2)),x)","-\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(-\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"-((3^(1/2)*1i + 3)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) + ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i - 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)","B"
201,1,289,18,0.105869,"\text{Not used}","int(-(2*x + x^2 - 2)/((x^2 + 2)*(- x^3 - 1)^(1/2)),x)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\left(-\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)+\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-1+\sqrt{2}\,1{}\mathrm{i}};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i + 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) - ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)) + ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(2^(1/2)*1i - 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2))","B"
202,1,632,30,2.822279,"\text{Not used}","int(-(2*x + x^2 - 2)/((x^3 + 1)^(1/2)*(d + d*x + x^2 + 2)),x)","-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{\sqrt{d^2-4\,d-8}}{2}-\frac{d}{2}+1};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d-\left(d-2\right)\,\left(\frac{d}{2}-\frac{\sqrt{d^2-4\,d-8}}{2}\right)+4\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\sqrt{d^2-4\,d-8}\,\left(\frac{\sqrt{d^2-4\,d-8}}{2}-\frac{d}{2}+1\right)}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{d}{2}+\frac{\sqrt{d^2-4\,d-8}}{2}-1};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d-\left(d-2\right)\,\left(\frac{d}{2}+\frac{\sqrt{d^2-4\,d-8}}{2}\right)+4\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\sqrt{d^2-4\,d-8}\,\left(\frac{d}{2}+\frac{\sqrt{d^2-4\,d-8}}{2}-1\right)}","Not used",1,"- (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2) - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/((d^2 - 4*d - 8)^(1/2)/2 - d/2 + 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d - (d - 2)*(d/2 - (d^2 - 4*d - 8)^(1/2)/2) + 4))/((x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)*(d^2 - 4*d - 8)^(1/2)*((d^2 - 4*d - 8)^(1/2)/2 - d/2 + 1)) - (2*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(d/2 + (d^2 - 4*d - 8)^(1/2)/2 - 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d - (d - 2)*(d/2 + (d^2 - 4*d - 8)^(1/2)/2) + 4))/((x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)*(d^2 - 4*d - 8)^(1/2)*(d/2 + (d^2 - 4*d - 8)^(1/2)/2 - 1))","B"
203,1,677,38,0.140952,"\text{Not used}","int((2*x - x^2 + 2)/((1 - x^3)^(1/2)*(d*x - d + x^2 + 2)),x)","\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{d}{2}-\frac{\sqrt{d^2+4\,d-8}}{2}+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d+\left(d+2\right)\,\left(\frac{d}{2}-\frac{\sqrt{d^2+4\,d-8}}{2}\right)-4\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{d}{2}-\frac{\sqrt{d^2+4\,d-8}}{2}+1\right)\,\sqrt{d^2+4\,d-8}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{d}{2}+\frac{\sqrt{d^2+4\,d-8}}{2}+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d+\left(d+2\right)\,\left(\frac{d}{2}+\frac{\sqrt{d^2+4\,d-8}}{2}\right)-4\right)}{\sqrt{1-x^3}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{d}{2}+\frac{\sqrt{d^2+4\,d-8}}{2}+1\right)\,\sqrt{d^2+4\,d-8}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) + (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(d/2 - (4*d + d^2 - 8)^(1/2)/2 + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d + (d + 2)*(d/2 - (4*d + d^2 - 8)^(1/2)/2) - 4))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)*(d/2 - (4*d + d^2 - 8)^(1/2)/2 + 1)*(4*d + d^2 - 8)^(1/2)) - (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(d/2 + (4*d + d^2 - 8)^(1/2)/2 + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d + (d + 2)*(d/2 + (4*d + d^2 - 8)^(1/2)/2) - 4))/((1 - x^3)^(1/2)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)*(d/2 + (4*d + d^2 - 8)^(1/2)/2 + 1)*(4*d + d^2 - 8)^(1/2))","B"
204,1,629,36,2.800851,"\text{Not used}","int((2*x - x^2 + 2)/((x^3 - 1)^(1/2)*(d*x - d + x^2 + 2)),x)","\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}+\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{d}{2}-\frac{\sqrt{d^2+4\,d-8}}{2}+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d+\left(d+2\right)\,\left(\frac{d}{2}-\frac{\sqrt{d^2+4\,d-8}}{2}\right)-4\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{d}{2}-\frac{\sqrt{d^2+4\,d-8}}{2}+1\right)\,\sqrt{d^2+4\,d-8}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{d}{2}+\frac{\sqrt{d^2+4\,d-8}}{2}+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d+\left(d+2\right)\,\left(\frac{d}{2}+\frac{\sqrt{d^2+4\,d-8}}{2}\right)-4\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{d}{2}+\frac{\sqrt{d^2+4\,d-8}}{2}+1\right)\,\sqrt{d^2+4\,d-8}}","Not used",1,"(2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2) + (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(d/2 - (4*d + d^2 - 8)^(1/2)/2 + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d + (d + 2)*(d/2 - (4*d + d^2 - 8)^(1/2)/2) - 4))/((((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)*(d/2 - (4*d + d^2 - 8)^(1/2)/2 + 1)*(4*d + d^2 - 8)^(1/2)) - (2*((3^(1/2)*1i)/2 + 3/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(d/2 + (4*d + d^2 - 8)^(1/2)/2 + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d + (d + 2)*(d/2 + (4*d + d^2 - 8)^(1/2)/2) - 4))/((((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)*(d/2 + (4*d + d^2 - 8)^(1/2)/2 + 1)*(4*d + d^2 - 8)^(1/2))","B"
205,1,680,32,0.120488,"\text{Not used}","int(-(2*x + x^2 - 2)/((- x^3 - 1)^(1/2)*(d + d*x + x^2 + 2)),x)","-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{\sqrt{d^2-4\,d-8}}{2}-\frac{d}{2}+1};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d-\left(d-2\right)\,\left(\frac{d}{2}-\frac{\sqrt{d^2-4\,d-8}}{2}\right)+4\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\sqrt{d^2-4\,d-8}\,\left(\frac{\sqrt{d^2-4\,d-8}}{2}-\frac{d}{2}+1\right)}-\frac{2\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3+1}\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{d}{2}+\frac{\sqrt{d^2-4\,d-8}}{2}-1};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)\,\left(d-\left(d-2\right)\,\left(\frac{d}{2}+\frac{\sqrt{d^2-4\,d-8}}{2}\right)+4\right)}{\sqrt{-x^3-1}\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\,\sqrt{d^2-4\,d-8}\,\left(\frac{d}{2}+\frac{\sqrt{d^2-4\,d-8}}{2}-1\right)}","Not used",1,"- (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)) - (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/((d^2 - 4*d - 8)^(1/2)/2 - d/2 + 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d - (d - 2)*(d/2 - (d^2 - 4*d - 8)^(1/2)/2) + 4))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)*(d^2 - 4*d - 8)^(1/2)*((d^2 - 4*d - 8)^(1/2)/2 - d/2 + 1)) - (2*((3^(1/2)*1i)/2 + 3/2)*(x^3 + 1)^(1/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(d/2 + (d^2 - 4*d - 8)^(1/2)/2 - 1), asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2))*(d - (d - 2)*(d/2 + (d^2 - 4*d - 8)^(1/2)/2) + 4))/((- x^3 - 1)^(1/2)*(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)*(d^2 - 4*d - 8)^(1/2)*(d/2 + (d^2 - 4*d - 8)^(1/2)/2 - 1))","B"
206,0,-1,355,0.000000,"\text{Not used}","int((a + c*x^4)^(1/2)*(d + e*x)^3,x)","\int \sqrt{c\,x^4+a}\,{\left(d+e\,x\right)}^3 \,d x","Not used",1,"int((a + c*x^4)^(1/2)*(d + e*x)^3, x)","F"
207,0,-1,326,0.000000,"\text{Not used}","int((a + c*x^4)^(1/2)*(d + e*x)^2,x)","\int \sqrt{c\,x^4+a}\,{\left(d+e\,x\right)}^2 \,d x","Not used",1,"int((a + c*x^4)^(1/2)*(d + e*x)^2, x)","F"
208,0,-1,158,0.000000,"\text{Not used}","int((a + c*x^4)^(1/2)*(d + e*x),x)","\int \sqrt{c\,x^4+a}\,\left(d+e\,x\right) \,d x","Not used",1,"int((a + c*x^4)^(1/2)*(d + e*x), x)","F"
209,1,37,105,2.643806,"\text{Not used}","int((a + c*x^4)^(1/2),x)","\frac{x\,\sqrt{c\,x^4+a}\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{2},\frac{1}{4};\ \frac{5}{4};\ -\frac{c\,x^4}{a}\right)}{\sqrt{\frac{c\,x^4}{a}+1}}","Not used",1,"(x*(a + c*x^4)^(1/2)*hypergeom([-1/2, 1/4], 5/4, -(c*x^4)/a))/((c*x^4)/a + 1)^(1/2)","B"
210,0,-1,730,0.000000,"\text{Not used}","int((a + c*x^4)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{c\,x^4+a}}{d+e\,x} \,d x","Not used",1,"int((a + c*x^4)^(1/2)/(d + e*x), x)","F"
211,0,-1,1221,0.000000,"\text{Not used}","int((a + c*x^4)^(1/2)/(d + e*x)^2,x)","\int \frac{\sqrt{c\,x^4+a}}{{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int((a + c*x^4)^(1/2)/(d + e*x)^2, x)","F"
212,0,-1,295,0.000000,"\text{Not used}","int((d + e*x)^3/(a + c*x^4)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{\sqrt{c\,x^4+a}} \,d x","Not used",1,"int((d + e*x)^3/(a + c*x^4)^(1/2), x)","F"
213,0,-1,263,0.000000,"\text{Not used}","int((d + e*x)^2/(a + c*x^4)^(1/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{\sqrt{c\,x^4+a}} \,d x","Not used",1,"int((d + e*x)^2/(a + c*x^4)^(1/2), x)","F"
214,0,-1,121,0.000000,"\text{Not used}","int((d + e*x)/(a + c*x^4)^(1/2),x)","\int \frac{d+e\,x}{\sqrt{c\,x^4+a}} \,d x","Not used",1,"int((d + e*x)/(a + c*x^4)^(1/2), x)","F"
215,1,37,88,2.630187,"\text{Not used}","int(1/(a + c*x^4)^(1/2),x)","\frac{x\,\sqrt{\frac{c\,x^4}{a}+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{1}{2};\ \frac{5}{4};\ -\frac{c\,x^4}{a}\right)}{\sqrt{c\,x^4+a}}","Not used",1,"(x*((c*x^4)/a + 1)^(1/2)*hypergeom([1/4, 1/2], 5/4, -(c*x^4)/a))/(a + c*x^4)^(1/2)","B"
216,0,-1,405,0.000000,"\text{Not used}","int(1/((a + c*x^4)^(1/2)*(d + e*x)),x)","\int \frac{1}{\sqrt{c\,x^4+a}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((a + c*x^4)^(1/2)*(d + e*x)), x)","F"
217,0,-1,610,0.000000,"\text{Not used}","int(1/((a + c*x^4)^(1/2)*(d + e*x)^2),x)","\int \frac{1}{\sqrt{c\,x^4+a}\,{\left(d+e\,x\right)}^2} \,d x","Not used",1,"int(1/((a + c*x^4)^(1/2)*(d + e*x)^2), x)","F"
218,0,-1,659,0.000000,"\text{Not used}","int(1/((a + c*x^4)^(1/2)*(d + e*x)^3),x)","\int \frac{1}{\sqrt{c\,x^4+a}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int(1/((a + c*x^4)^(1/2)*(d + e*x)^3), x)","F"
219,0,-1,298,0.000000,"\text{Not used}","int((d + e*x)^3/(a + c*x^4)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^3}{{\left(c\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^3/(a + c*x^4)^(3/2), x)","F"
220,0,-1,270,0.000000,"\text{Not used}","int((d + e*x)^2/(a + c*x^4)^(3/2),x)","\int \frac{{\left(d+e\,x\right)}^2}{{\left(c\,x^4+a\right)}^{3/2}} \,d x","Not used",1,"int((d + e*x)^2/(a + c*x^4)^(3/2), x)","F"
221,1,57,114,2.876795,"\text{Not used}","int((d + e*x)/(a + c*x^4)^(3/2),x)","\frac{e\,x^2}{2\,a\,\sqrt{c\,x^4+a}}+\frac{d\,x\,{\left(\frac{c\,x^4}{a}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{3}{2};\ \frac{5}{4};\ -\frac{c\,x^4}{a}\right)}{{\left(c\,x^4+a\right)}^{3/2}}","Not used",1,"(e*x^2)/(2*a*(a + c*x^4)^(1/2)) + (d*x*((c*x^4)/a + 1)^(3/2)*hypergeom([1/4, 3/2], 5/4, -(c*x^4)/a))/(a + c*x^4)^(3/2)","B"
222,1,37,108,2.659448,"\text{Not used}","int(1/(a + c*x^4)^(3/2),x)","\frac{x\,{\left(\frac{c\,x^4}{a}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{4},\frac{3}{2};\ \frac{5}{4};\ -\frac{c\,x^4}{a}\right)}{{\left(c\,x^4+a\right)}^{3/2}}","Not used",1,"(x*((c*x^4)/a + 1)^(3/2)*hypergeom([1/4, 3/2], 5/4, -(c*x^4)/a))/(a + c*x^4)^(3/2)","B"
223,0,-1,818,0.000000,"\text{Not used}","int(1/((a + c*x^4)^(3/2)*(d + e*x)),x)","\int \frac{1}{{\left(c\,x^4+a\right)}^{3/2}\,\left(d+e\,x\right)} \,d x","Not used",1,"int(1/((a + c*x^4)^(3/2)*(d + e*x)), x)","F"
224,0,-1,349,0.000000,"\text{Not used}","int((x^3*(c + d*x)^n)/(a + b*x^4),x)","\int \frac{x^3\,{\left(c+d\,x\right)}^n}{b\,x^4+a} \,d x","Not used",1,"int((x^3*(c + d*x)^n)/(a + b*x^4), x)","F"
225,0,-1,349,0.000000,"\text{Not used}","int((x^3*(c + d*x)^(n + 1))/(a + b*x^4),x)","\int \frac{x^3\,{\left(c+d\,x\right)}^{n+1}}{b\,x^4+a} \,d x","Not used",1,"int((x^3*(c + d*x)^(n + 1))/(a + b*x^4), x)","F"
226,0,-1,1605,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(1/2)*(c + d*x + e*x^2)),x)","\int \frac{1}{\sqrt{b\,x^4+a}\,\left(e\,x^2+d\,x+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(1/2)*(c + d*x + e*x^2)), x)","F"
227,1,234,161,2.973307,"\text{Not used}","int(x^m*(c*(a + b*x^2)^2)^(3/2),x)","\frac{x^m\,\left(\frac{3\,a^2\,c\,x^3\,\sqrt{c\,{\left(b\,x^2+a\right)}^2}\,\left(m^3+13\,m^2+47\,m+35\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{b^2\,c\,x^7\,\sqrt{c\,{\left(b\,x^2+a\right)}^2}\,\left(m^3+9\,m^2+23\,m+15\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{3\,a\,b\,c\,x^5\,\sqrt{c\,{\left(b\,x^2+a\right)}^2}\,\left(m^3+11\,m^2+31\,m+21\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{a^3\,c\,x\,\sqrt{c\,{\left(b\,x^2+a\right)}^2}\,\left(m^3+15\,m^2+71\,m+105\right)}{b\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}\right)}{\frac{a}{b}+x^2}","Not used",1,"(x^m*((3*a^2*c*x^3*(c*(a + b*x^2)^2)^(1/2)*(47*m + 13*m^2 + m^3 + 35))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (b^2*c*x^7*(c*(a + b*x^2)^2)^(1/2)*(23*m + 9*m^2 + m^3 + 15))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (3*a*b*c*x^5*(c*(a + b*x^2)^2)^(1/2)*(31*m + 11*m^2 + m^3 + 21))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (a^3*c*x*(c*(a + b*x^2)^2)^(1/2)*(71*m + 15*m^2 + m^3 + 105))/(b*(176*m + 86*m^2 + 16*m^3 + m^4 + 105))))/(a/b + x^2)","B"
228,0,-1,143,0.000000,"\text{Not used}","int(x^5*(c*(a + b*x^2)^2)^(3/2),x)","\int x^5\,{\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2} \,d x","Not used",1,"int(x^5*(c*(a + b*x^2)^2)^(3/2), x)","F"
229,0,-1,143,0.000000,"\text{Not used}","int(x^4*(c*(a + b*x^2)^2)^(3/2),x)","\int x^4\,{\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2} \,d x","Not used",1,"int(x^4*(c*(a + b*x^2)^2)^(3/2), x)","F"
230,1,50,66,2.830715,"\text{Not used}","int(x^3*(c*(a + b*x^2)^2)^(3/2),x)","\frac{\left(-a^2+3\,a\,b\,x^2+4\,b^2\,x^4\right)\,{\left(c\,a^2+2\,c\,a\,b\,x^2+c\,b^2\,x^4\right)}^{3/2}}{40\,b^2}","Not used",1,"((4*b^2*x^4 - a^2 + 3*a*b*x^2)*(a^2*c + b^2*c*x^4 + 2*a*b*c*x^2)^(3/2))/(40*b^2)","B"
231,0,-1,143,0.000000,"\text{Not used}","int(x^2*(c*(a + b*x^2)^2)^(3/2),x)","\int x^2\,{\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2} \,d x","Not used",1,"int(x^2*(c*(a + b*x^2)^2)^(3/2), x)","F"
232,1,40,32,2.835259,"\text{Not used}","int(x*(c*(a + b*x^2)^2)^(3/2),x)","\frac{\left(b^2\,x^2+a\,b\right)\,{\left(c\,a^2+2\,c\,a\,b\,x^2+c\,b^2\,x^4\right)}^{3/2}}{8\,b^2}","Not used",1,"((a*b + b^2*x^2)*(a^2*c + b^2*c*x^4 + 2*a*b*c*x^2)^(3/2))/(8*b^2)","B"
233,0,-1,135,0.000000,"\text{Not used}","int((c*(a + b*x^2)^2)^(3/2),x)","\int {\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2} \,d x","Not used",1,"int((c*(a + b*x^2)^2)^(3/2), x)","F"
234,0,-1,139,0.000000,"\text{Not used}","int((c*(a + b*x^2)^2)^(3/2)/x,x)","\int \frac{{\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2}}{x} \,d x","Not used",1,"int((c*(a + b*x^2)^2)^(3/2)/x, x)","F"
235,0,-1,134,0.000000,"\text{Not used}","int((c*(a + b*x^2)^2)^(3/2)/x^2,x)","\int \frac{{\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2}}{x^2} \,d x","Not used",1,"int((c*(a + b*x^2)^2)^(3/2)/x^2, x)","F"
236,0,-1,140,0.000000,"\text{Not used}","int((c*(a + b*x^2)^2)^(3/2)/x^3,x)","\int \frac{{\left(c\,{\left(b\,x^2+a\right)}^2\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((c*(a + b*x^2)^2)^(3/2)/x^3, x)","F"
237,0,-1,253,0.000000,"\text{Not used}","int(x^2*(c*(a + b*x^2)^3)^(3/2),x)","\int x^2\,{\left(c\,{\left(b\,x^2+a\right)}^3\right)}^{3/2} \,d x","Not used",1,"int(x^2*(c*(a + b*x^2)^3)^(3/2), x)","F"
238,1,62,32,2.707508,"\text{Not used}","int(x*(c*(a + b*x^2)^3)^(3/2),x)","\sqrt{c\,{\left(b\,x^2+a\right)}^3}\,\left(\frac{a^4\,c}{11\,b}+\frac{4\,a^3\,c\,x^2}{11}+\frac{b^3\,c\,x^8}{11}+\frac{6\,a^2\,b\,c\,x^4}{11}+\frac{4\,a\,b^2\,c\,x^6}{11}\right)","Not used",1,"(c*(a + b*x^2)^3)^(1/2)*((a^4*c)/(11*b) + (4*a^3*c*x^2)/11 + (b^3*c*x^8)/11 + (6*a^2*b*c*x^4)/11 + (4*a*b^2*c*x^6)/11)","B"
239,0,-1,207,0.000000,"\text{Not used}","int((c*(a + b*x^2)^3)^(3/2),x)","\int {\left(c\,{\left(b\,x^2+a\right)}^3\right)}^{3/2} \,d x","Not used",1,"int((c*(a + b*x^2)^3)^(3/2), x)","F"
240,0,-1,192,0.000000,"\text{Not used}","int((c*(a + b*x^2)^3)^(3/2)/x,x)","\int \frac{{\left(c\,{\left(b\,x^2+a\right)}^3\right)}^{3/2}}{x} \,d x","Not used",1,"int((c*(a + b*x^2)^3)^(3/2)/x, x)","F"
241,0,-1,208,0.000000,"\text{Not used}","int((c*(a + b*x^2)^3)^(3/2)/x^2,x)","\int \frac{{\left(c\,{\left(b\,x^2+a\right)}^3\right)}^{3/2}}{x^2} \,d x","Not used",1,"int((c*(a + b*x^2)^3)^(3/2)/x^2, x)","F"
242,0,-1,202,0.000000,"\text{Not used}","int((c*(a + b*x^2)^3)^(3/2)/x^3,x)","\int \frac{{\left(c\,{\left(b\,x^2+a\right)}^3\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((c*(a + b*x^2)^3)^(3/2)/x^3, x)","F"
243,0,-1,77,0.000000,"\text{Not used}","int(x^2*(c/(a + b*x^2))^(3/2),x)","\int x^2\,{\left(\frac{c}{b\,x^2+a}\right)}^{3/2} \,d x","Not used",1,"int(x^2*(c/(a + b*x^2))^(3/2), x)","F"
244,1,19,21,2.644343,"\text{Not used}","int(x*(c/(a + b*x^2))^(3/2),x)","-\frac{c\,\sqrt{\frac{c}{b\,x^2+a}}}{b}","Not used",1,"-(c*(c/(a + b*x^2))^(1/2))/b","B"
245,1,19,21,2.738524,"\text{Not used}","int((c/(a + b*x^2))^(3/2),x)","\frac{c\,x\,\sqrt{\frac{c}{b\,x^2+a}}}{a}","Not used",1,"(c*x*(c/(a + b*x^2))^(1/2))/a","B"
246,0,-1,71,0.000000,"\text{Not used}","int((c/(a + b*x^2))^(3/2)/x,x)","\int \frac{{\left(\frac{c}{b\,x^2+a}\right)}^{3/2}}{x} \,d x","Not used",1,"int((c/(a + b*x^2))^(3/2)/x, x)","F"
247,1,54,48,2.829639,"\text{Not used}","int((c/(a + b*x^2))^(3/2)/x^2,x)","-\frac{\left(\frac{b\,c}{a}+\frac{2\,b^2\,c\,x^2}{a^2}\right)\,\sqrt{\frac{c}{b\,x^2+a}}\,\left(\frac{a}{b}+x^2\right)}{b\,x^3+a\,x}","Not used",1,"-(((b*c)/a + (2*b^2*c*x^2)/a^2)*(c/(a + b*x^2))^(1/2)*(a/b + x^2))/(a*x + b*x^3)","B"
248,0,-1,104,0.000000,"\text{Not used}","int((c/(a + b*x^2))^(3/2)/x^3,x)","\int \frac{{\left(\frac{c}{b\,x^2+a}\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((c/(a + b*x^2))^(3/2)/x^3, x)","F"
249,1,109,138,2.964745,"\text{Not used}","int(x^7*(c*(a + b*x^2)^(1/2))^(3/2),x)","\sqrt{c\,\sqrt{b\,x^2+a}}\,\left(\frac{2\,c\,x^8\,\sqrt{b\,x^2+a}}{19}-\frac{256\,a^4\,c\,\sqrt{b\,x^2+a}}{7315\,b^4}+\frac{2\,a\,c\,x^6\,\sqrt{b\,x^2+a}}{95\,b}-\frac{24\,a^2\,c\,x^4\,\sqrt{b\,x^2+a}}{1045\,b^2}+\frac{192\,a^3\,c\,x^2\,\sqrt{b\,x^2+a}}{7315\,b^3}\right)","Not used",1,"(c*(a + b*x^2)^(1/2))^(1/2)*((2*c*x^8*(a + b*x^2)^(1/2))/19 - (256*a^4*c*(a + b*x^2)^(1/2))/(7315*b^4) + (2*a*c*x^6*(a + b*x^2)^(1/2))/(95*b) - (24*a^2*c*x^4*(a + b*x^2)^(1/2))/(1045*b^2) + (192*a^3*c*x^2*(a + b*x^2)^(1/2))/(7315*b^3))","B"
250,1,88,102,2.901406,"\text{Not used}","int(x^5*(c*(a + b*x^2)^(1/2))^(3/2),x)","\sqrt{c\,\sqrt{b\,x^2+a}}\,\left(\frac{2\,c\,x^6\,\sqrt{b\,x^2+a}}{15}+\frac{64\,a^3\,c\,\sqrt{b\,x^2+a}}{1155\,b^3}+\frac{2\,a\,c\,x^4\,\sqrt{b\,x^2+a}}{55\,b}-\frac{16\,a^2\,c\,x^2\,\sqrt{b\,x^2+a}}{385\,b^2}\right)","Not used",1,"(c*(a + b*x^2)^(1/2))^(1/2)*((2*c*x^6*(a + b*x^2)^(1/2))/15 + (64*a^3*c*(a + b*x^2)^(1/2))/(1155*b^3) + (2*a*c*x^4*(a + b*x^2)^(1/2))/(55*b) - (16*a^2*c*x^2*(a + b*x^2)^(1/2))/(385*b^2))","B"
251,1,67,66,2.885392,"\text{Not used}","int(x^3*(c*(a + b*x^2)^(1/2))^(3/2),x)","\sqrt{c\,\sqrt{b\,x^2+a}}\,\left(\frac{2\,c\,x^4\,\sqrt{b\,x^2+a}}{11}-\frac{8\,a^2\,c\,\sqrt{b\,x^2+a}}{77\,b^2}+\frac{6\,a\,c\,x^2\,\sqrt{b\,x^2+a}}{77\,b}\right)","Not used",1,"(c*(a + b*x^2)^(1/2))^(1/2)*((2*c*x^4*(a + b*x^2)^(1/2))/11 - (8*a^2*c*(a + b*x^2)^(1/2))/(77*b^2) + (6*a*c*x^2*(a + b*x^2)^(1/2))/(77*b))","B"
252,1,28,36,2.768897,"\text{Not used}","int(x*(c*(a + b*x^2)^(1/2))^(3/2),x)","\frac{2\,c\,{\left(b\,x^2+a\right)}^{3/2}\,\sqrt{c\,\sqrt{b\,x^2+a}}}{7\,b}","Not used",1,"(2*c*(a + b*x^2)^(3/2)*(c*(a + b*x^2)^(1/2))^(1/2))/(7*b)","B"
253,0,-1,117,0.000000,"\text{Not used}","int((c*(a + b*x^2)^(1/2))^(3/2)/x,x)","\int \frac{{\left(c\,\sqrt{b\,x^2+a}\right)}^{3/2}}{x} \,d x","Not used",1,"int((c*(a + b*x^2)^(1/2))^(3/2)/x, x)","F"
254,0,-1,133,0.000000,"\text{Not used}","int((c*(a + b*x^2)^(1/2))^(3/2)/x^3,x)","\int \frac{{\left(c\,\sqrt{b\,x^2+a}\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((c*(a + b*x^2)^(1/2))^(3/2)/x^3, x)","F"
255,0,-1,152,0.000000,"\text{Not used}","int(x^2*(c*(a + b*x^2)^(1/2))^(3/2),x)","\int x^2\,{\left(c\,\sqrt{b\,x^2+a}\right)}^{3/2} \,d x","Not used",1,"int(x^2*(c*(a + b*x^2)^(1/2))^(3/2), x)","F"
256,0,-1,119,0.000000,"\text{Not used}","int((c*(a + b*x^2)^(1/2))^(3/2),x)","\int {\left(c\,\sqrt{b\,x^2+a}\right)}^{3/2} \,d x","Not used",1,"int((c*(a + b*x^2)^(1/2))^(3/2), x)","F"
257,0,-1,115,0.000000,"\text{Not used}","int((c*(a + b*x^2)^(1/2))^(3/2)/x^2,x)","\int \frac{{\left(c\,\sqrt{b\,x^2+a}\right)}^{3/2}}{x^2} \,d x","Not used",1,"int((c*(a + b*x^2)^(1/2))^(3/2)/x^2, x)","F"
258,0,-1,154,0.000000,"\text{Not used}","int((c*(a + b*x^2)^(1/2))^(3/2)/x^4,x)","\int \frac{{\left(c\,\sqrt{b\,x^2+a}\right)}^{3/2}}{x^4} \,d x","Not used",1,"int((c*(a + b*x^2)^(1/2))^(3/2)/x^4, x)","F"
259,0,-1,71,0.000000,"\text{Not used}","int((-(a - x)*(b - x))^(1/2),x)","\int \sqrt{-\left(a-x\right)\,\left(b-x\right)} \,d x","Not used",1,"int((-(a - x)*(b - x))^(1/2), x)","F"
260,0,-1,48,0.000000,"\text{Not used}","int((-(x^2 - 1)*(x^2 + 3))^(1/2),x)","\int \sqrt{-\left(x^2-1\right)\,\left(x^2+3\right)} \,d x","Not used",1,"int((-(x^2 - 1)*(x^2 + 3))^(1/2), x)","F"
261,0,-1,32,0.000000,"\text{Not used}","int(1/(-(a - x)*(b - x))^(1/2),x)","\int \frac{1}{\sqrt{-\left(a-x\right)\,\left(b-x\right)}} \,d x","Not used",1,"int(1/(-(a - x)*(b - x))^(1/2), x)","F"
262,0,-1,12,0.000000,"\text{Not used}","int(1/(-(x^2 - 1)*(x^2 + 3))^(1/2),x)","\int \frac{1}{\sqrt{-\left(x^2-1\right)\,\left(x^2+3\right)}} \,d x","Not used",1,"int(1/(-(x^2 - 1)*(x^2 + 3))^(1/2), x)","F"
263,0,-1,244,0.000000,"\text{Not used}","int(x^5*((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int x^5\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}} \,d x","Not used",1,"int(x^5*((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
264,0,-1,161,0.000000,"\text{Not used}","int(x^3*((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int x^3\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}} \,d x","Not used",1,"int(x^3*((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
265,0,-1,103,0.000000,"\text{Not used}","int(x*((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int x\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}} \,d x","Not used",1,"int(x*((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
266,0,-1,112,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x, x)","F"
267,0,-1,127,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^3,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x^3} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^3, x)","F"
268,0,-1,208,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^5,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x^5} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^5, x)","F"
269,0,-1,318,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^7,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x^7} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^7, x)","F"
270,0,-1,357,0.000000,"\text{Not used}","int(x^4*((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int x^4\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}} \,d x","Not used",1,"int(x^4*((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
271,0,-1,266,0.000000,"\text{Not used}","int(x^2*((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int x^2\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}} \,d x","Not used",1,"int(x^2*((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
272,0,-1,194,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
273,0,-1,239,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^2,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x^2} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^2, x)","F"
274,0,-1,321,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^4,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x^4} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^4, x)","F"
275,0,-1,424,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^6,x)","\int \frac{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}}{x^6} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(1/2)/x^6, x)","F"
276,0,-1,282,0.000000,"\text{Not used}","int(x^5*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int x^5\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^5*((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
277,0,-1,199,0.000000,"\text{Not used}","int(x^3*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int x^3\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^3*((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
278,0,-1,141,0.000000,"\text{Not used}","int(x*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int x\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x*((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
279,0,-1,151,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x, x)","F"
280,0,-1,165,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^3,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x^3} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^3, x)","F"
281,0,-1,256,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^5,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x^5} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^5, x)","F"
282,0,-1,366,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^7,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x^7} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^7, x)","F"
283,0,-1,391,0.000000,"\text{Not used}","int(x^4*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int x^4\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^4*((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
284,0,-1,310,0.000000,"\text{Not used}","int(x^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int x^2\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
285,0,-1,262,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int {\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
286,0,-1,307,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^2,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x^2} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^2, x)","F"
287,0,-1,383,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^4,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x^4} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^4, x)","F"
288,0,-1,480,0.000000,"\text{Not used}","int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^6,x)","\int \frac{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}}{x^6} \,d x","Not used",1,"int(((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^6, x)","F"
289,1,55,51,2.666374,"\text{Not used}","int(x*(-(x^2 - 1)/(x^2 + 1))^(1/2),x)","-\mathrm{atan}\left(\sqrt{-\frac{x^2-1}{x^2+1}}\right)-\frac{\sqrt{-\frac{x^2-1}{x^2+1}}}{\frac{x^2-1}{x^2+1}-1}","Not used",1,"- atan((-(x^2 - 1)/(x^2 + 1))^(1/2)) - (-(x^2 - 1)/(x^2 + 1))^(1/2)/((x^2 - 1)/(x^2 + 1) - 1)","B"
290,1,88,72,0.209801,"\text{Not used}","int(x*(-(7*x^2 - 5)/(5*x^2 + 7))^(1/2),x)","-\frac{37\,\sqrt{35}\,\mathrm{atan}\left(\frac{\sqrt{5}\,\sqrt{7}\,\sqrt{-\frac{7\,x^2-5}{5\,x^2+7}}}{7}\right)}{175}-\frac{37\,\sqrt{5}\,\sqrt{7}\,\sqrt{35}\,\sqrt{-\frac{7\,x^2-5}{5\,x^2+7}}}{1225\,\left(\frac{5\,x^2-\frac{25}{7}}{5\,x^2+7}-1\right)}","Not used",1,"- (37*35^(1/2)*atan((5^(1/2)*7^(1/2)*(-(7*x^2 - 5)/(5*x^2 + 7))^(1/2))/7))/175 - (37*5^(1/2)*7^(1/2)*35^(1/2)*(-(7*x^2 - 5)/(5*x^2 + 7))^(1/2))/(1225*((5*x^2 - 25/7)/(5*x^2 + 7) - 1))","B"
291,1,56,53,2.674193,"\text{Not used}","int(x^2*(-(x^3 - 1)/(x^3 + 1))^(1/2),x)","-\frac{2\,\mathrm{atan}\left(\sqrt{-\frac{x^3-1}{x^3+1}}\right)}{3}-\frac{2\,\sqrt{-\frac{x^3-1}{x^3+1}}}{\frac{3\,\left(x^3-1\right)}{x^3+1}-3}","Not used",1,"- (2*atan((-(x^3 - 1)/(x^3 + 1))^(1/2)))/3 - (2*(-(x^3 - 1)/(x^3 + 1))^(1/2))/((3*(x^3 - 1))/(x^3 + 1) - 3)","B"
292,1,101,113,2.658415,"\text{Not used}","int(x^8*(-(x^3 - 1)/(x^3 + 1))^(1/2),x)","\frac{2\,\sqrt{-\frac{x^3-1}{x^3+1}}}{9}-\frac{\mathrm{atan}\left(\sqrt{-\frac{x^3-1}{x^3+1}}\right)}{3}+\frac{x^3\,\sqrt{-\frac{x^3-1}{x^3+1}}}{18}-\frac{x^6\,\sqrt{-\frac{x^3-1}{x^3+1}}}{18}+\frac{x^9\,\sqrt{-\frac{x^3-1}{x^3+1}}}{9}","Not used",1,"(2*(-(x^3 - 1)/(x^3 + 1))^(1/2))/9 - atan((-(x^3 - 1)/(x^3 + 1))^(1/2))/3 + (x^3*(-(x^3 - 1)/(x^3 + 1))^(1/2))/18 - (x^6*(-(x^3 - 1)/(x^3 + 1))^(1/2))/18 + (x^9*(-(x^3 - 1)/(x^3 + 1))^(1/2))/9","B"
293,1,134,106,2.994134,"\text{Not used}","int(x^9*(-(7*x^5 - 5)/(5*x^5 + 7))^(1/2),x)","\frac{2257\,\sqrt{35}\,\mathrm{atan}\left(\frac{\sqrt{5}\,\sqrt{7}\,\sqrt{-\frac{7\,x^5-5}{5\,x^5+7}}}{7}\right)}{30625}-\frac{43\,\sqrt{5}\,\sqrt{7}\,\sqrt{35}\,\sqrt{-\frac{7\,x^5-5}{5\,x^5+7}}}{4375}-\frac{37\,\sqrt{5}\,\sqrt{7}\,\sqrt{35}\,x^5\,\sqrt{-\frac{7\,x^5-5}{5\,x^5+7}}}{12250}+\frac{\sqrt{5}\,\sqrt{7}\,\sqrt{35}\,x^{10}\,\sqrt{-\frac{7\,x^5-5}{5\,x^5+7}}}{350}","Not used",1,"(2257*35^(1/2)*atan((5^(1/2)*7^(1/2)*(-(7*x^5 - 5)/(5*x^5 + 7))^(1/2))/7))/30625 - (43*5^(1/2)*7^(1/2)*35^(1/2)*(-(7*x^5 - 5)/(5*x^5 + 7))^(1/2))/4375 - (37*5^(1/2)*7^(1/2)*35^(1/2)*x^5*(-(7*x^5 - 5)/(5*x^5 + 7))^(1/2))/12250 + (5^(1/2)*7^(1/2)*35^(1/2)*x^10*(-(7*x^5 - 5)/(5*x^5 + 7))^(1/2))/350","B"
294,0,-1,52,0.000000,"\text{Not used}","int((x^2/(x^2 - 1))^(1/2)/(x^2 + 1),x)","\int \frac{\sqrt{\frac{x^2}{x^2-1}}}{x^2+1} \,d x","Not used",1,"int((x^2/(x^2 - 1))^(1/2)/(x^2 + 1), x)","F"
295,0,-1,68,0.000000,"\text{Not used}","int((x^2/(a + x^2*(a + 1) - 1))^(1/2)/(x^2 + 1),x)","\int \frac{\sqrt{\frac{x^2}{\left(a+1\right)\,x^2+a-1}}}{x^2+1} \,d x","Not used",1,"int((x^2/(a + x^2*(a + 1) - 1))^(1/2)/(x^2 + 1), x)","F"
296,0,-1,281,0.000000,"\text{Not used}","int(x^5/((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \frac{x^5}{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(x^5/((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
297,0,-1,169,0.000000,"\text{Not used}","int(x^3/((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \frac{x^3}{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(x^3/((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
298,0,-1,106,0.000000,"\text{Not used}","int(x/((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \frac{x}{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(x/((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
299,0,-1,112,0.000000,"\text{Not used}","int(1/(x*((e*(a + b*x^2))/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x*((e*(a + b*x^2))/(c + d*x^2))^(1/2)), x)","F"
300,0,-1,130,0.000000,"\text{Not used}","int(1/(x^3*((e*(a + b*x^2))/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^3\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^3*((e*(a + b*x^2))/(c + d*x^2))^(1/2)), x)","F"
301,0,-1,218,0.000000,"\text{Not used}","int(1/(x^5*((e*(a + b*x^2))/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^5\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^5*((e*(a + b*x^2))/(c + d*x^2))^(1/2)), x)","F"
302,0,-1,403,0.000000,"\text{Not used}","int(x^4/((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \frac{x^4}{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(x^4/((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
303,0,-1,312,0.000000,"\text{Not used}","int(x^2/((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \frac{x^2}{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(x^2/((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
304,0,-1,252,0.000000,"\text{Not used}","int(1/((e*(a + b*x^2))/(c + d*x^2))^(1/2),x)","\int \frac{1}{\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(1/((e*(a + b*x^2))/(c + d*x^2))^(1/2), x)","F"
305,0,-1,289,0.000000,"\text{Not used}","int(1/(x^2*((e*(a + b*x^2))/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^2\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^2*((e*(a + b*x^2))/(c + d*x^2))^(1/2)), x)","F"
306,0,-1,375,0.000000,"\text{Not used}","int(1/(x^4*((e*(a + b*x^2))/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^4\,\sqrt{\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^4*((e*(a + b*x^2))/(c + d*x^2))^(1/2)), x)","F"
307,0,-1,354,0.000000,"\text{Not used}","int(x^5/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int \frac{x^5}{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^5/((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
308,0,-1,202,0.000000,"\text{Not used}","int(x^3/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int \frac{x^3}{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^3/((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
309,0,-1,146,0.000000,"\text{Not used}","int(x/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int \frac{x}{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x/((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
310,0,-1,152,0.000000,"\text{Not used}","int(1/(x*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x*((e*(a + b*x^2))/(c + d*x^2))^(3/2)), x)","F"
311,0,-1,170,0.000000,"\text{Not used}","int(1/(x^3*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^3\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^3*((e*(a + b*x^2))/(c + d*x^2))^(3/2)), x)","F"
312,0,-1,255,0.000000,"\text{Not used}","int(1/(x^5*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^5\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^5*((e*(a + b*x^2))/(c + d*x^2))^(3/2)), x)","F"
313,0,-1,453,0.000000,"\text{Not used}","int(x^4/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int \frac{x^4}{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^4/((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
314,0,-1,378,0.000000,"\text{Not used}","int(x^2/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int \frac{x^2}{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^2/((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
315,0,-1,327,0.000000,"\text{Not used}","int(1/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x)","\int \frac{1}{{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*(a + b*x^2))/(c + d*x^2))^(3/2), x)","F"
316,0,-1,380,0.000000,"\text{Not used}","int(1/(x^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^2\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2)), x)","F"
317,0,-1,444,0.000000,"\text{Not used}","int(1/(x^4*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^4\,{\left(\frac{e\,\left(b\,x^2+a\right)}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^4*((e*(a + b*x^2))/(c + d*x^2))^(3/2)), x)","F"
318,0,-1,216,0.000000,"\text{Not used}","int(x^5*(a + b/(c + d*x^2))^(1/2),x)","\int x^5\,\sqrt{a+\frac{b}{d\,x^2+c}} \,d x","Not used",1,"int(x^5*(a + b/(c + d*x^2))^(1/2), x)","F"
319,0,-1,141,0.000000,"\text{Not used}","int(x^3*(a + b/(c + d*x^2))^(1/2),x)","\int x^3\,\sqrt{a+\frac{b}{d\,x^2+c}} \,d x","Not used",1,"int(x^3*(a + b/(c + d*x^2))^(1/2), x)","F"
320,1,120,69,3.007154,"\text{Not used}","int(x*(a + b/(c + d*x^2))^(1/2),x)","\frac{\sqrt{\frac{b\,\left(d\,x^2+c\right)+a\,{\left(d\,x^2+c\right)}^2}{{\left(d\,x^2+c\right)}^2}}\,\left(d\,x^2+c\right)\,\left(\frac{b\,\ln\left(\frac{\frac{b}{2}+a\,\left(d\,x^2+c\right)+\sqrt{a}\,\sqrt{b\,\left(d\,x^2+c\right)+a\,{\left(d\,x^2+c\right)}^2}}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b\,\left(d\,x^2+c\right)+a\,{\left(d\,x^2+c\right)}^2}}+2\right)}{4\,d}","Not used",1,"(((b*(c + d*x^2) + a*(c + d*x^2)^2)/(c + d*x^2)^2)^(1/2)*(c + d*x^2)*((b*log((b/2 + a*(c + d*x^2) + a^(1/2)*(b*(c + d*x^2) + a*(c + d*x^2)^2)^(1/2))/a^(1/2)))/(a^(1/2)*(b*(c + d*x^2) + a*(c + d*x^2)^2)^(1/2)) + 2))/(4*d)","B"
321,0,-1,96,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x, x)","F"
322,0,-1,104,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x^3,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x^3} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x^3, x)","F"
323,0,-1,174,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x^5,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x^5} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x^5, x)","F"
324,0,-1,265,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x^7,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x^7} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x^7, x)","F"
325,0,-1,368,0.000000,"\text{Not used}","int(x^4*(a + b/(c + d*x^2))^(1/2),x)","\int x^4\,\sqrt{a+\frac{b}{d\,x^2+c}} \,d x","Not used",1,"int(x^4*(a + b/(c + d*x^2))^(1/2), x)","F"
326,0,-1,282,0.000000,"\text{Not used}","int(x^2*(a + b/(c + d*x^2))^(1/2),x)","\int x^2\,\sqrt{a+\frac{b}{d\,x^2+c}} \,d x","Not used",1,"int(x^2*(a + b/(c + d*x^2))^(1/2), x)","F"
327,0,-1,213,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2),x)","\int \sqrt{a+\frac{b}{d\,x^2+c}} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2), x)","F"
328,0,-1,265,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x^2,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x^2} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x^2, x)","F"
329,0,-1,362,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x^4,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x^4} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x^4, x)","F"
330,0,-1,466,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(1/2)/x^6,x)","\int \frac{\sqrt{a+\frac{b}{d\,x^2+c}}}{x^6} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(1/2)/x^6, x)","F"
331,0,-1,249,0.000000,"\text{Not used}","int(x^5*(a + b/(c + d*x^2))^(3/2),x)","\int x^5\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^5*(a + b/(c + d*x^2))^(3/2), x)","F"
332,0,-1,172,0.000000,"\text{Not used}","int(x^3*(a + b/(c + d*x^2))^(3/2),x)","\int x^3\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^3*(a + b/(c + d*x^2))^(3/2), x)","F"
333,1,61,94,3.738585,"\text{Not used}","int(x*(a + b/(c + d*x^2))^(3/2),x)","-\frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}\,\left(d\,x^2+c\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{a\,\left(d\,x^2+c\right)}{b}\right)}{d\,{\left(\frac{a\,\left(d\,x^2+c\right)}{b}+1\right)}^{3/2}}","Not used",1,"-((a + b/(c + d*x^2))^(3/2)*(c + d*x^2)*hypergeom([-3/2, -1/2], 1/2, -(a*(c + d*x^2))/b))/(d*((a*(c + d*x^2))/b + 1)^(3/2))","B"
334,0,-1,126,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x, x)","F"
335,0,-1,138,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x^3,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x^3} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x^3, x)","F"
336,0,-1,205,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x^5,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x^5} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x^5, x)","F"
337,0,-1,292,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x^7,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x^7} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x^7, x)","F"
338,0,-1,405,0.000000,"\text{Not used}","int(x^4*(a + b/(c + d*x^2))^(3/2),x)","\int x^4\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^4*(a + b/(c + d*x^2))^(3/2), x)","F"
339,0,-1,331,0.000000,"\text{Not used}","int(x^2*(a + b/(c + d*x^2))^(3/2),x)","\int x^2\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int(x^2*(a + b/(c + d*x^2))^(3/2), x)","F"
340,0,-1,260,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2),x)","\int {\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2), x)","F"
341,0,-1,312,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x^2,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x^2} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x^2, x)","F"
342,0,-1,388,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x^4,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x^4} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x^4, x)","F"
343,0,-1,494,0.000000,"\text{Not used}","int((a + b/(c + d*x^2))^(3/2)/x^6,x)","\int \frac{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}{x^6} \,d x","Not used",1,"int((a + b/(c + d*x^2))^(3/2)/x^6, x)","F"
344,0,-1,225,0.000000,"\text{Not used}","int(x^5/(a + b/(c + d*x^2))^(1/2),x)","\int \frac{x^5}{\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(x^5/(a + b/(c + d*x^2))^(1/2), x)","F"
345,0,-1,148,0.000000,"\text{Not used}","int(x^3/(a + b/(c + d*x^2))^(1/2),x)","\int \frac{x^3}{\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(x^3/(a + b/(c + d*x^2))^(1/2), x)","F"
346,1,111,72,3.341603,"\text{Not used}","int(x/(a + b/(c + d*x^2))^(1/2),x)","\frac{\sqrt{\frac{a\,\left(d\,x^2+c\right)}{b}+1}\,\left(d\,x^2+c\right)\,\left(\frac{3\,\sqrt{b}\,\sqrt{b+a\,\left(d\,x^2+c\right)}}{2\,a\,\left(d\,x^2+c\right)}+\frac{b^{3/2}\,\mathrm{asin}\left(\frac{\sqrt{a}\,\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{\sqrt{b}}\right)\,3{}\mathrm{i}}{2\,a^{3/2}\,{\left(d\,x^2+c\right)}^{3/2}}\right)}{3\,d\,\sqrt{a+\frac{b}{d\,x^2+c}}}","Not used",1,"(((a*(c + d*x^2))/b + 1)^(1/2)*(c + d*x^2)*((b^(3/2)*asin((a^(1/2)*(c + d*x^2)^(1/2)*1i)/b^(1/2))*3i)/(2*a^(3/2)*(c + d*x^2)^(3/2)) + (3*b^(1/2)*(b + a*(c + d*x^2))^(1/2))/(2*a*(c + d*x^2))))/(3*d*(a + b/(c + d*x^2))^(1/2))","B"
347,0,-1,96,0.000000,"\text{Not used}","int(1/(x*(a + b/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x*(a + b/(c + d*x^2))^(1/2)), x)","F"
348,0,-1,108,0.000000,"\text{Not used}","int(1/(x^3*(a + b/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^3\,\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^3*(a + b/(c + d*x^2))^(1/2)), x)","F"
349,0,-1,177,0.000000,"\text{Not used}","int(1/(x^5*(a + b/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^5\,\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^5*(a + b/(c + d*x^2))^(1/2)), x)","F"
350,0,-1,443,0.000000,"\text{Not used}","int(x^4/(a + b/(c + d*x^2))^(1/2),x)","\int \frac{x^4}{\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(x^4/(a + b/(c + d*x^2))^(1/2), x)","F"
351,0,-1,354,0.000000,"\text{Not used}","int(x^2/(a + b/(c + d*x^2))^(1/2),x)","\int \frac{x^2}{\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(x^2/(a + b/(c + d*x^2))^(1/2), x)","F"
352,0,-1,286,0.000000,"\text{Not used}","int(1/(a + b/(c + d*x^2))^(1/2),x)","\int \frac{1}{\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(a + b/(c + d*x^2))^(1/2), x)","F"
353,0,-1,343,0.000000,"\text{Not used}","int(1/(x^2*(a + b/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^2\,\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^2*(a + b/(c + d*x^2))^(1/2)), x)","F"
354,0,-1,435,0.000000,"\text{Not used}","int(1/(x^4*(a + b/(c + d*x^2))^(1/2)),x)","\int \frac{1}{x^4\,\sqrt{a+\frac{b}{d\,x^2+c}}} \,d x","Not used",1,"int(1/(x^4*(a + b/(c + d*x^2))^(1/2)), x)","F"
355,0,-1,310,0.000000,"\text{Not used}","int(x^5/(a + b/(c + d*x^2))^(3/2),x)","\int \frac{x^5}{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^5/(a + b/(c + d*x^2))^(3/2), x)","F"
356,0,-1,187,0.000000,"\text{Not used}","int(x^3/(a + b/(c + d*x^2))^(3/2),x)","\int \frac{x^3}{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^3/(a + b/(c + d*x^2))^(3/2), x)","F"
357,1,61,100,3.930106,"\text{Not used}","int(x/(a + b/(c + d*x^2))^(3/2),x)","\frac{{\left(\frac{a\,\left(d\,x^2+c\right)}{b}+1\right)}^{3/2}\,\left(d\,x^2+c\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{2},\frac{5}{2};\ \frac{7}{2};\ -\frac{a\,\left(d\,x^2+c\right)}{b}\right)}{5\,d\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}}","Not used",1,"(((a*(c + d*x^2))/b + 1)^(3/2)*(c + d*x^2)*hypergeom([3/2, 5/2], 7/2, -(a*(c + d*x^2))/b))/(5*d*(a + b/(c + d*x^2))^(3/2))","B"
358,0,-1,134,0.000000,"\text{Not used}","int(1/(x*(a + b/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x*(a + b/(c + d*x^2))^(3/2)), x)","F"
359,0,-1,146,0.000000,"\text{Not used}","int(1/(x^3*(a + b/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^3\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^3*(a + b/(c + d*x^2))^(3/2)), x)","F"
360,0,-1,212,0.000000,"\text{Not used}","int(1/(x^5*(a + b/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^5\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^5*(a + b/(c + d*x^2))^(3/2)), x)","F"
361,0,-1,482,0.000000,"\text{Not used}","int(x^4/(a + b/(c + d*x^2))^(3/2),x)","\int \frac{x^4}{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^4/(a + b/(c + d*x^2))^(3/2), x)","F"
362,0,-1,409,0.000000,"\text{Not used}","int(x^2/(a + b/(c + d*x^2))^(3/2),x)","\int \frac{x^2}{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(x^2/(a + b/(c + d*x^2))^(3/2), x)","F"
363,0,-1,356,0.000000,"\text{Not used}","int(1/(a + b/(c + d*x^2))^(3/2),x)","\int \frac{1}{{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b/(c + d*x^2))^(3/2), x)","F"
364,0,-1,410,0.000000,"\text{Not used}","int(1/(x^2*(a + b/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^2\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*(a + b/(c + d*x^2))^(3/2)), x)","F"
365,0,-1,490,0.000000,"\text{Not used}","int(1/(x^4*(a + b/(c + d*x^2))^(3/2)),x)","\int \frac{1}{x^4\,{\left(a+\frac{b}{d\,x^2+c}\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^4*(a + b/(c + d*x^2))^(3/2)), x)","F"
366,0,-1,75,0.000000,"\text{Not used}","int((a*x^23)^(1/2)/(x^5 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^{23}}}{\sqrt{x^5+1}} \,d x","Not used",1,"int((a*x^23)^(1/2)/(x^5 + 1)^(1/2), x)","F"
367,0,-1,50,0.000000,"\text{Not used}","int((a*x^13)^(1/2)/(x^5 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^{13}}}{\sqrt{x^5+1}} \,d x","Not used",1,"int((a*x^13)^(1/2)/(x^5 + 1)^(1/2), x)","F"
368,0,-1,24,0.000000,"\text{Not used}","int((a*x^3)^(1/2)/(x^5 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^3}}{\sqrt{x^5+1}} \,d x","Not used",1,"int((a*x^3)^(1/2)/(x^5 + 1)^(1/2), x)","F"
369,1,17,23,2.692529,"\text{Not used}","int((a/x^7)^(1/2)/(x^5 + 1)^(1/2),x)","-\frac{2\,x\,\sqrt{x^5+1}\,\sqrt{\frac{a}{x^7}}}{5}","Not used",1,"-(2*x*(x^5 + 1)^(1/2)*(a/x^7)^(1/2))/5","B"
370,1,29,49,2.671826,"\text{Not used}","int((a/x^17)^(1/2)/(x^5 + 1)^(1/2),x)","\frac{\sqrt{\frac{a}{x^{17}}}\,\left(\frac{4\,x^{11}}{15}+\frac{2\,x^6}{15}-\frac{2\,x}{15}\right)}{\sqrt{x^5+1}}","Not used",1,"((a/x^17)^(1/2)*((2*x^6)/15 - (2*x)/15 + (4*x^11)/15))/(x^5 + 1)^(1/2)","B"
371,0,-1,37,0.000000,"\text{Not used}","int(-(a*x^6)^(1/2)/(x*(x^4 - 1)),x)","-\int \frac{\sqrt{a\,x^6}}{x\,\left(x^4-1\right)} \,d x","Not used",1,"-int((a*x^6)^(1/2)/(x*(x^4 - 1)), x)","F"
372,0,-1,37,0.000000,"\text{Not used}","int((a*x^6)^(1/2)/(x - x^5),x)","\int \frac{\sqrt{a\,x^6}}{x-x^5} \,d x","Not used",1,"int((a*x^6)^(1/2)/(x - x^5), x)","F"
373,0,-1,71,0.000000,"\text{Not used}","int(-(a*x^6)^(3/2)/(x*(x^4 - 1)),x)","-\int \frac{{\left(a\,x^6\right)}^{3/2}}{x\,\left(x^4-1\right)} \,d x","Not used",1,"-int((a*x^6)^(3/2)/(x*(x^4 - 1)), x)","F"
374,0,-1,49,0.000000,"\text{Not used}","int((a*x^6)^(1/2)/(x*(x^4 - 1)) - 1/(x^4 - 1),x)","\int \frac{\sqrt{a\,x^6}}{x\,\left(x^4-1\right)}-\frac{1}{x^4-1} \,d x","Not used",1,"int((a*x^6)^(1/2)/(x*(x^4 - 1)) - 1/(x^4 - 1), x)","F"
375,0,-1,49,0.000000,"\text{Not used}","int(- 1/(x^4 - 1) - (a*x^6)^(1/2)/(x - x^5),x)","\int -\frac{1}{x^4-1}-\frac{\sqrt{a\,x^6}}{x-x^5} \,d x","Not used",1,"int(- 1/(x^4 - 1) - (a*x^6)^(1/2)/(x - x^5), x)","F"
376,0,-1,44,0.000000,"\text{Not used}","int((a*x^3)^(1/2)/(x - x^3),x)","\int \frac{\sqrt{a\,x^3}}{x-x^3} \,d x","Not used",1,"int((a*x^3)^(1/2)/(x - x^3), x)","F"
377,0,-1,44,0.000000,"\text{Not used}","int((a*x^4)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^4}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((a*x^4)^(1/2)/(x^2 + 1)^(1/2), x)","F"
378,0,-1,83,0.000000,"\text{Not used}","int((a*x^3)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^3}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((a*x^3)^(1/2)/(x^2 + 1)^(1/2), x)","F"
379,1,19,22,2.674164,"\text{Not used}","int((a*x^2)^(1/2)/(x^2 + 1)^(1/2),x)","\frac{\sqrt{a}\,\sqrt{x^2+1}\,\sqrt{x^2}}{x}","Not used",1,"(a^(1/2)*(x^2 + 1)^(1/2)*(x^2)^(1/2))/x","B"
380,0,-1,131,0.000000,"\text{Not used}","int((a*x)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((a*x)^(1/2)/(x^2 + 1)^(1/2), x)","F"
381,0,-1,54,0.000000,"\text{Not used}","int((a/x)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((a/x)^(1/2)/(x^2 + 1)^(1/2), x)","F"
382,0,-1,22,0.000000,"\text{Not used}","int((a/x^2)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((a/x^2)^(1/2)/(x^2 + 1)^(1/2), x)","F"
383,0,-1,159,0.000000,"\text{Not used}","int((a/x^3)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((a/x^3)^(1/2)/(x^2 + 1)^(1/2), x)","F"
384,1,18,21,2.870377,"\text{Not used}","int((a/x^4)^(1/2)/(x^2 + 1)^(1/2),x)","-\sqrt{a}\,x\,\sqrt{x^2+1}\,\sqrt{\frac{1}{x^4}}","Not used",1,"-a^(1/2)*x*(x^2 + 1)^(1/2)*(1/x^4)^(1/2)","B"
385,1,20,25,2.911778,"\text{Not used}","int((a*x^4)^(1/2)/(x^3 + 1)^(1/2),x)","\frac{2\,\sqrt{a}\,\sqrt{x^3+1}\,\sqrt{x^4}}{3\,x^2}","Not used",1,"(2*a^(1/2)*(x^3 + 1)^(1/2)*(x^4)^(1/2))/(3*x^2)","B"
386,0,-1,292,0.000000,"\text{Not used}","int((a*x^3)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^3}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a*x^3)^(1/2)/(x^3 + 1)^(1/2), x)","F"
387,0,-1,260,0.000000,"\text{Not used}","int((a*x^2)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^2}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a*x^2)^(1/2)/(x^3 + 1)^(1/2), x)","F"
388,0,-1,23,0.000000,"\text{Not used}","int((a*x)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{a\,x}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a*x)^(1/2)/(x^3 + 1)^(1/2), x)","F"
389,0,-1,116,0.000000,"\text{Not used}","int((a/x)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a/x)^(1/2)/(x^3 + 1)^(1/2), x)","F"
390,0,-1,24,0.000000,"\text{Not used}","int((a/x^2)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a/x^2)^(1/2)/(x^3 + 1)^(1/2), x)","F"
391,0,-1,312,0.000000,"\text{Not used}","int((a/x^3)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a/x^3)^(1/2)/(x^3 + 1)^(1/2), x)","F"
392,0,-1,281,0.000000,"\text{Not used}","int((a/x^4)^(1/2)/(x^3 + 1)^(1/2),x)","\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{x^3+1}} \,d x","Not used",1,"int((a/x^4)^(1/2)/(x^3 + 1)^(1/2), x)","F"
393,0,-1,37,0.000000,"\text{Not used}","int((a*x^(2*n))^(1/2)/(x^n + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^{2\,n}}}{\sqrt{x^n+1}} \,d x","Not used",1,"int((a*x^(2*n))^(1/2)/(x^n + 1)^(1/2), x)","F"
394,0,-1,48,0.000000,"\text{Not used}","int((a*x^n)^(1/2)/(x^n + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^n}}{\sqrt{x^n+1}} \,d x","Not used",1,"int((a*x^n)^(1/2)/(x^n + 1)^(1/2), x)","F"
395,0,-1,52,0.000000,"\text{Not used}","int((a*x^(n/2))^(1/2)/(x^n + 1)^(1/2),x)","\int \frac{\sqrt{a\,x^{n/2}}}{\sqrt{x^n+1}} \,d x","Not used",1,"int((a*x^(n/2))^(1/2)/(x^n + 1)^(1/2), x)","F"
396,1,43,34,2.888365,"\text{Not used}","int((a*x^(2*n))^(1/2)/(x^n + 1)^(1/2) + (2*(a*x^(2*n))^(1/2))/(x^n*(x^n + 1)^(1/2)*(n + 2)),x)","\frac{\sqrt{a\,x^{2\,n}}\,\left(\frac{2\,x}{n+2}+\frac{2\,x^{n+1}}{n+2}\right)}{x^n\,\sqrt{x^n+1}}","Not used",1,"((a*x^(2*n))^(1/2)*((2*x)/(n + 2) + (2*x^(n + 1))/(n + 2)))/(x^n*(x^n + 1)^(1/2))","B"
397,0,-1,114,0.000000,"\text{Not used}","int((a*x)^(1/2)/((e + f*x)^(1/2)*(d + e*x)^(1/2)),x)","\int \frac{\sqrt{a\,x}}{\sqrt{e+f\,x}\,\sqrt{d+e\,x}} \,d x","Not used",1,"int((a*x)^(1/2)/((e + f*x)^(1/2)*(d + e*x)^(1/2)), x)","F"
398,1,16,16,3.399901,"\text{Not used}","int((a*x^m)^r,x)","\frac{x\,{\left(a\,x^m\right)}^r}{m\,r+1}","Not used",1,"(x*(a*x^m)^r)/(m*r + 1)","B"
399,1,26,26,2.917589,"\text{Not used}","int((a*x^m)^r*(b*x^n)^s,x)","\frac{x\,{\left(a\,x^m\right)}^r\,{\left(b\,x^n\right)}^s}{m\,r+n\,s+1}","Not used",1,"(x*(a*x^m)^r*(b*x^n)^s)/(m*r + n*s + 1)","B"
400,1,36,36,3.102705,"\text{Not used}","int((a*x^m)^r*(b*x^n)^s*(c*x^p)^t,x)","\frac{x\,{\left(a\,x^m\right)}^r\,{\left(b\,x^n\right)}^s\,{\left(c\,x^p\right)}^t}{m\,r+n\,s+p\,t+1}","Not used",1,"(x*(a*x^m)^r*(b*x^n)^s*(c*x^p)^t)/(m*r + n*s + p*t + 1)","B"
401,1,179,147,2.954175,"\text{Not used}","int(x^2/((a + b*x)^(1/2) + (c + b*x)^(1/2)),x)","\frac{2\,x^3\,\sqrt{a+b\,x}}{7\,\left(a-c\right)}-\frac{2\,x^3\,\sqrt{c+b\,x}}{7\,\left(a-c\right)}+\frac{16\,a^3\,\sqrt{a+b\,x}}{105\,b^3\,\left(a-c\right)}-\frac{16\,c^3\,\sqrt{c+b\,x}}{105\,b^3\,\left(a-c\right)}+\frac{2\,a\,x^2\,\sqrt{a+b\,x}}{35\,b\,\left(a-c\right)}-\frac{8\,a^2\,x\,\sqrt{a+b\,x}}{105\,b^2\,\left(a-c\right)}-\frac{2\,c\,x^2\,\sqrt{c+b\,x}}{35\,b\,\left(a-c\right)}+\frac{8\,c^2\,x\,\sqrt{c+b\,x}}{105\,b^2\,\left(a-c\right)}","Not used",1,"(2*x^3*(a + b*x)^(1/2))/(7*(a - c)) - (2*x^3*(c + b*x)^(1/2))/(7*(a - c)) + (16*a^3*(a + b*x)^(1/2))/(105*b^3*(a - c)) - (16*c^3*(c + b*x)^(1/2))/(105*b^3*(a - c)) + (2*a*x^2*(a + b*x)^(1/2))/(35*b*(a - c)) - (8*a^2*x*(a + b*x)^(1/2))/(105*b^2*(a - c)) - (2*c*x^2*(c + b*x)^(1/2))/(35*b*(a - c)) + (8*c^2*x*(c + b*x)^(1/2))/(105*b^2*(a - c))","B"
402,1,129,95,2.702951,"\text{Not used}","int(x/((a + b*x)^(1/2) + (c + b*x)^(1/2)),x)","\frac{2\,x^2\,\sqrt{a+b\,x}}{5\,\left(a-c\right)}-\frac{2\,x^2\,\sqrt{c+b\,x}}{5\,\left(a-c\right)}-\frac{4\,a^2\,\sqrt{a+b\,x}}{15\,b^2\,\left(a-c\right)}+\frac{4\,c^2\,\sqrt{c+b\,x}}{15\,b^2\,\left(a-c\right)}+\frac{2\,a\,x\,\sqrt{a+b\,x}}{15\,b\,\left(a-c\right)}-\frac{2\,c\,x\,\sqrt{c+b\,x}}{15\,b\,\left(a-c\right)}","Not used",1,"(2*x^2*(a + b*x)^(1/2))/(5*(a - c)) - (2*x^2*(c + b*x)^(1/2))/(5*(a - c)) - (4*a^2*(a + b*x)^(1/2))/(15*b^2*(a - c)) + (4*c^2*(c + b*x)^(1/2))/(15*b^2*(a - c)) + (2*a*x*(a + b*x)^(1/2))/(15*b*(a - c)) - (2*c*x*(c + b*x)^(1/2))/(15*b*(a - c))","B"
403,1,79,47,2.705746,"\text{Not used}","int(1/((a + b*x)^(1/2) + (c + b*x)^(1/2)),x)","\frac{2\,x\,\sqrt{a+b\,x}}{3\,\left(a-c\right)}-\frac{2\,x\,\sqrt{c+b\,x}}{3\,\left(a-c\right)}+\frac{2\,a\,\sqrt{a+b\,x}}{3\,b\,\left(a-c\right)}-\frac{2\,c\,\sqrt{c+b\,x}}{3\,b\,\left(a-c\right)}","Not used",1,"(2*x*(a + b*x)^(1/2))/(3*(a - c)) - (2*x*(c + b*x)^(1/2))/(3*(a - c)) + (2*a*(a + b*x)^(1/2))/(3*b*(a - c)) - (2*c*(c + b*x)^(1/2))/(3*b*(a - c))","B"
404,1,2983,97,18.079565,"\text{Not used}","int(1/(x*((a + b*x)^(1/2) + (c + b*x)^(1/2))),x)","-\frac{c^2\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)-4\,c^{3/2}\,\sqrt{c+b\,x}+4\,c^2-c^{3/2}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\sqrt{a+b\,x}-c^{3/2}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\sqrt{c+b\,x}+\mathrm{atan}\left(\frac{-a^{7/2}\,c\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^3\,c^{3/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^2\,c^{5/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^2\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a\,c^3\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^3\,c\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{3/2}\,c^{5/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^{3/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^2\,c^2\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,4{}\mathrm{i}-a^{3/2}\,c^{5/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^{5/2}\,c^{3/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}}{2\,a^5\,c^{3/2}-4\,a^4\,c^{5/2}+2\,a^{5/2}\,c^4+2\,a^3\,c^{7/2}-4\,a^{7/2}\,c^3+2\,a^{9/2}\,c^2-2\,a^2\,c^4\,\sqrt{a+b\,x}+4\,a^3\,c^3\,\sqrt{a+b\,x}-2\,a^4\,c^2\,\sqrt{a+b\,x}-2\,a^{3/2}\,c^{9/2}\,\sqrt{a+b\,x}+2\,a^{5/2}\,c^{7/2}\,\sqrt{a+b\,x}+2\,a^{7/2}\,c^{5/2}\,\sqrt{a+b\,x}-2\,a^{9/2}\,c^{3/2}\,\sqrt{a+b\,x}+2\,a^2\,c^4\,\sqrt{c+b\,x}-4\,a^3\,c^3\,\sqrt{c+b\,x}+2\,a^4\,c^2\,\sqrt{c+b\,x}}\right)\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}}{\sqrt{c}\,\left(\sqrt{a}-\sqrt{c}\right)\,{\left(\sqrt{a}+\sqrt{c}\right)}^2\,\left(\sqrt{a+b\,x}+\sqrt{c+b\,x}-\sqrt{a}-\sqrt{c}\right)}+\frac{4\,a^{3/2}\,\sqrt{c}\,\sqrt{c+b\,x}-4\,a^{3/2}\,c-8\,a\,c^{3/2}-3\,a\,c^{3/2}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)-3\,a^{3/2}\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)+8\,a\,c\,\sqrt{c+b\,x}-a^2\,\sqrt{c}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)+a^{3/2}\,\sqrt{c}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\sqrt{a+b\,x}+a^{3/2}\,\sqrt{c}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\sqrt{c+b\,x}+2\,a\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\sqrt{a+b\,x}+2\,a\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\sqrt{c+b\,x}+\mathrm{atan}\left(\frac{-a^{7/2}\,c\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^3\,c^{3/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^2\,c^{5/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^2\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a\,c^3\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^3\,c\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{3/2}\,c^{5/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^{3/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^2\,c^2\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,4{}\mathrm{i}-a^{3/2}\,c^{5/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^{5/2}\,c^{3/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}}{2\,a^5\,c^{3/2}-4\,a^4\,c^{5/2}+2\,a^{5/2}\,c^4+2\,a^3\,c^{7/2}-4\,a^{7/2}\,c^3+2\,a^{9/2}\,c^2-2\,a^2\,c^4\,\sqrt{a+b\,x}+4\,a^3\,c^3\,\sqrt{a+b\,x}-2\,a^4\,c^2\,\sqrt{a+b\,x}-2\,a^{3/2}\,c^{9/2}\,\sqrt{a+b\,x}+2\,a^{5/2}\,c^{7/2}\,\sqrt{a+b\,x}+2\,a^{7/2}\,c^{5/2}\,\sqrt{a+b\,x}-2\,a^{9/2}\,c^{3/2}\,\sqrt{a+b\,x}+2\,a^2\,c^4\,\sqrt{c+b\,x}-4\,a^3\,c^3\,\sqrt{c+b\,x}+2\,a^4\,c^2\,\sqrt{c+b\,x}}\right)\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{-a^{7/2}\,c\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^3\,c^{3/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^2\,c^{5/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^2\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a\,c^3\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^3\,c\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{3/2}\,c^{5/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^{3/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^2\,c^2\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,4{}\mathrm{i}-a^{3/2}\,c^{5/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^{5/2}\,c^{3/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}}{2\,a^5\,c^{3/2}-4\,a^4\,c^{5/2}+2\,a^{5/2}\,c^4+2\,a^3\,c^{7/2}-4\,a^{7/2}\,c^3+2\,a^{9/2}\,c^2-2\,a^2\,c^4\,\sqrt{a+b\,x}+4\,a^3\,c^3\,\sqrt{a+b\,x}-2\,a^4\,c^2\,\sqrt{a+b\,x}-2\,a^{3/2}\,c^{9/2}\,\sqrt{a+b\,x}+2\,a^{5/2}\,c^{7/2}\,\sqrt{a+b\,x}+2\,a^{7/2}\,c^{5/2}\,\sqrt{a+b\,x}-2\,a^{9/2}\,c^{3/2}\,\sqrt{a+b\,x}+2\,a^2\,c^4\,\sqrt{c+b\,x}-4\,a^3\,c^3\,\sqrt{c+b\,x}+2\,a^4\,c^2\,\sqrt{c+b\,x}}\right)\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-\sqrt{c}\,\mathrm{atan}\left(\frac{-a^{7/2}\,c\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^3\,c^{3/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^2\,c^{5/2}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^2\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a\,c^3\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^3\,c\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{3/2}\,c^{5/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}+a^{5/2}\,c^{3/2}\,\sqrt{a+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^2\,c^2\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,4{}\mathrm{i}-a^{3/2}\,c^{5/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}-a^{5/2}\,c^{3/2}\,\sqrt{c+b\,x}\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}}{2\,a^5\,c^{3/2}-4\,a^4\,c^{5/2}+2\,a^{5/2}\,c^4+2\,a^3\,c^{7/2}-4\,a^{7/2}\,c^3+2\,a^{9/2}\,c^2-2\,a^2\,c^4\,\sqrt{a+b\,x}+4\,a^3\,c^3\,\sqrt{a+b\,x}-2\,a^4\,c^2\,\sqrt{a+b\,x}-2\,a^{3/2}\,c^{9/2}\,\sqrt{a+b\,x}+2\,a^{5/2}\,c^{7/2}\,\sqrt{a+b\,x}+2\,a^{7/2}\,c^{5/2}\,\sqrt{a+b\,x}-2\,a^{9/2}\,c^{3/2}\,\sqrt{a+b\,x}+2\,a^2\,c^4\,\sqrt{c+b\,x}-4\,a^3\,c^3\,\sqrt{c+b\,x}+2\,a^4\,c^2\,\sqrt{c+b\,x}}\right)\,\sqrt{a^3\,c-2\,a^2\,c^2+a\,c^3}\,2{}\mathrm{i}}{\sqrt{a}\,\sqrt{c}\,\left(\sqrt{a}-\sqrt{c}\right)\,{\left(\sqrt{a}+\sqrt{c}\right)}^2\,\left(\sqrt{a+b\,x}+\sqrt{c+b\,x}-\sqrt{a}-\sqrt{c}\right)}","Not used",1,"(atan((a^2*c^(5/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^3*c^(3/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(7/2)*c*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^2*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a*c^3*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^3*c*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(3/2)*c^(5/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^(3/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^2*c^2*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*4i - a^(3/2)*c^(5/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(5/2)*c^(3/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i)/(2*a^5*c^(3/2) - 4*a^4*c^(5/2) + 2*a^(5/2)*c^4 + 2*a^3*c^(7/2) - 4*a^(7/2)*c^3 + 2*a^(9/2)*c^2 - 2*a^2*c^4*(a + b*x)^(1/2) + 4*a^3*c^3*(a + b*x)^(1/2) - 2*a^4*c^2*(a + b*x)^(1/2) - 2*a^(3/2)*c^(9/2)*(a + b*x)^(1/2) + 2*a^(5/2)*c^(7/2)*(a + b*x)^(1/2) + 2*a^(7/2)*c^(5/2)*(a + b*x)^(1/2) - 2*a^(9/2)*c^(3/2)*(a + b*x)^(1/2) + 2*a^2*c^4*(c + b*x)^(1/2) - 4*a^3*c^3*(c + b*x)^(1/2) + 2*a^4*c^2*(c + b*x)^(1/2)))*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - 4*a^(3/2)*c - 8*a*c^(3/2) + atan((a^2*c^(5/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^3*c^(3/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(7/2)*c*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^2*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a*c^3*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^3*c*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(3/2)*c^(5/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^(3/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^2*c^2*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*4i - a^(3/2)*c^(5/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(5/2)*c^(3/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i)/(2*a^5*c^(3/2) - 4*a^4*c^(5/2) + 2*a^(5/2)*c^4 + 2*a^3*c^(7/2) - 4*a^(7/2)*c^3 + 2*a^(9/2)*c^2 - 2*a^2*c^4*(a + b*x)^(1/2) + 4*a^3*c^3*(a + b*x)^(1/2) - 2*a^4*c^2*(a + b*x)^(1/2) - 2*a^(3/2)*c^(9/2)*(a + b*x)^(1/2) + 2*a^(5/2)*c^(7/2)*(a + b*x)^(1/2) + 2*a^(7/2)*c^(5/2)*(a + b*x)^(1/2) - 2*a^(9/2)*c^(3/2)*(a + b*x)^(1/2) + 2*a^2*c^4*(c + b*x)^(1/2) - 4*a^3*c^3*(c + b*x)^(1/2) + 2*a^4*c^2*(c + b*x)^(1/2)))*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + 4*a^(3/2)*c^(1/2)*(c + b*x)^(1/2) - 3*a*c^(3/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2))) - 3*a^(3/2)*c*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2))) + 8*a*c*(c + b*x)^(1/2) - c^(1/2)*atan((a^2*c^(5/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^3*c^(3/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(7/2)*c*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^2*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a*c^3*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^3*c*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(3/2)*c^(5/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^(3/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^2*c^2*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*4i - a^(3/2)*c^(5/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(5/2)*c^(3/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i)/(2*a^5*c^(3/2) - 4*a^4*c^(5/2) + 2*a^(5/2)*c^4 + 2*a^3*c^(7/2) - 4*a^(7/2)*c^3 + 2*a^(9/2)*c^2 - 2*a^2*c^4*(a + b*x)^(1/2) + 4*a^3*c^3*(a + b*x)^(1/2) - 2*a^4*c^2*(a + b*x)^(1/2) - 2*a^(3/2)*c^(9/2)*(a + b*x)^(1/2) + 2*a^(5/2)*c^(7/2)*(a + b*x)^(1/2) + 2*a^(7/2)*c^(5/2)*(a + b*x)^(1/2) - 2*a^(9/2)*c^(3/2)*(a + b*x)^(1/2) + 2*a^2*c^4*(c + b*x)^(1/2) - 4*a^3*c^3*(c + b*x)^(1/2) + 2*a^4*c^2*(c + b*x)^(1/2)))*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^2*c^(1/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2))) + a^(3/2)*c^(1/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(a + b*x)^(1/2) + a^(3/2)*c^(1/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(c + b*x)^(1/2) + 2*a*c*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(a + b*x)^(1/2) + 2*a*c*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(c + b*x)^(1/2))/(a^(1/2)*c^(1/2)*(a^(1/2) - c^(1/2))*(a^(1/2) + c^(1/2))^2*((a + b*x)^(1/2) + (c + b*x)^(1/2) - a^(1/2) - c^(1/2))) - (c^2*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2))) - 4*c^(3/2)*(c + b*x)^(1/2) + 4*c^2 + atan((a^2*c^(5/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^3*c^(3/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(7/2)*c*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^2*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a*c^3*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^3*c*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(3/2)*c^(5/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i + a^(5/2)*c^(3/2)*(a + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^2*c^2*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*4i - a^(3/2)*c^(5/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - a^(5/2)*c^(3/2)*(c + b*x)^(1/2)*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i)/(2*a^5*c^(3/2) - 4*a^4*c^(5/2) + 2*a^(5/2)*c^4 + 2*a^3*c^(7/2) - 4*a^(7/2)*c^3 + 2*a^(9/2)*c^2 - 2*a^2*c^4*(a + b*x)^(1/2) + 4*a^3*c^3*(a + b*x)^(1/2) - 2*a^4*c^2*(a + b*x)^(1/2) - 2*a^(3/2)*c^(9/2)*(a + b*x)^(1/2) + 2*a^(5/2)*c^(7/2)*(a + b*x)^(1/2) + 2*a^(7/2)*c^(5/2)*(a + b*x)^(1/2) - 2*a^(9/2)*c^(3/2)*(a + b*x)^(1/2) + 2*a^2*c^4*(c + b*x)^(1/2) - 4*a^3*c^3*(c + b*x)^(1/2) + 2*a^4*c^2*(c + b*x)^(1/2)))*(a*c^3 + a^3*c - 2*a^2*c^2)^(1/2)*2i - c^(3/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(a + b*x)^(1/2) - c^(3/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(c + b*x)^(1/2))/(c^(1/2)*(a^(1/2) - c^(1/2))*(a^(1/2) + c^(1/2))^2*((a + b*x)^(1/2) + (c + b*x)^(1/2) - a^(1/2) - c^(1/2)))","B"
405,1,2642,103,18.883896,"\text{Not used}","int(1/(x^2*((a + b*x)^(1/2) + (c + b*x)^(1/2))),x)","-\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\left(\frac{b}{2\,\sqrt{a}\,c}-\frac{b\,\left(\sqrt{a}+\sqrt{c}\right)}{2\,c\,\left(a-c\right)}\right)-\frac{\frac{\sqrt{a}\,b}{4\,\left(a\,c-a^2\right)}-\frac{b\,\sqrt{c}}{4\,\left(a\,c-c^2\right)}-\frac{\left(\frac{\sqrt{a}\,\left(\frac{b\,a^2}{4}+\frac{b\,a\,c}{4}-\frac{b\,c^2}{4}\right)}{a^3\,c-a^2\,c^2}-\frac{\sqrt{c}\,\left(-\frac{b\,a^2}{4}+\frac{b\,a\,c}{4}+\frac{b\,c^2}{4}\right)}{a\,c^3-a^2\,c^2}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}+\frac{\left(\frac{\sqrt{a}\,\left(\frac{a\,b}{4}-\frac{3\,b\,c}{4}\right)}{a\,c^2-a^2\,c}-\frac{\sqrt{c}\,\left(\frac{3\,a\,b}{4}-\frac{b\,c}{4}\right)}{a\,c^2-a^2\,c}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}}{\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3}-\frac{\left(a+c\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}}-\frac{b\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{4\,\sqrt{a}\,\sqrt{c}\,\left(\sqrt{a}-\sqrt{c}\right)\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{a^3\,b\,c^{7/2}-a^{7/2}\,b\,c^3-a^2\,b\,c^{9/2}+a^{9/2}\,b\,c^2}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(2\,a^{3/2}\,b\,c^5-2\,a^5\,b\,c^{3/2}+2\,a^4\,b\,c^{5/2}-2\,a^{5/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}-\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\left(\frac{a^{5/2}\,c^{11/2}-a^{7/2}\,c^{9/2}-a^{9/2}\,c^{7/2}+a^{11/2}\,c^{5/2}}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^6\,c^2-12\,a^5\,c^3+16\,a^4\,c^4-12\,a^3\,c^5+4\,a^2\,c^6\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}\right)\,1{}\mathrm{i}}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}+\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{a^3\,b\,c^{7/2}-a^{7/2}\,b\,c^3-a^2\,b\,c^{9/2}+a^{9/2}\,b\,c^2}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(2\,a^{3/2}\,b\,c^5-2\,a^5\,b\,c^{3/2}+2\,a^4\,b\,c^{5/2}-2\,a^{5/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}+\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\left(\frac{a^{5/2}\,c^{11/2}-a^{7/2}\,c^{9/2}-a^{9/2}\,c^{7/2}+a^{11/2}\,c^{5/2}}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^6\,c^2-12\,a^5\,c^3+16\,a^4\,c^4-12\,a^3\,c^5+4\,a^2\,c^6\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}\right)\,1{}\mathrm{i}}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}}{\frac{\frac{a^{3/2}\,b^2\,c^{7/2}}{2}-a^{5/2}\,b^2\,c^{5/2}+\frac{a^{7/2}\,b^2\,c^{3/2}}{2}}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(a^{3/2}\,b^2\,c^{7/2}-2\,a^{5/2}\,b^2\,c^{5/2}+a^{7/2}\,b^2\,c^{3/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}-\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{a^3\,b\,c^{7/2}-a^{7/2}\,b\,c^3-a^2\,b\,c^{9/2}+a^{9/2}\,b\,c^2}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(2\,a^{3/2}\,b\,c^5-2\,a^5\,b\,c^{3/2}+2\,a^4\,b\,c^{5/2}-2\,a^{5/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}-\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\left(\frac{a^{5/2}\,c^{11/2}-a^{7/2}\,c^{9/2}-a^{9/2}\,c^{7/2}+a^{11/2}\,c^{5/2}}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^6\,c^2-12\,a^5\,c^3+16\,a^4\,c^4-12\,a^3\,c^5+4\,a^2\,c^6\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}\right)}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}+\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{a^3\,b\,c^{7/2}-a^{7/2}\,b\,c^3-a^2\,b\,c^{9/2}+a^{9/2}\,b\,c^2}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(2\,a^{3/2}\,b\,c^5-2\,a^5\,b\,c^{3/2}+2\,a^4\,b\,c^{5/2}-2\,a^{5/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}+\frac{b\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\left(\frac{a^{5/2}\,c^{11/2}-a^{7/2}\,c^{9/2}-a^{9/2}\,c^{7/2}+a^{11/2}\,c^{5/2}}{a^5\,c^3-2\,a^4\,c^4+a^3\,c^5}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^6\,c^2-12\,a^5\,c^3+16\,a^4\,c^4-12\,a^3\,c^5+4\,a^2\,c^6\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^5\,c^3-2\,a^4\,c^4+a^3\,c^5\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}\right)}{2\,\left(2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}\right)}}\right)\,\left(a\,\sqrt{c}+\sqrt{a}\,c\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,1{}\mathrm{i}}{2\,a^2\,c^3-2\,a^3\,c^2+a^{3/2}\,c^{7/2}-a^{7/2}\,c^{3/2}}","Not used",1,"(b*atan(((b*(a*c^(1/2) + a^(1/2)*c)*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((a^3*b*c^(7/2) - a^(7/2)*b*c^3 - a^2*b*c^(9/2) + a^(9/2)*b*c^2)/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(2*a^(3/2)*b*c^5 - 2*a^5*b*c^(3/2) + 2*a^4*b*c^(5/2) - 2*a^(5/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)) - (b*(a*c^(1/2) + a^(1/2)*c)*((a^(5/2)*c^(11/2) - a^(7/2)*c^(9/2) - a^(9/2)*c^(7/2) + a^(11/2)*c^(5/2))/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^6 - 12*a^3*c^5 + 16*a^4*c^4 - 12*a^5*c^3 + 4*a^6*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2))/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2))))*1i)/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2))) + (b*(a*c^(1/2) + a^(1/2)*c)*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((a^3*b*c^(7/2) - a^(7/2)*b*c^3 - a^2*b*c^(9/2) + a^(9/2)*b*c^2)/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(2*a^(3/2)*b*c^5 - 2*a^5*b*c^(3/2) + 2*a^4*b*c^(5/2) - 2*a^(5/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)) + (b*(a*c^(1/2) + a^(1/2)*c)*((a^(5/2)*c^(11/2) - a^(7/2)*c^(9/2) - a^(9/2)*c^(7/2) + a^(11/2)*c^(5/2))/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^6 - 12*a^3*c^5 + 16*a^4*c^4 - 12*a^5*c^3 + 4*a^6*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2))/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2))))*1i)/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2))))/(((a^(3/2)*b^2*c^(7/2))/2 - a^(5/2)*b^2*c^(5/2) + (a^(7/2)*b^2*c^(3/2))/2)/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(a^(3/2)*b^2*c^(7/2) - 2*a^(5/2)*b^2*c^(5/2) + a^(7/2)*b^2*c^(3/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)) - (b*(a*c^(1/2) + a^(1/2)*c)*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((a^3*b*c^(7/2) - a^(7/2)*b*c^3 - a^2*b*c^(9/2) + a^(9/2)*b*c^2)/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(2*a^(3/2)*b*c^5 - 2*a^5*b*c^(3/2) + 2*a^4*b*c^(5/2) - 2*a^(5/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)) - (b*(a*c^(1/2) + a^(1/2)*c)*((a^(5/2)*c^(11/2) - a^(7/2)*c^(9/2) - a^(9/2)*c^(7/2) + a^(11/2)*c^(5/2))/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^6 - 12*a^3*c^5 + 16*a^4*c^4 - 12*a^5*c^3 + 4*a^6*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2))/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2)))))/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2))) + (b*(a*c^(1/2) + a^(1/2)*c)*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((a^3*b*c^(7/2) - a^(7/2)*b*c^3 - a^2*b*c^(9/2) + a^(9/2)*b*c^2)/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(2*a^(3/2)*b*c^5 - 2*a^5*b*c^(3/2) + 2*a^4*b*c^(5/2) - 2*a^(5/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)) + (b*(a*c^(1/2) + a^(1/2)*c)*((a^(5/2)*c^(11/2) - a^(7/2)*c^(9/2) - a^(9/2)*c^(7/2) + a^(11/2)*c^(5/2))/(a^3*c^5 - 2*a^4*c^4 + a^5*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^6 - 12*a^3*c^5 + 16*a^4*c^4 - 12*a^5*c^3 + 4*a^6*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^5 - 2*a^4*c^4 + a^5*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2))/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2)))))/(2*(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2)))))*(a*c^(1/2) + a^(1/2)*c)*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*1i)/(2*a^2*c^3 - 2*a^3*c^2 + a^(3/2)*c^(7/2) - a^(7/2)*c^(3/2)) - ((a^(1/2)*b)/(4*(a*c - a^2)) - (b*c^(1/2))/(4*(a*c - c^2)) - (((a^(1/2)*((a^2*b)/4 - (b*c^2)/4 + (a*b*c)/4))/(a^3*c - a^2*c^2) - (c^(1/2)*((b*c^2)/4 - (a^2*b)/4 + (a*b*c)/4))/(a*c^3 - a^2*c^2))*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 + (((a^(1/2)*((a*b)/4 - (3*b*c)/4))/(a*c^2 - a^2*c) - (c^(1/2)*((3*a*b)/4 - (b*c)/4))/(a*c^2 - a^2*c))*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)))/(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)) + ((a + b*x)^(1/2) - a^(1/2))^3/((c + b*x)^(1/2) - c^(1/2))^3 - ((a + c)*((a + b*x)^(1/2) - a^(1/2))^2)/(a^(1/2)*c^(1/2)*((c + b*x)^(1/2) - c^(1/2))^2)) - log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(b/(2*a^(1/2)*c) - (b*(a^(1/2) + c^(1/2)))/(2*c*(a - c))) - (b*((a + b*x)^(1/2) - a^(1/2)))/(4*a^(1/2)*c^(1/2)*(a^(1/2) - c^(1/2))*((c + b*x)^(1/2) - c^(1/2)))","B"
406,1,1358,228,81.167177,"\text{Not used}","int(x^2/((a + b*x)^(1/2) + (c + b*x)^(1/2))^2,x)","\frac{x^3\,\left(a+c\right)}{3\,{\left(a-c\right)}^2}-\frac{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{15}\,\left(\frac{5\,a^2}{16}+\frac{3\,a\,c}{8}+\frac{5\,c^2}{16}\right)}{b^3\,{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{15}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(-\frac{115\,a^4}{48}+\frac{23\,a^3\,c}{12}+\frac{349\,a^2\,c^2}{8}+\frac{23\,a\,c^3}{12}-\frac{115\,c^4}{48}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{13}\,\left(-\frac{115\,a^4}{48}+\frac{23\,a^3\,c}{12}+\frac{349\,a^2\,c^2}{8}+\frac{23\,a\,c^3}{12}-\frac{115\,c^4}{48}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{13}\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5\,\left(\frac{383\,a^4}{48}+\frac{3917\,a^3\,c}{12}+\frac{7279\,a^2\,c^2}{8}+\frac{3917\,a\,c^3}{12}+\frac{383\,c^4}{48}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^5\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{11}\,\left(\frac{383\,a^4}{48}+\frac{3917\,a^3\,c}{12}+\frac{7279\,a^2\,c^2}{8}+\frac{3917\,a\,c^3}{12}+\frac{383\,c^4}{48}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{11}\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^7\,\left(\frac{2789\,a^4}{48}+\frac{17567\,a^3\,c}{12}+\frac{28213\,a^2\,c^2}{8}+\frac{17567\,a\,c^3}{12}+\frac{2789\,c^4}{48}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^7\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^9\,\left(\frac{2789\,a^4}{48}+\frac{17567\,a^3\,c}{12}+\frac{28213\,a^2\,c^2}{8}+\frac{17567\,a\,c^3}{12}+\frac{2789\,c^4}{48}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^9\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(\frac{5\,a^2}{16}+\frac{3\,a\,c}{8}+\frac{5\,c^2}{16}\right)}{b^3\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)}-\frac{\sqrt{a}\,\sqrt{c}\,\left(192\,a^2\,c+192\,a\,c^2\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^4\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}-\frac{\sqrt{a}\,\sqrt{c}\,\left(192\,a^2\,c+192\,a\,c^2\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{12}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{12}\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}-\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(256\,a^3+\frac{5120\,a^2\,c}{3}+\frac{5120\,a\,c^2}{3}+256\,c^3\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^6\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}-\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{10}\,\left(256\,a^3+\frac{5120\,a^2\,c}{3}+\frac{5120\,a\,c^2}{3}+256\,c^3\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{10}\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}-\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8\,\left(512\,a^3+\frac{10112\,a^2\,c}{3}+\frac{10112\,a\,c^2}{3}+512\,c^3\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^8\,\left(a^2\,b^3-2\,a\,b^3\,c+b^3\,c^2\right)}}{\frac{28\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^4}-\frac{8\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}-\frac{56\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^6}+\frac{70\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^8}-\frac{56\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{10}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{10}}+\frac{28\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{12}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{12}}-\frac{8\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{14}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{14}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{16}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{16}}+1}+\frac{b\,x^4}{2\,{\left(a-c\right)}^2}+\frac{\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\left(5\,a^2+6\,a\,c+5\,c^2\right)}{16\,b^3}","Not used",1,"(x^3*(a + c))/(3*(a - c)^2) - ((((a + b*x)^(1/2) - a^(1/2))^15*((3*a*c)/8 + (5*a^2)/16 + (5*c^2)/16))/(b^3*((c + b*x)^(1/2) - c^(1/2))^15) + (((a + b*x)^(1/2) - a^(1/2))^3*((23*a*c^3)/12 + (23*a^3*c)/12 - (115*a^4)/48 - (115*c^4)/48 + (349*a^2*c^2)/8))/(((c + b*x)^(1/2) - c^(1/2))^3*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) + (((a + b*x)^(1/2) - a^(1/2))^13*((23*a*c^3)/12 + (23*a^3*c)/12 - (115*a^4)/48 - (115*c^4)/48 + (349*a^2*c^2)/8))/(((c + b*x)^(1/2) - c^(1/2))^13*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) + (((a + b*x)^(1/2) - a^(1/2))^5*((3917*a*c^3)/12 + (3917*a^3*c)/12 + (383*a^4)/48 + (383*c^4)/48 + (7279*a^2*c^2)/8))/(((c + b*x)^(1/2) - c^(1/2))^5*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) + (((a + b*x)^(1/2) - a^(1/2))^11*((3917*a*c^3)/12 + (3917*a^3*c)/12 + (383*a^4)/48 + (383*c^4)/48 + (7279*a^2*c^2)/8))/(((c + b*x)^(1/2) - c^(1/2))^11*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) + (((a + b*x)^(1/2) - a^(1/2))^7*((17567*a*c^3)/12 + (17567*a^3*c)/12 + (2789*a^4)/48 + (2789*c^4)/48 + (28213*a^2*c^2)/8))/(((c + b*x)^(1/2) - c^(1/2))^7*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) + (((a + b*x)^(1/2) - a^(1/2))^9*((17567*a*c^3)/12 + (17567*a^3*c)/12 + (2789*a^4)/48 + (2789*c^4)/48 + (28213*a^2*c^2)/8))/(((c + b*x)^(1/2) - c^(1/2))^9*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) + (((a + b*x)^(1/2) - a^(1/2))*((3*a*c)/8 + (5*a^2)/16 + (5*c^2)/16))/(b^3*((c + b*x)^(1/2) - c^(1/2))) - (a^(1/2)*c^(1/2)*(192*a*c^2 + 192*a^2*c)*((a + b*x)^(1/2) - a^(1/2))^4)/(((c + b*x)^(1/2) - c^(1/2))^4*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) - (a^(1/2)*c^(1/2)*(192*a*c^2 + 192*a^2*c)*((a + b*x)^(1/2) - a^(1/2))^12)/(((c + b*x)^(1/2) - c^(1/2))^12*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) - (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^6*((5120*a*c^2)/3 + (5120*a^2*c)/3 + 256*a^3 + 256*c^3))/(((c + b*x)^(1/2) - c^(1/2))^6*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) - (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^10*((5120*a*c^2)/3 + (5120*a^2*c)/3 + 256*a^3 + 256*c^3))/(((c + b*x)^(1/2) - c^(1/2))^10*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)) - (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^8*((10112*a*c^2)/3 + (10112*a^2*c)/3 + 512*a^3 + 512*c^3))/(((c + b*x)^(1/2) - c^(1/2))^8*(a^2*b^3 + b^3*c^2 - 2*a*b^3*c)))/((28*((a + b*x)^(1/2) - a^(1/2))^4)/((c + b*x)^(1/2) - c^(1/2))^4 - (8*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 - (56*((a + b*x)^(1/2) - a^(1/2))^6)/((c + b*x)^(1/2) - c^(1/2))^6 + (70*((a + b*x)^(1/2) - a^(1/2))^8)/((c + b*x)^(1/2) - c^(1/2))^8 - (56*((a + b*x)^(1/2) - a^(1/2))^10)/((c + b*x)^(1/2) - c^(1/2))^10 + (28*((a + b*x)^(1/2) - a^(1/2))^12)/((c + b*x)^(1/2) - c^(1/2))^12 - (8*((a + b*x)^(1/2) - a^(1/2))^14)/((c + b*x)^(1/2) - c^(1/2))^14 + ((a + b*x)^(1/2) - a^(1/2))^16/((c + b*x)^(1/2) - c^(1/2))^16 + 1) + (b*x^4)/(2*(a - c)^2) + (atanh(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(6*a*c + 5*a^2 + 5*c^2))/(16*b^3)","B"
407,1,1012,165,37.520779,"\text{Not used}","int(x/((a + b*x)^(1/2) + (c + b*x)^(1/2))^2,x)","\frac{\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(\frac{a}{2}+\frac{c}{2}\right)}{b^2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{11}\,\left(\frac{a}{2}+\frac{c}{2}\right)}{b^2\,{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{11}}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(\frac{17\,a^3}{6}+\frac{101\,a^2\,c}{2}+\frac{101\,a\,c^2}{2}+\frac{17\,c^3}{6}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^9\,\left(\frac{17\,a^3}{6}+\frac{101\,a^2\,c}{2}+\frac{101\,a\,c^2}{2}+\frac{17\,c^3}{6}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^9\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5\,\left(19\,a^3+269\,a^2\,c+269\,a\,c^2+19\,c^3\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^5\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^7\,\left(19\,a^3+269\,a^2\,c+269\,a\,c^2+19\,c^3\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^7\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}+\frac{16\,a^{3/2}\,c^{3/2}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}+\frac{16\,a^{3/2}\,c^{3/2}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{10}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{10}\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(64\,a^2+192\,a\,c+64\,c^2\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^4\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8\,\left(64\,a^2+192\,a\,c+64\,c^2\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^8\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(128\,a^2+\frac{1312\,a\,c}{3}+128\,c^2\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^6\,\left(a^2\,b^2-2\,a\,b^2\,c+b^2\,c^2\right)}}{\frac{15\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^4}-\frac{6\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}-\frac{20\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^6}+\frac{15\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^8}-\frac{6\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{10}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{10}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{12}}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^{12}}+1}-\frac{\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\left(a+c\right)}{2\,b^2}+\frac{x^2\,\left(a+c\right)}{2\,{\left(a-c\right)}^2}+\frac{2\,b\,x^3}{3\,{\left(a-c\right)}^2}","Not used",1,"((((a + b*x)^(1/2) - a^(1/2))*(a/2 + c/2))/(b^2*((c + b*x)^(1/2) - c^(1/2))) + (((a + b*x)^(1/2) - a^(1/2))^11*(a/2 + c/2))/(b^2*((c + b*x)^(1/2) - c^(1/2))^11) - (((a + b*x)^(1/2) - a^(1/2))^3*((101*a*c^2)/2 + (101*a^2*c)/2 + (17*a^3)/6 + (17*c^3)/6))/(((c + b*x)^(1/2) - c^(1/2))^3*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) - (((a + b*x)^(1/2) - a^(1/2))^9*((101*a*c^2)/2 + (101*a^2*c)/2 + (17*a^3)/6 + (17*c^3)/6))/(((c + b*x)^(1/2) - c^(1/2))^9*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) - (((a + b*x)^(1/2) - a^(1/2))^5*(269*a*c^2 + 269*a^2*c + 19*a^3 + 19*c^3))/(((c + b*x)^(1/2) - c^(1/2))^5*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) - (((a + b*x)^(1/2) - a^(1/2))^7*(269*a*c^2 + 269*a^2*c + 19*a^3 + 19*c^3))/(((c + b*x)^(1/2) - c^(1/2))^7*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) + (16*a^(3/2)*c^(3/2)*((a + b*x)^(1/2) - a^(1/2))^2)/(((c + b*x)^(1/2) - c^(1/2))^2*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) + (16*a^(3/2)*c^(3/2)*((a + b*x)^(1/2) - a^(1/2))^10)/(((c + b*x)^(1/2) - c^(1/2))^10*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) + (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^4*(192*a*c + 64*a^2 + 64*c^2))/(((c + b*x)^(1/2) - c^(1/2))^4*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) + (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^8*(192*a*c + 64*a^2 + 64*c^2))/(((c + b*x)^(1/2) - c^(1/2))^8*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)) + (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^6*((1312*a*c)/3 + 128*a^2 + 128*c^2))/(((c + b*x)^(1/2) - c^(1/2))^6*(a^2*b^2 + b^2*c^2 - 2*a*b^2*c)))/((15*((a + b*x)^(1/2) - a^(1/2))^4)/((c + b*x)^(1/2) - c^(1/2))^4 - (6*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 - (20*((a + b*x)^(1/2) - a^(1/2))^6)/((c + b*x)^(1/2) - c^(1/2))^6 + (15*((a + b*x)^(1/2) - a^(1/2))^8)/((c + b*x)^(1/2) - c^(1/2))^8 - (6*((a + b*x)^(1/2) - a^(1/2))^10)/((c + b*x)^(1/2) - c^(1/2))^10 + ((a + b*x)^(1/2) - a^(1/2))^12/((c + b*x)^(1/2) - c^(1/2))^12 + 1) - (atanh(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(a + c))/(2*b^2) + (x^2*(a + c))/(2*(a - c)^2) + (2*b*x^3)/(3*(a - c)^2)","B"
408,1,110,63,0.239252,"\text{Not used}","int(1/((a + b*x)^(1/2) + (c + b*x)^(1/2))^2,x)","\frac{b\,x^2}{{\left(a-c\right)}^2}+\frac{x\,\left(a+c\right)}{{\left(a-c\right)}^2}+\frac{\ln\left(a+c+2\,\sqrt{a+b\,x}\,\sqrt{c+b\,x}+2\,b\,x\right)\,{\left(a\,b-b\,c\right)}^2}{4\,b^3\,{\left(a-c\right)}^2}-\frac{2\,\sqrt{a+b\,x}\,\sqrt{c+b\,x}\,\left(\frac{x}{2}+\frac{a\,b+b\,c}{4\,b^2}\right)}{{\left(a-c\right)}^2}","Not used",1,"(b*x^2)/(a - c)^2 + (x*(a + c))/(a - c)^2 + (log(a + c + 2*(a + b*x)^(1/2)*(c + b*x)^(1/2) + 2*b*x)*(a*b - b*c)^2)/(4*b^3*(a - c)^2) - (2*(a + b*x)^(1/2)*(c + b*x)^(1/2)*(x/2 + (a*b + b*c)/(4*b^2)))/(a - c)^2","B"
409,1,524,133,11.140825,"\text{Not used}","int(1/(x*((a + b*x)^(1/2) + (c + b*x)^(1/2))^2),x)","\frac{2\,b\,x}{{\left(a-c\right)}^2}-\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}+1\right)\,\left(\frac{4\,c}{{\left(a-c\right)}^2}+\frac{2}{a-c}\right)-\frac{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(4\,a+4\,c\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3\,\left(a^2-2\,a\,c+c^2\right)}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a+4\,c\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^2-2\,a\,c+c^2\right)}-\frac{16\,\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2\,\left(a^2-2\,a\,c+c^2\right)}}{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^4}-\frac{2\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}+1}+\frac{2\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}-1\right)\,\left(a+c\right)}{{\left(a-c\right)}^2}+\frac{\ln\left(x\right)\,\left(a+c\right)}{a^2-2\,a\,c+c^2}+\frac{2\,\sqrt{a}\,\sqrt{c}\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)}{{\left(a-c\right)}^2}-\frac{2\,\sqrt{a}\,\sqrt{c}\,\ln\left(\frac{a\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}-\sqrt{a}\,\sqrt{c}+\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}-\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}\right)}{a^2-2\,a\,c+c^2}","Not used",1,"(2*b*x)/(a - c)^2 - log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)) + 1)*((4*c)/(a - c)^2 + 2/(a - c)) - ((((a + b*x)^(1/2) - a^(1/2))^3*(4*a + 4*c))/(((c + b*x)^(1/2) - c^(1/2))^3*(a^2 - 2*a*c + c^2)) + (((a + b*x)^(1/2) - a^(1/2))*(4*a + 4*c))/(((c + b*x)^(1/2) - c^(1/2))*(a^2 - 2*a*c + c^2)) - (16*a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^2)/(((c + b*x)^(1/2) - c^(1/2))^2*(a^2 - 2*a*c + c^2)))/(((a + b*x)^(1/2) - a^(1/2))^4/((c + b*x)^(1/2) - c^(1/2))^4 - (2*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 + 1) + (2*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)) - 1)*(a + c))/(a - c)^2 + (log(x)*(a + c))/(a^2 - 2*a*c + c^2) + (2*a^(1/2)*c^(1/2)*log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2))))/(a - c)^2 - (2*a^(1/2)*c^(1/2)*log((a*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)) - a^(1/2)*c^(1/2) + (c*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)) - (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2))/(a^2 - 2*a*c + c^2)","B"
410,1,7637,141,28.822418,"\text{Not used}","int(1/(x^2*((a + b*x)^(1/2) + (c + b*x)^(1/2))^2),x)","\frac{2\,b\,\ln\left(x\right)}{a^2-2\,a\,c+c^2}-\frac{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(\frac{b\,a^2}{2}-\frac{3\,b\,a\,c}{2}+\frac{b\,c^2}{2}\right)}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2\,\left(a^3\,c-2\,a^2\,c^2+a\,c^3\right)}-\frac{b}{2\,\left(a^2-2\,a\,c+c^2\right)}+\frac{\sqrt{a}\,\sqrt{c}\,\left(\frac{a\,b}{2}+\frac{b\,c}{2}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^3\,c-2\,a^2\,c^2+a\,c^3\right)}}{\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3}-\frac{\left(a+c\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}}-\frac{\ln\left(\frac{a\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}-\sqrt{a}\,\sqrt{c}+\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}-\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,b\,\sqrt{c}\right)}{a^3\,c-2\,a^2\,c^2+a\,c^3}-\frac{a+c}{x\,\left(a^2-2\,a\,c+c^2\right)}+\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,b\,\sqrt{c}\right)}{a^3\,c-2\,a^2\,c^2+a\,c^3}+\frac{b\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{2\,{\left(a-c\right)}^2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{4\,\left(4\,a^{12}\,b^3\,c^4+8\,a^{11}\,b^3\,c^5-32\,a^{10}\,b^3\,c^6-8\,a^9\,b^3\,c^7+56\,a^8\,b^3\,c^8-8\,a^7\,b^3\,c^9-32\,a^6\,b^3\,c^{10}+8\,a^5\,b^3\,c^{11}+4\,a^4\,b^3\,c^{12}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,b\,\left(\frac{4\,\left(-4\,b\,a^{15}\,c^5+16\,b\,a^{14}\,c^6+12\,b\,a^{13}\,c^7-192\,b\,a^{12}\,c^8+504\,b\,a^{11}\,c^9-672\,b\,a^{10}\,c^{10}+504\,b\,a^9\,c^{11}-192\,b\,a^8\,c^{12}+12\,b\,a^7\,c^{13}+16\,b\,a^6\,c^{14}-4\,b\,a^5\,c^{15}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(a^{9/2}\,c^{35/2}-8\,a^{11/2}\,c^{33/2}+27\,a^{13/2}\,c^{31/2}-49\,a^{15/2}\,c^{29/2}+50\,a^{17/2}\,c^{27/2}-27\,a^{19/2}\,c^{25/2}+6\,a^{21/2}\,c^{23/2}+6\,a^{23/2}\,c^{21/2}-27\,a^{25/2}\,c^{19/2}+50\,a^{27/2}\,c^{17/2}-49\,a^{29/2}\,c^{15/2}+27\,a^{31/2}\,c^{13/2}-8\,a^{33/2}\,c^{11/2}+a^{35/2}\,c^{9/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{18}\,c^4-47\,a^{17}\,c^5+268\,a^{16}\,c^6-982\,a^{15}\,c^7+2564\,a^{14}\,c^8-4993\,a^{13}\,c^9+7404\,a^{12}\,c^{10}-8436\,a^{11}\,c^{11}+7404\,a^{10}\,c^{12}-4993\,a^9\,c^{13}+2564\,a^8\,c^{14}-982\,a^7\,c^{15}+268\,a^6\,c^{16}-47\,a^5\,c^{17}+4\,a^4\,c^{18}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{7/2}\,b\,c^{33/2}-43\,a^{9/2}\,b\,c^{31/2}+231\,a^{11/2}\,b\,c^{29/2}-749\,a^{13/2}\,b\,c^{27/2}+1505\,a^{15/2}\,b\,c^{25/2}-1770\,a^{17/2}\,b\,c^{23/2}+822\,a^{19/2}\,b\,c^{21/2}+822\,a^{21/2}\,b\,c^{19/2}-1770\,a^{23/2}\,b\,c^{17/2}+1505\,a^{25/2}\,b\,c^{15/2}-749\,a^{27/2}\,b\,c^{13/2}+231\,a^{29/2}\,b\,c^{11/2}-43\,a^{31/2}\,b\,c^{9/2}+4\,a^{33/2}\,b\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{4\,\left(a^{7/2}\,b^2\,c^{29/2}+12\,a^{9/2}\,b^2\,c^{27/2}-100\,a^{11/2}\,b^2\,c^{25/2}+285\,a^{13/2}\,b^2\,c^{23/2}-390\,a^{15/2}\,b^2\,c^{21/2}+192\,a^{17/2}\,b^2\,c^{19/2}+192\,a^{19/2}\,b^2\,c^{17/2}-390\,a^{21/2}\,b^2\,c^{15/2}+285\,a^{23/2}\,b^2\,c^{13/2}-100\,a^{25/2}\,b^2\,c^{11/2}+12\,a^{27/2}\,b^2\,c^{9/2}+a^{29/2}\,b^2\,c^{7/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,a^{14}\,b^2\,c^4-570\,a^{13}\,b^2\,c^5+2053\,a^{12}\,b^2\,c^6-4568\,a^{11}\,b^2\,c^7+7090\,a^{10}\,b^2\,c^8-8156\,a^9\,b^2\,c^9+7090\,a^8\,b^2\,c^{10}-4568\,a^7\,b^2\,c^{11}+2053\,a^6\,b^2\,c^{12}-570\,a^5\,b^2\,c^{13}+73\,a^4\,b^2\,c^{14}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^3\,c^{25/2}-427\,a^{9/2}\,b^3\,c^{23/2}+1256\,a^{11/2}\,b^3\,c^{21/2}-1856\,a^{13/2}\,b^3\,c^{19/2}+962\,a^{15/2}\,b^3\,c^{17/2}+962\,a^{17/2}\,b^3\,c^{15/2}-1856\,a^{19/2}\,b^3\,c^{13/2}+1256\,a^{21/2}\,b^3\,c^{11/2}-427\,a^{23/2}\,b^3\,c^{9/2}+65\,a^{25/2}\,b^3\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)\,4{}\mathrm{i}}{{\left(a-c\right)}^2}+\frac{b\,\left(\frac{4\,\left(4\,a^{12}\,b^3\,c^4+8\,a^{11}\,b^3\,c^5-32\,a^{10}\,b^3\,c^6-8\,a^9\,b^3\,c^7+56\,a^8\,b^3\,c^8-8\,a^7\,b^3\,c^9-32\,a^6\,b^3\,c^{10}+8\,a^5\,b^3\,c^{11}+4\,a^4\,b^3\,c^{12}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(a^{7/2}\,b^2\,c^{29/2}+12\,a^{9/2}\,b^2\,c^{27/2}-100\,a^{11/2}\,b^2\,c^{25/2}+285\,a^{13/2}\,b^2\,c^{23/2}-390\,a^{15/2}\,b^2\,c^{21/2}+192\,a^{17/2}\,b^2\,c^{19/2}+192\,a^{19/2}\,b^2\,c^{17/2}-390\,a^{21/2}\,b^2\,c^{15/2}+285\,a^{23/2}\,b^2\,c^{13/2}-100\,a^{25/2}\,b^2\,c^{11/2}+12\,a^{27/2}\,b^2\,c^{9/2}+a^{29/2}\,b^2\,c^{7/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(-4\,b\,a^{15}\,c^5+16\,b\,a^{14}\,c^6+12\,b\,a^{13}\,c^7-192\,b\,a^{12}\,c^8+504\,b\,a^{11}\,c^9-672\,b\,a^{10}\,c^{10}+504\,b\,a^9\,c^{11}-192\,b\,a^8\,c^{12}+12\,b\,a^7\,c^{13}+16\,b\,a^6\,c^{14}-4\,b\,a^5\,c^{15}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}-\frac{4\,b\,\left(\frac{4\,\left(a^{9/2}\,c^{35/2}-8\,a^{11/2}\,c^{33/2}+27\,a^{13/2}\,c^{31/2}-49\,a^{15/2}\,c^{29/2}+50\,a^{17/2}\,c^{27/2}-27\,a^{19/2}\,c^{25/2}+6\,a^{21/2}\,c^{23/2}+6\,a^{23/2}\,c^{21/2}-27\,a^{25/2}\,c^{19/2}+50\,a^{27/2}\,c^{17/2}-49\,a^{29/2}\,c^{15/2}+27\,a^{31/2}\,c^{13/2}-8\,a^{33/2}\,c^{11/2}+a^{35/2}\,c^{9/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{18}\,c^4-47\,a^{17}\,c^5+268\,a^{16}\,c^6-982\,a^{15}\,c^7+2564\,a^{14}\,c^8-4993\,a^{13}\,c^9+7404\,a^{12}\,c^{10}-8436\,a^{11}\,c^{11}+7404\,a^{10}\,c^{12}-4993\,a^9\,c^{13}+2564\,a^8\,c^{14}-982\,a^7\,c^{15}+268\,a^6\,c^{16}-47\,a^5\,c^{17}+4\,a^4\,c^{18}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{7/2}\,b\,c^{33/2}-43\,a^{9/2}\,b\,c^{31/2}+231\,a^{11/2}\,b\,c^{29/2}-749\,a^{13/2}\,b\,c^{27/2}+1505\,a^{15/2}\,b\,c^{25/2}-1770\,a^{17/2}\,b\,c^{23/2}+822\,a^{19/2}\,b\,c^{21/2}+822\,a^{21/2}\,b\,c^{19/2}-1770\,a^{23/2}\,b\,c^{17/2}+1505\,a^{25/2}\,b\,c^{15/2}-749\,a^{27/2}\,b\,c^{13/2}+231\,a^{29/2}\,b\,c^{11/2}-43\,a^{31/2}\,b\,c^{9/2}+4\,a^{33/2}\,b\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,a^{14}\,b^2\,c^4-570\,a^{13}\,b^2\,c^5+2053\,a^{12}\,b^2\,c^6-4568\,a^{11}\,b^2\,c^7+7090\,a^{10}\,b^2\,c^8-8156\,a^9\,b^2\,c^9+7090\,a^8\,b^2\,c^{10}-4568\,a^7\,b^2\,c^{11}+2053\,a^6\,b^2\,c^{12}-570\,a^5\,b^2\,c^{13}+73\,a^4\,b^2\,c^{14}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^3\,c^{25/2}-427\,a^{9/2}\,b^3\,c^{23/2}+1256\,a^{11/2}\,b^3\,c^{21/2}-1856\,a^{13/2}\,b^3\,c^{19/2}+962\,a^{15/2}\,b^3\,c^{17/2}+962\,a^{17/2}\,b^3\,c^{15/2}-1856\,a^{19/2}\,b^3\,c^{13/2}+1256\,a^{21/2}\,b^3\,c^{11/2}-427\,a^{23/2}\,b^3\,c^{9/2}+65\,a^{25/2}\,b^3\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)\,4{}\mathrm{i}}{{\left(a-c\right)}^2}}{\frac{8\,\left(14\,a^{7/2}\,b^4\,c^{21/2}-14\,a^{9/2}\,b^4\,c^{19/2}-42\,a^{11/2}\,b^4\,c^{17/2}+42\,a^{13/2}\,b^4\,c^{15/2}+42\,a^{15/2}\,b^4\,c^{13/2}-42\,a^{17/2}\,b^4\,c^{11/2}-14\,a^{19/2}\,b^4\,c^{9/2}+14\,a^{21/2}\,b^4\,c^{7/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(4\,a^{12}\,b^3\,c^4+8\,a^{11}\,b^3\,c^5-32\,a^{10}\,b^3\,c^6-8\,a^9\,b^3\,c^7+56\,a^8\,b^3\,c^8-8\,a^7\,b^3\,c^9-32\,a^6\,b^3\,c^{10}+8\,a^5\,b^3\,c^{11}+4\,a^4\,b^3\,c^{12}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,b\,\left(\frac{4\,\left(-4\,b\,a^{15}\,c^5+16\,b\,a^{14}\,c^6+12\,b\,a^{13}\,c^7-192\,b\,a^{12}\,c^8+504\,b\,a^{11}\,c^9-672\,b\,a^{10}\,c^{10}+504\,b\,a^9\,c^{11}-192\,b\,a^8\,c^{12}+12\,b\,a^7\,c^{13}+16\,b\,a^6\,c^{14}-4\,b\,a^5\,c^{15}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(a^{9/2}\,c^{35/2}-8\,a^{11/2}\,c^{33/2}+27\,a^{13/2}\,c^{31/2}-49\,a^{15/2}\,c^{29/2}+50\,a^{17/2}\,c^{27/2}-27\,a^{19/2}\,c^{25/2}+6\,a^{21/2}\,c^{23/2}+6\,a^{23/2}\,c^{21/2}-27\,a^{25/2}\,c^{19/2}+50\,a^{27/2}\,c^{17/2}-49\,a^{29/2}\,c^{15/2}+27\,a^{31/2}\,c^{13/2}-8\,a^{33/2}\,c^{11/2}+a^{35/2}\,c^{9/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{18}\,c^4-47\,a^{17}\,c^5+268\,a^{16}\,c^6-982\,a^{15}\,c^7+2564\,a^{14}\,c^8-4993\,a^{13}\,c^9+7404\,a^{12}\,c^{10}-8436\,a^{11}\,c^{11}+7404\,a^{10}\,c^{12}-4993\,a^9\,c^{13}+2564\,a^8\,c^{14}-982\,a^7\,c^{15}+268\,a^6\,c^{16}-47\,a^5\,c^{17}+4\,a^4\,c^{18}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{7/2}\,b\,c^{33/2}-43\,a^{9/2}\,b\,c^{31/2}+231\,a^{11/2}\,b\,c^{29/2}-749\,a^{13/2}\,b\,c^{27/2}+1505\,a^{15/2}\,b\,c^{25/2}-1770\,a^{17/2}\,b\,c^{23/2}+822\,a^{19/2}\,b\,c^{21/2}+822\,a^{21/2}\,b\,c^{19/2}-1770\,a^{23/2}\,b\,c^{17/2}+1505\,a^{25/2}\,b\,c^{15/2}-749\,a^{27/2}\,b\,c^{13/2}+231\,a^{29/2}\,b\,c^{11/2}-43\,a^{31/2}\,b\,c^{9/2}+4\,a^{33/2}\,b\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{4\,\left(a^{7/2}\,b^2\,c^{29/2}+12\,a^{9/2}\,b^2\,c^{27/2}-100\,a^{11/2}\,b^2\,c^{25/2}+285\,a^{13/2}\,b^2\,c^{23/2}-390\,a^{15/2}\,b^2\,c^{21/2}+192\,a^{17/2}\,b^2\,c^{19/2}+192\,a^{19/2}\,b^2\,c^{17/2}-390\,a^{21/2}\,b^2\,c^{15/2}+285\,a^{23/2}\,b^2\,c^{13/2}-100\,a^{25/2}\,b^2\,c^{11/2}+12\,a^{27/2}\,b^2\,c^{9/2}+a^{29/2}\,b^2\,c^{7/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,a^{14}\,b^2\,c^4-570\,a^{13}\,b^2\,c^5+2053\,a^{12}\,b^2\,c^6-4568\,a^{11}\,b^2\,c^7+7090\,a^{10}\,b^2\,c^8-8156\,a^9\,b^2\,c^9+7090\,a^8\,b^2\,c^{10}-4568\,a^7\,b^2\,c^{11}+2053\,a^6\,b^2\,c^{12}-570\,a^5\,b^2\,c^{13}+73\,a^4\,b^2\,c^{14}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^3\,c^{25/2}-427\,a^{9/2}\,b^3\,c^{23/2}+1256\,a^{11/2}\,b^3\,c^{21/2}-1856\,a^{13/2}\,b^3\,c^{19/2}+962\,a^{15/2}\,b^3\,c^{17/2}+962\,a^{17/2}\,b^3\,c^{15/2}-1856\,a^{19/2}\,b^3\,c^{13/2}+1256\,a^{21/2}\,b^3\,c^{11/2}-427\,a^{23/2}\,b^3\,c^{9/2}+65\,a^{25/2}\,b^3\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{4\,b\,\left(\frac{4\,\left(4\,a^{12}\,b^3\,c^4+8\,a^{11}\,b^3\,c^5-32\,a^{10}\,b^3\,c^6-8\,a^9\,b^3\,c^7+56\,a^8\,b^3\,c^8-8\,a^7\,b^3\,c^9-32\,a^6\,b^3\,c^{10}+8\,a^5\,b^3\,c^{11}+4\,a^4\,b^3\,c^{12}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(a^{7/2}\,b^2\,c^{29/2}+12\,a^{9/2}\,b^2\,c^{27/2}-100\,a^{11/2}\,b^2\,c^{25/2}+285\,a^{13/2}\,b^2\,c^{23/2}-390\,a^{15/2}\,b^2\,c^{21/2}+192\,a^{17/2}\,b^2\,c^{19/2}+192\,a^{19/2}\,b^2\,c^{17/2}-390\,a^{21/2}\,b^2\,c^{15/2}+285\,a^{23/2}\,b^2\,c^{13/2}-100\,a^{25/2}\,b^2\,c^{11/2}+12\,a^{27/2}\,b^2\,c^{9/2}+a^{29/2}\,b^2\,c^{7/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}+\frac{4\,b\,\left(\frac{4\,\left(-4\,b\,a^{15}\,c^5+16\,b\,a^{14}\,c^6+12\,b\,a^{13}\,c^7-192\,b\,a^{12}\,c^8+504\,b\,a^{11}\,c^9-672\,b\,a^{10}\,c^{10}+504\,b\,a^9\,c^{11}-192\,b\,a^8\,c^{12}+12\,b\,a^7\,c^{13}+16\,b\,a^6\,c^{14}-4\,b\,a^5\,c^{15}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}-\frac{4\,b\,\left(\frac{4\,\left(a^{9/2}\,c^{35/2}-8\,a^{11/2}\,c^{33/2}+27\,a^{13/2}\,c^{31/2}-49\,a^{15/2}\,c^{29/2}+50\,a^{17/2}\,c^{27/2}-27\,a^{19/2}\,c^{25/2}+6\,a^{21/2}\,c^{23/2}+6\,a^{23/2}\,c^{21/2}-27\,a^{25/2}\,c^{19/2}+50\,a^{27/2}\,c^{17/2}-49\,a^{29/2}\,c^{15/2}+27\,a^{31/2}\,c^{13/2}-8\,a^{33/2}\,c^{11/2}+a^{35/2}\,c^{9/2}\right)}{a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{18}\,c^4-47\,a^{17}\,c^5+268\,a^{16}\,c^6-982\,a^{15}\,c^7+2564\,a^{14}\,c^8-4993\,a^{13}\,c^9+7404\,a^{12}\,c^{10}-8436\,a^{11}\,c^{11}+7404\,a^{10}\,c^{12}-4993\,a^9\,c^{13}+2564\,a^8\,c^{14}-982\,a^7\,c^{15}+268\,a^6\,c^{16}-47\,a^5\,c^{17}+4\,a^4\,c^{18}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{7/2}\,b\,c^{33/2}-43\,a^{9/2}\,b\,c^{31/2}+231\,a^{11/2}\,b\,c^{29/2}-749\,a^{13/2}\,b\,c^{27/2}+1505\,a^{15/2}\,b\,c^{25/2}-1770\,a^{17/2}\,b\,c^{23/2}+822\,a^{19/2}\,b\,c^{21/2}+822\,a^{21/2}\,b\,c^{19/2}-1770\,a^{23/2}\,b\,c^{17/2}+1505\,a^{25/2}\,b\,c^{15/2}-749\,a^{27/2}\,b\,c^{13/2}+231\,a^{29/2}\,b\,c^{11/2}-43\,a^{31/2}\,b\,c^{9/2}+4\,a^{33/2}\,b\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,a^{14}\,b^2\,c^4-570\,a^{13}\,b^2\,c^5+2053\,a^{12}\,b^2\,c^6-4568\,a^{11}\,b^2\,c^7+7090\,a^{10}\,b^2\,c^8-8156\,a^9\,b^2\,c^9+7090\,a^8\,b^2\,c^{10}-4568\,a^7\,b^2\,c^{11}+2053\,a^6\,b^2\,c^{12}-570\,a^5\,b^2\,c^{13}+73\,a^4\,b^2\,c^{14}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^3\,c^{25/2}-427\,a^{9/2}\,b^3\,c^{23/2}+1256\,a^{11/2}\,b^3\,c^{21/2}-1856\,a^{13/2}\,b^3\,c^{19/2}+962\,a^{15/2}\,b^3\,c^{17/2}+962\,a^{17/2}\,b^3\,c^{15/2}-1856\,a^{19/2}\,b^3\,c^{13/2}+1256\,a^{21/2}\,b^3\,c^{11/2}-427\,a^{23/2}\,b^3\,c^{9/2}+65\,a^{25/2}\,b^3\,c^{7/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}\right)}{{\left(a-c\right)}^2}+\frac{4\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(-112\,a^{10}\,b^4\,c^4+224\,a^9\,b^4\,c^5+112\,a^8\,b^4\,c^6-448\,a^7\,b^4\,c^7+112\,a^6\,b^4\,c^8+224\,a^5\,b^4\,c^9-112\,a^4\,b^4\,c^{10}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^{15}\,c^7-8\,a^{14}\,c^8+28\,a^{13}\,c^9-56\,a^{12}\,c^{10}+70\,a^{11}\,c^{11}-56\,a^{10}\,c^{12}+28\,a^9\,c^{13}-8\,a^8\,c^{14}+a^7\,c^{15}\right)}}\right)\,8{}\mathrm{i}}{{\left(a-c\right)}^2}","Not used",1,"(2*b*log(x))/(a^2 - 2*a*c + c^2) - ((((a + b*x)^(1/2) - a^(1/2))^2*((a^2*b)/2 + (b*c^2)/2 - (3*a*b*c)/2))/(((c + b*x)^(1/2) - c^(1/2))^2*(a*c^3 + a^3*c - 2*a^2*c^2)) - b/(2*(a^2 - 2*a*c + c^2)) + (a^(1/2)*c^(1/2)*((a*b)/2 + (b*c)/2)*((a + b*x)^(1/2) - a^(1/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a*c^3 + a^3*c - 2*a^2*c^2)))/(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)) + ((a + b*x)^(1/2) - a^(1/2))^3/((c + b*x)^(1/2) - c^(1/2))^3 - ((a + c)*((a + b*x)^(1/2) - a^(1/2))^2)/(a^(1/2)*c^(1/2)*((c + b*x)^(1/2) - c^(1/2))^2)) + (b*atan(((b*((4*(4*a^4*b^3*c^12 + 8*a^5*b^3*c^11 - 32*a^6*b^3*c^10 - 8*a^7*b^3*c^9 + 56*a^8*b^3*c^8 - 8*a^9*b^3*c^7 - 32*a^10*b^3*c^6 + 8*a^11*b^3*c^5 + 4*a^12*b^3*c^4))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*b*((4*(16*a^6*b*c^14 - 4*a^5*b*c^15 + 12*a^7*b*c^13 - 192*a^8*b*c^12 + 504*a^9*b*c^11 - 672*a^10*b*c^10 + 504*a^11*b*c^9 - 192*a^12*b*c^8 + 12*a^13*b*c^7 + 16*a^14*b*c^6 - 4*a^15*b*c^5))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(a^(9/2)*c^(35/2) - 8*a^(11/2)*c^(33/2) + 27*a^(13/2)*c^(31/2) - 49*a^(15/2)*c^(29/2) + 50*a^(17/2)*c^(27/2) - 27*a^(19/2)*c^(25/2) + 6*a^(21/2)*c^(23/2) + 6*a^(23/2)*c^(21/2) - 27*a^(25/2)*c^(19/2) + 50*a^(27/2)*c^(17/2) - 49*a^(29/2)*c^(15/2) + 27*a^(31/2)*c^(13/2) - 8*a^(33/2)*c^(11/2) + a^(35/2)*c^(9/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) - (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^4*c^18 - 47*a^5*c^17 + 268*a^6*c^16 - 982*a^7*c^15 + 2564*a^8*c^14 - 4993*a^9*c^13 + 7404*a^10*c^12 - 8436*a^11*c^11 + 7404*a^12*c^10 - 4993*a^13*c^9 + 2564*a^14*c^8 - 982*a^15*c^7 + 268*a^16*c^6 - 47*a^17*c^5 + 4*a^18*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 + (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^(7/2)*b*c^(33/2) - 43*a^(9/2)*b*c^(31/2) + 231*a^(11/2)*b*c^(29/2) - 749*a^(13/2)*b*c^(27/2) + 1505*a^(15/2)*b*c^(25/2) - 1770*a^(17/2)*b*c^(23/2) + 822*a^(19/2)*b*c^(21/2) + 822*a^(21/2)*b*c^(19/2) - 1770*a^(23/2)*b*c^(17/2) + 1505*a^(25/2)*b*c^(15/2) - 749*a^(27/2)*b*c^(13/2) + 231*a^(29/2)*b*c^(11/2) - 43*a^(31/2)*b*c^(9/2) + 4*a^(33/2)*b*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (4*(a^(7/2)*b^2*c^(29/2) + 12*a^(9/2)*b^2*c^(27/2) - 100*a^(11/2)*b^2*c^(25/2) + 285*a^(13/2)*b^2*c^(23/2) - 390*a^(15/2)*b^2*c^(21/2) + 192*a^(17/2)*b^2*c^(19/2) + 192*a^(19/2)*b^2*c^(17/2) - 390*a^(21/2)*b^2*c^(15/2) + 285*a^(23/2)*b^2*c^(13/2) - 100*a^(25/2)*b^2*c^(11/2) + 12*a^(27/2)*b^2*c^(9/2) + a^(29/2)*b^2*c^(7/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (2*((a + b*x)^(1/2) - a^(1/2))*(73*a^4*b^2*c^14 - 570*a^5*b^2*c^13 + 2053*a^6*b^2*c^12 - 4568*a^7*b^2*c^11 + 7090*a^8*b^2*c^10 - 8156*a^9*b^2*c^9 + 7090*a^10*b^2*c^8 - 4568*a^11*b^2*c^7 + 2053*a^12*b^2*c^6 - 570*a^13*b^2*c^5 + 73*a^14*b^2*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^3*c^(25/2) - 427*a^(9/2)*b^3*c^(23/2) + 1256*a^(11/2)*b^3*c^(21/2) - 1856*a^(13/2)*b^3*c^(19/2) + 962*a^(15/2)*b^3*c^(17/2) + 962*a^(17/2)*b^3*c^(15/2) - 1856*a^(19/2)*b^3*c^(13/2) + 1256*a^(21/2)*b^3*c^(11/2) - 427*a^(23/2)*b^3*c^(9/2) + 65*a^(25/2)*b^3*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7)))*4i)/(a - c)^2 + (b*((4*(4*a^4*b^3*c^12 + 8*a^5*b^3*c^11 - 32*a^6*b^3*c^10 - 8*a^7*b^3*c^9 + 56*a^8*b^3*c^8 - 8*a^9*b^3*c^7 - 32*a^10*b^3*c^6 + 8*a^11*b^3*c^5 + 4*a^12*b^3*c^4))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(a^(7/2)*b^2*c^(29/2) + 12*a^(9/2)*b^2*c^(27/2) - 100*a^(11/2)*b^2*c^(25/2) + 285*a^(13/2)*b^2*c^(23/2) - 390*a^(15/2)*b^2*c^(21/2) + 192*a^(17/2)*b^2*c^(19/2) + 192*a^(19/2)*b^2*c^(17/2) - 390*a^(21/2)*b^2*c^(15/2) + 285*a^(23/2)*b^2*c^(13/2) - 100*a^(25/2)*b^2*c^(11/2) + 12*a^(27/2)*b^2*c^(9/2) + a^(29/2)*b^2*c^(7/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(16*a^6*b*c^14 - 4*a^5*b*c^15 + 12*a^7*b*c^13 - 192*a^8*b*c^12 + 504*a^9*b*c^11 - 672*a^10*b*c^10 + 504*a^11*b*c^9 - 192*a^12*b*c^8 + 12*a^13*b*c^7 + 16*a^14*b*c^6 - 4*a^15*b*c^5))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) - (4*b*((4*(a^(9/2)*c^(35/2) - 8*a^(11/2)*c^(33/2) + 27*a^(13/2)*c^(31/2) - 49*a^(15/2)*c^(29/2) + 50*a^(17/2)*c^(27/2) - 27*a^(19/2)*c^(25/2) + 6*a^(21/2)*c^(23/2) + 6*a^(23/2)*c^(21/2) - 27*a^(25/2)*c^(19/2) + 50*a^(27/2)*c^(17/2) - 49*a^(29/2)*c^(15/2) + 27*a^(31/2)*c^(13/2) - 8*a^(33/2)*c^(11/2) + a^(35/2)*c^(9/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) - (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^4*c^18 - 47*a^5*c^17 + 268*a^6*c^16 - 982*a^7*c^15 + 2564*a^8*c^14 - 4993*a^9*c^13 + 7404*a^10*c^12 - 8436*a^11*c^11 + 7404*a^12*c^10 - 4993*a^13*c^9 + 2564*a^14*c^8 - 982*a^15*c^7 + 268*a^16*c^6 - 47*a^17*c^5 + 4*a^18*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 + (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^(7/2)*b*c^(33/2) - 43*a^(9/2)*b*c^(31/2) + 231*a^(11/2)*b*c^(29/2) - 749*a^(13/2)*b*c^(27/2) + 1505*a^(15/2)*b*c^(25/2) - 1770*a^(17/2)*b*c^(23/2) + 822*a^(19/2)*b*c^(21/2) + 822*a^(21/2)*b*c^(19/2) - 1770*a^(23/2)*b*c^(17/2) + 1505*a^(25/2)*b*c^(15/2) - 749*a^(27/2)*b*c^(13/2) + 231*a^(29/2)*b*c^(11/2) - 43*a^(31/2)*b*c^(9/2) + 4*a^(33/2)*b*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(73*a^4*b^2*c^14 - 570*a^5*b^2*c^13 + 2053*a^6*b^2*c^12 - 4568*a^7*b^2*c^11 + 7090*a^8*b^2*c^10 - 8156*a^9*b^2*c^9 + 7090*a^10*b^2*c^8 - 4568*a^11*b^2*c^7 + 2053*a^12*b^2*c^6 - 570*a^13*b^2*c^5 + 73*a^14*b^2*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^3*c^(25/2) - 427*a^(9/2)*b^3*c^(23/2) + 1256*a^(11/2)*b^3*c^(21/2) - 1856*a^(13/2)*b^3*c^(19/2) + 962*a^(15/2)*b^3*c^(17/2) + 962*a^(17/2)*b^3*c^(15/2) - 1856*a^(19/2)*b^3*c^(13/2) + 1256*a^(21/2)*b^3*c^(11/2) - 427*a^(23/2)*b^3*c^(9/2) + 65*a^(25/2)*b^3*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7)))*4i)/(a - c)^2)/((8*(14*a^(7/2)*b^4*c^(21/2) - 14*a^(9/2)*b^4*c^(19/2) - 42*a^(11/2)*b^4*c^(17/2) + 42*a^(13/2)*b^4*c^(15/2) + 42*a^(15/2)*b^4*c^(13/2) - 42*a^(17/2)*b^4*c^(11/2) - 14*a^(19/2)*b^4*c^(9/2) + 14*a^(21/2)*b^4*c^(7/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(4*a^4*b^3*c^12 + 8*a^5*b^3*c^11 - 32*a^6*b^3*c^10 - 8*a^7*b^3*c^9 + 56*a^8*b^3*c^8 - 8*a^9*b^3*c^7 - 32*a^10*b^3*c^6 + 8*a^11*b^3*c^5 + 4*a^12*b^3*c^4))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*b*((4*(16*a^6*b*c^14 - 4*a^5*b*c^15 + 12*a^7*b*c^13 - 192*a^8*b*c^12 + 504*a^9*b*c^11 - 672*a^10*b*c^10 + 504*a^11*b*c^9 - 192*a^12*b*c^8 + 12*a^13*b*c^7 + 16*a^14*b*c^6 - 4*a^15*b*c^5))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(a^(9/2)*c^(35/2) - 8*a^(11/2)*c^(33/2) + 27*a^(13/2)*c^(31/2) - 49*a^(15/2)*c^(29/2) + 50*a^(17/2)*c^(27/2) - 27*a^(19/2)*c^(25/2) + 6*a^(21/2)*c^(23/2) + 6*a^(23/2)*c^(21/2) - 27*a^(25/2)*c^(19/2) + 50*a^(27/2)*c^(17/2) - 49*a^(29/2)*c^(15/2) + 27*a^(31/2)*c^(13/2) - 8*a^(33/2)*c^(11/2) + a^(35/2)*c^(9/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) - (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^4*c^18 - 47*a^5*c^17 + 268*a^6*c^16 - 982*a^7*c^15 + 2564*a^8*c^14 - 4993*a^9*c^13 + 7404*a^10*c^12 - 8436*a^11*c^11 + 7404*a^12*c^10 - 4993*a^13*c^9 + 2564*a^14*c^8 - 982*a^15*c^7 + 268*a^16*c^6 - 47*a^17*c^5 + 4*a^18*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 + (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^(7/2)*b*c^(33/2) - 43*a^(9/2)*b*c^(31/2) + 231*a^(11/2)*b*c^(29/2) - 749*a^(13/2)*b*c^(27/2) + 1505*a^(15/2)*b*c^(25/2) - 1770*a^(17/2)*b*c^(23/2) + 822*a^(19/2)*b*c^(21/2) + 822*a^(21/2)*b*c^(19/2) - 1770*a^(23/2)*b*c^(17/2) + 1505*a^(25/2)*b*c^(15/2) - 749*a^(27/2)*b*c^(13/2) + 231*a^(29/2)*b*c^(11/2) - 43*a^(31/2)*b*c^(9/2) + 4*a^(33/2)*b*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (4*(a^(7/2)*b^2*c^(29/2) + 12*a^(9/2)*b^2*c^(27/2) - 100*a^(11/2)*b^2*c^(25/2) + 285*a^(13/2)*b^2*c^(23/2) - 390*a^(15/2)*b^2*c^(21/2) + 192*a^(17/2)*b^2*c^(19/2) + 192*a^(19/2)*b^2*c^(17/2) - 390*a^(21/2)*b^2*c^(15/2) + 285*a^(23/2)*b^2*c^(13/2) - 100*a^(25/2)*b^2*c^(11/2) + 12*a^(27/2)*b^2*c^(9/2) + a^(29/2)*b^2*c^(7/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (2*((a + b*x)^(1/2) - a^(1/2))*(73*a^4*b^2*c^14 - 570*a^5*b^2*c^13 + 2053*a^6*b^2*c^12 - 4568*a^7*b^2*c^11 + 7090*a^8*b^2*c^10 - 8156*a^9*b^2*c^9 + 7090*a^10*b^2*c^8 - 4568*a^11*b^2*c^7 + 2053*a^12*b^2*c^6 - 570*a^13*b^2*c^5 + 73*a^14*b^2*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^3*c^(25/2) - 427*a^(9/2)*b^3*c^(23/2) + 1256*a^(11/2)*b^3*c^(21/2) - 1856*a^(13/2)*b^3*c^(19/2) + 962*a^(15/2)*b^3*c^(17/2) + 962*a^(17/2)*b^3*c^(15/2) - 1856*a^(19/2)*b^3*c^(13/2) + 1256*a^(21/2)*b^3*c^(11/2) - 427*a^(23/2)*b^3*c^(9/2) + 65*a^(25/2)*b^3*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (4*b*((4*(4*a^4*b^3*c^12 + 8*a^5*b^3*c^11 - 32*a^6*b^3*c^10 - 8*a^7*b^3*c^9 + 56*a^8*b^3*c^8 - 8*a^9*b^3*c^7 - 32*a^10*b^3*c^6 + 8*a^11*b^3*c^5 + 4*a^12*b^3*c^4))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(a^(7/2)*b^2*c^(29/2) + 12*a^(9/2)*b^2*c^(27/2) - 100*a^(11/2)*b^2*c^(25/2) + 285*a^(13/2)*b^2*c^(23/2) - 390*a^(15/2)*b^2*c^(21/2) + 192*a^(17/2)*b^2*c^(19/2) + 192*a^(19/2)*b^2*c^(17/2) - 390*a^(21/2)*b^2*c^(15/2) + 285*a^(23/2)*b^2*c^(13/2) - 100*a^(25/2)*b^2*c^(11/2) + 12*a^(27/2)*b^2*c^(9/2) + a^(29/2)*b^2*c^(7/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) + (4*b*((4*(16*a^6*b*c^14 - 4*a^5*b*c^15 + 12*a^7*b*c^13 - 192*a^8*b*c^12 + 504*a^9*b*c^11 - 672*a^10*b*c^10 + 504*a^11*b*c^9 - 192*a^12*b*c^8 + 12*a^13*b*c^7 + 16*a^14*b*c^6 - 4*a^15*b*c^5))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) - (4*b*((4*(a^(9/2)*c^(35/2) - 8*a^(11/2)*c^(33/2) + 27*a^(13/2)*c^(31/2) - 49*a^(15/2)*c^(29/2) + 50*a^(17/2)*c^(27/2) - 27*a^(19/2)*c^(25/2) + 6*a^(21/2)*c^(23/2) + 6*a^(23/2)*c^(21/2) - 27*a^(25/2)*c^(19/2) + 50*a^(27/2)*c^(17/2) - 49*a^(29/2)*c^(15/2) + 27*a^(31/2)*c^(13/2) - 8*a^(33/2)*c^(11/2) + a^(35/2)*c^(9/2)))/(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7) - (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^4*c^18 - 47*a^5*c^17 + 268*a^6*c^16 - 982*a^7*c^15 + 2564*a^8*c^14 - 4993*a^9*c^13 + 7404*a^10*c^12 - 8436*a^11*c^11 + 7404*a^12*c^10 - 4993*a^13*c^9 + 2564*a^14*c^8 - 982*a^15*c^7 + 268*a^16*c^6 - 47*a^17*c^5 + 4*a^18*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 + (2*((a + b*x)^(1/2) - a^(1/2))*(4*a^(7/2)*b*c^(33/2) - 43*a^(9/2)*b*c^(31/2) + 231*a^(11/2)*b*c^(29/2) - 749*a^(13/2)*b*c^(27/2) + 1505*a^(15/2)*b*c^(25/2) - 1770*a^(17/2)*b*c^(23/2) + 822*a^(19/2)*b*c^(21/2) + 822*a^(21/2)*b*c^(19/2) - 1770*a^(23/2)*b*c^(17/2) + 1505*a^(25/2)*b*c^(15/2) - 749*a^(27/2)*b*c^(13/2) + 231*a^(29/2)*b*c^(11/2) - 43*a^(31/2)*b*c^(9/2) + 4*a^(33/2)*b*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(73*a^4*b^2*c^14 - 570*a^5*b^2*c^13 + 2053*a^6*b^2*c^12 - 4568*a^7*b^2*c^11 + 7090*a^8*b^2*c^10 - 8156*a^9*b^2*c^9 + 7090*a^10*b^2*c^8 - 4568*a^11*b^2*c^7 + 2053*a^12*b^2*c^6 - 570*a^13*b^2*c^5 + 73*a^14*b^2*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^3*c^(25/2) - 427*a^(9/2)*b^3*c^(23/2) + 1256*a^(11/2)*b^3*c^(21/2) - 1856*a^(13/2)*b^3*c^(19/2) + 962*a^(15/2)*b^3*c^(17/2) + 962*a^(17/2)*b^3*c^(15/2) - 1856*a^(19/2)*b^3*c^(13/2) + 1256*a^(21/2)*b^3*c^(11/2) - 427*a^(23/2)*b^3*c^(9/2) + 65*a^(25/2)*b^3*c^(7/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))/(a - c)^2 + (4*((a + b*x)^(1/2) - a^(1/2))*(224*a^5*b^4*c^9 - 112*a^4*b^4*c^10 + 112*a^6*b^4*c^8 - 448*a^7*b^4*c^7 + 112*a^8*b^4*c^6 + 224*a^9*b^4*c^5 - 112*a^10*b^4*c^4))/(((c + b*x)^(1/2) - c^(1/2))*(a^7*c^15 - 8*a^8*c^14 + 28*a^9*c^13 - 56*a^10*c^12 + 70*a^11*c^11 - 56*a^12*c^10 + 28*a^13*c^9 - 8*a^14*c^8 + a^15*c^7))))*8i)/(a - c)^2 - (log((a*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)) - a^(1/2)*c^(1/2) + (c*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)) - (a^(1/2)*c^(1/2)*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2)*(a^(1/2)*b*c^(3/2) + a^(3/2)*b*c^(1/2)))/(a*c^3 + a^3*c - 2*a^2*c^2) - (a + c)/(x*(a^2 - 2*a*c + c^2)) + (log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) + a^(3/2)*b*c^(1/2)))/(a*c^3 + a^3*c - 2*a^2*c^2) + (b*((a + b*x)^(1/2) - a^(1/2)))/(2*(a - c)^2*((c + b*x)^(1/2) - c^(1/2)))","B"
411,1,529,375,3.303264,"\text{Not used}","int(x^2/((a + b*x)^(1/2) + (c + b*x)^(1/2))^3,x)","\frac{x^3\,\left(\frac{64\,b\,c}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)\,\sqrt{c+b\,x}}{7\,b}-\frac{x^3\,\left(\frac{64\,a\,b}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)\,\sqrt{a+b\,x}}{7\,b}-\frac{8\,c^2\,\left(\frac{2\,c\,\left(3\,a+c\right)}{{\left(a-c\right)}^3}+\frac{6\,c\,\left(\frac{64\,b\,c}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)}{7\,b}\right)\,\sqrt{c+b\,x}}{15\,b^3}-\frac{x^2\,\left(\frac{2\,c\,\left(3\,a+c\right)}{{\left(a-c\right)}^3}+\frac{6\,c\,\left(\frac{64\,b\,c}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)}{7\,b}\right)\,\sqrt{c+b\,x}}{5\,b}+\frac{8\,a^2\,\left(\frac{2\,\left(a^2+3\,c\,a\right)}{{\left(a-c\right)}^3}+\frac{6\,a\,\left(\frac{64\,a\,b}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)}{7\,b}\right)\,\sqrt{a+b\,x}}{15\,b^3}+\frac{x^2\,\left(\frac{2\,\left(a^2+3\,c\,a\right)}{{\left(a-c\right)}^3}+\frac{6\,a\,\left(\frac{64\,a\,b}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)}{7\,b}\right)\,\sqrt{a+b\,x}}{5\,b}+\frac{8\,b\,x^4\,\sqrt{a+b\,x}}{9\,{\left(a-c\right)}^3}-\frac{8\,b\,x^4\,\sqrt{c+b\,x}}{9\,{\left(a-c\right)}^3}+\frac{4\,c\,x\,\left(\frac{2\,c\,\left(3\,a+c\right)}{{\left(a-c\right)}^3}+\frac{6\,c\,\left(\frac{64\,b\,c}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)}{7\,b}\right)\,\sqrt{c+b\,x}}{15\,b^2}-\frac{4\,a\,x\,\left(\frac{2\,\left(a^2+3\,c\,a\right)}{{\left(a-c\right)}^3}+\frac{6\,a\,\left(\frac{64\,a\,b}{9\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)}{7\,b}\right)\,\sqrt{a+b\,x}}{15\,b^2}","Not used",1,"(x^3*((64*b*c)/(9*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3)*(c + b*x)^(1/2))/(7*b) - (x^3*((64*a*b)/(9*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3)*(a + b*x)^(1/2))/(7*b) - (8*c^2*((2*c*(3*a + c))/(a - c)^3 + (6*c*((64*b*c)/(9*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3))/(7*b))*(c + b*x)^(1/2))/(15*b^3) - (x^2*((2*c*(3*a + c))/(a - c)^3 + (6*c*((64*b*c)/(9*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3))/(7*b))*(c + b*x)^(1/2))/(5*b) + (8*a^2*((2*(3*a*c + a^2))/(a - c)^3 + (6*a*((64*a*b)/(9*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3))/(7*b))*(a + b*x)^(1/2))/(15*b^3) + (x^2*((2*(3*a*c + a^2))/(a - c)^3 + (6*a*((64*a*b)/(9*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3))/(7*b))*(a + b*x)^(1/2))/(5*b) + (8*b*x^4*(a + b*x)^(1/2))/(9*(a - c)^3) - (8*b*x^4*(c + b*x)^(1/2))/(9*(a - c)^3) + (4*c*x*((2*c*(3*a + c))/(a - c)^3 + (6*c*((64*b*c)/(9*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3))/(7*b))*(c + b*x)^(1/2))/(15*b^2) - (4*a*x*((2*(3*a*c + a^2))/(a - c)^3 + (6*a*((64*a*b)/(9*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3))/(7*b))*(a + b*x)^(1/2))/(15*b^2)","B"
412,1,385,261,3.211429,"\text{Not used}","int(x/((a + b*x)^(1/2) + (c + b*x)^(1/2))^3,x)","\frac{x^2\,\left(\frac{48\,b\,c}{7\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)\,\sqrt{c+b\,x}}{5\,b}-\frac{x^2\,\left(\frac{48\,a\,b}{7\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)\,\sqrt{a+b\,x}}{5\,b}-\frac{2\,a\,\left(\frac{2\,a\,\left(a+3\,c\right)}{{\left(a-c\right)}^3}+\frac{4\,a\,\left(\frac{48\,a\,b}{7\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)}{5\,b}\right)\,\sqrt{a+b\,x}}{3\,b^2}+\frac{8\,b\,x^3\,\sqrt{a+b\,x}}{7\,{\left(a-c\right)}^3}+\frac{2\,c\,\left(\frac{2\,c\,\left(3\,a+c\right)}{{\left(a-c\right)}^3}+\frac{4\,c\,\left(\frac{48\,b\,c}{7\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)}{5\,b}\right)\,\sqrt{c+b\,x}}{3\,b^2}-\frac{8\,b\,x^3\,\sqrt{c+b\,x}}{7\,{\left(a-c\right)}^3}+\frac{x\,\left(\frac{2\,a\,\left(a+3\,c\right)}{{\left(a-c\right)}^3}+\frac{4\,a\,\left(\frac{48\,a\,b}{7\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)}{5\,b}\right)\,\sqrt{a+b\,x}}{3\,b}-\frac{x\,\left(\frac{2\,c\,\left(3\,a+c\right)}{{\left(a-c\right)}^3}+\frac{4\,c\,\left(\frac{48\,b\,c}{7\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)}{5\,b}\right)\,\sqrt{c+b\,x}}{3\,b}","Not used",1,"(x^2*((48*b*c)/(7*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3)*(c + b*x)^(1/2))/(5*b) - (x^2*((48*a*b)/(7*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3)*(a + b*x)^(1/2))/(5*b) - (2*a*((2*a*(a + 3*c))/(a - c)^3 + (4*a*((48*a*b)/(7*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3))/(5*b))*(a + b*x)^(1/2))/(3*b^2) + (8*b*x^3*(a + b*x)^(1/2))/(7*(a - c)^3) + (2*c*((2*c*(3*a + c))/(a - c)^3 + (4*c*((48*b*c)/(7*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3))/(5*b))*(c + b*x)^(1/2))/(3*b^2) - (8*b*x^3*(c + b*x)^(1/2))/(7*(a - c)^3) + (x*((2*a*(a + 3*c))/(a - c)^3 + (4*a*((48*a*b)/(7*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3))/(5*b))*(a + b*x)^(1/2))/(3*b) - (x*((2*c*(3*a + c))/(a - c)^3 + (4*c*((48*b*c)/(7*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3))/(5*b))*(c + b*x)^(1/2))/(3*b)","B"
413,1,252,64,2.994934,"\text{Not used}","int(1/((a + b*x)^(1/2) + (c + b*x)^(1/2))^3,x)","\frac{\left(\frac{2\,\left(a^2+3\,c\,a\right)}{{\left(a-c\right)}^3}+\frac{2\,a\,\left(\frac{32\,a\,b}{5\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)}{3\,b}\right)\,\sqrt{a+b\,x}}{b}-\frac{\left(\frac{2\,c\,\left(3\,a+c\right)}{{\left(a-c\right)}^3}+\frac{2\,c\,\left(\frac{32\,b\,c}{5\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)}{3\,b}\right)\,\sqrt{c+b\,x}}{b}+\frac{8\,b\,x^2\,\sqrt{a+b\,x}}{5\,{\left(a-c\right)}^3}-\frac{8\,b\,x^2\,\sqrt{c+b\,x}}{5\,{\left(a-c\right)}^3}-\frac{x\,\left(\frac{32\,a\,b}{5\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(5\,a+3\,c\right)}{{\left(a-c\right)}^3}\right)\,\sqrt{a+b\,x}}{3\,b}+\frac{x\,\left(\frac{32\,b\,c}{5\,{\left(a-c\right)}^3}-\frac{2\,b\,\left(3\,a+5\,c\right)}{{\left(a-c\right)}^3}\right)\,\sqrt{c+b\,x}}{3\,b}","Not used",1,"(((2*(3*a*c + a^2))/(a - c)^3 + (2*a*((32*a*b)/(5*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3))/(3*b))*(a + b*x)^(1/2))/b - (((2*c*(3*a + c))/(a - c)^3 + (2*c*((32*b*c)/(5*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3))/(3*b))*(c + b*x)^(1/2))/b + (8*b*x^2*(a + b*x)^(1/2))/(5*(a - c)^3) - (8*b*x^2*(c + b*x)^(1/2))/(5*(a - c)^3) - (x*((32*a*b)/(5*(a - c)^3) - (2*b*(5*a + 3*c))/(a - c)^3)*(a + b*x)^(1/2))/(3*b) + (x*((32*b*c)/(5*(a - c)^3) - (2*b*(3*a + 5*c))/(a - c)^3)*(c + b*x)^(1/2))/(3*b)","B"
414,1,4060,157,27.722238,"\text{Not used}","int(1/(x*((a + b*x)^(1/2) + (c + b*x)^(1/2))^3),x)","\frac{\frac{\left(\frac{\sqrt{a}\,\left(16\,a+16\,c\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}+\frac{\sqrt{c}\,\left(16\,a+16\,c\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}+\frac{\left(\frac{\sqrt{a}\,\left(12\,a+20\,c\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}+\frac{\sqrt{c}\,\left(20\,a+12\,c\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}+\frac{\sqrt{a}\,\left(\frac{28\,a}{3}+12\,c\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}+\frac{\sqrt{c}\,\left(12\,a+\frac{28\,c}{3}\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}}{\frac{3\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}+\frac{3\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3}+1}+\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\left(a\,\left(\sqrt{a}+3\,\sqrt{c}\right)+c\,\left(3\,\sqrt{a}+\sqrt{c}\right)\right)}{a^3-3\,a^2\,c+3\,a\,c^2-c^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{6\,a\,c^{11/2}-6\,a^{11/2}\,c+2\,a^{3/2}\,c^5-2\,a^5\,c^{3/2}+12\,a^3\,c^{7/2}-12\,a^{7/2}\,c^3-16\,a^2\,c^{9/2}+16\,a^{9/2}\,c^2}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}+\frac{\left(\frac{\sqrt{a}\,c^{15/2}-5\,a^{3/2}\,c^{13/2}+9\,a^{5/2}\,c^{11/2}-5\,a^{7/2}\,c^{9/2}-5\,a^{9/2}\,c^{7/2}+9\,a^{11/2}\,c^{5/2}-5\,a^{13/2}\,c^{3/2}+a^{15/2}\,\sqrt{c}}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(a^9\,c-7\,a^8\,c^2+22\,a^7\,c^3-41\,a^6\,c^4+50\,a^5\,c^5-41\,a^4\,c^6+22\,a^3\,c^7-7\,a^2\,c^8+a\,c^9\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(3\,a^{3/2}\,c^7-3\,a^7\,c^{3/2}+8\,a^6\,c^{5/2}-8\,a^{5/2}\,c^6-6\,a^5\,c^{7/2}+6\,a^{7/2}\,c^5+a^3\,c^{11/2}-a^{11/2}\,c^3\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)\,1{}\mathrm{i}}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}-\frac{\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{\left(\frac{\sqrt{a}\,c^{15/2}-5\,a^{3/2}\,c^{13/2}+9\,a^{5/2}\,c^{11/2}-5\,a^{7/2}\,c^{9/2}-5\,a^{9/2}\,c^{7/2}+9\,a^{11/2}\,c^{5/2}-5\,a^{13/2}\,c^{3/2}+a^{15/2}\,\sqrt{c}}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(a^9\,c-7\,a^8\,c^2+22\,a^7\,c^3-41\,a^6\,c^4+50\,a^5\,c^5-41\,a^4\,c^6+22\,a^3\,c^7-7\,a^2\,c^8+a\,c^9\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}-\frac{6\,a\,c^{11/2}-6\,a^{11/2}\,c+2\,a^{3/2}\,c^5-2\,a^5\,c^{3/2}+12\,a^3\,c^{7/2}-12\,a^{7/2}\,c^3-16\,a^2\,c^{9/2}+16\,a^{9/2}\,c^2}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(3\,a^{3/2}\,c^7-3\,a^7\,c^{3/2}+8\,a^6\,c^{5/2}-8\,a^{5/2}\,c^6-6\,a^5\,c^{7/2}+6\,a^{7/2}\,c^5+a^3\,c^{11/2}-a^{11/2}\,c^3\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)\,1{}\mathrm{i}}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}}{\frac{2\,\left(\sqrt{a}\,c^{9/2}-4\,a^{3/2}\,c^{7/2}+6\,a^{5/2}\,c^{5/2}-4\,a^{7/2}\,c^{3/2}+a^{9/2}\,\sqrt{c}\right)}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}-\frac{\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{6\,a\,c^{11/2}-6\,a^{11/2}\,c+2\,a^{3/2}\,c^5-2\,a^5\,c^{3/2}+12\,a^3\,c^{7/2}-12\,a^{7/2}\,c^3-16\,a^2\,c^{9/2}+16\,a^{9/2}\,c^2}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}+\frac{\left(\frac{\sqrt{a}\,c^{15/2}-5\,a^{3/2}\,c^{13/2}+9\,a^{5/2}\,c^{11/2}-5\,a^{7/2}\,c^{9/2}-5\,a^{9/2}\,c^{7/2}+9\,a^{11/2}\,c^{5/2}-5\,a^{13/2}\,c^{3/2}+a^{15/2}\,\sqrt{c}}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(a^9\,c-7\,a^8\,c^2+22\,a^7\,c^3-41\,a^6\,c^4+50\,a^5\,c^5-41\,a^4\,c^6+22\,a^3\,c^7-7\,a^2\,c^8+a\,c^9\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(3\,a^{3/2}\,c^7-3\,a^7\,c^{3/2}+8\,a^6\,c^{5/2}-8\,a^{5/2}\,c^6-6\,a^5\,c^{7/2}+6\,a^{7/2}\,c^5+a^3\,c^{11/2}-a^{11/2}\,c^3\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}-\frac{\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{\left(\frac{\sqrt{a}\,c^{15/2}-5\,a^{3/2}\,c^{13/2}+9\,a^{5/2}\,c^{11/2}-5\,a^{7/2}\,c^{9/2}-5\,a^{9/2}\,c^{7/2}+9\,a^{11/2}\,c^{5/2}-5\,a^{13/2}\,c^{3/2}+a^{15/2}\,\sqrt{c}}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(a^9\,c-7\,a^8\,c^2+22\,a^7\,c^3-41\,a^6\,c^4+50\,a^5\,c^5-41\,a^4\,c^6+22\,a^3\,c^7-7\,a^2\,c^8+a\,c^9\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}-\frac{6\,a\,c^{11/2}-6\,a^{11/2}\,c+2\,a^{3/2}\,c^5-2\,a^5\,c^{3/2}+12\,a^3\,c^{7/2}-12\,a^{7/2}\,c^3-16\,a^2\,c^{9/2}+16\,a^{9/2}\,c^2}{a^7\,c-6\,a^6\,c^2+15\,a^5\,c^3-20\,a^4\,c^4+15\,a^3\,c^5-6\,a^2\,c^6+a\,c^7}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(3\,a^{3/2}\,c^7-3\,a^7\,c^{3/2}+8\,a^6\,c^{5/2}-8\,a^{5/2}\,c^6-6\,a^5\,c^{7/2}+6\,a^{7/2}\,c^5+a^3\,c^{11/2}-a^{11/2}\,c^3\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}\right)\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}+\frac{4\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(6\,a^3\,c^4-a^6\,c-5\,a^2\,c^5-a\,c^6+6\,a^4\,c^3-5\,a^5\,c^2+3\,a^{3/2}\,c^{11/2}+4\,a^{5/2}\,c^{9/2}-14\,a^{7/2}\,c^{7/2}+4\,a^{9/2}\,c^{5/2}+3\,a^{11/2}\,c^{3/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^8\,c^2-6\,a^7\,c^3+15\,a^6\,c^4-20\,a^5\,c^5+15\,a^4\,c^6-6\,a^3\,c^7+a^2\,c^8\right)}}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\sqrt{a}\,c^3-3\,a^{5/2}\,c-3\,a\,c^{5/2}+a^3\,\sqrt{c}+2\,a^2\,c^{3/2}+2\,a^{3/2}\,c^2\right)\,2{}\mathrm{i}}{-a^6\,c+5\,a^5\,c^2-10\,a^4\,c^3+10\,a^3\,c^4-5\,a^2\,c^5+a\,c^6}","Not used",1,"((((a^(1/2)*(16*a + 16*c))/(3*a*c^2 - 3*a^2*c + a^3 - c^3) + (c^(1/2)*(16*a + 16*c))/(3*a*c^2 - 3*a^2*c + a^3 - c^3))*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)) + (((a^(1/2)*(12*a + 20*c))/(3*a*c^2 - 3*a^2*c + a^3 - c^3) + (c^(1/2)*(20*a + 12*c))/(3*a*c^2 - 3*a^2*c + a^3 - c^3))*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 + (a^(1/2)*((28*a)/3 + 12*c))/(3*a*c^2 - 3*a^2*c + a^3 - c^3) + (c^(1/2)*(12*a + (28*c)/3))/(3*a*c^2 - 3*a^2*c + a^3 - c^3))/((3*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)) + (3*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 + ((a + b*x)^(1/2) - a^(1/2))^3/((c + b*x)^(1/2) - c^(1/2))^3 + 1) + (log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(a*(a^(1/2) + 3*c^(1/2)) + c*(3*a^(1/2) + c^(1/2))))/(3*a*c^2 - 3*a^2*c + a^3 - c^3) + (atan(((((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((6*a*c^(11/2) - 6*a^(11/2)*c + 2*a^(3/2)*c^5 - 2*a^5*c^(3/2) + 12*a^3*c^(7/2) - 12*a^(7/2)*c^3 - 16*a^2*c^(9/2) + 16*a^(9/2)*c^2)/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) + (((a^(1/2)*c^(15/2) - 5*a^(3/2)*c^(13/2) + 9*a^(5/2)*c^(11/2) - 5*a^(7/2)*c^(9/2) - 5*a^(9/2)*c^(7/2) + 9*a^(11/2)*c^(5/2) - 5*a^(13/2)*c^(3/2) + a^(15/2)*c^(1/2))/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(a*c^9 + a^9*c - 7*a^2*c^8 + 22*a^3*c^7 - 41*a^4*c^6 + 50*a^5*c^5 - 41*a^6*c^4 + 22*a^7*c^3 - 7*a^8*c^2))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2))/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(3*a^(3/2)*c^7 - 3*a^7*c^(3/2) + 8*a^6*c^(5/2) - 8*a^(5/2)*c^6 - 6*a^5*c^(7/2) + 6*a^(7/2)*c^5 + a^3*c^(11/2) - a^(11/2)*c^3))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2)*1i)/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) - (((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((((a^(1/2)*c^(15/2) - 5*a^(3/2)*c^(13/2) + 9*a^(5/2)*c^(11/2) - 5*a^(7/2)*c^(9/2) - 5*a^(9/2)*c^(7/2) + 9*a^(11/2)*c^(5/2) - 5*a^(13/2)*c^(3/2) + a^(15/2)*c^(1/2))/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(a*c^9 + a^9*c - 7*a^2*c^8 + 22*a^3*c^7 - 41*a^4*c^6 + 50*a^5*c^5 - 41*a^6*c^4 + 22*a^7*c^3 - 7*a^8*c^2))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2))/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) - (6*a*c^(11/2) - 6*a^(11/2)*c + 2*a^(3/2)*c^5 - 2*a^5*c^(3/2) + 12*a^3*c^(7/2) - 12*a^(7/2)*c^3 - 16*a^2*c^(9/2) + 16*a^(9/2)*c^2)/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(3*a^(3/2)*c^7 - 3*a^7*c^(3/2) + 8*a^6*c^(5/2) - 8*a^(5/2)*c^6 - 6*a^5*c^(7/2) + 6*a^(7/2)*c^5 + a^3*c^(11/2) - a^(11/2)*c^3))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2)*1i)/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2))/((2*(a^(1/2)*c^(9/2) - 4*a^(3/2)*c^(7/2) + 6*a^(5/2)*c^(5/2) - 4*a^(7/2)*c^(3/2) + a^(9/2)*c^(1/2)))/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) - (((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((6*a*c^(11/2) - 6*a^(11/2)*c + 2*a^(3/2)*c^5 - 2*a^5*c^(3/2) + 12*a^3*c^(7/2) - 12*a^(7/2)*c^3 - 16*a^2*c^(9/2) + 16*a^(9/2)*c^2)/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) + (((a^(1/2)*c^(15/2) - 5*a^(3/2)*c^(13/2) + 9*a^(5/2)*c^(11/2) - 5*a^(7/2)*c^(9/2) - 5*a^(9/2)*c^(7/2) + 9*a^(11/2)*c^(5/2) - 5*a^(13/2)*c^(3/2) + a^(15/2)*c^(1/2))/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(a*c^9 + a^9*c - 7*a^2*c^8 + 22*a^3*c^7 - 41*a^4*c^6 + 50*a^5*c^5 - 41*a^6*c^4 + 22*a^7*c^3 - 7*a^8*c^2))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2))/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(3*a^(3/2)*c^7 - 3*a^7*c^(3/2) + 8*a^6*c^(5/2) - 8*a^(5/2)*c^6 - 6*a^5*c^(7/2) + 6*a^(7/2)*c^5 + a^3*c^(11/2) - a^(11/2)*c^3))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2))/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) - (((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((((a^(1/2)*c^(15/2) - 5*a^(3/2)*c^(13/2) + 9*a^(5/2)*c^(11/2) - 5*a^(7/2)*c^(9/2) - 5*a^(9/2)*c^(7/2) + 9*a^(11/2)*c^(5/2) - 5*a^(13/2)*c^(3/2) + a^(15/2)*c^(1/2))/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(a*c^9 + a^9*c - 7*a^2*c^8 + 22*a^3*c^7 - 41*a^4*c^6 + 50*a^5*c^5 - 41*a^6*c^4 + 22*a^7*c^3 - 7*a^8*c^2))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2))/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) - (6*a*c^(11/2) - 6*a^(11/2)*c + 2*a^(3/2)*c^5 - 2*a^5*c^(3/2) + 12*a^3*c^(7/2) - 12*a^(7/2)*c^3 - 16*a^2*c^(9/2) + 16*a^(9/2)*c^2)/(a*c^7 + a^7*c - 6*a^2*c^6 + 15*a^3*c^5 - 20*a^4*c^4 + 15*a^5*c^3 - 6*a^6*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(3*a^(3/2)*c^7 - 3*a^7*c^(3/2) + 8*a^6*c^(5/2) - 8*a^(5/2)*c^6 - 6*a^5*c^(7/2) + 6*a^(7/2)*c^5 + a^3*c^(11/2) - a^(11/2)*c^3))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2)))*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2))/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2) + (4*((a + b*x)^(1/2) - a^(1/2))*(6*a^3*c^4 - a^6*c - 5*a^2*c^5 - a*c^6 + 6*a^4*c^3 - 5*a^5*c^2 + 3*a^(3/2)*c^(11/2) + 4*a^(5/2)*c^(9/2) - 14*a^(7/2)*c^(7/2) + 4*a^(9/2)*c^(5/2) + 3*a^(11/2)*c^(3/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^2*c^8 - 6*a^3*c^7 + 15*a^4*c^6 - 20*a^5*c^5 + 15*a^6*c^4 - 6*a^7*c^3 + a^8*c^2))))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a^(1/2)*c^3 - 3*a^(5/2)*c - 3*a*c^(5/2) + a^3*c^(1/2) + 2*a^2*c^(3/2) + 2*a^(3/2)*c^2)*2i)/(a*c^6 - a^6*c - 5*a^2*c^5 + 10*a^3*c^4 - 10*a^4*c^3 + 5*a^5*c^2)","B"
415,1,4681,162,33.215178,"\text{Not used}","int(1/(x^2*((a + b*x)^(1/2) + (c + b*x)^(1/2))^3),x)","-\frac{\frac{\sqrt{a}\,\left(\frac{3\,a\,b}{4}+\frac{b\,c}{4}\right)}{-a^4+3\,a^3\,c-3\,a^2\,c^2+a\,c^3}-\frac{\sqrt{c}\,\left(\frac{a\,b}{4}+\frac{3\,b\,c}{4}\right)}{a^3\,c-3\,a^2\,c^2+3\,a\,c^3-c^4}-\frac{\left(\frac{\sqrt{a}\,\left(\frac{3\,b\,a^3}{4}+17\,b\,a^2\,c-\frac{b\,a\,c^2}{2}-\frac{b\,c^3}{4}\right)}{a^5\,c-3\,a^4\,c^2+3\,a^3\,c^3-a^2\,c^4}+\frac{\sqrt{c}\,\left(\frac{b\,a^3}{4}+\frac{b\,a^2\,c}{2}-17\,b\,a\,c^2-\frac{3\,b\,c^3}{4}\right)}{-a^4\,c^2+3\,a^3\,c^3-3\,a^2\,c^4+a\,c^5}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3}+\frac{\left(\frac{\sqrt{a}\,\left(-b\,a^3+15\,b\,a^2\,c+\frac{75\,b\,a\,c^2}{4}+\frac{b\,c^3}{4}\right)}{a^5\,c-3\,a^4\,c^2+3\,a^3\,c^3-a^2\,c^4}-\frac{\sqrt{c}\,\left(\frac{b\,a^3}{4}+\frac{75\,b\,a^2\,c}{4}+15\,b\,a\,c^2-b\,c^3\right)}{-a^4\,c^2+3\,a^3\,c^3-3\,a^2\,c^4+a\,c^5}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}+\frac{\left(\frac{\sqrt{a}\,\left(\frac{b\,a^2}{4}+\frac{67\,b\,a\,c}{4}-2\,b\,c^2\right)}{-a^4\,c+3\,a^3\,c^2-3\,a^2\,c^3+a\,c^4}+\frac{\sqrt{c}\,\left(-2\,b\,a^2+\frac{67\,b\,a\,c}{4}+\frac{b\,c^2}{4}\right)}{-a^4\,c+3\,a^3\,c^2-3\,a^2\,c^3+a\,c^4}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{c+b\,x}-\sqrt{c}}}{\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^4}-\frac{\left(\frac{a+c}{\sqrt{a}\,\sqrt{c}}-1\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^2}-\frac{\left(\frac{a+c}{\sqrt{a}\,\sqrt{c}}-1\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+b\,x}-\sqrt{c}\right)}^3}}-\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{c+b\,x}-\sqrt{c}}\right)\,\left(3\,a^2\,b\,\sqrt{c}+3\,\sqrt{a}\,b\,c^2+a\,c\,\left(9\,\sqrt{a}\,b+9\,b\,\sqrt{c}\right)\right)}{-2\,a^4\,c+6\,a^3\,c^2-6\,a^2\,c^3+2\,a\,c^4}-\frac{b\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{4\,\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{a}-\sqrt{c}\right)}^3\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{9\,a^6\,b\,c^{7/2}-9\,a^{7/2}\,b\,c^6-24\,a^5\,b\,c^{9/2}+24\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4-3\,a^2\,b\,c^{15/2}+3\,a^{15/2}\,b\,c^2}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(6\,a^{3/2}\,b\,c^8-6\,a^8\,b\,c^{3/2}+36\,a^6\,b\,c^{7/2}-36\,a^{7/2}\,b\,c^6-48\,a^5\,b\,c^{9/2}+48\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}-\frac{3\,b\,\left(\frac{a^{5/2}\,c^{19/2}-5\,a^{7/2}\,c^{17/2}+9\,a^{9/2}\,c^{15/2}-5\,a^{11/2}\,c^{13/2}-5\,a^{13/2}\,c^{11/2}+9\,a^{15/2}\,c^{9/2}-5\,a^{17/2}\,c^{7/2}+a^{19/2}\,c^{5/2}}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{10}\,c^2-28\,a^9\,c^3+88\,a^8\,c^4-164\,a^7\,c^5+200\,a^6\,c^6-164\,a^5\,c^7+88\,a^4\,c^8-28\,a^3\,c^9+4\,a^2\,c^{10}\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}\right)\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)\,3{}\mathrm{i}}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}+\frac{b\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{9\,a^6\,b\,c^{7/2}-9\,a^{7/2}\,b\,c^6-24\,a^5\,b\,c^{9/2}+24\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4-3\,a^2\,b\,c^{15/2}+3\,a^{15/2}\,b\,c^2}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(6\,a^{3/2}\,b\,c^8-6\,a^8\,b\,c^{3/2}+36\,a^6\,b\,c^{7/2}-36\,a^{7/2}\,b\,c^6-48\,a^5\,b\,c^{9/2}+48\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}+\frac{3\,b\,\left(\frac{a^{5/2}\,c^{19/2}-5\,a^{7/2}\,c^{17/2}+9\,a^{9/2}\,c^{15/2}-5\,a^{11/2}\,c^{13/2}-5\,a^{13/2}\,c^{11/2}+9\,a^{15/2}\,c^{9/2}-5\,a^{17/2}\,c^{7/2}+a^{19/2}\,c^{5/2}}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{10}\,c^2-28\,a^9\,c^3+88\,a^8\,c^4-164\,a^7\,c^5+200\,a^6\,c^6-164\,a^5\,c^7+88\,a^4\,c^8-28\,a^3\,c^9+4\,a^2\,c^{10}\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}\right)\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)\,3{}\mathrm{i}}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}}{\frac{\frac{9\,a^{3/2}\,b^2\,c^{11/2}}{2}-18\,a^{5/2}\,b^2\,c^{9/2}+27\,a^{7/2}\,b^2\,c^{7/2}-18\,a^{9/2}\,b^2\,c^{5/2}+\frac{9\,a^{11/2}\,b^2\,c^{3/2}}{2}}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(72\,a^3\,b^2\,c^4-72\,a^2\,b^2\,c^5+72\,a^4\,b^2\,c^3-72\,a^5\,b^2\,c^2+27\,a^{3/2}\,b^2\,c^{11/2}+36\,a^{5/2}\,b^2\,c^{9/2}-126\,a^{7/2}\,b^2\,c^{7/2}+36\,a^{9/2}\,b^2\,c^{5/2}+27\,a^{11/2}\,b^2\,c^{3/2}\right)}{\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}-\frac{3\,b\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{9\,a^6\,b\,c^{7/2}-9\,a^{7/2}\,b\,c^6-24\,a^5\,b\,c^{9/2}+24\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4-3\,a^2\,b\,c^{15/2}+3\,a^{15/2}\,b\,c^2}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(6\,a^{3/2}\,b\,c^8-6\,a^8\,b\,c^{3/2}+36\,a^6\,b\,c^{7/2}-36\,a^{7/2}\,b\,c^6-48\,a^5\,b\,c^{9/2}+48\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}-\frac{3\,b\,\left(\frac{a^{5/2}\,c^{19/2}-5\,a^{7/2}\,c^{17/2}+9\,a^{9/2}\,c^{15/2}-5\,a^{11/2}\,c^{13/2}-5\,a^{13/2}\,c^{11/2}+9\,a^{15/2}\,c^{9/2}-5\,a^{17/2}\,c^{7/2}+a^{19/2}\,c^{5/2}}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{10}\,c^2-28\,a^9\,c^3+88\,a^8\,c^4-164\,a^7\,c^5+200\,a^6\,c^6-164\,a^5\,c^7+88\,a^4\,c^8-28\,a^3\,c^9+4\,a^2\,c^{10}\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}\right)\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}+\frac{3\,b\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(\frac{9\,a^6\,b\,c^{7/2}-9\,a^{7/2}\,b\,c^6-24\,a^5\,b\,c^{9/2}+24\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4-3\,a^2\,b\,c^{15/2}+3\,a^{15/2}\,b\,c^2}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(6\,a^{3/2}\,b\,c^8-6\,a^8\,b\,c^{3/2}+36\,a^6\,b\,c^{7/2}-36\,a^{7/2}\,b\,c^6-48\,a^5\,b\,c^{9/2}+48\,a^{9/2}\,b\,c^5+18\,a^4\,b\,c^{11/2}-18\,a^{11/2}\,b\,c^4\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}+\frac{3\,b\,\left(\frac{a^{5/2}\,c^{19/2}-5\,a^{7/2}\,c^{17/2}+9\,a^{9/2}\,c^{15/2}-5\,a^{11/2}\,c^{13/2}-5\,a^{13/2}\,c^{11/2}+9\,a^{15/2}\,c^{9/2}-5\,a^{17/2}\,c^{7/2}+a^{19/2}\,c^{5/2}}{a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,a^{10}\,c^2-28\,a^9\,c^3+88\,a^8\,c^4-164\,a^7\,c^5+200\,a^6\,c^6-164\,a^5\,c^7+88\,a^4\,c^8-28\,a^3\,c^9+4\,a^2\,c^{10}\right)}{2\,\left(\sqrt{c+b\,x}-\sqrt{c}\right)\,\left(a^9\,c^3-6\,a^8\,c^4+15\,a^7\,c^5-20\,a^6\,c^6+15\,a^5\,c^7-6\,a^4\,c^8+a^3\,c^9\right)}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}\right)\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)}{2\,\left(-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7\right)}}\right)\,\sqrt{\left(\sqrt{a}\,c^{3/2}-2\,a\,c+a^{3/2}\,\sqrt{c}\right)\,\left(2\,a\,c+\sqrt{a}\,c^{3/2}+a^{3/2}\,\sqrt{c}\right)}\,\left(a\,c^{7/2}+a^{7/2}\,c-3\,a^3\,c^{3/2}-3\,a^{3/2}\,c^3+2\,a^2\,c^{5/2}+2\,a^{5/2}\,c^2\right)\,3{}\mathrm{i}}{-a^7\,c^2+5\,a^6\,c^3-10\,a^5\,c^4+10\,a^4\,c^5-5\,a^3\,c^6+a^2\,c^7}","Not used",1,"(b*atan(((b*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((9*a^6*b*c^(7/2) - 9*a^(7/2)*b*c^6 - 24*a^5*b*c^(9/2) + 24*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4 - 3*a^2*b*c^(15/2) + 3*a^(15/2)*b*c^2)/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(6*a^(3/2)*b*c^8 - 6*a^8*b*c^(3/2) + 36*a^6*b*c^(7/2) - 36*a^(7/2)*b*c^6 - 48*a^5*b*c^(9/2) + 48*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)) - (3*b*((a^(5/2)*c^(19/2) - 5*a^(7/2)*c^(17/2) + 9*a^(9/2)*c^(15/2) - 5*a^(11/2)*c^(13/2) - 5*a^(13/2)*c^(11/2) + 9*a^(15/2)*c^(9/2) - 5*a^(17/2)*c^(7/2) + a^(19/2)*c^(5/2))/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^10 - 28*a^3*c^9 + 88*a^4*c^8 - 164*a^5*c^7 + 200*a^6*c^6 - 164*a^7*c^5 + 88*a^8*c^4 - 28*a^9*c^3 + 4*a^10*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2))/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)))*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2)*3i)/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)) + (b*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((9*a^6*b*c^(7/2) - 9*a^(7/2)*b*c^6 - 24*a^5*b*c^(9/2) + 24*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4 - 3*a^2*b*c^(15/2) + 3*a^(15/2)*b*c^2)/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(6*a^(3/2)*b*c^8 - 6*a^8*b*c^(3/2) + 36*a^6*b*c^(7/2) - 36*a^(7/2)*b*c^6 - 48*a^5*b*c^(9/2) + 48*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)) + (3*b*((a^(5/2)*c^(19/2) - 5*a^(7/2)*c^(17/2) + 9*a^(9/2)*c^(15/2) - 5*a^(11/2)*c^(13/2) - 5*a^(13/2)*c^(11/2) + 9*a^(15/2)*c^(9/2) - 5*a^(17/2)*c^(7/2) + a^(19/2)*c^(5/2))/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^10 - 28*a^3*c^9 + 88*a^4*c^8 - 164*a^5*c^7 + 200*a^6*c^6 - 164*a^7*c^5 + 88*a^8*c^4 - 28*a^9*c^3 + 4*a^10*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2))/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)))*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2)*3i)/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)))/(((9*a^(3/2)*b^2*c^(11/2))/2 - 18*a^(5/2)*b^2*c^(9/2) + 27*a^(7/2)*b^2*c^(7/2) - 18*a^(9/2)*b^2*c^(5/2) + (9*a^(11/2)*b^2*c^(3/2))/2)/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(72*a^3*b^2*c^4 - 72*a^2*b^2*c^5 + 72*a^4*b^2*c^3 - 72*a^5*b^2*c^2 + 27*a^(3/2)*b^2*c^(11/2) + 36*a^(5/2)*b^2*c^(9/2) - 126*a^(7/2)*b^2*c^(7/2) + 36*a^(9/2)*b^2*c^(5/2) + 27*a^(11/2)*b^2*c^(3/2)))/(((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)) - (3*b*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((9*a^6*b*c^(7/2) - 9*a^(7/2)*b*c^6 - 24*a^5*b*c^(9/2) + 24*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4 - 3*a^2*b*c^(15/2) + 3*a^(15/2)*b*c^2)/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(6*a^(3/2)*b*c^8 - 6*a^8*b*c^(3/2) + 36*a^6*b*c^(7/2) - 36*a^(7/2)*b*c^6 - 48*a^5*b*c^(9/2) + 48*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)) - (3*b*((a^(5/2)*c^(19/2) - 5*a^(7/2)*c^(17/2) + 9*a^(9/2)*c^(15/2) - 5*a^(11/2)*c^(13/2) - 5*a^(13/2)*c^(11/2) + 9*a^(15/2)*c^(9/2) - 5*a^(17/2)*c^(7/2) + a^(19/2)*c^(5/2))/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^10 - 28*a^3*c^9 + 88*a^4*c^8 - 164*a^5*c^7 + 200*a^6*c^6 - 164*a^7*c^5 + 88*a^8*c^4 - 28*a^9*c^3 + 4*a^10*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2))/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)))*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2))/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)) + (3*b*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*((9*a^6*b*c^(7/2) - 9*a^(7/2)*b*c^6 - 24*a^5*b*c^(9/2) + 24*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4 - 3*a^2*b*c^(15/2) + 3*a^(15/2)*b*c^2)/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) + (((a + b*x)^(1/2) - a^(1/2))*(6*a^(3/2)*b*c^8 - 6*a^8*b*c^(3/2) + 36*a^6*b*c^(7/2) - 36*a^(7/2)*b*c^6 - 48*a^5*b*c^(9/2) + 48*a^(9/2)*b*c^5 + 18*a^4*b*c^(11/2) - 18*a^(11/2)*b*c^4))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)) + (3*b*((a^(5/2)*c^(19/2) - 5*a^(7/2)*c^(17/2) + 9*a^(9/2)*c^(15/2) - 5*a^(11/2)*c^(13/2) - 5*a^(13/2)*c^(11/2) + 9*a^(15/2)*c^(9/2) - 5*a^(17/2)*c^(7/2) + a^(19/2)*c^(5/2))/(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3) - (((a + b*x)^(1/2) - a^(1/2))*(4*a^2*c^10 - 28*a^3*c^9 + 88*a^4*c^8 - 164*a^5*c^7 + 200*a^6*c^6 - 164*a^7*c^5 + 88*a^8*c^4 - 28*a^9*c^3 + 4*a^10*c^2))/(2*((c + b*x)^(1/2) - c^(1/2))*(a^3*c^9 - 6*a^4*c^8 + 15*a^5*c^7 - 20*a^6*c^6 + 15*a^7*c^5 - 6*a^8*c^4 + a^9*c^3)))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2))/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2)))*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2))/(2*(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2))))*((a^(1/2)*c^(3/2) - 2*a*c + a^(3/2)*c^(1/2))*(2*a*c + a^(1/2)*c^(3/2) + a^(3/2)*c^(1/2)))^(1/2)*(a*c^(7/2) + a^(7/2)*c - 3*a^3*c^(3/2) - 3*a^(3/2)*c^3 + 2*a^2*c^(5/2) + 2*a^(5/2)*c^2)*3i)/(a^2*c^7 - 5*a^3*c^6 + 10*a^4*c^5 - 10*a^5*c^4 + 5*a^6*c^3 - a^7*c^2) - (log(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)))*(3*a^2*b*c^(1/2) + 3*a^(1/2)*b*c^2 + a*c*(9*a^(1/2)*b + 9*b*c^(1/2))))/(2*a*c^4 - 2*a^4*c - 6*a^2*c^3 + 6*a^3*c^2) - ((a^(1/2)*((3*a*b)/4 + (b*c)/4))/(a*c^3 + 3*a^3*c - a^4 - 3*a^2*c^2) - (c^(1/2)*((a*b)/4 + (3*b*c)/4))/(3*a*c^3 + a^3*c - c^4 - 3*a^2*c^2) - (((a^(1/2)*((3*a^3*b)/4 - (b*c^3)/4 - (a*b*c^2)/2 + 17*a^2*b*c))/(a^5*c - a^2*c^4 + 3*a^3*c^3 - 3*a^4*c^2) + (c^(1/2)*((a^3*b)/4 - (3*b*c^3)/4 - 17*a*b*c^2 + (a^2*b*c)/2))/(a*c^5 - 3*a^2*c^4 + 3*a^3*c^3 - a^4*c^2))*((a + b*x)^(1/2) - a^(1/2))^3)/((c + b*x)^(1/2) - c^(1/2))^3 + (((a^(1/2)*((b*c^3)/4 - a^3*b + (75*a*b*c^2)/4 + 15*a^2*b*c))/(a^5*c - a^2*c^4 + 3*a^3*c^3 - 3*a^4*c^2) - (c^(1/2)*((a^3*b)/4 - b*c^3 + 15*a*b*c^2 + (75*a^2*b*c)/4))/(a*c^5 - 3*a^2*c^4 + 3*a^3*c^3 - a^4*c^2))*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 + (((a^(1/2)*((a^2*b)/4 - 2*b*c^2 + (67*a*b*c)/4))/(a*c^4 - a^4*c - 3*a^2*c^3 + 3*a^3*c^2) + (c^(1/2)*((b*c^2)/4 - 2*a^2*b + (67*a*b*c)/4))/(a*c^4 - a^4*c - 3*a^2*c^3 + 3*a^3*c^2))*((a + b*x)^(1/2) - a^(1/2)))/((c + b*x)^(1/2) - c^(1/2)))/(((a + b*x)^(1/2) - a^(1/2))/((c + b*x)^(1/2) - c^(1/2)) + ((a + b*x)^(1/2) - a^(1/2))^4/((c + b*x)^(1/2) - c^(1/2))^4 - (((a + c)/(a^(1/2)*c^(1/2)) - 1)*((a + b*x)^(1/2) - a^(1/2))^2)/((c + b*x)^(1/2) - c^(1/2))^2 - (((a + c)/(a^(1/2)*c^(1/2)) - 1)*((a + b*x)^(1/2) - a^(1/2))^3)/((c + b*x)^(1/2) - c^(1/2))^3) - (b*((a + b*x)^(1/2) - a^(1/2)))/(4*a^(1/2)*c^(1/2)*(a^(1/2) - c^(1/2))^3*((c + b*x)^(1/2) - c^(1/2)))","B"
416,1,21,21,2.968411,"\text{Not used}","int(1/((x + 1)^(1/2) + x^(1/2)),x)","\frac{2\,x\,\sqrt{x+1}}{3}+\frac{2\,\sqrt{x+1}}{3}-\frac{2\,x^{3/2}}{3}","Not used",1,"(2*x*(x + 1)^(1/2))/3 + (2*(x + 1)^(1/2))/3 - (2*x^(3/2))/3","B"
417,1,21,21,2.937035,"\text{Not used}","int(1/((x - 1)^(1/2) + x^(1/2)),x)","\frac{2\,\sqrt{x-1}}{3}-\frac{2\,x\,\sqrt{x-1}}{3}+\frac{2\,x^{3/2}}{3}","Not used",1,"(2*(x - 1)^(1/2))/3 - (2*x*(x - 1)^(1/2))/3 + (2*x^(3/2))/3","B"
418,1,15,23,2.837705,"\text{Not used}","int(1/((x - 1)^(1/2) + (x + 1)^(1/2)),x)","\frac{{\left(x+1\right)}^{3/2}}{3}-\frac{{\left(x-1\right)}^{3/2}}{3}","Not used",1,"(x + 1)^(3/2)/3 - (x - 1)^(3/2)/3","B"
419,1,45,38,3.020874,"\text{Not used}","int(x^3*((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","\frac{x^4}{2}-\frac{\sqrt{1-x}\,\left(-\frac{2\,x^5}{5}-\frac{2\,x^4}{5}+\frac{2\,x^3}{15}+\frac{2\,x^2}{15}+\frac{4\,x}{15}+\frac{4}{15}\right)}{\sqrt{x+1}}","Not used",1,"x^4/2 - ((1 - x)^(1/2)*((4*x)/15 + (2*x^2)/15 + (2*x^3)/15 - (2*x^4)/5 - (2*x^5)/5 + 4/15))/(x + 1)^(1/2)","B"
420,1,563,48,14.085934,"\text{Not used}","int(x^2*((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","\frac{\frac{4\,\left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-\frac{28\,{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}-\frac{4\,{\left(\sqrt{1-x}-1\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}}{\frac{4\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{6\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{{\left(\sqrt{1-x}-1\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}+1}-\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\frac{\frac{3\,\left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}+\frac{23\,{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}-\frac{333\,{\left(\sqrt{1-x}-1\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}+\frac{671\,{\left(\sqrt{1-x}-1\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}-\frac{671\,{\left(\sqrt{1-x}-1\right)}^9}{{\left(\sqrt{x+1}-1\right)}^9}+\frac{333\,{\left(\sqrt{1-x}-1\right)}^{11}}{{\left(\sqrt{x+1}-1\right)}^{11}}-\frac{23\,{\left(\sqrt{1-x}-1\right)}^{13}}{{\left(\sqrt{x+1}-1\right)}^{13}}-\frac{3\,{\left(\sqrt{1-x}-1\right)}^{15}}{{\left(\sqrt{x+1}-1\right)}^{15}}}{\frac{8\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{56\,{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{1-x}-1\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}+\frac{56\,{\left(\sqrt{1-x}-1\right)}^{10}}{{\left(\sqrt{x+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^{12}}{{\left(\sqrt{x+1}-1\right)}^{12}}+\frac{8\,{\left(\sqrt{1-x}-1\right)}^{14}}{{\left(\sqrt{x+1}-1\right)}^{14}}+\frac{{\left(\sqrt{1-x}-1\right)}^{16}}{{\left(\sqrt{x+1}-1\right)}^{16}}+1}+\frac{2\,x^3}{3}","Not used",1,"((4*((1 - x)^(1/2) - 1))/((x + 1)^(1/2) - 1) - (28*((1 - x)^(1/2) - 1)^3)/((x + 1)^(1/2) - 1)^3 + (28*((1 - x)^(1/2) - 1)^5)/((x + 1)^(1/2) - 1)^5 - (4*((1 - x)^(1/2) - 1)^7)/((x + 1)^(1/2) - 1)^7)/((4*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + (6*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + (4*((1 - x)^(1/2) - 1)^6)/((x + 1)^(1/2) - 1)^6 + ((1 - x)^(1/2) - 1)^8/((x + 1)^(1/2) - 1)^8 + 1) - atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - ((3*((1 - x)^(1/2) - 1))/((x + 1)^(1/2) - 1) + (23*((1 - x)^(1/2) - 1)^3)/((x + 1)^(1/2) - 1)^3 - (333*((1 - x)^(1/2) - 1)^5)/((x + 1)^(1/2) - 1)^5 + (671*((1 - x)^(1/2) - 1)^7)/((x + 1)^(1/2) - 1)^7 - (671*((1 - x)^(1/2) - 1)^9)/((x + 1)^(1/2) - 1)^9 + (333*((1 - x)^(1/2) - 1)^11)/((x + 1)^(1/2) - 1)^11 - (23*((1 - x)^(1/2) - 1)^13)/((x + 1)^(1/2) - 1)^13 - (3*((1 - x)^(1/2) - 1)^15)/((x + 1)^(1/2) - 1)^15)/((8*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + (28*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + (56*((1 - x)^(1/2) - 1)^6)/((x + 1)^(1/2) - 1)^6 + (70*((1 - x)^(1/2) - 1)^8)/((x + 1)^(1/2) - 1)^8 + (56*((1 - x)^(1/2) - 1)^10)/((x + 1)^(1/2) - 1)^10 + (28*((1 - x)^(1/2) - 1)^12)/((x + 1)^(1/2) - 1)^12 + (8*((1 - x)^(1/2) - 1)^14)/((x + 1)^(1/2) - 1)^14 + ((1 - x)^(1/2) - 1)^16/((x + 1)^(1/2) - 1)^16 + 1) + (2*x^3)/3","B"
421,1,33,19,2.977292,"\text{Not used}","int(x*((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","x^2-\frac{\sqrt{1-x}\,\left(-\frac{2\,x^3}{3}-\frac{2\,x^2}{3}+\frac{2\,x}{3}+\frac{2}{3}\right)}{\sqrt{x+1}}","Not used",1,"x^2 - ((1 - x)^(1/2)*((2*x)/3 - (2*x^2)/3 - (2*x^3)/3 + 2/3))/(x + 1)^(1/2)","B"
422,1,206,19,7.724782,"\text{Not used}","int(((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","2\,x-4\,\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\frac{\frac{4\,\left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-\frac{28\,{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}-\frac{4\,{\left(\sqrt{1-x}-1\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}}{\frac{4\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{6\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{{\left(\sqrt{1-x}-1\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}+1}","Not used",1,"2*x - 4*atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - ((4*((1 - x)^(1/2) - 1))/((x + 1)^(1/2) - 1) - (28*((1 - x)^(1/2) - 1)^3)/((x + 1)^(1/2) - 1)^3 + (28*((1 - x)^(1/2) - 1)^5)/((x + 1)^(1/2) - 1)^5 - (4*((1 - x)^(1/2) - 1)^7)/((x + 1)^(1/2) - 1)^7)/((4*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + (6*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + (4*((1 - x)^(1/2) - 1)^6)/((x + 1)^(1/2) - 1)^6 + ((1 - x)^(1/2) - 1)^8/((x + 1)^(1/2) - 1)^8 + 1)","B"
423,1,122,32,4.097515,"\text{Not used}","int(((x + 1)^(1/2) + (1 - x)^(1/2))^2/x,x)","2\,\ln\left(\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-1\right)-2\,\ln\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)+2\,\ln\left(x\right)+\frac{16\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2\,\left(\frac{2\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+1\right)}","Not used",1,"2*log(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - 1) - 2*log(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) + 2*log(x) + (16*((1 - x)^(1/2) - 1)^2)/(((x + 1)^(1/2) - 1)^2*((2*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + ((1 - x)^(1/2) - 1)^4/((x + 1)^(1/2) - 1)^4 + 1))","B"
424,1,120,26,3.794618,"\text{Not used}","int(((x + 1)^(1/2) + (1 - x)^(1/2))^2/x^2,x)","8\,\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\frac{\frac{5\,{\left(\sqrt{1-x}-1\right)}^2}{2\,{\left(\sqrt{x+1}-1\right)}^2}-\frac{1}{2}}{\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}-\frac{{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}}-\frac{\sqrt{1-x}-1}{2\,\left(\sqrt{x+1}-1\right)}-\frac{2}{x}","Not used",1,"8*atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - ((5*((1 - x)^(1/2) - 1)^2)/(2*((x + 1)^(1/2) - 1)^2) - 1/2)/(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1) - ((1 - x)^(1/2) - 1)^3/((x + 1)^(1/2) - 1)^3) - ((1 - x)^(1/2) - 1)/(2*((x + 1)^(1/2) - 1)) - 2/x","B"
425,1,189,34,4.878698,"\text{Not used}","int(((x + 1)^(1/2) + (1 - x)^(1/2))^2/x^3,x)","\ln\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\ln\left(\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-1\right)+\frac{{\left(\sqrt{1-x}-1\right)}^2}{16\,{\left(\sqrt{x+1}-1\right)}^2}-\frac{\frac{{\left(\sqrt{1-x}-1\right)}^2}{8\,{\left(\sqrt{x+1}-1\right)}^2}+\frac{15\,{\left(\sqrt{1-x}-1\right)}^4}{16\,{\left(\sqrt{x+1}-1\right)}^4}-\frac{1}{16}}{\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-\frac{2\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}}-\frac{1}{x^2}","Not used",1,"log(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - log(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - 1) + ((1 - x)^(1/2) - 1)^2/(16*((x + 1)^(1/2) - 1)^2) - (((1 - x)^(1/2) - 1)^2/(8*((x + 1)^(1/2) - 1)^2) + (15*((1 - x)^(1/2) - 1)^4)/(16*((x + 1)^(1/2) - 1)^4) - 1/16)/(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - (2*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + ((1 - x)^(1/2) - 1)^6/((x + 1)^(1/2) - 1)^6) - 1/x^2","B"
426,1,179,147,2.919766,"\text{Not used}","int(x^3/((a + b*x)^(1/2) + (a + c*x)^(1/2)),x)","\frac{2\,x^3\,\sqrt{a+b\,x}}{7\,\left(b-c\right)}-\frac{2\,x^3\,\sqrt{a+c\,x}}{7\,\left(b-c\right)}+\frac{16\,a^3\,\sqrt{a+b\,x}}{105\,b^3\,\left(b-c\right)}-\frac{16\,a^3\,\sqrt{a+c\,x}}{105\,c^3\,\left(b-c\right)}+\frac{2\,a\,x^2\,\sqrt{a+b\,x}}{35\,b\,\left(b-c\right)}-\frac{8\,a^2\,x\,\sqrt{a+b\,x}}{105\,b^2\,\left(b-c\right)}-\frac{2\,a\,x^2\,\sqrt{a+c\,x}}{35\,c\,\left(b-c\right)}+\frac{8\,a^2\,x\,\sqrt{a+c\,x}}{105\,c^2\,\left(b-c\right)}","Not used",1,"(2*x^3*(a + b*x)^(1/2))/(7*(b - c)) - (2*x^3*(a + c*x)^(1/2))/(7*(b - c)) + (16*a^3*(a + b*x)^(1/2))/(105*b^3*(b - c)) - (16*a^3*(a + c*x)^(1/2))/(105*c^3*(b - c)) + (2*a*x^2*(a + b*x)^(1/2))/(35*b*(b - c)) - (8*a^2*x*(a + b*x)^(1/2))/(105*b^2*(b - c)) - (2*a*x^2*(a + c*x)^(1/2))/(35*c*(b - c)) + (8*a^2*x*(a + c*x)^(1/2))/(105*c^2*(b - c))","B"
427,1,129,95,2.861615,"\text{Not used}","int(x^2/((a + b*x)^(1/2) + (a + c*x)^(1/2)),x)","\frac{2\,x^2\,\sqrt{a+b\,x}}{5\,\left(b-c\right)}-\frac{2\,x^2\,\sqrt{a+c\,x}}{5\,\left(b-c\right)}-\frac{4\,a^2\,\sqrt{a+b\,x}}{15\,b^2\,\left(b-c\right)}+\frac{4\,a^2\,\sqrt{a+c\,x}}{15\,c^2\,\left(b-c\right)}+\frac{2\,a\,x\,\sqrt{a+b\,x}}{15\,b\,\left(b-c\right)}-\frac{2\,a\,x\,\sqrt{a+c\,x}}{15\,c\,\left(b-c\right)}","Not used",1,"(2*x^2*(a + b*x)^(1/2))/(5*(b - c)) - (2*x^2*(a + c*x)^(1/2))/(5*(b - c)) - (4*a^2*(a + b*x)^(1/2))/(15*b^2*(b - c)) + (4*a^2*(a + c*x)^(1/2))/(15*c^2*(b - c)) + (2*a*x*(a + b*x)^(1/2))/(15*b*(b - c)) - (2*a*x*(a + c*x)^(1/2))/(15*c*(b - c))","B"
428,1,79,47,2.905815,"\text{Not used}","int(x/((a + b*x)^(1/2) + (a + c*x)^(1/2)),x)","\frac{2\,x\,\sqrt{a+b\,x}}{3\,\left(b-c\right)}-\frac{2\,x\,\sqrt{a+c\,x}}{3\,\left(b-c\right)}+\frac{2\,a\,\sqrt{a+b\,x}}{3\,b\,\left(b-c\right)}-\frac{2\,a\,\sqrt{a+c\,x}}{3\,c\,\left(b-c\right)}","Not used",1,"(2*x*(a + b*x)^(1/2))/(3*(b - c)) - (2*x*(a + c*x)^(1/2))/(3*(b - c)) + (2*a*(a + b*x)^(1/2))/(3*b*(b - c)) - (2*a*(a + c*x)^(1/2))/(3*c*(b - c))","B"
429,1,213,97,4.330184,"\text{Not used}","int(1/((a + b*x)^(1/2) + (a + c*x)^(1/2)),x)","-\frac{2\,\sqrt{a}\,c\,\left(\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}+\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}\right)-2\,\sqrt{a}\,b\,\left(\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}+4\right)}{\left(b-c\right)\,\left(b-\frac{c\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}\right)}","Not used",1,"-(2*a^(1/2)*c*((2*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) + (log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2) - 2*a^(1/2)*b*(log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2))) - (2*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) + 4))/((b - c)*(b - (c*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2))","B"
430,1,1637,103,10.926113,"\text{Not used}","int(1/(x*((a + b*x)^(1/2) + (a + c*x)^(1/2))),x)","\frac{2\,a\,b-2\,a\,c+a\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)-2\,\sqrt{a}\,b\,\sqrt{a+c\,x}+2\,\sqrt{a}\,c\,\sqrt{a+b\,x}+a\,b\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)+b\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\sqrt{a+b\,x}\,\sqrt{a+c\,x}+c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\sqrt{a+b\,x}\,\sqrt{a+c\,x}-\sqrt{a}\,b\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\sqrt{a+b\,x}-\sqrt{a}\,b\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\sqrt{a+c\,x}-\sqrt{a}\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\sqrt{a+b\,x}-\sqrt{a}\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\sqrt{a+c\,x}+a\,b\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,2{}\mathrm{i}-a\,c\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,2{}\mathrm{i}+b\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,\sqrt{a+b\,x}\,\sqrt{a+c\,x}\,2{}\mathrm{i}-c\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,\sqrt{a+b\,x}\,\sqrt{a+c\,x}\,2{}\mathrm{i}-\sqrt{a}\,b\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,\sqrt{a+b\,x}\,2{}\mathrm{i}-\sqrt{a}\,b\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,\sqrt{a+c\,x}\,2{}\mathrm{i}+\sqrt{a}\,c\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,\sqrt{a+b\,x}\,2{}\mathrm{i}+\sqrt{a}\,c\,\mathrm{atan}\left(\frac{b^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-b^3\,\sqrt{a+c\,x}\,1{}\mathrm{i}+c^3\,\sqrt{a+b\,x}\,1{}\mathrm{i}-\sqrt{a}\,c^3\,1{}\mathrm{i}+\sqrt{a}\,b\,c^2\,1{}\mathrm{i}-b\,c^2\,\sqrt{a+c\,x}\,1{}\mathrm{i}}{b^3\,\sqrt{a+b\,x}-b^3\,\sqrt{a+c\,x}-c^3\,\sqrt{a+b\,x}+\sqrt{a}\,c^3-\sqrt{a}\,b\,c^2+b\,c^2\,\sqrt{a+c\,x}}\right)\,\sqrt{a+c\,x}\,2{}\mathrm{i}}{2\,\sqrt{a}\,\left(b-c\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}","Not used",1,"(2*a*b - 2*a*c + a*c*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2))) - 2*a^(1/2)*b*(a + c*x)^(1/2) + 2*a^(1/2)*c*(a + b*x)^(1/2) + a*b*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*2i - a*c*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*2i + a*b*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2))) + b*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*(a + b*x)^(1/2)*(a + c*x)^(1/2)*2i - c*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*(a + b*x)^(1/2)*(a + c*x)^(1/2)*2i + b*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a + b*x)^(1/2)*(a + c*x)^(1/2) + c*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a + b*x)^(1/2)*(a + c*x)^(1/2) - a^(1/2)*b*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*(a + b*x)^(1/2)*2i - a^(1/2)*b*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*(a + c*x)^(1/2)*2i + a^(1/2)*c*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*(a + b*x)^(1/2)*2i + a^(1/2)*c*atan((b^3*(a + b*x)^(1/2)*1i - b^3*(a + c*x)^(1/2)*1i + c^3*(a + b*x)^(1/2)*1i - a^(1/2)*c^3*1i + a^(1/2)*b*c^2*1i - b*c^2*(a + c*x)^(1/2)*1i)/(b^3*(a + b*x)^(1/2) - b^3*(a + c*x)^(1/2) - c^3*(a + b*x)^(1/2) + a^(1/2)*c^3 - a^(1/2)*b*c^2 + b*c^2*(a + c*x)^(1/2)))*(a + c*x)^(1/2)*2i - a^(1/2)*b*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a + b*x)^(1/2) - a^(1/2)*b*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a + c*x)^(1/2) - a^(1/2)*c*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a + b*x)^(1/2) - a^(1/2)*c*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a + c*x)^(1/2))/(2*a^(1/2)*(b - c)*((a + b*x)^(1/2) - a^(1/2))*((a + c*x)^(1/2) - a^(1/2)))","B"
431,1,1610,171,11.846860,"\text{Not used}","int(1/(x^2*((a + b*x)^(1/2) + (a + c*x)^(1/2))),x)","\frac{\frac{a^{3/2}\,b^3}{16\,\left(a^3\,c^2-a^3\,b\,c\right)}+\frac{a^{3/2}\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(\frac{b^3}{4}-\frac{7\,b^2\,c}{16}+\frac{b\,c^2}{4}\right)}{\left(a^3\,c^2-a^3\,b\,c\right)\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{a^{3/2}\,\left(\frac{b^3}{16}+\frac{c\,b^2}{16}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\left(a^3\,c^2-a^3\,b\,c\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}+\frac{\left(\frac{b^2}{8}-\frac{c^2}{8}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{a^{3/2}\,c\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}}{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}-\frac{\left(b+c\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{c\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+\frac{b\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{c\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}}-\frac{\left(\frac{c\,\left(b+c\right)}{4\,a^{3/2}\,\left(b-c\right)}-\frac{c\,\left(b^2-c^2\right)}{4\,a^{3/2}\,{\left(b-c\right)}^2}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(a^{3/2}\,b^2+a^{3/2}\,c^2\right)}{8\,a^3\,b-8\,a^3\,c}+\frac{c^2\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{16\,a^{3/2}\,\left(b-c\right)\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{\mathrm{atan}\left(\frac{\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(\frac{64\,a^6\,b^3-64\,a^6\,b\,c^2}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(64\,a^6\,b^3-128\,a^6\,b^2\,c+128\,a^6\,b\,c^2-64\,a^6\,c^3\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)}{8\,a^3}-\frac{16\,a^3\,b^4+16\,a^3\,b\,c^3}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}+\frac{\left(8\,a^3\,b^4+8\,a^3\,c^4\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)\,1{}\mathrm{i}}{8\,a^3}-\frac{\left(b+c\right)\,\left(\frac{16\,a^3\,b^4+16\,a^3\,b\,c^3}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}+\frac{\left(b+c\right)\,\left(\frac{64\,a^6\,b^3-64\,a^6\,b\,c^2}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(64\,a^6\,b^3-128\,a^6\,b^2\,c+128\,a^6\,b\,c^2-64\,a^6\,c^3\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)}{8\,a^3}-\frac{\left(8\,a^3\,b^4+8\,a^3\,c^4\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)\,1{}\mathrm{i}}{8\,a^3}}{\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(\frac{64\,a^6\,b^3-64\,a^6\,b\,c^2}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(64\,a^6\,b^3-128\,a^6\,b^2\,c+128\,a^6\,b\,c^2-64\,a^6\,c^3\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)}{8\,a^3}-\frac{16\,a^3\,b^4+16\,a^3\,b\,c^3}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}+\frac{\left(8\,a^3\,b^4+8\,a^3\,c^4\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)}{8\,a^3}-\frac{b\,c^4-b^5}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)}+\frac{\left(b+c\right)\,\left(\frac{16\,a^3\,b^4+16\,a^3\,b\,c^3}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}+\frac{\left(b+c\right)\,\left(\frac{64\,a^6\,b^3-64\,a^6\,b\,c^2}{64\,\left(a^6\,c^3-a^6\,b\,c^2\right)}-\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(64\,a^6\,b^3-128\,a^6\,b^2\,c+128\,a^6\,b\,c^2-64\,a^6\,c^3\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)}{8\,a^3}-\frac{\left(8\,a^3\,b^4+8\,a^3\,c^4\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{32\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)}{8\,a^3}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(-b^4\,c-b^3\,c^2+b^2\,c^3+b\,c^4\right)}{16\,\left(a^6\,c^3-a^6\,b\,c^2\right)\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}}\right)\,\left(a^{3/2}\,b+a^{3/2}\,c\right)\,1{}\mathrm{i}}{4\,a^3}","Not used",1,"((a^(3/2)*b^3)/(16*(a^3*c^2 - a^3*b*c)) + (a^(3/2)*((a + b*x)^(1/2) - a^(1/2))^2*((b*c^2)/4 - (7*b^2*c)/16 + b^3/4))/((a^3*c^2 - a^3*b*c)*((a + c*x)^(1/2) - a^(1/2))^2) - (a^(3/2)*((b^2*c)/16 + b^3/16)*((a + b*x)^(1/2) - a^(1/2)))/((a^3*c^2 - a^3*b*c)*((a + c*x)^(1/2) - a^(1/2))) + ((b^2/8 - c^2/8)*((a + b*x)^(1/2) - a^(1/2))^3)/(a^(3/2)*c*((a + c*x)^(1/2) - a^(1/2))^3))/(((a + b*x)^(1/2) - a^(1/2))^4/((a + c*x)^(1/2) - a^(1/2))^4 - ((b + c)*((a + b*x)^(1/2) - a^(1/2))^3)/(c*((a + c*x)^(1/2) - a^(1/2))^3) + (b*((a + b*x)^(1/2) - a^(1/2))^2)/(c*((a + c*x)^(1/2) - a^(1/2))^2)) - (((c*(b + c))/(4*a^(3/2)*(b - c)) - (c*(b^2 - c^2))/(4*a^(3/2)*(b - c)^2))*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(a^(3/2)*b^2 + a^(3/2)*c^2))/(8*a^3*b - 8*a^3*c) + (atan((((b + c)*(((b + c)*((64*a^6*b^3 - 64*a^6*b*c^2)/(64*(a^6*c^3 - a^6*b*c^2)) - (((a + b*x)^(1/2) - a^(1/2))*(64*a^6*b^3 - 64*a^6*c^3 + 128*a^6*b*c^2 - 128*a^6*b^2*c))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))/(8*a^3) - (16*a^3*b^4 + 16*a^3*b*c^3)/(64*(a^6*c^3 - a^6*b*c^2)) + ((8*a^3*b^4 + 8*a^3*c^4)*((a + b*x)^(1/2) - a^(1/2)))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2))))*1i)/(8*a^3) - ((b + c)*((16*a^3*b^4 + 16*a^3*b*c^3)/(64*(a^6*c^3 - a^6*b*c^2)) + ((b + c)*((64*a^6*b^3 - 64*a^6*b*c^2)/(64*(a^6*c^3 - a^6*b*c^2)) - (((a + b*x)^(1/2) - a^(1/2))*(64*a^6*b^3 - 64*a^6*c^3 + 128*a^6*b*c^2 - 128*a^6*b^2*c))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))/(8*a^3) - ((8*a^3*b^4 + 8*a^3*c^4)*((a + b*x)^(1/2) - a^(1/2)))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2))))*1i)/(8*a^3))/(((b + c)*(((b + c)*((64*a^6*b^3 - 64*a^6*b*c^2)/(64*(a^6*c^3 - a^6*b*c^2)) - (((a + b*x)^(1/2) - a^(1/2))*(64*a^6*b^3 - 64*a^6*c^3 + 128*a^6*b*c^2 - 128*a^6*b^2*c))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))/(8*a^3) - (16*a^3*b^4 + 16*a^3*b*c^3)/(64*(a^6*c^3 - a^6*b*c^2)) + ((8*a^3*b^4 + 8*a^3*c^4)*((a + b*x)^(1/2) - a^(1/2)))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))/(8*a^3) - (b*c^4 - b^5)/(32*(a^6*c^3 - a^6*b*c^2)) + ((b + c)*((16*a^3*b^4 + 16*a^3*b*c^3)/(64*(a^6*c^3 - a^6*b*c^2)) + ((b + c)*((64*a^6*b^3 - 64*a^6*b*c^2)/(64*(a^6*c^3 - a^6*b*c^2)) - (((a + b*x)^(1/2) - a^(1/2))*(64*a^6*b^3 - 64*a^6*c^3 + 128*a^6*b*c^2 - 128*a^6*b^2*c))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))/(8*a^3) - ((8*a^3*b^4 + 8*a^3*c^4)*((a + b*x)^(1/2) - a^(1/2)))/(32*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))/(8*a^3) + (((a + b*x)^(1/2) - a^(1/2))*(b*c^4 - b^4*c + b^2*c^3 - b^3*c^2))/(16*(a^6*c^3 - a^6*b*c^2)*((a + c*x)^(1/2) - a^(1/2)))))*(a^(3/2)*b + a^(3/2)*c)*1i)/(4*a^3) + (c^2*((a + b*x)^(1/2) - a^(1/2))^2)/(16*a^(3/2)*(b - c)*((a + c*x)^(1/2) - a^(1/2))^2)","B"
432,1,1107,195,18.151293,"\text{Not used}","int(x^3/((a + b*x)^(1/2) + (a + c*x)^(1/2))^2,x)","\frac{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(128\,a^3\,b^3\,c+\frac{1312\,a^3\,b^2\,c^2}{3}+128\,a^3\,b\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^6}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^7\,\left(19\,a^3\,b^3\,c+269\,a^3\,b^2\,c^2+269\,a^3\,b\,c^3+19\,a^3\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^7}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5\,\left(19\,a^3\,b^4+269\,a^3\,b^3\,c+269\,a^3\,b^2\,c^2+19\,a^3\,b\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(64\,a^3\,b^4+192\,a^3\,b^3\,c+64\,a^3\,b^2\,c^2\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8\,\left(64\,a^3\,b^2\,c^2+192\,a^3\,b\,c^3+64\,a^3\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^8}+\frac{16\,a^3\,b^4\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{16\,a^3\,c^4\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{10}}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^{10}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{11}\,\left(a^3\,b^3\,c^3-a^3\,b^2\,c^4-a^3\,b\,c^5+a^3\,c^6\right)}{2\,b^2\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^{11}}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(17\,a^3\,b^5+303\,a^3\,b^4\,c+303\,a^3\,b^3\,c^2+17\,a^3\,b^2\,c^3\right)}{6\,c\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^9\,\left(17\,a^3\,b^3\,c^2+303\,a^3\,b^2\,c^3+303\,a^3\,b\,c^4+17\,a^3\,c^5\right)}{6\,b\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^9}+\frac{\left(a^3\,b+a^3\,c\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(b^5-2\,b^4\,c+b^3\,c^2\right)}{2\,c^2\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}}{b^8-2\,b^7\,c+b^6\,c^2+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{12}\,\left(b^2\,c^6-2\,b\,c^7+c^8\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^{12}}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(6\,b^7\,c-12\,b^6\,c^2+6\,b^5\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^{10}\,\left(6\,b^3\,c^5-12\,b^2\,c^6+6\,b\,c^7\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^{10}}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(15\,b^6\,c^2-30\,b^5\,c^3+15\,b^4\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8\,\left(15\,b^4\,c^4-30\,b^3\,c^5+15\,b^2\,c^6\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^8}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(20\,b^5\,c^3-40\,b^4\,c^4+20\,b^3\,c^5\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^6}}+\frac{x^3\,\left(b+c\right)}{3\,{\left(b-c\right)}^2}+\frac{a\,x^2}{{\left(b-c\right)}^2}-\frac{a^3\,\mathrm{atanh}\left(\frac{\sqrt{c}\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}\right)\,\left(b+c\right)}{2\,b^{5/2}\,c^{5/2}}","Not used",1,"((((a + b*x)^(1/2) - a^(1/2))^6*(128*a^3*b*c^3 + 128*a^3*b^3*c + (1312*a^3*b^2*c^2)/3))/((a + c*x)^(1/2) - a^(1/2))^6 - (((a + b*x)^(1/2) - a^(1/2))^7*(19*a^3*c^4 + 269*a^3*b*c^3 + 19*a^3*b^3*c + 269*a^3*b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^7 - (((a + b*x)^(1/2) - a^(1/2))^5*(19*a^3*b^4 + 19*a^3*b*c^3 + 269*a^3*b^3*c + 269*a^3*b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^5 + (((a + b*x)^(1/2) - a^(1/2))^4*(64*a^3*b^4 + 192*a^3*b^3*c + 64*a^3*b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^4 + (((a + b*x)^(1/2) - a^(1/2))^8*(64*a^3*c^4 + 192*a^3*b*c^3 + 64*a^3*b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^8 + (16*a^3*b^4*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 + (16*a^3*c^4*((a + b*x)^(1/2) - a^(1/2))^10)/((a + c*x)^(1/2) - a^(1/2))^10 + (((a + b*x)^(1/2) - a^(1/2))^11*(a^3*c^6 - a^3*b*c^5 - a^3*b^2*c^4 + a^3*b^3*c^3))/(2*b^2*((a + c*x)^(1/2) - a^(1/2))^11) - (((a + b*x)^(1/2) - a^(1/2))^3*(17*a^3*b^5 + 303*a^3*b^4*c + 17*a^3*b^2*c^3 + 303*a^3*b^3*c^2))/(6*c*((a + c*x)^(1/2) - a^(1/2))^3) - (((a + b*x)^(1/2) - a^(1/2))^9*(17*a^3*c^5 + 303*a^3*b*c^4 + 303*a^3*b^2*c^3 + 17*a^3*b^3*c^2))/(6*b*((a + c*x)^(1/2) - a^(1/2))^9) + ((a^3*b + a^3*c)*((a + b*x)^(1/2) - a^(1/2))*(b^5 - 2*b^4*c + b^3*c^2))/(2*c^2*((a + c*x)^(1/2) - a^(1/2))))/(b^8 - 2*b^7*c + b^6*c^2 + (((a + b*x)^(1/2) - a^(1/2))^12*(c^8 - 2*b*c^7 + b^2*c^6))/((a + c*x)^(1/2) - a^(1/2))^12 - (((a + b*x)^(1/2) - a^(1/2))^2*(6*b^7*c + 6*b^5*c^3 - 12*b^6*c^2))/((a + c*x)^(1/2) - a^(1/2))^2 - (((a + b*x)^(1/2) - a^(1/2))^10*(6*b*c^7 - 12*b^2*c^6 + 6*b^3*c^5))/((a + c*x)^(1/2) - a^(1/2))^10 + (((a + b*x)^(1/2) - a^(1/2))^4*(15*b^4*c^4 - 30*b^5*c^3 + 15*b^6*c^2))/((a + c*x)^(1/2) - a^(1/2))^4 + (((a + b*x)^(1/2) - a^(1/2))^8*(15*b^2*c^6 - 30*b^3*c^5 + 15*b^4*c^4))/((a + c*x)^(1/2) - a^(1/2))^8 - (((a + b*x)^(1/2) - a^(1/2))^6*(20*b^3*c^5 - 40*b^4*c^4 + 20*b^5*c^3))/((a + c*x)^(1/2) - a^(1/2))^6) + (x^3*(b + c))/(3*(b - c)^2) + (a*x^2)/(b - c)^2 - (a^3*atanh((c^(1/2)*((a + b*x)^(1/2) - a^(1/2)))/(b^(1/2)*((a + c*x)^(1/2) - a^(1/2))))*(b + c))/(2*b^(5/2)*c^(5/2))","B"
433,1,129,142,0.246227,"\text{Not used}","int(x^2/((a + b*x)^(1/2) + (a + c*x)^(1/2))^2,x)","\frac{2\,a\,x}{{\left(b-c\right)}^2}+\frac{x^2\,\left(b+c\right)}{2\,{\left(b-c\right)}^2}-\frac{2\,\left(\frac{x}{2}+\frac{a\,b+a\,c}{4\,b\,c}\right)\,\sqrt{a+b\,x}\,\sqrt{a+c\,x}}{{\left(b-c\right)}^2}+\frac{\ln\left(a\,b+a\,c+2\,b\,c\,x+2\,\sqrt{b}\,\sqrt{c}\,\sqrt{a+b\,x}\,\sqrt{a+c\,x}\right)\,{\left(a\,b-a\,c\right)}^2}{4\,b^{3/2}\,c^{3/2}\,{\left(b-c\right)}^2}","Not used",1,"(2*a*x)/(b - c)^2 + (x^2*(b + c))/(2*(b - c)^2) - (2*(x/2 + (a*b + a*c)/(4*b*c))*(a + b*x)^(1/2)*(a + c*x)^(1/2))/(b - c)^2 + (log(a*b + a*c + 2*b*c*x + 2*b^(1/2)*c^(1/2)*(a + b*x)^(1/2)*(a + c*x)^(1/2))*(a*b - a*c)^2)/(4*b^(3/2)*c^(3/2)*(b - c)^2)","B"
434,1,5098,135,19.761095,"\text{Not used}","int(x/((a + b*x)^(1/2) + (a + c*x)^(1/2))^2,x)","\frac{2\,a\,\ln\left(x\right)}{b^2-2\,b\,c+c^2}-\frac{\frac{\left(4\,a\,c^2+4\,a\,b\,c\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+\frac{\left(4\,a\,b^2+4\,a\,c\,b\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{16\,a\,b\,c\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}}{b^4-2\,b^3\,c+b^2\,c^2-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(2\,b^3\,c-4\,b^2\,c^2+2\,b\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(b^2\,c^2-2\,b\,c^3+c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}}-\frac{2\,a\,\ln\left(\frac{\left(\sqrt{a+b\,x}-\sqrt{a+c\,x}\right)\,\left(b-\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{b^2-2\,b\,c+c^2}+\frac{2\,a\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{{\left(b-c\right)}^2}+\frac{x\,\left(b+c\right)}{{\left(b-c\right)}^2}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(32\,a^3\,b^8\,c^4-64\,a^3\,b^7\,c^5+8\,a^3\,b^6\,c^6+240\,a^3\,b^5\,c^7+8\,a^3\,b^4\,c^8-64\,a^3\,b^3\,c^9+32\,a^3\,b^2\,c^{10}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}-\frac{4\,\left(4\,a^3\,b^7\,c^5+44\,a^3\,b^6\,c^6+44\,a^3\,b^5\,c^7+4\,a^3\,b^4\,c^8\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(4\,a^2\,b^{10}\,c^4+2\,a^2\,b^9\,c^5-18\,a^2\,b^8\,c^6+12\,a^2\,b^7\,c^7+12\,a^2\,b^6\,c^8-18\,a^2\,b^5\,c^9+2\,a^2\,b^4\,c^{10}+4\,a^2\,b^3\,c^{11}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(16\,a^2\,b^{10}\,c^4-32\,a^2\,b^9\,c^5+36\,a^2\,b^8\,c^6-64\,a^2\,b^7\,c^7+88\,a^2\,b^6\,c^8-64\,a^2\,b^5\,c^9+36\,a^2\,b^4\,c^{10}-32\,a^2\,b^3\,c^{11}+16\,a^2\,b^2\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(a\,b^{11}\,c^5+7\,a\,b^{10}\,c^6-27\,a\,b^9\,c^7+19\,a\,b^8\,c^8+19\,a\,b^7\,c^9-27\,a\,b^6\,c^{10}+7\,a\,b^5\,c^{11}+a\,b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(8\,a\,b^{11}\,c^5-54\,a\,b^{10}\,c^6+212\,a\,b^9\,c^7-490\,a\,b^8\,c^8+648\,a\,b^7\,c^9-490\,a\,b^6\,c^{10}+212\,a\,b^5\,c^{11}-54\,a\,b^4\,c^{12}+8\,a\,b^3\,c^{13}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)\,2{}\mathrm{i}}{b^3\,c-2\,b^2\,c^2+b\,c^3}-\frac{a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(4\,a^3\,b^7\,c^5+44\,a^3\,b^6\,c^6+44\,a^3\,b^5\,c^7+4\,a^3\,b^4\,c^8\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(32\,a^3\,b^8\,c^4-64\,a^3\,b^7\,c^5+8\,a^3\,b^6\,c^6+240\,a^3\,b^5\,c^7+8\,a^3\,b^4\,c^8-64\,a^3\,b^3\,c^9+32\,a^3\,b^2\,c^{10}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(4\,a^2\,b^{10}\,c^4+2\,a^2\,b^9\,c^5-18\,a^2\,b^8\,c^6+12\,a^2\,b^7\,c^7+12\,a^2\,b^6\,c^8-18\,a^2\,b^5\,c^9+2\,a^2\,b^4\,c^{10}+4\,a^2\,b^3\,c^{11}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(16\,a^2\,b^{10}\,c^4-32\,a^2\,b^9\,c^5+36\,a^2\,b^8\,c^6-64\,a^2\,b^7\,c^7+88\,a^2\,b^6\,c^8-64\,a^2\,b^5\,c^9+36\,a^2\,b^4\,c^{10}-32\,a^2\,b^3\,c^{11}+16\,a^2\,b^2\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(8\,a\,b^{11}\,c^5-54\,a\,b^{10}\,c^6+212\,a\,b^9\,c^7-490\,a\,b^8\,c^8+648\,a\,b^7\,c^9-490\,a\,b^6\,c^{10}+212\,a\,b^5\,c^{11}-54\,a\,b^4\,c^{12}+8\,a\,b^3\,c^{13}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}-\frac{4\,\left(a\,b^{11}\,c^5+7\,a\,b^{10}\,c^6-27\,a\,b^9\,c^7+19\,a\,b^8\,c^8+19\,a\,b^7\,c^9-27\,a\,b^6\,c^{10}+7\,a\,b^5\,c^{11}+a\,b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)\,2{}\mathrm{i}}{b^3\,c-2\,b^2\,c^2+b\,c^3}}{\frac{4\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(128\,a^4\,b^5\,c^5+256\,a^4\,b^4\,c^6+128\,a^4\,b^3\,c^7\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}-\frac{8\,\left(16\,a^4\,b^6\,c^4+56\,a^4\,b^5\,c^5+56\,a^4\,b^4\,c^6+16\,a^4\,b^3\,c^7\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(32\,a^3\,b^8\,c^4-64\,a^3\,b^7\,c^5+8\,a^3\,b^6\,c^6+240\,a^3\,b^5\,c^7+8\,a^3\,b^4\,c^8-64\,a^3\,b^3\,c^9+32\,a^3\,b^2\,c^{10}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}-\frac{4\,\left(4\,a^3\,b^7\,c^5+44\,a^3\,b^6\,c^6+44\,a^3\,b^5\,c^7+4\,a^3\,b^4\,c^8\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(4\,a^2\,b^{10}\,c^4+2\,a^2\,b^9\,c^5-18\,a^2\,b^8\,c^6+12\,a^2\,b^7\,c^7+12\,a^2\,b^6\,c^8-18\,a^2\,b^5\,c^9+2\,a^2\,b^4\,c^{10}+4\,a^2\,b^3\,c^{11}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(16\,a^2\,b^{10}\,c^4-32\,a^2\,b^9\,c^5+36\,a^2\,b^8\,c^6-64\,a^2\,b^7\,c^7+88\,a^2\,b^6\,c^8-64\,a^2\,b^5\,c^9+36\,a^2\,b^4\,c^{10}-32\,a^2\,b^3\,c^{11}+16\,a^2\,b^2\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(a\,b^{11}\,c^5+7\,a\,b^{10}\,c^6-27\,a\,b^9\,c^7+19\,a\,b^8\,c^8+19\,a\,b^7\,c^9-27\,a\,b^6\,c^{10}+7\,a\,b^5\,c^{11}+a\,b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(8\,a\,b^{11}\,c^5-54\,a\,b^{10}\,c^6+212\,a\,b^9\,c^7-490\,a\,b^8\,c^8+648\,a\,b^7\,c^9-490\,a\,b^6\,c^{10}+212\,a\,b^5\,c^{11}-54\,a\,b^4\,c^{12}+8\,a\,b^3\,c^{13}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(4\,a^3\,b^7\,c^5+44\,a^3\,b^6\,c^6+44\,a^3\,b^5\,c^7+4\,a^3\,b^4\,c^8\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(32\,a^3\,b^8\,c^4-64\,a^3\,b^7\,c^5+8\,a^3\,b^6\,c^6+240\,a^3\,b^5\,c^7+8\,a^3\,b^4\,c^8-64\,a^3\,b^3\,c^9+32\,a^3\,b^2\,c^{10}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(4\,a^2\,b^{10}\,c^4+2\,a^2\,b^9\,c^5-18\,a^2\,b^8\,c^6+12\,a^2\,b^7\,c^7+12\,a^2\,b^6\,c^8-18\,a^2\,b^5\,c^9+2\,a^2\,b^4\,c^{10}+4\,a^2\,b^3\,c^{11}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(16\,a^2\,b^{10}\,c^4-32\,a^2\,b^9\,c^5+36\,a^2\,b^8\,c^6-64\,a^2\,b^7\,c^7+88\,a^2\,b^6\,c^8-64\,a^2\,b^5\,c^9+36\,a^2\,b^4\,c^{10}-32\,a^2\,b^3\,c^{11}+16\,a^2\,b^2\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(8\,a\,b^{11}\,c^5-54\,a\,b^{10}\,c^6+212\,a\,b^9\,c^7-490\,a\,b^8\,c^8+648\,a\,b^7\,c^9-490\,a\,b^6\,c^{10}+212\,a\,b^5\,c^{11}-54\,a\,b^4\,c^{12}+8\,a\,b^3\,c^{13}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}-\frac{4\,\left(a\,b^{11}\,c^5+7\,a\,b^{10}\,c^6-27\,a\,b^9\,c^7+19\,a\,b^8\,c^8+19\,a\,b^7\,c^9-27\,a\,b^6\,c^{10}+7\,a\,b^5\,c^{11}+a\,b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,a\,\sqrt{b\,c}\,\left(b+c\right)\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}\right)}{b^3\,c-2\,b^2\,c^2+b\,c^3}}\right)\,\sqrt{b\,c}\,\left(b+c\right)\,4{}\mathrm{i}}{b^3\,c-2\,b^2\,c^2+b\,c^3}","Not used",1,"(2*a*log(x))/(b^2 - 2*b*c + c^2) - (((4*a*c^2 + 4*a*b*c)*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3 + ((4*a*b^2 + 4*a*b*c)*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (16*a*b*c*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2)/(b^4 - 2*b^3*c + b^2*c^2 - (((a + b*x)^(1/2) - a^(1/2))^2*(2*b*c^3 + 2*b^3*c - 4*b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^2 + (((a + b*x)^(1/2) - a^(1/2))^4*(c^4 - 2*b*c^3 + b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^4) - (2*a*log((((a + b*x)^(1/2) - (a + c*x)^(1/2))*(b - (c*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2))))/((a + c*x)^(1/2) - a^(1/2))))/(b^2 - 2*b*c + c^2) + (2*a*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2))))/(b - c)^2 + (x*(b + c))/(b - c)^2 + (a*atan(((a*(b*c)^(1/2)*(b + c)*((2*((a + b*x)^(1/2) - a^(1/2))*(32*a^3*b^2*c^10 - 64*a^3*b^3*c^9 + 8*a^3*b^4*c^8 + 240*a^3*b^5*c^7 + 8*a^3*b^6*c^6 - 64*a^3*b^7*c^5 + 32*a^3*b^8*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) - (4*(4*a^3*b^4*c^8 + 44*a^3*b^5*c^7 + 44*a^3*b^6*c^6 + 4*a^3*b^7*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*a^2*b^3*c^11 + 2*a^2*b^4*c^10 - 18*a^2*b^5*c^9 + 12*a^2*b^6*c^8 + 12*a^2*b^7*c^7 - 18*a^2*b^8*c^6 + 2*a^2*b^9*c^5 + 4*a^2*b^10*c^4))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(16*a^2*b^2*c^12 - 32*a^2*b^3*c^11 + 36*a^2*b^4*c^10 - 64*a^2*b^5*c^9 + 88*a^2*b^6*c^8 - 64*a^2*b^7*c^7 + 36*a^2*b^8*c^6 - 32*a^2*b^9*c^5 + 16*a^2*b^10*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((4*(a*b^4*c^12 + 7*a*b^5*c^11 - 27*a*b^6*c^10 + 19*a*b^7*c^9 + 19*a*b^8*c^8 - 27*a*b^9*c^7 + 7*a*b^10*c^6 + a*b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(8*a*b^3*c^13 - 54*a*b^4*c^12 + 212*a*b^5*c^11 - 490*a*b^6*c^10 + 648*a*b^7*c^9 - 490*a*b^8*c^8 + 212*a*b^9*c^7 - 54*a*b^10*c^6 + 8*a*b^11*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2))*2i)/(b*c^3 + b^3*c - 2*b^2*c^2) - (a*(b*c)^(1/2)*(b + c)*((4*(4*a^3*b^4*c^8 + 44*a^3*b^5*c^7 + 44*a^3*b^6*c^6 + 4*a^3*b^7*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(32*a^3*b^2*c^10 - 64*a^3*b^3*c^9 + 8*a^3*b^4*c^8 + 240*a^3*b^5*c^7 + 8*a^3*b^6*c^6 - 64*a^3*b^7*c^5 + 32*a^3*b^8*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*a^2*b^3*c^11 + 2*a^2*b^4*c^10 - 18*a^2*b^5*c^9 + 12*a^2*b^6*c^8 + 12*a^2*b^7*c^7 - 18*a^2*b^8*c^6 + 2*a^2*b^9*c^5 + 4*a^2*b^10*c^4))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(16*a^2*b^2*c^12 - 32*a^2*b^3*c^11 + 36*a^2*b^4*c^10 - 64*a^2*b^5*c^9 + 88*a^2*b^6*c^8 - 64*a^2*b^7*c^7 + 36*a^2*b^8*c^6 - 32*a^2*b^9*c^5 + 16*a^2*b^10*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((2*((a + b*x)^(1/2) - a^(1/2))*(8*a*b^3*c^13 - 54*a*b^4*c^12 + 212*a*b^5*c^11 - 490*a*b^6*c^10 + 648*a*b^7*c^9 - 490*a*b^8*c^8 + 212*a*b^9*c^7 - 54*a*b^10*c^6 + 8*a*b^11*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) - (4*(a*b^4*c^12 + 7*a*b^5*c^11 - 27*a*b^6*c^10 + 19*a*b^7*c^9 + 19*a*b^8*c^8 - 27*a*b^9*c^7 + 7*a*b^10*c^6 + a*b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2))*2i)/(b*c^3 + b^3*c - 2*b^2*c^2))/((4*((a + b*x)^(1/2) - a^(1/2))*(128*a^4*b^3*c^7 + 256*a^4*b^4*c^6 + 128*a^4*b^5*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) - (8*(16*a^4*b^3*c^7 + 56*a^4*b^4*c^6 + 56*a^4*b^5*c^5 + 16*a^4*b^6*c^4))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*a*(b*c)^(1/2)*(b + c)*((2*((a + b*x)^(1/2) - a^(1/2))*(32*a^3*b^2*c^10 - 64*a^3*b^3*c^9 + 8*a^3*b^4*c^8 + 240*a^3*b^5*c^7 + 8*a^3*b^6*c^6 - 64*a^3*b^7*c^5 + 32*a^3*b^8*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) - (4*(4*a^3*b^4*c^8 + 44*a^3*b^5*c^7 + 44*a^3*b^6*c^6 + 4*a^3*b^7*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*a^2*b^3*c^11 + 2*a^2*b^4*c^10 - 18*a^2*b^5*c^9 + 12*a^2*b^6*c^8 + 12*a^2*b^7*c^7 - 18*a^2*b^8*c^6 + 2*a^2*b^9*c^5 + 4*a^2*b^10*c^4))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(16*a^2*b^2*c^12 - 32*a^2*b^3*c^11 + 36*a^2*b^4*c^10 - 64*a^2*b^5*c^9 + 88*a^2*b^6*c^8 - 64*a^2*b^7*c^7 + 36*a^2*b^8*c^6 - 32*a^2*b^9*c^5 + 16*a^2*b^10*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((4*(a*b^4*c^12 + 7*a*b^5*c^11 - 27*a*b^6*c^10 + 19*a*b^7*c^9 + 19*a*b^8*c^8 - 27*a*b^9*c^7 + 7*a*b^10*c^6 + a*b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(8*a*b^3*c^13 - 54*a*b^4*c^12 + 212*a*b^5*c^11 - 490*a*b^6*c^10 + 648*a*b^7*c^9 - 490*a*b^8*c^8 + 212*a*b^9*c^7 - 54*a*b^10*c^6 + 8*a*b^11*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*a^3*b^4*c^8 + 44*a^3*b^5*c^7 + 44*a^3*b^6*c^6 + 4*a^3*b^7*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(32*a^3*b^2*c^10 - 64*a^3*b^3*c^9 + 8*a^3*b^4*c^8 + 240*a^3*b^5*c^7 + 8*a^3*b^6*c^6 - 64*a^3*b^7*c^5 + 32*a^3*b^8*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*a^2*b^3*c^11 + 2*a^2*b^4*c^10 - 18*a^2*b^5*c^9 + 12*a^2*b^6*c^8 + 12*a^2*b^7*c^7 - 18*a^2*b^8*c^6 + 2*a^2*b^9*c^5 + 4*a^2*b^10*c^4))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) - (2*((a + b*x)^(1/2) - a^(1/2))*(16*a^2*b^2*c^12 - 32*a^2*b^3*c^11 + 36*a^2*b^4*c^10 - 64*a^2*b^5*c^9 + 88*a^2*b^6*c^8 - 64*a^2*b^7*c^7 + 36*a^2*b^8*c^6 - 32*a^2*b^9*c^5 + 16*a^2*b^10*c^4))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) + (2*a*(b*c)^(1/2)*(b + c)*((2*((a + b*x)^(1/2) - a^(1/2))*(8*a*b^3*c^13 - 54*a*b^4*c^12 + 212*a*b^5*c^11 - 490*a*b^6*c^10 + 648*a*b^7*c^9 - 490*a*b^8*c^8 + 212*a*b^9*c^7 - 54*a*b^10*c^6 + 8*a*b^11*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)) - (4*(a*b^4*c^12 + 7*a*b^5*c^11 - 27*a*b^6*c^10 + 19*a*b^7*c^9 + 19*a*b^8*c^8 - 27*a*b^9*c^7 + 7*a*b^10*c^6 + a*b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*a*(b*c)^(1/2)*(b + c)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))/(b*c^3 + b^3*c - 2*b^2*c^2)))*(b*c)^(1/2)*(b + c)*4i)/(b*c^3 + b^3*c - 2*b^2*c^2)","B"
435,1,4285,138,17.443759,"\text{Not used}","int(1/((a + b*x)^(1/2) + (a + c*x)^(1/2))^2,x)","\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(b+c\right)}{{\left(b-c\right)}^2}-\frac{\frac{\left(b^2+c\,b\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-b^2+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(b^2-3\,b\,c+c^2\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}}{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(2\,b^2\,c-4\,b\,c^2+2\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(-2\,b^3+2\,b^2\,c+2\,b\,c^2-2\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(2\,b^3-4\,b^2\,c+2\,b\,c^2\right)}{\sqrt{a+c\,x}-\sqrt{a}}}+\frac{\ln\left(x\right)\,\left(b+c\right)}{b^2-2\,b\,c+c^2}-\frac{\ln\left(\frac{\left(\sqrt{a+b\,x}-\sqrt{a+c\,x}\right)\,\left(b-\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(b+c\right)}{b^2-2\,b\,c+c^2}-\frac{2\,a}{x\,\left(b^2-2\,b\,c+c^2\right)}+\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{2\,{\left(b-c\right)}^2\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b\,c}\,\left(\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(b^{11}\,c^5+16\,b^{10}\,c^6-42\,b^9\,c^7+25\,b^8\,c^8+25\,b^7\,c^9-42\,b^6\,c^{10}+16\,b^5\,c^{11}+b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(4\,b^{11}\,c^6-36\,b^9\,c^8+64\,b^8\,c^9-36\,b^7\,c^{10}+4\,b^5\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{12}\,c^5-27\,b^{11}\,c^6+99\,b^{10}\,c^7-175\,b^9\,c^8+99\,b^8\,c^9+99\,b^7\,c^{10}-175\,b^6\,c^{11}+99\,b^5\,c^{12}-27\,b^4\,c^{13}+4\,b^3\,c^{14}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,b^{10}\,c^6-278\,b^9\,c^7+503\,b^8\,c^8-596\,b^7\,c^9+503\,b^6\,c^{10}-278\,b^5\,c^{11}+73\,b^4\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{4\,\left(4\,b^9\,c^6+24\,b^8\,c^7+40\,b^7\,c^8+24\,b^6\,c^9+4\,b^5\,c^{10}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,b^9\,c^6-167\,b^8\,c^7+198\,b^7\,c^8+198\,b^6\,c^9-167\,b^5\,c^{10}+65\,b^4\,c^{11}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)\,4{}\mathrm{i}}{{\left(b-c\right)}^2}-\frac{\sqrt{b\,c}\,\left(\frac{4\,\left(4\,b^9\,c^6+24\,b^8\,c^7+40\,b^7\,c^8+24\,b^6\,c^9+4\,b^5\,c^{10}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(b^{11}\,c^5+16\,b^{10}\,c^6-42\,b^9\,c^7+25\,b^8\,c^8+25\,b^7\,c^9-42\,b^6\,c^{10}+16\,b^5\,c^{11}+b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{4\,\left(4\,b^{11}\,c^6-36\,b^9\,c^8+64\,b^8\,c^9-36\,b^7\,c^{10}+4\,b^5\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{12}\,c^5-27\,b^{11}\,c^6+99\,b^{10}\,c^7-175\,b^9\,c^8+99\,b^8\,c^9+99\,b^7\,c^{10}-175\,b^6\,c^{11}+99\,b^5\,c^{12}-27\,b^4\,c^{13}+4\,b^3\,c^{14}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,b^{10}\,c^6-278\,b^9\,c^7+503\,b^8\,c^8-596\,b^7\,c^9+503\,b^6\,c^{10}-278\,b^5\,c^{11}+73\,b^4\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,b^9\,c^6-167\,b^8\,c^7+198\,b^7\,c^8+198\,b^6\,c^9-167\,b^5\,c^{10}+65\,b^4\,c^{11}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)\,4{}\mathrm{i}}{{\left(b-c\right)}^2}}{\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(b^{11}\,c^5+16\,b^{10}\,c^6-42\,b^9\,c^7+25\,b^8\,c^8+25\,b^7\,c^9-42\,b^6\,c^{10}+16\,b^5\,c^{11}+b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(4\,b^{11}\,c^6-36\,b^9\,c^8+64\,b^8\,c^9-36\,b^7\,c^{10}+4\,b^5\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{12}\,c^5-27\,b^{11}\,c^6+99\,b^{10}\,c^7-175\,b^9\,c^8+99\,b^8\,c^9+99\,b^7\,c^{10}-175\,b^6\,c^{11}+99\,b^5\,c^{12}-27\,b^4\,c^{13}+4\,b^3\,c^{14}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,b^{10}\,c^6-278\,b^9\,c^7+503\,b^8\,c^8-596\,b^7\,c^9+503\,b^6\,c^{10}-278\,b^5\,c^{11}+73\,b^4\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{4\,\left(4\,b^9\,c^6+24\,b^8\,c^7+40\,b^7\,c^8+24\,b^6\,c^9+4\,b^5\,c^{10}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,b^9\,c^6-167\,b^8\,c^7+198\,b^7\,c^8+198\,b^6\,c^9-167\,b^5\,c^{10}+65\,b^4\,c^{11}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{8\,\left(14\,b^8\,c^6+42\,b^7\,c^7+42\,b^6\,c^8+14\,b^5\,c^9\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(4\,b^9\,c^6+24\,b^8\,c^7+40\,b^7\,c^8+24\,b^6\,c^9+4\,b^5\,c^{10}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(b^{11}\,c^5+16\,b^{10}\,c^6-42\,b^9\,c^7+25\,b^8\,c^8+25\,b^7\,c^9-42\,b^6\,c^{10}+16\,b^5\,c^{11}+b^4\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\sqrt{b\,c}\,\left(\frac{4\,\left(-b^{13}\,c^5+4\,b^{12}\,c^6-5\,b^{11}\,c^7+b^{10}\,c^8+b^9\,c^9+b^8\,c^{10}+b^7\,c^{11}-5\,b^6\,c^{12}+4\,b^5\,c^{13}-b^4\,c^{14}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{13}\,c^5-31\,b^{12}\,c^6+120\,b^{11}\,c^7-300\,b^{10}\,c^8+516\,b^9\,c^9-618\,b^8\,c^{10}+516\,b^7\,c^{11}-300\,b^6\,c^{12}+120\,b^5\,c^{13}-31\,b^4\,c^{14}+4\,b^3\,c^{15}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{4\,\left(4\,b^{11}\,c^6-36\,b^9\,c^8+64\,b^8\,c^9-36\,b^7\,c^{10}+4\,b^5\,c^{12}\right)}{b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4}+\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(4\,b^{12}\,c^5-27\,b^{11}\,c^6+99\,b^{10}\,c^7-175\,b^9\,c^8+99\,b^8\,c^9+99\,b^7\,c^{10}-175\,b^6\,c^{11}+99\,b^5\,c^{12}-27\,b^4\,c^{13}+4\,b^3\,c^{14}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(73\,b^{10}\,c^6-278\,b^9\,c^7+503\,b^8\,c^8-596\,b^7\,c^9+503\,b^6\,c^{10}-278\,b^5\,c^{11}+73\,b^4\,c^{12}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}-\frac{2\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(65\,b^9\,c^6-167\,b^8\,c^7+198\,b^7\,c^8+198\,b^6\,c^9-167\,b^5\,c^{10}+65\,b^4\,c^{11}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}\right)}{{\left(b-c\right)}^2}+\frac{4\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(112\,b^7\,c^7+224\,b^6\,c^8+112\,b^5\,c^9\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(b^4-4\,b^3\,c+6\,b^2\,c^2-4\,b\,c^3+c^4\right)}}\right)\,\sqrt{b\,c}\,8{}\mathrm{i}}{{\left(b-c\right)}^2}","Not used",1,"(atan((((b*c)^(1/2)*((4*(b*c)^(1/2)*((4*(b^4*c^12 + 16*b^5*c^11 - 42*b^6*c^10 + 25*b^7*c^9 + 25*b^8*c^8 - 42*b^9*c^7 + 16*b^10*c^6 + b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(4*b^5*c^12 - 36*b^7*c^10 + 64*b^8*c^9 - 36*b^9*c^8 + 4*b^11*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^14 - 27*b^4*c^13 + 99*b^5*c^12 - 175*b^6*c^11 + 99*b^7*c^10 + 99*b^8*c^9 - 175*b^9*c^8 + 99*b^10*c^7 - 27*b^11*c^6 + 4*b^12*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(73*b^4*c^12 - 278*b^5*c^11 + 503*b^6*c^10 - 596*b^7*c^9 + 503*b^8*c^8 - 278*b^9*c^7 + 73*b^10*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (4*(4*b^5*c^10 + 24*b^6*c^9 + 40*b^7*c^8 + 24*b^8*c^7 + 4*b^9*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(65*b^4*c^11 - 167*b^5*c^10 + 198*b^6*c^9 + 198*b^7*c^8 - 167*b^8*c^7 + 65*b^9*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)))*4i)/(b - c)^2 - ((b*c)^(1/2)*((4*(4*b^5*c^10 + 24*b^6*c^9 + 40*b^7*c^8 + 24*b^8*c^7 + 4*b^9*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(b^4*c^12 + 16*b^5*c^11 - 42*b^6*c^10 + 25*b^7*c^9 + 25*b^8*c^8 - 42*b^9*c^7 + 16*b^10*c^6 + b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(b*c)^(1/2)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (4*(4*b^5*c^12 - 36*b^7*c^10 + 64*b^8*c^9 - 36*b^9*c^8 + 4*b^11*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^14 - 27*b^4*c^13 + 99*b^5*c^12 - 175*b^6*c^11 + 99*b^7*c^10 + 99*b^8*c^9 - 175*b^9*c^8 + 99*b^10*c^7 - 27*b^11*c^6 + 4*b^12*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(73*b^4*c^12 - 278*b^5*c^11 + 503*b^6*c^10 - 596*b^7*c^9 + 503*b^8*c^8 - 278*b^9*c^7 + 73*b^10*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(65*b^4*c^11 - 167*b^5*c^10 + 198*b^6*c^9 + 198*b^7*c^8 - 167*b^8*c^7 + 65*b^9*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2)))*4i)/(b - c)^2)/((4*(b*c)^(1/2)*((4*(b*c)^(1/2)*((4*(b^4*c^12 + 16*b^5*c^11 - 42*b^6*c^10 + 25*b^7*c^9 + 25*b^8*c^8 - 42*b^9*c^7 + 16*b^10*c^6 + b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(4*b^5*c^12 - 36*b^7*c^10 + 64*b^8*c^9 - 36*b^9*c^8 + 4*b^11*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^14 - 27*b^4*c^13 + 99*b^5*c^12 - 175*b^6*c^11 + 99*b^7*c^10 + 99*b^8*c^9 - 175*b^9*c^8 + 99*b^10*c^7 - 27*b^11*c^6 + 4*b^12*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(73*b^4*c^12 - 278*b^5*c^11 + 503*b^6*c^10 - 596*b^7*c^9 + 503*b^8*c^8 - 278*b^9*c^7 + 73*b^10*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (4*(4*b^5*c^10 + 24*b^6*c^9 + 40*b^7*c^8 + 24*b^8*c^7 + 4*b^9*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(65*b^4*c^11 - 167*b^5*c^10 + 198*b^6*c^9 + 198*b^7*c^8 - 167*b^8*c^7 + 65*b^9*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (8*(14*b^5*c^9 + 42*b^6*c^8 + 42*b^7*c^7 + 14*b^8*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(4*b^5*c^10 + 24*b^6*c^9 + 40*b^7*c^8 + 24*b^8*c^7 + 4*b^9*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(b^4*c^12 + 16*b^5*c^11 - 42*b^6*c^10 + 25*b^7*c^9 + 25*b^8*c^8 - 42*b^9*c^7 + 16*b^10*c^6 + b^11*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (4*(b*c)^(1/2)*((4*(b*c)^(1/2)*((4*(4*b^5*c^13 - b^4*c^14 - 5*b^6*c^12 + b^7*c^11 + b^8*c^10 + b^9*c^9 + b^10*c^8 - 5*b^11*c^7 + 4*b^12*c^6 - b^13*c^5))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^15 - 31*b^4*c^14 + 120*b^5*c^13 - 300*b^6*c^12 + 516*b^7*c^11 - 618*b^8*c^10 + 516*b^9*c^9 - 300*b^10*c^8 + 120*b^11*c^7 - 31*b^12*c^6 + 4*b^13*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (4*(4*b^5*c^12 - 36*b^7*c^10 + 64*b^8*c^9 - 36*b^9*c^8 + 4*b^11*c^6))/(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2) + (2*((a + b*x)^(1/2) - a^(1/2))*(4*b^3*c^14 - 27*b^4*c^13 + 99*b^5*c^12 - 175*b^6*c^11 + 99*b^7*c^10 + 99*b^8*c^9 - 175*b^9*c^8 + 99*b^10*c^7 - 27*b^11*c^6 + 4*b^12*c^5))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(73*b^4*c^12 - 278*b^5*c^11 + 503*b^6*c^10 - 596*b^7*c^9 + 503*b^8*c^8 - 278*b^9*c^7 + 73*b^10*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 - (2*((a + b*x)^(1/2) - a^(1/2))*(65*b^4*c^11 - 167*b^5*c^10 + 198*b^6*c^9 + 198*b^7*c^8 - 167*b^8*c^7 + 65*b^9*c^6))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))/(b - c)^2 + (4*((a + b*x)^(1/2) - a^(1/2))*(112*b^5*c^9 + 224*b^6*c^8 + 112*b^7*c^7))/(((a + c*x)^(1/2) - a^(1/2))*(b^4 - 4*b^3*c - 4*b*c^3 + c^4 + 6*b^2*c^2))))*(b*c)^(1/2)*8i)/(b - c)^2 - (((b*c + b^2)*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - b^2 + (((a + b*x)^(1/2) - a^(1/2))^2*(b^2 - 3*b*c + c^2))/((a + c*x)^(1/2) - a^(1/2))^2)/((((a + b*x)^(1/2) - a^(1/2))^3*(2*b^2*c - 4*b*c^2 + 2*c^3))/((a + c*x)^(1/2) - a^(1/2))^3 + (((a + b*x)^(1/2) - a^(1/2))^2*(2*b*c^2 + 2*b^2*c - 2*b^3 - 2*c^3))/((a + c*x)^(1/2) - a^(1/2))^2 + (((a + b*x)^(1/2) - a^(1/2))*(2*b*c^2 - 4*b^2*c + 2*b^3))/((a + c*x)^(1/2) - a^(1/2))) + (log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(b + c))/(b - c)^2 + (log(x)*(b + c))/(b^2 - 2*b*c + c^2) - (log((((a + b*x)^(1/2) - (a + c*x)^(1/2))*(b - (c*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2))))/((a + c*x)^(1/2) - a^(1/2)))*(b + c))/(b^2 - 2*b*c + c^2) - (2*a)/(x*(b^2 - 2*b*c + c^2)) + (c*((a + b*x)^(1/2) - a^(1/2)))/(2*(b - c)^2*((a + c*x)^(1/2) - a^(1/2)))","B"
436,1,787,123,12.319555,"\text{Not used}","int(1/(x*((a + b*x)^(1/2) + (a + c*x)^(1/2))^2),x)","\frac{\ln\left(\frac{\left(\sqrt{a+b\,x}-\sqrt{a+c\,x}\right)\,\left(b-\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{4\,a}-\frac{\frac{b^4}{2}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(-\frac{b^4}{2}+4\,b^3\,c+\frac{3\,b^2\,c^2}{2}+4\,b\,c^3-\frac{c^4}{2}\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}-\frac{\left(2\,b^4+2\,c\,b^3\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{\left(b^2\,c^2+b\,c^3\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(\frac{5\,b^4}{2}+6\,b^3\,c+\frac{5\,b^2\,c^2}{2}\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(b^4+6\,b^3\,c+6\,b^2\,c^2+b\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}}{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(8\,a\,b^4+16\,a\,b^3\,c-48\,a\,b^2\,c^2+16\,a\,b\,c^3+8\,a\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(16\,a\,b^4-16\,a\,b^3\,c-16\,a\,b^2\,c^2+16\,a\,b\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5\,\left(16\,a\,b^3\,c-16\,a\,b^2\,c^2-16\,a\,b\,c^3+16\,a\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(8\,a\,b^4-16\,a\,b^3\,c+8\,a\,b^2\,c^2\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(8\,a\,b^2\,c^2-16\,a\,b\,c^3+8\,a\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^6}}-\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{4\,a}-\frac{a+x\,\left(b+c\right)}{x^2\,\left(b^2-2\,b\,c+c^2\right)}-\frac{c^2\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{16\,a\,{\left(b-c\right)}^2\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{c\,\left(b+c\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{8\,a\,{\left(b-c\right)}^2\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}","Not used",1,"log((((a + b*x)^(1/2) - (a + c*x)^(1/2))*(b - (c*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2))))/((a + c*x)^(1/2) - a^(1/2)))/(4*a) - (b^4/2 + (((a + b*x)^(1/2) - a^(1/2))^4*(4*b*c^3 + 4*b^3*c - b^4/2 - c^4/2 + (3*b^2*c^2)/2))/((a + c*x)^(1/2) - a^(1/2))^4 - ((2*b^3*c + 2*b^4)*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - ((b*c^3 + b^2*c^2)*((a + b*x)^(1/2) - a^(1/2))^5)/((a + c*x)^(1/2) - a^(1/2))^5 + (((a + b*x)^(1/2) - a^(1/2))^2*(6*b^3*c + (5*b^4)/2 + (5*b^2*c^2)/2))/((a + c*x)^(1/2) - a^(1/2))^2 - (((a + b*x)^(1/2) - a^(1/2))^3*(b*c^3 + 6*b^3*c + b^4 + 6*b^2*c^2))/((a + c*x)^(1/2) - a^(1/2))^3)/((((a + b*x)^(1/2) - a^(1/2))^4*(8*a*b^4 + 8*a*c^4 - 48*a*b^2*c^2 + 16*a*b*c^3 + 16*a*b^3*c))/((a + c*x)^(1/2) - a^(1/2))^4 - (((a + b*x)^(1/2) - a^(1/2))^3*(16*a*b^4 - 16*a*b^2*c^2 + 16*a*b*c^3 - 16*a*b^3*c))/((a + c*x)^(1/2) - a^(1/2))^3 - (((a + b*x)^(1/2) - a^(1/2))^5*(16*a*c^4 - 16*a*b^2*c^2 - 16*a*b*c^3 + 16*a*b^3*c))/((a + c*x)^(1/2) - a^(1/2))^5 + (((a + b*x)^(1/2) - a^(1/2))^2*(8*a*b^4 + 8*a*b^2*c^2 - 16*a*b^3*c))/((a + c*x)^(1/2) - a^(1/2))^2 + (((a + b*x)^(1/2) - a^(1/2))^6*(8*a*c^4 + 8*a*b^2*c^2 - 16*a*b*c^3))/((a + c*x)^(1/2) - a^(1/2))^6) - log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))/(4*a) - (a + x*(b + c))/(x^2*(b^2 - 2*b*c + c^2)) - (c^2*((a + b*x)^(1/2) - a^(1/2))^2)/(16*a*(b - c)^2*((a + c*x)^(1/2) - a^(1/2))^2) + (c*(b + c)*((a + b*x)^(1/2) - a^(1/2)))/(8*a*(b - c)^2*((a + c*x)^(1/2) - a^(1/2)))","B"
437,1,1290,174,18.735308,"\text{Not used}","int(1/(x^2*((a + b*x)^(1/2) + (a + c*x)^(1/2))^2),x)","\frac{\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(b+c\right)}{8\,a^2}-\frac{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^7\,\left(3\,b^5\,c-15\,b^4\,c^2+3\,b^3\,c^3+3\,b^2\,c^4-15\,b\,c^5+3\,c^6\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^7}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5\,\left(-b^6+26\,b^5\,c+4\,b^4\,c^2+4\,b^3\,c^3+26\,b^2\,c^4-b\,c^5\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}-\frac{b^6}{3}+\frac{\left(b^6+c\,b^5\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8\,\left(b^4\,c^2-6\,b^3\,c^3+7\,b^2\,c^4-6\,b\,c^5+c^6\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^8}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(-\frac{5\,b^6}{3}+6\,b^5\,c+30\,b^4\,c^2-24\,b^3\,c^3+30\,b^2\,c^4+6\,b\,c^5-\frac{5\,c^6}{3}\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^6}-\frac{\left(\frac{17\,b^6}{3}+\frac{17\,b^3\,c^3}{3}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2\,\left(b^6-4\,b^5\,c+b^4\,c^2\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(5\,b^6+18\,b^5\,c-6\,b^4\,c^2+18\,b^3\,c^3+5\,b^2\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}}{\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5\,\left(96\,a^2\,b^5+96\,a^2\,b^4\,c-384\,a^2\,b^3\,c^2+96\,a^2\,b^2\,c^3+96\,a^2\,b\,c^4\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^8\,\left(96\,a^2\,b^3\,c^2-96\,a^2\,b^2\,c^3-96\,a^2\,b\,c^4+96\,a^2\,c^5\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^8}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6\,\left(32\,a^2\,b^5+224\,a^2\,b^4\,c-256\,a^2\,b^3\,c^2-256\,a^2\,b^2\,c^3+224\,a^2\,b\,c^4+32\,a^2\,c^5\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^6}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4\,\left(96\,a^2\,b^5-96\,a^2\,b^4\,c-96\,a^2\,b^3\,c^2+96\,a^2\,b^2\,c^3\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^7\,\left(96\,a^2\,b^4\,c+96\,a^2\,b^3\,c^2-384\,a^2\,b^2\,c^3+96\,a^2\,b\,c^4+96\,a^2\,c^5\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^7}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3\,\left(32\,a^2\,b^5-64\,a^2\,b^4\,c+32\,a^2\,b^3\,c^2\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^9\,\left(32\,a^2\,b^2\,c^3-64\,a^2\,b\,c^4+32\,a^2\,c^5\right)}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^9}}-\frac{\left(\frac{c\,\left(3\,b^2+8\,b\,c+3\,c^2\right)}{16\,a^2\,{\left(b-c\right)}^2}-\frac{c\,\left(4\,b^2+17\,b\,c+4\,c^2\right)}{32\,a^2\,{\left(b-c\right)}^2}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{\ln\left(\frac{\left(\sqrt{a+b\,x}-\sqrt{a+c\,x}\right)\,\left(b-\frac{c\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(b+c\right)}{8\,a^2}-\frac{\frac{2\,a}{3}+x\,\left(\frac{b}{2}+\frac{c}{2}\right)}{x^3\,\left(b^2-2\,b\,c+c^2\right)}+\frac{c^3\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{96\,a^2\,{\left(b-c\right)}^2\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}","Not used",1,"(log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*(b + c))/(8*a^2) - ((((a + b*x)^(1/2) - a^(1/2))^7*(3*b^5*c - 15*b*c^5 + 3*c^6 + 3*b^2*c^4 + 3*b^3*c^3 - 15*b^4*c^2))/((a + c*x)^(1/2) - a^(1/2))^7 - (((a + b*x)^(1/2) - a^(1/2))^5*(26*b^5*c - b*c^5 - b^6 + 26*b^2*c^4 + 4*b^3*c^3 + 4*b^4*c^2))/((a + c*x)^(1/2) - a^(1/2))^5 - b^6/3 + ((b^5*c + b^6)*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (((a + b*x)^(1/2) - a^(1/2))^8*(c^6 - 6*b*c^5 + 7*b^2*c^4 - 6*b^3*c^3 + b^4*c^2))/((a + c*x)^(1/2) - a^(1/2))^8 + (((a + b*x)^(1/2) - a^(1/2))^6*(6*b*c^5 + 6*b^5*c - (5*b^6)/3 - (5*c^6)/3 + 30*b^2*c^4 - 24*b^3*c^3 + 30*b^4*c^2))/((a + c*x)^(1/2) - a^(1/2))^6 - (((17*b^6)/3 + (17*b^3*c^3)/3)*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3 + (((a + b*x)^(1/2) - a^(1/2))^2*(b^6 - 4*b^5*c + b^4*c^2))/((a + c*x)^(1/2) - a^(1/2))^2 + (((a + b*x)^(1/2) - a^(1/2))^4*(18*b^5*c + 5*b^6 + 5*b^2*c^4 + 18*b^3*c^3 - 6*b^4*c^2))/((a + c*x)^(1/2) - a^(1/2))^4)/((((a + b*x)^(1/2) - a^(1/2))^5*(96*a^2*b^5 + 96*a^2*b*c^4 + 96*a^2*b^4*c + 96*a^2*b^2*c^3 - 384*a^2*b^3*c^2))/((a + c*x)^(1/2) - a^(1/2))^5 - (((a + b*x)^(1/2) - a^(1/2))^8*(96*a^2*c^5 - 96*a^2*b*c^4 - 96*a^2*b^2*c^3 + 96*a^2*b^3*c^2))/((a + c*x)^(1/2) - a^(1/2))^8 - (((a + b*x)^(1/2) - a^(1/2))^6*(32*a^2*b^5 + 32*a^2*c^5 + 224*a^2*b*c^4 + 224*a^2*b^4*c - 256*a^2*b^2*c^3 - 256*a^2*b^3*c^2))/((a + c*x)^(1/2) - a^(1/2))^6 - (((a + b*x)^(1/2) - a^(1/2))^4*(96*a^2*b^5 - 96*a^2*b^4*c + 96*a^2*b^2*c^3 - 96*a^2*b^3*c^2))/((a + c*x)^(1/2) - a^(1/2))^4 + (((a + b*x)^(1/2) - a^(1/2))^7*(96*a^2*c^5 + 96*a^2*b*c^4 + 96*a^2*b^4*c - 384*a^2*b^2*c^3 + 96*a^2*b^3*c^2))/((a + c*x)^(1/2) - a^(1/2))^7 + (((a + b*x)^(1/2) - a^(1/2))^3*(32*a^2*b^5 - 64*a^2*b^4*c + 32*a^2*b^3*c^2))/((a + c*x)^(1/2) - a^(1/2))^3 + (((a + b*x)^(1/2) - a^(1/2))^9*(32*a^2*c^5 - 64*a^2*b*c^4 + 32*a^2*b^2*c^3))/((a + c*x)^(1/2) - a^(1/2))^9) - (((c*(8*b*c + 3*b^2 + 3*c^2))/(16*a^2*(b - c)^2) - (c*(17*b*c + 4*b^2 + 4*c^2))/(32*a^2*(b - c)^2))*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (log((((a + b*x)^(1/2) - (a + c*x)^(1/2))*(b - (c*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2))))/((a + c*x)^(1/2) - a^(1/2)))*(b + c))/(8*a^2) - ((2*a)/3 + x*(b/2 + c/2))/(x^3*(b^2 - 2*b*c + c^2)) + (c^3*((a + b*x)^(1/2) - a^(1/2))^3)/(96*a^2*(b - c)^2*((a + c*x)^(1/2) - a^(1/2))^3)","B"
438,1,429,277,3.342075,"\text{Not used}","int(x^4/((a + b*x)^(1/2) + (a + c*x)^(1/2))^3,x)","\frac{x^2\,\left(\frac{12\,a\,\left(3\,b+c\right)}{7\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(3\,b+5\,c\right)}{{\left(b-c\right)}^3}\right)\,\sqrt{a+c\,x}}{5\,c}-\frac{2\,a\,\left(\frac{8\,a^2}{{\left(b-c\right)}^3}-\frac{4\,a\,\left(\frac{2\,a\,\left(5\,b+3\,c\right)}{{\left(b-c\right)}^3}-\frac{12\,a\,\left(b^2+3\,c\,b\right)}{7\,b\,{\left(b-c\right)}^3}\right)}{5\,b}\right)\,\sqrt{a+b\,x}}{3\,b^2}+\frac{x\,\left(\frac{8\,a^2}{{\left(b-c\right)}^3}-\frac{4\,a\,\left(\frac{2\,a\,\left(5\,b+3\,c\right)}{{\left(b-c\right)}^3}-\frac{12\,a\,\left(b^2+3\,c\,b\right)}{7\,b\,{\left(b-c\right)}^3}\right)}{5\,b}\right)\,\sqrt{a+b\,x}}{3\,b}+\frac{2\,a\,\left(\frac{8\,a^2}{{\left(b-c\right)}^3}+\frac{4\,a\,\left(\frac{12\,a\,\left(3\,b+c\right)}{7\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(3\,b+5\,c\right)}{{\left(b-c\right)}^3}\right)}{5\,c}\right)\,\sqrt{a+c\,x}}{3\,c^2}+\frac{x^2\,\left(\frac{2\,a\,\left(5\,b+3\,c\right)}{{\left(b-c\right)}^3}-\frac{12\,a\,\left(b^2+3\,c\,b\right)}{7\,b\,{\left(b-c\right)}^3}\right)\,\sqrt{a+b\,x}}{5\,b}-\frac{x\,\left(\frac{8\,a^2}{{\left(b-c\right)}^3}+\frac{4\,a\,\left(\frac{12\,a\,\left(3\,b+c\right)}{7\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(3\,b+5\,c\right)}{{\left(b-c\right)}^3}\right)}{5\,c}\right)\,\sqrt{a+c\,x}}{3\,c}-\frac{2\,x^3\,\left(3\,b+c\right)\,\sqrt{a+c\,x}}{7\,{\left(b-c\right)}^3}+\frac{2\,x^3\,\left(b^2+3\,c\,b\right)\,\sqrt{a+b\,x}}{7\,b\,{\left(b-c\right)}^3}","Not used",1,"(x^2*((12*a*(3*b + c))/(7*(b - c)^3) - (2*a*(3*b + 5*c))/(b - c)^3)*(a + c*x)^(1/2))/(5*c) - (2*a*((8*a^2)/(b - c)^3 - (4*a*((2*a*(5*b + 3*c))/(b - c)^3 - (12*a*(3*b*c + b^2))/(7*b*(b - c)^3)))/(5*b))*(a + b*x)^(1/2))/(3*b^2) + (x*((8*a^2)/(b - c)^3 - (4*a*((2*a*(5*b + 3*c))/(b - c)^3 - (12*a*(3*b*c + b^2))/(7*b*(b - c)^3)))/(5*b))*(a + b*x)^(1/2))/(3*b) + (2*a*((8*a^2)/(b - c)^3 + (4*a*((12*a*(3*b + c))/(7*(b - c)^3) - (2*a*(3*b + 5*c))/(b - c)^3))/(5*c))*(a + c*x)^(1/2))/(3*c^2) + (x^2*((2*a*(5*b + 3*c))/(b - c)^3 - (12*a*(3*b*c + b^2))/(7*b*(b - c)^3))*(a + b*x)^(1/2))/(5*b) - (x*((8*a^2)/(b - c)^3 + (4*a*((12*a*(3*b + c))/(7*(b - c)^3) - (2*a*(3*b + 5*c))/(b - c)^3))/(5*c))*(a + c*x)^(1/2))/(3*c) - (2*x^3*(3*b + c)*(a + c*x)^(1/2))/(7*(b - c)^3) + (2*x^3*(3*b*c + b^2)*(a + b*x)^(1/2))/(7*b*(b - c)^3)","B"
439,1,268,163,3.360241,"\text{Not used}","int(x^3/((a + b*x)^(1/2) + (a + c*x)^(1/2))^3,x)","\frac{\left(\frac{8\,a^2}{{\left(b-c\right)}^3}+\frac{2\,a\,\left(\frac{8\,a\,\left(b+3\,c\right)}{5\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(5\,b+3\,c\right)}{{\left(b-c\right)}^3}\right)}{3\,b}\right)\,\sqrt{a+b\,x}}{b}-\frac{\left(\frac{8\,a^2}{{\left(b-c\right)}^3}+\frac{2\,a\,\left(\frac{8\,a\,\left(3\,b+c\right)}{5\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(3\,b+5\,c\right)}{{\left(b-c\right)}^3}\right)}{3\,c}\right)\,\sqrt{a+c\,x}}{c}-\frac{x\,\left(\frac{8\,a\,\left(b+3\,c\right)}{5\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(5\,b+3\,c\right)}{{\left(b-c\right)}^3}\right)\,\sqrt{a+b\,x}}{3\,b}+\frac{x\,\left(\frac{8\,a\,\left(3\,b+c\right)}{5\,{\left(b-c\right)}^3}-\frac{2\,a\,\left(3\,b+5\,c\right)}{{\left(b-c\right)}^3}\right)\,\sqrt{a+c\,x}}{3\,c}+\frac{2\,x^2\,\left(b+3\,c\right)\,\sqrt{a+b\,x}}{5\,{\left(b-c\right)}^3}-\frac{2\,x^2\,\left(3\,b+c\right)\,\sqrt{a+c\,x}}{5\,{\left(b-c\right)}^3}","Not used",1,"(((8*a^2)/(b - c)^3 + (2*a*((8*a*(b + 3*c))/(5*(b - c)^3) - (2*a*(5*b + 3*c))/(b - c)^3))/(3*b))*(a + b*x)^(1/2))/b - (((8*a^2)/(b - c)^3 + (2*a*((8*a*(3*b + c))/(5*(b - c)^3) - (2*a*(3*b + 5*c))/(b - c)^3))/(3*c))*(a + c*x)^(1/2))/c - (x*((8*a*(b + 3*c))/(5*(b - c)^3) - (2*a*(5*b + 3*c))/(b - c)^3)*(a + b*x)^(1/2))/(3*b) + (x*((8*a*(3*b + c))/(5*(b - c)^3) - (2*a*(3*b + 5*c))/(b - c)^3)*(a + c*x)^(1/2))/(3*c) + (2*x^2*(b + 3*c)*(a + b*x)^(1/2))/(5*(b - c)^3) - (2*x^2*(3*b + c)*(a + c*x)^(1/2))/(5*(b - c)^3)","B"
440,1,762,155,7.022673,"\text{Not used}","int(x^2/((a + b*x)^(1/2) + (a + c*x)^(1/2))^3,x)","\frac{4\,a^{3/2}\,b^4-\frac{4\,a^{3/2}\,c^4\,\left(\frac{4\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}-\frac{15\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}+\frac{24\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}+\frac{6\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^6}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^6}\right)}{3}-\frac{4\,a^{3/2}\,b^2\,c^2\,\left(\frac{24\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}+\frac{12\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{12\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}-\frac{15\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}+\frac{18\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-3\right)}{3}+\frac{4\,a^{3/2}\,b\,c^3\,\left(\frac{6\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{12\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+\frac{66\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}-\frac{24\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^5}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^5}+\frac{18\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}\right)}{3}+\frac{4\,a^{3/2}\,b^3\,c\,\left(6\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)-\frac{24\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}+\frac{6\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{4\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}+26\right)}{3}}{c\,{\left(b-c\right)}^3\,{\left(b-\frac{c\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}\right)}^3}","Not used",1,"(4*a^(3/2)*b^4 - (4*a^(3/2)*c^4*((4*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3 - (15*((a + b*x)^(1/2) - a^(1/2))^4)/((a + c*x)^(1/2) - a^(1/2))^4 + (24*((a + b*x)^(1/2) - a^(1/2))^5)/((a + c*x)^(1/2) - a^(1/2))^5 + (6*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2))^6)/((a + c*x)^(1/2) - a^(1/2))^6))/3 - (4*a^(3/2)*b^2*c^2*((24*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) + (12*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 + (12*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3 - (15*((a + b*x)^(1/2) - a^(1/2))^4)/((a + c*x)^(1/2) - a^(1/2))^4 + (18*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 - 3))/3 + (4*a^(3/2)*b*c^3*((6*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 - (12*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3 + (66*((a + b*x)^(1/2) - a^(1/2))^4)/((a + c*x)^(1/2) - a^(1/2))^4 - (24*((a + b*x)^(1/2) - a^(1/2))^5)/((a + c*x)^(1/2) - a^(1/2))^5 + (18*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2))^4)/((a + c*x)^(1/2) - a^(1/2))^4))/3 + (4*a^(3/2)*b^3*c*(6*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2))) - (24*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) + (6*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 - (4*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3 + 26))/3)/(c*(b - c)^3*(b - (c*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2)^3)","B"
441,1,559,157,7.488186,"\text{Not used}","int(x/((a + b*x)^(1/2) + (a + c*x)^(1/2))^3,x)","\frac{2\,\sqrt{a}\,b^2\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(\frac{8\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{2\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{3\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}+1\right)-2\,\sqrt{a}\,c^2\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(\frac{2\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^4}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^4}+\frac{3\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}\right)+2\,\sqrt{a}\,b\,c\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(\frac{8\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{14\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}+\frac{3\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a+c\,x}-\sqrt{a}}-\frac{3\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^3}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^3}\right)}{{\left(b-c\right)}^3\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)\,\left(b-\frac{c\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}\right)}","Not used",1,"(2*a^(1/2)*b^2*((a + c*x)^(1/2) - a^(1/2))*((8*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (2*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 + (3*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) + 1) - 2*a^(1/2)*c^2*((a + c*x)^(1/2) - a^(1/2))*((2*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 - ((a + b*x)^(1/2) - a^(1/2))^4/((a + c*x)^(1/2) - a^(1/2))^4 + (3*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3) + 2*a^(1/2)*b*c*((a + c*x)^(1/2) - a^(1/2))*((8*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (14*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2 + (3*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2)))/((a + c*x)^(1/2) - a^(1/2)) - (3*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2)))*((a + b*x)^(1/2) - a^(1/2))^3)/((a + c*x)^(1/2) - a^(1/2))^3))/((b - c)^3*((a + b*x)^(1/2) - a^(1/2))*(b - (c*((a + b*x)^(1/2) - a^(1/2))^2)/((a + c*x)^(1/2) - a^(1/2))^2))","B"
442,1,287,164,5.743497,"\text{Not used}","int(1/((a + b*x)^(1/2) + (a + c*x)^(1/2))^3,x)","\frac{c^2\,{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}{4\,\sqrt{a}\,{\left(b-c\right)}^3\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}-\frac{\left(\frac{\sqrt{a}\,b^2}{4\,\left(a\,b^3-3\,a\,b^2\,c+3\,a\,b\,c^2-a\,c^3\right)}-\frac{\sqrt{a}\,\left(b^2+c\,b\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\left(\sqrt{a+c\,x}-\sqrt{a}\right)\,\left(a\,b^3-3\,a\,b^2\,c+3\,a\,b\,c^2-a\,c^3\right)}\right)\,{\left(\sqrt{a+c\,x}-\sqrt{a}\right)}^2}{{\left(\sqrt{a+b\,x}-\sqrt{a}\right)}^2}+\frac{3\,b\,c\,\ln\left(\frac{\sqrt{a+b\,x}-\sqrt{a}}{\sqrt{a+c\,x}-\sqrt{a}}\right)}{\sqrt{a}\,\left(b^3-3\,b^2\,c+3\,b\,c^2-c^3\right)}-\frac{c\,\left(b+c\right)\,\left(\sqrt{a+b\,x}-\sqrt{a}\right)}{\sqrt{a}\,{\left(b-c\right)}^3\,\left(\sqrt{a+c\,x}-\sqrt{a}\right)}","Not used",1,"(c^2*((a + b*x)^(1/2) - a^(1/2))^2)/(4*a^(1/2)*(b - c)^3*((a + c*x)^(1/2) - a^(1/2))^2) - (((a^(1/2)*b^2)/(4*(a*b^3 - a*c^3 + 3*a*b*c^2 - 3*a*b^2*c)) - (a^(1/2)*(b*c + b^2)*((a + b*x)^(1/2) - a^(1/2)))/(((a + c*x)^(1/2) - a^(1/2))*(a*b^3 - a*c^3 + 3*a*b*c^2 - 3*a*b^2*c)))*((a + c*x)^(1/2) - a^(1/2))^2)/((a + b*x)^(1/2) - a^(1/2))^2 + (3*b*c*log(((a + b*x)^(1/2) - a^(1/2))/((a + c*x)^(1/2) - a^(1/2))))/(a^(1/2)*(3*b*c^2 - 3*b^2*c + b^3 - c^3)) - (c*(b + c)*((a + b*x)^(1/2) - a^(1/2)))/(a^(1/2)*(b - c)^3*((a + c*x)^(1/2) - a^(1/2)))","B"
443,1,209,31,8.122455,"\text{Not used}","int(((x + 1)^(1/2) + (1 - x)^(1/2))*(1 - x)^(1/2),x)","x-2\,\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\frac{\frac{2\,\left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-\frac{14\,{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{14\,{\left(\sqrt{1-x}-1\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}-\frac{2\,{\left(\sqrt{1-x}-1\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}}{\frac{4\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{6\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{{\left(\sqrt{1-x}-1\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}+1}-\frac{x^2}{2}","Not used",1,"x - 2*atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - ((2*((1 - x)^(1/2) - 1))/((x + 1)^(1/2) - 1) - (14*((1 - x)^(1/2) - 1)^3)/((x + 1)^(1/2) - 1)^3 + (14*((1 - x)^(1/2) - 1)^5)/((x + 1)^(1/2) - 1)^5 - (2*((1 - x)^(1/2) - 1)^7)/((x + 1)^(1/2) - 1)^7)/((4*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + (6*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + (4*((1 - x)^(1/2) - 1)^6)/((x + 1)^(1/2) - 1)^6 + ((1 - x)^(1/2) - 1)^8/((x + 1)^(1/2) - 1)^8 + 1) - x^2/2","B"
444,1,42,38,3.064592,"\text{Not used}","int(-x^3*((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","\sqrt{1-x}\,\left(\frac{4\,\sqrt{x+1}}{15}+\frac{2\,x^2\,\sqrt{x+1}}{15}-\frac{2\,x^4\,\sqrt{x+1}}{5}\right)-\frac{x^4}{2}","Not used",1,"(1 - x)^(1/2)*((4*(x + 1)^(1/2))/15 + (2*x^2*(x + 1)^(1/2))/15 - (2*x^4*(x + 1)^(1/2))/5) - x^4/2","B"
445,1,381,48,10.394269,"\text{Not used}","int(-x^2*((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\frac{\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}-\frac{35\,{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{273\,{\left(\sqrt{1-x}-1\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}-\frac{715\,{\left(\sqrt{1-x}-1\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}+\frac{715\,{\left(\sqrt{1-x}-1\right)}^9}{{\left(\sqrt{x+1}-1\right)}^9}-\frac{273\,{\left(\sqrt{1-x}-1\right)}^{11}}{{\left(\sqrt{x+1}-1\right)}^{11}}+\frac{35\,{\left(\sqrt{1-x}-1\right)}^{13}}{{\left(\sqrt{x+1}-1\right)}^{13}}-\frac{{\left(\sqrt{1-x}-1\right)}^{15}}{{\left(\sqrt{x+1}-1\right)}^{15}}}{\frac{8\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{56\,{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{1-x}-1\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}+\frac{56\,{\left(\sqrt{1-x}-1\right)}^{10}}{{\left(\sqrt{x+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^{12}}{{\left(\sqrt{x+1}-1\right)}^{12}}+\frac{8\,{\left(\sqrt{1-x}-1\right)}^{14}}{{\left(\sqrt{x+1}-1\right)}^{14}}+\frac{{\left(\sqrt{1-x}-1\right)}^{16}}{{\left(\sqrt{x+1}-1\right)}^{16}}+1}-\frac{2\,x^3}{3}","Not used",1,"atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - (((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1) - (35*((1 - x)^(1/2) - 1)^3)/((x + 1)^(1/2) - 1)^3 + (273*((1 - x)^(1/2) - 1)^5)/((x + 1)^(1/2) - 1)^5 - (715*((1 - x)^(1/2) - 1)^7)/((x + 1)^(1/2) - 1)^7 + (715*((1 - x)^(1/2) - 1)^9)/((x + 1)^(1/2) - 1)^9 - (273*((1 - x)^(1/2) - 1)^11)/((x + 1)^(1/2) - 1)^11 + (35*((1 - x)^(1/2) - 1)^13)/((x + 1)^(1/2) - 1)^13 - ((1 - x)^(1/2) - 1)^15/((x + 1)^(1/2) - 1)^15)/((8*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + (28*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + (56*((1 - x)^(1/2) - 1)^6)/((x + 1)^(1/2) - 1)^6 + (70*((1 - x)^(1/2) - 1)^8)/((x + 1)^(1/2) - 1)^8 + (56*((1 - x)^(1/2) - 1)^10)/((x + 1)^(1/2) - 1)^10 + (28*((1 - x)^(1/2) - 1)^12)/((x + 1)^(1/2) - 1)^12 + (8*((1 - x)^(1/2) - 1)^14)/((x + 1)^(1/2) - 1)^14 + ((1 - x)^(1/2) - 1)^16/((x + 1)^(1/2) - 1)^16 + 1) - (2*x^3)/3","B"
446,1,25,21,3.061435,"\text{Not used}","int(-x*((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","-x^2-\frac{2\,\left(x^2-1\right)\,\sqrt{1-x}\,\sqrt{x+1}}{3}","Not used",1,"- x^2 - (2*(x^2 - 1)*(1 - x)^(1/2)*(x + 1)^(1/2))/3","B"
447,1,205,22,3.714393,"\text{Not used}","int(-((x + 1)^(1/2) + (1 - x)^(1/2))^2,x)","4\,\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-2\,x+\frac{\frac{4\,\left(\sqrt{1-x}-1\right)}{\sqrt{x+1}-1}-\frac{28\,{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{28\,{\left(\sqrt{1-x}-1\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}-\frac{4\,{\left(\sqrt{1-x}-1\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}}{\frac{4\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{6\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{{\left(\sqrt{1-x}-1\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}+1}","Not used",1,"4*atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - 2*x + ((4*((1 - x)^(1/2) - 1))/((x + 1)^(1/2) - 1) - (28*((1 - x)^(1/2) - 1)^3)/((x + 1)^(1/2) - 1)^3 + (28*((1 - x)^(1/2) - 1)^5)/((x + 1)^(1/2) - 1)^5 - (4*((1 - x)^(1/2) - 1)^7)/((x + 1)^(1/2) - 1)^7)/((4*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + (6*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + (4*((1 - x)^(1/2) - 1)^6)/((x + 1)^(1/2) - 1)^6 + ((1 - x)^(1/2) - 1)^8/((x + 1)^(1/2) - 1)^8 + 1)","B"
448,1,122,32,4.127359,"\text{Not used}","int(-((x + 1)^(1/2) + (1 - x)^(1/2))^2/x,x)","2\,\ln\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-2\,\ln\left(\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-1\right)-2\,\ln\left(x\right)-\frac{16\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2\,\left(\frac{2\,{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+\frac{{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+1\right)}","Not used",1,"2*log(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - 2*log(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - 1) - 2*log(x) - (16*((1 - x)^(1/2) - 1)^2)/(((x + 1)^(1/2) - 1)^2*((2*((1 - x)^(1/2) - 1)^2)/((x + 1)^(1/2) - 1)^2 + ((1 - x)^(1/2) - 1)^4/((x + 1)^(1/2) - 1)^4 + 1))","B"
449,1,118,26,3.786977,"\text{Not used}","int(-((x + 1)^(1/2) + (1 - x)^(1/2))^2/x^2,x)","\frac{\frac{5\,{\left(\sqrt{1-x}-1\right)}^2}{2\,{\left(\sqrt{x+1}-1\right)}^2}-\frac{1}{2}}{\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}-\frac{{\left(\sqrt{1-x}-1\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}}-8\,\mathrm{atan}\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)+\frac{\sqrt{1-x}-1}{2\,\left(\sqrt{x+1}-1\right)}+\frac{2}{x}","Not used",1,"((5*((1 - x)^(1/2) - 1)^2)/(2*((x + 1)^(1/2) - 1)^2) - 1/2)/(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1) - ((1 - x)^(1/2) - 1)^3/((x + 1)^(1/2) - 1)^3) - 8*atan(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) + ((1 - x)^(1/2) - 1)/(2*((x + 1)^(1/2) - 1)) + 2/x","B"
450,1,186,33,4.776579,"\text{Not used}","int(-((x + 1)^(1/2) + (1 - x)^(1/2))^2/x^3,x)","\ln\left(\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-1\right)-\ln\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)-\frac{{\left(\sqrt{1-x}-1\right)}^2}{16\,{\left(\sqrt{x+1}-1\right)}^2}+\frac{\frac{{\left(\sqrt{1-x}-1\right)}^2}{8\,{\left(\sqrt{x+1}-1\right)}^2}+\frac{15\,{\left(\sqrt{1-x}-1\right)}^4}{16\,{\left(\sqrt{x+1}-1\right)}^4}-\frac{1}{16}}{\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-\frac{2\,{\left(\sqrt{1-x}-1\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{{\left(\sqrt{1-x}-1\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}}+\frac{1}{x^2}","Not used",1,"log(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - 1) - log(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) - ((1 - x)^(1/2) - 1)^2/(16*((x + 1)^(1/2) - 1)^2) + (((1 - x)^(1/2) - 1)^2/(8*((x + 1)^(1/2) - 1)^2) + (15*((1 - x)^(1/2) - 1)^4)/(16*((x + 1)^(1/2) - 1)^4) - 1/16)/(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - (2*((1 - x)^(1/2) - 1)^4)/((x + 1)^(1/2) - 1)^4 + ((1 - x)^(1/2) - 1)^6/((x + 1)^(1/2) - 1)^6) + 1/x^2","B"
451,1,93,28,4.493051,"\text{Not used}","int(((x + 1)^(1/2) + (1 - x)^(1/2))/((x + 1)^(1/2) - (1 - x)^(1/2)),x)","\ln\left(\frac{{\left(\sqrt{1-x}-1\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}-1\right)-\ln\left(\frac{\sqrt{1-x}-1}{\sqrt{x+1}-1}\right)+\ln\left(x\right)-\frac{8\,\left(x-2\,\sqrt{x+1}+2\right)\,\left(x+2\,\sqrt{1-x}-2\right)}{{\left(2\,\sqrt{x+1}+2\,\sqrt{1-x}-4\right)}^2}","Not used",1,"log(((1 - x)^(1/2) - 1)^2/((x + 1)^(1/2) - 1)^2 - 1) - log(((1 - x)^(1/2) - 1)/((x + 1)^(1/2) - 1)) + log(x) - (8*(x - 2*(x + 1)^(1/2) + 2)*(x + 2*(1 - x)^(1/2) - 2))/(2*(x + 1)^(1/2) + 2*(1 - x)^(1/2) - 4)^2","B"
452,1,200,33,10.853289,"\text{Not used}","int(-((x - 1)^(1/2) - (x + 1)^(1/2))/((x - 1)^(1/2) + (x + 1)^(1/2)),x)","\mathrm{acosh}\left(x\right)-2\,\mathrm{atanh}\left(\frac{\sqrt{x-1}-\mathrm{i}}{\sqrt{x+1}-1}\right)+\frac{\frac{14\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{14\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{x+1}-1\right)}^5}+\frac{2\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{x+1}-1\right)}^7}+\frac{2\,\left(\sqrt{x-1}-\mathrm{i}\right)}{\sqrt{x+1}-1}}{1+\frac{6\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}-\frac{4\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}}+\frac{x^2}{2}","Not used",1,"acosh(x) - 2*atanh(((x - 1)^(1/2) - 1i)/((x + 1)^(1/2) - 1)) + ((14*((x - 1)^(1/2) - 1i)^3)/((x + 1)^(1/2) - 1)^3 + (14*((x - 1)^(1/2) - 1i)^5)/((x + 1)^(1/2) - 1)^5 + (2*((x - 1)^(1/2) - 1i)^7)/((x + 1)^(1/2) - 1)^7 + (2*((x - 1)^(1/2) - 1i))/((x + 1)^(1/2) - 1))/((6*((x - 1)^(1/2) - 1i)^4)/((x + 1)^(1/2) - 1)^4 - (4*((x - 1)^(1/2) - 1i)^2)/((x + 1)^(1/2) - 1)^2 - (4*((x - 1)^(1/2) - 1i)^6)/((x + 1)^(1/2) - 1)^6 + ((x - 1)^(1/2) - 1i)^8/((x + 1)^(1/2) - 1)^8 + 1) + x^2/2","B"
453,0,-1,121,0.000000,"\text{Not used}","int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^n,x)","\int {\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^n \,d x","Not used",1,"int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^n, x)","F"
454,0,-1,175,0.000000,"\text{Not used}","int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^3,x)","\int {\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^3 \,d x","Not used",1,"int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^3, x)","F"
455,1,210,136,4.657135,"\text{Not used}","int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^2,x)","\left\{\begin{array}{cl} x\,{\left(d+\sqrt{a}\,f\right)}^2 & \text{\ if\ \ }e=0\\ x\,\left(d^2+a\,f^2\right)+\frac{2\,e^2\,x^3}{3}+d\,e\,x^2+\frac{2\,a\,f^3\,\sqrt{a+\frac{e^2\,x^2}{f^2}}}{e}-\frac{2\,f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\,\left(2\,a\,f^2-e^2\,x^2\right)}{3\,e}+d\,f\,x\,\sqrt{a+\frac{e^2\,x^2}{f^2}}+\frac{2\,a\,d\,f\,\ln\left(x\,\sqrt{\frac{e^2}{f^2}}+\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}{\sqrt{\frac{e^2}{f^2}}}-\frac{a\,d\,e^2\,\ln\left(2\,x\,\sqrt{\frac{e^2}{f^2}}+2\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}{f\,{\left(\frac{e^2}{f^2}\right)}^{3/2}} & \text{\ if\ \ }e\neq 0 \end{array}\right.","Not used",1,"piecewise(e == 0, x*(d + a^(1/2)*f)^2, e ~= 0, x*(a*f^2 + d^2) + (2*e^2*x^3)/3 + d*e*x^2 + (2*a*f^3*(a + (e^2*x^2)/f^2)^(1/2))/e - (2*f*(a + (e^2*x^2)/f^2)^(1/2)*(2*a*f^2 - e^2*x^2))/(3*e) + d*f*x*(a + (e^2*x^2)/f^2)^(1/2) + (2*a*d*f*log(x*(e^2/f^2)^(1/2) + (a + (e^2*x^2)/f^2)^(1/2)))/(e^2/f^2)^(1/2) - (a*d*e^2*log(2*x*(e^2/f^2)^(1/2) + 2*(a + (e^2*x^2)/f^2)^(1/2)))/(f*(e^2/f^2)^(3/2)))","B"
456,1,136,68,3.888138,"\text{Not used}","int(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2),x)","\left\{\begin{array}{cl} x\,\left(d+\sqrt{a}\,f\right) & \text{\ if\ \ }e=0\\ d\,x+\frac{e\,x^2}{2}+\frac{f\,x\,\sqrt{a+\frac{e^2\,x^2}{f^2}}}{2}+\frac{a\,e^2\,\ln\left(x\,\sqrt{\frac{e^2}{f^2}}+\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}{f\,{\left(\frac{e^2}{f^2}\right)}^{3/2}}-\frac{a\,e^2\,\ln\left(2\,x\,\sqrt{\frac{e^2}{f^2}}+2\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}{2\,f\,{\left(\frac{e^2}{f^2}\right)}^{3/2}} & \text{\ if\ \ }e\neq 0 \end{array}\right.","Not used",1,"piecewise(e == 0, x*(d + a^(1/2)*f), e ~= 0, d*x + (e*x^2)/2 + (f*x*(a + (e^2*x^2)/f^2)^(1/2))/2 + (a*e^2*log(x*(e^2/f^2)^(1/2) + (a + (e^2*x^2)/f^2)^(1/2)))/(f*(e^2/f^2)^(3/2)) - (a*e^2*log(2*x*(e^2/f^2)^(1/2) + 2*(a + (e^2*x^2)/f^2)^(1/2)))/(2*f*(e^2/f^2)^(3/2)))","B"
457,0,-1,117,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2)),x)","\int \frac{1}{d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2)), x)","F"
458,0,-1,151,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^2,x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^2} \,d x","Not used",1,"int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^2, x)","F"
459,0,-1,193,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^3,x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^3} \,d x","Not used",1,"int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^3, x)","F"
460,0,-1,225,0.000000,"\text{Not used}","int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(5/2),x)","\int {\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^{5/2} \,d x","Not used",1,"int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(5/2), x)","F"
461,0,-1,183,0.000000,"\text{Not used}","int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(3/2),x)","\int {\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^{3/2} \,d x","Not used",1,"int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(3/2), x)","F"
462,0,-1,147,0.000000,"\text{Not used}","int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(1/2),x)","\int \sqrt{d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}} \,d x","Not used",1,"int((d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(1/2), x)","F"
463,0,-1,147,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(1/2), x)","F"
464,0,-1,158,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(3/2),x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^{3/2}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(3/2), x)","F"
465,0,-1,199,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(5/2),x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}}\right)}^{5/2}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + (e^2*x^2)/f^2)^(1/2))^(5/2), x)","F"
466,0,-1,41,0.000000,"\text{Not used}","int((x - (x^2 - 4)^(1/2))^(1/2),x)","\int \sqrt{x-\sqrt{x^2-4}} \,d x","Not used",1,"int((x - (x^2 - 4)^(1/2))^(1/2), x)","F"
467,0,-1,69,0.000000,"\text{Not used}","int((a*x + b*(c + (a^2*x^2)/b^2)^(1/2))^(1/2),x)","\int \sqrt{a\,x+b\,\sqrt{c+\frac{a^2\,x^2}{b^2}}} \,d x","Not used",1,"int((a*x + b*(c + (a^2*x^2)/b^2)^(1/2))^(1/2), x)","F"
468,0,-1,45,0.000000,"\text{Not used}","int(((1 - x^2)^(1/2) + 1)^(1/2),x)","\int \sqrt{\sqrt{1-x^2}+1} \,d x","Not used",1,"int(((1 - x^2)^(1/2) + 1)^(1/2), x)","F"
469,0,-1,41,0.000000,"\text{Not used}","int(((x^2 + 1)^(1/2) + 1)^(1/2),x)","\int \sqrt{\sqrt{x^2+1}+1} \,d x","Not used",1,"int(((x^2 + 1)^(1/2) + 1)^(1/2), x)","F"
470,0,-1,41,0.000000,"\text{Not used}","int(((x^2 + 25)^(1/2) + 5)^(1/2),x)","\int \sqrt{\sqrt{x^2+25}+5} \,d x","Not used",1,"int(((x^2 + 25)^(1/2) + 5)^(1/2), x)","F"
471,0,-1,66,0.000000,"\text{Not used}","int((a + b*(c*x^2 + a^2/b^2)^(1/2))^(1/2),x)","\int \sqrt{a+b\,\sqrt{c\,x^2+\frac{a^2}{b^2}}} \,d x","Not used",1,"int((a + b*(c*x^2 + a^2/b^2)^(1/2))^(1/2), x)","F"
472,0,-1,166,0.000000,"\text{Not used}","int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^n,x)","\int {\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^n \,d x","Not used",1,"int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^n, x)","F"
473,0,-1,303,0.000000,"\text{Not used}","int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^3,x)","\int {\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^3 \,d x","Not used",1,"int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^3, x)","F"
474,0,-1,237,0.000000,"\text{Not used}","int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^2,x)","\int {\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^2 \,d x","Not used",1,"int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^2, x)","F"
475,0,-1,118,0.000000,"\text{Not used}","int(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2),x)","\int d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}} \,d x","Not used",1,"int(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2), x)","F"
476,0,-1,215,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2)),x)","\int \frac{1}{d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2)), x)","F"
477,0,-1,266,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^2,x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^2} \,d x","Not used",1,"int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^2, x)","F"
478,0,-1,330,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^3,x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^3} \,d x","Not used",1,"int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^3, x)","F"
479,0,-1,370,0.000000,"\text{Not used}","int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(5/2),x)","\int {\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^{5/2} \,d x","Not used",1,"int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(5/2), x)","F"
480,0,-1,302,0.000000,"\text{Not used}","int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(3/2),x)","\int {\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^{3/2} \,d x","Not used",1,"int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(3/2), x)","F"
481,0,-1,233,0.000000,"\text{Not used}","int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(1/2),x)","\int \sqrt{d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}} \,d x","Not used",1,"int((d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(1/2), x)","F"
482,0,-1,244,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(1/2), x)","F"
483,0,-1,269,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(3/2),x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^{3/2}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(3/2), x)","F"
484,0,-1,335,0.000000,"\text{Not used}","int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(5/2),x)","\int \frac{1}{{\left(d+e\,x+f\,\sqrt{a+b\,x+\frac{e^2\,x^2}{f^2}}\right)}^{5/2}} \,d x","Not used",1,"int(1/(d + e*x + f*(a + b*x + (e^2*x^2)/f^2)^(1/2))^(5/2), x)","F"
485,0,-1,164,0.000000,"\text{Not used}","int((a + x^2)^2*(x + (a + x^2)^(1/2))^n,x)","\int {\left(x^2+a\right)}^2\,{\left(x+\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((a + x^2)^2*(x + (a + x^2)^(1/2))^n, x)","F"
486,0,-1,108,0.000000,"\text{Not used}","int((a + x^2)*(x + (a + x^2)^(1/2))^n,x)","\int \left(x^2+a\right)\,{\left(x+\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((a + x^2)*(x + (a + x^2)^(1/2))^n, x)","F"
487,0,-1,52,0.000000,"\text{Not used}","int((x + (a + x^2)^(1/2))^n,x)","\int {\left(x+\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((x + (a + x^2)^(1/2))^n, x)","F"
488,0,-1,59,0.000000,"\text{Not used}","int((x + (a + x^2)^(1/2))^n/(a + x^2),x)","\int \frac{{\left(x+\sqrt{x^2+a}\right)}^n}{x^2+a} \,d x","Not used",1,"int((x + (a + x^2)^(1/2))^n/(a + x^2), x)","F"
489,0,-1,59,0.000000,"\text{Not used}","int((x + (a + x^2)^(1/2))^n/(a + x^2)^2,x)","\int \frac{{\left(x+\sqrt{x^2+a}\right)}^n}{{\left(x^2+a\right)}^2} \,d x","Not used",1,"int((x + (a + x^2)^(1/2))^n/(a + x^2)^2, x)","F"
490,0,-1,176,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n*(a + x^2)^2,x)","\int {\left(x-\sqrt{x^2+a}\right)}^n\,{\left(x^2+a\right)}^2 \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n*(a + x^2)^2, x)","F"
491,0,-1,116,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n*(a + x^2),x)","\int {\left(x-\sqrt{x^2+a}\right)}^n\,\left(x^2+a\right) \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n*(a + x^2), x)","F"
492,0,-1,56,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n,x)","\int {\left(x-\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n, x)","F"
493,0,-1,63,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n/(a + x^2),x)","\int \frac{{\left(x-\sqrt{x^2+a}\right)}^n}{x^2+a} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n/(a + x^2), x)","F"
494,0,-1,63,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n/(a + x^2)^2,x)","\int \frac{{\left(x-\sqrt{x^2+a}\right)}^n}{{\left(x^2+a\right)}^2} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n/(a + x^2)^2, x)","F"
495,0,-1,187,0.000000,"\text{Not used}","int((a + x^2)^(5/2)*(x + (a + x^2)^(1/2))^n,x)","\int {\left(x^2+a\right)}^{5/2}\,{\left(x+\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((a + x^2)^(5/2)*(x + (a + x^2)^(1/2))^n, x)","F"
496,0,-1,131,0.000000,"\text{Not used}","int((a + x^2)^(3/2)*(x + (a + x^2)^(1/2))^n,x)","\int {\left(x^2+a\right)}^{3/2}\,{\left(x+\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((a + x^2)^(3/2)*(x + (a + x^2)^(1/2))^n, x)","F"
497,0,-1,75,0.000000,"\text{Not used}","int((a + x^2)^(1/2)*(x + (a + x^2)^(1/2))^n,x)","\int \sqrt{x^2+a}\,{\left(x+\sqrt{x^2+a}\right)}^n \,d x","Not used",1,"int((a + x^2)^(1/2)*(x + (a + x^2)^(1/2))^n, x)","F"
498,1,15,17,3.000243,"\text{Not used}","int((x + (a + x^2)^(1/2))^n/(a + x^2)^(1/2),x)","\frac{{\left(x+\sqrt{x^2+a}\right)}^n}{n}","Not used",1,"(x + (a + x^2)^(1/2))^n/n","B"
499,0,-1,59,0.000000,"\text{Not used}","int((x + (a + x^2)^(1/2))^n/(a + x^2)^(3/2),x)","\int \frac{{\left(x+\sqrt{x^2+a}\right)}^n}{{\left(x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((x + (a + x^2)^(1/2))^n/(a + x^2)^(3/2), x)","F"
500,0,-1,59,0.000000,"\text{Not used}","int((x + (a + x^2)^(1/2))^n/(a + x^2)^(5/2),x)","\int \frac{{\left(x+\sqrt{x^2+a}\right)}^n}{{\left(x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((x + (a + x^2)^(1/2))^n/(a + x^2)^(5/2), x)","F"
501,0,-1,201,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n*(a + x^2)^(5/2),x)","\int {\left(x-\sqrt{x^2+a}\right)}^n\,{\left(x^2+a\right)}^{5/2} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n*(a + x^2)^(5/2), x)","F"
502,0,-1,141,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n*(a + x^2)^(3/2),x)","\int {\left(x-\sqrt{x^2+a}\right)}^n\,{\left(x^2+a\right)}^{3/2} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n*(a + x^2)^(3/2), x)","F"
503,0,-1,81,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n*(a + x^2)^(1/2),x)","\int {\left(x-\sqrt{x^2+a}\right)}^n\,\sqrt{x^2+a} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n*(a + x^2)^(1/2), x)","F"
504,1,18,20,3.192952,"\text{Not used}","int((x - (a + x^2)^(1/2))^n/(a + x^2)^(1/2),x)","-\frac{{\left(x-\sqrt{x^2+a}\right)}^n}{n}","Not used",1,"-(x - (a + x^2)^(1/2))^n/n","B"
505,0,-1,63,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n/(a + x^2)^(3/2),x)","\int \frac{{\left(x-\sqrt{x^2+a}\right)}^n}{{\left(x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n/(a + x^2)^(3/2), x)","F"
506,0,-1,63,0.000000,"\text{Not used}","int((x - (a + x^2)^(1/2))^n/(a + x^2)^(5/2),x)","\int \frac{{\left(x-\sqrt{x^2+a}\right)}^n}{{\left(x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((x - (a + x^2)^(1/2))^n/(a + x^2)^(5/2), x)","F"
507,0,-1,365,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^2,x)","\int {\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n\,{\left(a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}\right)}^2 \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^2, x)","F"
508,0,-1,239,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2),x)","\int {\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n\,\left(a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}\right) \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2), x)","F"
509,0,-1,107,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n,x)","\int {\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n, x)","F"
510,0,-1,122,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2),x)","\int \frac{{\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n}{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2), x)","F"
511,0,-1,122,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^2,x)","\int \frac{{\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n}{{\left(a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}\right)}^2} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^2, x)","F"
512,0,-1,107,0.000000,"\text{Not used}","int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n,x)","\int {\left(d+e\,x+f\,\sqrt{\frac{a\,f^2+e\,x\,\left(2\,d+e\,x\right)}{f^2}}\right)}^n \,d x","Not used",1,"int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n, x)","F"
513,0,-1,122,0.000000,"\text{Not used}","int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2),x)","\int \frac{{\left(d+e\,x+f\,\sqrt{\frac{a\,f^2+e\,x\,\left(2\,d+e\,x\right)}{f^2}}\right)}^n}{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}} \,d x","Not used",1,"int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2), x)","F"
514,0,-1,297,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(3/2),x)","\int {\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n\,{\left(a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}\right)}^{3/2} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(3/2), x)","F"
515,0,-1,171,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2),x)","\int {\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2), x)","F"
516,1,41,41,3.084443,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2),x)","\frac{f\,{\left(d+e\,x+f\,\sqrt{\frac{e^2\,x^2+2\,d\,e\,x+a\,f^2}{f^2}}\right)}^n}{e\,n}","Not used",1,"(f*(d + e*x + f*((a*f^2 + e^2*x^2 + 2*d*e*x)/f^2)^(1/2))^n)/(e*n)","B"
517,0,-1,122,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(3/2),x)","\int \frac{{\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n}{{\left(a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}\right)}^{3/2}} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(3/2), x)","F"
518,1,39,41,3.076223,"\text{Not used}","int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n/((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2),x)","\frac{f\,{\left(d+e\,x+f\,\sqrt{\frac{a\,f^2+e\,x\,\left(2\,d+e\,x\right)}{f^2}}\right)}^n}{e\,n}","Not used",1,"(f*(d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n)/(e*n)","B"
519,0,-1,327,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a*g + (e^2*g*x^2)/f^2 + (2*d*e*g*x)/f^2)^(1/2),x)","\int {\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n\,\sqrt{a\,g+\frac{e^2\,g\,x^2}{f^2}+\frac{2\,d\,e\,g\,x}{f^2}} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n*(a*g + (e^2*g*x^2)/f^2 + (2*d*e*g*x)/f^2)^(1/2), x)","F"
520,0,-1,93,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a*g + (e^2*g*x^2)/f^2 + (2*d*e*g*x)/f^2)^(1/2),x)","\int \frac{{\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n}{\sqrt{a\,g+\frac{e^2\,g\,x^2}{f^2}+\frac{2\,d\,e\,g\,x}{f^2}}} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a*g + (e^2*g*x^2)/f^2 + (2*d*e*g*x)/f^2)^(1/2), x)","F"
521,0,-1,177,0.000000,"\text{Not used}","int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a*g + (e^2*g*x^2)/f^2 + (2*d*e*g*x)/f^2)^(3/2),x)","\int \frac{{\left(d+f\,\sqrt{a+\frac{e^2\,x^2}{f^2}+\frac{2\,d\,e\,x}{f^2}}+e\,x\right)}^n}{{\left(a\,g+\frac{e^2\,g\,x^2}{f^2}+\frac{2\,d\,e\,g\,x}{f^2}\right)}^{3/2}} \,d x","Not used",1,"int((d + f*(a + (e^2*x^2)/f^2 + (2*d*e*x)/f^2)^(1/2) + e*x)^n/(a*g + (e^2*g*x^2)/f^2 + (2*d*e*g*x)/f^2)^(3/2), x)","F"
522,0,-1,93,0.000000,"\text{Not used}","int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n/((a*f^2*g + e*g*x*(2*d + e*x))/f^2)^(1/2),x)","\int \frac{{\left(d+e\,x+f\,\sqrt{\frac{a\,f^2+e\,x\,\left(2\,d+e\,x\right)}{f^2}}\right)}^n}{\sqrt{\frac{a\,g\,f^2+e\,g\,x\,\left(2\,d+e\,x\right)}{f^2}}} \,d x","Not used",1,"int((d + e*x + f*((a*f^2 + e*x*(2*d + e*x))/f^2)^(1/2))^n/((a*f^2*g + e*g*x*(2*d + e*x))/f^2)^(1/2), x)","F"
523,0,-1,191,0.000000,"\text{Not used}","int(1/((c + d*x^2)^(1/2)*(e + f*x^2)^(1/2)*(a + b*x)),x)","\int \frac{1}{\sqrt{d\,x^2+c}\,\sqrt{f\,x^2+e}\,\left(a+b\,x\right)} \,d x","Not used",1,"int(1/((c + d*x^2)^(1/2)*(e + f*x^2)^(1/2)*(a + b*x)), x)","F"
524,1,50,81,3.113004,"\text{Not used}","int((e - 2*f*x^2)/(e^2 + 4*f^2*x^4 + 4*d*f*x^2 + 4*e*f*x^2),x)","\frac{\mathrm{atan}\left(\frac{2\,f^{3/2}\,x^3+2\,d\,\sqrt{f}\,x+e\,\sqrt{f}\,x}{\sqrt{d}\,e}\right)-\mathrm{atan}\left(\frac{\sqrt{f}\,x}{\sqrt{d}}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"(atan((2*f^(3/2)*x^3 + 2*d*f^(1/2)*x + e*f^(1/2)*x)/(d^(1/2)*e)) - atan((f^(1/2)*x)/d^(1/2)))/(2*d^(1/2)*f^(1/2))","B"
525,1,28,73,3.140944,"\text{Not used}","int((e - 2*f*x^2)/(e^2 + 4*f^2*x^4 - 4*d*f*x^2 + 4*e*f*x^2),x)","\frac{\mathrm{atanh}\left(\frac{2\,\sqrt{d}\,\sqrt{f}\,x}{2\,f\,x^2+e}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"atanh((2*d^(1/2)*f^(1/2)*x)/(e + 2*f*x^2))/(2*d^(1/2)*f^(1/2))","B"
526,1,54,38,3.315317,"\text{Not used}","int((e - 4*f*x^3)/(e^2 + 4*f^2*x^6 + 4*d*f*x^2 + 4*e*f*x^3),x)","\frac{\mathrm{atan}\left(\frac{2\,f^{3/2}\,x^5+2\,d\,\sqrt{f}\,x+e\,\sqrt{f}\,x^2}{\sqrt{d}\,e}\right)-\mathrm{atan}\left(\frac{\sqrt{f}\,x^2}{\sqrt{d}}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"(atan((2*f^(3/2)*x^5 + 2*d*f^(1/2)*x + e*f^(1/2)*x^2)/(d^(1/2)*e)) - atan((f^(1/2)*x^2)/d^(1/2)))/(2*d^(1/2)*f^(1/2))","B"
527,1,67,38,3.117874,"\text{Not used}","int((e - 4*f*x^3)/(e^2 + 4*f^2*x^6 - 4*d*f*x^2 + 4*e*f*x^3),x)","-\frac{\mathrm{atanh}\left(\frac{-32\,f\,d^2\,x+27\,e^3+54\,f\,e^2\,x^3}{16\,d^{3/2}\,e\,\sqrt{f}+32\,d^{3/2}\,f^{3/2}\,x^3-54\,\sqrt{d}\,e^2\,\sqrt{f}\,x}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"-atanh((27*e^3 - 32*d^2*f*x + 54*e^2*f*x^3)/(16*d^(3/2)*e*f^(1/2) + 32*d^(3/2)*f^(3/2)*x^3 - 54*d^(1/2)*e^2*f^(1/2)*x))/(2*d^(1/2)*f^(1/2))","B"
528,1,196,38,3.418761,"\text{Not used}","int((e - 2*f*x^n*(n - 1))/(e^2 + 4*f^2*x^(2*n) + 4*d*f*x^2 + 4*e*f*x^n),x)","\frac{\ln\left(-\frac{e+2\,f\,x^n-2\,f\,n\,x^n}{4\,f^2}-\frac{e^2\,n-4\,d\,f\,x^2+4\,d\,f\,n\,x^2+2\,e\,f\,n\,x^n}{8\,\sqrt{-d}\,f^{5/2}\,x}\right)}{4\,\sqrt{-d}\,\sqrt{f}}-\frac{\mathrm{atan}\left(\frac{x\,\left(8\,d\,f\,n^2-16\,d\,f\,n+8\,d\,f\right)}{4\,\sqrt{d}\,\sqrt{f}\,\left(e\,n-e\,n^2\right)}\right)}{2\,\sqrt{d}\,\sqrt{f}}-\frac{\ln\left(\frac{e^2\,n-4\,d\,f\,x^2+4\,d\,f\,n\,x^2+2\,e\,f\,n\,x^n}{8\,\sqrt{-d}\,f^{5/2}\,x}-\frac{e+2\,f\,x^n-2\,f\,n\,x^n}{4\,f^2}\right)}{4\,\sqrt{-d}\,\sqrt{f}}","Not used",1,"log(- (e + 2*f*x^n - 2*f*n*x^n)/(4*f^2) - (e^2*n - 4*d*f*x^2 + 4*d*f*n*x^2 + 2*e*f*n*x^n)/(8*(-d)^(1/2)*f^(5/2)*x))/(4*(-d)^(1/2)*f^(1/2)) - atan((x*(8*d*f - 16*d*f*n + 8*d*f*n^2))/(4*d^(1/2)*f^(1/2)*(e*n - e*n^2)))/(2*d^(1/2)*f^(1/2)) - log((e^2*n - 4*d*f*x^2 + 4*d*f*n*x^2 + 2*e*f*n*x^n)/(8*(-d)^(1/2)*f^(5/2)*x) - (e + 2*f*x^n - 2*f*n*x^n)/(4*f^2))/(4*(-d)^(1/2)*f^(1/2))","B"
529,1,139,38,5.302221,"\text{Not used}","int((e - 2*f*x^n*(n - 1))/(e^2 + 4*f^2*x^(2*n) - 4*d*f*x^2 + 4*e*f*x^n),x)","\frac{\ln\left(\frac{\left(e+2\,f\,x^n+2\,\sqrt{d}\,\sqrt{f}\,x\right)\,\left(e\,n+2\,\sqrt{d}\,\sqrt{f}\,x-2\,\sqrt{d}\,\sqrt{f}\,n\,x\right)}{x}\right)}{4\,\sqrt{d}\,\sqrt{f}}-\frac{\ln\left(\frac{\left(e+2\,f\,x^n-2\,\sqrt{d}\,\sqrt{f}\,x\right)\,\left(e\,n-2\,\sqrt{d}\,\sqrt{f}\,x+2\,\sqrt{d}\,\sqrt{f}\,n\,x\right)}{x}\right)}{4\,\sqrt{d}\,\sqrt{f}}-\frac{\mathrm{atan}\left(\frac{2\,\sqrt{d}\,\sqrt{f}\,x\,\left(n\,1{}\mathrm{i}-\mathrm{i}\right)}{e\,n}\right)\,1{}\mathrm{i}}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"log(((e + 2*f*x^n + 2*d^(1/2)*f^(1/2)*x)*(e*n + 2*d^(1/2)*f^(1/2)*x - 2*d^(1/2)*f^(1/2)*n*x))/x)/(4*d^(1/2)*f^(1/2)) - log(((e + 2*f*x^n - 2*d^(1/2)*f^(1/2)*x)*(e*n - 2*d^(1/2)*f^(1/2)*x + 2*d^(1/2)*f^(1/2)*n*x))/x)/(4*d^(1/2)*f^(1/2)) - (atan((2*d^(1/2)*f^(1/2)*x*(n*1i - 1i))/(e*n))*1i)/(2*d^(1/2)*f^(1/2))","B"
530,1,42,42,3.099586,"\text{Not used}","int(x/(e^2 + 4*f^2*x^4 + 4*d*f*x^4 + 4*e*f*x^2),x)","\frac{\mathrm{atan}\left(\frac{e\,\sqrt{f}+2\,f^{3/2}\,x^2+2\,d\,\sqrt{f}\,x^2}{\sqrt{d}\,e}\right)}{4\,\sqrt{d}\,e\,\sqrt{f}}","Not used",1,"atan((e*f^(1/2) + 2*f^(3/2)*x^2 + 2*d*f^(1/2)*x^2)/(d^(1/2)*e))/(4*d^(1/2)*e*f^(1/2))","B"
531,1,199,44,3.106687,"\text{Not used}","int(x/(e^2 + 4*f^2*x^4 - 4*d*f*x^4 + 4*e*f*x^2),x)","\frac{\mathrm{atanh}\left(\frac{16\,d^{3/2}\,f^{3/2}\,x^2}{\frac{8\,e\,f^3}{d}-32\,f^3\,x^2-16\,e\,f^2+16\,d\,f^2\,x^2+8\,d\,e\,f+\frac{16\,f^4\,x^2}{d}}-\frac{32\,\sqrt{d}\,f^{5/2}\,x^2}{\frac{8\,e\,f^3}{d}-32\,f^3\,x^2-16\,e\,f^2+16\,d\,f^2\,x^2+8\,d\,e\,f+\frac{16\,f^4\,x^2}{d}}+\frac{16\,f^{7/2}\,x^2}{\sqrt{d}\,\left(\frac{8\,e\,f^3}{d}-32\,f^3\,x^2-16\,e\,f^2+16\,d\,f^2\,x^2+8\,d\,e\,f+\frac{16\,f^4\,x^2}{d}\right)}\right)}{4\,\sqrt{d}\,e\,\sqrt{f}}","Not used",1,"atanh((16*d^(3/2)*f^(3/2)*x^2)/((8*e*f^3)/d - 32*f^3*x^2 - 16*e*f^2 + 16*d*f^2*x^2 + 8*d*e*f + (16*f^4*x^2)/d) - (32*d^(1/2)*f^(5/2)*x^2)/((8*e*f^3)/d - 32*f^3*x^2 - 16*e*f^2 + 16*d*f^2*x^2 + 8*d*e*f + (16*f^4*x^2)/d) + (16*f^(7/2)*x^2)/(d^(1/2)*((8*e*f^3)/d - 32*f^3*x^2 - 16*e*f^2 + 16*d*f^2*x^2 + 8*d*e*f + (16*f^4*x^2)/d)))/(4*d^(1/2)*e*f^(1/2))","B"
532,1,278,40,3.209018,"\text{Not used}","int((x^2*(3*e + 2*f*x^2))/(e^2 + 4*f^2*x^4 + 4*d*f*x^6 + 4*e*f*x^2),x)","\frac{\mathrm{atan}\left(\frac{2\,f^2\,x+2\,d\,f\,x^3-d\,e\,x}{\sqrt{d}\,e\,\sqrt{f}}\right)-\mathrm{atan}\left(\frac{1984\,d^{3/2}\,f^{9/2}\,x^3}{432\,d^2\,e^2\,f^2-128\,d\,e\,f^4}+\frac{1728\,d^{5/2}\,f^{7/2}\,x^5}{432\,d^2\,e^2\,f^2-128\,d\,e\,f^4}+\frac{512\,\sqrt{d}\,f^{13/2}\,x^3}{128\,d\,e^2\,f^4-432\,d^2\,e^3\,f^2}+\frac{512\,d^{3/2}\,f^{11/2}\,x^5}{128\,d\,e^2\,f^4-432\,d^2\,e^3\,f^2}-\frac{256\,\sqrt{d}\,f^{11/2}\,x}{432\,d^2\,e^2\,f^2-128\,d\,e\,f^4}+\frac{864\,d^{3/2}\,e\,f^{7/2}\,x}{432\,d^2\,e^2\,f^2-128\,d\,e\,f^4}-\frac{864\,d^{5/2}\,e\,f^{5/2}\,x^3}{432\,d^2\,e^2\,f^2-128\,d\,e\,f^4}\right)+\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{f}}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"(atan((2*f^2*x + 2*d*f*x^3 - d*e*x)/(d^(1/2)*e*f^(1/2))) - atan((1984*d^(3/2)*f^(9/2)*x^3)/(432*d^2*e^2*f^2 - 128*d*e*f^4) + (1728*d^(5/2)*f^(7/2)*x^5)/(432*d^2*e^2*f^2 - 128*d*e*f^4) + (512*d^(1/2)*f^(13/2)*x^3)/(128*d*e^2*f^4 - 432*d^2*e^3*f^2) + (512*d^(3/2)*f^(11/2)*x^5)/(128*d*e^2*f^4 - 432*d^2*e^3*f^2) - (256*d^(1/2)*f^(11/2)*x)/(432*d^2*e^2*f^2 - 128*d*e*f^4) + (864*d^(3/2)*e*f^(7/2)*x)/(432*d^2*e^2*f^2 - 128*d*e*f^4) - (864*d^(5/2)*e*f^(5/2)*x^3)/(432*d^2*e^2*f^2 - 128*d*e*f^4)) + atan((d^(1/2)*x)/f^(1/2)))/(2*d^(1/2)*f^(1/2))","B"
533,1,30,40,3.142540,"\text{Not used}","int((x^2*(3*e + 2*f*x^2))/(e^2 + 4*f^2*x^4 - 4*d*f*x^6 + 4*e*f*x^2),x)","\frac{\mathrm{atanh}\left(\frac{2\,\sqrt{d}\,\sqrt{f}\,x^3}{2\,f\,x^2+e}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"atanh((2*d^(1/2)*f^(1/2)*x^3)/(e + 2*f*x^2))/(2*d^(1/2)*f^(1/2))","B"
534,0,-1,42,0.000000,"\text{Not used}","int((x^m*(e*(m + 1) + 2*f*x^2*(m - 1)))/(e^2 + 4*f^2*x^4 + 4*e*f*x^2 + 4*d*f*x^(2*m + 2)),x)","\int \frac{x^m\,\left(2\,f\,\left(m-1\right)\,x^2+e\,\left(m+1\right)\right)}{e^2+4\,f^2\,x^4+4\,e\,f\,x^2+4\,d\,f\,x^{2\,m+2}} \,d x","Not used",1,"int((x^m*(e*(m + 1) + 2*f*x^2*(m - 1)))/(e^2 + 4*f^2*x^4 + 4*e*f*x^2 + 4*d*f*x^(2*m + 2)), x)","F"
535,0,-1,42,0.000000,"\text{Not used}","int((x^m*(e*(m + 1) + 2*f*x^2*(m - 1)))/(e^2 + 4*f^2*x^4 + 4*e*f*x^2 - 4*d*f*x^(2*m + 2)),x)","\int \frac{x^m\,\left(2\,f\,\left(m-1\right)\,x^2+e\,\left(m+1\right)\right)}{e^2+4\,f^2\,x^4+4\,e\,f\,x^2-4\,d\,f\,x^{2\,m+2}} \,d x","Not used",1,"int((x^m*(e*(m + 1) + 2*f*x^2*(m - 1)))/(e^2 + 4*f^2*x^4 + 4*e*f*x^2 - 4*d*f*x^(2*m + 2)), x)","F"
536,1,233,40,3.487633,"\text{Not used}","int((x*(2*e - 2*f*x^3))/(e^2 + 4*f^2*x^6 + 4*d*f*x^4 + 4*e*f*x^3),x)","\frac{\mathrm{atan}\left(\frac{128\,d^{7/2}\,\sqrt{f}\,x^2}{64\,d^3\,e+729\,f\,e^3}-\frac{216\,d^{3/2}\,e^2\,\sqrt{f}}{64\,d^3\,e+729\,f\,e^3}+\frac{128\,d^{5/2}\,f^{3/2}\,x^4}{64\,d^3\,e+729\,f\,e^3}+\frac{216\,d^{3/2}\,e\,\sqrt{f}}{64\,d^3+729\,f\,e^2}+\frac{729\,d^{3/2}\,e^2\,f^{3/2}\,x}{64\,d^5+729\,f\,d^2\,e^2}+\frac{1458\,d^{3/2}\,e\,f^{5/2}\,x^4}{64\,d^5+729\,f\,d^2\,e^2}+\frac{64\,d^{5/2}\,e\,\sqrt{f}\,x}{64\,d^3\,e+729\,f\,e^3}+\frac{1458\,d^{3/2}\,e\,f^{3/2}\,x^2}{64\,d^4+729\,f\,d\,e^2}\right)-\mathrm{atan}\left(\frac{\sqrt{f}\,x}{\sqrt{d}}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"(atan((128*d^(7/2)*f^(1/2)*x^2)/(64*d^3*e + 729*e^3*f) - (216*d^(3/2)*e^2*f^(1/2))/(64*d^3*e + 729*e^3*f) + (128*d^(5/2)*f^(3/2)*x^4)/(64*d^3*e + 729*e^3*f) + (216*d^(3/2)*e*f^(1/2))/(729*e^2*f + 64*d^3) + (729*d^(3/2)*e^2*f^(3/2)*x)/(64*d^5 + 729*d^2*e^2*f) + (1458*d^(3/2)*e*f^(5/2)*x^4)/(64*d^5 + 729*d^2*e^2*f) + (64*d^(5/2)*e*f^(1/2)*x)/(64*d^3*e + 729*e^3*f) + (1458*d^(3/2)*e*f^(3/2)*x^2)/(64*d^4 + 729*d*e^2*f)) - atan((f^(1/2)*x)/d^(1/2)))/(2*d^(1/2)*f^(1/2))","B"
537,1,67,40,3.381421,"\text{Not used}","int((x*(2*e - 2*f*x^3))/(e^2 + 4*f^2*x^6 - 4*d*f*x^4 + 4*e*f*x^3),x)","-\frac{\mathrm{atanh}\left(\frac{27\,e^2\,\sqrt{f}+54\,e\,f^{3/2}\,x^3-16\,d^2\,\sqrt{f}\,x^2}{8\,d^{3/2}\,e+16\,d^{3/2}\,f\,x^3-54\,\sqrt{d}\,e\,f\,x^2}\right)}{2\,\sqrt{d}\,\sqrt{f}}","Not used",1,"-atanh((27*e^2*f^(1/2) + 54*e*f^(3/2)*x^3 - 16*d^2*f^(1/2)*x^2)/(8*d^(3/2)*e + 16*d^(3/2)*f*x^3 - 54*d^(1/2)*e*f*x^2))/(2*d^(1/2)*f^(1/2))","B"
538,1,42,42,3.433163,"\text{Not used}","int(x^2/(e^2 + 4*f^2*x^6 + 4*d*f*x^6 + 4*e*f*x^3),x)","\frac{\mathrm{atan}\left(\frac{e\,\sqrt{f}+2\,f^{3/2}\,x^3+2\,d\,\sqrt{f}\,x^3}{\sqrt{d}\,e}\right)}{6\,\sqrt{d}\,e\,\sqrt{f}}","Not used",1,"atan((e*f^(1/2) + 2*f^(3/2)*x^3 + 2*d*f^(1/2)*x^3)/(d^(1/2)*e))/(6*d^(1/2)*e*f^(1/2))","B"
539,1,923,44,3.527000,"\text{Not used}","int(x^2/(e^2 + 4*f^2*x^6 - 4*d*f*x^6 + 4*e*f*x^3),x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(x^3\,\left(32\,d^3\,f^3-96\,d^2\,f^4+96\,d\,f^5-32\,f^6\right)+\frac{x^3\,\left(-64\,e\,d^3\,f^4+192\,e\,d^2\,f^5-192\,e\,d\,f^6+64\,e\,f^7\right)+16\,e^2\,f^6-48\,d\,e^2\,f^5+48\,d^2\,e^2\,f^4-16\,d^3\,e^2\,f^3-\frac{\frac{x^3\,\left(-384\,d^3\,e^2\,f^5+1152\,d^2\,e^2\,f^6-1152\,d\,e^2\,f^7+384\,e^2\,f^8\right)}{12}+16\,e^3\,f^7-48\,d\,e^3\,f^6+48\,d^2\,e^3\,f^5-16\,d^3\,e^3\,f^4}{\sqrt{d}\,e\,\sqrt{f}}}{\sqrt{d}\,e\,\sqrt{f}}\right)\,1{}\mathrm{i}}{\sqrt{d}\,e\,\sqrt{f}}+\frac{\left(x^3\,\left(32\,d^3\,f^3-96\,d^2\,f^4+96\,d\,f^5-32\,f^6\right)-\frac{x^3\,\left(-64\,e\,d^3\,f^4+192\,e\,d^2\,f^5-192\,e\,d\,f^6+64\,e\,f^7\right)+16\,e^2\,f^6-48\,d\,e^2\,f^5+48\,d^2\,e^2\,f^4-16\,d^3\,e^2\,f^3+\frac{\frac{x^3\,\left(-384\,d^3\,e^2\,f^5+1152\,d^2\,e^2\,f^6-1152\,d\,e^2\,f^7+384\,e^2\,f^8\right)}{12}+16\,e^3\,f^7-48\,d\,e^3\,f^6+48\,d^2\,e^3\,f^5-16\,d^3\,e^3\,f^4}{\sqrt{d}\,e\,\sqrt{f}}}{\sqrt{d}\,e\,\sqrt{f}}\right)\,1{}\mathrm{i}}{\sqrt{d}\,e\,\sqrt{f}}}{\frac{x^3\,\left(32\,d^3\,f^3-96\,d^2\,f^4+96\,d\,f^5-32\,f^6\right)+\frac{x^3\,\left(-64\,e\,d^3\,f^4+192\,e\,d^2\,f^5-192\,e\,d\,f^6+64\,e\,f^7\right)+16\,e^2\,f^6-48\,d\,e^2\,f^5+48\,d^2\,e^2\,f^4-16\,d^3\,e^2\,f^3-\frac{\frac{x^3\,\left(-384\,d^3\,e^2\,f^5+1152\,d^2\,e^2\,f^6-1152\,d\,e^2\,f^7+384\,e^2\,f^8\right)}{12}+16\,e^3\,f^7-48\,d\,e^3\,f^6+48\,d^2\,e^3\,f^5-16\,d^3\,e^3\,f^4}{\sqrt{d}\,e\,\sqrt{f}}}{\sqrt{d}\,e\,\sqrt{f}}}{\sqrt{d}\,e\,\sqrt{f}}-\frac{x^3\,\left(32\,d^3\,f^3-96\,d^2\,f^4+96\,d\,f^5-32\,f^6\right)-\frac{x^3\,\left(-64\,e\,d^3\,f^4+192\,e\,d^2\,f^5-192\,e\,d\,f^6+64\,e\,f^7\right)+16\,e^2\,f^6-48\,d\,e^2\,f^5+48\,d^2\,e^2\,f^4-16\,d^3\,e^2\,f^3+\frac{\frac{x^3\,\left(-384\,d^3\,e^2\,f^5+1152\,d^2\,e^2\,f^6-1152\,d\,e^2\,f^7+384\,e^2\,f^8\right)}{12}+16\,e^3\,f^7-48\,d\,e^3\,f^6+48\,d^2\,e^3\,f^5-16\,d^3\,e^3\,f^4}{\sqrt{d}\,e\,\sqrt{f}}}{\sqrt{d}\,e\,\sqrt{f}}}{\sqrt{d}\,e\,\sqrt{f}}}\right)\,1{}\mathrm{i}}{6\,\sqrt{d}\,e\,\sqrt{f}}","Not used",1,"(atan((((x^3*(96*d*f^5 - 32*f^6 - 96*d^2*f^4 + 32*d^3*f^3) + (x^3*(64*e*f^7 + 192*d^2*e*f^5 - 64*d^3*e*f^4 - 192*d*e*f^6) + 16*e^2*f^6 - 48*d*e^2*f^5 + 48*d^2*e^2*f^4 - 16*d^3*e^2*f^3 - ((x^3*(384*e^2*f^8 - 1152*d*e^2*f^7 + 1152*d^2*e^2*f^6 - 384*d^3*e^2*f^5))/12 + 16*e^3*f^7 - 48*d*e^3*f^6 + 48*d^2*e^3*f^5 - 16*d^3*e^3*f^4)/(d^(1/2)*e*f^(1/2)))/(d^(1/2)*e*f^(1/2)))*1i)/(d^(1/2)*e*f^(1/2)) + ((x^3*(96*d*f^5 - 32*f^6 - 96*d^2*f^4 + 32*d^3*f^3) - (x^3*(64*e*f^7 + 192*d^2*e*f^5 - 64*d^3*e*f^4 - 192*d*e*f^6) + 16*e^2*f^6 - 48*d*e^2*f^5 + 48*d^2*e^2*f^4 - 16*d^3*e^2*f^3 + ((x^3*(384*e^2*f^8 - 1152*d*e^2*f^7 + 1152*d^2*e^2*f^6 - 384*d^3*e^2*f^5))/12 + 16*e^3*f^7 - 48*d*e^3*f^6 + 48*d^2*e^3*f^5 - 16*d^3*e^3*f^4)/(d^(1/2)*e*f^(1/2)))/(d^(1/2)*e*f^(1/2)))*1i)/(d^(1/2)*e*f^(1/2)))/((x^3*(96*d*f^5 - 32*f^6 - 96*d^2*f^4 + 32*d^3*f^3) + (x^3*(64*e*f^7 + 192*d^2*e*f^5 - 64*d^3*e*f^4 - 192*d*e*f^6) + 16*e^2*f^6 - 48*d*e^2*f^5 + 48*d^2*e^2*f^4 - 16*d^3*e^2*f^3 - ((x^3*(384*e^2*f^8 - 1152*d*e^2*f^7 + 1152*d^2*e^2*f^6 - 384*d^3*e^2*f^5))/12 + 16*e^3*f^7 - 48*d*e^3*f^6 + 48*d^2*e^3*f^5 - 16*d^3*e^3*f^4)/(d^(1/2)*e*f^(1/2)))/(d^(1/2)*e*f^(1/2)))/(d^(1/2)*e*f^(1/2)) - (x^3*(96*d*f^5 - 32*f^6 - 96*d^2*f^4 + 32*d^3*f^3) - (x^3*(64*e*f^7 + 192*d^2*e*f^5 - 64*d^3*e*f^4 - 192*d*e*f^6) + 16*e^2*f^6 - 48*d*e^2*f^5 + 48*d^2*e^2*f^4 - 16*d^3*e^2*f^3 + ((x^3*(384*e^2*f^8 - 1152*d*e^2*f^7 + 1152*d^2*e^2*f^6 - 384*d^3*e^2*f^5))/12 + 16*e^3*f^7 - 48*d*e^3*f^6 + 48*d^2*e^3*f^5 - 16*d^3*e^3*f^4)/(d^(1/2)*e*f^(1/2)))/(d^(1/2)*e*f^(1/2)))/(d^(1/2)*e*f^(1/2))))*1i)/(6*d^(1/2)*e*f^(1/2))","B"
540,0,-1,42,0.000000,"\text{Not used}","int((x^m*(e*(m + 1) + 2*f*x^3*(m - 2)))/(e^2 + 4*f^2*x^6 + 4*e*f*x^3 + 4*d*f*x^(2*m + 2)),x)","\int \frac{x^m\,\left(2\,f\,\left(m-2\right)\,x^3+e\,\left(m+1\right)\right)}{e^2+4\,f^2\,x^6+4\,e\,f\,x^3+4\,d\,f\,x^{2\,m+2}} \,d x","Not used",1,"int((x^m*(e*(m + 1) + 2*f*x^3*(m - 2)))/(e^2 + 4*f^2*x^6 + 4*e*f*x^3 + 4*d*f*x^(2*m + 2)), x)","F"
541,0,-1,42,0.000000,"\text{Not used}","int((x^m*(e*(m + 1) + 2*f*x^3*(m - 2)))/(e^2 + 4*f^2*x^6 + 4*e*f*x^3 - 4*d*f*x^(2*m + 2)),x)","\int \frac{x^m\,\left(2\,f\,\left(m-2\right)\,x^3+e\,\left(m+1\right)\right)}{e^2+4\,f^2\,x^6+4\,e\,f\,x^3-4\,d\,f\,x^{2\,m+2}} \,d x","Not used",1,"int((x^m*(e*(m + 1) + 2*f*x^3*(m - 2)))/(e^2 + 4*f^2*x^6 + 4*e*f*x^3 - 4*d*f*x^(2*m + 2)), x)","F"
542,0,-1,42,0.000000,"\text{Not used}","int((x^m*(e*(m + 1) + 2*f*x^n*(m - n + 1)))/(e^2 + 4*f^2*x^(2*n) + 4*d*f*x^(2*m + 2) + 4*e*f*x^n),x)","\int \frac{x^m\,\left(e\,\left(m+1\right)+2\,f\,x^n\,\left(m-n+1\right)\right)}{e^2+4\,f^2\,x^{2\,n}+4\,d\,f\,x^{2\,m+2}+4\,e\,f\,x^n} \,d x","Not used",1,"int((x^m*(e*(m + 1) + 2*f*x^n*(m - n + 1)))/(e^2 + 4*f^2*x^(2*n) + 4*d*f*x^(2*m + 2) + 4*e*f*x^n), x)","F"
543,0,-1,42,0.000000,"\text{Not used}","int((x^m*(e*(m + 1) + 2*f*x^n*(m - n + 1)))/(e^2 + 4*f^2*x^(2*n) - 4*d*f*x^(2*m + 2) + 4*e*f*x^n),x)","\int \frac{x^m\,\left(e\,\left(m+1\right)+2\,f\,x^n\,\left(m-n+1\right)\right)}{e^2+4\,f^2\,x^{2\,n}-4\,d\,f\,x^{2\,m+2}+4\,e\,f\,x^n} \,d x","Not used",1,"int((x^m*(e*(m + 1) + 2*f*x^n*(m - n + 1)))/(e^2 + 4*f^2*x^(2*n) - 4*d*f*x^(2*m + 2) + 4*e*f*x^n), x)","F"
544,1,167,134,3.644102,"\text{Not used}","int(x^5/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2),x)","\frac{x^4}{4\,b\,c}-\sqrt{b\,x^2+a}\,\left(\frac{d^3}{b^3\,c^4}-\frac{2\,a\,d}{b^3\,c^2}\right)-\frac{d\,{\left(b\,x^2+a\right)}^{3/2}}{3\,b^3\,c^2}-\frac{x^2\,\left(a\,c^2-d^2\right)}{2\,b^2\,c^3}+\frac{\mathrm{atanh}\left(\frac{c\,\sqrt{b\,x^2+a}}{d}\right)\,{\left(a\,c^2-d^2\right)}^2}{b^3\,c^5}+\frac{\ln\left(b\,c^2\,x^2+a\,c^2-d^2\right)\,\left(a^2\,c^4-2\,a\,c^2\,d^2+d^4\right)}{2\,b^3\,c^5}","Not used",1,"x^4/(4*b*c) - (a + b*x^2)^(1/2)*(d^3/(b^3*c^4) - (2*a*d)/(b^3*c^2)) - (d*(a + b*x^2)^(3/2))/(3*b^3*c^2) - (x^2*(a*c^2 - d^2))/(2*b^2*c^3) + (atanh((c*(a + b*x^2)^(1/2))/d)*(a*c^2 - d^2)^2)/(b^3*c^5) + (log(a*c^2 - d^2 + b*c^2*x^2)*(d^4 + a^2*c^4 - 2*a*c^2*d^2))/(2*b^3*c^5)","B"
545,1,123,69,3.497916,"\text{Not used}","int(x^3/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2),x)","\frac{x^2}{2\,b\,c}-\frac{d\,\sqrt{b\,x^2+a}}{b^2\,c^2}+\frac{\mathrm{atanh}\left(\frac{c\,\left(a\,c^2-d^2\right)\,\sqrt{b\,x^2+a}}{d^3-a\,c^2\,d}\right)\,\left(a\,c^2-d^2\right)}{b^2\,c^3}-\frac{\ln\left(b\,c^2\,x^2+a\,c^2-d^2\right)\,\left(a\,c^2-d^2\right)}{2\,b^2\,c^3}","Not used",1,"x^2/(2*b*c) - (d*(a + b*x^2)^(1/2))/(b^2*c^2) + (atanh((c*(a*c^2 - d^2)*(a + b*x^2)^(1/2))/(d^3 - a*c^2*d))*(a*c^2 - d^2))/(b^2*c^3) - (log(a*c^2 - d^2 + b*c^2*x^2)*(a*c^2 - d^2))/(2*b^2*c^3)","B"
546,1,45,23,3.468774,"\text{Not used}","int(x/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2),x)","\frac{\mathrm{atanh}\left(\frac{c\,\sqrt{b\,x^2+a}}{d}\right)+\frac{\ln\left(b\,c^2\,x^2+a\,c^2-d^2\right)}{2}}{b\,c}","Not used",1,"(atanh((c*(a + b*x^2)^(1/2))/d) + log(a*c^2 - d^2 + b*c^2*x^2)/2)/(b*c)","B"
547,1,1270,88,3.947724,"\text{Not used}","int(1/(x*(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2)),x)","\frac{c\,\ln\left(x\right)}{a\,c^2-d^2}-\frac{c\,\mathrm{atan}\left(\frac{\frac{c\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}+\frac{c\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d-\frac{c\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{2\,\left(a\,c^2-d^2\right)}\right)}{2\,\left(a\,c^2-d^2\right)}\right)\,1{}\mathrm{i}}{2\,\left(a\,c^2-d^2\right)}+\frac{c\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}-\frac{c\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d+\frac{c\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{2\,\left(a\,c^2-d^2\right)}\right)}{2\,\left(a\,c^2-d^2\right)}\right)\,1{}\mathrm{i}}{2\,\left(a\,c^2-d^2\right)}}{\frac{c\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}+\frac{c\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d-\frac{c\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{2\,\left(a\,c^2-d^2\right)}\right)}{2\,\left(a\,c^2-d^2\right)}\right)}{2\,\left(a\,c^2-d^2\right)}-\frac{c\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}-\frac{c\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d+\frac{c\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{2\,\left(a\,c^2-d^2\right)}\right)}{2\,\left(a\,c^2-d^2\right)}\right)}{2\,\left(a\,c^2-d^2\right)}}\right)\,1{}\mathrm{i}}{a\,c^2-d^2}-\frac{c\,\ln\left(b\,c^2\,x^2+a\,c^2-d^2\right)}{2\,a\,c^2-2\,d^2}-\frac{d\,\mathrm{atan}\left(\frac{\frac{d\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}+\frac{d\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d-\frac{d\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)\,1{}\mathrm{i}}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}+\frac{d\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}-\frac{d\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d+\frac{d\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)\,1{}\mathrm{i}}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}}{\frac{d\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}+\frac{d\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d-\frac{d\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}-\frac{d\,\left(4\,c^6\,d^2\,\sqrt{b\,x^2+a}-\frac{d\,\left(4\,c^4\,d^5-8\,a\,c^6\,d^3+4\,a^2\,c^8\,d+\frac{d\,\sqrt{b\,x^2+a}\,\left(8\,a^3\,c^{10}-8\,a^2\,c^8\,d^2-8\,a\,c^6\,d^4+8\,c^4\,d^6\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}\right)}{\sqrt{a}\,\left(2\,a\,c^2-2\,d^2\right)}}\right)\,1{}\mathrm{i}}{\sqrt{a}\,\left(a\,c^2-d^2\right)}","Not used",1,"(c*log(x))/(a*c^2 - d^2) - (c*atan(((c*(4*c^6*d^2*(a + b*x^2)^(1/2) + (c*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d - (c*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(2*(a*c^2 - d^2))))/(2*(a*c^2 - d^2)))*1i)/(2*(a*c^2 - d^2)) + (c*(4*c^6*d^2*(a + b*x^2)^(1/2) - (c*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d + (c*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(2*(a*c^2 - d^2))))/(2*(a*c^2 - d^2)))*1i)/(2*(a*c^2 - d^2)))/((c*(4*c^6*d^2*(a + b*x^2)^(1/2) + (c*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d - (c*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(2*(a*c^2 - d^2))))/(2*(a*c^2 - d^2))))/(2*(a*c^2 - d^2)) - (c*(4*c^6*d^2*(a + b*x^2)^(1/2) - (c*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d + (c*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(2*(a*c^2 - d^2))))/(2*(a*c^2 - d^2))))/(2*(a*c^2 - d^2))))*1i)/(a*c^2 - d^2) - (c*log(a*c^2 - d^2 + b*c^2*x^2))/(2*a*c^2 - 2*d^2) - (d*atan(((d*(4*c^6*d^2*(a + b*x^2)^(1/2) + (d*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d - (d*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(a^(1/2)*(2*a*c^2 - 2*d^2))))/(a^(1/2)*(2*a*c^2 - 2*d^2)))*1i)/(a^(1/2)*(2*a*c^2 - 2*d^2)) + (d*(4*c^6*d^2*(a + b*x^2)^(1/2) - (d*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d + (d*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(a^(1/2)*(2*a*c^2 - 2*d^2))))/(a^(1/2)*(2*a*c^2 - 2*d^2)))*1i)/(a^(1/2)*(2*a*c^2 - 2*d^2)))/((d*(4*c^6*d^2*(a + b*x^2)^(1/2) + (d*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d - (d*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(a^(1/2)*(2*a*c^2 - 2*d^2))))/(a^(1/2)*(2*a*c^2 - 2*d^2))))/(a^(1/2)*(2*a*c^2 - 2*d^2)) - (d*(4*c^6*d^2*(a + b*x^2)^(1/2) - (d*(4*c^4*d^5 - 8*a*c^6*d^3 + 4*a^2*c^8*d + (d*(a + b*x^2)^(1/2)*(8*a^3*c^10 + 8*c^4*d^6 - 8*a*c^6*d^4 - 8*a^2*c^8*d^2))/(a^(1/2)*(2*a*c^2 - 2*d^2))))/(a^(1/2)*(2*a*c^2 - 2*d^2))))/(a^(1/2)*(2*a*c^2 - 2*d^2))))*1i)/(a^(1/2)*(a*c^2 - d^2))","B"
548,1,4602,151,5.563470,"\text{Not used}","int(1/(x^3*(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2)),x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,b\,a^6\,c^{14}\,d-18\,b\,a^5\,c^{12}\,d^3+32\,b\,a^4\,c^{10}\,d^5-28\,b\,a^3\,c^8\,d^7+12\,b\,a^2\,c^6\,d^9-2\,b\,a\,c^4\,d^{11}}{16\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}-\frac{\sqrt{b\,x^2+a}\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{512\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}}{16\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}+\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,b^2\,c^{10}\,d^2-6\,a\,b^2\,c^8\,d^4+b^2\,c^6\,d^6\right)}{32\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,1{}\mathrm{i}}{a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8}-\frac{\left(\frac{\left(\frac{4\,b\,a^6\,c^{14}\,d-18\,b\,a^5\,c^{12}\,d^3+32\,b\,a^4\,c^{10}\,d^5-28\,b\,a^3\,c^8\,d^7+12\,b\,a^2\,c^6\,d^9-2\,b\,a\,c^4\,d^{11}}{16\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}+\frac{\sqrt{b\,x^2+a}\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{512\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}}{16\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}-\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,b^2\,c^{10}\,d^2-6\,a\,b^2\,c^8\,d^4+b^2\,c^6\,d^6\right)}{32\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,1{}\mathrm{i}}{a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8}}{\frac{\frac{b^3\,c^8\,d^5}{2}-\frac{3\,a\,b^3\,c^{10}\,d^3}{2}}{a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6}+\frac{\left(\frac{\left(\frac{4\,b\,a^6\,c^{14}\,d-18\,b\,a^5\,c^{12}\,d^3+32\,b\,a^4\,c^{10}\,d^5-28\,b\,a^3\,c^8\,d^7+12\,b\,a^2\,c^6\,d^9-2\,b\,a\,c^4\,d^{11}}{16\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}-\frac{\sqrt{b\,x^2+a}\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{512\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}}{16\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}+\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,b^2\,c^{10}\,d^2-6\,a\,b^2\,c^8\,d^4+b^2\,c^6\,d^6\right)}{32\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}}{a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8}+\frac{\left(\frac{\left(\frac{4\,b\,a^6\,c^{14}\,d-18\,b\,a^5\,c^{12}\,d^3+32\,b\,a^4\,c^{10}\,d^5-28\,b\,a^3\,c^8\,d^7+12\,b\,a^2\,c^6\,d^9-2\,b\,a\,c^4\,d^{11}}{16\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}+\frac{\sqrt{b\,x^2+a}\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{512\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}}{16\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}-\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,b^2\,c^{10}\,d^2-6\,a\,b^2\,c^8\,d^4+b^2\,c^6\,d^6\right)}{32\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}}{a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8}}\right)\,\sqrt{16\,\left(9\,a^2\,b^2\,c^4\,d^2-6\,a\,b^2\,c^2\,d^4+b^2\,d^6\right)\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}\,1{}\mathrm{i}}{8\,\left(a^7\,c^8-4\,a^6\,c^6\,d^2+6\,a^5\,c^4\,d^4-4\,a^4\,c^2\,d^6+a^3\,d^8\right)}-\frac{c}{2\,x^2\,\left(a\,c^2-d^2\right)}-\frac{b\,c^3\,\ln\left(x\right)}{a^2\,c^4-2\,a\,c^2\,d^2+d^4}+\frac{b\,c^3\,\ln\left(b\,c^2\,x^2+a\,c^2-d^2\right)}{2\,a^2\,c^4-4\,a\,c^2\,d^2+2\,d^4}-\frac{d\,\sqrt{b\,x^2+a}}{2\,x^2\,\left(a\,d^2-a^2\,c^2\right)}+\frac{b\,c^3\,\mathrm{atan}\left(\frac{\frac{c^3\,\left(\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,c^{10}\,d^2-6\,a\,c^8\,d^4+c^6\,d^6\right)}{2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}+\frac{c^3\,\left(\frac{-16\,a^6\,c^{14}\,d+72\,a^5\,c^{12}\,d^3-128\,a^4\,c^{10}\,d^5+112\,a^3\,c^8\,d^7-48\,a^2\,c^6\,d^9+8\,a\,c^4\,d^{11}}{4\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}-\frac{c^3\,\sqrt{b\,x^2+a}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{4\,{\left(a\,c^2-d^2\right)}^2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)}{2\,{\left(a\,c^2-d^2\right)}^2}\right)\,1{}\mathrm{i}}{2\,{\left(a\,c^2-d^2\right)}^2}+\frac{c^3\,\left(\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,c^{10}\,d^2-6\,a\,c^8\,d^4+c^6\,d^6\right)}{2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}-\frac{c^3\,\left(\frac{-16\,a^6\,c^{14}\,d+72\,a^5\,c^{12}\,d^3-128\,a^4\,c^{10}\,d^5+112\,a^3\,c^8\,d^7-48\,a^2\,c^6\,d^9+8\,a\,c^4\,d^{11}}{4\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}+\frac{c^3\,\sqrt{b\,x^2+a}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{4\,{\left(a\,c^2-d^2\right)}^2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)}{2\,{\left(a\,c^2-d^2\right)}^2}\right)\,1{}\mathrm{i}}{2\,{\left(a\,c^2-d^2\right)}^2}}{\frac{c^8\,d^5-3\,a\,c^{10}\,d^3}{2\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}-\frac{c^3\,\left(\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,c^{10}\,d^2-6\,a\,c^8\,d^4+c^6\,d^6\right)}{2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}+\frac{c^3\,\left(\frac{-16\,a^6\,c^{14}\,d+72\,a^5\,c^{12}\,d^3-128\,a^4\,c^{10}\,d^5+112\,a^3\,c^8\,d^7-48\,a^2\,c^6\,d^9+8\,a\,c^4\,d^{11}}{4\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}-\frac{c^3\,\sqrt{b\,x^2+a}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{4\,{\left(a\,c^2-d^2\right)}^2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)}{2\,{\left(a\,c^2-d^2\right)}^2}\right)}{2\,{\left(a\,c^2-d^2\right)}^2}+\frac{c^3\,\left(\frac{\sqrt{b\,x^2+a}\,\left(13\,a^2\,c^{10}\,d^2-6\,a\,c^8\,d^4+c^6\,d^6\right)}{2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}-\frac{c^3\,\left(\frac{-16\,a^6\,c^{14}\,d+72\,a^5\,c^{12}\,d^3-128\,a^4\,c^{10}\,d^5+112\,a^3\,c^8\,d^7-48\,a^2\,c^6\,d^9+8\,a\,c^4\,d^{11}}{4\,\left(a^5\,c^6-3\,a^4\,c^4\,d^2+3\,a^3\,c^2\,d^4-a^2\,d^6\right)}+\frac{c^3\,\sqrt{b\,x^2+a}\,\left(16\,a^7\,c^{14}-48\,a^6\,c^{12}\,d^2+32\,a^5\,c^{10}\,d^4+32\,a^4\,c^8\,d^6-48\,a^3\,c^6\,d^8+16\,a^2\,c^4\,d^{10}\right)}{4\,{\left(a\,c^2-d^2\right)}^2\,\left(a^4\,c^4-2\,a^3\,c^2\,d^2+a^2\,d^4\right)}\right)}{2\,{\left(a\,c^2-d^2\right)}^2}\right)}{2\,{\left(a\,c^2-d^2\right)}^2}}\right)\,1{}\mathrm{i}}{{\left(a\,c^2-d^2\right)}^2}","Not used",1,"(atan(((((((12*a^2*b*c^6*d^9 - 28*a^3*b*c^8*d^7 + 32*a^4*b*c^10*d^5 - 18*a^5*b*c^12*d^3 - 2*a*b*c^4*d^11 + 4*a^6*b*c^14*d)/(16*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) - ((a + b*x^2)^(1/2)*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(512*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2))/(16*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)) + ((a + b*x^2)^(1/2)*(b^2*c^6*d^6 - 6*a*b^2*c^8*d^4 + 13*a^2*b^2*c^10*d^2))/(32*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*1i)/(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2) - (((((12*a^2*b*c^6*d^9 - 28*a^3*b*c^8*d^7 + 32*a^4*b*c^10*d^5 - 18*a^5*b*c^12*d^3 - 2*a*b*c^4*d^11 + 4*a^6*b*c^14*d)/(16*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) + ((a + b*x^2)^(1/2)*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(512*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2))/(16*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)) - ((a + b*x^2)^(1/2)*(b^2*c^6*d^6 - 6*a*b^2*c^8*d^4 + 13*a^2*b^2*c^10*d^2))/(32*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*1i)/(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))/(((b^3*c^8*d^5)/2 - (3*a*b^3*c^10*d^3)/2)/(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2) + (((((12*a^2*b*c^6*d^9 - 28*a^3*b*c^8*d^7 + 32*a^4*b*c^10*d^5 - 18*a^5*b*c^12*d^3 - 2*a*b*c^4*d^11 + 4*a^6*b*c^14*d)/(16*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) - ((a + b*x^2)^(1/2)*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(512*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2))/(16*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)) + ((a + b*x^2)^(1/2)*(b^2*c^6*d^6 - 6*a*b^2*c^8*d^4 + 13*a^2*b^2*c^10*d^2))/(32*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2))/(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2) + (((((12*a^2*b*c^6*d^9 - 28*a^3*b*c^8*d^7 + 32*a^4*b*c^10*d^5 - 18*a^5*b*c^12*d^3 - 2*a*b*c^4*d^11 + 4*a^6*b*c^14*d)/(16*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) + ((a + b*x^2)^(1/2)*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(512*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2))/(16*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)) - ((a + b*x^2)^(1/2)*(b^2*c^6*d^6 - 6*a*b^2*c^8*d^4 + 13*a^2*b^2*c^10*d^2))/(32*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2))/(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)))*(16*(b^2*d^6 - 6*a*b^2*c^2*d^4 + 9*a^2*b^2*c^4*d^2)*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2))^(1/2)*1i)/(8*(a^7*c^8 + a^3*d^8 - 4*a^4*c^2*d^6 + 6*a^5*c^4*d^4 - 4*a^6*c^6*d^2)) - c/(2*x^2*(a*c^2 - d^2)) - (b*c^3*log(x))/(d^4 + a^2*c^4 - 2*a*c^2*d^2) + (b*c^3*log(a*c^2 - d^2 + b*c^2*x^2))/(2*d^4 + 2*a^2*c^4 - 4*a*c^2*d^2) - (d*(a + b*x^2)^(1/2))/(2*x^2*(a*d^2 - a^2*c^2)) + (b*c^3*atan(((c^3*(((a + b*x^2)^(1/2)*(c^6*d^6 - 6*a*c^8*d^4 + 13*a^2*c^10*d^2))/(2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)) + (c^3*((8*a*c^4*d^11 - 16*a^6*c^14*d - 48*a^2*c^6*d^9 + 112*a^3*c^8*d^7 - 128*a^4*c^10*d^5 + 72*a^5*c^12*d^3)/(4*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) - (c^3*(a + b*x^2)^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(4*(a*c^2 - d^2)^2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2))))/(2*(a*c^2 - d^2)^2))*1i)/(2*(a*c^2 - d^2)^2) + (c^3*(((a + b*x^2)^(1/2)*(c^6*d^6 - 6*a*c^8*d^4 + 13*a^2*c^10*d^2))/(2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)) - (c^3*((8*a*c^4*d^11 - 16*a^6*c^14*d - 48*a^2*c^6*d^9 + 112*a^3*c^8*d^7 - 128*a^4*c^10*d^5 + 72*a^5*c^12*d^3)/(4*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) + (c^3*(a + b*x^2)^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(4*(a*c^2 - d^2)^2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2))))/(2*(a*c^2 - d^2)^2))*1i)/(2*(a*c^2 - d^2)^2))/((c^8*d^5 - 3*a*c^10*d^3)/(2*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) - (c^3*(((a + b*x^2)^(1/2)*(c^6*d^6 - 6*a*c^8*d^4 + 13*a^2*c^10*d^2))/(2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)) + (c^3*((8*a*c^4*d^11 - 16*a^6*c^14*d - 48*a^2*c^6*d^9 + 112*a^3*c^8*d^7 - 128*a^4*c^10*d^5 + 72*a^5*c^12*d^3)/(4*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) - (c^3*(a + b*x^2)^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(4*(a*c^2 - d^2)^2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2))))/(2*(a*c^2 - d^2)^2)))/(2*(a*c^2 - d^2)^2) + (c^3*(((a + b*x^2)^(1/2)*(c^6*d^6 - 6*a*c^8*d^4 + 13*a^2*c^10*d^2))/(2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2)) - (c^3*((8*a*c^4*d^11 - 16*a^6*c^14*d - 48*a^2*c^6*d^9 + 112*a^3*c^8*d^7 - 128*a^4*c^10*d^5 + 72*a^5*c^12*d^3)/(4*(a^5*c^6 - a^2*d^6 + 3*a^3*c^2*d^4 - 3*a^4*c^4*d^2)) + (c^3*(a + b*x^2)^(1/2)*(16*a^7*c^14 + 16*a^2*c^4*d^10 - 48*a^3*c^6*d^8 + 32*a^4*c^8*d^6 + 32*a^5*c^10*d^4 - 48*a^6*c^12*d^2))/(4*(a*c^2 - d^2)^2*(a^4*c^4 + a^2*d^4 - 2*a^3*c^2*d^2))))/(2*(a*c^2 - d^2)^2)))/(2*(a*c^2 - d^2)^2)))*1i)/(a*c^2 - d^2)^2","B"
549,0,-1,147,0.000000,"\text{Not used}","int(x^2/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2),x)","\int \frac{x^2}{a\,c+d\,\sqrt{b\,x^2+a}+b\,c\,x^2} \,d x","Not used",1,"int(x^2/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2), x)","F"
550,0,-1,103,0.000000,"\text{Not used}","int(1/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2),x)","\left\{\begin{array}{cl} \frac{\mathrm{atan}\left(\frac{b\,c\,x}{\sqrt{a\,b\,c^2-b\,d^2}}\right)}{\sqrt{a\,b\,c^2-b\,d^2}}-\frac{d\,x}{\sqrt{a}\,\left(a\,c^2-d^2\right)} & \text{\ if\ \ }b=0\vee d=0\\ \frac{\mathrm{atan}\left(\frac{b\,c\,x}{\sqrt{a\,b\,c^2-b\,d^2}}\right)}{\sqrt{a\,b\,c^2-b\,d^2}}-\frac{d\,\mathrm{atan}\left(\frac{x\,\sqrt{a\,b\,c^2-b\,\left(a\,c^2-d^2\right)}}{\sqrt{a\,c^2-d^2}\,\sqrt{b\,x^2+a}}\right)}{\sqrt{-\left(a\,c^2-d^2\right)\,\left(b\,\left(a\,c^2-d^2\right)-a\,b\,c^2\right)}} & \text{\ if\ \ }0<b\,d^2\\ \frac{\mathrm{atan}\left(\frac{b\,c\,x}{\sqrt{a\,b\,c^2-b\,d^2}}\right)}{\sqrt{a\,b\,c^2-b\,d^2}}-\frac{d\,\ln\left(\frac{\sqrt{\left(a\,c^2-d^2\right)\,\left(b\,x^2+a\right)}+x\,\sqrt{b\,\left(a\,c^2-d^2\right)-a\,b\,c^2}}{\sqrt{\left(a\,c^2-d^2\right)\,\left(b\,x^2+a\right)}-x\,\sqrt{b\,\left(a\,c^2-d^2\right)-a\,b\,c^2}}\right)}{2\,\sqrt{\left(a\,c^2-d^2\right)\,\left(b\,\left(a\,c^2-d^2\right)-a\,b\,c^2\right)}} & \text{\ if\ \ }b\,d^2<0\\ \int \frac{1}{a\,c+d\,\sqrt{b\,x^2+a}+b\,c\,x^2} \,d x & \text{\ if\ \ }b\,d^2\notin \mathbb{R} \end{array}\right.","Not used",1,"piecewise(b == 0 | d == 0, atan((b*c*x)/(- b*d^2 + a*b*c^2)^(1/2))/(- b*d^2 + a*b*c^2)^(1/2) - (d*x)/(a^(1/2)*(a*c^2 - d^2)), 0 < b*d^2, atan((b*c*x)/(- b*d^2 + a*b*c^2)^(1/2))/(- b*d^2 + a*b*c^2)^(1/2) - (d*atan((x*(- b*(a*c^2 - d^2) + a*b*c^2)^(1/2))/((a*c^2 - d^2)^(1/2)*(a + b*x^2)^(1/2))))/(-(a*c^2 - d^2)*(b*(a*c^2 - d^2) - a*b*c^2))^(1/2), b*d^2 < 0, atan((b*c*x)/(- b*d^2 + a*b*c^2)^(1/2))/(- b*d^2 + a*b*c^2)^(1/2) - (d*log((((a*c^2 - d^2)*(a + b*x^2))^(1/2) + x*(b*(a*c^2 - d^2) - a*b*c^2)^(1/2))/(((a*c^2 - d^2)*(a + b*x^2))^(1/2) - x*(b*(a*c^2 - d^2) - a*b*c^2)^(1/2))))/(2*((a*c^2 - d^2)*(b*(a*c^2 - d^2) - a*b*c^2))^(1/2)), ~in(b*d^2, 'real'), int(1/(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2), x))","F"
551,0,-1,160,0.000000,"\text{Not used}","int(1/(x^2*(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2)),x)","\int \frac{1}{x^2\,\left(a\,c+d\,\sqrt{b\,x^2+a}+b\,c\,x^2\right)} \,d x","Not used",1,"int(1/(x^2*(a*c + d*(a + b*x^2)^(1/2) + b*c*x^2)), x)","F"
552,1,200,140,3.740369,"\text{Not used}","int(x^8/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3),x)","\frac{\left(\frac{2\,d\,\left(a\,c^2-d^2\right)}{b^2\,c^4}+\frac{4\,a\,d}{3\,b^2\,c^2}\right)\,\sqrt{b\,x^3+a}}{3\,b}+\frac{x^6}{6\,b\,c}-\frac{x^3\,\left(a\,c^2-d^2\right)}{3\,b^2\,c^3}+\frac{\ln\left(\frac{d+c\,\sqrt{b\,x^3+a}}{d-c\,\sqrt{b\,x^3+a}}\right)\,{\left(a\,c^2-d^2\right)}^2}{3\,b^3\,c^5}+\frac{\ln\left(b\,c^2\,x^3+a\,c^2-d^2\right)\,\left(a^2\,c^4-2\,a\,c^2\,d^2+d^4\right)}{3\,b^3\,c^5}-\frac{2\,d\,x^3\,\sqrt{b\,x^3+a}}{9\,b^2\,c^2}","Not used",1,"(((2*d*(a*c^2 - d^2))/(b^2*c^4) + (4*a*d)/(3*b^2*c^2))*(a + b*x^3)^(1/2))/(3*b) + x^6/(6*b*c) - (x^3*(a*c^2 - d^2))/(3*b^2*c^3) + (log((d + c*(a + b*x^3)^(1/2))/(d - c*(a + b*x^3)^(1/2)))*(a*c^2 - d^2)^2)/(3*b^3*c^5) + (log(a*c^2 - d^2 + b*c^2*x^3)*(d^4 + a^2*c^4 - 2*a*c^2*d^2))/(3*b^3*c^5) - (2*d*x^3*(a + b*x^3)^(1/2))/(9*b^2*c^2)","B"
553,1,119,73,3.563576,"\text{Not used}","int(x^5/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3),x)","\frac{x^3}{3\,b\,c}-\frac{2\,d\,\sqrt{b\,x^3+a}}{3\,b^2\,c^2}+\frac{\ln\left(\frac{d-c\,\sqrt{b\,x^3+a}}{d+c\,\sqrt{b\,x^3+a}}\right)\,\left(a\,c^2-d^2\right)}{3\,b^2\,c^3}-\frac{\ln\left(b\,c^2\,x^3+a\,c^2-d^2\right)\,\left(a\,c^2-d^2\right)}{3\,b^2\,c^3}","Not used",1,"x^3/(3*b*c) - (2*d*(a + b*x^3)^(1/2))/(3*b^2*c^2) + (log((d - c*(a + b*x^3)^(1/2))/(d + c*(a + b*x^3)^(1/2)))*(a*c^2 - d^2))/(3*b^2*c^3) - (log(a*c^2 - d^2 + b*c^2*x^3)*(a*c^2 - d^2))/(3*b^2*c^3)","B"
554,1,60,26,3.507619,"\text{Not used}","int(x^2/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3),x)","\frac{\ln\left(\frac{d+c\,\sqrt{b\,x^3+a}}{d-c\,\sqrt{b\,x^3+a}}\right)+\ln\left(b\,c^2\,x^3+a\,c^2-d^2\right)}{3\,b\,c}","Not used",1,"(log((d + c*(a + b*x^3)^(1/2))/(d - c*(a + b*x^3)^(1/2))) + log(a*c^2 - d^2 + b*c^2*x^3))/(3*b*c)","B"
555,1,156,93,4.308489,"\text{Not used}","int(1/(x*(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3)),x)","\frac{c\,\ln\left(x\right)}{a\,c^2-d^2}+\frac{c\,\ln\left(\frac{d-c\,\sqrt{b\,x^3+a}}{d+c\,\sqrt{b\,x^3+a}}\right)}{3\,\left(a\,c^2-d^2\right)}-\frac{c\,\ln\left(b\,c^2\,x^3+a\,c^2-d^2\right)}{3\,a\,c^2-3\,d^2}+\frac{d\,\ln\left(\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,{\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}^3}{x^6}\right)}{3\,\sqrt{a}\,\left(a\,c^2-d^2\right)}","Not used",1,"(c*log(x))/(a*c^2 - d^2) + (c*log((d - c*(a + b*x^3)^(1/2))/(d + c*(a + b*x^3)^(1/2))))/(3*(a*c^2 - d^2)) - (c*log(a*c^2 - d^2 + b*c^2*x^3))/(3*a*c^2 - 3*d^2) + (d*log((((a + b*x^3)^(1/2) - a^(1/2))*((a + b*x^3)^(1/2) + a^(1/2))^3)/x^6))/(3*a^(1/2)*(a*c^2 - d^2))","B"
556,1,248,154,5.463482,"\text{Not used}","int(1/(x^4*(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3)),x)","\frac{b\,c^3\,\ln\left(b\,c^2\,x^3+a\,c^2-d^2\right)}{3\,a^2\,c^4-6\,a\,c^2\,d^2+3\,d^4}-\frac{b\,c^3\,\ln\left(x\right)}{a^2\,c^4-2\,a\,c^2\,d^2+d^4}-\frac{c}{3\,x^3\,\left(a\,c^2-d^2\right)}+\frac{b\,c^3\,\ln\left(\frac{d+c\,\sqrt{b\,x^3+a}}{d-c\,\sqrt{b\,x^3+a}}\right)}{3\,{\left(a\,c^2-d^2\right)}^2}+\frac{d\,\sqrt{b\,x^3+a}}{3\,a\,x^3\,\left(a\,c^2-d^2\right)}+\frac{b\,d\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)\,\left(3\,a\,c^2-d^2\right)}{6\,a^{3/2}\,{\left(a\,c^2-d^2\right)}^2}","Not used",1,"(b*c^3*log(a*c^2 - d^2 + b*c^2*x^3))/(3*d^4 + 3*a^2*c^4 - 6*a*c^2*d^2) - (b*c^3*log(x))/(d^4 + a^2*c^4 - 2*a*c^2*d^2) - c/(3*x^3*(a*c^2 - d^2)) + (b*c^3*log((d + c*(a + b*x^3)^(1/2))/(d - c*(a + b*x^3)^(1/2))))/(3*(a*c^2 - d^2)^2) + (d*(a + b*x^3)^(1/2))/(3*a*x^3*(a*c^2 - d^2)) + (b*d*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6)*(3*a*c^2 - d^2))/(6*a^(3/2)*(a*c^2 - d^2)^2)","B"
557,0,-1,311,0.000000,"\text{Not used}","int(x^3/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3),x)","\int \frac{x^3}{a\,c+d\,\sqrt{b\,x^3+a}+b\,c\,x^3} \,d x","Not used",1,"int(x^3/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3), x)","F"
558,0,-1,304,0.000000,"\text{Not used}","int(x/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3),x)","\int \frac{x}{a\,c+d\,\sqrt{b\,x^3+a}+b\,c\,x^3} \,d x","Not used",1,"int(x/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3), x)","F"
559,0,-1,300,0.000000,"\text{Not used}","int(1/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3),x)","\int \frac{1}{a\,c+d\,\sqrt{b\,x^3+a}+b\,c\,x^3} \,d x","Not used",1,"int(1/(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3), x)","F"
560,0,-1,319,0.000000,"\text{Not used}","int(1/(x^2*(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3)),x)","\int \frac{1}{x^2\,\left(a\,c+d\,\sqrt{b\,x^3+a}+b\,c\,x^3\right)} \,d x","Not used",1,"int(1/(x^2*(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3)), x)","F"
561,0,-1,324,0.000000,"\text{Not used}","int(1/(x^3*(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3)),x)","\int \frac{1}{x^3\,\left(a\,c+d\,\sqrt{b\,x^3+a}+b\,c\,x^3\right)} \,d x","Not used",1,"int(1/(x^3*(a*c + d*(a + b*x^3)^(1/2) + b*c*x^3)), x)","F"
562,0,-1,135,0.000000,"\text{Not used}","int(1/(a*c + d*(a + b*x^n)^(1/2) + b*c*x^n),x)","\int \frac{1}{a\,c+d\,\sqrt{a+b\,x^n}+b\,c\,x^n} \,d x","Not used",1,"int(1/(a*c + d*(a + b*x^n)^(1/2) + b*c*x^n), x)","F"
563,0,-1,167,0.000000,"\text{Not used}","int(x^m/(a*c + d*(a + b*x^n)^(1/2) + b*c*x^n),x)","\int \frac{x^m}{a\,c+d\,\sqrt{a+b\,x^n}+b\,c\,x^n} \,d x","Not used",1,"int(x^m/(a*c + d*(a + b*x^n)^(1/2) + b*c*x^n), x)","F"
564,1,25,27,3.346056,"\text{Not used}","int(x^(n - 1)/(a*c + d*(a + b*x^n)^(1/2) + b*c*x^n),x)","\frac{2\,\ln\left(d+c\,\sqrt{a+b\,x^n}\right)}{b\,c\,n}","Not used",1,"(2*log(d + c*(a + b*x^n)^(1/2)))/(b*c*n)","B"
565,1,6,8,0.047171,"\text{Not used}","int(1/(x^(1/2) + 4*x^(3/2)),x)","\mathrm{atan}\left(2\,\sqrt{x}\right)","Not used",1,"atan(2*x^(1/2))","B"
566,1,9,13,3.080258,"\text{Not used}","int(1/(x^(1/2) - x^(5/2)),x)","\mathrm{atan}\left(\sqrt{x}\right)+\mathrm{atanh}\left(\sqrt{x}\right)","Not used",1,"atan(x^(1/2)) + atanh(x^(1/2))","B"
567,1,19,27,3.103269,"\text{Not used}","int(1/(x^(1/2) - x^(1/4)),x)","4\,\ln\left(x^{1/4}-1\right)+2\,\sqrt{x}+4\,x^{1/4}","Not used",1,"4*log(x^(1/4) - 1) + 2*x^(1/2) + 4*x^(1/4)","B"
568,1,24,32,0.029945,"\text{Not used}","int(1/(x^(1/2) + x^(1/3)),x)","2\,\sqrt{x}-6\,\ln\left(x^{1/6}+1\right)-3\,x^{1/3}+6\,x^{1/6}","Not used",1,"2*x^(1/2) - 6*log(x^(1/6) + 1) - 3*x^(1/3) + 6*x^(1/6)","B"
569,1,19,25,0.032209,"\text{Not used}","int(1/(x^(1/2) + x^(1/4)),x)","4\,\ln\left(x^{1/4}+1\right)+2\,\sqrt{x}-4\,x^{1/4}","Not used",1,"4*log(x^(1/4) + 1) + 2*x^(1/2) - 4*x^(1/4)","B"
570,1,14,20,0.076575,"\text{Not used}","int(-1/(x^(1/3) - x^(2/3)),x)","3\,\ln\left(x^{1/3}-1\right)+3\,x^{1/3}","Not used",1,"3*log(x^(1/3) - 1) + 3*x^(1/3)","B"
571,1,73,62,3.076270,"\text{Not used}","int(1/(x^(1/2) + 1/x^(1/4)),x)","\frac{4\,\ln\left(16\,x^{1/4}+16\right)}{3}+\ln\left(9\,{\left(-\frac{2}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)}^2+16\,x^{1/4}\right)\,\left(-\frac{2}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)-\ln\left(9\,{\left(\frac{2}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)}^2+16\,x^{1/4}\right)\,\left(\frac{2}{3}+\frac{\sqrt{3}\,2{}\mathrm{i}}{3}\right)+2\,\sqrt{x}","Not used",1,"(4*log(16*x^(1/4) + 16))/3 + log(9*((3^(1/2)*2i)/3 - 2/3)^2 + 16*x^(1/4))*((3^(1/2)*2i)/3 - 2/3) - log(9*((3^(1/2)*2i)/3 + 2/3)^2 + 16*x^(1/4))*((3^(1/2)*2i)/3 + 2/3) + 2*x^(1/2)","B"
572,1,49,73,0.035693,"\text{Not used}","int(1/(x^(1/3) + x^(1/4)),x)","12\,\ln\left(x^{1/12}+1\right)+2\,\sqrt{x}+3\,x^{1/3}-4\,x^{1/4}+\frac{3\,x^{2/3}}{2}+6\,x^{1/6}-12\,x^{1/12}-\frac{12\,x^{5/12}}{5}-\frac{12\,x^{7/12}}{7}","Not used",1,"12*log(x^(1/12) + 1) + 2*x^(1/2) + 3*x^(1/3) - 4*x^(1/4) + (3*x^(2/3))/2 + 6*x^(1/6) - 12*x^(1/12) - (12*x^(5/12))/5 - (12*x^(7/12))/7","B"
573,1,82,130,0.153082,"\text{Not used}","int(1/(1/x^(1/3) + 1/x^(1/4)),x)","4\,x^{1/4}-12\,\ln\left(x^{1/12}+1\right)-2\,\sqrt{x}-3\,x^{1/3}-x-\frac{3\,x^{2/3}}{2}-6\,x^{1/6}+\frac{4\,x^{3/4}}{3}+\frac{4\,x^{5/4}}{5}-\frac{6\,x^{5/6}}{5}+12\,x^{1/12}-\frac{6\,x^{7/6}}{7}+\frac{12\,x^{5/12}}{5}+\frac{12\,x^{7/12}}{7}+\frac{12\,x^{11/12}}{11}+\frac{12\,x^{13/12}}{13}","Not used",1,"4*x^(1/4) - 12*log(x^(1/12) + 1) - 2*x^(1/2) - 3*x^(1/3) - x - (3*x^(2/3))/2 - 6*x^(1/6) + (4*x^(3/4))/3 + (4*x^(5/4))/5 - (6*x^(5/6))/5 + 12*x^(1/12) - (6*x^(7/6))/7 + (12*x^(5/12))/5 + (12*x^(7/12))/7 + (12*x^(11/12))/11 + (12*x^(13/12))/13","B"
574,1,223,200,0.122336,"\text{Not used}","int(1/(x^(1/2) - 1/x^(1/3)),x)","\frac{6\,\ln\left(1296\,x^{1/6}-1296\right)}{5}-\ln\left(-750\,x^{1/6}\,{\left(\frac{3\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}}{10}-\frac{3\,\sqrt{5}}{10}+\frac{3}{10}\right)}^3-1296\right)\,\left(\frac{3\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}}{10}-\frac{3\,\sqrt{5}}{10}+\frac{3}{10}\right)+\ln\left(750\,x^{1/6}\,{\left(\frac{3\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}}{10}+\frac{3\,\sqrt{5}}{10}-\frac{3}{10}\right)}^3-1296\right)\,\left(\frac{3\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}}{10}+\frac{3\,\sqrt{5}}{10}-\frac{3}{10}\right)-\ln\left(-750\,x^{1/6}\,{\left(\frac{3\,\sqrt{5}}{10}-\frac{3\,\sqrt{2}\,\sqrt{\sqrt{5}-5}}{10}+\frac{3}{10}\right)}^3-1296\right)\,\left(\frac{3\,\sqrt{5}}{10}-\frac{3\,\sqrt{2}\,\sqrt{\sqrt{5}-5}}{10}+\frac{3}{10}\right)-\ln\left(-750\,x^{1/6}\,{\left(\frac{3\,\sqrt{5}}{10}+\frac{3\,\sqrt{2}\,\sqrt{\sqrt{5}-5}}{10}+\frac{3}{10}\right)}^3-1296\right)\,\left(\frac{3\,\sqrt{5}}{10}+\frac{3\,\sqrt{2}\,\sqrt{\sqrt{5}-5}}{10}+\frac{3}{10}\right)+2\,\sqrt{x}","Not used",1,"(6*log(1296*x^(1/6) - 1296))/5 - log(- 750*x^(1/6)*((3*2^(1/2)*(- 5^(1/2) - 5)^(1/2))/10 - (3*5^(1/2))/10 + 3/10)^3 - 1296)*((3*2^(1/2)*(- 5^(1/2) - 5)^(1/2))/10 - (3*5^(1/2))/10 + 3/10) + log(750*x^(1/6)*((3*2^(1/2)*(- 5^(1/2) - 5)^(1/2))/10 + (3*5^(1/2))/10 - 3/10)^3 - 1296)*((3*2^(1/2)*(- 5^(1/2) - 5)^(1/2))/10 + (3*5^(1/2))/10 - 3/10) - log(- 750*x^(1/6)*((3*5^(1/2))/10 - (3*2^(1/2)*(5^(1/2) - 5)^(1/2))/10 + 3/10)^3 - 1296)*((3*5^(1/2))/10 - (3*2^(1/2)*(5^(1/2) - 5)^(1/2))/10 + 3/10) - log(- 750*x^(1/6)*((3*5^(1/2))/10 + (3*2^(1/2)*(5^(1/2) - 5)^(1/2))/10 + 3/10)^3 - 1296)*((3*5^(1/2))/10 + (3*2^(1/2)*(5^(1/2) - 5)^(1/2))/10 + 3/10) + 2*x^(1/2)","B"
575,1,6,8,0.139025,"\text{Not used}","int(x^(1/2)/(x + x^2),x)","2\,\mathrm{atan}\left(\sqrt{x}\right)","Not used",1,"2*atan(x^(1/2))","B"
576,1,15,19,0.041822,"\text{Not used}","int(x/(x + 4*x^(1/2)),x)","x+32\,\ln\left(\sqrt{x}+4\right)-8\,\sqrt{x}","Not used",1,"x + 32*log(x^(1/2) + 4) - 8*x^(1/2)","B"
577,1,42,108,0.084944,"\text{Not used}","int(x^(1/2)/(x + x^(1/3)),x)","2\,\sqrt{x}+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x^{1/6}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{3}{2}+\frac{3}{2}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x^{1/6}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{3}{2}-\frac{3}{2}{}\mathrm{i}\right)","Not used",1,"2*x^(1/2) - 2^(1/2)*atan(2^(1/2)*x^(1/6)*(1/2 + 1i/2))*(3/2 + 3i/2) - 2^(1/2)*atan(2^(1/2)*x^(1/6)*(1/2 - 1i/2))*(3/2 - 3i/2)","B"
578,1,78,76,3.079764,"\text{Not used}","int(x^(1/3)/(x^(1/2) + x^(1/4)),x)","4\,\ln\left(144\,x^{1/12}+144\right)-\ln\left(18-36\,x^{1/12}+\sqrt{3}\,18{}\mathrm{i}\right)\,\left(2+\sqrt{3}\,2{}\mathrm{i}\right)+\ln\left(36\,x^{1/12}-18+\sqrt{3}\,18{}\mathrm{i}\right)\,\left(-2+\sqrt{3}\,2{}\mathrm{i}\right)+3\,x^{1/3}+\frac{6\,x^{5/6}}{5}-12\,x^{1/12}-\frac{12\,x^{7/12}}{7}","Not used",1,"4*log(144*x^(1/12) + 144) - log(3^(1/2)*18i - 36*x^(1/12) + 18)*(3^(1/2)*2i + 2) + log(3^(1/2)*18i + 36*x^(1/12) - 18)*(3^(1/2)*2i - 2) + 3*x^(1/3) + (6*x^(5/6))/5 - 12*x^(1/12) - (12*x^(7/12))/7","B"
579,1,75,119,0.151803,"\text{Not used}","int(x^(1/2)/(x^(1/3) + x^(1/4)),x)","x+12\,\ln\left(x^{1/12}+1\right)+2\,\sqrt{x}+3\,x^{1/3}-4\,x^{1/4}+\frac{3\,x^{2/3}}{2}+6\,x^{1/6}-\frac{4\,x^{3/4}}{3}+\frac{6\,x^{5/6}}{5}-12\,x^{1/12}+\frac{6\,x^{7/6}}{7}-\frac{12\,x^{5/12}}{5}-\frac{12\,x^{7/12}}{7}-\frac{12\,x^{11/12}}{11}-\frac{12\,x^{13/12}}{13}","Not used",1,"x + 12*log(x^(1/12) + 1) + 2*x^(1/2) + 3*x^(1/3) - 4*x^(1/4) + (3*x^(2/3))/2 + 6*x^(1/6) - (4*x^(3/4))/3 + (6*x^(5/6))/5 - 12*x^(1/12) + (6*x^(7/6))/7 - (12*x^(5/12))/5 - (12*x^(7/12))/7 - (12*x^(11/12))/11 - (12*x^(13/12))/13","B"
580,1,208,201,0.060757,"\text{Not used}","int(x^(1/2)/(x^(1/2) - 1/x^(1/3)),x)","x+\frac{6\,\ln\left(1296\,x^{1/6}-1296\right)}{5}-\ln\left(270\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}-270\,\sqrt{5}+1080\,x^{1/6}+270\right)\,\left(\frac{3\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}}{10}-\frac{3\,\sqrt{5}}{10}+\frac{3}{10}\right)+\ln\left(270\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}+270\,\sqrt{5}-1080\,x^{1/6}-270\right)\,\left(\frac{3\,\sqrt{2}\,\sqrt{-\sqrt{5}-5}}{10}+\frac{3\,\sqrt{5}}{10}-\frac{3}{10}\right)+6\,x^{1/6}-\ln\left(270\,\sqrt{5}+1080\,x^{1/6}-270\,\sqrt{2}\,\sqrt{\sqrt{5}-5}+270\right)\,\left(\frac{3\,\sqrt{5}}{10}-\frac{3\,\sqrt{2}\,\sqrt{\sqrt{5}-5}}{10}+\frac{3}{10}\right)-\ln\left(270\,\sqrt{5}+1080\,x^{1/6}+270\,\sqrt{2}\,\sqrt{\sqrt{5}-5}+270\right)\,\left(\frac{3\,\sqrt{5}}{10}+\frac{3\,\sqrt{2}\,\sqrt{\sqrt{5}-5}}{10}+\frac{3}{10}\right)","Not used",1,"x + (6*log(1296*x^(1/6) - 1296))/5 - log(270*2^(1/2)*(- 5^(1/2) - 5)^(1/2) - 270*5^(1/2) + 1080*x^(1/6) + 270)*((3*2^(1/2)*(- 5^(1/2) - 5)^(1/2))/10 - (3*5^(1/2))/10 + 3/10) + log(270*2^(1/2)*(- 5^(1/2) - 5)^(1/2) + 270*5^(1/2) - 1080*x^(1/6) - 270)*((3*2^(1/2)*(- 5^(1/2) - 5)^(1/2))/10 + (3*5^(1/2))/10 - 3/10) + 6*x^(1/6) - log(270*5^(1/2) + 1080*x^(1/6) - 270*2^(1/2)*(5^(1/2) - 5)^(1/2) + 270)*((3*5^(1/2))/10 - (3*2^(1/2)*(5^(1/2) - 5)^(1/2))/10 + 3/10) - log(270*5^(1/2) + 1080*x^(1/6) + 270*2^(1/2)*(5^(1/2) - 5)^(1/2) + 270)*((3*5^(1/2))/10 + (3*2^(1/2)*(5^(1/2) - 5)^(1/2))/10 + 3/10)","B"
581,1,32,36,3.257230,"\text{Not used}","int((x^m*(b - a/x)^(1/2))/(a - b*x)^(1/2),x)","\frac{2\,x^{m+1}\,\sqrt{b-\frac{a}{x}}}{\left(2\,m+1\right)\,\sqrt{a-b\,x}}","Not used",1,"(2*x^(m + 1)*(b - a/x)^(1/2))/((2*m + 1)*(a - b*x)^(1/2))","B"
582,1,23,29,3.096180,"\text{Not used}","int((x^2*(b - a/x)^(1/2))/(a - b*x)^(1/2),x)","\frac{2\,x^3\,\sqrt{b-\frac{a}{x}}}{5\,\sqrt{a-b\,x}}","Not used",1,"(2*x^3*(b - a/x)^(1/2))/(5*(a - b*x)^(1/2))","B"
583,1,23,29,3.064387,"\text{Not used}","int((x*(b - a/x)^(1/2))/(a - b*x)^(1/2),x)","\frac{2\,x^2\,\sqrt{b-\frac{a}{x}}}{3\,\sqrt{a-b\,x}}","Not used",1,"(2*x^2*(b - a/x)^(1/2))/(3*(a - b*x)^(1/2))","B"
584,1,21,25,3.044296,"\text{Not used}","int((b - a/x)^(1/2)/(a - b*x)^(1/2),x)","\frac{2\,x\,\sqrt{b-\frac{a}{x}}}{\sqrt{a-b\,x}}","Not used",1,"(2*x*(b - a/x)^(1/2))/(a - b*x)^(1/2)","B"
585,1,20,24,3.079245,"\text{Not used}","int((b - a/x)^(1/2)/(x*(a - b*x)^(1/2)),x)","-\frac{2\,\sqrt{b-\frac{a}{x}}}{\sqrt{a-b\,x}}","Not used",1,"-(2*(b - a/x)^(1/2))/(a - b*x)^(1/2)","B"
586,1,23,29,3.102442,"\text{Not used}","int((b - a/x)^(1/2)/(x^2*(a - b*x)^(1/2)),x)","-\frac{2\,\sqrt{b-\frac{a}{x}}}{3\,x\,\sqrt{a-b\,x}}","Not used",1,"-(2*(b - a/x)^(1/2))/(3*x*(a - b*x)^(1/2))","B"
587,0,-1,80,0.000000,"\text{Not used}","int((a + b/x)^m*(c + d*x)^n,x)","\int {\left(a+\frac{b}{x}\right)}^m\,{\left(c+d\,x\right)}^n \,d x","Not used",1,"int((a + b/x)^m*(c + d*x)^n, x)","F"
588,0,-1,138,0.000000,"\text{Not used}","int((a + b/x)^m*(c + d*x)^2,x)","\int {\left(a+\frac{b}{x}\right)}^m\,{\left(c+d\,x\right)}^2 \,d x","Not used",1,"int((a + b/x)^m*(c + d*x)^2, x)","F"
589,0,-1,79,0.000000,"\text{Not used}","int((a + b/x)^m*(c + d*x),x)","\int {\left(a+\frac{b}{x}\right)}^m\,\left(c+d\,x\right) \,d x","Not used",1,"int((a + b/x)^m*(c + d*x), x)","F"
590,1,51,40,3.134925,"\text{Not used}","int((a + b/x)^m,x)","-\frac{x\,{\left(a+\frac{b}{x}\right)}^m\,{{}}_2{\mathrm{F}}_1\left(1-m,-m;\ 2-m;\ -\frac{a\,x}{b}\right)}{{\left(\frac{a\,x}{b}+1\right)}^m\,\left(m-1\right)}","Not used",1,"-(x*(a + b/x)^m*hypergeom([1 - m, -m], 2 - m, -(a*x)/b))/(((a*x)/b + 1)^m*(m - 1))","B"
591,0,-1,101,0.000000,"\text{Not used}","int((a + b/x)^m/(c + d*x),x)","\int \frac{{\left(a+\frac{b}{x}\right)}^m}{c+d\,x} \,d x","Not used",1,"int((a + b/x)^m/(c + d*x), x)","F"
592,0,-1,56,0.000000,"\text{Not used}","int((a + b/x)^m/(c + d*x)^2,x)","\int \frac{{\left(a+\frac{b}{x}\right)}^m}{{\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b/x)^m/(c + d*x)^2, x)","F"
593,0,-1,112,0.000000,"\text{Not used}","int((a + b/x)^m/(c + d*x)^3,x)","\int \frac{{\left(a+\frac{b}{x}\right)}^m}{{\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b/x)^m/(c + d*x)^3, x)","F"
594,0,-1,185,0.000000,"\text{Not used}","int((a + b/x)^m/(c + d*x)^4,x)","\int \frac{{\left(a+\frac{b}{x}\right)}^m}{{\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b/x)^m/(c + d*x)^4, x)","F"
595,1,29,33,3.357937,"\text{Not used}","int((x^m*(b - a/x^2)^(1/2))/(a - b*x^2)^(1/2),x)","\frac{x^{m+1}\,\sqrt{b-\frac{a}{x^2}}}{m\,\sqrt{a-b\,x^2}}","Not used",1,"(x^(m + 1)*(b - a/x^2)^(1/2))/(m*(a - b*x^2)^(1/2))","B"
596,1,25,31,3.136934,"\text{Not used}","int((x^2*(b - a/x^2)^(1/2))/(a - b*x^2)^(1/2),x)","\frac{x^3\,\sqrt{b-\frac{a}{x^2}}}{2\,\sqrt{a-b\,x^2}}","Not used",1,"(x^3*(b - a/x^2)^(1/2))/(2*(a - b*x^2)^(1/2))","B"
597,1,27,28,3.104563,"\text{Not used}","int((x*(b - a/x^2)^(1/2))/(a - b*x^2)^(1/2),x)","\frac{\sqrt{b\,x^2-a}\,\sqrt{x^2}}{\sqrt{a-b\,x^2}}","Not used",1,"((b*x^2 - a)^(1/2)*(x^2)^(1/2))/(a - b*x^2)^(1/2)","B"
598,0,-1,28,0.000000,"\text{Not used}","int((b - a/x^2)^(1/2)/(a - b*x^2)^(1/2),x)","\int \frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b\,x^2}} \,d x","Not used",1,"int((b - a/x^2)^(1/2)/(a - b*x^2)^(1/2), x)","F"
599,1,22,26,3.344673,"\text{Not used}","int((b - a/x^2)^(1/2)/(x*(a - b*x^2)^(1/2)),x)","-\frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b\,x^2}}","Not used",1,"-(b - a/x^2)^(1/2)/(a - b*x^2)^(1/2)","B"
600,1,25,31,3.464808,"\text{Not used}","int((b - a/x^2)^(1/2)/(x^2*(a - b*x^2)^(1/2)),x)","-\frac{\sqrt{b-\frac{a}{x^2}}}{2\,x\,\sqrt{a-b\,x^2}}","Not used",1,"-(b - a/x^2)^(1/2)/(2*x*(a - b*x^2)^(1/2))","B"
601,0,-1,406,0.000000,"\text{Not used}","int((c + d*x)^(3/2)/(a + b/x^2)^(1/2),x)","\int \frac{{\left(c+d\,x\right)}^{3/2}}{\sqrt{a+\frac{b}{x^2}}} \,d x","Not used",1,"int((c + d*x)^(3/2)/(a + b/x^2)^(1/2), x)","F"
602,1,11,15,3.519294,"\text{Not used}","int((x^3 - 1)/(x^4 - 4*x)^(2/3),x)","\frac{3\,{\left(x^4-4\,x\right)}^{1/3}}{4}","Not used",1,"(3*(x^4 - 4*x)^(1/3))/4","B"
603,1,19,17,3.162716,"\text{Not used}","int(-(x^2 - 2)*(6*x - x^3)^(1/4),x)","-\frac{4\,x\,\left(x^2-6\right)\,{\left(6\,x-x^3\right)}^{1/4}}{15}","Not used",1,"-(4*x*(x^2 - 6)*(6*x - x^3)^(1/4))/15","B"
604,1,11,15,3.097815,"\text{Not used}","int((5*x + x^5)^(1/2)*(x^4 + 1),x)","\frac{2\,{\left(x^5+5\,x\right)}^{3/2}}{15}","Not used",1,"(2*(5*x + x^5)^(3/2))/15","B"
605,1,11,15,3.108203,"\text{Not used}","int((2*x + x^5)^(1/2)*(5*x^4 + 2),x)","\frac{2\,{\left(x^5+2\,x\right)}^{3/2}}{3}","Not used",1,"(2*(2*x + x^5)^(3/2))/3","B"
606,1,10,13,3.232468,"\text{Not used}","int((x + 3*x^2)/(x^2 + 2*x^3)^(1/2),x)","\left|x\right|\,\sqrt{2\,x+1}","Not used",1,"abs(x)*(2*x + 1)^(1/2)","B"
607,1,32,44,0.111305,"\text{Not used}","int(((1 - 5*x)^(1/3) + 2)/((1 - 5*x)^(1/3) + 3),x)","x+\frac{27\,\ln\left({\left(1-5\,x\right)}^{1/3}+3\right)}{5}-\frac{9\,{\left(1-5\,x\right)}^{1/3}}{5}+\frac{3\,{\left(1-5\,x\right)}^{2/3}}{10}","Not used",1,"x + (27*log((1 - 5*x)^(1/3) + 3))/5 - (9*(1 - 5*x)^(1/3))/5 + (3*(1 - 5*x)^(2/3))/10","B"
608,1,15,21,3.005382,"\text{Not used}","int((x^(1/2) + 1)/(x^(1/2) - 1),x)","x+4\,\ln\left(\sqrt{x}-1\right)+4\,\sqrt{x}","Not used",1,"x + 4*log(x^(1/2) - 1) + 4*x^(1/2)","B"
609,1,25,33,3.095322,"\text{Not used}","int(-((3*x + 2)^(1/2) - 1)/((3*x + 2)^(1/2) + 1),x)","\frac{4\,\sqrt{3\,x+2}}{3}-\frac{4\,\ln\left(\sqrt{3\,x+2}+1\right)}{3}-x","Not used",1,"(4*(3*x + 2)^(1/2))/3 - (4*log((3*x + 2)^(1/2) + 1))/3 - x","B"
610,1,29,33,3.024099,"\text{Not used}","int(((a + b*x)^(1/2) - 1)/((a + b*x)^(1/2) + 1),x)","x+\frac{4\,\ln\left(\sqrt{a+b\,x}+1\right)}{b}-\frac{4\,\sqrt{a+b\,x}}{b}","Not used",1,"x + (4*log((a + b*x)^(1/2) + 1))/b - (4*(a + b*x)^(1/2))/b","B"
611,1,10,10,3.272766,"\text{Not used}","int((a + b*n*x^(n - 1))/(b*x^n + a*x),x)","\ln\left(b\,x^n+a\,x\right)","Not used",1,"log(b*x^n + a*x)","B"
612,1,39,17,3.368126,"\text{Not used}","int((a + b*n*x^(n - 1))/(x^n*(b + a*x^(1 - n))),x)","-\frac{\ln\left(b+a\,x^{1-n}\right)-2\,n\,\mathrm{atanh}\left(\frac{2\,a\,x^{1-n}}{b}+1\right)}{n-1}","Not used",1,"-(log(b + a*x^(1 - n)) - 2*n*atanh((2*a*x^(1 - n))/b + 1))/(n - 1)","B"
613,-1,-1,37,0.000000,"\text{Not used}","int(x*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(2*a*d + x^4*(6*b*g + 6*c*f + b*g*m + 2*c*f*m + 3*b*g*n + 2*c*f*n) + x^2*(4*a*f + 4*b*e + 4*c*d + b*e*m + 2*c*d*m + 2*a*f*n + b*e*n) + x*(3*a*e + 3*b*d + b*d*m + a*e*n) + x^3*(5*a*g + 5*b*f + 5*c*e + b*f*m + 2*c*e*m + 3*a*g*n + 2*b*f*n + c*e*n) + c*g*x^5*(2*m + 3*n + 7)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
614,-1,-1,35,0.000000,"\text{Not used}","int((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(a*d + x^4*(5*b*g + 5*c*f + b*g*m + 2*c*f*m + 3*b*g*n + 2*c*f*n) + x^2*(3*a*f + 3*b*e + 3*c*d + b*e*m + 2*c*d*m + 2*a*f*n + b*e*n) + x*(2*a*e + 2*b*d + b*d*m + a*e*n) + x^3*(4*a*g + 4*b*f + 4*c*e + b*f*m + 2*c*e*m + 3*a*g*n + 2*b*f*n + c*e*n) + c*g*x^5*(2*m + 3*n + 6)),x)","\text{Hanged}","Not used",1,"\text{Hanged}","F(-1)"
615,1,148,34,9.777505,"\text{Not used}","int((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(a*e + b*d + x^3*(4*b*g + 4*c*f + b*g*m + 2*c*f*m + 3*b*g*n + 2*c*f*n) + x^2*(3*a*g + 3*b*f + 3*c*e + b*f*m + 2*c*e*m + 3*a*g*n + 2*b*f*n + c*e*n) + x*(2*a*f + 2*b*e + 2*c*d + b*e*m + 2*c*d*m + 2*a*f*n + b*e*n) + b*d*m + a*e*n + c*g*x^4*(2*m + 3*n + 5)),x)","{\left(g\,x^3+f\,x^2+e\,x+d\right)}^n\,\left(x^4\,\left(b\,g+c\,f\right)\,{\left(c\,x^2+b\,x+a\right)}^m+x^2\,{\left(c\,x^2+b\,x+a\right)}^m\,\left(a\,f+b\,e+c\,d\right)+x^3\,{\left(c\,x^2+b\,x+a\right)}^m\,\left(a\,g+b\,f+c\,e\right)+a\,d\,{\left(c\,x^2+b\,x+a\right)}^m+x\,\left(a\,e+b\,d\right)\,{\left(c\,x^2+b\,x+a\right)}^m+c\,g\,x^5\,{\left(c\,x^2+b\,x+a\right)}^m\right)","Not used",1,"(d + e*x + f*x^2 + g*x^3)^n*(x^4*(b*g + c*f)*(a + b*x + c*x^2)^m + x^2*(a + b*x + c*x^2)^m*(a*f + b*e + c*d) + x^3*(a + b*x + c*x^2)^m*(a*g + b*f + c*e) + a*d*(a + b*x + c*x^2)^m + x*(a*e + b*d)*(a + b*x + c*x^2)^m + c*g*x^5*(a + b*x + c*x^2)^m)","B"
616,1,37,37,9.680395,"\text{Not used}","int(((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(x^4*(3*b*g + 3*c*f + b*g*m + 2*c*f*m + 3*b*g*n + 2*c*f*n) - a*d + x^2*(a*f + b*e + c*d + b*e*m + 2*c*d*m + 2*a*f*n + b*e*n) + x*(b*d*m + a*e*n) + x^3*(2*a*g + 2*b*f + 2*c*e + b*f*m + 2*c*e*m + 3*a*g*n + 2*b*f*n + c*e*n) + c*g*x^5*(2*m + 3*n + 4)))/x^2,x)","\frac{{\left(c\,x^2+b\,x+a\right)}^{m+1}\,{\left(g\,x^3+f\,x^2+e\,x+d\right)}^{n+1}}{x}","Not used",1,"((a + b*x + c*x^2)^(m + 1)*(d + e*x + f*x^2 + g*x^3)^(n + 1))/x","B"
617,1,146,37,9.216183,"\text{Not used}","int(((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(x^4*(2*b*g + 2*c*f + b*g*m + 2*c*f*m + 3*b*g*n + 2*c*f*n) - 2*a*d - x*(a*e + b*d - b*d*m - a*e*n) + x^2*(b*e*m + 2*c*d*m + 2*a*f*n + b*e*n) + x^3*(a*g + b*f + c*e + b*f*m + 2*c*e*m + 3*a*g*n + 2*b*f*n + c*e*n) + c*g*x^5*(2*m + 3*n + 3)))/x^3,x)","{\left(c\,x^2+b\,x+a\right)}^m\,{\left(g\,x^3+f\,x^2+e\,x+d\right)}^n\,\left(a\,f+b\,e+c\,d+c\,g\,x^3+a\,g\,x+b\,f\,x+c\,e\,x+b\,g\,x^2+c\,f\,x^2\right)+\frac{\left(a\,e+b\,d\right)\,{\left(c\,x^2+b\,x+a\right)}^m\,{\left(g\,x^3+f\,x^2+e\,x+d\right)}^n}{x}+\frac{a\,d\,{\left(c\,x^2+b\,x+a\right)}^m\,{\left(g\,x^3+f\,x^2+e\,x+d\right)}^n}{x^2}","Not used",1,"(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(a*f + b*e + c*d + c*g*x^3 + a*g*x + b*f*x + c*e*x + b*g*x^2 + c*f*x^2) + ((a*e + b*d)*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x + (a*d*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x^2","B"
618,1,167,185,3.369854,"\text{Not used}","int(x^3*(a + b*(c + d*x)^(1/2))^2,x)","\frac{b^2\,{\left(c+d\,x\right)}^5}{5\,d^4}-\frac{\left(6\,b^2\,c-2\,a^2\right)\,{\left(c+d\,x\right)}^4}{8\,d^4}+\frac{\left(6\,a^2\,c^2-2\,b^2\,c^3\right)\,{\left(c+d\,x\right)}^2}{4\,d^4}-\frac{a^2\,c^3\,x}{d^3}+\frac{4\,a\,b\,{\left(c+d\,x\right)}^{9/2}}{9\,d^4}+\frac{c\,\left(b^2\,c-a^2\right)\,{\left(c+d\,x\right)}^3}{d^4}-\frac{4\,a\,b\,c^3\,{\left(c+d\,x\right)}^{3/2}}{3\,d^4}+\frac{12\,a\,b\,c^2\,{\left(c+d\,x\right)}^{5/2}}{5\,d^4}-\frac{12\,a\,b\,c\,{\left(c+d\,x\right)}^{7/2}}{7\,d^4}","Not used",1,"(b^2*(c + d*x)^5)/(5*d^4) - ((6*b^2*c - 2*a^2)*(c + d*x)^4)/(8*d^4) + ((6*a^2*c^2 - 2*b^2*c^3)*(c + d*x)^2)/(4*d^4) - (a^2*c^3*x)/d^3 + (4*a*b*(c + d*x)^(9/2))/(9*d^4) + (c*(b^2*c - a^2)*(c + d*x)^3)/d^4 - (4*a*b*c^3*(c + d*x)^(3/2))/(3*d^4) + (12*a*b*c^2*(c + d*x)^(5/2))/(5*d^4) - (12*a*b*c*(c + d*x)^(7/2))/(7*d^4)","B"
619,1,124,138,0.062518,"\text{Not used}","int(x^2*(a + b*(c + d*x)^(1/2))^2,x)","\frac{b^2\,{\left(c+d\,x\right)}^4}{4\,d^3}-\frac{\left(4\,a^2\,c-2\,b^2\,c^2\right)\,{\left(c+d\,x\right)}^2}{4\,d^3}-\frac{\left(4\,b^2\,c-2\,a^2\right)\,{\left(c+d\,x\right)}^3}{6\,d^3}+\frac{a^2\,c^2\,x}{d^2}+\frac{4\,a\,b\,{\left(c+d\,x\right)}^{7/2}}{7\,d^3}+\frac{4\,a\,b\,c^2\,{\left(c+d\,x\right)}^{3/2}}{3\,d^3}-\frac{8\,a\,b\,c\,{\left(c+d\,x\right)}^{5/2}}{5\,d^3}","Not used",1,"(b^2*(c + d*x)^4)/(4*d^3) - ((4*a^2*c - 2*b^2*c^2)*(c + d*x)^2)/(4*d^3) - ((4*b^2*c - 2*a^2)*(c + d*x)^3)/(6*d^3) + (a^2*c^2*x)/d^2 + (4*a*b*(c + d*x)^(7/2))/(7*d^3) + (4*a*b*c^2*(c + d*x)^(3/2))/(3*d^3) - (8*a*b*c*(c + d*x)^(5/2))/(5*d^3)","B"
620,1,79,89,0.030119,"\text{Not used}","int(x*(a + b*(c + d*x)^(1/2))^2,x)","\frac{b^2\,{\left(c+d\,x\right)}^3}{3\,d^2}-\frac{\left(2\,b^2\,c-2\,a^2\right)\,{\left(c+d\,x\right)}^2}{4\,d^2}+\frac{4\,a\,b\,{\left(c+d\,x\right)}^{5/2}}{5\,d^2}-\frac{a^2\,c\,x}{d}-\frac{4\,a\,b\,c\,{\left(c+d\,x\right)}^{3/2}}{3\,d^2}","Not used",1,"(b^2*(c + d*x)^3)/(3*d^2) - ((2*b^2*c - 2*a^2)*(c + d*x)^2)/(4*d^2) + (4*a*b*(c + d*x)^(5/2))/(5*d^2) - (a^2*c*x)/d - (4*a*b*c*(c + d*x)^(3/2))/(3*d^2)","B"
621,1,36,41,0.045750,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^2,x)","\frac{3\,b^2\,{\left(c+d\,x\right)}^2+8\,a\,b\,{\left(c+d\,x\right)}^{3/2}+6\,a^2\,d\,x}{6\,d}","Not used",1,"(3*b^2*(c + d*x)^2 + 8*a*b*(c + d*x)^(3/2) + 6*a^2*d*x)/(6*d)","B"
622,1,130,57,0.088310,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^2/x,x)","\ln\left(\left(2\,a^2+2\,c\,b^2\right)\,\sqrt{c+d\,x}-2\,{\left(a+b\,\sqrt{c}\right)}^2\,\sqrt{c+d\,x}+4\,a\,b\,c\right)\,{\left(a+b\,\sqrt{c}\right)}^2+\ln\left(\left(2\,a^2+2\,c\,b^2\right)\,\sqrt{c+d\,x}-2\,{\left(a-b\,\sqrt{c}\right)}^2\,\sqrt{c+d\,x}+4\,a\,b\,c\right)\,{\left(a-b\,\sqrt{c}\right)}^2+4\,a\,b\,\sqrt{c+d\,x}+b^2\,d\,x","Not used",1,"log((2*b^2*c + 2*a^2)*(c + d*x)^(1/2) - 2*(a + b*c^(1/2))^2*(c + d*x)^(1/2) + 4*a*b*c)*(a + b*c^(1/2))^2 + log((2*b^2*c + 2*a^2)*(c + d*x)^(1/2) - 2*(a - b*c^(1/2))^2*(c + d*x)^(1/2) + 4*a*b*c)*(a - b*c^(1/2))^2 + 4*a*b*(c + d*x)^(1/2) + b^2*d*x","B"
623,1,131,54,0.123902,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^2/x^2,x)","b\,d\,\ln\left(2\,b\,d\,\left(b+\frac{a}{\sqrt{c}}\right)\,\sqrt{c+d\,x}-2\,b^2\,d\,\sqrt{c+d\,x}-2\,a\,b\,d\right)\,\left(b+\frac{a}{\sqrt{c}}\right)-\frac{a^2\,d+b^2\,c\,d+2\,a\,b\,d\,\sqrt{c+d\,x}}{d\,x}+b\,d\,\ln\left(2\,b\,d\,\left(b-\frac{a}{\sqrt{c}}\right)\,\sqrt{c+d\,x}-2\,b^2\,d\,\sqrt{c+d\,x}-2\,a\,b\,d\right)\,\left(b-\frac{a}{\sqrt{c}}\right)","Not used",1,"b*d*log(2*b*d*(b + a/c^(1/2))*(c + d*x)^(1/2) - 2*b^2*d*(c + d*x)^(1/2) - 2*a*b*d)*(b + a/c^(1/2)) - (a^2*d + b^2*c*d + 2*a*b*d*(c + d*x)^(1/2))/(d*x) + b*d*log(2*b*d*(b - a/c^(1/2))*(c + d*x)^(1/2) - 2*b^2*d*(c + d*x)^(1/2) - 2*a*b*d)*(b - a/c^(1/2))","B"
624,1,80,80,3.399561,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^2/x^3,x)","\frac{a\,b\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}}{\sqrt{c}}\right)}{2\,c^{3/2}}-\frac{b^2\,c}{2\,x^2}-\frac{b^2\,d}{x}-\frac{a\,b\,\sqrt{c+d\,x}}{2\,x^2}-\frac{a\,b\,{\left(c+d\,x\right)}^{3/2}}{2\,c\,x^2}-\frac{a^2}{2\,x^2}","Not used",1,"(a*b*d^2*atanh((c + d*x)^(1/2)/c^(1/2)))/(2*c^(3/2)) - (b^2*c)/(2*x^2) - (b^2*d)/x - (a*b*(c + d*x)^(1/2))/(2*x^2) - (a*b*(c + d*x)^(3/2))/(2*c*x^2) - a^2/(2*x^2)","B"
625,0,-1,326,0.000000,"\text{Not used}","int(x^3*(a + b*(c + d*x)^(1/2))^(1/2),x)","\int x^3\,\sqrt{a+b\,\sqrt{c+d\,x}} \,d x","Not used",1,"int(x^3*(a + b*(c + d*x)^(1/2))^(1/2), x)","F"
626,0,-1,224,0.000000,"\text{Not used}","int(x^2*(a + b*(c + d*x)^(1/2))^(1/2),x)","\int x^2\,\sqrt{a+b\,\sqrt{c+d\,x}} \,d x","Not used",1,"int(x^2*(a + b*(c + d*x)^(1/2))^(1/2), x)","F"
627,0,-1,133,0.000000,"\text{Not used}","int(x*(a + b*(c + d*x)^(1/2))^(1/2),x)","\int x\,\sqrt{a+b\,\sqrt{c+d\,x}} \,d x","Not used",1,"int(x*(a + b*(c + d*x)^(1/2))^(1/2), x)","F"
628,1,44,56,3.394543,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^(1/2),x)","\frac{4\,{\left(a+b\,\sqrt{c+d\,x}\right)}^{5/2}}{5\,b^2\,d}-\frac{4\,a\,{\left(a+b\,\sqrt{c+d\,x}\right)}^{3/2}}{3\,b^2\,d}","Not used",1,"(4*(a + b*(c + d*x)^(1/2))^(5/2))/(5*b^2*d) - (4*a*(a + b*(c + d*x)^(1/2))^(3/2))/(3*b^2*d)","B"
629,0,-1,116,0.000000,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^(1/2)/x,x)","\int \frac{\sqrt{a+b\,\sqrt{c+d\,x}}}{x} \,d x","Not used",1,"int((a + b*(c + d*x)^(1/2))^(1/2)/x, x)","F"
630,0,-1,137,0.000000,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^(1/2)/x^2,x)","\int \frac{\sqrt{a+b\,\sqrt{c+d\,x}}}{x^2} \,d x","Not used",1,"int((a + b*(c + d*x)^(1/2))^(1/2)/x^2, x)","F"
631,0,-1,224,0.000000,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^(1/2)/x^3,x)","\int \frac{\sqrt{a+b\,\sqrt{c+d\,x}}}{x^3} \,d x","Not used",1,"int((a + b*(c + d*x)^(1/2))^(1/2)/x^3, x)","F"
632,1,317,230,0.069350,"\text{Not used}","int(x^3/(a + b*(c + d*x)^(1/2)),x)","\frac{2\,{\left(c+d\,x\right)}^{7/2}}{7\,b\,d^4}-\left(\frac{a^2\,\left(\frac{a^2\,\left(\frac{6\,c}{b\,d^4}-\frac{2\,a^2}{b^3\,d^4}\right)}{b^2}-\frac{6\,c^2}{b\,d^4}\right)}{b^2}+\frac{2\,c^3}{b\,d^4}\right)\,\sqrt{c+d\,x}-\left(\frac{a^2\,\left(\frac{6\,c}{b\,d^4}-\frac{2\,a^2}{b^3\,d^4}\right)}{3\,b^2}-\frac{2\,c^2}{b\,d^4}\right)\,{\left(c+d\,x\right)}^{3/2}-\left(\frac{6\,c}{5\,b\,d^4}-\frac{2\,a^2}{5\,b^3\,d^4}\right)\,{\left(c+d\,x\right)}^{5/2}+\frac{a\,\left(\frac{6\,c}{b\,d^4}-\frac{2\,a^2}{b^3\,d^4}\right)\,{\left(c+d\,x\right)}^2}{4\,b}-\frac{a\,{\left(c+d\,x\right)}^3}{3\,b^2\,d^4}-\frac{\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(2\,a^7-6\,a^5\,b^2\,c+6\,a^3\,b^4\,c^2-2\,a\,b^6\,c^3\right)}{b^8\,d^4}+\frac{a\,d\,x\,\left(\frac{a^2\,\left(\frac{6\,c}{b\,d^4}-\frac{2\,a^2}{b^3\,d^4}\right)}{b^2}-\frac{6\,c^2}{b\,d^4}\right)}{2\,b}","Not used",1,"(2*(c + d*x)^(7/2))/(7*b*d^4) - ((a^2*((a^2*((6*c)/(b*d^4) - (2*a^2)/(b^3*d^4)))/b^2 - (6*c^2)/(b*d^4)))/b^2 + (2*c^3)/(b*d^4))*(c + d*x)^(1/2) - ((a^2*((6*c)/(b*d^4) - (2*a^2)/(b^3*d^4)))/(3*b^2) - (2*c^2)/(b*d^4))*(c + d*x)^(3/2) - ((6*c)/(5*b*d^4) - (2*a^2)/(5*b^3*d^4))*(c + d*x)^(5/2) + (a*((6*c)/(b*d^4) - (2*a^2)/(b^3*d^4))*(c + d*x)^2)/(4*b) - (a*(c + d*x)^3)/(3*b^2*d^4) - (log(a + b*(c + d*x)^(1/2))*(2*a^7 - 6*a^5*b^2*c - 2*a*b^6*c^3 + 6*a^3*b^4*c^2))/(b^8*d^4) + (a*d*x*((a^2*((6*c)/(b*d^4) - (2*a^2)/(b^3*d^4)))/b^2 - (6*c^2)/(b*d^4)))/(2*b)","B"
633,1,184,151,3.212666,"\text{Not used}","int(x^2/(a + b*(c + d*x)^(1/2)),x)","\frac{2\,{\left(c+d\,x\right)}^{5/2}}{5\,b\,d^3}-\left(\frac{a^2\,\left(\frac{4\,c}{b\,d^3}-\frac{2\,a^2}{b^3\,d^3}\right)}{b^2}-\frac{2\,c^2}{b\,d^3}\right)\,\sqrt{c+d\,x}-\left(\frac{4\,c}{3\,b\,d^3}-\frac{2\,a^2}{3\,b^3\,d^3}\right)\,{\left(c+d\,x\right)}^{3/2}-\frac{\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(2\,a^5-4\,a^3\,b^2\,c+2\,a\,b^4\,c^2\right)}{b^6\,d^3}-\frac{a\,{\left(c+d\,x\right)}^2}{2\,b^2\,d^3}+\frac{a\,d\,x\,\left(\frac{4\,c}{b\,d^3}-\frac{2\,a^2}{b^3\,d^3}\right)}{2\,b}","Not used",1,"(2*(c + d*x)^(5/2))/(5*b*d^3) - ((a^2*((4*c)/(b*d^3) - (2*a^2)/(b^3*d^3)))/b^2 - (2*c^2)/(b*d^3))*(c + d*x)^(1/2) - ((4*c)/(3*b*d^3) - (2*a^2)/(3*b^3*d^3))*(c + d*x)^(3/2) - (log(a + b*(c + d*x)^(1/2))*(2*a^5 - 4*a^3*b^2*c + 2*a*b^4*c^2))/(b^6*d^3) - (a*(c + d*x)^2)/(2*b^2*d^3) + (a*d*x*((4*c)/(b*d^3) - (2*a^2)/(b^3*d^3)))/(2*b)","B"
634,1,89,90,0.054125,"\text{Not used}","int(x/(a + b*(c + d*x)^(1/2)),x)","\frac{2\,{\left(c+d\,x\right)}^{3/2}}{3\,b\,d^2}-\left(\frac{2\,c}{b\,d^2}-\frac{2\,a^2}{b^3\,d^2}\right)\,\sqrt{c+d\,x}-\frac{\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(2\,a^3-2\,a\,b^2\,c\right)}{b^4\,d^2}-\frac{a\,x}{b^2\,d}","Not used",1,"(2*(c + d*x)^(3/2))/(3*b*d^2) - ((2*c)/(b*d^2) - (2*a^2)/(b^3*d^2))*(c + d*x)^(1/2) - (log(a + b*(c + d*x)^(1/2))*(2*a^3 - 2*a*b^2*c))/(b^4*d^2) - (a*x)/(b^2*d)","B"
635,1,33,41,0.052980,"\text{Not used}","int(1/(a + b*(c + d*x)^(1/2)),x)","-\frac{2\,\left(a\,\ln\left(a+b\,\sqrt{c+d\,x}\right)-b\,\sqrt{c+d\,x}\right)}{b^2\,d}","Not used",1,"-(2*(a*log(a + b*(c + d*x)^(1/2)) - b*(c + d*x)^(1/2)))/(b^2*d)","B"
636,1,181,82,3.281971,"\text{Not used}","int(1/(x*(a + b*(c + d*x)^(1/2))),x)","\frac{\ln\left(2\,b^3\,c^{3/2}-2\,b^3\,c\,\sqrt{c+d\,x}-6\,a\,b^2\,c+6\,a\,b^2\,\sqrt{c}\,\sqrt{c+d\,x}\right)}{a+b\,\sqrt{c}}+\frac{\ln\left(-2\,b^3\,c^{3/2}-2\,b^3\,c\,\sqrt{c+d\,x}-6\,a\,b^2\,c-6\,a\,b^2\,\sqrt{c}\,\sqrt{c+d\,x}\right)}{a-b\,\sqrt{c}}+\frac{2\,a\,\ln\left(4\,b^5\,c^2\,\sqrt{c+d\,x}-36\,a^3\,b^2\,c+4\,a\,b^4\,c^2-36\,a^2\,b^3\,c\,\sqrt{c+d\,x}\right)}{b^2\,c-a^2}","Not used",1,"log(2*b^3*c^(3/2) - 2*b^3*c*(c + d*x)^(1/2) - 6*a*b^2*c + 6*a*b^2*c^(1/2)*(c + d*x)^(1/2))/(a + b*c^(1/2)) + log(- 2*b^3*c^(3/2) - 2*b^3*c*(c + d*x)^(1/2) - 6*a*b^2*c - 6*a*b^2*c^(1/2)*(c + d*x)^(1/2))/(a - b*c^(1/2)) + (2*a*log(4*b^5*c^2*(c + d*x)^(1/2) - 36*a^3*b^2*c + 4*a*b^4*c^2 - 36*a^2*b^3*c*(c + d*x)^(1/2)))/(b^2*c - a^2)","B"
637,1,220,130,3.591036,"\text{Not used}","int(1/(x^2*(a + b*(c + d*x)^(1/2))),x)","\frac{\ln\left(\sqrt{c+d\,x}-\sqrt{c}\right)\,\left(4\,a\,b^2\,c\,d-b\,\sqrt{c}\,d\,\left(2\,a^2+2\,c\,b^2\right)\right)}{4\,a^4\,c-8\,a^2\,b^2\,c^2+4\,b^4\,c^3}+\frac{\ln\left(\sqrt{c+d\,x}+\sqrt{c}\right)\,\left(4\,a\,b^2\,c\,d+b\,\sqrt{c}\,d\,\left(2\,a^2+2\,c\,b^2\right)\right)}{4\,a^4\,c-8\,a^2\,b^2\,c^2+4\,b^4\,c^3}+\frac{\frac{a\,d}{b^2\,c-a^2}-\frac{b\,d\,\sqrt{c+d\,x}}{b^2\,c-a^2}}{d\,x}-\frac{2\,a\,b^2\,d\,\ln\left(a+b\,\sqrt{c+d\,x}\right)}{{\left(b^2\,c-a^2\right)}^2}","Not used",1,"(log((c + d*x)^(1/2) - c^(1/2))*(4*a*b^2*c*d - b*c^(1/2)*d*(2*b^2*c + 2*a^2)))/(4*a^4*c + 4*b^4*c^3 - 8*a^2*b^2*c^2) + (log((c + d*x)^(1/2) + c^(1/2))*(4*a*b^2*c*d + b*c^(1/2)*d*(2*b^2*c + 2*a^2)))/(4*a^4*c + 4*b^4*c^3 - 8*a^2*b^2*c^2) + ((a*d)/(b^2*c - a^2) - (b*d*(c + d*x)^(1/2))/(b^2*c - a^2))/(d*x) - (2*a*b^2*d*log(a + b*(c + d*x)^(1/2)))/(b^2*c - a^2)^2","B"
638,1,1094,204,5.008792,"\text{Not used}","int(1/(x^3*(a + b*(c + d*x)^(1/2))),x)","\frac{\ln\left(\frac{b^5\,d^4\,{\left(a^2+3\,c\,b^2\right)}^2\,\sqrt{c+d\,x}}{16\,c^2\,{\left(b^2\,c-a^2\right)}^4}-\frac{a\,b^4\,d^4\,\left(-a^4+2\,a^2\,b^2\,c+15\,b^4\,c^2\right)}{16\,c^2\,{\left(b^2\,c-a^2\right)}^4}-\frac{b\,d^2\,\sqrt{c^3}\,\left(\frac{b^2\,d^2\,\left(3\,b^2\,c-a^2\right)}{4\,c\,\left(b^2\,c-a^2\right)}+\frac{b^2\,d^2\,\sqrt{c^3}\,\left(a^2\,\sqrt{c+d\,x}+4\,a\,b\,c+3\,b^2\,c\,\sqrt{c+d\,x}\right)\,\left(3\,b^4\,c^2-a^4+6\,a^2\,b^2\,c+8\,a\,b^3\,\sqrt{c^3}\right)}{4\,c^3\,{\left(b^2\,c-a^2\right)}^3}-\frac{a\,b^3\,d^2\,\left(9\,b^2\,c-a^2\right)\,\sqrt{c+d\,x}}{2\,c\,{\left(b^2\,c-a^2\right)}^2}\right)\,\left(3\,b^4\,c^2-a^4+6\,a^2\,b^2\,c+8\,a\,b^3\,\sqrt{c^3}\right)}{8\,c^3\,{\left(b^2\,c-a^2\right)}^3}\right)\,\left(8\,a\,b^4\,c^3\,d^2-a^4\,b\,d^2\,\sqrt{c^3}+3\,b^5\,c^2\,d^2\,\sqrt{c^3}+6\,a^2\,b^3\,c\,d^2\,\sqrt{c^3}\right)}{8\,\left(a^6\,c^3-3\,a^4\,b^2\,c^4+3\,a^2\,b^4\,c^5-b^6\,c^6\right)}-\frac{\frac{a^3\,d^2-3\,a\,b^2\,c\,d^2}{2\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}-\frac{\left(a^2\,b\,d^2+3\,c\,b^3\,d^2\right)\,{\left(c+d\,x\right)}^{3/2}}{4\,c\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}+\frac{b\,d^2\,\left(5\,b^2\,c-a^2\right)\,\sqrt{c+d\,x}}{4\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}+\frac{a\,b^2\,d^2\,\left(c+d\,x\right)}{a^4-2\,a^2\,b^2\,c+b^4\,c^2}}{{\left(c+d\,x\right)}^2-2\,c\,\left(c+d\,x\right)+c^2}+\frac{\ln\left(\frac{b^5\,d^4\,{\left(a^2+3\,c\,b^2\right)}^2\,\sqrt{c+d\,x}}{16\,c^2\,{\left(b^2\,c-a^2\right)}^4}-\frac{a\,b^4\,d^4\,\left(-a^4+2\,a^2\,b^2\,c+15\,b^4\,c^2\right)}{16\,c^2\,{\left(b^2\,c-a^2\right)}^4}-\frac{b\,d^2\,\sqrt{c^3}\,\left(\frac{b^2\,d^2\,\left(3\,b^2\,c-a^2\right)}{4\,c\,\left(b^2\,c-a^2\right)}+\frac{b^2\,d^2\,\sqrt{c^3}\,\left(a^2\,\sqrt{c+d\,x}+4\,a\,b\,c+3\,b^2\,c\,\sqrt{c+d\,x}\right)\,\left(a^4-3\,b^4\,c^2-6\,a^2\,b^2\,c+8\,a\,b^3\,\sqrt{c^3}\right)}{4\,c^3\,{\left(b^2\,c-a^2\right)}^3}-\frac{a\,b^3\,d^2\,\left(9\,b^2\,c-a^2\right)\,\sqrt{c+d\,x}}{2\,c\,{\left(b^2\,c-a^2\right)}^2}\right)\,\left(a^4-3\,b^4\,c^2-6\,a^2\,b^2\,c+8\,a\,b^3\,\sqrt{c^3}\right)}{8\,c^3\,{\left(b^2\,c-a^2\right)}^3}\right)\,\left(8\,a\,b^4\,c^3\,d^2+a^4\,b\,d^2\,\sqrt{c^3}-3\,b^5\,c^2\,d^2\,\sqrt{c^3}-6\,a^2\,b^3\,c\,d^2\,\sqrt{c^3}\right)}{8\,\left(a^6\,c^3-3\,a^4\,b^2\,c^4+3\,a^2\,b^4\,c^5-b^6\,c^6\right)}+\frac{2\,a\,b^4\,d^2\,\ln\left(a+b\,\sqrt{c+d\,x}\right)}{{\left(b^2\,c-a^2\right)}^3}","Not used",1,"(log((b^5*d^4*(3*b^2*c + a^2)^2*(c + d*x)^(1/2))/(16*c^2*(b^2*c - a^2)^4) - (a*b^4*d^4*(15*b^4*c^2 - a^4 + 2*a^2*b^2*c))/(16*c^2*(b^2*c - a^2)^4) - (b*d^2*(c^3)^(1/2)*((b^2*d^2*(3*b^2*c - a^2))/(4*c*(b^2*c - a^2)) + (b^2*d^2*(c^3)^(1/2)*(a^2*(c + d*x)^(1/2) + 4*a*b*c + 3*b^2*c*(c + d*x)^(1/2))*(3*b^4*c^2 - a^4 + 6*a^2*b^2*c + 8*a*b^3*(c^3)^(1/2)))/(4*c^3*(b^2*c - a^2)^3) - (a*b^3*d^2*(9*b^2*c - a^2)*(c + d*x)^(1/2))/(2*c*(b^2*c - a^2)^2))*(3*b^4*c^2 - a^4 + 6*a^2*b^2*c + 8*a*b^3*(c^3)^(1/2)))/(8*c^3*(b^2*c - a^2)^3))*(8*a*b^4*c^3*d^2 - a^4*b*d^2*(c^3)^(1/2) + 3*b^5*c^2*d^2*(c^3)^(1/2) + 6*a^2*b^3*c*d^2*(c^3)^(1/2)))/(8*(a^6*c^3 - b^6*c^6 - 3*a^4*b^2*c^4 + 3*a^2*b^4*c^5)) - ((a^3*d^2 - 3*a*b^2*c*d^2)/(2*(a^4 + b^4*c^2 - 2*a^2*b^2*c)) - ((a^2*b*d^2 + 3*b^3*c*d^2)*(c + d*x)^(3/2))/(4*c*(a^4 + b^4*c^2 - 2*a^2*b^2*c)) + (b*d^2*(5*b^2*c - a^2)*(c + d*x)^(1/2))/(4*(a^4 + b^4*c^2 - 2*a^2*b^2*c)) + (a*b^2*d^2*(c + d*x))/(a^4 + b^4*c^2 - 2*a^2*b^2*c))/((c + d*x)^2 - 2*c*(c + d*x) + c^2) + (log((b^5*d^4*(3*b^2*c + a^2)^2*(c + d*x)^(1/2))/(16*c^2*(b^2*c - a^2)^4) - (a*b^4*d^4*(15*b^4*c^2 - a^4 + 2*a^2*b^2*c))/(16*c^2*(b^2*c - a^2)^4) - (b*d^2*(c^3)^(1/2)*((b^2*d^2*(3*b^2*c - a^2))/(4*c*(b^2*c - a^2)) + (b^2*d^2*(c^3)^(1/2)*(a^2*(c + d*x)^(1/2) + 4*a*b*c + 3*b^2*c*(c + d*x)^(1/2))*(a^4 - 3*b^4*c^2 - 6*a^2*b^2*c + 8*a*b^3*(c^3)^(1/2)))/(4*c^3*(b^2*c - a^2)^3) - (a*b^3*d^2*(9*b^2*c - a^2)*(c + d*x)^(1/2))/(2*c*(b^2*c - a^2)^2))*(a^4 - 3*b^4*c^2 - 6*a^2*b^2*c + 8*a*b^3*(c^3)^(1/2)))/(8*c^3*(b^2*c - a^2)^3))*(8*a*b^4*c^3*d^2 + a^4*b*d^2*(c^3)^(1/2) - 3*b^5*c^2*d^2*(c^3)^(1/2) - 6*a^2*b^3*c*d^2*(c^3)^(1/2)))/(8*(a^6*c^3 - b^6*c^6 - 3*a^4*b^2*c^4 + 3*a^2*b^4*c^5)) + (2*a*b^4*d^2*log(a + b*(c + d*x)^(1/2)))/(b^2*c - a^2)^3","B"
639,1,461,240,0.094493,"\text{Not used}","int(x^3/(a + b*(c + d*x)^(1/2))^2,x)","\left(\frac{4\,a^3}{3\,b^5\,d^4}+\frac{2\,a\,\left(\frac{6\,c}{b^2\,d^4}-\frac{6\,a^2}{b^4\,d^4}\right)}{3\,b}\right)\,{\left(c+d\,x\right)}^{3/2}-\left(\frac{3\,c}{2\,b^2\,d^4}-\frac{3\,a^2}{2\,b^4\,d^4}\right)\,{\left(c+d\,x\right)}^2-\left(\frac{2\,a\,\left(\frac{a^2\,\left(\frac{6\,c}{b^2\,d^4}-\frac{6\,a^2}{b^4\,d^4}\right)}{b^2}-\frac{2\,a\,\left(\frac{4\,a^3}{b^5\,d^4}+\frac{2\,a\,\left(\frac{6\,c}{b^2\,d^4}-\frac{6\,a^2}{b^4\,d^4}\right)}{b}\right)}{b}+\frac{6\,c^2}{b^2\,d^4}\right)}{b}+\frac{a^2\,\left(\frac{4\,a^3}{b^5\,d^4}+\frac{2\,a\,\left(\frac{6\,c}{b^2\,d^4}-\frac{6\,a^2}{b^4\,d^4}\right)}{b}\right)}{b^2}\right)\,\sqrt{c+d\,x}+\frac{{\left(c+d\,x\right)}^3}{3\,b^2\,d^4}+\frac{2\,\left(a^7-3\,a^5\,b^2\,c+3\,a^3\,b^4\,c^2-a\,b^6\,c^3\right)}{b\,\left(b^8\,d^4\,\sqrt{c+d\,x}+a\,b^7\,d^4\right)}+d\,x\,\left(\frac{a^2\,\left(\frac{6\,c}{b^2\,d^4}-\frac{6\,a^2}{b^4\,d^4}\right)}{2\,b^2}-\frac{a\,\left(\frac{4\,a^3}{b^5\,d^4}+\frac{2\,a\,\left(\frac{6\,c}{b^2\,d^4}-\frac{6\,a^2}{b^4\,d^4}\right)}{b}\right)}{b}+\frac{3\,c^2}{b^2\,d^4}\right)+\frac{\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(14\,a^6-30\,a^4\,b^2\,c+18\,a^2\,b^4\,c^2-2\,b^6\,c^3\right)}{b^8\,d^4}-\frac{4\,a\,{\left(c+d\,x\right)}^{5/2}}{5\,b^3\,d^4}","Not used",1,"((4*a^3)/(3*b^5*d^4) + (2*a*((6*c)/(b^2*d^4) - (6*a^2)/(b^4*d^4)))/(3*b))*(c + d*x)^(3/2) - ((3*c)/(2*b^2*d^4) - (3*a^2)/(2*b^4*d^4))*(c + d*x)^2 - ((2*a*((a^2*((6*c)/(b^2*d^4) - (6*a^2)/(b^4*d^4)))/b^2 - (2*a*((4*a^3)/(b^5*d^4) + (2*a*((6*c)/(b^2*d^4) - (6*a^2)/(b^4*d^4)))/b))/b + (6*c^2)/(b^2*d^4)))/b + (a^2*((4*a^3)/(b^5*d^4) + (2*a*((6*c)/(b^2*d^4) - (6*a^2)/(b^4*d^4)))/b))/b^2)*(c + d*x)^(1/2) + (c + d*x)^3/(3*b^2*d^4) + (2*(a^7 - 3*a^5*b^2*c - a*b^6*c^3 + 3*a^3*b^4*c^2))/(b*(b^8*d^4*(c + d*x)^(1/2) + a*b^7*d^4)) + d*x*((a^2*((6*c)/(b^2*d^4) - (6*a^2)/(b^4*d^4)))/(2*b^2) - (a*((4*a^3)/(b^5*d^4) + (2*a*((6*c)/(b^2*d^4) - (6*a^2)/(b^4*d^4)))/b))/b + (3*c^2)/(b^2*d^4)) + (log(a + b*(c + d*x)^(1/2))*(14*a^6 - 2*b^6*c^3 - 30*a^4*b^2*c + 18*a^2*b^4*c^2))/(b^8*d^4) - (4*a*(c + d*x)^(5/2))/(5*b^3*d^4)","B"
640,1,197,166,3.197140,"\text{Not used}","int(x^2/(a + b*(c + d*x)^(1/2))^2,x)","\left(\frac{4\,a^3}{b^5\,d^3}+\frac{2\,a\,\left(\frac{4\,c}{b^2\,d^3}-\frac{6\,a^2}{b^4\,d^3}\right)}{b}\right)\,\sqrt{c+d\,x}+\frac{2\,\left(a^5-2\,a^3\,b^2\,c+a\,b^4\,c^2\right)}{b\,\left(b^6\,d^3\,\sqrt{c+d\,x}+a\,b^5\,d^3\right)}+\frac{{\left(c+d\,x\right)}^2}{2\,b^2\,d^3}-d\,x\,\left(\frac{2\,c}{b^2\,d^3}-\frac{3\,a^2}{b^4\,d^3}\right)-\frac{4\,a\,{\left(c+d\,x\right)}^{3/2}}{3\,b^3\,d^3}+\frac{\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(10\,a^4-12\,a^2\,b^2\,c+2\,b^4\,c^2\right)}{b^6\,d^3}","Not used",1,"((4*a^3)/(b^5*d^3) + (2*a*((4*c)/(b^2*d^3) - (6*a^2)/(b^4*d^3)))/b)*(c + d*x)^(1/2) + (2*(a^5 - 2*a^3*b^2*c + a*b^4*c^2))/(b*(b^6*d^3*(c + d*x)^(1/2) + a*b^5*d^3)) + (c + d*x)^2/(2*b^2*d^3) - d*x*((2*c)/(b^2*d^3) - (3*a^2)/(b^4*d^3)) - (4*a*(c + d*x)^(3/2))/(3*b^3*d^3) + (log(a + b*(c + d*x)^(1/2))*(10*a^4 + 2*b^4*c^2 - 12*a^2*b^2*c))/(b^6*d^3)","B"
641,1,98,95,0.061673,"\text{Not used}","int(x/(a + b*(c + d*x)^(1/2))^2,x)","\frac{x}{b^2\,d}+\frac{2\,\left(a^3-a\,b^2\,c\right)}{b\,\left(b^4\,d^2\,\sqrt{c+d\,x}+a\,b^3\,d^2\right)}-\frac{\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(2\,b^2\,c-6\,a^2\right)}{b^4\,d^2}-\frac{4\,a\,\sqrt{c+d\,x}}{b^3\,d^2}","Not used",1,"x/(b^2*d) + (2*(a^3 - a*b^2*c))/(b*(b^4*d^2*(c + d*x)^(1/2) + a*b^3*d^2)) - (log(a + b*(c + d*x)^(1/2))*(2*b^2*c - 6*a^2))/(b^4*d^2) - (4*a*(c + d*x)^(1/2))/(b^3*d^2)","B"
642,1,43,47,0.047426,"\text{Not used}","int(1/(a + b*(c + d*x)^(1/2))^2,x)","\frac{2\,\ln\left(a+b\,\sqrt{c+d\,x}\right)}{b^2\,d}+\frac{2\,a}{b^2\,\left(a\,d+b\,d\,\sqrt{c+d\,x}\right)}","Not used",1,"(2*log(a + b*(c + d*x)^(1/2)))/(b^2*d) + (2*a)/(b^2*(a*d + b*d*(c + d*x)^(1/2)))","B"
643,1,125,129,3.510658,"\text{Not used}","int(1/(x*(a + b*(c + d*x)^(1/2))^2),x)","\frac{\ln\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{{\left(a+b\,\sqrt{c}\right)}^2}+\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(\frac{2}{b^2\,c-a^2}-\frac{4\,b^2\,c}{{\left(b^2\,c-a^2\right)}^2}\right)+\frac{\ln\left(\sqrt{c+d\,x}+\sqrt{c}\right)}{{\left(a-b\,\sqrt{c}\right)}^2}-\frac{2\,a}{\left(b^2\,c-a^2\right)\,\left(a+b\,\sqrt{c+d\,x}\right)}","Not used",1,"log((c + d*x)^(1/2) - c^(1/2))/(a + b*c^(1/2))^2 + log(a + b*(c + d*x)^(1/2))*(2/(b^2*c - a^2) - (4*b^2*c)/(b^2*c - a^2)^2) + log((c + d*x)^(1/2) + c^(1/2))/(a - b*c^(1/2))^2 - (2*a)/((b^2*c - a^2)*(a + b*(c + d*x)^(1/2)))","B"
644,1,275,202,0.731457,"\text{Not used}","int(1/(x^2*(a + b*(c + d*x)^(1/2))^2),x)","\frac{b\,d\,\ln\left(\sqrt{c+d\,x}+\sqrt{c}\right)}{a^3\,\sqrt{c}-b^3\,c^2+3\,a\,b^2\,c^{3/2}-3\,a^2\,b\,c}-\frac{\frac{a\,d\,\left(a^2+3\,c\,b^2\right)}{{\left(b^2\,c-a^2\right)}^2}+\frac{b\,d\,\sqrt{c+d\,x}}{b^2\,c-a^2}-\frac{4\,a\,b^2\,d\,\left(c+d\,x\right)}{a^4-2\,a^2\,b^2\,c+b^4\,c^2}}{b\,{\left(c+d\,x\right)}^{3/2}-a\,c+a\,\left(c+d\,x\right)-b\,c\,\sqrt{c+d\,x}}-\frac{b\,d\,\ln\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{a^3\,\sqrt{c}+b^3\,c^2+3\,a\,b^2\,c^{3/2}+3\,a^2\,b\,c}-\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(\frac{6\,b^2\,d}{{\left(b^2\,c-a^2\right)}^2}-\frac{8\,b^4\,c\,d}{{\left(b^2\,c-a^2\right)}^3}\right)","Not used",1,"(b*d*log((c + d*x)^(1/2) + c^(1/2)))/(a^3*c^(1/2) - b^3*c^2 + 3*a*b^2*c^(3/2) - 3*a^2*b*c) - ((a*d*(3*b^2*c + a^2))/(b^2*c - a^2)^2 + (b*d*(c + d*x)^(1/2))/(b^2*c - a^2) - (4*a*b^2*d*(c + d*x))/(a^4 + b^4*c^2 - 2*a^2*b^2*c))/(b*(c + d*x)^(3/2) - a*c + a*(c + d*x) - b*c*(c + d*x)^(1/2)) - (b*d*log((c + d*x)^(1/2) - c^(1/2)))/(a^3*c^(1/2) + b^3*c^2 + 3*a*b^2*c^(3/2) + 3*a^2*b*c) - log(a + b*(c + d*x)^(1/2))*((6*b^2*d)/(b^2*c - a^2)^2 - (8*b^4*c*d)/(b^2*c - a^2)^3)","B"
645,1,1441,306,5.963530,"\text{Not used}","int(1/(x^3*(a + b*(c + d*x)^(1/2))^2),x)","\frac{\frac{\left(5\,a^3\,b^2\,d^2+19\,c\,a\,b^4\,d^2\right)\,\left(c+d\,x\right)}{2\,\left(b^2\,c-a^2\right)\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}+\frac{\left(a^3\,b^2\,d^2+11\,c\,a\,b^4\,d^2\right)\,{\left(c+d\,x\right)}^2}{2\,c\,\left(a^6-3\,a^4\,b^2\,c+3\,a^2\,b^4\,c^2-b^6\,c^3\right)}-\frac{a\,\left(-a^4\,d^2+6\,a^2\,b^2\,c\,d^2+7\,b^4\,c^2\,d^2\right)}{2\,\left(b^2\,c-a^2\right)\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}+\frac{b\,\left(a^2\,d^2+2\,c\,b^2\,d^2\right)\,{\left(c+d\,x\right)}^{3/2}}{2\,c\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}-\frac{3\,b^3\,c\,d^2\,\sqrt{c+d\,x}}{2\,\left(a^4-2\,a^2\,b^2\,c+b^4\,c^2\right)}}{a\,{\left(c+d\,x\right)}^2+b\,{\left(c+d\,x\right)}^{5/2}+a\,c^2-2\,a\,c\,\left(c+d\,x\right)-2\,b\,c\,{\left(c+d\,x\right)}^{3/2}+b\,c^2\,\sqrt{c+d\,x}}+\ln\left(a+b\,\sqrt{c+d\,x}\right)\,\left(\frac{10\,b^4\,d^2}{{\left(b^2\,c-a^2\right)}^3}-\frac{12\,b^6\,c\,d^2}{{\left(b^2\,c-a^2\right)}^4}\right)+\frac{\ln\left(\frac{a\,b^4\,d^4\,\left(a^6+2\,a^4\,b^2\,c-103\,a^2\,b^4\,c^2-44\,b^6\,c^3\right)}{4\,c^2\,{\left(b^2\,c-a^2\right)}^6}-\frac{b\,d^2\,\left(\frac{b^2\,d^2\,\left(a^2\,\sqrt{c+d\,x}+4\,a\,b\,c+3\,b^2\,c\,\sqrt{c+d\,x}\right)\,\left(a^5\,\sqrt{c^3}+4\,b^5\,c^4+20\,a^2\,b^3\,c^3-10\,a^3\,b^2\,c\,\sqrt{c^3}-15\,a\,b^4\,c^2\,\sqrt{c^3}\right)}{2\,c^3\,{\left(b^2\,c-a^2\right)}^4}-\frac{b^3\,d^2\,\sqrt{c+d\,x}\,\left(-a^4+19\,a^2\,b^2\,c+6\,b^4\,c^2\right)}{c\,{\left(b^2\,c-a^2\right)}^3}+\frac{a\,b^2\,d^2\,\left(7\,b^2\,c-a^2\right)}{2\,c\,{\left(b^2\,c-a^2\right)}^2}\right)\,\left(a^5\,\sqrt{c^3}+4\,b^5\,c^4+20\,a^2\,b^3\,c^3-10\,a^3\,b^2\,c\,\sqrt{c^3}-15\,a\,b^4\,c^2\,\sqrt{c^3}\right)}{4\,c^3\,{\left(b^2\,c-a^2\right)}^4}+\frac{a^2\,b^5\,d^4\,{\left(a^2+11\,c\,b^2\right)}^2\,\sqrt{c+d\,x}}{4\,c^2\,{\left(b^2\,c-a^2\right)}^6}\right)\,\left(4\,b^6\,c^4\,d^2+20\,a^2\,b^4\,c^3\,d^2+a^5\,b\,d^2\,\sqrt{c^3}-10\,a^3\,b^3\,c\,d^2\,\sqrt{c^3}-15\,a\,b^5\,c^2\,d^2\,\sqrt{c^3}\right)}{4\,\left(a^8\,c^3-4\,a^6\,b^2\,c^4+6\,a^4\,b^4\,c^5-4\,a^2\,b^6\,c^6+b^8\,c^7\right)}+\frac{\ln\left(\frac{a\,b^4\,d^4\,\left(a^6+2\,a^4\,b^2\,c-103\,a^2\,b^4\,c^2-44\,b^6\,c^3\right)}{4\,c^2\,{\left(b^2\,c-a^2\right)}^6}-\frac{b\,d^2\,\left(\frac{b^2\,d^2\,\left(a^2\,\sqrt{c+d\,x}+4\,a\,b\,c+3\,b^2\,c\,\sqrt{c+d\,x}\right)\,\left(4\,b^5\,c^4-a^5\,\sqrt{c^3}+20\,a^2\,b^3\,c^3+10\,a^3\,b^2\,c\,\sqrt{c^3}+15\,a\,b^4\,c^2\,\sqrt{c^3}\right)}{2\,c^3\,{\left(b^2\,c-a^2\right)}^4}-\frac{b^3\,d^2\,\sqrt{c+d\,x}\,\left(-a^4+19\,a^2\,b^2\,c+6\,b^4\,c^2\right)}{c\,{\left(b^2\,c-a^2\right)}^3}+\frac{a\,b^2\,d^2\,\left(7\,b^2\,c-a^2\right)}{2\,c\,{\left(b^2\,c-a^2\right)}^2}\right)\,\left(4\,b^5\,c^4-a^5\,\sqrt{c^3}+20\,a^2\,b^3\,c^3+10\,a^3\,b^2\,c\,\sqrt{c^3}+15\,a\,b^4\,c^2\,\sqrt{c^3}\right)}{4\,c^3\,{\left(b^2\,c-a^2\right)}^4}+\frac{a^2\,b^5\,d^4\,{\left(a^2+11\,c\,b^2\right)}^2\,\sqrt{c+d\,x}}{4\,c^2\,{\left(b^2\,c-a^2\right)}^6}\right)\,\left(4\,b^6\,c^4\,d^2+20\,a^2\,b^4\,c^3\,d^2-a^5\,b\,d^2\,\sqrt{c^3}+10\,a^3\,b^3\,c\,d^2\,\sqrt{c^3}+15\,a\,b^5\,c^2\,d^2\,\sqrt{c^3}\right)}{4\,\left(a^8\,c^3-4\,a^6\,b^2\,c^4+6\,a^4\,b^4\,c^5-4\,a^2\,b^6\,c^6+b^8\,c^7\right)}","Not used",1,"(((5*a^3*b^2*d^2 + 19*a*b^4*c*d^2)*(c + d*x))/(2*(b^2*c - a^2)*(a^4 + b^4*c^2 - 2*a^2*b^2*c)) + ((a^3*b^2*d^2 + 11*a*b^4*c*d^2)*(c + d*x)^2)/(2*c*(a^6 - b^6*c^3 - 3*a^4*b^2*c + 3*a^2*b^4*c^2)) - (a*(7*b^4*c^2*d^2 - a^4*d^2 + 6*a^2*b^2*c*d^2))/(2*(b^2*c - a^2)*(a^4 + b^4*c^2 - 2*a^2*b^2*c)) + (b*(a^2*d^2 + 2*b^2*c*d^2)*(c + d*x)^(3/2))/(2*c*(a^4 + b^4*c^2 - 2*a^2*b^2*c)) - (3*b^3*c*d^2*(c + d*x)^(1/2))/(2*(a^4 + b^4*c^2 - 2*a^2*b^2*c)))/(a*(c + d*x)^2 + b*(c + d*x)^(5/2) + a*c^2 - 2*a*c*(c + d*x) - 2*b*c*(c + d*x)^(3/2) + b*c^2*(c + d*x)^(1/2)) + log(a + b*(c + d*x)^(1/2))*((10*b^4*d^2)/(b^2*c - a^2)^3 - (12*b^6*c*d^2)/(b^2*c - a^2)^4) + (log((a*b^4*d^4*(a^6 - 44*b^6*c^3 + 2*a^4*b^2*c - 103*a^2*b^4*c^2))/(4*c^2*(b^2*c - a^2)^6) - (b*d^2*((b^2*d^2*(a^2*(c + d*x)^(1/2) + 4*a*b*c + 3*b^2*c*(c + d*x)^(1/2))*(a^5*(c^3)^(1/2) + 4*b^5*c^4 + 20*a^2*b^3*c^3 - 10*a^3*b^2*c*(c^3)^(1/2) - 15*a*b^4*c^2*(c^3)^(1/2)))/(2*c^3*(b^2*c - a^2)^4) - (b^3*d^2*(c + d*x)^(1/2)*(6*b^4*c^2 - a^4 + 19*a^2*b^2*c))/(c*(b^2*c - a^2)^3) + (a*b^2*d^2*(7*b^2*c - a^2))/(2*c*(b^2*c - a^2)^2))*(a^5*(c^3)^(1/2) + 4*b^5*c^4 + 20*a^2*b^3*c^3 - 10*a^3*b^2*c*(c^3)^(1/2) - 15*a*b^4*c^2*(c^3)^(1/2)))/(4*c^3*(b^2*c - a^2)^4) + (a^2*b^5*d^4*(11*b^2*c + a^2)^2*(c + d*x)^(1/2))/(4*c^2*(b^2*c - a^2)^6))*(4*b^6*c^4*d^2 + 20*a^2*b^4*c^3*d^2 + a^5*b*d^2*(c^3)^(1/2) - 10*a^3*b^3*c*d^2*(c^3)^(1/2) - 15*a*b^5*c^2*d^2*(c^3)^(1/2)))/(4*(a^8*c^3 + b^8*c^7 - 4*a^6*b^2*c^4 + 6*a^4*b^4*c^5 - 4*a^2*b^6*c^6)) + (log((a*b^4*d^4*(a^6 - 44*b^6*c^3 + 2*a^4*b^2*c - 103*a^2*b^4*c^2))/(4*c^2*(b^2*c - a^2)^6) - (b*d^2*((b^2*d^2*(a^2*(c + d*x)^(1/2) + 4*a*b*c + 3*b^2*c*(c + d*x)^(1/2))*(4*b^5*c^4 - a^5*(c^3)^(1/2) + 20*a^2*b^3*c^3 + 10*a^3*b^2*c*(c^3)^(1/2) + 15*a*b^4*c^2*(c^3)^(1/2)))/(2*c^3*(b^2*c - a^2)^4) - (b^3*d^2*(c + d*x)^(1/2)*(6*b^4*c^2 - a^4 + 19*a^2*b^2*c))/(c*(b^2*c - a^2)^3) + (a*b^2*d^2*(7*b^2*c - a^2))/(2*c*(b^2*c - a^2)^2))*(4*b^5*c^4 - a^5*(c^3)^(1/2) + 20*a^2*b^3*c^3 + 10*a^3*b^2*c*(c^3)^(1/2) + 15*a*b^4*c^2*(c^3)^(1/2)))/(4*c^3*(b^2*c - a^2)^4) + (a^2*b^5*d^4*(11*b^2*c + a^2)^2*(c + d*x)^(1/2))/(4*c^2*(b^2*c - a^2)^6))*(4*b^6*c^4*d^2 + 20*a^2*b^4*c^3*d^2 - a^5*b*d^2*(c^3)^(1/2) + 10*a^3*b^3*c*d^2*(c^3)^(1/2) + 15*a*b^5*c^2*d^2*(c^3)^(1/2)))/(4*(a^8*c^3 + b^8*c^7 - 4*a^6*b^2*c^4 + 6*a^4*b^4*c^5 - 4*a^2*b^6*c^6))","B"
646,0,-1,324,0.000000,"\text{Not used}","int(x^3/(a + b*(c + d*x)^(1/2))^(1/2),x)","\int \frac{x^3}{\sqrt{a+b\,\sqrt{c+d\,x}}} \,d x","Not used",1,"int(x^3/(a + b*(c + d*x)^(1/2))^(1/2), x)","F"
647,0,-1,222,0.000000,"\text{Not used}","int(x^2/(a + b*(c + d*x)^(1/2))^(1/2),x)","\int \frac{x^2}{\sqrt{a+b\,\sqrt{c+d\,x}}} \,d x","Not used",1,"int(x^2/(a + b*(c + d*x)^(1/2))^(1/2), x)","F"
648,0,-1,131,0.000000,"\text{Not used}","int(x/(a + b*(c + d*x)^(1/2))^(1/2),x)","\int \frac{x}{\sqrt{a+b\,\sqrt{c+d\,x}}} \,d x","Not used",1,"int(x/(a + b*(c + d*x)^(1/2))^(1/2), x)","F"
649,1,44,54,3.258234,"\text{Not used}","int(1/(a + b*(c + d*x)^(1/2))^(1/2),x)","\frac{4\,{\left(a+b\,\sqrt{c+d\,x}\right)}^{3/2}}{3\,b^2\,d}-\frac{4\,a\,\sqrt{a+b\,\sqrt{c+d\,x}}}{b^2\,d}","Not used",1,"(4*(a + b*(c + d*x)^(1/2))^(3/2))/(3*b^2*d) - (4*a*(a + b*(c + d*x)^(1/2))^(1/2))/(b^2*d)","B"
650,0,-1,97,0.000000,"\text{Not used}","int(1/(x*(a + b*(c + d*x)^(1/2))^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+b\,\sqrt{c+d\,x}}} \,d x","Not used",1,"int(1/(x*(a + b*(c + d*x)^(1/2))^(1/2)), x)","F"
651,0,-1,163,0.000000,"\text{Not used}","int(1/(x^2*(a + b*(c + d*x)^(1/2))^(1/2)),x)","\int \frac{1}{x^2\,\sqrt{a+b\,\sqrt{c+d\,x}}} \,d x","Not used",1,"int(1/(x^2*(a + b*(c + d*x)^(1/2))^(1/2)), x)","F"
652,0,-1,261,0.000000,"\text{Not used}","int(1/(x^3*(a + b*(c + d*x)^(1/2))^(1/2)),x)","\int \frac{1}{x^3\,\sqrt{a+b\,\sqrt{c+d\,x}}} \,d x","Not used",1,"int(1/(x^3*(a + b*(c + d*x)^(1/2))^(1/2)), x)","F"
653,0,-1,350,0.000000,"\text{Not used}","int(x^3*(a + b*(c + d*x)^(1/2))^p,x)","\int x^3\,{\left(a+b\,\sqrt{c+d\,x}\right)}^p \,d x","Not used",1,"int(x^3*(a + b*(c + d*x)^(1/2))^p, x)","F"
654,0,-1,242,0.000000,"\text{Not used}","int(x^2*(a + b*(c + d*x)^(1/2))^p,x)","\int x^2\,{\left(a+b\,\sqrt{c+d\,x}\right)}^p \,d x","Not used",1,"int(x^2*(a + b*(c + d*x)^(1/2))^p, x)","F"
655,0,-1,145,0.000000,"\text{Not used}","int(x*(a + b*(c + d*x)^(1/2))^p,x)","\int x\,{\left(a+b\,\sqrt{c+d\,x}\right)}^p \,d x","Not used",1,"int(x*(a + b*(c + d*x)^(1/2))^p, x)","F"
656,1,146,62,3.583104,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^p,x)","\left\{\begin{array}{cl} -\frac{2\,a\,\ln\left(a+b\,\sqrt{c+d\,x}\right)-2\,b\,\sqrt{c+d\,x}}{b^2\,d} & \text{\ if\ \ }p=-1\\ \frac{2\,\left(\ln\left(a+b\,\sqrt{c+d\,x}\right)+\frac{a}{a+b\,\sqrt{c+d\,x}}\right)}{b^2\,d} & \text{\ if\ \ }p=-2\\ \frac{4\,{\left(a+b\,\sqrt{c+d\,x}\right)}^{p+2}}{b^2\,d\,\left(2\,p+4\right)}-\frac{4\,a\,{\left(a+b\,\sqrt{c+d\,x}\right)}^{p+1}}{b^2\,d\,\left(2\,p+2\right)} & \text{\ if\ \ }p\neq -1\wedge p\neq -2 \end{array}\right.","Not used",1,"piecewise(p == -1, -(2*a*log(a + b*(c + d*x)^(1/2)) - 2*b*(c + d*x)^(1/2))/(b^2*d), p == -2, (2*(log(a + b*(c + d*x)^(1/2)) + a/(a + b*(c + d*x)^(1/2))))/(b^2*d), p ~= -1 & p ~= -2, (4*(a + b*(c + d*x)^(1/2))^(p + 2))/(b^2*d*(2*p + 4)) - (4*a*(a + b*(c + d*x)^(1/2))^(p + 1))/(b^2*d*(2*p + 2)))","B"
657,0,-1,139,0.000000,"\text{Not used}","int((a + b*(c + d*x)^(1/2))^p/x,x)","\int \frac{{\left(a+b\,\sqrt{c+d\,x}\right)}^p}{x} \,d x","Not used",1,"int((a + b*(c + d*x)^(1/2))^p/x, x)","F"
658,0,-1,93,0.000000,"\text{Not used}","int((a + b*(c*x)^n)^(5/2)/x,x)","\int \frac{{\left(a+b\,{\left(c\,x\right)}^n\right)}^{5/2}}{x} \,d x","Not used",1,"int((a + b*(c*x)^n)^(5/2)/x, x)","F"
659,0,-1,70,0.000000,"\text{Not used}","int((a + b*(c*x)^n)^(3/2)/x,x)","\int \frac{{\left(a+b\,{\left(c\,x\right)}^n\right)}^{3/2}}{x} \,d x","Not used",1,"int((a + b*(c*x)^n)^(3/2)/x, x)","F"
660,0,-1,49,0.000000,"\text{Not used}","int((a + b*(c*x)^n)^(1/2)/x,x)","\int \frac{\sqrt{a+b\,{\left(c\,x\right)}^n}}{x} \,d x","Not used",1,"int((a + b*(c*x)^n)^(1/2)/x, x)","F"
661,0,-1,30,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*x)^n)^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+b\,{\left(c\,x\right)}^n}} \,d x","Not used",1,"int(1/(x*(a + b*(c*x)^n)^(1/2)), x)","F"
662,0,-1,52,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*x)^n)^(3/2)),x)","\int \frac{1}{x\,{\left(a+b\,{\left(c\,x\right)}^n\right)}^{3/2}} \,d x","Not used",1,"int(1/(x*(a + b*(c*x)^n)^(3/2)), x)","F"
663,0,-1,75,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*x)^n)^(5/2)),x)","\int \frac{1}{x\,{\left(a+b\,{\left(c\,x\right)}^n\right)}^{5/2}} \,d x","Not used",1,"int(1/(x*(a + b*(c*x)^n)^(5/2)), x)","F"
664,0,-1,101,0.000000,"\text{Not used}","int((b*(c*x)^n - a)^(5/2)/x,x)","\int \frac{{\left(b\,{\left(c\,x\right)}^n-a\right)}^{5/2}}{x} \,d x","Not used",1,"int((b*(c*x)^n - a)^(5/2)/x, x)","F"
665,0,-1,76,0.000000,"\text{Not used}","int((b*(c*x)^n - a)^(3/2)/x,x)","\int \frac{{\left(b\,{\left(c\,x\right)}^n-a\right)}^{3/2}}{x} \,d x","Not used",1,"int((b*(c*x)^n - a)^(3/2)/x, x)","F"
666,0,-1,53,0.000000,"\text{Not used}","int((b*(c*x)^n - a)^(1/2)/x,x)","\int \frac{\sqrt{b\,{\left(c\,x\right)}^n-a}}{x} \,d x","Not used",1,"int((b*(c*x)^n - a)^(1/2)/x, x)","F"
667,0,-1,32,0.000000,"\text{Not used}","int(1/(x*(b*(c*x)^n - a)^(1/2)),x)","\int \frac{1}{x\,\sqrt{b\,{\left(c\,x\right)}^n-a}} \,d x","Not used",1,"int(1/(x*(b*(c*x)^n - a)^(1/2)), x)","F"
668,0,-1,56,0.000000,"\text{Not used}","int(1/(x*(b*(c*x)^n - a)^(3/2)),x)","\int \frac{1}{x\,{\left(b\,{\left(c\,x\right)}^n-a\right)}^{3/2}} \,d x","Not used",1,"int(1/(x*(b*(c*x)^n - a)^(3/2)), x)","F"
669,0,-1,81,0.000000,"\text{Not used}","int(1/(x*(b*(c*x)^n - a)^(5/2)),x)","\int \frac{1}{x\,{\left(b\,{\left(c\,x\right)}^n-a\right)}^{5/2}} \,d x","Not used",1,"int(1/(x*(b*(c*x)^n - a)^(5/2)), x)","F"
670,1,17,23,3.108079,"\text{Not used}","int(1/(x*(a + b*x)^(1/2)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"-(2*atanh((a + b*x)^(1/2)/a^(1/2)))/a^(1/2)","B"
671,0,-1,30,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*x)^m)^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+b\,{\left(c\,x\right)}^m}} \,d x","Not used",1,"int(1/(x*(a + b*(c*x)^m)^(1/2)), x)","F"
672,0,-1,37,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*(d*x)^m)^n)^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+b\,{\left(c\,{\left(d\,x\right)}^m\right)}^n}} \,d x","Not used",1,"int(1/(x*(a + b*(c*(d*x)^m)^n)^(1/2)), x)","F"
673,0,-1,44,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*(d*(e*x)^m)^n)^p)^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+b\,{\left(c\,{\left(d\,{\left(e\,x\right)}^m\right)}^n\right)}^p}} \,d x","Not used",1,"int(1/(x*(a + b*(c*(d*(e*x)^m)^n)^p)^(1/2)), x)","F"
674,0,-1,51,0.000000,"\text{Not used}","int(1/(x*(a + b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2)),x)","\int \frac{1}{x\,\sqrt{a+b\,{\left(c\,{\left(d\,{\left(e\,{\left(f\,x\right)}^m\right)}^n\right)}^p\right)}^q}} \,d x","Not used",1,"int(1/(x*(a + b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2)), x)","F"
675,1,54,76,3.501656,"\text{Not used}","int(((1/x^2 - 1)^(1/2)*(x^2 - 1)^3)/x,x)","\sqrt{\frac{1}{x^2}-1}-\frac{35\,\mathrm{atan}\left(\sqrt{\frac{1}{x^2}-1}\right)}{16}+\frac{19\,x^6\,\sqrt{\frac{1}{x^2}-1}}{16}+\frac{17\,x^6\,{\left(\frac{1}{x^2}-1\right)}^{3/2}}{6}+\frac{29\,x^6\,{\left(\frac{1}{x^2}-1\right)}^{5/2}}{16}","Not used",1,"(1/x^2 - 1)^(1/2) - (35*atan((1/x^2 - 1)^(1/2)))/16 + (19*x^6*(1/x^2 - 1)^(1/2))/16 + (17*x^6*(1/x^2 - 1)^(3/2))/6 + (29*x^6*(1/x^2 - 1)^(5/2))/16","B"
676,1,44,60,3.355307,"\text{Not used}","int(((1/x^2 - 1)^(1/2)*(x^2 - 1)^2)/x,x)","\frac{15\,\mathrm{atan}\left(\sqrt{\frac{1}{x^2}-1}\right)}{8}-\sqrt{\frac{1}{x^2}-1}-\frac{7\,x^4\,\sqrt{\frac{1}{x^2}-1}}{8}-\frac{9\,x^4\,{\left(\frac{1}{x^2}-1\right)}^{3/2}}{8}","Not used",1,"(15*atan((1/x^2 - 1)^(1/2)))/8 - (1/x^2 - 1)^(1/2) - (7*x^4*(1/x^2 - 1)^(1/2))/8 - (9*x^4*(1/x^2 - 1)^(3/2))/8","B"
677,1,30,44,3.574578,"\text{Not used}","int(((1/x^2 - 1)^(1/2)*(x^2 - 1))/x,x)","\sqrt{\frac{1}{x^2}-1}-\frac{3\,\mathrm{atan}\left(\sqrt{\frac{1}{x^2}-1}\right)}{2}+\frac{x^2\,\sqrt{\frac{1}{x^2}-1}}{2}","Not used",1,"(1/x^2 - 1)^(1/2) - (3*atan((1/x^2 - 1)^(1/2)))/2 + (x^2*(1/x^2 - 1)^(1/2))/2","B"
678,1,14,9,3.176372,"\text{Not used}","int((1/x^2 - 1)^(1/2)/(x*(x^2 - 1)),x)","\frac{\sqrt{1-x^2}}{\left|x\right|}","Not used",1,"(1 - x^2)^(1/2)/abs(x)","B"
679,1,25,21,3.107457,"\text{Not used}","int((1/x^2 - 1)^(1/2)/(x*(x^2 - 1)^2),x)","\frac{x\,\sqrt{\frac{1}{x^2}-1}\,\left(2\,x^2-1\right)}{x-x^3}","Not used",1,"(x*(1/x^2 - 1)^(1/2)*(2*x^2 - 1))/(x - x^3)","B"
680,1,28,34,3.093372,"\text{Not used}","int((1/x^2 - 1)^(1/2)/(x*(x^2 - 1)^3),x)","\frac{\sqrt{\frac{1}{x^2}-1}\,\left(8\,x^4-12\,x^2+3\right)}{3\,{\left(x^2-1\right)}^2}","Not used",1,"((1/x^2 - 1)^(1/2)*(8*x^4 - 12*x^2 + 3))/(3*(x^2 - 1)^2)","B"
681,1,18,9,3.107896,"\text{Not used}","int((x*(1/x^2 + 1)^(1/2))/(x^2 + 1)^2,x)","\frac{x^2\,\sqrt{\frac{1}{x^2}+1}}{x^2+1}","Not used",1,"(x^2*(1/x^2 + 1)^(1/2))/(x^2 + 1)","B"
682,1,18,9,3.096592,"\text{Not used}","int(1/(x*(1/x^2 + 1)^(1/2)*(x^2 + 1)),x)","\frac{x^2\,\sqrt{\frac{1}{x^2}+1}}{x^2+1}","Not used",1,"(x^2*(1/x^2 + 1)^(1/2))/(x^2 + 1)","B"
683,1,26,18,3.381238,"\text{Not used}","int(x/(a + b*x^2 + (a + b*x^2)^(1/2)),x)","\frac{\mathrm{atanh}\left(\sqrt{b\,x^2+a}\right)+\frac{\ln\left(b\,x^2+a-1\right)}{2}}{b}","Not used",1,"(atanh((a + b*x^2)^(1/2)) + log(a + b*x^2 - 1)/2)/b","B"
684,1,10,16,3.344628,"\text{Not used}","int(-x/((x^2)^(1/3) - x^2),x)","\frac{3\,\ln\left({\left(x^2\right)}^{2/3}-1\right)}{4}","Not used",1,"(3*log((x^2)^(2/3) - 1))/4","B"
685,1,26,44,0.089987,"\text{Not used}","int(x*(x^2 + 1)^3*(2*x^2 + x^4 + 2)^(1/2),x)","\frac{{\left(x^4+2\,x^2+2\right)}^{3/2}\,\left(3\,x^4+6\,x^2+1\right)}{30}","Not used",1,"((2*x^2 + x^4 + 2)^(3/2)*(6*x^2 + 3*x^4 + 1))/30","B"
686,1,124,121,3.273207,"\text{Not used}","int(x^5*(1 - x^3)^(1/2)*(x^9 + 1)^2,x)","\frac{84374\,x^6\,\sqrt{1-x^3}}{765765}-\frac{173014\,x^3\,\sqrt{1-x^3}}{2297295}-\frac{8864\,x^9\,\sqrt{1-x^3}}{459459}-\frac{1108\,x^{12}\,\sqrt{1-x^3}}{65637}+\frac{1436\,x^{15}\,\sqrt{1-x^3}}{12155}-\frac{28\,x^{18}\,\sqrt{1-x^3}}{9945}-\frac{2\,x^{21}\,\sqrt{1-x^3}}{765}+\frac{2\,x^{24}\,\sqrt{1-x^3}}{51}-\frac{346028\,\sqrt{1-x^3}}{2297295}","Not used",1,"(84374*x^6*(1 - x^3)^(1/2))/765765 - (173014*x^3*(1 - x^3)^(1/2))/2297295 - (8864*x^9*(1 - x^3)^(1/2))/459459 - (1108*x^12*(1 - x^3)^(1/2))/65637 + (1436*x^15*(1 - x^3)^(1/2))/12155 - (28*x^18*(1 - x^3)^(1/2))/9945 - (2*x^21*(1 - x^3)^(1/2))/765 + (2*x^24*(1 - x^3)^(1/2))/51 - (346028*(1 - x^3)^(1/2))/2297295","B"
687,1,42,50,3.760856,"\text{Not used}","int(x/(a + b*x^2)^(3/2) + x/((x^2 + 1)*(a + b*x^2)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}-\frac{1}{b\,\sqrt{b\,x^2+a}}","Not used",1,"- atanh((a + b*x^2)^(1/2)/(a - b)^(1/2))/(a - b)^(1/2) - 1/(b*(a + b*x^2)^(1/2))","B"
688,1,96,50,4.515672,"\text{Not used}","int((x*(a + b*x^2 + x^2 + 1))/((x^2 + 1)*(a + b*x^2)^(3/2)),x)","\frac{1}{\sqrt{b\,x^2+a}\,\left(a-b\right)}-\frac{a}{\sqrt{b\,x^2+a}\,\left(a\,b-b^2\right)}-\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a-b}}\right)}{{\left(a-b\right)}^{3/2}}+\frac{b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a-b}}\right)}{{\left(a-b\right)}^{3/2}}","Not used",1,"1/((a + b*x^2)^(1/2)*(a - b)) - a/((a + b*x^2)^(1/2)*(a*b - b^2)) - (a*atanh((a + b*x^2)^(1/2)/(a - b)^(1/2)))/(a - b)^(3/2) + (b*atanh((a + b*x^2)^(1/2)/(a - b)^(1/2)))/(a - b)^(3/2)","B"
689,1,56,68,3.687784,"\text{Not used}","int(x/(a + b*x^2)^(3/2) + x/(a + b*x^2)^(5/2) + x/((x^2 + 1)*(a + b*x^2)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}-\frac{1}{b\,\sqrt{b\,x^2+a}}-\frac{1}{3\,b\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"- atanh((a + b*x^2)^(1/2)/(a - b)^(1/2))/(a - b)^(1/2) - 1/(b*(a + b*x^2)^(1/2)) - 1/(3*b*(a + b*x^2)^(3/2))","B"
690,1,50,68,3.899418,"\text{Not used}","int((x*(a + a*x^2 + b*x^2 + b*x^4 + a^2 + x^2 + b^2*x^4 + 2*a*b*x^2 + 1))/((x^2 + 1)*(a + b*x^2)^(5/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}-\frac{b\,x^2+a+\frac{1}{3}}{b\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"- atanh((a + b*x^2)^(1/2)/(a - b)^(1/2))/(a - b)^(1/2) - (a + b*x^2 + 1/3)/(b*(a + b*x^2)^(3/2))","B"
691,1,39,34,3.329359,"\text{Not used}","int(1/(x + x^(1/2))^(1/2),x)","\frac{2\,\sqrt{x}\,\left(\sqrt{x}+1\right)+x^{1/4}\,\mathrm{asin}\left(x^{1/4}\,1{}\mathrm{i}\right)\,\sqrt{\sqrt{x}+1}\,2{}\mathrm{i}}{\sqrt{x+\sqrt{x}}}","Not used",1,"(2*x^(1/2)*(x^(1/2) + 1) + x^(1/4)*asin(x^(1/4)*1i)*(x^(1/2) + 1)^(1/2)*2i)/(x + x^(1/2))^(1/2)","B"
692,1,27,74,3.161580,"\text{Not used}","int((x + x^(1/2))^(1/2),x)","\frac{4\,x\,\sqrt{x+\sqrt{x}}\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{2},\frac{5}{2};\ \frac{7}{2};\ -\sqrt{x}\right)}{5\,\sqrt{\sqrt{x}+1}}","Not used",1,"(4*x*(x + x^(1/2))^(1/2)*hypergeom([-1/2, 5/2], 7/2, -x^(1/2)))/(5*(x^(1/2) + 1)^(1/2))","B"
693,1,13,19,0.029903,"\text{Not used}","int((-x)^(1/2)*(x + (-x)^(1/2)),x)","\frac{2\,{\left(-x\right)}^{5/2}}{5}-\frac{x^2}{2}","Not used",1,"(2*(-x)^(5/2))/5 - x^2/2","B"
694,1,162,54,0.094581,"\text{Not used}","int((x^(1/4) + 5)/(x - 6),x)","\ln\left(11520\,x^{1/4}-\left(6^{1/4}+5\right)\,\left(2304\,x^{1/4}-2304\,6^{1/4}+11520\right)+57600\right)\,\left(6^{1/4}+5\right)-\ln\left(\left(6^{1/4}-5\right)\,\left(2304\,6^{1/4}+2304\,x^{1/4}+11520\right)+11520\,x^{1/4}+57600\right)\,\left(6^{1/4}-5\right)-\ln\left(11520\,x^{1/4}+\left(\sqrt{-\sqrt{6}}-5\right)\,\left(2304\,\sqrt{-\sqrt{6}}+2304\,x^{1/4}+11520\right)+57600\right)\,\left(\sqrt{-\sqrt{6}}-5\right)+\ln\left(11520\,x^{1/4}-\left(\sqrt{-\sqrt{6}}+5\right)\,\left(2304\,x^{1/4}-2304\,\sqrt{-\sqrt{6}}+11520\right)+57600\right)\,\left(\sqrt{-\sqrt{6}}+5\right)+4\,x^{1/4}","Not used",1,"log(11520*x^(1/4) - (6^(1/4) + 5)*(2304*x^(1/4) - 2304*6^(1/4) + 11520) + 57600)*(6^(1/4) + 5) - log((6^(1/4) - 5)*(2304*6^(1/4) + 2304*x^(1/4) + 11520) + 11520*x^(1/4) + 57600)*(6^(1/4) - 5) - log(11520*x^(1/4) + ((-6^(1/2))^(1/2) - 5)*(2304*(-6^(1/2))^(1/2) + 2304*x^(1/4) + 11520) + 57600)*((-6^(1/2))^(1/2) - 5) + log(11520*x^(1/4) - ((-6^(1/2))^(1/2) + 5)*(2304*x^(1/4) - 2304*(-6^(1/2))^(1/2) + 11520) + 57600)*((-6^(1/2))^(1/2) + 5) + 4*x^(1/4)","B"
695,1,12,14,0.188394,"\text{Not used}","int(1/((4 - x)^(1/2) - x + 4),x)","-2\,\ln\left(\sqrt{4-x}+1\right)","Not used",1,"-2*log((4 - x)^(1/2) + 1)","B"
696,1,71,61,3.238395,"\text{Not used}","int(1/(x - (x + 2)^(1/2) + 1),x)","\ln\left(2\,\sqrt{x+2}-\left(\frac{\sqrt{5}}{5}+1\right)\,\left(2\,\sqrt{x+2}-1\right)\right)\,\left(\frac{\sqrt{5}}{5}+1\right)-\ln\left(2\,\sqrt{x+2}+\left(\frac{\sqrt{5}}{5}-1\right)\,\left(2\,\sqrt{x+2}-1\right)\right)\,\left(\frac{\sqrt{5}}{5}-1\right)","Not used",1,"log(2*(x + 2)^(1/2) - (5^(1/2)/5 + 1)*(2*(x + 2)^(1/2) - 1))*(5^(1/2)/5 + 1) - log(2*(x + 2)^(1/2) + (5^(1/2)/5 - 1)*(2*(x + 2)^(1/2) - 1))*(5^(1/2)/5 - 1)","B"
697,1,32,37,0.066019,"\text{Not used}","int(1/(x + (x + 1)^(1/2) + 4),x)","\ln\left(x+\sqrt{x+1}+4\right)-\frac{2\,\sqrt{11}\,\mathrm{atan}\left(\frac{\sqrt{11}}{11}+\frac{2\,\sqrt{11}\,\sqrt{x+1}}{11}\right)}{11}","Not used",1,"log(x + (x + 1)^(1/2) + 4) - (2*11^(1/2)*atan(11^(1/2)/11 + (2*11^(1/2)*(x + 1)^(1/2))/11))/11","B"
698,1,71,61,0.118658,"\text{Not used}","int(1/(x - (x + 1)^(1/2)),x)","\ln\left(2\,\sqrt{x+1}-\left(\frac{\sqrt{5}}{5}+1\right)\,\left(2\,\sqrt{x+1}-1\right)\right)\,\left(\frac{\sqrt{5}}{5}+1\right)-\ln\left(2\,\sqrt{x+1}+\left(\frac{\sqrt{5}}{5}-1\right)\,\left(2\,\sqrt{x+1}-1\right)\right)\,\left(\frac{\sqrt{5}}{5}-1\right)","Not used",1,"log(2*(x + 1)^(1/2) - (5^(1/2)/5 + 1)*(2*(x + 1)^(1/2) - 1))*(5^(1/2)/5 + 1) - log(2*(x + 1)^(1/2) + (5^(1/2)/5 - 1)*(2*(x + 1)^(1/2) - 1))*(5^(1/2)/5 - 1)","B"
699,1,25,31,3.082652,"\text{Not used}","int(1/(x - (x + 2)^(1/2)),x)","\frac{2\,\ln\left(\frac{2\,\sqrt{x+2}}{3}+\frac{2}{3}\right)}{3}+\frac{4\,\ln\left(\frac{4}{3}-\frac{2\,\sqrt{x+2}}{3}\right)}{3}","Not used",1,"(2*log((2*(x + 2)^(1/2))/3 + 2/3))/3 + (4*log(4/3 - (2*(x + 2)^(1/2))/3))/3","B"
700,1,79,65,3.158046,"\text{Not used}","int(1/(x - (1 - x)^(1/2)),x)","\ln\left(2\,\sqrt{1-x}-\left(\frac{\sqrt{5}}{5}+1\right)\,\left(2\,\sqrt{1-x}+1\right)\right)\,\left(\frac{\sqrt{5}}{5}+1\right)-\ln\left(2\,\sqrt{1-x}+\left(\frac{\sqrt{5}}{5}-1\right)\,\left(2\,\sqrt{1-x}+1\right)\right)\,\left(\frac{\sqrt{5}}{5}-1\right)","Not used",1,"log(2*(1 - x)^(1/2) - (5^(1/2)/5 + 1)*(2*(1 - x)^(1/2) + 1))*(5^(1/2)/5 + 1) - log(2*(1 - x)^(1/2) + (5^(1/2)/5 - 1)*(2*(1 - x)^(1/2) + 1))*(5^(1/2)/5 - 1)","B"
701,0,-1,62,0.000000,"\text{Not used}","int((x + x^(1/2) + 1)^(1/2),x)","\int \sqrt{x+\sqrt{x}+1} \,d x","Not used",1,"int((x + x^(1/2) + 1)^(1/2), x)","F"
702,0,-1,75,0.000000,"\text{Not used}","int((x + (x + 1)^(1/2) + 1)^(1/2),x)","\int \sqrt{x+\sqrt{x+1}+1} \,d x","Not used",1,"int((x + (x + 1)^(1/2) + 1)^(1/2), x)","F"
703,0,-1,68,0.000000,"\text{Not used}","int((x + (x - 1)^(1/2))^(1/2),x)","\int \sqrt{x+\sqrt{x-1}} \,d x","Not used",1,"int((x + (x - 1)^(1/2))^(1/2), x)","F"
704,0,-1,80,0.000000,"\text{Not used}","int((2*x + (2*x - 1)^(1/2))^(1/2),x)","\int \sqrt{2\,x+\sqrt{2\,x-1}} \,d x","Not used",1,"int((2*x + (2*x - 1)^(1/2))^(1/2), x)","F"
705,0,-1,109,0.000000,"\text{Not used}","int((3*x + (8*x - 7)^(1/2))^(1/2),x)","\int \sqrt{3\,x+\sqrt{8\,x-7}} \,d x","Not used",1,"int((3*x + (8*x - 7)^(1/2))^(1/2), x)","F"
706,0,-1,47,0.000000,"\text{Not used}","int(1/(x + (x + 1)^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{x+\sqrt{x+1}}} \,d x","Not used",1,"int(1/(x + (x + 1)^(1/2))^(1/2), x)","F"
707,1,102,67,3.090371,"\text{Not used}","int((x + 1)/(x + (6*x - 9)^(1/2) + 4),x)","x+3\,\ln\left(\left(6\,\sqrt{6\,x-9}+\left(-3+\sqrt{6}\,2{}\mathrm{i}\right)\,\left(2\,\sqrt{6\,x-9}+6\right)+66\right)\,\left(6\,\sqrt{6\,x-9}-\left(3+\sqrt{6}\,2{}\mathrm{i}\right)\,\left(2\,\sqrt{6\,x-9}+6\right)+66\right)\right)+4\,\sqrt{6}\,\mathrm{atan}\left(\frac{\sqrt{6}\,\sqrt{6\,x-9}}{12}+\frac{\sqrt{6}}{4}\right)-2\,\sqrt{6\,x-9}","Not used",1,"x + 3*log((6*(6*x - 9)^(1/2) + (6^(1/2)*2i - 3)*(2*(6*x - 9)^(1/2) + 6) + 66)*(6*(6*x - 9)^(1/2) - (6^(1/2)*2i + 3)*(2*(6*x - 9)^(1/2) + 6) + 66)) + 4*6^(1/2)*atan((6^(1/2)*(6*x - 9)^(1/2))/12 + 6^(1/2)/4) - 2*(6*x - 9)^(1/2)","B"
708,1,118,71,0.033390,"\text{Not used}","int(-(x - 12)/(x + (6*x - 9)^(1/2) + 4),x)","2\,\sqrt{6\,x-9}+10\,\ln\left(\left(\left(2\,\sqrt{6\,x-9}+6\right)\,\left(-10+\frac{\sqrt{2}\,\sqrt{3}\,21{}\mathrm{i}}{4}\right)+20\,\sqrt{6\,x-9}-66\right)\,\left(\left(2\,\sqrt{6\,x-9}+6\right)\,\left(10+\frac{\sqrt{2}\,\sqrt{3}\,21{}\mathrm{i}}{4}\right)-20\,\sqrt{6\,x-9}+66\right)\right)-x-\frac{21\,\sqrt{2}\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{3}}{4}+\frac{\sqrt{2}\,\sqrt{3}\,\sqrt{6\,x-9}}{12}\right)}{2}","Not used",1,"10*log(((2*(6*x - 9)^(1/2) + 6)*((2^(1/2)*3^(1/2)*21i)/4 - 10) + 20*(6*x - 9)^(1/2) - 66)*((2*(6*x - 9)^(1/2) + 6)*((2^(1/2)*3^(1/2)*21i)/4 + 10) - 20*(6*x - 9)^(1/2) + 66)) - x + 2*(6*x - 9)^(1/2) - (21*2^(1/2)*3^(1/2)*atan((2^(1/2)*3^(1/2))/4 + (2^(1/2)*3^(1/2)*(6*x - 9)^(1/2))/12))/2","B"
709,1,43,52,3.170443,"\text{Not used}","int((x^3 - 1)/(x^(1/2)*(x^2 + 1)),x)","\frac{2\,x^{3/2}}{3}-\frac{\sqrt{2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{x}}{2}+\frac{\sqrt{2}\,x^{3/2}}{2}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{x}}{2}\right)\right)}{2}","Not used",1,"(2*x^(3/2))/3 - (2^(1/2)*(2*atan((2^(1/2)*x^(1/2))/2 + (2^(1/2)*x^(3/2))/2) + 2*atan((2^(1/2)*x^(1/2))/2)))/2","B"
710,0,-1,20,0.000000,"\text{Not used}","int(1/(2*(x - (x - 1)^(1/2))^(1/2)*(x - 1)^(1/2)),x)","\int \frac{1}{2\,\sqrt{x-\sqrt{x-1}}\,\sqrt{x-1}} \,d x","Not used",1,"int(1/(2*(x - (x - 1)^(1/2))^(1/2)*(x - 1)^(1/2)), x)","F"
711,1,53,43,3.105116,"\text{Not used}","int(-(x^(7/2) + 1)/(x^2 - 1),x)","-\ln\left(10\,\sqrt{x}-10\right)-2\,\sqrt{x}-\frac{2\,x^{5/2}}{5}+\ln\left(1+\sqrt{x}\,\left(-3-\mathrm{i}\right)-3{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)+\ln\left(1+\sqrt{x}\,\left(-3+1{}\mathrm{i}\right)+3{}\mathrm{i}\right)\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)","Not used",1,"log((1 - 3i) - x^(1/2)*(3 + 1i))*(1/2 + 1i/2) - log(10*x^(1/2) - 10) + log((1 + 3i) - x^(1/2)*(3 - 1i))*(1/2 - 1i/2) - 2*x^(1/2) - (2*x^(5/2))/5","B"
712,1,88,116,0.127010,"\text{Not used}","int((2*x + 4)/((2*x - 1)^(1/2) + (2*x - 1)^(1/3)),x)","6\,\sqrt{2\,x-1}-18\,\ln\left({\left(2\,x-1\right)}^{1/6}+1\right)-x-9\,{\left(2\,x-1\right)}^{1/3}-\frac{3\,{\left(2\,x-1\right)}^{2/3}}{4}+\frac{{\left(2\,x-1\right)}^{3/2}}{3}+18\,{\left(2\,x-1\right)}^{1/6}-\frac{3\,{\left(2\,x-1\right)}^{4/3}}{8}+\frac{3\,{\left(2\,x-1\right)}^{5/6}}{5}+\frac{3\,{\left(2\,x-1\right)}^{7/6}}{7}","Not used",1,"6*(2*x - 1)^(1/2) - 18*log((2*x - 1)^(1/6) + 1) - x - 9*(2*x - 1)^(1/3) - (3*(2*x - 1)^(2/3))/4 + (2*x - 1)^(3/2)/3 + 18*(2*x - 1)^(1/6) - (3*(2*x - 1)^(4/3))/8 + (3*(2*x - 1)^(5/6))/5 + (3*(2*x - 1)^(7/6))/7","B"
713,0,-1,83,0.000000,"\text{Not used}","int(1/((x^(1/2) + 1)^(1/2) + 2)^(1/2),x)","\int \frac{1}{\sqrt{\sqrt{\sqrt{x}+1}+2}} \,d x","Not used",1,"int(1/((x^(1/2) + 1)^(1/2) + 2)^(1/2), x)","F"
714,0,-1,64,0.000000,"\text{Not used}","int(((x^(1/2) + 4)^(1/2) + 2)^(1/2),x)","\int \sqrt{\sqrt{\sqrt{x}+4}+2} \,d x","Not used",1,"int(((x^(1/2) + 4)^(1/2) + 2)^(1/2), x)","F"
715,0,-1,82,0.000000,"\text{Not used}","int((2 - ((5*x - 9)^(1/2) + 4)^(1/2))^(1/2),x)","\int \sqrt{2-\sqrt{\sqrt{5\,x-9}+4}} \,d x","Not used",1,"int((2 - ((5*x - 9)^(1/2) + 4)^(1/2))^(1/2), x)","F"
716,0,-1,83,0.000000,"\text{Not used}","int(1/((x^(1/2) + 1)^(1/2) + 2)^(1/2),x)","\int \frac{1}{\sqrt{\sqrt{\sqrt{x}+1}+2}} \,d x","Not used",1,"int(1/((x^(1/2) + 1)^(1/2) + 2)^(1/2), x)","F"
717,0,-1,190,0.000000,"\text{Not used}","int((((x^(1/2) + 1)^(1/2) + 1)^(1/2) + 1)^(1/2),x)","\int \sqrt{\sqrt{\sqrt{\sqrt{x}+1}+1}+1} \,d x","Not used",1,"int((((x^(1/2) + 1)^(1/2) + 1)^(1/2) + 1)^(1/2), x)","F"
718,0,-1,233,0.000000,"\text{Not used}","int((((2*x^(1/2) - 1)^(1/2) + 3)^(1/2) + 2)^(1/2),x)","\int \sqrt{\sqrt{\sqrt{2\,\sqrt{x}-1}+3}+2} \,d x","Not used",1,"int((((2*x^(1/2) - 1)^(1/2) + 3)^(1/2) + 2)^(1/2), x)","F"
719,0,-1,160,0.000000,"\text{Not used}","int(x*(((x - 1)^(1/2) + 1)^(1/2) + 1)^(1/2),x)","\int x\,\sqrt{\sqrt{\sqrt{x-1}+1}+1} \,d x","Not used",1,"int(x*(((x - 1)^(1/2) + 1)^(1/2) + 1)^(1/2), x)","F"
720,0,-1,20,0.000000,"\text{Not used}","int(1/((x - (x - 1)^(1/2))^(1/2)*(x - 1)^(1/2)),x)","\int \frac{1}{\sqrt{x-\sqrt{x-1}}\,\sqrt{x-1}} \,d x","Not used",1,"int(1/((x - (x - 1)^(1/2))^(1/2)*(x - 1)^(1/2)), x)","F"
721,0,-1,44,0.000000,"\text{Not used}","int(1/(x + (2*x - 1)^(1/2) + 1)^(1/2),x)","\int \frac{1}{\sqrt{x+\sqrt{2\,x-1}+1}} \,d x","Not used",1,"int(1/(x + (2*x - 1)^(1/2) + 1)^(1/2), x)","F"
722,1,50,54,3.099770,"\text{Not used}","int((q + p*x)/((f + (b + a*x)^(1/2))*(b + a*x)^(1/2)),x)","\frac{\ln\left(f+\sqrt{b+a\,x}\right)\,\left(2\,p\,f^2+2\,a\,q-2\,b\,p\right)}{a^2}+\frac{p\,x}{a}-\frac{2\,f\,p\,\sqrt{b+a\,x}}{a^2}","Not used",1,"(log(f + (b + a*x)^(1/2))*(2*a*q - 2*b*p + 2*f^2*p))/a^2 + (p*x)/a - (2*f*p*(b + a*x)^(1/2))/a^2","B"
723,0,-1,70,0.000000,"\text{Not used}","int((1 - x^(1/2) - x)^(1/2),x)","\int \sqrt{1-\sqrt{x}-x} \,d x","Not used",1,"int((1 - x^(1/2) - x)^(1/2), x)","F"
724,1,15,19,3.043364,"\text{Not used}","int((x + 6*x^(1/2) + 9)/(x + 4*x^(1/2)),x)","x+2\,\ln\left(\sqrt{x}+4\right)+4\,\sqrt{x}","Not used",1,"x + 2*log(x^(1/2) + 4) + 4*x^(1/2)","B"
725,1,47,77,0.048056,"\text{Not used}","int((8*x^(7/2) - 6)/(9*x^(1/2) - 5),x)","\frac{125000\,x}{4782969}-\frac{280728140\,\ln\left(\sqrt{x}-\frac{5}{9}\right)}{387420489}+\frac{2500\,x^2}{59049}-\frac{56145628\,\sqrt{x}}{43046721}+\frac{200\,x^3}{2187}+\frac{2\,x^4}{9}+\frac{50000\,x^{3/2}}{1594323}+\frac{400\,x^{5/2}}{6561}+\frac{80\,x^{7/2}}{567}","Not used",1,"(125000*x)/4782969 - (280728140*log(x^(1/2) - 5/9))/387420489 + (2500*x^2)/59049 - (56145628*x^(1/2))/43046721 + (200*x^3)/2187 + (2*x^4)/9 + (50000*x^(3/2))/1594323 + (400*x^(5/2))/6561 + (80*x^(7/2))/567","B"
726,1,255,80,0.104097,"\text{Not used}","int(((x^3 + 1)*(x + 1)^(1/2))/(x^2 + 1),x)","\frac{2\,{\left(x+1\right)}^{5/2}}{5}-\frac{2\,{\left(x+1\right)}^{3/2}}{3}-2\,\sqrt{x+1}-\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{x+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}-64}-\frac{\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{x+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}-64}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}+\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}\right)+\mathrm{atan}\left(\frac{\sqrt{2}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{x+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}+64}+\frac{\sqrt{2}\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{x+1}\,64{}\mathrm{i}}{256\,\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}+64}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}-\sqrt{\frac{\sqrt{2}}{4}-\frac{1}{4}}\,2{}\mathrm{i}\right)","Not used",1,"(2*(x + 1)^(5/2))/5 - (2*(x + 1)^(3/2))/3 - 2*(x + 1)^(1/2) - atan((2^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2)*(x + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) - 64) - (2^(1/2)*(2^(1/2)/4 - 1/4)^(1/2)*(x + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) - 64))*((- 2^(1/2)/4 - 1/4)^(1/2)*2i + (2^(1/2)/4 - 1/4)^(1/2)*2i) + atan((2^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2)*(x + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) + 64) + (2^(1/2)*(2^(1/2)/4 - 1/4)^(1/2)*(x + 1)^(1/2)*64i)/(256*(2^(1/2)/4 - 1/4)^(1/2)*(- 2^(1/2)/4 - 1/4)^(1/2) + 64))*((- 2^(1/2)/4 - 1/4)^(1/2)*2i - (2^(1/2)/4 - 1/4)^(1/2)*2i)","B"
727,0,-1,89,0.000000,"\text{Not used}","int((x - x^(1/2) - 1)^(1/2)/(x^(1/2)*(x - 1)),x)","\int \frac{\sqrt{x-\sqrt{x}-1}}{\sqrt{x}\,\left(x-1\right)} \,d x","Not used",1,"int((x - x^(1/2) - 1)^(1/2)/(x^(1/2)*(x - 1)), x)","F"
728,0,-1,61,0.000000,"\text{Not used}","int((2*(x + 1)^(1/2) + 1)/(x*(x + (x + 1)^(1/2))^(1/2)*(x + 1)^(1/2)),x)","\int \frac{2\,\sqrt{x+1}+1}{x\,\sqrt{x+\sqrt{x+1}}\,\sqrt{x+1}} \,d x","Not used",1,"int((2*(x + 1)^(1/2) + 1)/(x*(x + (x + 1)^(1/2))^(1/2)*(x + 1)^(1/2)), x)","F"
729,1,14,8,0.158381,"\text{Not used}","int(1/(x^(1/2)*(x + 1)^(1/2)),x)","4\,\mathrm{atanh}\left(\frac{\sqrt{x+1}-1}{\sqrt{x}}\right)","Not used",1,"4*atanh(((x + 1)^(1/2) - 1)/x^(1/2))","B"
730,1,12,8,0.063890,"\text{Not used}","int((x/(x + 1))^(1/2)/x,x)","2\,\mathrm{atanh}\left(\sqrt{\frac{x}{x+1}}\right)","Not used",1,"2*atanh((x/(x + 1))^(1/2))","B"
731,1,26,22,3.718734,"\text{Not used}","int(x^(1/2)/(x + 1)^(1/2),x)","\sqrt{x}\,\sqrt{x+1}-2\,\mathrm{atanh}\left(\frac{\sqrt{x}}{\sqrt{x+1}-1}\right)","Not used",1,"x^(1/2)*(x + 1)^(1/2) - 2*atanh(x^(1/2)/((x + 1)^(1/2) - 1))","B"
732,1,35,22,3.123620,"\text{Not used}","int((x/(x + 1))^(1/2),x)","-\mathrm{atanh}\left(\sqrt{\frac{x}{x+1}}\right)-\frac{\sqrt{\frac{x}{x+1}}}{\frac{x}{x+1}-1}","Not used",1,"- atanh((x/(x + 1))^(1/2)) - (x/(x + 1))^(1/2)/(x/(x + 1) - 1)","B"
733,1,138,36,5.090140,"\text{Not used}","int((x - 1)^(1/2)/(x^2*(x + 1)^(1/2)),x)","-\ln\left(\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}+\ln\left(\frac{\sqrt{x-1}-\mathrm{i}}{\sqrt{x+1}-1}\right)\,1{}\mathrm{i}-\frac{\sqrt{x-1}-\mathrm{i}}{4\,\left(\sqrt{x+1}-1\right)}-\frac{\frac{5\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+1}{\frac{4\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{4\,\left(\sqrt{x-1}-\mathrm{i}\right)}{\sqrt{x+1}-1}}","Not used",1,"log(((x - 1)^(1/2) - 1i)/((x + 1)^(1/2) - 1))*1i - log(((x - 1)^(1/2) - 1i)^2/((x + 1)^(1/2) - 1)^2 + 1)*1i - ((x - 1)^(1/2) - 1i)/(4*((x + 1)^(1/2) - 1)) - ((5*((x - 1)^(1/2) - 1i)^2)/((x + 1)^(1/2) - 1)^2 + 1)/((4*((x - 1)^(1/2) - 1i)^3)/((x + 1)^(1/2) - 1)^3 + (4*((x - 1)^(1/2) - 1i))/((x + 1)^(1/2) - 1))","B"
734,1,41,36,0.059946,"\text{Not used}","int(((x - 1)/(x + 1))^(1/2)/x^2,x)","2\,\mathrm{atan}\left(\sqrt{\frac{x-1}{x+1}}\right)-\frac{2\,\sqrt{\frac{x-1}{x+1}}}{\frac{x-1}{x+1}+1}","Not used",1,"2*atan(((x - 1)/(x + 1))^(1/2)) - (2*((x - 1)/(x + 1))^(1/2))/((x - 1)/(x + 1) + 1)","B"
735,1,473,69,12.863047,"\text{Not used}","int((x^3*(x - 1)^(1/2))/(x + 1)^(1/2),x)","\frac{3\,\mathrm{atanh}\left(\frac{\sqrt{x-1}-\mathrm{i}}{\sqrt{x+1}-1}\right)}{2}+\frac{\frac{23\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^3}{2\,{\left(\sqrt{x+1}-1\right)}^3}-\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^4\,64{}\mathrm{i}}{{\left(\sqrt{x+1}-1\right)}^4}+\frac{333\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{x+1}-1\right)}^5}+\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^6\,256{}\mathrm{i}}{3\,{\left(\sqrt{x+1}-1\right)}^6}+\frac{671\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{x+1}-1\right)}^7}-\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^8\,128{}\mathrm{i}}{3\,{\left(\sqrt{x+1}-1\right)}^8}+\frac{671\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^9}{2\,{\left(\sqrt{x+1}-1\right)}^9}+\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^{10}\,256{}\mathrm{i}}{3\,{\left(\sqrt{x+1}-1\right)}^{10}}+\frac{333\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{x+1}-1\right)}^{11}}-\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^{12}\,64{}\mathrm{i}}{{\left(\sqrt{x+1}-1\right)}^{12}}+\frac{23\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{x+1}-1\right)}^{13}}-\frac{3\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^{15}}{2\,{\left(\sqrt{x+1}-1\right)}^{15}}-\frac{3\,\left(\sqrt{x-1}-\mathrm{i}\right)}{2\,\left(\sqrt{x+1}-1\right)}}{1+\frac{28\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{x+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{x+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{x+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{x+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{x+1}-1\right)}^{14}}+\frac{{\left(\sqrt{x-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{x+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}}","Not used",1,"(3*atanh(((x - 1)^(1/2) - 1i)/((x + 1)^(1/2) - 1)))/2 + ((23*((x - 1)^(1/2) - 1i)^3)/(2*((x + 1)^(1/2) - 1)^3) - (((x - 1)^(1/2) - 1i)^4*64i)/((x + 1)^(1/2) - 1)^4 + (333*((x - 1)^(1/2) - 1i)^5)/(2*((x + 1)^(1/2) - 1)^5) + (((x - 1)^(1/2) - 1i)^6*256i)/(3*((x + 1)^(1/2) - 1)^6) + (671*((x - 1)^(1/2) - 1i)^7)/(2*((x + 1)^(1/2) - 1)^7) - (((x - 1)^(1/2) - 1i)^8*128i)/(3*((x + 1)^(1/2) - 1)^8) + (671*((x - 1)^(1/2) - 1i)^9)/(2*((x + 1)^(1/2) - 1)^9) + (((x - 1)^(1/2) - 1i)^10*256i)/(3*((x + 1)^(1/2) - 1)^10) + (333*((x - 1)^(1/2) - 1i)^11)/(2*((x + 1)^(1/2) - 1)^11) - (((x - 1)^(1/2) - 1i)^12*64i)/((x + 1)^(1/2) - 1)^12 + (23*((x - 1)^(1/2) - 1i)^13)/(2*((x + 1)^(1/2) - 1)^13) - (3*((x - 1)^(1/2) - 1i)^15)/(2*((x + 1)^(1/2) - 1)^15) - (3*((x - 1)^(1/2) - 1i))/(2*((x + 1)^(1/2) - 1)))/((28*((x - 1)^(1/2) - 1i)^4)/((x + 1)^(1/2) - 1)^4 - (8*((x - 1)^(1/2) - 1i)^2)/((x + 1)^(1/2) - 1)^2 - (56*((x - 1)^(1/2) - 1i)^6)/((x + 1)^(1/2) - 1)^6 + (70*((x - 1)^(1/2) - 1i)^8)/((x + 1)^(1/2) - 1)^8 - (56*((x - 1)^(1/2) - 1i)^10)/((x + 1)^(1/2) - 1)^10 + (28*((x - 1)^(1/2) - 1i)^12)/((x + 1)^(1/2) - 1)^12 - (8*((x - 1)^(1/2) - 1i)^14)/((x + 1)^(1/2) - 1)^14 + ((x - 1)^(1/2) - 1i)^16/((x + 1)^(1/2) - 1)^16 + 1)","B"
736,1,119,69,0.049671,"\text{Not used}","int(x^3*((x - 1)/(x + 1))^(1/2),x)","\frac{3\,\mathrm{atanh}\left(\sqrt{\frac{x-1}{x+1}}\right)}{4}-\frac{\frac{3\,\sqrt{\frac{x-1}{x+1}}}{4}-\frac{49\,{\left(\frac{x-1}{x+1}\right)}^{3/2}}{12}+\frac{31\,{\left(\frac{x-1}{x+1}\right)}^{5/2}}{12}-\frac{13\,{\left(\frac{x-1}{x+1}\right)}^{7/2}}{4}}{\frac{6\,{\left(x-1\right)}^2}{{\left(x+1\right)}^2}-\frac{4\,\left(x-1\right)}{x+1}-\frac{4\,{\left(x-1\right)}^3}{{\left(x+1\right)}^3}+\frac{{\left(x-1\right)}^4}{{\left(x+1\right)}^4}+1}","Not used",1,"(3*atanh(((x - 1)/(x + 1))^(1/2)))/4 - ((3*((x - 1)/(x + 1))^(1/2))/4 - (49*((x - 1)/(x + 1))^(3/2))/12 + (31*((x - 1)/(x + 1))^(5/2))/12 - (13*((x - 1)/(x + 1))^(7/2))/4)/((6*(x - 1)^2)/(x + 1)^2 - (4*(x - 1))/(x + 1) - (4*(x - 1)^3)/(x + 1)^3 + (x - 1)^4/(x + 1)^4 + 1)","B"
737,1,13,15,0.178958,"\text{Not used}","int((-x/(x + 1))^(1/2)/x,x)","2\,\mathrm{atan}\left(\sqrt{-\frac{x}{x+1}}\right)","Not used",1,"2*atan((-x/(x + 1))^(1/2))","B"
738,1,15,18,3.139350,"\text{Not used}","int((-(x - 1)/(x + 1))^(1/2)/(x - 1),x)","2\,\mathrm{atan}\left(\sqrt{-\frac{x-1}{x+1}}\right)","Not used",1,"2*atan((-(x - 1)/(x + 1))^(1/2))","B"
739,1,36,24,0.180323,"\text{Not used}","int(((a + b*x)/(c - b*x))^(1/2)/(a + b*x),x)","-\frac{2\,\sqrt{-b}\,\mathrm{atanh}\left(\frac{\sqrt{-b}\,\sqrt{\frac{a+b\,x}{c-b\,x}}}{\sqrt{b}}\right)}{b^{3/2}}","Not used",1,"-(2*(-b)^(1/2)*atanh(((-b)^(1/2)*((a + b*x)/(c - b*x))^(1/2))/b^(1/2)))/b^(3/2)","B"
740,1,31,41,0.204281,"\text{Not used}","int(((a + b*x)/(c + d*x))^(1/2)/(a + b*x),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{d}\,\sqrt{\frac{a+b\,x}{c+d\,x}}}{\sqrt{b}}\right)}{\sqrt{b}\,\sqrt{d}}","Not used",1,"(2*atanh((d^(1/2)*((a + b*x)/(c + d*x))^(1/2))/b^(1/2)))/(b^(1/2)*d^(1/2))","B"
741,1,37,32,3.126908,"\text{Not used}","int((-x/(x + 1))^(1/2),x)","-\mathrm{atan}\left(\sqrt{-\frac{x}{x+1}}\right)-\frac{\sqrt{-\frac{x}{x+1}}}{\frac{x}{x+1}-1}","Not used",1,"- atan((-x/(x + 1))^(1/2)) - (-x/(x + 1))^(1/2)/(x/(x + 1) - 1)","B"
742,1,43,38,0.030301,"\text{Not used}","int((-(x - 1)/(x + 1))^(1/2),x)","-2\,\mathrm{atan}\left(\sqrt{-\frac{x-1}{x+1}}\right)-\frac{2\,\sqrt{-\frac{x-1}{x+1}}}{\frac{x-1}{x+1}-1}","Not used",1,"- 2*atan((-(x - 1)/(x + 1))^(1/2)) - (2*(-(x - 1)/(x + 1))^(1/2))/((x - 1)/(x + 1) - 1)","B"
743,1,49,42,3.170904,"\text{Not used}","int(((a + x)/(a - x))^(1/2),x)","2\,a\,\mathrm{atan}\left(\sqrt{\frac{a+x}{a-x}}\right)-\frac{2\,a\,\sqrt{\frac{a+x}{a-x}}}{\frac{a+x}{a-x}+1}","Not used",1,"2*a*atan(((a + x)/(a - x))^(1/2)) - (2*a*((a + x)/(a - x))^(1/2))/((a + x)/(a - x) + 1)","B"
744,1,51,41,0.050438,"\text{Not used}","int((-(a - x)/(a + x))^(1/2),x)","\frac{2\,a\,\sqrt{-\frac{a-x}{a+x}}}{\frac{a-x}{a+x}+1}-2\,a\,\mathrm{atanh}\left(\sqrt{-\frac{a-x}{a+x}}\right)","Not used",1,"(2*a*(-(a - x)/(a + x))^(1/2))/((a - x)/(a + x) + 1) - 2*a*atanh((-(a - x)/(a + x))^(1/2))","B"
745,1,90,76,0.273437,"\text{Not used}","int(((a + b*x)/(c + d*x))^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{d}\,\sqrt{\frac{a+b\,x}{c+d\,x}}}{\sqrt{b}}\right)\,\left(a\,d-b\,c\right)}{\sqrt{b}\,d^{3/2}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{\frac{a+b\,x}{c+d\,x}}}{b\,d\,\left(\frac{d\,\left(a+b\,x\right)}{b\,\left(c+d\,x\right)}-1\right)}","Not used",1,"(atanh((d^(1/2)*((a + b*x)/(c + d*x))^(1/2))/b^(1/2))*(a*d - b*c))/(b^(1/2)*d^(3/2)) + ((a*d - b*c)*((a + b*x)/(c + d*x))^(1/2))/(b*d*((d*(a + b*x))/(b*(c + d*x)) - 1))","B"
746,1,57,49,3.164202,"\text{Not used}","int(((x - 1)/(3*x + 5))^(1/2),x)","-\frac{8\,\sqrt{3}\,\mathrm{atanh}\left(\sqrt{3}\,\sqrt{\frac{x-1}{3\,x+5}}\right)}{9}-\frac{8\,\sqrt{\frac{x-1}{3\,x+5}}}{3\,\left(\frac{3\,x-3}{3\,x+5}-1\right)}","Not used",1,"- (8*3^(1/2)*atanh(3^(1/2)*((x - 1)/(3*x + 5))^(1/2)))/9 - (8*((x - 1)/(3*x + 5))^(1/2))/(3*((3*x - 3)/(3*x + 5) - 1))","B"
747,1,74,46,3.238754,"\text{Not used}","int(((5*x - 1)/(7*x + 1))^(1/2)/x^2,x)","12\,\mathrm{atan}\left(\frac{\sqrt{5}\,\sqrt{7}\,\sqrt{35}\,\sqrt{\frac{5\,x-1}{7\,x+1}}}{35}\right)-\frac{12\,\sqrt{5}\,\sqrt{7}\,\sqrt{35}\,\sqrt{\frac{5\,x-1}{7\,x+1}}}{25\,\left(\frac{7\,x-\frac{7}{5}}{7\,x+1}+\frac{7}{5}\right)}","Not used",1,"12*atan((5^(1/2)*7^(1/2)*35^(1/2)*((5*x - 1)/(7*x + 1))^(1/2))/35) - (12*5^(1/2)*7^(1/2)*35^(1/2)*((5*x - 1)/(7*x + 1))^(1/2))/(25*((7*x - 7/5)/(7*x + 1) + 7/5))","B"
748,1,17,20,0.057439,"\text{Not used}","int(x/((-(x - 1)/(x + 1))^(1/2)*(x + 1)),x)","-\sqrt{-\frac{x-1}{x+1}}\,\left(x+1\right)","Not used",1,"-(-(x - 1)/(x + 1))^(1/2)*(x + 1)","B"
749,0,-1,18,0.000000,"\text{Not used}","int(x/((x + 1)*(2/(x + 1) - 1)^(1/2)),x)","\int \frac{x}{\left(x+1\right)\,\sqrt{\frac{2}{x+1}-1}} \,d x","Not used",1,"int(x/((x + 1)*(2/(x + 1) - 1)^(1/2)), x)","F"
750,1,62,54,0.088920,"\text{Not used}","int(x/(((x + 2)/(x + 3))^(1/2)*(x + 1)),x)","2\,\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2}\,\sqrt{\frac{x+2}{x+3}}\right)-\frac{\sqrt{\frac{x+2}{x+3}}}{\frac{x+2}{x+3}-1}-\mathrm{atanh}\left(\sqrt{\frac{x+2}{x+3}}\right)","Not used",1,"2*2^(1/2)*atanh(2^(1/2)*((x + 2)/(x + 3))^(1/2)) - ((x + 2)/(x + 3))^(1/2)/((x + 2)/(x + 3) - 1) - atanh(((x + 2)/(x + 3))^(1/2))","B"
751,1,15,11,3.125152,"\text{Not used}","int((1/x + 1)^(1/2)/(x + 1)^2,x)","\frac{2\,x\,\sqrt{\frac{1}{x}+1}}{x+1}","Not used",1,"(2*x*(1/x + 1)^(1/2))/(x + 1)","B"
752,0,-1,29,0.000000,"\text{Not used}","int((1/x + 1)^(1/2)/(1 - x^2)^(1/2),x)","\int \frac{\sqrt{\frac{1}{x}+1}}{\sqrt{1-x^2}} \,d x","Not used",1,"int((1/x + 1)^(1/2)/(1 - x^2)^(1/2), x)","F"
753,0,-1,180,0.000000,"\text{Not used}","int(1/(x + (3 - x^2 - 2*x)^(1/2)),x)","\int \frac{1}{x+\sqrt{-x^2-2\,x+3}} \,d x","Not used",1,"int(1/(x + (3 - x^2 - 2*x)^(1/2)), x)","F"
754,0,-1,172,0.000000,"\text{Not used}","int(1/(x + (3 - x^2 - 2*x)^(1/2))^2,x)","\int \frac{1}{{\left(x+\sqrt{-x^2-2\,x+3}\right)}^2} \,d x","Not used",1,"int(1/(x + (3 - x^2 - 2*x)^(1/2))^2, x)","F"
755,0,-1,307,0.000000,"\text{Not used}","int(1/(x + (3 - x^2 - 2*x)^(1/2))^3,x)","\int \frac{1}{{\left(x+\sqrt{-x^2-2\,x+3}\right)}^3} \,d x","Not used",1,"int(1/(x + (3 - x^2 - 2*x)^(1/2))^3, x)","F"
756,0,-1,65,0.000000,"\text{Not used}","int(1/(x + (x^2 - 2*x - 3)^(1/2)),x)","\frac{x}{2}-\frac{3\,\ln\left(x+\frac{3}{2}\right)}{4}-\int \frac{\sqrt{x^2-2\,x-3}}{2\,x+3} \,d x","Not used",1,"x/2 - (3*log(x + 3/2))/4 - int((x^2 - 2*x - 3)^(1/2)/(2*x + 3), x)","F"
757,0,-1,83,0.000000,"\text{Not used}","int(1/(x + (x^2 - 2*x - 3)^(1/2))^2,x)","\int \frac{1}{{\left(x+\sqrt{x^2-2\,x-3}\right)}^2} \,d x","Not used",1,"int(1/(x + (x^2 - 2*x - 3)^(1/2))^2, x)","F"
758,0,-1,101,0.000000,"\text{Not used}","int(1/(x + (x^2 - 2*x - 3)^(1/2))^3,x)","\int \frac{1}{{\left(x+\sqrt{x^2-2\,x-3}\right)}^3} \,d x","Not used",1,"int(1/(x + (x^2 - 2*x - 3)^(1/2))^3, x)","F"
759,0,-1,108,0.000000,"\text{Not used}","int(1/(x + (- 4*x - x^2 - 3)^(1/2)),x)","\int \frac{1}{x+\sqrt{-x^2-4\,x-3}} \,d x","Not used",1,"int(1/(x + (- 4*x - x^2 - 3)^(1/2)), x)","F"
760,0,-1,87,0.000000,"\text{Not used}","int(1/(x + (- 4*x - x^2 - 3)^(1/2))^2,x)","\int \frac{1}{{\left(x+\sqrt{-x^2-4\,x-3}\right)}^2} \,d x","Not used",1,"int(1/(x + (- 4*x - x^2 - 3)^(1/2))^2, x)","F"
761,0,-1,149,0.000000,"\text{Not used}","int(1/(x + (- 4*x - x^2 - 3)^(1/2))^3,x)","\int \frac{1}{{\left(x+\sqrt{-x^2-4\,x-3}\right)}^3} \,d x","Not used",1,"int(1/(x + (- 4*x - x^2 - 3)^(1/2))^3, x)","F"
762,1,38,42,0.182519,"\text{Not used}","int(x^3*(2*x + 1)*(x + 1)^3*(1 - 2*x^3 - x^4 - x^2)^(1/2),x)","-\frac{\left(3\,x^4+6\,x^3+3\,x^2+2\right)\,{\left(-x^4-2\,x^3-x^2+1\right)}^{3/2}}{15}","Not used",1,"-((3*x^2 + 6*x^3 + 3*x^4 + 2)*(1 - 2*x^3 - x^4 - x^2)^(3/2))/15","B"
763,1,51,42,3.420860,"\text{Not used}","int((2*x + 1)*(1 - (x + x^2)^2)^(1/2)*(x + x^2)^3,x)","\sqrt{1-{\left(x^2+x\right)}^2}\,\left(\frac{x^8}{5}+\frac{4\,x^7}{5}+\frac{6\,x^6}{5}+\frac{4\,x^5}{5}+\frac{2\,x^4}{15}-\frac{2\,x^3}{15}-\frac{x^2}{15}-\frac{2}{15}\right)","Not used",1,"(1 - (x + x^2)^2)^(1/2)*((2*x^4)/15 - (2*x^3)/15 - x^2/15 + (4*x^5)/5 + (6*x^6)/5 + (4*x^7)/5 + x^8/5 - 2/15)","B"
764,0,-1,102,0.000000,"\text{Not used}","int((8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int {\left(-x^4+4\,x^3-8\,x^2+8\,x\right)}^{3/2} \,d x","Not used",1,"int((8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
765,0,-1,62,0.000000,"\text{Not used}","int((8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int \sqrt{-x^4+4\,x^3-8\,x^2+8\,x} \,d x","Not used",1,"int((8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
766,0,-1,17,0.000000,"\text{Not used}","int(1/(8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int \frac{1}{\sqrt{-x^4+4\,x^3-8\,x^2+8\,x}} \,d x","Not used",1,"int(1/(8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
767,0,-1,73,0.000000,"\text{Not used}","int(1/(8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int \frac{1}{{\left(-x^4+4\,x^3-8\,x^2+8\,x\right)}^{3/2}} \,d x","Not used",1,"int(1/(8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
768,0,-1,109,0.000000,"\text{Not used}","int(1/(8*x - 8*x^2 + 4*x^3 - x^4)^(5/2),x)","\int \frac{1}{{\left(-x^4+4\,x^3-8\,x^2+8\,x\right)}^{5/2}} \,d x","Not used",1,"int(1/(8*x - 8*x^2 + 4*x^3 - x^4)^(5/2), x)","F"
769,0,-1,102,0.000000,"\text{Not used}","int((-x*(x - 2)*(x^2 - 2*x + 4))^(3/2),x)","\int {\left(-x\,\left(x-2\right)\,\left(x^2-2\,x+4\right)\right)}^{3/2} \,d x","Not used",1,"int((-x*(x - 2)*(x^2 - 2*x + 4))^(3/2), x)","F"
770,0,-1,62,0.000000,"\text{Not used}","int((-x*(x - 2)*(x^2 - 2*x + 4))^(1/2),x)","\int \sqrt{-x\,\left(x-2\right)\,\left(x^2-2\,x+4\right)} \,d x","Not used",1,"int((-x*(x - 2)*(x^2 - 2*x + 4))^(1/2), x)","F"
771,0,-1,17,0.000000,"\text{Not used}","int(1/(-x*(x - 2)*(x^2 - 2*x + 4))^(1/2),x)","\int \frac{1}{\sqrt{-x\,\left(x-2\right)\,\left(x^2-2\,x+4\right)}} \,d x","Not used",1,"int(1/(-x*(x - 2)*(x^2 - 2*x + 4))^(1/2), x)","F"
772,0,-1,73,0.000000,"\text{Not used}","int(1/(-x*(x - 2)*(x^2 - 2*x + 4))^(3/2),x)","\int \frac{1}{{\left(-x\,\left(x-2\right)\,\left(x^2-2\,x+4\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(-x*(x - 2)*(x^2 - 2*x + 4))^(3/2), x)","F"
773,0,-1,109,0.000000,"\text{Not used}","int(1/(-x*(x - 2)*(x^2 - 2*x + 4))^(5/2),x)","\int \frac{1}{{\left(-x\,\left(x-2\right)\,\left(x^2-2\,x+4\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(-x*(x - 2)*(x^2 - 2*x + 4))^(5/2), x)","F"
774,0,-1,730,0.000000,"\text{Not used}","int((4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(3/2),x)","\int {\left(4\,c^2\,x^2+4\,c\,d\,x^3+4\,a\,c+d^2\,x^4\right)}^{3/2} \,d x","Not used",1,"int((4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(3/2), x)","F"
775,0,-1,622,0.000000,"\text{Not used}","int((4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(1/2),x)","\int \sqrt{4\,c^2\,x^2+4\,c\,d\,x^3+4\,a\,c+d^2\,x^4} \,d x","Not used",1,"int((4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(1/2), x)","F"
776,0,-1,227,0.000000,"\text{Not used}","int(1/(4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(1/2),x)","\int \frac{1}{\sqrt{4\,c^2\,x^2+4\,c\,d\,x^3+4\,a\,c+d^2\,x^4}} \,d x","Not used",1,"int(1/(4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(1/2), x)","F"
777,0,-1,674,0.000000,"\text{Not used}","int(1/(4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(3/2),x)","\int \frac{1}{{\left(4\,c^2\,x^2+4\,c\,d\,x^3+4\,a\,c+d^2\,x^4\right)}^{3/2}} \,d x","Not used",1,"int(1/(4*a*c + 4*c^2*x^2 + d^2*x^4 + 4*c*d*x^3)^(3/2), x)","F"
778,0,-1,663,0.000000,"\text{Not used}","int((8*a*e^2 - d^3*x + 8*e^3*x^4 + 8*d*e^2*x^3)^(1/2),x)","\int \sqrt{-d^3\,x+8\,d\,e^2\,x^3+8\,e^3\,x^4+8\,a\,e^2} \,d x","Not used",1,"int((8*a*e^2 - d^3*x + 8*e^3*x^4 + 8*d*e^2*x^3)^(1/2), x)","F"
779,0,-1,235,0.000000,"\text{Not used}","int(1/(8*a*e^2 - d^3*x + 8*e^3*x^4 + 8*d*e^2*x^3)^(1/2),x)","\int \frac{1}{\sqrt{-d^3\,x+8\,d\,e^2\,x^3+8\,e^3\,x^4+8\,a\,e^2}} \,d x","Not used",1,"int(1/(8*a*e^2 - d^3*x + 8*e^3*x^4 + 8*d*e^2*x^3)^(1/2), x)","F"
780,0,-1,748,0.000000,"\text{Not used}","int(1/(8*a*e^2 - d^3*x + 8*e^3*x^4 + 8*d*e^2*x^3)^(3/2),x)","\int \frac{1}{{\left(-d^3\,x+8\,d\,e^2\,x^3+8\,e^3\,x^4+8\,a\,e^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(8*a*e^2 - d^3*x + 8*e^3*x^4 + 8*d*e^2*x^3)^(3/2), x)","F"
781,0,-1,452,0.000000,"\text{Not used}","int((a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int {\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{3/2} \,d x","Not used",1,"int((a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
782,0,-1,397,0.000000,"\text{Not used}","int((a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int \sqrt{-x^4+4\,x^3-8\,x^2+8\,x+a} \,d x","Not used",1,"int((a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
783,0,-1,144,0.000000,"\text{Not used}","int(1/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int \frac{1}{\sqrt{-x^4+4\,x^3-8\,x^2+8\,x+a}} \,d x","Not used",1,"int(1/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
784,0,-1,437,0.000000,"\text{Not used}","int(1/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int \frac{1}{{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
785,0,-1,517,0.000000,"\text{Not used}","int(1/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2),x)","\int \frac{1}{{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2), x)","F"
786,0,-1,558,0.000000,"\text{Not used}","int(x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int x\,{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{3/2} \,d x","Not used",1,"int(x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
787,0,-1,466,0.000000,"\text{Not used}","int(x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int x\,\sqrt{-x^4+4\,x^3-8\,x^2+8\,x+a} \,d x","Not used",1,"int(x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
788,0,-1,179,0.000000,"\text{Not used}","int(x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int \frac{x}{\sqrt{-x^4+4\,x^3-8\,x^2+8\,x+a}} \,d x","Not used",1,"int(x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
789,0,-1,474,0.000000,"\text{Not used}","int(x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int \frac{x}{{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
790,0,-1,591,0.000000,"\text{Not used}","int(x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2),x)","\int \frac{x}{{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2), x)","F"
791,0,-1,585,0.000000,"\text{Not used}","int(x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int x^2\,{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{3/2} \,d x","Not used",1,"int(x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
792,0,-1,485,0.000000,"\text{Not used}","int(x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int x^2\,\sqrt{-x^4+4\,x^3-8\,x^2+8\,x+a} \,d x","Not used",1,"int(x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
793,0,-1,388,0.000000,"\text{Not used}","int(x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2),x)","\int \frac{x^2}{\sqrt{-x^4+4\,x^3-8\,x^2+8\,x+a}} \,d x","Not used",1,"int(x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(1/2), x)","F"
794,0,-1,311,0.000000,"\text{Not used}","int(x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x)","\int \frac{x^2}{{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{3/2}} \,d x","Not used",1,"int(x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2), x)","F"
795,0,-1,582,0.000000,"\text{Not used}","int(x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2),x)","\int \frac{x^2}{{\left(-x^4+4\,x^3-8\,x^2+8\,x+a\right)}^{5/2}} \,d x","Not used",1,"int(x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2), x)","F"
796,0,-1,129,0.000000,"\text{Not used}","int(1/(8*x - x^3 + 8*x^4 + 8)^(1/2),x)","\int \frac{1}{\sqrt{8\,x^4-x^3+8\,x+8}} \,d x","Not used",1,"int(1/(8*x - x^3 + 8*x^4 + 8)^(1/2), x)","F"
797,0,-1,431,0.000000,"\text{Not used}","int(1/(8*x - x^3 + 8*x^4 + 8)^(3/2),x)","\int \frac{1}{{\left(8\,x^4-x^3+8\,x+8\right)}^{3/2}} \,d x","Not used",1,"int(1/(8*x - x^3 + 8*x^4 + 8)^(3/2), x)","F"
798,0,-1,108,0.000000,"\text{Not used}","int(1/(4*x + 4*x^2 + 4*x^4 + 1)^(1/2),x)","\int \frac{1}{\sqrt{4\,x^4+4\,x^2+4\,x+1}} \,d x","Not used",1,"int(1/(4*x + 4*x^2 + 4*x^4 + 1)^(1/2), x)","F"
799,0,-1,367,0.000000,"\text{Not used}","int(1/(4*x + 4*x^2 + 4*x^4 + 1)^(3/2),x)","\int \frac{1}{{\left(4\,x^4+4\,x^2+4\,x+1\right)}^{3/2}} \,d x","Not used",1,"int(1/(4*x + 4*x^2 + 4*x^4 + 1)^(3/2), x)","F"
800,0,-1,126,0.000000,"\text{Not used}","int(1/(24*x + 8*x^2 - 15*x^3 + 8*x^4 + 8)^(1/2),x)","\int \frac{1}{\sqrt{8\,x^4-15\,x^3+8\,x^2+24\,x+8}} \,d x","Not used",1,"int(1/(24*x + 8*x^2 - 15*x^3 + 8*x^4 + 8)^(1/2), x)","F"
801,0,-1,434,0.000000,"\text{Not used}","int(1/(24*x + 8*x^2 - 15*x^3 + 8*x^4 + 8)^(3/2),x)","\int \frac{1}{{\left(8\,x^4-15\,x^3+8\,x^2+24\,x+8\right)}^{3/2}} \,d x","Not used",1,"int(1/(24*x + 8*x^2 - 15*x^3 + 8*x^4 + 8)^(3/2), x)","F"
802,0,-1,577,0.000000,"\text{Not used}","int(1/(24*x + 8*x^2 - 15*x^3 + 8*x^4 + 8)^(5/2),x)","\int \frac{1}{{\left(8\,x^4-15\,x^3+8\,x^2+24\,x+8\right)}^{5/2}} \,d x","Not used",1,"int(1/(24*x + 8*x^2 - 15*x^3 + 8*x^4 + 8)^(5/2), x)","F"
803,0,-1,130,0.000000,"\text{Not used}","int(1/(15*x^3 - 44*x^2 - 6*x + 3*x^4 + 9)^(1/2),x)","\int \frac{1}{\sqrt{3\,x^4+15\,x^3-44\,x^2-6\,x+9}} \,d x","Not used",1,"int(1/(15*x^3 - 44*x^2 - 6*x + 3*x^4 + 9)^(1/2), x)","F"
804,0,-1,444,0.000000,"\text{Not used}","int(1/(15*x^3 - 44*x^2 - 6*x + 3*x^4 + 9)^(3/2),x)","\int \frac{1}{{\left(3\,x^4+15\,x^3-44\,x^2-6\,x+9\right)}^{3/2}} \,d x","Not used",1,"int(1/(15*x^3 - 44*x^2 - 6*x + 3*x^4 + 9)^(3/2), x)","F"
805,1,158,56,7.906406,"\text{Not used}","int((3/(x + 1)^(1/2) + 2*(3 - x)^(1/2))^2/x,x)","48\,\mathrm{atan}\left(\frac{\sqrt{3-x}-4\,\sqrt{3}+3\,\sqrt{3}\,\sqrt{x+1}}{\sqrt{x+1}-3\,\sqrt{3}\,\sqrt{3-x}+8}\right)-9\,\ln\left(x+1\right)-4\,x+21\,\ln\left(x\right)+12\,\sqrt{3}\,\ln\left(\frac{6\,x-12\,\sqrt{x+1}+4\,\sqrt{3}\,\sqrt{3-x}+2\,\sqrt{3}\,\sqrt{x+1}\,\sqrt{3-x}-6}{3\,x+6\,\sqrt{3}\,\sqrt{3-x}-18}\right)-12\,\sqrt{3}\,\ln\left(\frac{\sqrt{x+1}-1}{\sqrt{3}-\sqrt{3-x}}\right)","Not used",1,"48*atan(((3 - x)^(1/2) - 4*3^(1/2) + 3*3^(1/2)*(x + 1)^(1/2))/((x + 1)^(1/2) - 3*3^(1/2)*(3 - x)^(1/2) + 8)) - 9*log(x + 1) - 4*x + 21*log(x) + 12*3^(1/2)*log((6*x - 12*(x + 1)^(1/2) + 4*3^(1/2)*(3 - x)^(1/2) + 2*3^(1/2)*(x + 1)^(1/2)*(3 - x)^(1/2) - 6)/(3*x + 6*3^(1/2)*(3 - x)^(1/2) - 18)) - 12*3^(1/2)*log(((x + 1)^(1/2) - 1)/(3^(1/2) - (3 - x)^(1/2)))","B"
806,1,55,65,0.042864,"\text{Not used}","int((x + x^2 - 1)/((x^2 + 1)^(1/2) + 1),x)","\left(\frac{x}{2}+1\right)\,\sqrt{x^2+1}-\frac{\mathrm{asinh}\left(x\right)}{2}-\ln\left(x\right)-x+\frac{\sqrt{x^2+1}}{x}-\frac{1}{x}+\mathrm{atan}\left(\sqrt{x^2+1}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"atan((x^2 + 1)^(1/2)*1i)*1i - x - asinh(x)/2 - log(x) + (x/2 + 1)*(x^2 + 1)^(1/2) + (x^2 + 1)^(1/2)/x - 1/x","B"
807,1,52,53,0.044548,"\text{Not used}","int((x + x^2 - 1)/(x + (x^2 + 1)^(1/2) + 1),x)","\frac{x^2}{2}-\frac{\ln\left(x\right)}{2}-\sqrt{x^2+1}\,\left(\frac{x^2}{6}+\frac{x}{4}-\frac{1}{3}\right)-\frac{\mathrm{asinh}\left(x\right)}{4}+\frac{x^3}{6}+\frac{\mathrm{atan}\left(\sqrt{x^2+1}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(atan((x^2 + 1)^(1/2)*1i)*1i)/2 - asinh(x)/4 - log(x)/2 - (x^2 + 1)^(1/2)*(x/4 + x^2/6 - 1/3) + x^2/2 + x^3/6","B"
808,1,12,14,3.387368,"\text{Not used}","int((x + 2*(x - 1)^(1/2))/(x*(x - 1)^(1/2)),x)","2\,\ln\left(x\right)+2\,\sqrt{x-1}","Not used",1,"2*log(x) + 2*(x - 1)^(1/2)","B"
809,1,43,61,3.359515,"\text{Not used}","int((a + b*x^(2/3) + c*x^(1/2))^2,x)","a^2\,x+\frac{3\,b^2\,x^{7/3}}{7}+\frac{c^2\,x^2}{2}+\frac{6\,a\,b\,x^{5/3}}{5}+\frac{4\,a\,c\,x^{3/2}}{3}+\frac{12\,b\,c\,x^{13/6}}{13}","Not used",1,"a^2*x + (3*b^2*x^(7/3))/7 + (c^2*x^2)/2 + (6*a*b*x^(5/3))/5 + (4*a*c*x^(3/2))/3 + (12*b*c*x^(13/6))/13","B"
810,1,84,114,0.060019,"\text{Not used}","int((a + b*x^(2/3) + c*x^(1/2))^3,x)","a^3\,x+\frac{b^3\,x^3}{3}+\frac{2\,c^3\,x^{5/2}}{5}+\frac{9\,a^2\,b\,x^{5/3}}{5}+\frac{9\,a\,b^2\,x^{7/3}}{7}+\frac{3\,a\,c^2\,x^2}{2}+2\,a^2\,c\,x^{3/2}+\frac{9\,b\,c^2\,x^{8/3}}{8}+\frac{18\,b^2\,c\,x^{17/6}}{17}+\frac{36\,a\,b\,c\,x^{13/6}}{13}","Not used",1,"a^3*x + (b^3*x^3)/3 + (2*c^3*x^(5/2))/5 + (9*a^2*b*x^(5/3))/5 + (9*a*b^2*x^(7/3))/7 + (3*a*c^2*x^2)/2 + 2*a^2*c*x^(3/2) + (9*b*c^2*x^(8/3))/8 + (18*b^2*c*x^(17/6))/17 + (36*a*b*c*x^(13/6))/13","B"
811,1,46,58,4.083390,"\text{Not used}","int((x^2 - 1)/(x^3*(a - b + b/x^2)^(1/2)),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{a-b+\frac{b}{x^2}}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}+\frac{\sqrt{a-b+\frac{b}{x^2}}}{b}","Not used",1,"atanh((a - b + b/x^2)^(1/2)/(a - b)^(1/2))/(a - b)^(1/2) + (a - b + b/x^2)^(1/2)/b","B"
812,1,62,58,4.044972,"\text{Not used}","int((x^2 - 1)/(x^3*(a + b*(1/x^2 - 1))^(1/2)),x)","\frac{\sqrt{a+b\,\left(\frac{1}{x^2}-1\right)}}{b}+\frac{\ln\left(x^2\,\left(2\,a-2\,b+2\,\sqrt{a-b}\,\sqrt{a+b\,\left(\frac{1}{x^2}-1\right)}+\frac{b}{x^2}\right)\right)}{2\,\sqrt{a-b}}","Not used",1,"(a + b*(1/x^2 - 1))^(1/2)/b + log(x^2*(2*a - 2*b + 2*(a - b)^(1/2)*(a + b*(1/x^2 - 1))^(1/2) + b/x^2))/(2*(a - b)^(1/2))","B"
813,1,67,53,3.587936,"\text{Not used}","int((x + 1)/((x^2 + 4)*(x^2 + 9)^(1/2)),x)","\sqrt{5}\,\left(\ln\left(x-2{}\mathrm{i}\right)-\ln\left(\sqrt{5}\,\sqrt{x^2+9}+9+x\,2{}\mathrm{i}\right)\right)\,\left(\frac{1}{10}-\frac{1}{20}{}\mathrm{i}\right)+\sqrt{5}\,\left(\ln\left(x+2{}\mathrm{i}\right)-\ln\left(\sqrt{5}\,\sqrt{x^2+9}+9-x\,2{}\mathrm{i}\right)\right)\,\left(\frac{1}{10}+\frac{1}{20}{}\mathrm{i}\right)","Not used",1,"5^(1/2)*(log(x - 2i) - log(x*2i + 5^(1/2)*(x^2 + 9)^(1/2) + 9))*(1/10 - 1i/20) + 5^(1/2)*(log(x + 2i) - log(5^(1/2)*(x^2 + 9)^(1/2) - x*2i + 9))*(1/10 + 1i/20)","B"
814,1,23,23,0.030388,"\text{Not used}","int(x*((1 - x^2)^(1/2) + 1),x)","\frac{x^2}{2}+\sqrt{1-x^2}\,\left(\frac{x^2}{3}-\frac{1}{3}\right)","Not used",1,"x^2/2 + (1 - x^2)^(1/2)*(x^2/3 - 1/3)","B"
815,1,35,23,3.694770,"\text{Not used}","int(x*((1 - x)^(1/2)*(x + 1)^(1/2) + 1),x)","\frac{x^2}{2}-\frac{\sqrt{1-x}\,\left(-\frac{x^3}{3}-\frac{x^2}{3}+\frac{x}{3}+\frac{1}{3}\right)}{\sqrt{x+1}}","Not used",1,"x^2/2 - ((1 - x)^(1/2)*(x/3 - x^2/3 - x^3/3 + 1/3))/(x + 1)^(1/2)","B"
816,1,180,33,7.556503,"\text{Not used}","int(x*(1/((x + 2)^(1/2)*(x + 3)^(1/2)) + 1),x)","\frac{\frac{10\,\left(\sqrt{x+2}-\sqrt{2}\right)}{\sqrt{x+3}-\sqrt{3}}+\frac{10\,{\left(\sqrt{x+2}-\sqrt{2}\right)}^3}{{\left(\sqrt{x+3}-\sqrt{3}\right)}^3}-\frac{8\,\sqrt{6}\,{\left(\sqrt{x+2}-\sqrt{2}\right)}^2}{{\left(\sqrt{x+3}-\sqrt{3}\right)}^2}}{\frac{{\left(\sqrt{x+2}-\sqrt{2}\right)}^4}{{\left(\sqrt{x+3}-\sqrt{3}\right)}^4}-\frac{2\,{\left(\sqrt{x+2}-\sqrt{2}\right)}^2}{{\left(\sqrt{x+3}-\sqrt{3}\right)}^2}+1}-10\,\mathrm{atanh}\left(\frac{\sqrt{x+2}-\sqrt{2}}{\sqrt{x+3}-\sqrt{3}}\right)+\frac{x^2}{2}","Not used",1,"((10*((x + 2)^(1/2) - 2^(1/2)))/((x + 3)^(1/2) - 3^(1/2)) + (10*((x + 2)^(1/2) - 2^(1/2))^3)/((x + 3)^(1/2) - 3^(1/2))^3 - (8*6^(1/2)*((x + 2)^(1/2) - 2^(1/2))^2)/((x + 3)^(1/2) - 3^(1/2))^2)/(((x + 2)^(1/2) - 2^(1/2))^4/((x + 3)^(1/2) - 3^(1/2))^4 - (2*((x + 2)^(1/2) - 2^(1/2))^2)/((x + 3)^(1/2) - 3^(1/2))^2 + 1) - 10*atanh(((x + 2)^(1/2) - 2^(1/2))/((x + 3)^(1/2) - 3^(1/2))) + x^2/2","B"
817,0,-1,45,0.000000,"\text{Not used}","int(-(x - (x^6)^(1/2))/(x*(x^4 - 1)),x)","\int -\frac{x-\sqrt{x^6}}{x\,\left(x^4-1\right)} \,d x","Not used",1,"int(-(x - (x^6)^(1/2))/(x*(x^4 - 1)), x)","F"
818,0,-1,45,0.000000,"\text{Not used}","int(((x^6)^(1/2)/x - 1)/(x^4 - 1),x)","\int \frac{\frac{\sqrt{x^6}}{x}-1}{x^4-1} \,d x","Not used",1,"int(((x^6)^(1/2)/x - 1)/(x^4 - 1), x)","F"
819,0,-1,45,0.000000,"\text{Not used}","int((x - (x^6)^(1/2))/(x - x^5),x)","\int \frac{x-\sqrt{x^6}}{x-x^5} \,d x","Not used",1,"int((x - (x^6)^(1/2))/(x - x^5), x)","F"
820,0,-1,45,0.000000,"\text{Not used}","int(x/(x + (x^6)^(1/2)),x)","\int \frac{x}{x+\sqrt{x^6}} \,d x","Not used",1,"int(x/(x + (x^6)^(1/2)), x)","F"
821,0,-1,52,0.000000,"\text{Not used}","int(-((x^3)^(1/2) - x^(1/2))/(x - x^3),x)","-\int \frac{\sqrt{x^3}-\sqrt{x}}{x-x^3} \,d x","Not used",1,"-int(((x^3)^(1/2) - x^(1/2))/(x - x^3), x)","F"
822,0,-1,52,0.000000,"\text{Not used}","int(1/((x^3)^(1/2) + x^(1/2)),x)","\int \frac{1}{\sqrt{x^3}+\sqrt{x}} \,d x","Not used",1,"int(1/((x^3)^(1/2) + x^(1/2)), x)","F"
823,0,-1,68,0.000000,"\text{Not used}","int(1/((x - 1)^(1/2) + ((x - 1)^3)^(1/2)),x)","\int -\frac{\sqrt{x-1}-\sqrt{{\left(x-1\right)}^3}}{{\left(x-1\right)}^3-x+1} \,d x","Not used",1,"int(-((x - 1)^(1/2) - ((x - 1)^3)^(1/2))/((x - 1)^3 - x + 1), x)","F"
824,1,19,31,3.327417,"\text{Not used}","int(- 3/(5*x + 4)^2 - (4*x + 5)/((5*x + 4)^2*(1 - x^2)^(1/2)),x)","\frac{\sqrt{1-x^2}+\frac{3}{5}}{5\,x+4}","Not used",1,"((1 - x^2)^(1/2) + 3/5)/(5*x + 4)","B"
825,1,19,31,0.036278,"\text{Not used}","int(-(4*x + 3*(1 - x^2)^(1/2) + 5)/((5*x + 4)^2*(1 - x^2)^(1/2)),x)","\frac{\sqrt{1-x^2}+\frac{3}{5}}{5\,x+4}","Not used",1,"((1 - x^2)^(1/2) + 3/5)/(5*x + 4)","B"
826,1,19,31,0.065374,"\text{Not used}","int(-1/((4*x + 5)*(1 - x^2)^(1/2) + 3*x^2 - 3),x)","\frac{\sqrt{1-x^2}+\frac{3}{5}}{5\,x+4}","Not used",1,"((1 - x^2)^(1/2) + 3/5)/(5*x + 4)","B"
827,1,19,31,0.052779,"\text{Not used}","int(-1/(4*x*(1 - x^2)^(1/2) + 3*x^2 + 5*(1 - x^2)^(1/2) - 3),x)","\frac{\sqrt{1-x^2}+\frac{3}{5}}{5\,x+4}","Not used",1,"((1 - x^2)^(1/2) + 3/5)/(5*x + 4)","B"
828,1,19,31,3.323606,"\text{Not used}","int(((1 - x^2)^(1/2) - 1)/((1 - x^2)^(1/2)*(x - 2*(1 - x^2)^(1/2) + 2)^2),x)","\frac{\sqrt{1-x^2}+\frac{3}{5}}{5\,x+4}","Not used",1,"((1 - x^2)^(1/2) + 3/5)/(5*x + 4)","B"
829,0,-1,43,0.000000,"\text{Not used}","int((a + b*x^(n - 1))/(d*x^n + c*x),x)","\int \frac{a+b\,x^{n-1}}{d\,x^n+c\,x} \,d x","Not used",1,"int((a + b*x^(n - 1))/(d*x^n + c*x), x)","F"
830,1,31,42,3.387579,"\text{Not used}","int((2*x^2 + 1)^(1/2)/((2*x^2 + 1)^(1/2) + 1),x)","x-\frac{\sqrt{2}\,\mathrm{asinh}\left(\sqrt{2}\,x\right)}{2}+\frac{\frac{\sqrt{2}\,\sqrt{x^2+\frac{1}{2}}}{2}-\frac{1}{2}}{x}","Not used",1,"x - (2^(1/2)*asinh(2^(1/2)*x))/2 + ((2^(1/2)*(x^2 + 1/2)^(1/2))/2 - 1/2)/x","B"
831,1,60,65,3.443516,"\text{Not used}","int((4*x^2 - 1)^(1/2)/(x + (4*x^2 - 1)^(1/2)),x)","\frac{4\,x}{3}+\frac{\sqrt{3}\,\ln\left(x-\frac{\sqrt{3}}{3}\right)}{18}-\frac{\sqrt{3}\,\ln\left(x+\frac{\sqrt{3}}{3}\right)}{18}+\frac{\sqrt{3}\,\mathrm{atanh}\left(\sqrt{3}\,\sqrt{4\,x^2-1}\right)}{9}-\frac{\sqrt{4\,x^2-1}}{3}","Not used",1,"(4*x)/3 + (3^(1/2)*log(x - 3^(1/2)/3))/18 - (3^(1/2)*log(x + 3^(1/2)/3))/18 + (3^(1/2)*atanh(3^(1/2)*(4*x^2 - 1)^(1/2)))/9 - (4*x^2 - 1)^(1/2)/3","B"
832,0,-1,195,0.000000,"\text{Not used}","int((a + b*x + c*x^2)/((x^2 - 1)^(1/2)*(d + e*x)^3),x)","\int \frac{c\,x^2+b\,x+a}{\sqrt{x^2-1}\,{\left(d+e\,x\right)}^3} \,d x","Not used",1,"int((a + b*x + c*x^2)/((x^2 - 1)^(1/2)*(d + e*x)^3), x)","F"
833,1,20,28,3.849942,"\text{Not used}","int((2*x^8 + 1)/(x*(x^8 + 1)^(3/2)),x)","-\frac{\mathrm{atanh}\left(\sqrt{x^8+1}\right)}{4}-\frac{1}{4\,\sqrt{x^8+1}}","Not used",1,"- atanh((x^8 + 1)^(1/2))/4 - 1/(4*(x^8 + 1)^(1/2))","B"
834,0,-1,28,0.000000,"\text{Not used}","int(((x^8 + 1)^(1/2)*(2*x^8 + 1))/(x + 2*x^9 + x^17),x)","\int \frac{\sqrt{x^8+1}\,\left(2\,x^8+1\right)}{x^{17}+2\,x^9+x} \,d x","Not used",1,"int(((x^8 + 1)^(1/2)*(2*x^8 + 1))/(x + 2*x^9 + x^17), x)","F"
835,1,18,22,0.044475,"\text{Not used}","int(x/(1 - 9*x^2)^(1/2) - 9*x^2 + 1,x)","x-3\,x^3-\frac{\sqrt{\frac{1}{9}-x^2}}{3}","Not used",1,"x - 3*x^3 - (1/9 - x^2)^(1/2)/3","B"
836,1,18,22,0.028527,"\text{Not used}","int((x + (1 - 9*x^2)^(3/2))/(1 - 9*x^2)^(1/2),x)","x-3\,x^3-\frac{\sqrt{\frac{1}{9}-x^2}}{3}","Not used",1,"x - 3*x^3 - (1/9 - x^2)^(1/2)/3","B"
837,1,11,17,3.700168,"\text{Not used}","int(((x - 3*x^(1/2))^(2/3)*(2*x^(1/2) - 3))/x^(1/2),x)","\frac{6\,{\left(x-3\,\sqrt{x}\right)}^{5/3}}{5}","Not used",1,"(6*(x - 3*x^(1/2))^(5/3))/5","B"
838,0,-1,17,0.000000,"\text{Not used}","int((2*x - 9*x^(1/2) + 9)/(x - 3*x^(1/2))^(1/3),x)","\int \frac{2\,x-9\,\sqrt{x}+9}{{\left(x-3\,\sqrt{x}\right)}^{1/3}} \,d x","Not used",1,"int((2*x - 9*x^(1/2) + 9)/(x - 3*x^(1/2))^(1/3), x)","F"
839,1,6,10,0.010177,"\text{Not used}","int(1/(4 - 9*x^2)^(1/2),x)","\frac{\mathrm{asin}\left(\frac{3\,x}{2}\right)}{3}","Not used",1,"asin((3*x)/2)/3","B"
840,1,32,10,0.147643,"\text{Not used}","int(1/((2 - 3*x)^(1/2)*(3*x + 2)^(1/2)),x)","-\frac{4\,\mathrm{atan}\left(\frac{\sqrt{2}-\sqrt{2-3\,x}}{\sqrt{2}-\sqrt{3\,x+2}}\right)}{3}","Not used",1,"-(4*atan((2^(1/2) - (2 - 3*x)^(1/2))/(2^(1/2) - (3*x + 2)^(1/2))))/3","B"
841,1,6,10,0.012178,"\text{Not used}","int(1/(-(3*x - 2)*(3*x + 2))^(1/2),x)","\frac{\mathrm{asin}\left(\frac{3\,x}{2}\right)}{3}","Not used",1,"asin((3*x)/2)/3","B"
842,1,6,12,3.124940,"\text{Not used}","int(1/(15 - x^2 - 2*x)^(1/2),x)","\mathrm{asin}\left(\frac{x}{4}+\frac{1}{4}\right)","Not used",1,"asin(x/4 + 1/4)","B"
843,1,30,12,3.427964,"\text{Not used}","int(1/((3 - x)^(1/2)*(x + 5)^(1/2)),x)","4\,\mathrm{atan}\left(\frac{\sqrt{3}-\sqrt{3-x}}{\sqrt{x+5}-\sqrt{5}}\right)","Not used",1,"4*atan((3^(1/2) - (3 - x)^(1/2))/((x + 5)^(1/2) - 5^(1/2)))","B"
844,1,6,12,3.369524,"\text{Not used}","int(1/(-(x - 3)*(x + 5))^(1/2),x)","\mathrm{asin}\left(\frac{x}{4}+\frac{1}{4}\right)","Not used",1,"asin(x/4 + 1/4)","B"
845,1,4,4,3.184726,"\text{Not used}","int(1/(- 8*x - x^2 - 15)^(1/2),x)","\mathrm{asin}\left(x+4\right)","Not used",1,"asin(x + 4)","B"
846,1,33,4,0.082386,"\text{Not used}","int(1/((- x - 3)^(1/2)*(x + 5)^(1/2)),x)","4\,\mathrm{atan}\left(\frac{-\sqrt{-x-3}+\sqrt{3}\,1{}\mathrm{i}}{\sqrt{x+5}-\sqrt{5}}\right)","Not used",1,"4*atan((3^(1/2)*1i - (- x - 3)^(1/2))/((x + 5)^(1/2) - 5^(1/2)))","B"
847,1,4,4,3.362337,"\text{Not used}","int(1/(-(x + 3)*(x + 5))^(1/2),x)","\mathrm{asin}\left(x+4\right)","Not used",1,"asin(x + 4)","B"
848,1,7,11,0.025553,"\text{Not used}","int(1 - x^(1/2),x)","x-\frac{2\,x^{3/2}}{3}","Not used",1,"x - (2*x^(3/2))/3","B"
849,1,7,11,0.026096,"\text{Not used}","int(-(x - 1)/(x^(1/2) + 1),x)","x-\frac{2\,x^{3/2}}{3}","Not used",1,"x - (2*x^(3/2))/3","B"
850,0,-1,27,0.000000,"\text{Not used}","int((-1/(x^2 - 1))^(1/2),x)","\int \sqrt{-\frac{1}{x^2-1}} \,d x","Not used",1,"int((-1/(x^2 - 1))^(1/2), x)","F"
851,0,-1,27,0.000000,"\text{Not used}","int((-(x^2 + 1)/(x^4 - 1))^(1/2),x)","\int \sqrt{-\frac{x^2+1}{x^4-1}} \,d x","Not used",1,"int((-(x^2 + 1)/(x^4 - 1))^(1/2), x)","F"
852,0,-1,25,0.000000,"\text{Not used}","int((1/(x^2 - 1))^(1/2),x)","\int \sqrt{\frac{1}{x^2-1}} \,d x","Not used",1,"int((1/(x^2 - 1))^(1/2), x)","F"
853,0,-1,25,0.000000,"\text{Not used}","int(((x^2 + 1)/(x^4 - 1))^(1/2),x)","\int \sqrt{\frac{x^2+1}{x^4-1}} \,d x","Not used",1,"int(((x^2 + 1)/(x^4 - 1))^(1/2), x)","F"
854,1,9,11,0.193215,"\text{Not used}","int(1/(1 - x)^(1/2),x)","-2\,\sqrt{1-x}","Not used",1,"-2*(1 - x)^(1/2)","B"
855,1,16,11,3.556731,"\text{Not used}","int((x + 1)^(1/2)/(1 - x^2)^(1/2),x)","-\frac{2\,\sqrt{1-x^2}}{\sqrt{x+1}}","Not used",1,"-(2*(1 - x^2)^(1/2))/(x + 1)^(1/2)","B"
856,1,7,9,0.094961,"\text{Not used}","int(1/(x + 1)^(1/2),x)","2\,\sqrt{x+1}","Not used",1,"2*(x + 1)^(1/2)","B"
857,1,18,9,3.635318,"\text{Not used}","int((1 - x)^(1/2)/(1 - x^2)^(1/2),x)","\frac{2\,\sqrt{1-x^2}}{\sqrt{1-x}}","Not used",1,"(2*(1 - x^2)^(1/2))/(1 - x)^(1/2)","B"
858,1,9,13,3.507127,"\text{Not used}","int((1 - x)^(1/2),x)","-\frac{2\,{\left(1-x\right)}^{3/2}}{3}","Not used",1,"-(2*(1 - x)^(3/2))/3","B"
859,1,20,13,3.522690,"\text{Not used}","int((1 - x^2)^(1/2)/(x + 1)^(1/2),x)","\frac{\left(\frac{2\,x}{3}-\frac{2}{3}\right)\,\sqrt{1-x^2}}{\sqrt{x+1}}","Not used",1,"(((2*x)/3 - 2/3)*(1 - x^2)^(1/2))/(x + 1)^(1/2)","B"
860,1,7,11,3.419362,"\text{Not used}","int((x + 1)^(1/2),x)","\frac{2\,{\left(x+1\right)}^{3/2}}{3}","Not used",1,"(2*(x + 1)^(3/2))/3","B"
861,1,22,11,3.490576,"\text{Not used}","int((1 - x^2)^(1/2)/(1 - x)^(1/2),x)","\frac{\left(\frac{2\,x}{3}+\frac{2}{3}\right)\,\sqrt{1-x^2}}{\sqrt{1-x}}","Not used",1,"(((2*x)/3 + 2/3)*(1 - x^2)^(1/2))/(1 - x)^(1/2)","B"
862,1,172,35,6.135913,"\text{Not used}","int((3*x + 2)^(1/2)/(x + 1)^(1/2),x)","\frac{2\,\sqrt{3}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,\left(\sqrt{2}-\sqrt{3\,x+2}\right)}{3\,\left(\sqrt{x+1}-1\right)}\right)}{3}-\frac{\frac{30\,\left(\sqrt{2}-\sqrt{3\,x+2}\right)}{\sqrt{x+1}-1}+\frac{10\,{\left(\sqrt{2}-\sqrt{3\,x+2}\right)}^3}{{\left(\sqrt{x+1}-1\right)}^3}+\frac{24\,\sqrt{2}\,{\left(\sqrt{2}-\sqrt{3\,x+2}\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}}{\frac{{\left(\sqrt{2}-\sqrt{3\,x+2}\right)}^4}{{\left(\sqrt{x+1}-1\right)}^4}-\frac{6\,{\left(\sqrt{2}-\sqrt{3\,x+2}\right)}^2}{{\left(\sqrt{x+1}-1\right)}^2}+9}","Not used",1,"(2*3^(1/2)*atanh((3^(1/2)*(2^(1/2) - (3*x + 2)^(1/2)))/(3*((x + 1)^(1/2) - 1))))/3 - ((30*(2^(1/2) - (3*x + 2)^(1/2)))/((x + 1)^(1/2) - 1) + (10*(2^(1/2) - (3*x + 2)^(1/2))^3)/((x + 1)^(1/2) - 1)^3 + (24*2^(1/2)*(2^(1/2) - (3*x + 2)^(1/2))^2)/((x + 1)^(1/2) - 1)^2)/((2^(1/2) - (3*x + 2)^(1/2))^4/((x + 1)^(1/2) - 1)^4 - (6*(2^(1/2) - (3*x + 2)^(1/2))^2)/((x + 1)^(1/2) - 1)^2 + 9)","B"
863,0,-1,35,0.000000,"\text{Not used}","int(((3*x + 2)^(1/2)*(1 - x)^(1/2))/(1 - x^2)^(1/2),x)","\int \frac{\sqrt{3\,x+2}\,\sqrt{1-x}}{\sqrt{1-x^2}} \,d x","Not used",1,"int(((3*x + 2)^(1/2)*(1 - x)^(1/2))/(1 - x^2)^(1/2), x)","F"
864,0,-1,43,0.000000,"\text{Not used}","int((x + 1)^(3/2)/(x*(1 - x)^(3/2)),x)","\int \frac{{\left(x+1\right)}^{3/2}}{x\,{\left(1-x\right)}^{3/2}} \,d x","Not used",1,"int((x + 1)^(3/2)/(x*(1 - x)^(3/2)), x)","F"
865,1,37,35,3.203682,"\text{Not used}","int((x + 1)^3/(x*(1 - x^2)^(3/2)),x)","\ln\left(\sqrt{\frac{1}{x^2}-1}-\sqrt{\frac{1}{x^2}}\right)-\mathrm{asin}\left(x\right)-\frac{4\,\sqrt{1-x^2}}{x-1}","Not used",1,"log((1/x^2 - 1)^(1/2) - (1/x^2)^(1/2)) - asin(x) - (4*(1 - x^2)^(1/2))/(x - 1)","B"
866,0,-1,51,0.000000,"\text{Not used}","int((a*x + 1)^(3/2)/(x*(1 - a*x)^(3/2)),x)","\int \frac{{\left(a\,x+1\right)}^{3/2}}{x\,{\left(1-a\,x\right)}^{3/2}} \,d x","Not used",1,"int((a*x + 1)^(3/2)/(x*(1 - a*x)^(3/2)), x)","F"
867,1,82,45,3.491190,"\text{Not used}","int((a*x + 1)^3/(x*(1 - a^2*x^2)^(3/2)),x)","\frac{4\,a\,\sqrt{1-a^2\,x^2}}{\left(x\,\sqrt{-a^2}-\frac{\sqrt{-a^2}}{a}\right)\,\sqrt{-a^2}}-\frac{a\,\mathrm{asinh}\left(x\,\sqrt{-a^2}\right)}{\sqrt{-a^2}}-\mathrm{atanh}\left(\sqrt{1-a^2\,x^2}\right)","Not used",1,"(4*a*(1 - a^2*x^2)^(1/2))/((x*(-a^2)^(1/2) - (-a^2)^(1/2)/a)*(-a^2)^(1/2)) - (a*asinh(x*(-a^2)^(1/2)))/(-a^2)^(1/2) - atanh((1 - a^2*x^2)^(1/2))","B"
868,1,2,2,0.005932,"\text{Not used}","int(1/(1 - x^2)^(1/2),x)","\mathrm{asin}\left(x\right)","Not used",1,"asin(x)","B"
869,0,-1,2,0.000000,"\text{Not used}","int((x^2 + 1)^(1/2)/(1 - x^4)^(1/2),x)","\int \frac{\sqrt{x^2+1}}{\sqrt{1-x^4}} \,d x","Not used",1,"int((x^2 + 1)^(1/2)/(1 - x^4)^(1/2), x)","F"
870,1,2,2,0.028340,"\text{Not used}","int(1/(x^2 + 1)^(1/2),x)","\mathrm{asinh}\left(x\right)","Not used",1,"asinh(x)","B"
871,0,-1,2,0.000000,"\text{Not used}","int((1 - x^2)^(1/2)/(1 - x^4)^(1/2),x)","\int \frac{\sqrt{1-x^2}}{\sqrt{1-x^4}} \,d x","Not used",1,"int((1 - x^2)^(1/2)/(1 - x^4)^(1/2), x)","F"
872,1,17,23,0.030765,"\text{Not used}","int((1 - x^2)^(1/2),x)","\frac{\mathrm{asin}\left(x\right)}{2}+\frac{x\,\sqrt{1-x^2}}{2}","Not used",1,"asin(x)/2 + (x*(1 - x^2)^(1/2))/2","B"
873,0,-1,23,0.000000,"\text{Not used}","int((1 - x^4)^(1/2)/(x^2 + 1)^(1/2),x)","\int \frac{\sqrt{1-x^4}}{\sqrt{x^2+1}} \,d x","Not used",1,"int((1 - x^4)^(1/2)/(x^2 + 1)^(1/2), x)","F"
874,1,15,21,0.028333,"\text{Not used}","int((x^2 + 1)^(1/2),x)","\frac{\mathrm{asinh}\left(x\right)}{2}+\frac{x\,\sqrt{x^2+1}}{2}","Not used",1,"asinh(x)/2 + (x*(x^2 + 1)^(1/2))/2","B"
875,0,-1,21,0.000000,"\text{Not used}","int((1 - x^4)^(1/2)/(1 - x^2)^(1/2),x)","\int \frac{\sqrt{1-x^4}}{\sqrt{1-x^2}} \,d x","Not used",1,"int((1 - x^4)^(1/2)/(1 - x^2)^(1/2), x)","F"
876,1,54,49,4.672777,"\text{Not used}","int(((a + b + c*x^2)/d)^m,x)","\frac{x\,{\left(\frac{a+b}{d}+\frac{c\,x^2}{d}\right)}^m\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},-m;\ \frac{3}{2};\ -\frac{c\,x^2}{a+b}\right)}{{\left(\frac{c\,x^2}{a+b}+1\right)}^m}","Not used",1,"(x*((a + b)/d + (c*x^2)/d)^m*hypergeom([1/2, -m], 3/2, -(c*x^2)/(a + b)))/((c*x^2)/(a + b) + 1)^m","B"
877,1,20,28,0.034024,"\text{Not used}","int(1/(x - (x^2 + 1)^(1/2)),x)","-\frac{\mathrm{asinh}\left(x\right)}{2}-\frac{x\,\sqrt{x^2+1}}{2}-\frac{x^2}{2}","Not used",1,"- asinh(x)/2 - (x*(x^2 + 1)^(1/2))/2 - x^2/2","B"
878,1,105,37,0.143069,"\text{Not used}","int(1/(x - (1 - x^2)^(1/2)),x)","\frac{\ln\left(x-\frac{\sqrt{2}}{2}\right)}{4}+\frac{\ln\left(x+\frac{\sqrt{2}}{2}\right)}{4}-\frac{\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,x}{2}-1\right)\,1{}\mathrm{i}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\frac{\sqrt{2}}{2}}\right)}{4}+\frac{\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,x}{2}+1\right)\,1{}\mathrm{i}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{2}}{2}}\right)}{4}-\frac{\mathrm{asin}\left(x\right)}{2}","Not used",1,"log(x - 2^(1/2)/2)/4 + log(x + 2^(1/2)/2)/4 - log((2^(1/2)*((2^(1/2)*x)/2 - 1)*1i - (1 - x^2)^(1/2)*1i)/(x - 2^(1/2)/2))/4 + log((2^(1/2)*((2^(1/2)*x)/2 + 1)*1i + (1 - x^2)^(1/2)*1i)/(x + 2^(1/2)/2))/4 - asin(x)/2","B"
879,1,57,40,3.500681,"\text{Not used}","int(1/(x - (2*x^2 + 1)^(1/2)),x)","-\ln\left(x-\mathrm{i}\right)-\frac{\ln\left(x-\frac{\sqrt{2}\,\sqrt{x^2+\frac{1}{2}}}{2}+\frac{1}{2}{}\mathrm{i}\right)}{2}+\frac{\ln\left(x+\frac{\sqrt{2}\,\sqrt{x^2+\frac{1}{2}}}{2}-\frac{1}{2}{}\mathrm{i}\right)}{2}-\sqrt{2}\,\mathrm{asinh}\left(\sqrt{2}\,x\right)","Not used",1,"log(x + (2^(1/2)*(x^2 + 1/2)^(1/2))/2 - 1i/2)/2 - log(x - (2^(1/2)*(x^2 + 1/2)^(1/2))/2 + 1i/2)/2 - log(x - 1i) - 2^(1/2)*asinh(2^(1/2)*x)","B"
880,1,86,54,3.327870,"\text{Not used}","int((2*x + x^2*(2 - x^2)^(1/2) - x^3)/(2*x^2 - 2),x)","\frac{\ln\left(x-1\right)}{4}+\frac{\ln\left(x+1\right)}{4}-\frac{\ln\left(\frac{-x\,1{}\mathrm{i}+\sqrt{2-x^2}\,1{}\mathrm{i}+2{}\mathrm{i}}{x-1}\right)}{4}+\frac{\ln\left(\frac{x\,1{}\mathrm{i}+\sqrt{2-x^2}\,1{}\mathrm{i}+2{}\mathrm{i}}{x+1}\right)}{4}+\frac{x\,\sqrt{2-x^2}}{4}-\frac{x^2}{4}","Not used",1,"log(x - 1)/4 + log(x + 1)/4 - log(((2 - x^2)^(1/2)*1i - x*1i + 2i)/(x - 1))/4 + log((x*1i + (2 - x^2)^(1/2)*1i + 2i)/(x + 1))/4 + (x*(2 - x^2)^(1/2))/4 - x^2/4","B"
881,1,86,60,3.377495,"\text{Not used}","int((x*(2 - x^2)^(1/2))/(x - (2 - x^2)^(1/2)),x)","\frac{\ln\left(x-1\right)}{4}+\frac{\ln\left(x+1\right)}{4}-\frac{\ln\left(\frac{-x\,1{}\mathrm{i}+\sqrt{2-x^2}\,1{}\mathrm{i}+2{}\mathrm{i}}{x-1}\right)}{4}+\frac{\ln\left(\frac{x\,1{}\mathrm{i}+\sqrt{2-x^2}\,1{}\mathrm{i}+2{}\mathrm{i}}{x+1}\right)}{4}+\frac{x\,\sqrt{2-x^2}}{4}-\frac{x^2}{4}","Not used",1,"log(x - 1)/4 + log(x + 1)/4 - log(((2 - x^2)^(1/2)*1i - x*1i + 2i)/(x - 1))/4 + log((x*1i + (2 - x^2)^(1/2)*1i + 2i)/(x + 1))/4 + (x*(2 - x^2)^(1/2))/4 - x^2/4","B"
882,0,-1,51,0.000000,"\text{Not used}","int(-x/(x - (2*x - x^2)^(1/2)),x)","\int -\frac{x}{x-\sqrt{2\,x-x^2}} \,d x","Not used",1,"int(-x/(x - (2*x - x^2)^(1/2)), x)","F"
883,0,-1,51,0.000000,"\text{Not used}","int(-(x + (2*x - x^2)^(1/2))/(2*x - 2),x)","\int -\frac{x+\sqrt{2\,x-x^2}}{2\,x-2} \,d x","Not used",1,"int(-(x + (2*x - x^2)^(1/2))/(2*x - 2), x)","F"
884,1,56,51,4.781510,"\text{Not used}","int(-(x + x^(1/2)*(2 - x)^(1/2))/(2*x - 2),x)","\mathrm{atanh}\left(\frac{\sqrt{x}\,\left(\sqrt{2}-\sqrt{2-x}\right)}{x+\sqrt{2}\,\sqrt{2-x}-2}\right)-\frac{\ln\left(x-1\right)}{2}-\frac{x}{2}-\frac{\sqrt{x}\,\sqrt{2-x}}{2}","Not used",1,"atanh((x^(1/2)*(2^(1/2) - (2 - x)^(1/2)))/(x + 2^(1/2)*(2 - x)^(1/2) - 2)) - log(x - 1)/2 - x/2 - (x^(1/2)*(2 - x)^(1/2))/2","B"
885,1,56,54,0.061422,"\text{Not used}","int(x^(1/2)/((2 - x)^(1/2) - x^(1/2)),x)","\mathrm{atanh}\left(\frac{\sqrt{x}\,\left(\sqrt{2}-\sqrt{2-x}\right)}{x+\sqrt{2}\,\sqrt{2-x}-2}\right)-\frac{\ln\left(x-1\right)}{2}-\frac{x}{2}-\frac{\sqrt{x}\,\sqrt{2-x}}{2}","Not used",1,"atanh((x^(1/2)*(2^(1/2) - (2 - x)^(1/2)))/(x + 2^(1/2)*(2 - x)^(1/2) - 2)) - log(x - 1)/2 - x/2 - (x^(1/2)*(2 - x)^(1/2))/2","B"
886,1,20,27,3.419311,"\text{Not used}","int(1/((x^2 - 1)*(x + 1))^(2/3),x)","\frac{3\,{\left(\left(x^2-1\right)\,\left(x+1\right)\right)}^{1/3}}{2\,\left(x+1\right)}","Not used",1,"(3*((x^2 - 1)*(x + 1))^(1/3))/(2*(x + 1))","B"
887,1,138,14,3.380349,"\text{Not used}","int((x^2 - 1)/((x*(x^2 + 1))^(1/2)*(x^2 + 1)),x)","-\frac{2\,x}{\sqrt{x^3+x}}-\frac{\sqrt{1-x\,1{}\mathrm{i}}\,\sqrt{\frac{1}{2}+\frac{x\,1{}\mathrm{i}}{2}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{1-x\,1{}\mathrm{i}}\right)\middle|\frac{1}{2}\right)\,\sqrt{x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{\sqrt{x^3+x}}+\frac{\sqrt{1-x\,1{}\mathrm{i}}\,\sqrt{\frac{1}{2}+\frac{x\,1{}\mathrm{i}}{2}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{1-x\,1{}\mathrm{i}}\right)\middle|\frac{1}{2}\right)\,\sqrt{x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{\sqrt{x^3+x}}-\frac{\sqrt{1-x\,1{}\mathrm{i}}\,\sqrt{1+x\,1{}\mathrm{i}}\,\sqrt{-x\,1{}\mathrm{i}}\,\mathrm{E}\left(\mathrm{asin}\left(\sqrt{-x\,1{}\mathrm{i}}\right)\middle|-1\right)\,1{}\mathrm{i}}{\sqrt{x^3+x}}","Not used",1,"((1 - x*1i)^(1/2)*((x*1i)/2 + 1/2)^(1/2)*ellipticF(asin((1 - x*1i)^(1/2)), 1/2)*(x*1i)^(1/2)*2i)/(x + x^3)^(1/2) - ((1 - x*1i)^(1/2)*((x*1i)/2 + 1/2)^(1/2)*ellipticE(asin((1 - x*1i)^(1/2)), 1/2)*(x*1i)^(1/2)*2i)/(x + x^3)^(1/2) - (2*x)/(x + x^3)^(1/2) - ((1 - x*1i)^(1/2)*(x*1i + 1)^(1/2)*(-x*1i)^(1/2)*ellipticE(asin((-x*1i)^(1/2)), -1)*1i)/(x + x^3)^(1/2)","B"
888,1,10,12,0.051467,"\text{Not used}","int((x^2 - 1)/((x^2 + 1)*(x + x^3)^(1/2)),x)","-\frac{2\,x}{\sqrt{x^3+x}}","Not used",1,"-(2*x)/(x + x^3)^(1/2)","B"
889,1,48,36,3.492117,"\text{Not used}","int(((x^2 - 1)^2/(x*(x^2 + 1)))^(1/2)/(x^2 + 1),x)","-\frac{\left(2\,x^3+2\,x\right)\,\sqrt{\frac{1}{x^2+1}}\,\sqrt{{\left(x^2-1\right)}^2}\,\sqrt{\frac{1}{x}}}{\left(x^2-1\right)\,\left(x^2+1\right)}","Not used",1,"-((2*x + 2*x^3)*(1/(x^2 + 1))^(1/2)*((x^2 - 1)^2)^(1/2)*(1/x)^(1/2))/((x^2 - 1)*(x^2 + 1))","B"
890,1,43,33,3.493695,"\text{Not used}","int(((x^2 - 1)^2/(x + x^3))^(1/2)/(x^2 + 1),x)","-\frac{\sqrt{\frac{1}{x^3+x}}\,\left(2\,x^3+2\,x\right)\,\sqrt{{\left(x^2-1\right)}^2}}{\left(x^2-1\right)\,\left(x^2+1\right)}","Not used",1,"-((1/(x + x^3))^(1/2)*(2*x + 2*x^3)*((x^2 - 1)^2)^(1/2))/((x^2 - 1)*(x^2 + 1))","B"
891,0,-1,70,0.000000,"\text{Not used}","int(1/((a + b/x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{a+\frac{b}{x^2}}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b/x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
892,0,-1,83,0.000000,"\text{Not used}","int((x^4 - 2*x^2)^(1/2)/((x^2 - 1)*(x^2 + 2)),x)","\int \frac{\sqrt{x^4-2\,x^2}}{\left(x^2-1\right)\,\left(x^2+2\right)} \,d x","Not used",1,"int((x^4 - 2*x^2)^(1/2)/((x^2 - 1)*(x^2 + 2)), x)","F"
893,0,-1,47,0.000000,"\text{Not used}","int(-(1 - 1/(x^2 - 1)^2)^(1/2)/(x^2 - 2),x)","\int -\frac{\sqrt{1-\frac{1}{{\left(x^2-1\right)}^2}}}{x^2-2} \,d x","Not used",1,"int(-(1 - 1/(x^2 - 1)^2)^(1/2)/(x^2 - 2), x)","F"
894,0,-1,123,0.000000,"\text{Not used}","int((-(2*x^2 - x^4)/(x^2 - 1)^2)^(1/2)/(x^2 + 2),x)","\int \frac{\sqrt{-\frac{2\,x^2-x^4}{{\left(x^2-1\right)}^2}}}{x^2+2} \,d x","Not used",1,"int((-(2*x^2 - x^4)/(x^2 - 1)^2)^(1/2)/(x^2 + 2), x)","F"
895,0,-1,133,0.000000,"\text{Not used}","int(((2*x)/(x^2 + 1) + 1)^(5/2),x)","\int {\left(\frac{2\,x}{x^2+1}+1\right)}^{5/2} \,d x","Not used",1,"int(((2*x)/(x^2 + 1) + 1)^(5/2), x)","F"
896,0,-1,90,0.000000,"\text{Not used}","int(((2*x)/(x^2 + 1) + 1)^(3/2),x)","\int {\left(\frac{2\,x}{x^2+1}+1\right)}^{3/2} \,d x","Not used",1,"int(((2*x)/(x^2 + 1) + 1)^(3/2), x)","F"
897,0,-1,61,0.000000,"\text{Not used}","int(((2*x)/(x^2 + 1) + 1)^(1/2),x)","\int \sqrt{\frac{2\,x}{x^2+1}+1} \,d x","Not used",1,"int(((2*x)/(x^2 + 1) + 1)^(1/2), x)","F"
898,0,-1,109,0.000000,"\text{Not used}","int(1/((2*x)/(x^2 + 1) + 1)^(1/2),x)","\int \frac{1}{\sqrt{\frac{2\,x}{x^2+1}+1}} \,d x","Not used",1,"int(1/((2*x)/(x^2 + 1) + 1)^(1/2), x)","F"
899,0,-1,144,0.000000,"\text{Not used}","int(1/((2*x)/(x^2 + 1) + 1)^(3/2),x)","\int \frac{1}{{\left(\frac{2\,x}{x^2+1}+1\right)}^{3/2}} \,d x","Not used",1,"int(1/((2*x)/(x^2 + 1) + 1)^(3/2), x)","F"
900,1,23,28,3.515252,"\text{Not used}","int(((2*x)/(x^2 + 1) + 1)^(1/2)/(x^2 + 1),x)","\frac{\sqrt{\frac{2\,x}{x^2+1}+1}\,\left(x-1\right)}{x+1}","Not used",1,"(((2*x)/(x^2 + 1) + 1)^(1/2)*(x - 1))/(x + 1)","B"
901,0,-1,17,0.000000,"\text{Not used}","int(F(x)*(x - x^2)^(1/2),x)","\int F\left(x\right)\,\sqrt{x-x^2} \,d x","Not used",0,"int(F(x)*(x - x^2)^(1/2), x)","F"
902,0,-1,17,0.000000,"\text{Not used}","int(F(x)/(x - x^2)^(1/2),x)","\int \frac{F\left(x\right)}{\sqrt{x-x^2}} \,d x","Not used",0,"int(F(x)/(x - x^2)^(1/2), x)","F"
903,0,-1,17,0.000000,"\text{Not used}","int(x^(1/2)*F(x)*(1 - x)^(1/2),x)","\int \sqrt{x}\,F\left(x\right)\,\sqrt{1-x} \,d x","Not used",0,"int(x^(1/2)*F(x)*(1 - x)^(1/2), x)","F"
904,0,-1,17,0.000000,"\text{Not used}","int(F(x)/(x^(1/2)*(1 - x)^(1/2)),x)","\int \frac{F\left(x\right)}{\sqrt{x}\,\sqrt{1-x}} \,d x","Not used",0,"int(F(x)/(x^(1/2)*(1 - x)^(1/2)), x)","F"
905,0,-1,11,0.000000,"\text{Not used}","int(F((a + b*x)/x),x)","\int F\left(\frac{a+b\,x}{x}\right) \,d x","Not used",0,"int(F((a + b*x)/x), x)","F"
906,0,-1,11,0.000000,"\text{Not used}","int(F((a + b*x^2)/x^2),x)","\int F\left(\frac{b\,x^2+a}{x^2}\right) \,d x","Not used",0,"int(F((a + b*x^2)/x^2), x)","F"
907,0,-1,13,0.000000,"\text{Not used}","int(F(x/(a + b*x)),x)","\int F\left(\frac{x}{a+b\,x}\right) \,d x","Not used",0,"int(F(x/(a + b*x)), x)","F"
908,0,-1,17,0.000000,"\text{Not used}","int(F(x^2/(a + b*x^2)),x)","\int F\left(\frac{x^2}{b\,x^2+a}\right) \,d x","Not used",0,"int(F(x^2/(a + b*x^2)), x)","F"
909,0,-1,15,0.000000,"\text{Not used}","int(F(x^2/(a + b*x)^2),x)","\int F\left(\frac{x^2}{{\left(a+b\,x\right)}^2}\right) \,d x","Not used",0,"int(F(x^2/(a + b*x)^2), x)","F"
910,0,-1,17,0.000000,"\text{Not used}","int(F(x^4/(a + b*x^2)^2),x)","\int F\left(\frac{x^4}{{\left(b\,x^2+a\right)}^2}\right) \,d x","Not used",0,"int(F(x^4/(a + b*x^2)^2), x)","F"
911,0,-1,47,0.000000,"\text{Not used}","int(((a + b^2*x^4)^(1/2) + b*x^2)^(1/2)/(a + b^2*x^4)^(1/2),x)","\int \frac{\sqrt{\sqrt{b^2\,x^4+a}+b\,x^2}}{\sqrt{b^2\,x^4+a}} \,d x","Not used",1,"int(((a + b^2*x^4)^(1/2) + b*x^2)^(1/2)/(a + b^2*x^4)^(1/2), x)","F"
912,0,-1,48,0.000000,"\text{Not used}","int(((a + b^2*x^4)^(1/2) - b*x^2)^(1/2)/(a + b^2*x^4)^(1/2),x)","\int \frac{\sqrt{\sqrt{b^2\,x^4+a}-b\,x^2}}{\sqrt{b^2\,x^4+a}} \,d x","Not used",1,"int(((a + b^2*x^4)^(1/2) - b*x^2)^(1/2)/(a + b^2*x^4)^(1/2), x)","F"
913,0,-1,169,0.000000,"\text{Not used}","int((2*x^2 + (4*x^4 + 3)^(1/2))^(1/2)/((4*x^4 + 3)^(1/2)*(c + d*x)),x)","\int \frac{\sqrt{2\,x^2+\sqrt{4\,x^4+3}}}{\sqrt{4\,x^4+3}\,\left(c+d\,x\right)} \,d x","Not used",1,"int((2*x^2 + (4*x^4 + 3)^(1/2))^(1/2)/((4*x^4 + 3)^(1/2)*(c + d*x)), x)","F"
914,0,-1,268,0.000000,"\text{Not used}","int((2*x^2 + (4*x^4 + 3)^(1/2))^(1/2)/((4*x^4 + 3)^(1/2)*(c + d*x)^2),x)","\int \frac{\sqrt{2\,x^2+\sqrt{4\,x^4+3}}}{\sqrt{4\,x^4+3}\,{\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((2*x^2 + (4*x^4 + 3)^(1/2))^(1/2)/((4*x^4 + 3)^(1/2)*(c + d*x)^2), x)","F"
915,1,27,41,3.367375,"\text{Not used}","int((x - 4)/(x^(1/2)*(x^(1/3) + 1)),x)","30\,\mathrm{atan}\left(x^{1/6}\right)+2\,\sqrt{x}-30\,x^{1/6}-\frac{6\,x^{5/6}}{5}+\frac{6\,x^{7/6}}{7}","Not used",1,"30*atan(x^(1/6)) + 2*x^(1/2) - 30*x^(1/6) - (6*x^(5/6))/5 + (6*x^(7/6))/7","B"
916,1,22,26,3.360782,"\text{Not used}","int((x^(1/2) + 1)/(x^(5/6) + x^(7/6)),x)","6\,\mathrm{atan}\left(x^{1/6}\right)-3\,\ln\left(36\,x^{1/3}+36\right)+3\,x^{1/3}","Not used",1,"6*atan(x^(1/6)) - 3*log(36*x^(1/3) + 36) + 3*x^(1/3)","B"
917,1,42,42,0.025724,"\text{Not used}","int((x^(1/2) + 1)/(x^(1/2)*(x^(1/3) + 1)),x)","\frac{3\,x^{2/3}}{2}+3\,\ln\left(\left(-6+x^{1/6}\,6{}\mathrm{i}\right)\,\left(6+x^{1/6}\,6{}\mathrm{i}\right)\right)-3\,x^{1/3}-6\,\mathrm{atan}\left(x^{1/6}\right)+6\,x^{1/6}","Not used",1,"3*log((x^(1/6)*6i - 6)*(x^(1/6)*6i + 6)) - 6*atan(x^(1/6)) - 3*x^(1/3) + (3*x^(2/3))/2 + 6*x^(1/6)","B"
918,1,17,20,3.459546,"\text{Not used}","int((b/x^2 + 2)^(1/2)/(b + 2*x^2),x)","-\frac{\mathrm{asinh}\left(\frac{\sqrt{2}\,\sqrt{b}}{2\,x}\right)}{\sqrt{b}}","Not used",1,"-asinh((2^(1/2)*b^(1/2))/(2*x))/b^(1/2)","B"
919,1,21,20,3.469582,"\text{Not used}","int(-(2 - b/x^2)^(1/2)/(b - 2*x^2),x)","-\frac{\mathrm{asinh}\left(\frac{\sqrt{2}\,\sqrt{-b}}{2\,x}\right)}{\sqrt{-b}}","Not used",1,"-asinh((2^(1/2)*(-b)^(1/2))/(2*x))/(-b)^(1/2)","B"
920,0,-1,121,0.000000,"\text{Not used}","int((a + c/x^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{a+\frac{c}{x^2}}}{d+e\,x} \,d x","Not used",1,"int((a + c/x^2)^(1/2)/(d + e*x), x)","F"
921,0,-1,181,0.000000,"\text{Not used}","int((a + b/x + c/x^2)^(1/2)/(d + e*x),x)","\int \frac{\sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}{d+e\,x} \,d x","Not used",1,"int((a + b/x + c/x^2)^(1/2)/(d + e*x), x)","F"
922,1,16,26,3.541327,"\text{Not used}","int(((x^3)^(1/5) + x^(1/6))/x^(1/2),x)","\frac{10\,\sqrt{x}\,{\left(x^3\right)}^{1/5}}{11}+\frac{3\,x^{2/3}}{2}","Not used",1,"(10*x^(1/2)*(x^3)^(1/5))/11 + (3*x^(2/3))/2","B"
923,1,22,26,3.528870,"\text{Not used}","int((x + 2)/(4*x - x^2)^(1/2),x)","4\,\mathrm{asin}\left(\frac{x}{2}-1\right)-\sqrt{4\,x-x^2}","Not used",1,"4*asin(x/2 - 1) - (4*x - x^2)^(1/2)","B"
924,1,9,15,3.564542,"\text{Not used}","int((x + 3)/(6*x + x^2)^(1/3),x)","\frac{3\,{\left(x\,\left(x+6\right)\right)}^{2/3}}{4}","Not used",1,"(3*(x*(x + 6))^(2/3))/4","B"
925,1,18,22,3.503780,"\text{Not used}","int((x + 4)/(6*x - x^2)^(3/2),x)","\frac{7\,x-12}{9\,\sqrt{6\,x-x^2}}","Not used",1,"(7*x - 12)/(9*(6*x - x^2)^(1/2))","B"
926,0,-1,12,0.000000,"\text{Not used}","int(1/((2*x + x^2)^(1/2)*(x + 1)),x)","\int \frac{1}{\sqrt{x^2+2\,x}\,\left(x+1\right)} \,d x","Not used",1,"int(1/((2*x + x^2)^(1/2)*(x + 1)), x)","F"
927,0,-1,12,0.000000,"\text{Not used}","int(1/((2*x + 1)*(x + x^2)^(1/2)),x)","\int \frac{1}{\left(2\,x+1\right)\,\sqrt{x^2+x}} \,d x","Not used",1,"int(1/((2*x + 1)*(x + x^2)^(1/2)), x)","F"
928,1,10,15,3.639782,"\text{Not used}","int((x - 1)/(2*x - x^2)^(1/2),x)","-\sqrt{-x\,\left(x-2\right)}","Not used",1,"-(-x*(x - 2))^(1/2)","B"
929,0,-1,54,0.000000,"\text{Not used}","int((x - x^2)^(1/2)/(x + 1),x)","\int \frac{\sqrt{x-x^2}}{x+1} \,d x","Not used",1,"int((x - x^2)^(1/2)/(x + 1), x)","F"
930,1,27,59,3.532303,"\text{Not used}","int((x + x^(1/4))^(1/2),x)","\frac{8\,x\,\sqrt{x+x^{1/4}}\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{2},\frac{3}{2};\ \frac{5}{2};\ -x^{3/4}\right)}{9\,\sqrt{x^{3/4}+1}}","Not used",1,"(8*x*(x + x^(1/4))^(1/2)*hypergeom([-1/2, 3/2], 5/2, -x^(3/4)))/(9*(x^(3/4) + 1)^(1/2))","B"
931,1,27,59,3.543921,"\text{Not used}","int((x + x^(3/2))^(1/2),x)","\frac{2\,x\,\sqrt{x+x^{3/2}}\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{2},3;\ 4;\ -\sqrt{x}\right)}{3\,\sqrt{\sqrt{x}+1}}","Not used",1,"(2*x*(x + x^(3/2))^(1/2)*hypergeom([-1/2, 3], 4, -x^(1/2)))/(3*(x^(1/2) + 1)^(1/2))","B"
932,0,-1,94,0.000000,"\text{Not used}","int(x*(x + x^(3/2))^(1/2),x)","\int x\,\sqrt{x+x^{3/2}} \,d x","Not used",1,"int(x*(x + x^(3/2))^(1/2), x)","F"
933,1,19,18,3.499179,"\text{Not used}","int(-(x^2 - 1)*(-1/(x^2 - 2))^(1/2),x)","-\frac{x\,\left(x^2-2\right)\,\sqrt{-\frac{1}{x^2-2}}}{2}","Not used",1,"-(x*(x^2 - 2)*(-1/(x^2 - 2))^(1/2))/2","B"
934,0,-1,107,0.000000,"\text{Not used}","int((x^2 + x^3 - x^4)^(1/2),x)","\int \sqrt{-x^4+x^3+x^2} \,d x","Not used",1,"int((x^2 + x^3 - x^4)^(1/2), x)","F"
935,1,25,25,3.507648,"\text{Not used}","int(1/((a^2 + x^2)^3)^(1/2),x)","\frac{x\,\sqrt{{\left(a^2+x^2\right)}^3}}{a^2\,{\left(a^2+x^2\right)}^2}","Not used",1,"(x*((a^2 + x^2)^3)^(1/2))/(a^2*(a^2 + x^2)^2)","B"
936,1,35,42,3.448491,"\text{Not used}","int(x^(1/2)/(x + x^(1/2) + 1),x)","2\,\sqrt{x}-\frac{2\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}}{3}+\frac{2\,\sqrt{3}\,\sqrt{x}}{3}\right)}{3}-\ln\left(x+\sqrt{x}+1\right)","Not used",1,"2*x^(1/2) - (2*3^(1/2)*atan(3^(1/2)/3 + (2*3^(1/2)*x^(1/2))/3))/3 - log(x + x^(1/2) + 1)","B"
937,1,27,32,0.035244,"\text{Not used}","int(x/(x + x^(1/2) + 1),x)","x+\frac{4\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}}{3}+\frac{2\,\sqrt{3}\,\sqrt{x}}{3}\right)}{3}-2\,\sqrt{x}","Not used",1,"x + (4*3^(1/2)*atan(3^(1/2)/3 + (2*3^(1/2)*x^(1/2))/3))/3 - 2*x^(1/2)","B"
938,0,-1,76,0.000000,"\text{Not used}","int(1/(x^(1/2)*(x + x^(1/2) + 1)^(7/2)),x)","\int \frac{1}{\sqrt{x}\,{\left(x+\sqrt{x}+1\right)}^{7/2}} \,d x","Not used",1,"int(1/(x^(1/2)*(x + x^(1/2) + 1)^(7/2)), x)","F"
939,1,46,46,0.035717,"\text{Not used}","int((x - 1)/((x^2 + 1)^(1/2) + 1),x)","\sqrt{x^2+1}-\ln\left(x\right)-\mathrm{asinh}\left(x\right)+\frac{\sqrt{x^2+1}}{x}-\frac{1}{x}+\mathrm{atan}\left(\sqrt{x^2+1}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"atan((x^2 + 1)^(1/2)*1i)*1i - asinh(x) - log(x) + (x^2 + 1)^(1/2) + (x^2 + 1)^(1/2)/x - 1/x","B"
940,0,-1,20,0.000000,"\text{Not used}","int(1/((x^2 - 1)^(2/3)*(x + 1)^(2/3)),x)","\int \frac{1}{{\left(x^2-1\right)}^{2/3}\,{\left(x+1\right)}^{2/3}} \,d x","Not used",1,"int(1/((x^2 - 1)^(2/3)*(x + 1)^(2/3)), x)","F"
941,1,14,35,3.591114,"\text{Not used}","int((1 - x^6)^(2/3)/x^6 + (1 - x^6)^(2/3),x)","-\frac{{\left(1-x^6\right)}^{5/3}}{5\,x^5}","Not used",1,"-(1 - x^6)^(5/3)/(5*x^5)","B"
942,1,13,15,3.684032,"\text{Not used}","int((x^(m - 1)*(2*a*m + b*x^n*(2*m - n)))/(2*(a + b*x^n)^(3/2)),x)","\frac{x^m}{\sqrt{a+b\,x^n}}","Not used",1,"x^m/(a + b*x^n)^(1/2)","B"
943,1,37,53,0.042777,"\text{Not used}","int((x - 2*x^3)/(3*x + 2)^(1/2),x)","\frac{8\,{\left(3\,x+2\right)}^{5/2}}{135}-\frac{10\,{\left(3\,x+2\right)}^{3/2}}{81}-\frac{4\,\sqrt{3\,x+2}}{81}-\frac{4\,{\left(3\,x+2\right)}^{7/2}}{567}","Not used",1,"(8*(3*x + 2)^(5/2))/135 - (10*(3*x + 2)^(3/2))/81 - (4*(3*x + 2)^(1/2))/81 - (4*(3*x + 2)^(7/2))/567","B"
944,1,25,31,0.068524,"\text{Not used}","int(1/((x + 1)^(1/2) + (x + 1)^(1/4)),x)","4\,\ln\left({\left(x+1\right)}^{1/4}+1\right)+2\,\sqrt{x+1}-4\,{\left(x+1\right)}^{1/4}","Not used",1,"4*log((x + 1)^(1/4) + 1) + 2*(x + 1)^(1/2) - 4*(x + 1)^(1/4)","B"
945,1,9,11,3.516041,"\text{Not used}","int((2*x + 1)/(x + x^2)^(1/2),x)","2\,\sqrt{x\,\left(x+1\right)}","Not used",1,"2*(x*(x + 1))^(1/2)","B"
946,1,4,6,0.143151,"\text{Not used}","int(1/(2*x^(1/2)*(x + 1)),x)","\mathrm{atan}\left(\sqrt{x}\right)","Not used",1,"atan(x^(1/2))","B"
947,1,16,20,3.507611,"\text{Not used}","int(1/(x*(6*x - x^2)^(1/2)),x)","-\frac{\sqrt{6\,x-x^2}}{3\,x}","Not used",1,"-(6*x - x^2)^(1/2)/(3*x)","B"
948,1,11,17,0.024275,"\text{Not used}","int(x^(1/2)*(x^(1/2) + 1),x)","\frac{x^2}{2}+\frac{2\,x^{3/2}}{3}","Not used",1,"x^2/2 + (2*x^(3/2))/3","B"
949,1,12,19,0.024872,"\text{Not used}","int(-(x^(1/2) - 1)/x^(1/3),x)","-\frac{3\,x^{2/3}\,\left(4\,\sqrt{x}-7\right)}{14}","Not used",1,"-(3*x^(2/3)*(4*x^(1/2) - 7))/14","B"
950,1,27,41,0.027004,"\text{Not used}","int(x^(1/2)/(x^(1/3) + 1),x)","6\,\mathrm{atan}\left(x^{1/6}\right)+2\,\sqrt{x}-6\,x^{1/6}-\frac{6\,x^{5/6}}{5}+\frac{6\,x^{7/6}}{7}","Not used",1,"6*atan(x^(1/6)) + 2*x^(1/2) - 6*x^(1/6) - (6*x^(5/6))/5 + (6*x^(7/6))/7","B"
951,1,73,67,3.831592,"\text{Not used}","int((x^(1/2) + 1)^(1/3)/x,x)","2\,\ln\left({\left(\sqrt{x}+1\right)}^{1/3}-1\right)+6\,{\left(\sqrt{x}+1\right)}^{1/3}+\ln\left({\left(\sqrt{x}+1\right)}^{1/3}+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)-\ln\left({\left(\sqrt{x}+1\right)}^{1/3}+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)","Not used",1,"2*log((x^(1/2) + 1)^(1/3) - 1) + 6*(x^(1/2) + 1)^(1/3) + log((x^(1/2) + 1)^(1/3) - (3^(1/2)*1i)/2 + 1/2)*(3^(1/2)*1i - 1) - log((3^(1/2)*1i)/2 + (x^(1/2) + 1)^(1/3) + 1/2)*(3^(1/2)*1i + 1)","B"
952,1,7,11,0.002037,"\text{Not used}","int(1 - x^(1/2),x)","x-\frac{2\,x^{3/2}}{3}","Not used",1,"x - (2*x^(3/2))/3","B"
953,1,7,11,0.023352,"\text{Not used}","int(1 - x^(1/4),x)","x-\frac{4\,x^{5/4}}{5}","Not used",1,"x - (4*x^(5/4))/5","B"
954,1,7,11,0.026458,"\text{Not used}","int(-(x^(1/2) - 1)/(x^(1/4) + 1),x)","x-\frac{4\,x^{5/4}}{5}","Not used",1,"x - (4*x^(5/4))/5","B"
955,0,-1,61,0.000000,"\text{Not used}","int(1/((a + b*x)*(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{\left(a+b\,x\right)\,\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((a + b*x)*(c + d*x))^(1/2), x)","F"
956,0,-1,65,0.000000,"\text{Not used}","int(1/((a + b*x)*(c - d*x))^(1/2),x)","\int \frac{1}{\sqrt{\left(a+b\,x\right)\,\left(c-d\,x\right)}} \,d x","Not used",1,"int(1/((a + b*x)*(c - d*x))^(1/2), x)","F"
957,1,9,13,3.338696,"\text{Not used}","int(-1/(x^(1/2)*(x^2 - 1)),x)","\mathrm{atan}\left(\sqrt{x}\right)+\mathrm{atanh}\left(\sqrt{x}\right)","Not used",1,"atan(x^(1/2)) + atanh(x^(1/2))","B"
958,1,9,13,0.027410,"\text{Not used}","int(x^(1/2)/(x - x^3),x)","\mathrm{atan}\left(\sqrt{x}\right)+\mathrm{atanh}\left(\sqrt{x}\right)","Not used",1,"atan(x^(1/2)) + atanh(x^(1/2))","B"
959,1,233,72,4.234173,"\text{Not used}","int(x/(x*(3^(1/2) + 1) - 3^(1/2) + x^2 + 2),x)","\ln\left(x-\left(\frac{\frac{\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}+\frac{\sqrt{3}\,\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}}{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}+\frac{1}{2}\right)\,\left(2\,x+\sqrt{3}+1\right)\right)\,\left(\frac{\frac{\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}+\frac{\sqrt{3}\,\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}}{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}+\frac{1}{2}\right)-\ln\left(x+\left(\frac{\frac{\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}+\frac{\sqrt{3}\,\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}}{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}-\frac{1}{2}\right)\,\left(2\,x+\sqrt{3}+1\right)\right)\,\left(\frac{\frac{\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}+\frac{\sqrt{3}\,\sqrt{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}}{2}}{\left(\sqrt{3}-1\right)\,\left(\sqrt{3}+7\right)}-\frac{1}{2}\right)","Not used",1,"log(x - ((((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2)/2 + (3^(1/2)*((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2))/2)/((3^(1/2) - 1)*(3^(1/2) + 7)) + 1/2)*(2*x + 3^(1/2) + 1))*((((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2)/2 + (3^(1/2)*((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2))/2)/((3^(1/2) - 1)*(3^(1/2) + 7)) + 1/2) - log(x + ((((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2)/2 + (3^(1/2)*((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2))/2)/((3^(1/2) - 1)*(3^(1/2) + 7)) - 1/2)*(2*x + 3^(1/2) + 1))*((((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2)/2 + (3^(1/2)*((3^(1/2) - 1)*(3^(1/2) + 7))^(1/2))/2)/((3^(1/2) - 1)*(3^(1/2) + 7)) - 1/2)","B"
960,1,22,37,3.513320,"\text{Not used}","int((x^2 + x^3)^(1/2),x)","\frac{2\,\sqrt{x^3+x^2}\,\left(3\,x^2+x-2\right)}{15\,x}","Not used",1,"(2*(x^2 + x^3)^(1/2)*(x + 3*x^2 - 2))/(15*x)","B"
961,0,-1,12,0.000000,"\text{Not used}","int(1/((2*x + x^2)^(1/2)*(x + 1)),x)","\int \frac{1}{\sqrt{x^2+2\,x}\,\left(x+1\right)} \,d x","Not used",1,"int(1/((2*x + x^2)^(1/2)*(x + 1)), x)","F"
962,0,-1,95,0.000000,"\text{Not used}","int(x^(1/2)*(1 - x^(1/2) - x)^(1/2),x)","\int \sqrt{x}\,\sqrt{1-\sqrt{x}-x} \,d x","Not used",1,"int(x^(1/2)*(1 - x^(1/2) - x)^(1/2), x)","F"
963,1,16,35,3.506092,"\text{Not used}","int(((x - 3)^(1/2) + 1)^(1/3),x)","\left(x-3\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{3},2;\ 3;\ -\sqrt{x-3}\right)","Not used",1,"(x - 3)*hypergeom([-1/3, 2], 3, -(x - 3)^(1/2))","B"
964,1,24,37,3.578262,"\text{Not used}","int(1/((2*x - 1)^(1/2) + 3)^(1/2),x)","\frac{\sqrt{3}\,\left(2\,x-1\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},2;\ 3;\ -\frac{\sqrt{2\,x-1}}{3}\right)}{6}","Not used",1,"(3^(1/2)*(2*x - 1)*hypergeom([1/2, 2], 3, -(2*x - 1)^(1/2)/3))/6","B"
965,1,39,29,3.896980,"\text{Not used}","int((1 - x)^(1/2)/(x^(1/2) + 1),x)","\sqrt{x}\,\sqrt{1-x}-2\,\sqrt{1-x}-2\,\mathrm{atan}\left(\frac{\sqrt{x}}{\sqrt{1-x}-1}\right)","Not used",1,"x^(1/2)*(1 - x)^(1/2) - 2*(1 - x)^(1/2) - 2*atan(x^(1/2)/((1 - x)^(1/2) - 1))","B"
966,1,40,25,3.648329,"\text{Not used}","int(-(1 - x)^(1/2)/(x^(1/2) - 1),x)","2\,\mathrm{atan}\left(\frac{\sqrt{x}}{\sqrt{1-x}-1}\right)-2\,\sqrt{1-x}-\sqrt{x}\,\sqrt{1-x}","Not used",1,"2*atan(x^(1/2)/((1 - x)^(1/2) - 1)) - 2*(1 - x)^(1/2) - x^(1/2)*(1 - x)^(1/2)","B"
967,1,22,21,0.040608,"\text{Not used}","int(x/(x - (x^2 + 1)^(1/2)),x)","-\sqrt{x^2+1}\,\left(\frac{x^2}{3}+\frac{1}{3}\right)-\frac{x^3}{3}","Not used",1,"- (x^2 + 1)^(1/2)*(x^2/3 + 1/3) - x^3/3","B"
968,1,127,65,3.498785,"\text{Not used}","int(x/(x - (1 - x^2)^(1/2)),x)","\frac{x}{2}-\frac{\sqrt{2}\,\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,x}{2}-1\right)\,1{}\mathrm{i}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\frac{\sqrt{2}}{2}}\right)}{8}-\frac{\sqrt{2}\,\ln\left(\frac{\sqrt{2}\,\left(\frac{\sqrt{2}\,x}{2}+1\right)\,1{}\mathrm{i}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{2}}{2}}\right)}{8}+\frac{\sqrt{2}\,\ln\left(x-\frac{\sqrt{2}}{2}\right)}{8}-\frac{\sqrt{2}\,\ln\left(x+\frac{\sqrt{2}}{2}\right)}{8}+\frac{\sqrt{1-x^2}}{2}","Not used",1,"x/2 - (2^(1/2)*log((2^(1/2)*((2^(1/2)*x)/2 - 1)*1i - (1 - x^2)^(1/2)*1i)/(x - 2^(1/2)/2)))/8 - (2^(1/2)*log((2^(1/2)*((2^(1/2)*x)/2 + 1)*1i + (1 - x^2)^(1/2)*1i)/(x + 2^(1/2)/2)))/8 + (2^(1/2)*log(x - 2^(1/2)/2))/8 - (2^(1/2)*log(x + 2^(1/2)/2))/8 + (1 - x^2)^(1/2)/2","B"
969,1,64,31,0.188273,"\text{Not used}","int(x/(x - (2*x^2 + 1)^(1/2)),x)","-x-\sqrt{2}\,\sqrt{x^2+\frac{1}{2}}-\ln\left(x-\mathrm{i}\right)\,1{}\mathrm{i}+\frac{\ln\left(x-\frac{\sqrt{2}\,\sqrt{x^2+\frac{1}{2}}}{2}+\frac{1}{2}{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\frac{\ln\left(x+\frac{\sqrt{2}\,\sqrt{x^2+\frac{1}{2}}}{2}-\frac{1}{2}{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(log(x - (2^(1/2)*(x^2 + 1/2)^(1/2))/2 + 1i/2)*1i)/2 - log(x - 1i)*1i - x + (log(x + (2^(1/2)*(x^2 + 1/2)^(1/2))/2 - 1i/2)*1i)/2 - 2^(1/2)*(x^2 + 1/2)^(1/2)","B"
970,0,-1,82,0.000000,"\text{Not used}","int(x^(1/2)*(x + x^(1/2))^(1/2),x)","\int \sqrt{x}\,\sqrt{x+\sqrt{x}} \,d x","Not used",1,"int(x^(1/2)*(x + x^(1/2))^(1/2), x)","F"
971,1,95,74,3.412116,"\text{Not used}","int((x^(1/3) + 1)/(x^(1/2) + 1),x)","2\,\sqrt{x}+\ln\left(\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27+\sqrt{3}\,9{}\mathrm{i}\right)+36\,x^{1/6}+36\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)-\ln\left(\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(-27+\sqrt{3}\,9{}\mathrm{i}\right)+36\,x^{1/6}+36\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)-4\,\ln\left(36\,x^{1/6}+36\right)-3\,x^{1/3}+\frac{6\,x^{5/6}}{5}","Not used",1,"log((3^(1/2)*1i - 1)*(3^(1/2)*9i + 27) + 36*x^(1/6) + 36)*(3^(1/2)*1i - 1) - 4*log(36*x^(1/6) + 36) - log((3^(1/2)*1i + 1)*(3^(1/2)*9i - 27) + 36*x^(1/6) + 36)*(3^(1/2)*1i + 1) + 2*x^(1/2) - 3*x^(1/3) + (6*x^(5/6))/5","B"
972,1,130,115,0.087237,"\text{Not used}","int((x^(1/3) + 1)/(x^(1/4) + 1),x)","4\,x^{1/4}+\ln\left(\left(-2+\sqrt{3}\,2{}\mathrm{i}\right)\,\left(54-36\,x^{1/12}+\sqrt{3}\,18{}\mathrm{i}\right)-144\,x^{1/12}+144\right)\,\left(-2+\sqrt{3}\,2{}\mathrm{i}\right)-\ln\left(\left(2+\sqrt{3}\,2{}\mathrm{i}\right)\,\left(36\,x^{1/12}-54+\sqrt{3}\,18{}\mathrm{i}\right)-144\,x^{1/12}+144\right)\,\left(2+\sqrt{3}\,2{}\mathrm{i}\right)-2\,\sqrt{x}-3\,x^{1/3}-8\,\ln\left(144\,x^{1/12}+144\right)+\frac{4\,x^{3/4}}{3}-\frac{6\,x^{5/6}}{5}+12\,x^{1/12}+\frac{12\,x^{7/12}}{7}+\frac{12\,x^{13/12}}{13}","Not used",1,"log((3^(1/2)*2i - 2)*(3^(1/2)*18i - 36*x^(1/12) + 54) - 144*x^(1/12) + 144)*(3^(1/2)*2i - 2) - 8*log(144*x^(1/12) + 144) - log((3^(1/2)*2i + 2)*(3^(1/2)*18i + 36*x^(1/12) - 54) - 144*x^(1/12) + 144)*(3^(1/2)*2i + 2) - 2*x^(1/2) - 3*x^(1/3) + 4*x^(1/4) + (4*x^(3/4))/3 - (6*x^(5/6))/5 + 12*x^(1/12) + (12*x^(7/12))/7 + (12*x^(13/12))/13","B"
973,1,4,4,0.032472,"\text{Not used}","int(x^2/(x^2 + (1 - x^2)^(1/2) - 1),x)","x+\mathrm{asin}\left(x\right)","Not used",1,"x + asin(x)","B"
974,1,18,22,3.387060,"\text{Not used}","int(((x + 1)/x)^(1/2),x)","\mathrm{atanh}\left(\sqrt{\frac{1}{x}+1}\right)+x\,\sqrt{\frac{1}{x}+1}","Not used",1,"atanh((1/x + 1)^(1/2)) + x*(1/x + 1)^(1/2)","B"
975,1,20,24,0.036766,"\text{Not used}","int((-(x - 1)/x)^(1/2),x)","x\,\sqrt{\frac{1}{x}-1}-\mathrm{atan}\left(\sqrt{\frac{1}{x}-1}\right)","Not used",1,"x*(1/x - 1)^(1/2) - atan((1/x - 1)^(1/2))","B"
976,1,24,24,0.029977,"\text{Not used}","int(((x - 1)/x)^(1/2),x)","x\,\sqrt{1-\frac{1}{x}}-\mathrm{atanh}\left(\sqrt{1-\frac{1}{x}}\right)","Not used",1,"x*(1 - 1/x)^(1/2) - atanh((1 - 1/x)^(1/2))","B"
977,1,20,24,0.036748,"\text{Not used}","int(((x + 1)/x)^(1/2)/x,x)","2\,\mathrm{atanh}\left(\sqrt{\frac{1}{x}+1}\right)-2\,\sqrt{\frac{1}{x}+1}","Not used",1,"2*atanh((1/x + 1)^(1/2)) - 2*(1/x + 1)^(1/2)","B"
978,1,35,22,0.039561,"\text{Not used}","int((x/(x + 1))^(1/2),x)","-\mathrm{atanh}\left(\sqrt{\frac{x}{x+1}}\right)-\frac{\sqrt{\frac{x}{x+1}}}{\frac{x}{x+1}-1}","Not used",1,"- atanh((x/(x + 1))^(1/2)) - (x/(x + 1))^(1/2)/(x/(x + 1) - 1)","B"
979,1,23,29,3.367359,"\text{Not used}","int(1/(-(x + 1)/x)^(1/2),x)","\mathrm{atan}\left(\sqrt{-\frac{1}{x}-1}\right)-x\,\sqrt{-\frac{1}{x}-1}","Not used",1,"atan((- 1/x - 1)^(1/2)) - x*(- 1/x - 1)^(1/2)","B"
980,1,26,33,3.467567,"\text{Not used}","int((-x*(x - 4))^(1/2),x)","2\,\mathrm{asin}\left(\frac{x}{2}-1\right)+\left(\frac{x}{2}-1\right)\,\sqrt{4\,x-x^2}","Not used",1,"2*asin(x/2 - 1) + (x/2 - 1)*(4*x - x^2)^(1/2)","B"
981,1,6,8,0.013773,"\text{Not used}","int(1/(-x*(x - 1))^(1/2),x)","\mathrm{asin}\left(2\,x-1\right)","Not used",1,"asin(2*x - 1)","B"
982,1,13,13,3.517840,"\text{Not used}","int(x/(x*(x + 2))^(3/2),x)","\frac{\sqrt{x\,\left(x+2\right)}}{x+2}","Not used",1,"(x*(x + 2))^(1/2)/(x + 2)","B"
983,1,17,22,3.583148,"\text{Not used}","int(-(1/x + 1)^(1/2)/(x^2 - 1),x)","\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\sqrt{\frac{1}{x}+1}}{2}\right)","Not used",1,"2^(1/2)*atanh((2^(1/2)*(1/x + 1)^(1/2))/2)","B"
984,1,45,24,0.098898,"\text{Not used}","int(1/(5^(1/2) + 5^(1/2)*x^2 - x^2 + 1),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,x\,\left(\sqrt{5}+1\right)}{4\,\left(\frac{\sqrt{5}}{4}+\frac{1}{4}\right)\,\sqrt{\sqrt{5}+3}}\right)\,\left(\sqrt{5}+1\right)}{4\,\sqrt{\sqrt{5}+3}}","Not used",1,"(2^(1/2)*atan((2^(1/2)*x*(5^(1/2) + 1))/(4*(5^(1/2)/4 + 1/4)*(5^(1/2) + 3)^(1/2)))*(5^(1/2) + 1))/(4*(5^(1/2) + 3)^(1/2))","B"
985,1,28,28,3.472080,"\text{Not used}","int(1/(a*x + b*x^2)^(1/2),x)","\frac{\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{\sqrt{b}}","Not used",1,"log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2))/b^(1/2)","B"
986,1,28,28,3.528687,"\text{Not used}","int(1/(x*(a + b*x))^(1/2),x)","\frac{\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{\sqrt{b}}","Not used",1,"log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2))/b^(1/2)","B"
987,1,28,28,3.592903,"\text{Not used}","int(1/(x^2*(b + a/x))^(1/2),x)","\frac{\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{\sqrt{b}}","Not used",1,"log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2))/b^(1/2)","B"
988,1,28,28,3.528633,"\text{Not used}","int(1/(x^3*(a/x^2 + b/x))^(1/2),x)","\frac{\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{\sqrt{b}}","Not used",1,"log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2))/b^(1/2)","B"
989,1,28,28,3.523927,"\text{Not used}","int(1/((a*x^2 + b*x^3)/x)^(1/2),x)","\frac{\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{\sqrt{b}}","Not used",1,"log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2))/b^(1/2)","B"
990,1,28,28,3.515328,"\text{Not used}","int(1/((a*x^3 + b*x^4)/x^2)^(1/2),x)","\frac{\ln\left(\frac{\frac{a}{2}+b\,x}{\sqrt{b}}+\sqrt{b\,x^2+a\,x}\right)}{\sqrt{b}}","Not used",1,"log((a/2 + b*x)/b^(1/2) + (a*x + b*x^2)^(1/2))/b^(1/2)","B"
991,1,33,40,3.902761,"\text{Not used}","int(1/(a*c*x + b*c*x^2)^(1/2),x)","\frac{\ln\left(a\,c+2\,\sqrt{b\,c}\,\sqrt{c\,x\,\left(a+b\,x\right)}+2\,b\,c\,x\right)}{\sqrt{b\,c}}","Not used",1,"log(a*c + 2*(b*c)^(1/2)*(c*x*(a + b*x))^(1/2) + 2*b*c*x)/(b*c)^(1/2)","B"
992,1,33,40,3.556708,"\text{Not used}","int(1/(c*(a*x + b*x^2))^(1/2),x)","\frac{\ln\left(a\,c+2\,\sqrt{b\,c}\,\sqrt{c\,x\,\left(a+b\,x\right)}+2\,b\,c\,x\right)}{\sqrt{b\,c}}","Not used",1,"log(a*c + 2*(b*c)^(1/2)*(c*x*(a + b*x))^(1/2) + 2*b*c*x)/(b*c)^(1/2)","B"
993,1,33,40,3.474971,"\text{Not used}","int(1/(c*x*(a + b*x))^(1/2),x)","\frac{\ln\left(a\,c+2\,\sqrt{b\,c}\,\sqrt{c\,x\,\left(a+b\,x\right)}+2\,b\,c\,x\right)}{\sqrt{b\,c}}","Not used",1,"log(a*c + 2*(b*c)^(1/2)*(c*x*(a + b*x))^(1/2) + 2*b*c*x)/(b*c)^(1/2)","B"
994,1,33,40,3.653873,"\text{Not used}","int(1/(c*x^2*(b + a/x))^(1/2),x)","\frac{\ln\left(a\,c+2\,\sqrt{b\,c}\,\sqrt{c\,x\,\left(a+b\,x\right)}+2\,b\,c\,x\right)}{\sqrt{b\,c}}","Not used",1,"log(a*c + 2*(b*c)^(1/2)*(c*x*(a + b*x))^(1/2) + 2*b*c*x)/(b*c)^(1/2)","B"
995,0,-1,63,0.000000,"\text{Not used}","int((x*(x^2 - 1)^(1/2) - x^2 + 1)^(1/2),x)","\int \sqrt{x\,\sqrt{x^2-1}-x^2+1} \,d x","Not used",1,"int((x*(x^2 - 1)^(1/2) - x^2 + 1)^(1/2), x)","F"
996,0,-1,66,0.000000,"\text{Not used}","int((x^(1/2)*(x + 1)^(1/2) - x)^(1/2)/(x + 1)^(1/2),x)","\int \frac{\sqrt{\sqrt{x}\,\sqrt{x+1}-x}}{\sqrt{x+1}} \,d x","Not used",1,"int((x^(1/2)*(x + 1)^(1/2) - x)^(1/2)/(x + 1)^(1/2), x)","F"
997,1,649,78,4.379519,"\text{Not used}","int(-(x + 2*(x^2 + 1)^(1/2))/(x + (x^2 + 1)^(1/2) + x^3),x)","\frac{\ln\left(x+\frac{\sqrt{2}\,\sqrt{\sqrt{5}-1}}{2}\right)\,\left(\frac{\sqrt{5}}{2}-\frac{5}{2}\right)}{2\,\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}}-\frac{\ln\left(x-\frac{\sqrt{2}\,\sqrt{\sqrt{5}-1}}{2}\right)\,\left(\frac{\sqrt{5}}{2}-\frac{5}{2}\right)}{2\,\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}}+\frac{\ln\left(x-\frac{\sqrt{2}\,\sqrt{-\sqrt{5}-1}}{2}\right)\,\left(\frac{\sqrt{5}}{2}+\frac{5}{2}\right)}{2\,\sqrt{-\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}}-\frac{\ln\left(x+\frac{\sqrt{2}\,\sqrt{-\sqrt{5}-1}}{2}\right)\,\left(\frac{\sqrt{5}}{2}+\frac{5}{2}\right)}{2\,\sqrt{-\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}}-\frac{\left(\ln\left(x-\frac{\sqrt{2}\,\sqrt{\sqrt{5}-1}}{2}\right)-\ln\left(\frac{\sqrt{2}\,x\,\sqrt{\sqrt{5}-1}}{2}+\frac{\sqrt{2}\,\sqrt{x^2+1}\,\sqrt{\sqrt{5}+1}}{2}+1\right)\right)\,\left(\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}+2\,{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)}{\left(2\,\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)\,\sqrt{\frac{\sqrt{5}}{2}+\frac{1}{2}}}-\frac{\left(\ln\left(x+\frac{\sqrt{2}\,\sqrt{\sqrt{5}-1}}{2}\right)-\ln\left(\frac{\sqrt{2}\,\sqrt{x^2+1}\,\sqrt{\sqrt{5}+1}}{2}-\frac{\sqrt{2}\,x\,\sqrt{\sqrt{5}-1}}{2}+1\right)\right)\,\left(\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}+2\,{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)}{\left(2\,\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)\,\sqrt{\frac{\sqrt{5}}{2}+\frac{1}{2}}}+\frac{\left(\ln\left(\frac{\sqrt{2}\,\sqrt{x^2+1}\,\sqrt{1-\sqrt{5}}}{2}-\frac{\sqrt{2}\,x\,\sqrt{-\sqrt{5}-1}}{2}+1\right)-\ln\left(x+\frac{\sqrt{2}\,\sqrt{-\sqrt{5}-1}}{2}\right)\right)\,\left(\sqrt{-\frac{\sqrt{5}}{2}-\frac{1}{2}}+2\,{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)}{\left(2\,\sqrt{-\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)\,\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}+\frac{\left(\ln\left(\frac{\sqrt{2}\,x\,\sqrt{-\sqrt{5}-1}}{2}+\frac{\sqrt{2}\,\sqrt{x^2+1}\,\sqrt{1-\sqrt{5}}}{2}+1\right)-\ln\left(x-\frac{\sqrt{2}\,\sqrt{-\sqrt{5}-1}}{2}\right)\right)\,\left(\sqrt{-\frac{\sqrt{5}}{2}-\frac{1}{2}}+2\,{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)}{\left(2\,\sqrt{-\frac{\sqrt{5}}{2}-\frac{1}{2}}+4\,{\left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}^{3/2}\right)\,\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}","Not used",1,"(log(x + (2^(1/2)*(5^(1/2) - 1)^(1/2))/2)*(5^(1/2)/2 - 5/2))/(2*(5^(1/2)/2 - 1/2)^(1/2) + 4*(5^(1/2)/2 - 1/2)^(3/2)) - (log(x - (2^(1/2)*(5^(1/2) - 1)^(1/2))/2)*(5^(1/2)/2 - 5/2))/(2*(5^(1/2)/2 - 1/2)^(1/2) + 4*(5^(1/2)/2 - 1/2)^(3/2)) + (log(x - (2^(1/2)*(- 5^(1/2) - 1)^(1/2))/2)*(5^(1/2)/2 + 5/2))/(2*(- 5^(1/2)/2 - 1/2)^(1/2) + 4*(- 5^(1/2)/2 - 1/2)^(3/2)) - (log(x + (2^(1/2)*(- 5^(1/2) - 1)^(1/2))/2)*(5^(1/2)/2 + 5/2))/(2*(- 5^(1/2)/2 - 1/2)^(1/2) + 4*(- 5^(1/2)/2 - 1/2)^(3/2)) - ((log(x - (2^(1/2)*(5^(1/2) - 1)^(1/2))/2) - log((2^(1/2)*x*(5^(1/2) - 1)^(1/2))/2 + (2^(1/2)*(x^2 + 1)^(1/2)*(5^(1/2) + 1)^(1/2))/2 + 1))*((5^(1/2)/2 - 1/2)^(1/2) + 2*(5^(1/2)/2 - 1/2)^(3/2)))/((2*(5^(1/2)/2 - 1/2)^(1/2) + 4*(5^(1/2)/2 - 1/2)^(3/2))*(5^(1/2)/2 + 1/2)^(1/2)) - ((log(x + (2^(1/2)*(5^(1/2) - 1)^(1/2))/2) - log((2^(1/2)*(x^2 + 1)^(1/2)*(5^(1/2) + 1)^(1/2))/2 - (2^(1/2)*x*(5^(1/2) - 1)^(1/2))/2 + 1))*((5^(1/2)/2 - 1/2)^(1/2) + 2*(5^(1/2)/2 - 1/2)^(3/2)))/((2*(5^(1/2)/2 - 1/2)^(1/2) + 4*(5^(1/2)/2 - 1/2)^(3/2))*(5^(1/2)/2 + 1/2)^(1/2)) + ((log((2^(1/2)*(x^2 + 1)^(1/2)*(1 - 5^(1/2))^(1/2))/2 - (2^(1/2)*x*(- 5^(1/2) - 1)^(1/2))/2 + 1) - log(x + (2^(1/2)*(- 5^(1/2) - 1)^(1/2))/2))*((- 5^(1/2)/2 - 1/2)^(1/2) + 2*(- 5^(1/2)/2 - 1/2)^(3/2)))/((2*(- 5^(1/2)/2 - 1/2)^(1/2) + 4*(- 5^(1/2)/2 - 1/2)^(3/2))*(1/2 - 5^(1/2)/2)^(1/2)) + ((log((2^(1/2)*x*(- 5^(1/2) - 1)^(1/2))/2 + (2^(1/2)*(x^2 + 1)^(1/2)*(1 - 5^(1/2))^(1/2))/2 + 1) - log(x - (2^(1/2)*(- 5^(1/2) - 1)^(1/2))/2))*((- 5^(1/2)/2 - 1/2)^(1/2) + 2*(- 5^(1/2)/2 - 1/2)^(3/2)))/((2*(- 5^(1/2)/2 - 1/2)^(1/2) + 4*(- 5^(1/2)/2 - 1/2)^(3/2))*(1/2 - 5^(1/2)/2)^(1/2))","B"
998,0,-1,126,0.000000,"\text{Not used}","int((2*x + 1)/((x^2 + 1)*(2*x + x^2 + 2)^(1/2)),x)","\int \frac{2\,x+1}{\left(x^2+1\right)\,\sqrt{x^2+2\,x+2}} \,d x","Not used",1,"int((2*x + 1)/((x^2 + 1)*(2*x + x^2 + 2)^(1/2)), x)","F"
999,0,-1,22,0.000000,"\text{Not used}","int(1/(((x^4 + 1)^(1/2) - x^2)^(1/2)*(x^4 + 1)),x)","\int \frac{1}{\sqrt{\sqrt{x^4+1}-x^2}\,\left(x^4+1\right)} \,d x","Not used",1,"int(1/(((x^4 + 1)^(1/2) - x^2)^(1/2)*(x^4 + 1)), x)","F"
1000,0,-1,40,0.000000,"\text{Not used}","int(1/((a + b*x^4)*(d*(a + b*x^4)^(1/2) + c*x^2)^(1/2)),x)","\int \frac{1}{\left(b\,x^4+a\right)\,\sqrt{d\,\sqrt{b\,x^4+a}+c\,x^2}} \,d x","Not used",1,"int(1/((a + b*x^4)*(d*(a + b*x^4)^(1/2) + c*x^2)^(1/2)), x)","F"
1001,0,-1,41,0.000000,"\text{Not used}","int(1/((a + b*x^4)*(d*(a + b*x^4)^(1/2) - c*x^2)^(1/2)),x)","\int \frac{1}{\left(b\,x^4+a\right)\,\sqrt{d\,\sqrt{b\,x^4+a}-c\,x^2}} \,d x","Not used",1,"int(1/((a + b*x^4)*(d*(a + b*x^4)^(1/2) - c*x^2)^(1/2)), x)","F"
1002,0,-1,184,0.000000,"\text{Not used}","int(x/(a + b*c^4 + b*d^4*x^4 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + 4*b*c*d^3*x^3)^(1/2),x)","\int \frac{x}{\sqrt{b\,c^4+4\,b\,c^3\,d\,x+6\,b\,c^2\,d^2\,x^2+4\,b\,c\,d^3\,x^3+b\,d^4\,x^4+a}} \,d x","Not used",1,"int(x/(a + b*c^4 + b*d^4*x^4 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + 4*b*c*d^3*x^3)^(1/2), x)","F"
1003,0,-1,131,0.000000,"\text{Not used}","int(1/(a + b*c^4 + b*d^4*x^4 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + 4*b*c*d^3*x^3)^(1/2),x)","\int \frac{1}{\sqrt{b\,c^4+4\,b\,c^3\,d\,x+6\,b\,c^2\,d^2\,x^2+4\,b\,c\,d^3\,x^3+b\,d^4\,x^4+a}} \,d x","Not used",1,"int(1/(a + b*c^4 + b*d^4*x^4 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + 4*b*c*d^3*x^3)^(1/2), x)","F"
1004,0,-1,54,0.000000,"\text{Not used}","int((a - c*x^4)/((a*d + a*e*x^2 + c*d*x^4)*(a + b*x^2 + c*x^4)^(1/2)),x)","\int \frac{a-c\,x^4}{\left(c\,d\,x^4+a\,e\,x^2+a\,d\right)\,\sqrt{c\,x^4+b\,x^2+a}} \,d x","Not used",1,"int((a - c*x^4)/((a*d + a*e*x^2 + c*d*x^4)*(a + b*x^2 + c*x^4)^(1/2)), x)","F"
1005,0,-1,53,0.000000,"\text{Not used}","int((a - c*x^4)/((a*d + a*e*x^2 + c*d*x^4)*(a - b*x^2 + c*x^4)^(1/2)),x)","\int \frac{a-c\,x^4}{\left(c\,d\,x^4+a\,e\,x^2+a\,d\right)\,\sqrt{c\,x^4-b\,x^2+a}} \,d x","Not used",1,"int((a - c*x^4)/((a*d + a*e*x^2 + c*d*x^4)*(a - b*x^2 + c*x^4)^(1/2)), x)","F"
1006,0,-1,84,0.000000,"\text{Not used}","int(1/((x^3 + 8)*(x^2 - 2*x + 5)^(1/2)),x)","\int \frac{1}{\left(x^3+8\right)\,\sqrt{x^2-2\,x+5}} \,d x","Not used",1,"int(1/((x^3 + 8)*(x^2 - 2*x + 5)^(1/2)), x)","F"
1007,1,13,20,3.412930,"\text{Not used}","int((x^2/(x^2 + 1))^(1/2),x)","\frac{\sqrt{x^4+x^2}}{x}","Not used",1,"(x^2 + x^4)^(1/2)/x","B"
1008,0,-1,46,0.000000,"\text{Not used}","int((x^n/(x^n + 1))^(1/2),x)","\int \sqrt{\frac{x^n}{x^n+1}} \,d x","Not used",1,"int((x^n/(x^n + 1))^(1/2), x)","F"
1009,0,-1,88,0.000000,"\text{Not used}","int((e*f - e*f*x^2)/((a*d + b*d*x + a*d*x^2)*(a + b*x + a*x^4 + b*x^3 + c*x^2)^(1/2)),x)","\int \frac{e\,f-e\,f\,x^2}{\left(a\,d\,x^2+b\,d\,x+a\,d\right)\,\sqrt{a\,x^4+b\,x^3+c\,x^2+b\,x+a}} \,d x","Not used",1,"int((e*f - e*f*x^2)/((a*d + b*d*x + a*d*x^2)*(a + b*x + a*x^4 + b*x^3 + c*x^2)^(1/2)), x)","F"
1010,0,-1,88,0.000000,"\text{Not used}","int(-(e*f - e*f*x^2)/((a*d - b*d*x + a*d*x^2)*(b*x - a - a*x^4 + b*x^3 + c*x^2)^(1/2)),x)","\int -\frac{e\,f-e\,f\,x^2}{\left(a\,d\,x^2-b\,d\,x+a\,d\right)\,\sqrt{-a\,x^4+b\,x^3+c\,x^2+b\,x-a}} \,d x","Not used",1,"int(-(e*f - e*f*x^2)/((a*d - b*d*x + a*d*x^2)*(b*x - a - a*x^4 + b*x^3 + c*x^2)^(1/2)), x)","F"
1011,0,-1,46,0.000000,"\text{Not used}","int((a*x^2 + b*x*((a^2*x^2)/b^2 - a/b^2)^(1/2))^(1/2)/(x*((a^2*x^2)/b^2 - a/b^2)^(1/2)),x)","\int \frac{\sqrt{a\,x^2+b\,x\,\sqrt{\frac{a^2\,x^2}{b^2}-\frac{a}{b^2}}}}{x\,\sqrt{\frac{a^2\,x^2}{b^2}-\frac{a}{b^2}}} \,d x","Not used",1,"int((a*x^2 + b*x*((a^2*x^2)/b^2 - a/b^2)^(1/2))^(1/2)/(x*((a^2*x^2)/b^2 - a/b^2)^(1/2)), x)","F"
1012,0,-1,46,0.000000,"\text{Not used}","int((b*x*(a/b^2 + (a^2*x^2)/b^2)^(1/2) - a*x^2)^(1/2)/(x*(a/b^2 + (a^2*x^2)/b^2)^(1/2)),x)","\int \frac{\sqrt{b\,x\,\sqrt{\frac{a}{b^2}+\frac{a^2\,x^2}{b^2}}-a\,x^2}}{x\,\sqrt{\frac{a}{b^2}+\frac{a^2\,x^2}{b^2}}} \,d x","Not used",1,"int((b*x*(a/b^2 + (a^2*x^2)/b^2)^(1/2) - a*x^2)^(1/2)/(x*(a/b^2 + (a^2*x^2)/b^2)^(1/2)), x)","F"
1013,0,-1,46,0.000000,"\text{Not used}","int((x*(a*x + b*((a^2*x^2)/b^2 - a/b^2)^(1/2)))^(1/2)/(x*((a^2*x^2)/b^2 - a/b^2)^(1/2)),x)","\int \frac{\sqrt{x\,\left(a\,x+b\,\sqrt{\frac{a^2\,x^2}{b^2}-\frac{a}{b^2}}\right)}}{x\,\sqrt{\frac{a^2\,x^2}{b^2}-\frac{a}{b^2}}} \,d x","Not used",1,"int((x*(a*x + b*((a^2*x^2)/b^2 - a/b^2)^(1/2)))^(1/2)/(x*((a^2*x^2)/b^2 - a/b^2)^(1/2)), x)","F"
1014,0,-1,46,0.000000,"\text{Not used}","int((-x*(a*x - b*(a/b^2 + (a^2*x^2)/b^2)^(1/2)))^(1/2)/(x*(a/b^2 + (a^2*x^2)/b^2)^(1/2)),x)","\int \frac{\sqrt{-x\,\left(a\,x-b\,\sqrt{\frac{a}{b^2}+\frac{a^2\,x^2}{b^2}}\right)}}{x\,\sqrt{\frac{a}{b^2}+\frac{a^2\,x^2}{b^2}}} \,d x","Not used",1,"int((-x*(a*x - b*(a/b^2 + (a^2*x^2)/b^2)^(1/2)))^(1/2)/(x*(a/b^2 + (a^2*x^2)/b^2)^(1/2)), x)","F"
1015,1,132,19,6.097754,"\text{Not used}","int((x*(x - 1)^(1/2) + x*(x - 4)^(1/2) - 4*(x - 1)^(1/2) - (x - 4)^(1/2))/((x^2 - 5*x + 4)*((x - 1)^(1/2) + (x - 4)^(1/2) + 1)),x)","\frac{\ln\left(x-5\right)}{2}+2\,\mathrm{atanh}\left(\frac{\sqrt{x-1}-\sqrt{3}}{\sqrt{x-4}}\right)+\frac{7\,\mathrm{atanh}\left(\frac{4\,\left(\sqrt{x-1}-\sqrt{3}\right)}{\left(\frac{{\left(\sqrt{x-1}-\sqrt{3}\right)}^2}{x-4}+1\right)\,\sqrt{x-4}}\right)}{2}-\frac{5\,\mathrm{atanh}\left(\frac{194400\,\left(\sqrt{x-1}-\sqrt{3}\right)}{\left(\frac{48600\,{\left(\sqrt{x-1}-\sqrt{3}\right)}^2}{x-4}+48600\right)\,\sqrt{x-4}}\right)}{2}-\mathrm{atanh}\left(\sqrt{x-4}\right)+\mathrm{atanh}\left(\frac{\sqrt{x-1}}{2}\right)","Not used",1,"log(x - 5)/2 + 2*atanh(((x - 1)^(1/2) - 3^(1/2))/(x - 4)^(1/2)) + (7*atanh((4*((x - 1)^(1/2) - 3^(1/2)))/((((x - 1)^(1/2) - 3^(1/2))^2/(x - 4) + 1)*(x - 4)^(1/2))))/2 - (5*atanh((194400*((x - 1)^(1/2) - 3^(1/2)))/(((48600*((x - 1)^(1/2) - 3^(1/2))^2)/(x - 4) + 48600)*(x - 4)^(1/2))))/2 - atanh((x - 4)^(1/2)) + atanh((x - 1)^(1/2)/2)","B"
1016,0,-1,90,0.000000,"\text{Not used}","int(1/(x*(3*x + x^2 + 3)*(3*x + 3*x^2 + x^3 + 3)^(1/3)),x)","\int \frac{1}{x\,\left(x^2+3\,x+3\right)\,{\left(x^3+3\,x^2+3\,x+3\right)}^{1/3}} \,d x","Not used",1,"int(1/(x*(3*x + x^2 + 3)*(3*x + 3*x^2 + x^3 + 3)^(1/3)), x)","F"
1017,0,-1,103,0.000000,"\text{Not used}","int(-(x^2 - 1)/((1 - x^3)^(2/3)*(x^2 - x + 1)),x)","-\int \frac{x^2-1}{{\left(1-x^3\right)}^{2/3}\,\left(x^2-x+1\right)} \,d x","Not used",1,"-int((x^2 - 1)/((1 - x^3)^(2/3)*(x^2 - x + 1)), x)","F"
1018,0,-1,49,0.000000,"\text{Not used}","int(x^2/((x^4 - 1)^(1/2)*(x^4 + 1)),x)","\int \frac{x^2}{\sqrt{x^4-1}\,\left(x^4+1\right)} \,d x","Not used",1,"int(x^2/((x^4 - 1)^(1/2)*(x^4 + 1)), x)","F"
1019,0,-1,80,0.000000,"\text{Not used}","int((a - c*x^4)/((d + e*x^2)*(a*e + c*d*x^2)*(a + b*x^2 + c*x^4)^(1/2)),x)","\int \frac{a-c\,x^4}{\left(e\,x^2+d\right)\,\left(c\,d\,x^2+a\,e\right)\,\sqrt{c\,x^4+b\,x^2+a}} \,d x","Not used",1,"int((a - c*x^4)/((d + e*x^2)*(a*e + c*d*x^2)*(a + b*x^2 + c*x^4)^(1/2)), x)","F"
1020,1,1,1,0.004806,"\text{Not used}","int(x - (x^2 - 1)/(x + 1),x)","x","Not used",1,"x","B"
1021,1,549,122,3.924545,"\text{Not used}","int(1/(1/x + (1 - x^2)^(1/2)),x)","\mathrm{asin}\left(x\right)-\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)-1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}}-\sqrt{1-x^2}\,1{}\mathrm{i}}{\frac{\sqrt{3}}{2}-x+\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}+\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)-1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}-\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)+1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}-\frac{\ln\left(x-\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}{\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}-\frac{\ln\left(x+\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}{\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}+\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)+1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}+\frac{\ln\left(x-\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}{-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}+\frac{\ln\left(x+\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}{-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}","Not used",1,"asin(x) - log((((x*(3^(1/2)/2 + 1i/2) - 1)*1i)/(1 - (3^(1/2)/2 + 1i/2)^2)^(1/2) - (1 - x^2)^(1/2)*1i)/(3^(1/2)/2 - x + 1i/2))/((1 - (3^(1/2)/2 + 1i/2)^2)^(1/2)*(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i)) + log((((x*(3^(1/2)/2 - 1i/2) - 1)*1i)/(1 - (3^(1/2)/2 - 1i/2)^2)^(1/2) - (1 - x^2)^(1/2)*1i)/(x - 3^(1/2)/2 + 1i/2))/((1 - (3^(1/2)/2 - 1i/2)^2)^(1/2)*(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i)) - log((((x*(3^(1/2)/2 - 1i/2) + 1)*1i)/(1 - (3^(1/2)/2 - 1i/2)^2)^(1/2) + (1 - x^2)^(1/2)*1i)/(x + 3^(1/2)/2 - 1i/2))/((1 - (3^(1/2)/2 - 1i/2)^2)^(1/2)*(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i)) - (log(x - 3^(1/2)/2 - 1i/2)*(3^(1/2)/2 + 1i/2))/(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i) - (log(x + 3^(1/2)/2 + 1i/2)*(3^(1/2)/2 + 1i/2))/(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i) + log((((x*(3^(1/2)/2 + 1i/2) + 1)*1i)/(1 - (3^(1/2)/2 + 1i/2)^2)^(1/2) + (1 - x^2)^(1/2)*1i)/(x + 3^(1/2)/2 + 1i/2))/((1 - (3^(1/2)/2 + 1i/2)^2)^(1/2)*(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i)) + (log(x - 3^(1/2)/2 + 1i/2)*(3^(1/2)/2 - 1i/2))/(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i) + (log(x + 3^(1/2)/2 - 1i/2)*(3^(1/2)/2 - 1i/2))/(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i)","B"
1022,1,549,122,3.894576,"\text{Not used}","int((x*(1 - x^2)^(1/2))/(x - x^3 + (1 - x^2)^(1/2)),x)","\mathrm{asin}\left(x\right)-\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)-1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}}-\sqrt{1-x^2}\,1{}\mathrm{i}}{\frac{\sqrt{3}}{2}-x+\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}+\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)-1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}}-\sqrt{1-x^2}\,1{}\mathrm{i}}{x-\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}-\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)+1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}-\frac{\ln\left(x-\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}{\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}-\frac{\ln\left(x+\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}{\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}+\frac{\ln\left(\frac{\frac{\left(x\,\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)+1\right)\,1{}\mathrm{i}}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}}+\sqrt{1-x^2}\,1{}\mathrm{i}}{x+\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}}\right)}{\sqrt{1-{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^2}\,\left(\sqrt{3}-4\,{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}\right)}+\frac{\ln\left(x-\frac{\sqrt{3}}{2}+\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}{-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}+\frac{\ln\left(x+\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)\,\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}{-\sqrt{3}+4\,{\left(\frac{\sqrt{3}}{2}-\frac{1}{2}{}\mathrm{i}\right)}^3+1{}\mathrm{i}}","Not used",1,"asin(x) - log((((x*(3^(1/2)/2 + 1i/2) - 1)*1i)/(1 - (3^(1/2)/2 + 1i/2)^2)^(1/2) - (1 - x^2)^(1/2)*1i)/(3^(1/2)/2 - x + 1i/2))/((1 - (3^(1/2)/2 + 1i/2)^2)^(1/2)*(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i)) + log((((x*(3^(1/2)/2 - 1i/2) - 1)*1i)/(1 - (3^(1/2)/2 - 1i/2)^2)^(1/2) - (1 - x^2)^(1/2)*1i)/(x - 3^(1/2)/2 + 1i/2))/((1 - (3^(1/2)/2 - 1i/2)^2)^(1/2)*(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i)) - log((((x*(3^(1/2)/2 - 1i/2) + 1)*1i)/(1 - (3^(1/2)/2 - 1i/2)^2)^(1/2) + (1 - x^2)^(1/2)*1i)/(x + 3^(1/2)/2 - 1i/2))/((1 - (3^(1/2)/2 - 1i/2)^2)^(1/2)*(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i)) - (log(x - 3^(1/2)/2 - 1i/2)*(3^(1/2)/2 + 1i/2))/(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i) - (log(x + 3^(1/2)/2 + 1i/2)*(3^(1/2)/2 + 1i/2))/(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i) + log((((x*(3^(1/2)/2 + 1i/2) + 1)*1i)/(1 - (3^(1/2)/2 + 1i/2)^2)^(1/2) + (1 - x^2)^(1/2)*1i)/(x + 3^(1/2)/2 + 1i/2))/((1 - (3^(1/2)/2 + 1i/2)^2)^(1/2)*(3^(1/2) - 4*(3^(1/2)/2 + 1i/2)^3 + 1i)) + (log(x - 3^(1/2)/2 + 1i/2)*(3^(1/2)/2 - 1i/2))/(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i) + (log(x + 3^(1/2)/2 - 1i/2)*(3^(1/2)/2 - 1i/2))/(4*(3^(1/2)/2 - 1i/2)^3 - 3^(1/2) + 1i)","B"
1023,1,31,34,3.451608,"\text{Not used}","int((1 - x^4)^n/(x + x^2 + x^3 + 1)^n,x)","\frac{{\left(1-x^4\right)}^n\,\left(x-1\right)}{\left(n+1\right)\,{\left(x^3+x^2+x+1\right)}^n}","Not used",1,"((1 - x^4)^n*(x - 1))/((n + 1)*(x + x^2 + x^3 + 1)^n)","B"
1024,0,-1,177,0.000000,"\text{Not used}","int(x/(5308416*c^4*x^4 - 44375*b^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x)^(1/2),x)","\int \frac{x}{\sqrt{-44375\,b^4+576000\,b^3\,c\,x+576000\,b^2\,c^2\,x^2+5308416\,c^4\,x^4}} \,d x","Not used",1,"int(x/(5308416*c^4*x^4 - 44375*b^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x)^(1/2), x)","F"
1025,0,-1,100,0.000000,"\text{Not used}","int((4*x + 1)/(120*x + 64*x^2 + 64*x^3 + 64*x^4 + 9)^(1/2),x)","\int \frac{4\,x+1}{\sqrt{64\,x^4+64\,x^3+64\,x^2+120\,x+9}} \,d x","Not used",1,"int((4*x + 1)/(120*x + 64*x^2 + 64*x^3 + 64*x^4 + 9)^(1/2), x)","F"