1,0,0,0,0.000000," ","integrate(1/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1} {\left(x + 2^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 + 1)*(x + 2^(2/3))), x)","F",0
2,-2,0,0,0.000000," ","integrate(1/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
3,-2,0,0,0.000000," ","integrate(1/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
4,-2,0,0,0.000000," ","integrate(1/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
5,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate(1/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,0,0,0,0.000000," ","integrate(1/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(4*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
10,-2,0,0,0.000000," ","integrate(1/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
11,-2,0,0,0.000000," ","integrate(1/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
12,-2,0,0,0.000000," ","integrate(1/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
13,-2,0,0,0.000000," ","integrate(1/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
14,0,0,0,0.000000," ","integrate(1/(3+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} + 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 + 1)*(x + 3)), x)","F",0
15,0,0,0,0.000000," ","integrate(1/(3+x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} + 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 + 1)*(x + 3)), x)","F",0
16,0,0,0,0.000000," ","integrate(1/(3+x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{3} - 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(x^3 - 1)*(x + 3)), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(3+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{3} - 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^3 - 1)*(x + 3)), x)","F",0
18,0,0,0,0.000000," ","integrate(1/(d*x+c)/(d^3*x^3-c^3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(d^{3} x^{3} - c^{3}\right)}^{\frac{1}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((d^3*x^3 - c^3)^(1/3)*(d*x + c)), x)","F",0
19,0,0,0,0.000000," ","integrate(1/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(d^{3} x^{3} + 2 \, c^{3}\right)}^{\frac{1}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((d^3*x^3 + 2*c^3)^(1/3)*(d*x + c)), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(d*x+c)/(d^3*x^3+2*c^3)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(d^{3} x^{3} + 2 \, c^{3}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((d^3*x^3 + 2*c^3)^(2/3)*(d*x + c)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(1+2^(1/3)*x)/(x^3+1)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + 1\right)}^{\frac{2}{3}} {\left(2^{\frac{1}{3}} x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^3 + 1)^(2/3)*(2^(1/3)*x + 1)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(1-2^(1/3)*x)/(-x^3+1)^(2/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} {\left(2^{\frac{1}{3}} x - 1\right)}}\,{d x}"," ",0,"integrate(-1/((-x^3 + 1)^(2/3)*(2^(1/3)*x - 1)), x)","F",0
23,0,0,0,0.000000," ","integrate((d*x+c)^4*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{4}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x + c)^4, x)","F",0
24,0,0,0,0.000000," ","integrate((d*x+c)^3*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{3}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x + c)^3, x)","F",0
25,0,0,0,0.000000," ","integrate((d*x+c)^2*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{2}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x + c)^2, x)","F",0
26,0,0,0,0.000000," ","integrate((d*x+c)*(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)*(d*x + c), x)","F",0
27,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x + c}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/(d*x + c), x)","F",0
28,0,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^3 + a)^(1/3)/(d*x + c)^2, x)","F",0
29,0,0,0,0.000000," ","integrate((d*x+c)^4/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{4}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((d*x + c)^4/(b*x^3 + a)^(1/3), x)","F",0
30,0,0,0,0.000000," ","integrate((d*x+c)^3/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{3}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((d*x + c)^3/(b*x^3 + a)^(1/3), x)","F",0
31,0,0,0,0.000000," ","integrate((d*x+c)^2/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((d*x + c)^2/(b*x^3 + a)^(1/3), x)","F",0
32,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{d x + c}{{\left(b x^{3} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((d*x + c)/(b*x^3 + a)^(1/3), x)","F",0
33,0,0,0,0.000000," ","integrate(1/(d*x+c)/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*(d*x + c)), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*(d*x + c)^2), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(d*x+c)^3/(b*x^3+a)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(1/3)*(d*x + c)^3), x)","F",0
36,0,0,0,0.000000," ","integrate((d*x+c)^4/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{4}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x + c)^4/(b*x^3 + a)^(2/3), x)","F",0
37,0,0,0,0.000000," ","integrate((d*x+c)^3/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{3}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x + c)^3/(b*x^3 + a)^(2/3), x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)^2/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{2}}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x + c)^2/(b*x^3 + a)^(2/3), x)","F",0
39,0,0,0,0.000000," ","integrate((d*x+c)/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{d x + c}{{\left(b x^{3} + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((d*x + c)/(b*x^3 + a)^(2/3), x)","F",0
40,0,0,0,0.000000," ","integrate(1/(d*x+c)/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*(d*x + c)), x)","F",0
41,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*(d*x + c)^2), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(d*x+c)^3/(b*x^3+a)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{3}}\,{d x}"," ",0,"integrate(1/((b*x^3 + a)^(2/3)*(d*x + c)^3), x)","F",0
43,-2,0,0,0.000000," ","integrate((2^(2/3)-2*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
44,-2,0,0,0.000000," ","integrate((2^(2/3)+2*x)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
45,-2,0,0,0.000000," ","integrate((2^(2/3)+2*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
46,-2,0,0,0.000000," ","integrate((2^(2/3)-2*x)/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
47,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)-2*b^(1/3)*x)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)+2*b^(1/3)*x)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)+2*b^(1/3)*x)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((2^(2/3)*a^(1/3)-2*b^(1/3)*x)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,0,0,0,0.000000," ","integrate((-2*d*x+c)/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int -\frac{2 \, d x - c}{\sqrt{4 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(2*d*x - c)/(sqrt(4*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
52,-2,0,0,0.000000," ","integrate((2+3*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
53,-2,0,0,0.000000," ","integrate((2+3*x)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
54,-2,0,0,0.000000," ","integrate((2+3*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
55,0,0,0,0.000000," ","integrate((2+3*x)/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x + 2}{\sqrt{-x^{3} - 1} {\left(x + 2^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"integrate((3*x + 2)/(sqrt(-x^3 - 1)*(x + 2^(2/3))), x)","F",0
56,0,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{x^{3} + 1} {\left(x + 2^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(x^3 + 1)*(x + 2^(2/3))), x)","F",0
57,-2,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
58,-2,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
59,-2,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
60,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((f*x+e)/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{4 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(4*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
65,-2,0,0,0.000000," ","integrate(x/(2^(2/3)+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
66,-2,0,0,0.000000," ","integrate(x/(2^(2/3)-x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,0]:[1,0,0,-2]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
67,-2,0,0,0.000000," ","integrate(x/(2^(2/3)-x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[1]%%%} / %%%{%%{[1,0,0]:[1,0,0,-2]%%},[1]%%%} Error: Bad Argument Value","F(-2)",0
68,0,0,0,0.000000," ","integrate(x/(2^(2/3)+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{3} - 1} {\left(x + 2^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-x^3 - 1)*(x + 2^(2/3))), x)","F",0
69,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(x/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,0,0,0,0.000000," ","integrate(x/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{4 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(4*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
74,0,0,0,0.000000," ","integrate((1+x)/(2-x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + 1}{\sqrt{x^{3} + 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(-(x + 1)/(sqrt(x^3 + 1)*(x - 2)), x)","F",0
75,0,0,0,0.000000," ","integrate((1-x)/(2+x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 1}{\sqrt{-x^{3} + 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate(-(x - 1)/(sqrt(-x^3 + 1)*(x + 2)), x)","F",0
76,0,0,0,0.000000," ","integrate((1-x)/(2+x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - 1}{\sqrt{x^{3} - 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate(-(x - 1)/(sqrt(x^3 - 1)*(x + 2)), x)","F",0
77,0,0,0,0.000000," ","integrate((1+x)/(2-x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + 1}{\sqrt{-x^{3} - 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(-(x + 1)/(sqrt(-x^3 - 1)*(x - 2)), x)","F",0
78,-1,0,0,0.000000," ","integrate((a^(1/3)+b^(1/3)*x)/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((a^(1/3)-b^(1/3)*x)/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((a^(1/3)-b^(1/3)*x)/(2*a^(1/3)+b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((a^(1/3)+b^(1/3)*x)/(2*a^(1/3)-b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,0,0,0,0.000000," ","integrate((-2*d*x+c)/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int -\frac{2 \, d x - c}{\sqrt{-8 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(2*d*x - c)/(sqrt(-8*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
83,0,0,0,0.000000," ","integrate((f*x+e)/(2-x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{f x + e}{\sqrt{x^{3} + 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(-(f*x + e)/(sqrt(x^3 + 1)*(x - 2)), x)","F",0
84,0,0,0,0.000000," ","integrate((f*x+e)/(2+x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{-x^{3} + 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(-x^3 + 1)*(x + 2)), x)","F",0
85,0,0,0,0.000000," ","integrate((f*x+e)/(2+x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{x^{3} - 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(x^3 - 1)*(x + 2)), x)","F",0
86,0,0,0,0.000000," ","integrate((f*x+e)/(2-x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{f x + e}{\sqrt{-x^{3} - 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(-(f*x + e)/(sqrt(-x^3 - 1)*(x - 2)), x)","F",0
87,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)+b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((f*x+e)/(2*a^(1/3)-b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{-8 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(-8*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
92,0,0,0,0.000000," ","integrate(x/(2-x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x}{\sqrt{x^{3} + 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(-x/(sqrt(x^3 + 1)*(x - 2)), x)","F",0
93,0,0,0,0.000000," ","integrate(x/(2+x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{3} + 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-x^3 + 1)*(x + 2)), x)","F",0
94,0,0,0,0.000000," ","integrate(x/(2+x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} - 1} {\left(x + 2\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 - 1)*(x + 2)), x)","F",0
95,0,0,0,0.000000," ","integrate(x/(2-x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x}{\sqrt{-x^{3} - 1} {\left(x - 2\right)}}\,{d x}"," ",0,"integrate(-x/(sqrt(-x^3 - 1)*(x - 2)), x)","F",0
96,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)+b^(1/3)*x)/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(x/(2*a^(1/3)-b^(1/3)*x)/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,0.000000," ","integrate(x/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-8 \, d^{3} x^{3} + c^{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-8*d^3*x^3 + c^3)*(d*x + c)), x)","F",0
101,-2,0,0,0.000000," ","integrate((1+x+3^(1/2))/(1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[-1,-1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[-2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
102,-2,0,0,0.000000," ","integrate((1-x+3^(1/2))/(1-x-3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[-2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
103,-2,0,0,0.000000," ","integrate((1-x+3^(1/2))/(1-x-3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[-2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
104,-2,0,0,0.000000," ","integrate((1+x+3^(1/2))/(1+x-3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[-1,-1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[-2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
105,-1,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(1+(b/a)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.41index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
110,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(1-(b/a)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.42index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
111,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x+3^(1/2))/(1-(b/a)^(1/3)*x-3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.44index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
112,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x+3^(1/2))/(1+(b/a)^(1/3)*x-3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.45index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
113,-2,0,0,0.000000," ","integrate((1+x-3^(1/2))/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,-1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
114,-2,0,0,0.000000," ","integrate((1-x-3^(1/2))/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,-1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
115,-2,0,0,0.000000," ","integrate((1-x-3^(1/2))/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,-1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
116,-2,0,0,0.000000," ","integrate((1+x-3^(1/2))/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[1,-1]:[1,0,-3]%%},[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
117,-1,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(1+(b/a)^(1/3)*x+3^(1/2))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Value","F(-2)",0
122,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(1-(b/a)^(1/3)*x+3^(1/2))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Value","F(-2)",0
123,-2,0,0,0.000000," ","integrate((1-(b/a)^(1/3)*x-3^(1/2))/(1-(b/a)^(1/3)*x+3^(1/2))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Value","F(-2)",0
124,-2,0,0,0.000000," ","integrate((1+(b/a)^(1/3)*x-3^(1/2))/(1+(b/a)^(1/3)*x+3^(1/2))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.43index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
125,0,0,0,0.000000," ","integrate((1+x)/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{3} + 1} {\left(x + \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^3 + 1)*(x + sqrt(3) + 1)), x)","F",0
126,0,0,0,0.000000," ","integrate((1+x)/(1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + 1}{\sqrt{x^{3} + 1} {\left(x - \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^3 + 1)*(x - sqrt(3) + 1)), x)","F",0
127,-2,0,0,0.000000," ","integrate((f*x+e)/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
128,-2,0,0,0.000000," ","integrate((f*x+e)/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
129,-2,0,0,0.000000," ","integrate((f*x+e)/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
130,-2,0,0,0.000000," ","integrate((f*x+e)/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
131,-1,0,0,0.000000," ","integrate((f*x+e)/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((f*x+e)/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate((f*x+e)/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((f*x+e)/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,0,0,0,0.000000," ","integrate(x/(1+x+3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} + 1} {\left(x + \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 + 1)*(x + sqrt(3) + 1)), x)","F",0
136,0,0,0,0.000000," ","integrate(x/(1-x+3^(1/2))/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x}{\sqrt{-x^{3} + 1} {\left(x - \sqrt{3} - 1\right)}}\,{d x}"," ",0,"integrate(-x/(sqrt(-x^3 + 1)*(x - sqrt(3) - 1)), x)","F",0
137,-2,0,0,0.000000," ","integrate(x/(1-x+3^(1/2))/(x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
138,-2,0,0,0.000000," ","integrate(x/(1+x+3^(1/2))/(-x^3-1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[2]%%%} / %%%{%%{[2,4]:[1,0,-3]%%},[2]%%%} Error: Bad Argument Value","F(-2)",0
139,0,0,0,0.000000," ","integrate(x/(1+x-3^(1/2))/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} + 1} {\left(x - \sqrt{3} + 1\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 + 1)*(x - sqrt(3) + 1)), x)","F",0
140,-1,0,0,0.000000," ","integrate(x/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(x/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate(x/(-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(x/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/(d*x+c)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{x^{3} + 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/(sqrt(x^3 + 1)*(d*x + c)), x)","F",0
145,0,0,0,0.000000," ","integrate((1-x+3^(1/2))/(d*x+c)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} - 1}{\sqrt{-x^{3} + 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(x - sqrt(3) - 1)/(sqrt(-x^3 + 1)*(d*x + c)), x)","F",0
146,0,0,0,0.000000," ","integrate((1-x+3^(1/2))/(d*x+c)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} - 1}{\sqrt{x^{3} - 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(x - sqrt(3) - 1)/(sqrt(x^3 - 1)*(d*x + c)), x)","F",0
147,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{-x^{3} - 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/(sqrt(-x^3 - 1)*(d*x + c)), x)","F",0
148,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/(d*x+c)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{x^{3} + 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/(sqrt(x^3 + 1)*(d*x + c)), x)","F",0
149,0,0,0,0.000000," ","integrate((1-x-3^(1/2))/(d*x+c)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + \sqrt{3} - 1}{\sqrt{-x^{3} + 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(x + sqrt(3) - 1)/(sqrt(-x^3 + 1)*(d*x + c)), x)","F",0
150,0,0,0,0.000000," ","integrate((1-x-3^(1/2))/(d*x+c)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + \sqrt{3} - 1}{\sqrt{x^{3} - 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(x + sqrt(3) - 1)/(sqrt(x^3 - 1)*(d*x + c)), x)","F",0
151,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{-x^{3} - 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/(sqrt(-x^3 - 1)*(d*x + c)), x)","F",0
152,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/x/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{x^{3} + 1} x}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/(sqrt(x^3 + 1)*x), x)","F",0
153,0,0,0,0.000000," ","integrate((1-x+3^(1/2))/x/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} - 1}{\sqrt{-x^{3} + 1} x}\,{d x}"," ",0,"integrate(-(x - sqrt(3) - 1)/(sqrt(-x^3 + 1)*x), x)","F",0
154,0,0,0,0.000000," ","integrate((1-x+3^(1/2))/x/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x - \sqrt{3} - 1}{\sqrt{x^{3} - 1} x}\,{d x}"," ",0,"integrate(-(x - sqrt(3) - 1)/(sqrt(x^3 - 1)*x), x)","F",0
155,0,0,0,0.000000," ","integrate((1+x+3^(1/2))/x/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x + \sqrt{3} + 1}{\sqrt{-x^{3} - 1} x}\,{d x}"," ",0,"integrate((x + sqrt(3) + 1)/(sqrt(-x^3 - 1)*x), x)","F",0
156,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/x/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{x^{3} + 1} x}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/(sqrt(x^3 + 1)*x), x)","F",0
157,0,0,0,0.000000," ","integrate((1-x-3^(1/2))/x/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + \sqrt{3} - 1}{\sqrt{-x^{3} + 1} x}\,{d x}"," ",0,"integrate(-(x + sqrt(3) - 1)/(sqrt(-x^3 + 1)*x), x)","F",0
158,0,0,0,0.000000," ","integrate((1-x-3^(1/2))/x/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x + \sqrt{3} - 1}{\sqrt{x^{3} - 1} x}\,{d x}"," ",0,"integrate(-(x + sqrt(3) - 1)/(sqrt(x^3 - 1)*x), x)","F",0
159,0,0,0,0.000000," ","integrate((1+x-3^(1/2))/x/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x - \sqrt{3} + 1}{\sqrt{-x^{3} - 1} x}\,{d x}"," ",0,"integrate((x - sqrt(3) + 1)/(sqrt(-x^3 - 1)*x), x)","F",0
160,0,0,0,0.000000," ","integrate(x/(3+x)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} + 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 + 1)*(x + 3)), x)","F",0
161,0,0,0,0.000000," ","integrate(x/(3+x)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{3} + 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-x^3 + 1)*(x + 3)), x)","F",0
162,0,0,0,0.000000," ","integrate(x/(3+x)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{x^{3} - 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(x^3 - 1)*(x + 3)), x)","F",0
163,0,0,0,0.000000," ","integrate(x/(3+x)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{3} - 1} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-x^3 - 1)*(x + 3)), x)","F",0
164,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{x^{3} + 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(x^3 + 1)*(d*x + c)), x)","F",0
165,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{-x^{3} + 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(-x^3 + 1)*(d*x + c)), x)","F",0
166,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{x^{3} - 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(x^3 - 1)*(d*x + c)), x)","F",0
167,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{-x^{3} - 1} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(-x^3 - 1)*(d*x + c)), x)","F",0
168,0,0,0,0.000000," ","integrate((f*x+e)/x/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{x^{3} + 1} x}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(x^3 + 1)*x), x)","F",0
169,0,0,0,0.000000," ","integrate((f*x+e)/x/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{-x^{3} + 1} x}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(-x^3 + 1)*x), x)","F",0
170,0,0,0,0.000000," ","integrate((f*x+e)/x/(x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{x^{3} - 1} x}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(x^3 - 1)*x), x)","F",0
171,0,0,0,0.000000," ","integrate((f*x+e)/x/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int \frac{f x + e}{\sqrt{-x^{3} - 1} x}\,{d x}"," ",0,"integrate((f*x + e)/(sqrt(-x^3 - 1)*x), x)","F",0
172,0,0,0,0.000000," ","integrate((-d*x+c)/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x, algorithm=""giac"")","\int -\frac{d x - c}{{\left(d^{3} x^{3} + 2 \, c^{3}\right)}^{\frac{1}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(-(d*x - c)/((d^3*x^3 + 2*c^3)^(1/3)*(d*x + c)), x)","F",0
173,0,0,0,0.000000," ","integrate((f*x+e)/(d*x+c)/(d^3*x^3-c^3)^(1/3),x, algorithm=""giac"")","\int \frac{f x + e}{{\left(d^{3} x^{3} - c^{3}\right)}^{\frac{1}{3}} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((f*x + e)/((d^3*x^3 - c^3)^(1/3)*(d*x + c)), x)","F",0
174,1,835,0,0.398465," ","integrate(x^2*(b*x+a)^n*(d*x^3+c),x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{6} d n^{5} x^{6} + {\left(b x + a\right)}^{n} a b^{5} d n^{5} x^{5} + 15 \, {\left(b x + a\right)}^{n} b^{6} d n^{4} x^{6} + 10 \, {\left(b x + a\right)}^{n} a b^{5} d n^{4} x^{5} + 85 \, {\left(b x + a\right)}^{n} b^{6} d n^{3} x^{6} + {\left(b x + a\right)}^{n} b^{6} c n^{5} x^{3} - 5 \, {\left(b x + a\right)}^{n} a^{2} b^{4} d n^{4} x^{4} + 35 \, {\left(b x + a\right)}^{n} a b^{5} d n^{3} x^{5} + 225 \, {\left(b x + a\right)}^{n} b^{6} d n^{2} x^{6} + {\left(b x + a\right)}^{n} a b^{5} c n^{5} x^{2} + 18 \, {\left(b x + a\right)}^{n} b^{6} c n^{4} x^{3} - 30 \, {\left(b x + a\right)}^{n} a^{2} b^{4} d n^{3} x^{4} + 50 \, {\left(b x + a\right)}^{n} a b^{5} d n^{2} x^{5} + 274 \, {\left(b x + a\right)}^{n} b^{6} d n x^{6} + 16 \, {\left(b x + a\right)}^{n} a b^{5} c n^{4} x^{2} + 121 \, {\left(b x + a\right)}^{n} b^{6} c n^{3} x^{3} + 20 \, {\left(b x + a\right)}^{n} a^{3} b^{3} d n^{3} x^{3} - 55 \, {\left(b x + a\right)}^{n} a^{2} b^{4} d n^{2} x^{4} + 24 \, {\left(b x + a\right)}^{n} a b^{5} d n x^{5} + 120 \, {\left(b x + a\right)}^{n} b^{6} d x^{6} - 2 \, {\left(b x + a\right)}^{n} a^{2} b^{4} c n^{4} x + 89 \, {\left(b x + a\right)}^{n} a b^{5} c n^{3} x^{2} + 372 \, {\left(b x + a\right)}^{n} b^{6} c n^{2} x^{3} + 60 \, {\left(b x + a\right)}^{n} a^{3} b^{3} d n^{2} x^{3} - 30 \, {\left(b x + a\right)}^{n} a^{2} b^{4} d n x^{4} - 30 \, {\left(b x + a\right)}^{n} a^{2} b^{4} c n^{3} x + 194 \, {\left(b x + a\right)}^{n} a b^{5} c n^{2} x^{2} - 60 \, {\left(b x + a\right)}^{n} a^{4} b^{2} d n^{2} x^{2} + 508 \, {\left(b x + a\right)}^{n} b^{6} c n x^{3} + 40 \, {\left(b x + a\right)}^{n} a^{3} b^{3} d n x^{3} + 2 \, {\left(b x + a\right)}^{n} a^{3} b^{3} c n^{3} - 148 \, {\left(b x + a\right)}^{n} a^{2} b^{4} c n^{2} x + 120 \, {\left(b x + a\right)}^{n} a b^{5} c n x^{2} - 60 \, {\left(b x + a\right)}^{n} a^{4} b^{2} d n x^{2} + 240 \, {\left(b x + a\right)}^{n} b^{6} c x^{3} + 30 \, {\left(b x + a\right)}^{n} a^{3} b^{3} c n^{2} - 240 \, {\left(b x + a\right)}^{n} a^{2} b^{4} c n x + 120 \, {\left(b x + a\right)}^{n} a^{5} b d n x + 148 \, {\left(b x + a\right)}^{n} a^{3} b^{3} c n + 240 \, {\left(b x + a\right)}^{n} a^{3} b^{3} c - 120 \, {\left(b x + a\right)}^{n} a^{6} d}{b^{6} n^{6} + 21 \, b^{6} n^{5} + 175 \, b^{6} n^{4} + 735 \, b^{6} n^{3} + 1624 \, b^{6} n^{2} + 1764 \, b^{6} n + 720 \, b^{6}}"," ",0,"((b*x + a)^n*b^6*d*n^5*x^6 + (b*x + a)^n*a*b^5*d*n^5*x^5 + 15*(b*x + a)^n*b^6*d*n^4*x^6 + 10*(b*x + a)^n*a*b^5*d*n^4*x^5 + 85*(b*x + a)^n*b^6*d*n^3*x^6 + (b*x + a)^n*b^6*c*n^5*x^3 - 5*(b*x + a)^n*a^2*b^4*d*n^4*x^4 + 35*(b*x + a)^n*a*b^5*d*n^3*x^5 + 225*(b*x + a)^n*b^6*d*n^2*x^6 + (b*x + a)^n*a*b^5*c*n^5*x^2 + 18*(b*x + a)^n*b^6*c*n^4*x^3 - 30*(b*x + a)^n*a^2*b^4*d*n^3*x^4 + 50*(b*x + a)^n*a*b^5*d*n^2*x^5 + 274*(b*x + a)^n*b^6*d*n*x^6 + 16*(b*x + a)^n*a*b^5*c*n^4*x^2 + 121*(b*x + a)^n*b^6*c*n^3*x^3 + 20*(b*x + a)^n*a^3*b^3*d*n^3*x^3 - 55*(b*x + a)^n*a^2*b^4*d*n^2*x^4 + 24*(b*x + a)^n*a*b^5*d*n*x^5 + 120*(b*x + a)^n*b^6*d*x^6 - 2*(b*x + a)^n*a^2*b^4*c*n^4*x + 89*(b*x + a)^n*a*b^5*c*n^3*x^2 + 372*(b*x + a)^n*b^6*c*n^2*x^3 + 60*(b*x + a)^n*a^3*b^3*d*n^2*x^3 - 30*(b*x + a)^n*a^2*b^4*d*n*x^4 - 30*(b*x + a)^n*a^2*b^4*c*n^3*x + 194*(b*x + a)^n*a*b^5*c*n^2*x^2 - 60*(b*x + a)^n*a^4*b^2*d*n^2*x^2 + 508*(b*x + a)^n*b^6*c*n*x^3 + 40*(b*x + a)^n*a^3*b^3*d*n*x^3 + 2*(b*x + a)^n*a^3*b^3*c*n^3 - 148*(b*x + a)^n*a^2*b^4*c*n^2*x + 120*(b*x + a)^n*a*b^5*c*n*x^2 - 60*(b*x + a)^n*a^4*b^2*d*n*x^2 + 240*(b*x + a)^n*b^6*c*x^3 + 30*(b*x + a)^n*a^3*b^3*c*n^2 - 240*(b*x + a)^n*a^2*b^4*c*n*x + 120*(b*x + a)^n*a^5*b*d*n*x + 148*(b*x + a)^n*a^3*b^3*c*n + 240*(b*x + a)^n*a^3*b^3*c - 120*(b*x + a)^n*a^6*d)/(b^6*n^6 + 21*b^6*n^5 + 175*b^6*n^4 + 735*b^6*n^3 + 1624*b^6*n^2 + 1764*b^6*n + 720*b^6)","B",0
175,1,577,0,0.379390," ","integrate(x*(b*x+a)^n*(d*x^3+c),x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{5} d n^{4} x^{5} + {\left(b x + a\right)}^{n} a b^{4} d n^{4} x^{4} + 10 \, {\left(b x + a\right)}^{n} b^{5} d n^{3} x^{5} + 6 \, {\left(b x + a\right)}^{n} a b^{4} d n^{3} x^{4} + 35 \, {\left(b x + a\right)}^{n} b^{5} d n^{2} x^{5} + {\left(b x + a\right)}^{n} b^{5} c n^{4} x^{2} - 4 \, {\left(b x + a\right)}^{n} a^{2} b^{3} d n^{3} x^{3} + 11 \, {\left(b x + a\right)}^{n} a b^{4} d n^{2} x^{4} + 50 \, {\left(b x + a\right)}^{n} b^{5} d n x^{5} + {\left(b x + a\right)}^{n} a b^{4} c n^{4} x + 13 \, {\left(b x + a\right)}^{n} b^{5} c n^{3} x^{2} - 12 \, {\left(b x + a\right)}^{n} a^{2} b^{3} d n^{2} x^{3} + 6 \, {\left(b x + a\right)}^{n} a b^{4} d n x^{4} + 24 \, {\left(b x + a\right)}^{n} b^{5} d x^{5} + 12 \, {\left(b x + a\right)}^{n} a b^{4} c n^{3} x + 59 \, {\left(b x + a\right)}^{n} b^{5} c n^{2} x^{2} + 12 \, {\left(b x + a\right)}^{n} a^{3} b^{2} d n^{2} x^{2} - 8 \, {\left(b x + a\right)}^{n} a^{2} b^{3} d n x^{3} - {\left(b x + a\right)}^{n} a^{2} b^{3} c n^{3} + 47 \, {\left(b x + a\right)}^{n} a b^{4} c n^{2} x + 107 \, {\left(b x + a\right)}^{n} b^{5} c n x^{2} + 12 \, {\left(b x + a\right)}^{n} a^{3} b^{2} d n x^{2} - 12 \, {\left(b x + a\right)}^{n} a^{2} b^{3} c n^{2} + 60 \, {\left(b x + a\right)}^{n} a b^{4} c n x - 24 \, {\left(b x + a\right)}^{n} a^{4} b d n x + 60 \, {\left(b x + a\right)}^{n} b^{5} c x^{2} - 47 \, {\left(b x + a\right)}^{n} a^{2} b^{3} c n - 60 \, {\left(b x + a\right)}^{n} a^{2} b^{3} c + 24 \, {\left(b x + a\right)}^{n} a^{5} d}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"((b*x + a)^n*b^5*d*n^4*x^5 + (b*x + a)^n*a*b^4*d*n^4*x^4 + 10*(b*x + a)^n*b^5*d*n^3*x^5 + 6*(b*x + a)^n*a*b^4*d*n^3*x^4 + 35*(b*x + a)^n*b^5*d*n^2*x^5 + (b*x + a)^n*b^5*c*n^4*x^2 - 4*(b*x + a)^n*a^2*b^3*d*n^3*x^3 + 11*(b*x + a)^n*a*b^4*d*n^2*x^4 + 50*(b*x + a)^n*b^5*d*n*x^5 + (b*x + a)^n*a*b^4*c*n^4*x + 13*(b*x + a)^n*b^5*c*n^3*x^2 - 12*(b*x + a)^n*a^2*b^3*d*n^2*x^3 + 6*(b*x + a)^n*a*b^4*d*n*x^4 + 24*(b*x + a)^n*b^5*d*x^5 + 12*(b*x + a)^n*a*b^4*c*n^3*x + 59*(b*x + a)^n*b^5*c*n^2*x^2 + 12*(b*x + a)^n*a^3*b^2*d*n^2*x^2 - 8*(b*x + a)^n*a^2*b^3*d*n*x^3 - (b*x + a)^n*a^2*b^3*c*n^3 + 47*(b*x + a)^n*a*b^4*c*n^2*x + 107*(b*x + a)^n*b^5*c*n*x^2 + 12*(b*x + a)^n*a^3*b^2*d*n*x^2 - 12*(b*x + a)^n*a^2*b^3*c*n^2 + 60*(b*x + a)^n*a*b^4*c*n*x - 24*(b*x + a)^n*a^4*b*d*n*x + 60*(b*x + a)^n*b^5*c*x^2 - 47*(b*x + a)^n*a^2*b^3*c*n - 60*(b*x + a)^n*a^2*b^3*c + 24*(b*x + a)^n*a^5*d)/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
176,1,361,0,0.326772," ","integrate((b*x+a)^n*(d*x^3+c),x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{4} d n^{3} x^{4} + {\left(b x + a\right)}^{n} a b^{3} d n^{3} x^{3} + 6 \, {\left(b x + a\right)}^{n} b^{4} d n^{2} x^{4} + 3 \, {\left(b x + a\right)}^{n} a b^{3} d n^{2} x^{3} + 11 \, {\left(b x + a\right)}^{n} b^{4} d n x^{4} + {\left(b x + a\right)}^{n} b^{4} c n^{3} x - 3 \, {\left(b x + a\right)}^{n} a^{2} b^{2} d n^{2} x^{2} + 2 \, {\left(b x + a\right)}^{n} a b^{3} d n x^{3} + 6 \, {\left(b x + a\right)}^{n} b^{4} d x^{4} + {\left(b x + a\right)}^{n} a b^{3} c n^{3} + 9 \, {\left(b x + a\right)}^{n} b^{4} c n^{2} x - 3 \, {\left(b x + a\right)}^{n} a^{2} b^{2} d n x^{2} + 9 \, {\left(b x + a\right)}^{n} a b^{3} c n^{2} + 26 \, {\left(b x + a\right)}^{n} b^{4} c n x + 6 \, {\left(b x + a\right)}^{n} a^{3} b d n x + 26 \, {\left(b x + a\right)}^{n} a b^{3} c n + 24 \, {\left(b x + a\right)}^{n} b^{4} c x + 24 \, {\left(b x + a\right)}^{n} a b^{3} c - 6 \, {\left(b x + a\right)}^{n} a^{4} d}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"((b*x + a)^n*b^4*d*n^3*x^4 + (b*x + a)^n*a*b^3*d*n^3*x^3 + 6*(b*x + a)^n*b^4*d*n^2*x^4 + 3*(b*x + a)^n*a*b^3*d*n^2*x^3 + 11*(b*x + a)^n*b^4*d*n*x^4 + (b*x + a)^n*b^4*c*n^3*x - 3*(b*x + a)^n*a^2*b^2*d*n^2*x^2 + 2*(b*x + a)^n*a*b^3*d*n*x^3 + 6*(b*x + a)^n*b^4*d*x^4 + (b*x + a)^n*a*b^3*c*n^3 + 9*(b*x + a)^n*b^4*c*n^2*x - 3*(b*x + a)^n*a^2*b^2*d*n*x^2 + 9*(b*x + a)^n*a*b^3*c*n^2 + 26*(b*x + a)^n*b^4*c*n*x + 6*(b*x + a)^n*a^3*b*d*n*x + 26*(b*x + a)^n*a*b^3*c*n + 24*(b*x + a)^n*b^4*c*x + 24*(b*x + a)^n*a*b^3*c - 6*(b*x + a)^n*a^4*d)/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
177,0,0,0,0.000000," ","integrate((b*x+a)^n*(d*x^3+c)/x,x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)} {\left(b x + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((d*x^3 + c)*(b*x + a)^n/x, x)","F",0
178,1,2660,0,0.613227," ","integrate(x^2*(b*x+a)^n*(d*x^3+c)^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{9} d^{2} n^{8} x^{9} + {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{8} x^{8} + 36 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n^{7} x^{9} + 28 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{7} x^{8} + 546 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n^{6} x^{9} + 2 \, {\left(b x + a\right)}^{n} b^{9} c d n^{8} x^{6} - 8 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n^{7} x^{7} + 322 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{6} x^{8} + 4536 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n^{5} x^{9} + 2 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{8} x^{5} + 78 \, {\left(b x + a\right)}^{n} b^{9} c d n^{7} x^{6} - 168 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n^{6} x^{7} + 1960 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{5} x^{8} + 22449 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n^{4} x^{9} + 68 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{7} x^{5} + 1272 \, {\left(b x + a\right)}^{n} b^{9} c d n^{6} x^{6} + 56 \, {\left(b x + a\right)}^{n} a^{3} b^{6} d^{2} n^{6} x^{6} - 1400 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n^{5} x^{7} + 6769 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{4} x^{8} + 67284 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n^{3} x^{9} + {\left(b x + a\right)}^{n} b^{9} c^{2} n^{8} x^{3} - 10 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n^{7} x^{4} + 932 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{6} x^{5} + 11268 \, {\left(b x + a\right)}^{n} b^{9} c d n^{5} x^{6} + 840 \, {\left(b x + a\right)}^{n} a^{3} b^{6} d^{2} n^{5} x^{6} - 5880 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n^{4} x^{7} + 13132 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{3} x^{8} + 118124 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n^{2} x^{9} + {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{8} x^{2} + 42 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n^{7} x^{3} - 300 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n^{6} x^{4} + 6608 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{5} x^{5} - 336 \, {\left(b x + a\right)}^{n} a^{4} b^{5} d^{2} n^{5} x^{5} + 58938 \, {\left(b x + a\right)}^{n} b^{9} c d n^{4} x^{6} + 4760 \, {\left(b x + a\right)}^{n} a^{3} b^{6} d^{2} n^{4} x^{6} - 12992 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n^{3} x^{7} + 13068 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n^{2} x^{8} + 109584 \, {\left(b x + a\right)}^{n} b^{9} d^{2} n x^{9} + 40 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{7} x^{2} + 744 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n^{6} x^{3} + 40 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c d n^{6} x^{3} - 3460 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n^{5} x^{4} + 25898 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{4} x^{5} - 3360 \, {\left(b x + a\right)}^{n} a^{4} b^{5} d^{2} n^{4} x^{5} + 185022 \, {\left(b x + a\right)}^{n} b^{9} c d n^{3} x^{6} + 12600 \, {\left(b x + a\right)}^{n} a^{3} b^{6} d^{2} n^{3} x^{6} - 14112 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n^{2} x^{7} + 5040 \, {\left(b x + a\right)}^{n} a b^{8} d^{2} n x^{8} + 40320 \, {\left(b x + a\right)}^{n} b^{9} d^{2} x^{9} - 2 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n^{7} x + 664 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{6} x^{2} + 7218 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n^{5} x^{3} + 1080 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c d n^{5} x^{3} - 19200 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n^{4} x^{4} + 1680 \, {\left(b x + a\right)}^{n} a^{5} b^{4} d^{2} n^{4} x^{4} + 55532 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{3} x^{5} - 11760 \, {\left(b x + a\right)}^{n} a^{4} b^{5} d^{2} n^{3} x^{5} + 337228 \, {\left(b x + a\right)}^{n} b^{9} c d n^{2} x^{6} + 15344 \, {\left(b x + a\right)}^{n} a^{3} b^{6} d^{2} n^{2} x^{6} - 5760 \, {\left(b x + a\right)}^{n} a^{2} b^{7} d^{2} n x^{7} - 78 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n^{6} x + 5890 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{5} x^{2} - 120 \, {\left(b x + a\right)}^{n} a^{4} b^{5} c d n^{5} x^{2} + 41619 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n^{4} x^{3} + 10600 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c d n^{4} x^{3} - 52690 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n^{3} x^{4} + 10080 \, {\left(b x + a\right)}^{n} a^{5} b^{4} d^{2} n^{3} x^{4} + 59568 \, {\left(b x + a\right)}^{n} a b^{8} c d n^{2} x^{5} - 16800 \, {\left(b x + a\right)}^{n} a^{4} b^{5} d^{2} n^{2} x^{5} + 322032 \, {\left(b x + a\right)}^{n} b^{9} c d n x^{6} + 6720 \, {\left(b x + a\right)}^{n} a^{3} b^{6} d^{2} n x^{6} + 2 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} n^{6} - 1250 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n^{5} x + 29839 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{4} x^{2} - 3000 \, {\left(b x + a\right)}^{n} a^{4} b^{5} c d n^{4} x^{2} + 144468 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n^{3} x^{3} + 45000 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c d n^{3} x^{3} - 6720 \, {\left(b x + a\right)}^{n} a^{6} b^{3} d^{2} n^{3} x^{3} - 66900 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n^{2} x^{4} + 18480 \, {\left(b x + a\right)}^{n} a^{5} b^{4} d^{2} n^{2} x^{4} + 24192 \, {\left(b x + a\right)}^{n} a b^{8} c d n x^{5} - 8064 \, {\left(b x + a\right)}^{n} a^{4} b^{5} d^{2} n x^{5} + 120960 \, {\left(b x + a\right)}^{n} b^{9} c d x^{6} + 78 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} n^{5} - 10530 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n^{4} x + 240 \, {\left(b x + a\right)}^{n} a^{5} b^{4} c d n^{4} x + 84790 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{3} x^{2} - 25800 \, {\left(b x + a\right)}^{n} a^{4} b^{5} c d n^{3} x^{2} + 290276 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n^{2} x^{3} + 75760 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c d n^{2} x^{3} - 20160 \, {\left(b x + a\right)}^{n} a^{6} b^{3} d^{2} n^{2} x^{3} - 30240 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c d n x^{4} + 10080 \, {\left(b x + a\right)}^{n} a^{5} b^{4} d^{2} n x^{4} + 1250 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} n^{4} - 49148 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n^{3} x + 5760 \, {\left(b x + a\right)}^{n} a^{5} b^{4} c d n^{3} x + 120696 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n^{2} x^{2} - 83400 \, {\left(b x + a\right)}^{n} a^{4} b^{5} c d n^{2} x^{2} + 20160 \, {\left(b x + a\right)}^{n} a^{7} b^{2} d^{2} n^{2} x^{2} + 301872 \, {\left(b x + a\right)}^{n} b^{9} c^{2} n x^{3} + 40320 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c d n x^{3} - 13440 \, {\left(b x + a\right)}^{n} a^{6} b^{3} d^{2} n x^{3} + 10530 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} n^{3} - 240 \, {\left(b x + a\right)}^{n} a^{6} b^{3} c d n^{3} - 120432 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n^{2} x + 45840 \, {\left(b x + a\right)}^{n} a^{5} b^{4} c d n^{2} x + 60480 \, {\left(b x + a\right)}^{n} a b^{8} c^{2} n x^{2} - 60480 \, {\left(b x + a\right)}^{n} a^{4} b^{5} c d n x^{2} + 20160 \, {\left(b x + a\right)}^{n} a^{7} b^{2} d^{2} n x^{2} + 120960 \, {\left(b x + a\right)}^{n} b^{9} c^{2} x^{3} + 49148 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} n^{2} - 5760 \, {\left(b x + a\right)}^{n} a^{6} b^{3} c d n^{2} - 120960 \, {\left(b x + a\right)}^{n} a^{2} b^{7} c^{2} n x + 120960 \, {\left(b x + a\right)}^{n} a^{5} b^{4} c d n x - 40320 \, {\left(b x + a\right)}^{n} a^{8} b d^{2} n x + 120432 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} n - 45840 \, {\left(b x + a\right)}^{n} a^{6} b^{3} c d n + 120960 \, {\left(b x + a\right)}^{n} a^{3} b^{6} c^{2} - 120960 \, {\left(b x + a\right)}^{n} a^{6} b^{3} c d + 40320 \, {\left(b x + a\right)}^{n} a^{9} d^{2}}{b^{9} n^{9} + 45 \, b^{9} n^{8} + 870 \, b^{9} n^{7} + 9450 \, b^{9} n^{6} + 63273 \, b^{9} n^{5} + 269325 \, b^{9} n^{4} + 723680 \, b^{9} n^{3} + 1172700 \, b^{9} n^{2} + 1026576 \, b^{9} n + 362880 \, b^{9}}"," ",0,"((b*x + a)^n*b^9*d^2*n^8*x^9 + (b*x + a)^n*a*b^8*d^2*n^8*x^8 + 36*(b*x + a)^n*b^9*d^2*n^7*x^9 + 28*(b*x + a)^n*a*b^8*d^2*n^7*x^8 + 546*(b*x + a)^n*b^9*d^2*n^6*x^9 + 2*(b*x + a)^n*b^9*c*d*n^8*x^6 - 8*(b*x + a)^n*a^2*b^7*d^2*n^7*x^7 + 322*(b*x + a)^n*a*b^8*d^2*n^6*x^8 + 4536*(b*x + a)^n*b^9*d^2*n^5*x^9 + 2*(b*x + a)^n*a*b^8*c*d*n^8*x^5 + 78*(b*x + a)^n*b^9*c*d*n^7*x^6 - 168*(b*x + a)^n*a^2*b^7*d^2*n^6*x^7 + 1960*(b*x + a)^n*a*b^8*d^2*n^5*x^8 + 22449*(b*x + a)^n*b^9*d^2*n^4*x^9 + 68*(b*x + a)^n*a*b^8*c*d*n^7*x^5 + 1272*(b*x + a)^n*b^9*c*d*n^6*x^6 + 56*(b*x + a)^n*a^3*b^6*d^2*n^6*x^6 - 1400*(b*x + a)^n*a^2*b^7*d^2*n^5*x^7 + 6769*(b*x + a)^n*a*b^8*d^2*n^4*x^8 + 67284*(b*x + a)^n*b^9*d^2*n^3*x^9 + (b*x + a)^n*b^9*c^2*n^8*x^3 - 10*(b*x + a)^n*a^2*b^7*c*d*n^7*x^4 + 932*(b*x + a)^n*a*b^8*c*d*n^6*x^5 + 11268*(b*x + a)^n*b^9*c*d*n^5*x^6 + 840*(b*x + a)^n*a^3*b^6*d^2*n^5*x^6 - 5880*(b*x + a)^n*a^2*b^7*d^2*n^4*x^7 + 13132*(b*x + a)^n*a*b^8*d^2*n^3*x^8 + 118124*(b*x + a)^n*b^9*d^2*n^2*x^9 + (b*x + a)^n*a*b^8*c^2*n^8*x^2 + 42*(b*x + a)^n*b^9*c^2*n^7*x^3 - 300*(b*x + a)^n*a^2*b^7*c*d*n^6*x^4 + 6608*(b*x + a)^n*a*b^8*c*d*n^5*x^5 - 336*(b*x + a)^n*a^4*b^5*d^2*n^5*x^5 + 58938*(b*x + a)^n*b^9*c*d*n^4*x^6 + 4760*(b*x + a)^n*a^3*b^6*d^2*n^4*x^6 - 12992*(b*x + a)^n*a^2*b^7*d^2*n^3*x^7 + 13068*(b*x + a)^n*a*b^8*d^2*n^2*x^8 + 109584*(b*x + a)^n*b^9*d^2*n*x^9 + 40*(b*x + a)^n*a*b^8*c^2*n^7*x^2 + 744*(b*x + a)^n*b^9*c^2*n^6*x^3 + 40*(b*x + a)^n*a^3*b^6*c*d*n^6*x^3 - 3460*(b*x + a)^n*a^2*b^7*c*d*n^5*x^4 + 25898*(b*x + a)^n*a*b^8*c*d*n^4*x^5 - 3360*(b*x + a)^n*a^4*b^5*d^2*n^4*x^5 + 185022*(b*x + a)^n*b^9*c*d*n^3*x^6 + 12600*(b*x + a)^n*a^3*b^6*d^2*n^3*x^6 - 14112*(b*x + a)^n*a^2*b^7*d^2*n^2*x^7 + 5040*(b*x + a)^n*a*b^8*d^2*n*x^8 + 40320*(b*x + a)^n*b^9*d^2*x^9 - 2*(b*x + a)^n*a^2*b^7*c^2*n^7*x + 664*(b*x + a)^n*a*b^8*c^2*n^6*x^2 + 7218*(b*x + a)^n*b^9*c^2*n^5*x^3 + 1080*(b*x + a)^n*a^3*b^6*c*d*n^5*x^3 - 19200*(b*x + a)^n*a^2*b^7*c*d*n^4*x^4 + 1680*(b*x + a)^n*a^5*b^4*d^2*n^4*x^4 + 55532*(b*x + a)^n*a*b^8*c*d*n^3*x^5 - 11760*(b*x + a)^n*a^4*b^5*d^2*n^3*x^5 + 337228*(b*x + a)^n*b^9*c*d*n^2*x^6 + 15344*(b*x + a)^n*a^3*b^6*d^2*n^2*x^6 - 5760*(b*x + a)^n*a^2*b^7*d^2*n*x^7 - 78*(b*x + a)^n*a^2*b^7*c^2*n^6*x + 5890*(b*x + a)^n*a*b^8*c^2*n^5*x^2 - 120*(b*x + a)^n*a^4*b^5*c*d*n^5*x^2 + 41619*(b*x + a)^n*b^9*c^2*n^4*x^3 + 10600*(b*x + a)^n*a^3*b^6*c*d*n^4*x^3 - 52690*(b*x + a)^n*a^2*b^7*c*d*n^3*x^4 + 10080*(b*x + a)^n*a^5*b^4*d^2*n^3*x^4 + 59568*(b*x + a)^n*a*b^8*c*d*n^2*x^5 - 16800*(b*x + a)^n*a^4*b^5*d^2*n^2*x^5 + 322032*(b*x + a)^n*b^9*c*d*n*x^6 + 6720*(b*x + a)^n*a^3*b^6*d^2*n*x^6 + 2*(b*x + a)^n*a^3*b^6*c^2*n^6 - 1250*(b*x + a)^n*a^2*b^7*c^2*n^5*x + 29839*(b*x + a)^n*a*b^8*c^2*n^4*x^2 - 3000*(b*x + a)^n*a^4*b^5*c*d*n^4*x^2 + 144468*(b*x + a)^n*b^9*c^2*n^3*x^3 + 45000*(b*x + a)^n*a^3*b^6*c*d*n^3*x^3 - 6720*(b*x + a)^n*a^6*b^3*d^2*n^3*x^3 - 66900*(b*x + a)^n*a^2*b^7*c*d*n^2*x^4 + 18480*(b*x + a)^n*a^5*b^4*d^2*n^2*x^4 + 24192*(b*x + a)^n*a*b^8*c*d*n*x^5 - 8064*(b*x + a)^n*a^4*b^5*d^2*n*x^5 + 120960*(b*x + a)^n*b^9*c*d*x^6 + 78*(b*x + a)^n*a^3*b^6*c^2*n^5 - 10530*(b*x + a)^n*a^2*b^7*c^2*n^4*x + 240*(b*x + a)^n*a^5*b^4*c*d*n^4*x + 84790*(b*x + a)^n*a*b^8*c^2*n^3*x^2 - 25800*(b*x + a)^n*a^4*b^5*c*d*n^3*x^2 + 290276*(b*x + a)^n*b^9*c^2*n^2*x^3 + 75760*(b*x + a)^n*a^3*b^6*c*d*n^2*x^3 - 20160*(b*x + a)^n*a^6*b^3*d^2*n^2*x^3 - 30240*(b*x + a)^n*a^2*b^7*c*d*n*x^4 + 10080*(b*x + a)^n*a^5*b^4*d^2*n*x^4 + 1250*(b*x + a)^n*a^3*b^6*c^2*n^4 - 49148*(b*x + a)^n*a^2*b^7*c^2*n^3*x + 5760*(b*x + a)^n*a^5*b^4*c*d*n^3*x + 120696*(b*x + a)^n*a*b^8*c^2*n^2*x^2 - 83400*(b*x + a)^n*a^4*b^5*c*d*n^2*x^2 + 20160*(b*x + a)^n*a^7*b^2*d^2*n^2*x^2 + 301872*(b*x + a)^n*b^9*c^2*n*x^3 + 40320*(b*x + a)^n*a^3*b^6*c*d*n*x^3 - 13440*(b*x + a)^n*a^6*b^3*d^2*n*x^3 + 10530*(b*x + a)^n*a^3*b^6*c^2*n^3 - 240*(b*x + a)^n*a^6*b^3*c*d*n^3 - 120432*(b*x + a)^n*a^2*b^7*c^2*n^2*x + 45840*(b*x + a)^n*a^5*b^4*c*d*n^2*x + 60480*(b*x + a)^n*a*b^8*c^2*n*x^2 - 60480*(b*x + a)^n*a^4*b^5*c*d*n*x^2 + 20160*(b*x + a)^n*a^7*b^2*d^2*n*x^2 + 120960*(b*x + a)^n*b^9*c^2*x^3 + 49148*(b*x + a)^n*a^3*b^6*c^2*n^2 - 5760*(b*x + a)^n*a^6*b^3*c*d*n^2 - 120960*(b*x + a)^n*a^2*b^7*c^2*n*x + 120960*(b*x + a)^n*a^5*b^4*c*d*n*x - 40320*(b*x + a)^n*a^8*b*d^2*n*x + 120432*(b*x + a)^n*a^3*b^6*c^2*n - 45840*(b*x + a)^n*a^6*b^3*c*d*n + 120960*(b*x + a)^n*a^3*b^6*c^2 - 120960*(b*x + a)^n*a^6*b^3*c*d + 40320*(b*x + a)^n*a^9*d^2)/(b^9*n^9 + 45*b^9*n^8 + 870*b^9*n^7 + 9450*b^9*n^6 + 63273*b^9*n^5 + 269325*b^9*n^4 + 723680*b^9*n^3 + 1172700*b^9*n^2 + 1026576*b^9*n + 362880*b^9)","B",0
179,1,2034,0,0.614397," ","integrate(x*(b*x+a)^n*(d*x^3+c)^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{8} d^{2} n^{7} x^{8} + {\left(b x + a\right)}^{n} a b^{7} d^{2} n^{7} x^{7} + 28 \, {\left(b x + a\right)}^{n} b^{8} d^{2} n^{6} x^{8} + 21 \, {\left(b x + a\right)}^{n} a b^{7} d^{2} n^{6} x^{7} + 322 \, {\left(b x + a\right)}^{n} b^{8} d^{2} n^{5} x^{8} + 2 \, {\left(b x + a\right)}^{n} b^{8} c d n^{7} x^{5} - 7 \, {\left(b x + a\right)}^{n} a^{2} b^{6} d^{2} n^{6} x^{6} + 175 \, {\left(b x + a\right)}^{n} a b^{7} d^{2} n^{5} x^{7} + 1960 \, {\left(b x + a\right)}^{n} b^{8} d^{2} n^{4} x^{8} + 2 \, {\left(b x + a\right)}^{n} a b^{7} c d n^{7} x^{4} + 62 \, {\left(b x + a\right)}^{n} b^{8} c d n^{6} x^{5} - 105 \, {\left(b x + a\right)}^{n} a^{2} b^{6} d^{2} n^{5} x^{6} + 735 \, {\left(b x + a\right)}^{n} a b^{7} d^{2} n^{4} x^{7} + 6769 \, {\left(b x + a\right)}^{n} b^{8} d^{2} n^{3} x^{8} + 54 \, {\left(b x + a\right)}^{n} a b^{7} c d n^{6} x^{4} + 782 \, {\left(b x + a\right)}^{n} b^{8} c d n^{5} x^{5} + 42 \, {\left(b x + a\right)}^{n} a^{3} b^{5} d^{2} n^{5} x^{5} - 595 \, {\left(b x + a\right)}^{n} a^{2} b^{6} d^{2} n^{4} x^{6} + 1624 \, {\left(b x + a\right)}^{n} a b^{7} d^{2} n^{3} x^{7} + 13132 \, {\left(b x + a\right)}^{n} b^{8} d^{2} n^{2} x^{8} + {\left(b x + a\right)}^{n} b^{8} c^{2} n^{7} x^{2} - 8 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c d n^{6} x^{3} + 566 \, {\left(b x + a\right)}^{n} a b^{7} c d n^{5} x^{4} + 5162 \, {\left(b x + a\right)}^{n} b^{8} c d n^{4} x^{5} + 420 \, {\left(b x + a\right)}^{n} a^{3} b^{5} d^{2} n^{4} x^{5} - 1575 \, {\left(b x + a\right)}^{n} a^{2} b^{6} d^{2} n^{3} x^{6} + 1764 \, {\left(b x + a\right)}^{n} a b^{7} d^{2} n^{2} x^{7} + 13068 \, {\left(b x + a\right)}^{n} b^{8} d^{2} n x^{8} + {\left(b x + a\right)}^{n} a b^{7} c^{2} n^{7} x + 34 \, {\left(b x + a\right)}^{n} b^{8} c^{2} n^{6} x^{2} - 192 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c d n^{5} x^{3} + 2898 \, {\left(b x + a\right)}^{n} a b^{7} c d n^{4} x^{4} - 210 \, {\left(b x + a\right)}^{n} a^{4} b^{4} d^{2} n^{4} x^{4} + 19088 \, {\left(b x + a\right)}^{n} b^{8} c d n^{3} x^{5} + 1470 \, {\left(b x + a\right)}^{n} a^{3} b^{5} d^{2} n^{3} x^{5} - 1918 \, {\left(b x + a\right)}^{n} a^{2} b^{6} d^{2} n^{2} x^{6} + 720 \, {\left(b x + a\right)}^{n} a b^{7} d^{2} n x^{7} + 5040 \, {\left(b x + a\right)}^{n} b^{8} d^{2} x^{8} + 33 \, {\left(b x + a\right)}^{n} a b^{7} c^{2} n^{6} x + 478 \, {\left(b x + a\right)}^{n} b^{8} c^{2} n^{5} x^{2} + 24 \, {\left(b x + a\right)}^{n} a^{3} b^{5} c d n^{5} x^{2} - 1688 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c d n^{4} x^{3} + 7496 \, {\left(b x + a\right)}^{n} a b^{7} c d n^{3} x^{4} - 1260 \, {\left(b x + a\right)}^{n} a^{4} b^{4} d^{2} n^{3} x^{4} + 39128 \, {\left(b x + a\right)}^{n} b^{8} c d n^{2} x^{5} + 2100 \, {\left(b x + a\right)}^{n} a^{3} b^{5} d^{2} n^{2} x^{5} - 840 \, {\left(b x + a\right)}^{n} a^{2} b^{6} d^{2} n x^{6} - {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} n^{6} + 445 \, {\left(b x + a\right)}^{n} a b^{7} c^{2} n^{5} x + 3580 \, {\left(b x + a\right)}^{n} b^{8} c^{2} n^{4} x^{2} + 528 \, {\left(b x + a\right)}^{n} a^{3} b^{5} c d n^{4} x^{2} - 6528 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c d n^{3} x^{3} + 840 \, {\left(b x + a\right)}^{n} a^{5} b^{3} d^{2} n^{3} x^{3} + 9144 \, {\left(b x + a\right)}^{n} a b^{7} c d n^{2} x^{4} - 2310 \, {\left(b x + a\right)}^{n} a^{4} b^{4} d^{2} n^{2} x^{4} + 40608 \, {\left(b x + a\right)}^{n} b^{8} c d n x^{5} + 1008 \, {\left(b x + a\right)}^{n} a^{3} b^{5} d^{2} n x^{5} - 33 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} n^{5} + 3135 \, {\left(b x + a\right)}^{n} a b^{7} c^{2} n^{4} x - 48 \, {\left(b x + a\right)}^{n} a^{4} b^{4} c d n^{4} x + 15289 \, {\left(b x + a\right)}^{n} b^{8} c^{2} n^{3} x^{2} + 4008 \, {\left(b x + a\right)}^{n} a^{3} b^{5} c d n^{3} x^{2} - 10400 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c d n^{2} x^{3} + 2520 \, {\left(b x + a\right)}^{n} a^{5} b^{3} d^{2} n^{2} x^{3} + 4032 \, {\left(b x + a\right)}^{n} a b^{7} c d n x^{4} - 1260 \, {\left(b x + a\right)}^{n} a^{4} b^{4} d^{2} n x^{4} + 16128 \, {\left(b x + a\right)}^{n} b^{8} c d x^{5} - 445 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} n^{4} + 12154 \, {\left(b x + a\right)}^{n} a b^{7} c^{2} n^{3} x - 1008 \, {\left(b x + a\right)}^{n} a^{4} b^{4} c d n^{3} x + 36706 \, {\left(b x + a\right)}^{n} b^{8} c^{2} n^{2} x^{2} + 11568 \, {\left(b x + a\right)}^{n} a^{3} b^{5} c d n^{2} x^{2} - 2520 \, {\left(b x + a\right)}^{n} a^{6} b^{2} d^{2} n^{2} x^{2} - 5376 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c d n x^{3} + 1680 \, {\left(b x + a\right)}^{n} a^{5} b^{3} d^{2} n x^{3} - 3135 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} n^{3} + 48 \, {\left(b x + a\right)}^{n} a^{5} b^{3} c d n^{3} + 24552 \, {\left(b x + a\right)}^{n} a b^{7} c^{2} n^{2} x - 7008 \, {\left(b x + a\right)}^{n} a^{4} b^{4} c d n^{2} x + 44712 \, {\left(b x + a\right)}^{n} b^{8} c^{2} n x^{2} + 8064 \, {\left(b x + a\right)}^{n} a^{3} b^{5} c d n x^{2} - 2520 \, {\left(b x + a\right)}^{n} a^{6} b^{2} d^{2} n x^{2} - 12154 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} n^{2} + 1008 \, {\left(b x + a\right)}^{n} a^{5} b^{3} c d n^{2} + 20160 \, {\left(b x + a\right)}^{n} a b^{7} c^{2} n x - 16128 \, {\left(b x + a\right)}^{n} a^{4} b^{4} c d n x + 5040 \, {\left(b x + a\right)}^{n} a^{7} b d^{2} n x + 20160 \, {\left(b x + a\right)}^{n} b^{8} c^{2} x^{2} - 24552 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} n + 7008 \, {\left(b x + a\right)}^{n} a^{5} b^{3} c d n - 20160 \, {\left(b x + a\right)}^{n} a^{2} b^{6} c^{2} + 16128 \, {\left(b x + a\right)}^{n} a^{5} b^{3} c d - 5040 \, {\left(b x + a\right)}^{n} a^{8} d^{2}}{b^{8} n^{8} + 36 \, b^{8} n^{7} + 546 \, b^{8} n^{6} + 4536 \, b^{8} n^{5} + 22449 \, b^{8} n^{4} + 67284 \, b^{8} n^{3} + 118124 \, b^{8} n^{2} + 109584 \, b^{8} n + 40320 \, b^{8}}"," ",0,"((b*x + a)^n*b^8*d^2*n^7*x^8 + (b*x + a)^n*a*b^7*d^2*n^7*x^7 + 28*(b*x + a)^n*b^8*d^2*n^6*x^8 + 21*(b*x + a)^n*a*b^7*d^2*n^6*x^7 + 322*(b*x + a)^n*b^8*d^2*n^5*x^8 + 2*(b*x + a)^n*b^8*c*d*n^7*x^5 - 7*(b*x + a)^n*a^2*b^6*d^2*n^6*x^6 + 175*(b*x + a)^n*a*b^7*d^2*n^5*x^7 + 1960*(b*x + a)^n*b^8*d^2*n^4*x^8 + 2*(b*x + a)^n*a*b^7*c*d*n^7*x^4 + 62*(b*x + a)^n*b^8*c*d*n^6*x^5 - 105*(b*x + a)^n*a^2*b^6*d^2*n^5*x^6 + 735*(b*x + a)^n*a*b^7*d^2*n^4*x^7 + 6769*(b*x + a)^n*b^8*d^2*n^3*x^8 + 54*(b*x + a)^n*a*b^7*c*d*n^6*x^4 + 782*(b*x + a)^n*b^8*c*d*n^5*x^5 + 42*(b*x + a)^n*a^3*b^5*d^2*n^5*x^5 - 595*(b*x + a)^n*a^2*b^6*d^2*n^4*x^6 + 1624*(b*x + a)^n*a*b^7*d^2*n^3*x^7 + 13132*(b*x + a)^n*b^8*d^2*n^2*x^8 + (b*x + a)^n*b^8*c^2*n^7*x^2 - 8*(b*x + a)^n*a^2*b^6*c*d*n^6*x^3 + 566*(b*x + a)^n*a*b^7*c*d*n^5*x^4 + 5162*(b*x + a)^n*b^8*c*d*n^4*x^5 + 420*(b*x + a)^n*a^3*b^5*d^2*n^4*x^5 - 1575*(b*x + a)^n*a^2*b^6*d^2*n^3*x^6 + 1764*(b*x + a)^n*a*b^7*d^2*n^2*x^7 + 13068*(b*x + a)^n*b^8*d^2*n*x^8 + (b*x + a)^n*a*b^7*c^2*n^7*x + 34*(b*x + a)^n*b^8*c^2*n^6*x^2 - 192*(b*x + a)^n*a^2*b^6*c*d*n^5*x^3 + 2898*(b*x + a)^n*a*b^7*c*d*n^4*x^4 - 210*(b*x + a)^n*a^4*b^4*d^2*n^4*x^4 + 19088*(b*x + a)^n*b^8*c*d*n^3*x^5 + 1470*(b*x + a)^n*a^3*b^5*d^2*n^3*x^5 - 1918*(b*x + a)^n*a^2*b^6*d^2*n^2*x^6 + 720*(b*x + a)^n*a*b^7*d^2*n*x^7 + 5040*(b*x + a)^n*b^8*d^2*x^8 + 33*(b*x + a)^n*a*b^7*c^2*n^6*x + 478*(b*x + a)^n*b^8*c^2*n^5*x^2 + 24*(b*x + a)^n*a^3*b^5*c*d*n^5*x^2 - 1688*(b*x + a)^n*a^2*b^6*c*d*n^4*x^3 + 7496*(b*x + a)^n*a*b^7*c*d*n^3*x^4 - 1260*(b*x + a)^n*a^4*b^4*d^2*n^3*x^4 + 39128*(b*x + a)^n*b^8*c*d*n^2*x^5 + 2100*(b*x + a)^n*a^3*b^5*d^2*n^2*x^5 - 840*(b*x + a)^n*a^2*b^6*d^2*n*x^6 - (b*x + a)^n*a^2*b^6*c^2*n^6 + 445*(b*x + a)^n*a*b^7*c^2*n^5*x + 3580*(b*x + a)^n*b^8*c^2*n^4*x^2 + 528*(b*x + a)^n*a^3*b^5*c*d*n^4*x^2 - 6528*(b*x + a)^n*a^2*b^6*c*d*n^3*x^3 + 840*(b*x + a)^n*a^5*b^3*d^2*n^3*x^3 + 9144*(b*x + a)^n*a*b^7*c*d*n^2*x^4 - 2310*(b*x + a)^n*a^4*b^4*d^2*n^2*x^4 + 40608*(b*x + a)^n*b^8*c*d*n*x^5 + 1008*(b*x + a)^n*a^3*b^5*d^2*n*x^5 - 33*(b*x + a)^n*a^2*b^6*c^2*n^5 + 3135*(b*x + a)^n*a*b^7*c^2*n^4*x - 48*(b*x + a)^n*a^4*b^4*c*d*n^4*x + 15289*(b*x + a)^n*b^8*c^2*n^3*x^2 + 4008*(b*x + a)^n*a^3*b^5*c*d*n^3*x^2 - 10400*(b*x + a)^n*a^2*b^6*c*d*n^2*x^3 + 2520*(b*x + a)^n*a^5*b^3*d^2*n^2*x^3 + 4032*(b*x + a)^n*a*b^7*c*d*n*x^4 - 1260*(b*x + a)^n*a^4*b^4*d^2*n*x^4 + 16128*(b*x + a)^n*b^8*c*d*x^5 - 445*(b*x + a)^n*a^2*b^6*c^2*n^4 + 12154*(b*x + a)^n*a*b^7*c^2*n^3*x - 1008*(b*x + a)^n*a^4*b^4*c*d*n^3*x + 36706*(b*x + a)^n*b^8*c^2*n^2*x^2 + 11568*(b*x + a)^n*a^3*b^5*c*d*n^2*x^2 - 2520*(b*x + a)^n*a^6*b^2*d^2*n^2*x^2 - 5376*(b*x + a)^n*a^2*b^6*c*d*n*x^3 + 1680*(b*x + a)^n*a^5*b^3*d^2*n*x^3 - 3135*(b*x + a)^n*a^2*b^6*c^2*n^3 + 48*(b*x + a)^n*a^5*b^3*c*d*n^3 + 24552*(b*x + a)^n*a*b^7*c^2*n^2*x - 7008*(b*x + a)^n*a^4*b^4*c*d*n^2*x + 44712*(b*x + a)^n*b^8*c^2*n*x^2 + 8064*(b*x + a)^n*a^3*b^5*c*d*n*x^2 - 2520*(b*x + a)^n*a^6*b^2*d^2*n*x^2 - 12154*(b*x + a)^n*a^2*b^6*c^2*n^2 + 1008*(b*x + a)^n*a^5*b^3*c*d*n^2 + 20160*(b*x + a)^n*a*b^7*c^2*n*x - 16128*(b*x + a)^n*a^4*b^4*c*d*n*x + 5040*(b*x + a)^n*a^7*b*d^2*n*x + 20160*(b*x + a)^n*b^8*c^2*x^2 - 24552*(b*x + a)^n*a^2*b^6*c^2*n + 7008*(b*x + a)^n*a^5*b^3*c*d*n - 20160*(b*x + a)^n*a^2*b^6*c^2 + 16128*(b*x + a)^n*a^5*b^3*c*d - 5040*(b*x + a)^n*a^8*d^2)/(b^8*n^8 + 36*b^8*n^7 + 546*b^8*n^6 + 4536*b^8*n^5 + 22449*b^8*n^4 + 67284*b^8*n^3 + 118124*b^8*n^2 + 109584*b^8*n + 40320*b^8)","B",0
180,1,1477,0,0.497782," ","integrate((b*x+a)^n*(d*x^3+c)^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{7} d^{2} n^{6} x^{7} + {\left(b x + a\right)}^{n} a b^{6} d^{2} n^{6} x^{6} + 21 \, {\left(b x + a\right)}^{n} b^{7} d^{2} n^{5} x^{7} + 15 \, {\left(b x + a\right)}^{n} a b^{6} d^{2} n^{5} x^{6} + 175 \, {\left(b x + a\right)}^{n} b^{7} d^{2} n^{4} x^{7} + 2 \, {\left(b x + a\right)}^{n} b^{7} c d n^{6} x^{4} - 6 \, {\left(b x + a\right)}^{n} a^{2} b^{5} d^{2} n^{5} x^{5} + 85 \, {\left(b x + a\right)}^{n} a b^{6} d^{2} n^{4} x^{6} + 735 \, {\left(b x + a\right)}^{n} b^{7} d^{2} n^{3} x^{7} + 2 \, {\left(b x + a\right)}^{n} a b^{6} c d n^{6} x^{3} + 48 \, {\left(b x + a\right)}^{n} b^{7} c d n^{5} x^{4} - 60 \, {\left(b x + a\right)}^{n} a^{2} b^{5} d^{2} n^{4} x^{5} + 225 \, {\left(b x + a\right)}^{n} a b^{6} d^{2} n^{3} x^{6} + 1624 \, {\left(b x + a\right)}^{n} b^{7} d^{2} n^{2} x^{7} + 42 \, {\left(b x + a\right)}^{n} a b^{6} c d n^{5} x^{3} + 452 \, {\left(b x + a\right)}^{n} b^{7} c d n^{4} x^{4} + 30 \, {\left(b x + a\right)}^{n} a^{3} b^{4} d^{2} n^{4} x^{4} - 210 \, {\left(b x + a\right)}^{n} a^{2} b^{5} d^{2} n^{3} x^{5} + 274 \, {\left(b x + a\right)}^{n} a b^{6} d^{2} n^{2} x^{6} + 1764 \, {\left(b x + a\right)}^{n} b^{7} d^{2} n x^{7} + {\left(b x + a\right)}^{n} b^{7} c^{2} n^{6} x - 6 \, {\left(b x + a\right)}^{n} a^{2} b^{5} c d n^{5} x^{2} + 326 \, {\left(b x + a\right)}^{n} a b^{6} c d n^{4} x^{3} + 2112 \, {\left(b x + a\right)}^{n} b^{7} c d n^{3} x^{4} + 180 \, {\left(b x + a\right)}^{n} a^{3} b^{4} d^{2} n^{3} x^{4} - 300 \, {\left(b x + a\right)}^{n} a^{2} b^{5} d^{2} n^{2} x^{5} + 120 \, {\left(b x + a\right)}^{n} a b^{6} d^{2} n x^{6} + 720 \, {\left(b x + a\right)}^{n} b^{7} d^{2} x^{7} + {\left(b x + a\right)}^{n} a b^{6} c^{2} n^{6} + 27 \, {\left(b x + a\right)}^{n} b^{7} c^{2} n^{5} x - 114 \, {\left(b x + a\right)}^{n} a^{2} b^{5} c d n^{4} x^{2} + 1134 \, {\left(b x + a\right)}^{n} a b^{6} c d n^{3} x^{3} - 120 \, {\left(b x + a\right)}^{n} a^{4} b^{3} d^{2} n^{3} x^{3} + 5090 \, {\left(b x + a\right)}^{n} b^{7} c d n^{2} x^{4} + 330 \, {\left(b x + a\right)}^{n} a^{3} b^{4} d^{2} n^{2} x^{4} - 144 \, {\left(b x + a\right)}^{n} a^{2} b^{5} d^{2} n x^{5} + 27 \, {\left(b x + a\right)}^{n} a b^{6} c^{2} n^{5} + 295 \, {\left(b x + a\right)}^{n} b^{7} c^{2} n^{4} x + 12 \, {\left(b x + a\right)}^{n} a^{3} b^{4} c d n^{4} x - 750 \, {\left(b x + a\right)}^{n} a^{2} b^{5} c d n^{3} x^{2} + 1688 \, {\left(b x + a\right)}^{n} a b^{6} c d n^{2} x^{3} - 360 \, {\left(b x + a\right)}^{n} a^{4} b^{3} d^{2} n^{2} x^{3} + 5904 \, {\left(b x + a\right)}^{n} b^{7} c d n x^{4} + 180 \, {\left(b x + a\right)}^{n} a^{3} b^{4} d^{2} n x^{4} + 295 \, {\left(b x + a\right)}^{n} a b^{6} c^{2} n^{4} + 1665 \, {\left(b x + a\right)}^{n} b^{7} c^{2} n^{3} x + 216 \, {\left(b x + a\right)}^{n} a^{3} b^{4} c d n^{3} x - 1902 \, {\left(b x + a\right)}^{n} a^{2} b^{5} c d n^{2} x^{2} + 360 \, {\left(b x + a\right)}^{n} a^{5} b^{2} d^{2} n^{2} x^{2} + 840 \, {\left(b x + a\right)}^{n} a b^{6} c d n x^{3} - 240 \, {\left(b x + a\right)}^{n} a^{4} b^{3} d^{2} n x^{3} + 2520 \, {\left(b x + a\right)}^{n} b^{7} c d x^{4} + 1665 \, {\left(b x + a\right)}^{n} a b^{6} c^{2} n^{3} - 12 \, {\left(b x + a\right)}^{n} a^{4} b^{3} c d n^{3} + 5104 \, {\left(b x + a\right)}^{n} b^{7} c^{2} n^{2} x + 1284 \, {\left(b x + a\right)}^{n} a^{3} b^{4} c d n^{2} x - 1260 \, {\left(b x + a\right)}^{n} a^{2} b^{5} c d n x^{2} + 360 \, {\left(b x + a\right)}^{n} a^{5} b^{2} d^{2} n x^{2} + 5104 \, {\left(b x + a\right)}^{n} a b^{6} c^{2} n^{2} - 216 \, {\left(b x + a\right)}^{n} a^{4} b^{3} c d n^{2} + 8028 \, {\left(b x + a\right)}^{n} b^{7} c^{2} n x + 2520 \, {\left(b x + a\right)}^{n} a^{3} b^{4} c d n x - 720 \, {\left(b x + a\right)}^{n} a^{6} b d^{2} n x + 8028 \, {\left(b x + a\right)}^{n} a b^{6} c^{2} n - 1284 \, {\left(b x + a\right)}^{n} a^{4} b^{3} c d n + 5040 \, {\left(b x + a\right)}^{n} b^{7} c^{2} x + 5040 \, {\left(b x + a\right)}^{n} a b^{6} c^{2} - 2520 \, {\left(b x + a\right)}^{n} a^{4} b^{3} c d + 720 \, {\left(b x + a\right)}^{n} a^{7} d^{2}}{b^{7} n^{7} + 28 \, b^{7} n^{6} + 322 \, b^{7} n^{5} + 1960 \, b^{7} n^{4} + 6769 \, b^{7} n^{3} + 13132 \, b^{7} n^{2} + 13068 \, b^{7} n + 5040 \, b^{7}}"," ",0,"((b*x + a)^n*b^7*d^2*n^6*x^7 + (b*x + a)^n*a*b^6*d^2*n^6*x^6 + 21*(b*x + a)^n*b^7*d^2*n^5*x^7 + 15*(b*x + a)^n*a*b^6*d^2*n^5*x^6 + 175*(b*x + a)^n*b^7*d^2*n^4*x^7 + 2*(b*x + a)^n*b^7*c*d*n^6*x^4 - 6*(b*x + a)^n*a^2*b^5*d^2*n^5*x^5 + 85*(b*x + a)^n*a*b^6*d^2*n^4*x^6 + 735*(b*x + a)^n*b^7*d^2*n^3*x^7 + 2*(b*x + a)^n*a*b^6*c*d*n^6*x^3 + 48*(b*x + a)^n*b^7*c*d*n^5*x^4 - 60*(b*x + a)^n*a^2*b^5*d^2*n^4*x^5 + 225*(b*x + a)^n*a*b^6*d^2*n^3*x^6 + 1624*(b*x + a)^n*b^7*d^2*n^2*x^7 + 42*(b*x + a)^n*a*b^6*c*d*n^5*x^3 + 452*(b*x + a)^n*b^7*c*d*n^4*x^4 + 30*(b*x + a)^n*a^3*b^4*d^2*n^4*x^4 - 210*(b*x + a)^n*a^2*b^5*d^2*n^3*x^5 + 274*(b*x + a)^n*a*b^6*d^2*n^2*x^6 + 1764*(b*x + a)^n*b^7*d^2*n*x^7 + (b*x + a)^n*b^7*c^2*n^6*x - 6*(b*x + a)^n*a^2*b^5*c*d*n^5*x^2 + 326*(b*x + a)^n*a*b^6*c*d*n^4*x^3 + 2112*(b*x + a)^n*b^7*c*d*n^3*x^4 + 180*(b*x + a)^n*a^3*b^4*d^2*n^3*x^4 - 300*(b*x + a)^n*a^2*b^5*d^2*n^2*x^5 + 120*(b*x + a)^n*a*b^6*d^2*n*x^6 + 720*(b*x + a)^n*b^7*d^2*x^7 + (b*x + a)^n*a*b^6*c^2*n^6 + 27*(b*x + a)^n*b^7*c^2*n^5*x - 114*(b*x + a)^n*a^2*b^5*c*d*n^4*x^2 + 1134*(b*x + a)^n*a*b^6*c*d*n^3*x^3 - 120*(b*x + a)^n*a^4*b^3*d^2*n^3*x^3 + 5090*(b*x + a)^n*b^7*c*d*n^2*x^4 + 330*(b*x + a)^n*a^3*b^4*d^2*n^2*x^4 - 144*(b*x + a)^n*a^2*b^5*d^2*n*x^5 + 27*(b*x + a)^n*a*b^6*c^2*n^5 + 295*(b*x + a)^n*b^7*c^2*n^4*x + 12*(b*x + a)^n*a^3*b^4*c*d*n^4*x - 750*(b*x + a)^n*a^2*b^5*c*d*n^3*x^2 + 1688*(b*x + a)^n*a*b^6*c*d*n^2*x^3 - 360*(b*x + a)^n*a^4*b^3*d^2*n^2*x^3 + 5904*(b*x + a)^n*b^7*c*d*n*x^4 + 180*(b*x + a)^n*a^3*b^4*d^2*n*x^4 + 295*(b*x + a)^n*a*b^6*c^2*n^4 + 1665*(b*x + a)^n*b^7*c^2*n^3*x + 216*(b*x + a)^n*a^3*b^4*c*d*n^3*x - 1902*(b*x + a)^n*a^2*b^5*c*d*n^2*x^2 + 360*(b*x + a)^n*a^5*b^2*d^2*n^2*x^2 + 840*(b*x + a)^n*a*b^6*c*d*n*x^3 - 240*(b*x + a)^n*a^4*b^3*d^2*n*x^3 + 2520*(b*x + a)^n*b^7*c*d*x^4 + 1665*(b*x + a)^n*a*b^6*c^2*n^3 - 12*(b*x + a)^n*a^4*b^3*c*d*n^3 + 5104*(b*x + a)^n*b^7*c^2*n^2*x + 1284*(b*x + a)^n*a^3*b^4*c*d*n^2*x - 1260*(b*x + a)^n*a^2*b^5*c*d*n*x^2 + 360*(b*x + a)^n*a^5*b^2*d^2*n*x^2 + 5104*(b*x + a)^n*a*b^6*c^2*n^2 - 216*(b*x + a)^n*a^4*b^3*c*d*n^2 + 8028*(b*x + a)^n*b^7*c^2*n*x + 2520*(b*x + a)^n*a^3*b^4*c*d*n*x - 720*(b*x + a)^n*a^6*b*d^2*n*x + 8028*(b*x + a)^n*a*b^6*c^2*n - 1284*(b*x + a)^n*a^4*b^3*c*d*n + 5040*(b*x + a)^n*b^7*c^2*x + 5040*(b*x + a)^n*a*b^6*c^2 - 2520*(b*x + a)^n*a^4*b^3*c*d + 720*(b*x + a)^n*a^7*d^2)/(b^7*n^7 + 28*b^7*n^6 + 322*b^7*n^5 + 1960*b^7*n^4 + 6769*b^7*n^3 + 13132*b^7*n^2 + 13068*b^7*n + 5040*b^7)","B",0
181,0,0,0,0.000000," ","integrate((b*x+a)^n*(d*x^3+c)^2/x,x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{2} {\left(b x + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((d*x^3 + c)^2*(b*x + a)^n/x, x)","F",0
182,-2,0,0,0.000000," ","integrate(x^2*(b*x+a)^n*(d*x^3+c)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Polynomial exponent overflow. Error: Bad Argument Value","F(-2)",0
183,1,4934,0,0.717030," ","integrate(x*(b*x+a)^n*(d*x^3+c)^3,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{11} d^{3} n^{10} x^{11} + {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{10} x^{10} + 55 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{9} x^{11} + 45 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{9} x^{10} + 1320 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{8} x^{11} + 3 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{10} x^{8} - 10 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{9} x^{9} + 870 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{8} x^{10} + 18150 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{7} x^{11} + 3 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{10} x^{7} + 174 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{9} x^{8} - 360 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{8} x^{9} + 9450 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{7} x^{10} + 157773 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{6} x^{11} + 153 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{9} x^{7} + 4383 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{8} x^{8} + 90 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{8} x^{8} - 5460 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{7} x^{9} + 63273 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{6} x^{10} + 902055 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{5} x^{11} + 3 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{10} x^{5} - 21 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{9} x^{6} + 3312 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{8} x^{7} + 62946 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{7} x^{8} + 2520 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{7} x^{8} - 45360 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{6} x^{9} + 269325 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{5} x^{10} + 3416930 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{4} x^{11} + 3 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{10} x^{4} + 183 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{9} x^{5} - 945 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{8} x^{6} + 39762 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{7} x^{7} - 720 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n^{7} x^{7} + 568701 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{6} x^{8} + 28980 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{6} x^{8} - 224490 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{5} x^{9} + 723680 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{4} x^{10} + 8409500 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{3} x^{11} + 171 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{9} x^{4} + 4860 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{8} x^{5} + 126 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c d^{2} n^{8} x^{5} - 17514 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{7} x^{6} + 290367 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{6} x^{7} - 15120 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n^{6} x^{7} + 3363066 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{5} x^{8} + 176400 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{5} x^{8} - 672840 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{4} x^{9} + 1172700 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{3} x^{10} + 12753576 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n^{2} x^{11} + {\left(b x + a\right)}^{n} b^{11} c^{3} n^{10} x^{2} - 12 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{2} d n^{9} x^{3} + 4176 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{8} x^{4} + 73710 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{7} x^{5} + 5040 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c d^{2} n^{7} x^{5} - 173250 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{6} x^{6} + 5040 \, {\left(b x + a\right)}^{n} a^{5} b^{6} d^{3} n^{6} x^{6} + 1330497 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{5} x^{7} - 126000 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n^{5} x^{7} + 13114077 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{4} x^{8} + 609210 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{4} x^{8} - 1181240 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{3} x^{9} + 1026576 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n^{2} x^{10} + 10628640 \, {\left(b x + a\right)}^{n} b^{11} d^{3} n x^{11} + {\left(b x + a\right)}^{n} a b^{10} c^{3} n^{10} x + 64 \, {\left(b x + a\right)}^{n} b^{11} c^{3} n^{9} x^{2} - 648 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{2} d n^{8} x^{3} + 57006 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{7} x^{4} - 630 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c d^{2} n^{7} x^{4} + 703719 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{6} x^{5} + 79884 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c d^{2} n^{6} x^{5} - 993069 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{5} x^{6} + 75600 \, {\left(b x + a\right)}^{n} a^{5} b^{6} d^{3} n^{5} x^{6} + 3800598 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{4} x^{7} - 529200 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n^{4} x^{7} + 33074574 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{3} x^{8} + 1181880 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{3} x^{8} - 1095840 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n^{2} x^{9} + 362880 \, {\left(b x + a\right)}^{n} a b^{10} d^{3} n x^{10} + 3628800 \, {\left(b x + a\right)}^{n} b^{11} d^{3} x^{11} + 63 \, {\left(b x + a\right)}^{n} a b^{10} c^{3} n^{9} x + 1797 \, {\left(b x + a\right)}^{n} b^{11} c^{3} n^{8} x^{2} + 36 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c^{2} d n^{8} x^{2} - 14760 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{2} d n^{7} x^{3} + 475695 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{6} x^{4} - 22680 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c d^{2} n^{6} x^{4} + 4394079 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{5} x^{5} + 640080 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c d^{2} n^{5} x^{5} - 30240 \, {\left(b x + a\right)}^{n} a^{6} b^{5} d^{3} n^{5} x^{5} - 3355065 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{4} x^{6} + 428400 \, {\left(b x + a\right)}^{n} a^{5} b^{6} d^{3} n^{4} x^{6} + 6470388 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{3} x^{7} - 1169280 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n^{3} x^{7} + 51177636 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n^{2} x^{8} + 1176120 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n^{2} x^{8} - 403200 \, {\left(b x + a\right)}^{n} a^{2} b^{9} d^{3} n x^{9} - {\left(b x + a\right)}^{n} a^{2} b^{9} c^{3} n^{9} + 1734 \, {\left(b x + a\right)}^{n} a b^{10} c^{3} n^{8} x + 29076 \, {\left(b x + a\right)}^{n} b^{11} c^{3} n^{7} x^{2} + 1872 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c^{2} d n^{7} x^{2} - 183744 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{2} d n^{6} x^{3} + 2520 \, {\left(b x + a\right)}^{n} a^{5} b^{6} c d^{2} n^{6} x^{3} + 2491299 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{5} x^{4} - 308700 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c d^{2} n^{5} x^{4} + 18048210 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{4} x^{5} + 2758014 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c d^{2} n^{4} x^{5} - 302400 \, {\left(b x + a\right)}^{n} a^{6} b^{5} d^{3} n^{4} x^{5} - 6473796 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{3} x^{6} + 1134000 \, {\left(b x + a\right)}^{n} a^{5} b^{6} d^{3} n^{3} x^{6} + 5884920 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n^{2} x^{7} - 1270080 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n^{2} x^{7} + 43332840 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} n x^{8} + 453600 \, {\left(b x + a\right)}^{n} a^{3} b^{8} d^{3} n x^{8} - 63 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{3} n^{8} + 27342 \, {\left(b x + a\right)}^{n} a b^{10} c^{3} n^{7} x - 72 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c^{2} d n^{7} x + 299271 \, {\left(b x + a\right)}^{n} b^{11} c^{3} n^{6} x^{2} + 40536 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c^{2} d n^{6} x^{2} - 1351548 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{2} d n^{5} x^{3} + 83160 \, {\left(b x + a\right)}^{n} a^{5} b^{6} c d^{2} n^{5} x^{3} + 8083014 \, {\left(b x + a\right)}^{n} a b^{10} c^{2} d n^{4} x^{4} - 1965600 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c d^{2} n^{4} x^{4} + 151200 \, {\left(b x + a\right)}^{n} a^{7} b^{4} d^{3} n^{4} x^{4} + 47746140 \, {\left(b x + a\right)}^{n} b^{11} c^{2} d n^{3} x^{5} + 6340320 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c d^{2} n^{3} x^{5} - 1058400 \, {\left(b x + a\right)}^{n} a^{6} b^{5} d^{3} n^{3} x^{5} - 6449940 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c d^{2} n^{2} x^{6} + 1380960 \, {\left(b x + a\right)}^{n} a^{5} b^{6} d^{3} n^{2} x^{6} + 2138400 \, {\left(b x + a\right)}^{n} a b^{10} c d^{2} n x^{7} - 518400 \, {\left(b x + a\right)}^{n} a^{4} b^{7} d^{3} n x^{7} + 14968800 \, {\left(b x + a\right)}^{n} b^{11} c d^{2} x^{8} - 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17640288 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c^{2} d n^{2} x + 4520880 \, {\left(b x + a\right)}^{n} a^{7} b^{4} c d^{2} n^{2} x + 50292720 \, {\left(b x + a\right)}^{n} b^{11} c^{3} n x^{2} + 11975040 \, {\left(b x + a\right)}^{n} a^{3} b^{8} c^{2} d n x^{2} - 7484400 \, {\left(b x + a\right)}^{n} a^{6} b^{5} c d^{2} n x^{2} + 1814400 \, {\left(b x + a\right)}^{n} a^{9} b^{2} d^{3} n x^{2} - 19978308 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{3} n^{2} + 5365728 \, {\left(b x + a\right)}^{n} a^{5} b^{6} c^{2} d n^{2} - 453600 \, {\left(b x + a\right)}^{n} a^{8} b^{3} c d^{2} n^{2} + 19958400 \, {\left(b x + a\right)}^{n} a b^{10} c^{3} n x - 23950080 \, {\left(b x + a\right)}^{n} a^{4} b^{7} c^{2} d n x + 14968800 \, {\left(b x + a\right)}^{n} a^{7} b^{4} c d^{2} n x - 3628800 \, {\left(b x + a\right)}^{n} a^{10} b d^{3} n x + 19958400 \, {\left(b x + a\right)}^{n} b^{11} c^{3} x^{2} - 30334320 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{3} n + 17640288 \, {\left(b x + a\right)}^{n} a^{5} b^{6} c^{2} d n - 4520880 \, {\left(b x + a\right)}^{n} a^{8} b^{3} c d^{2} n - 19958400 \, {\left(b x + a\right)}^{n} a^{2} b^{9} c^{3} + 23950080 \, {\left(b x + a\right)}^{n} a^{5} b^{6} c^{2} d - 14968800 \, {\left(b x + a\right)}^{n} a^{8} b^{3} c d^{2} + 3628800 \, {\left(b x + a\right)}^{n} a^{11} d^{3}}{b^{11} n^{11} + 66 \, b^{11} n^{10} + 1925 \, b^{11} n^{9} + 32670 \, b^{11} n^{8} + 357423 \, b^{11} n^{7} + 2637558 \, b^{11} n^{6} + 13339535 \, b^{11} n^{5} + 45995730 \, b^{11} n^{4} + 105258076 \, b^{11} n^{3} + 150917976 \, b^{11} n^{2} + 120543840 \, b^{11} n + 39916800 \, b^{11}}"," ",0,"((b*x + a)^n*b^11*d^3*n^10*x^11 + (b*x + a)^n*a*b^10*d^3*n^10*x^10 + 55*(b*x + a)^n*b^11*d^3*n^9*x^11 + 45*(b*x + a)^n*a*b^10*d^3*n^9*x^10 + 1320*(b*x + a)^n*b^11*d^3*n^8*x^11 + 3*(b*x + a)^n*b^11*c*d^2*n^10*x^8 - 10*(b*x + a)^n*a^2*b^9*d^3*n^9*x^9 + 870*(b*x + a)^n*a*b^10*d^3*n^8*x^10 + 18150*(b*x + a)^n*b^11*d^3*n^7*x^11 + 3*(b*x + a)^n*a*b^10*c*d^2*n^10*x^7 + 174*(b*x + a)^n*b^11*c*d^2*n^9*x^8 - 360*(b*x + a)^n*a^2*b^9*d^3*n^8*x^9 + 9450*(b*x + a)^n*a*b^10*d^3*n^7*x^10 + 157773*(b*x + a)^n*b^11*d^3*n^6*x^11 + 153*(b*x + a)^n*a*b^10*c*d^2*n^9*x^7 + 4383*(b*x + a)^n*b^11*c*d^2*n^8*x^8 + 90*(b*x + a)^n*a^3*b^8*d^3*n^8*x^8 - 5460*(b*x + a)^n*a^2*b^9*d^3*n^7*x^9 + 63273*(b*x + a)^n*a*b^10*d^3*n^6*x^10 + 902055*(b*x + a)^n*b^11*d^3*n^5*x^11 + 3*(b*x + a)^n*b^11*c^2*d*n^10*x^5 - 21*(b*x + a)^n*a^2*b^9*c*d^2*n^9*x^6 + 3312*(b*x + a)^n*a*b^10*c*d^2*n^8*x^7 + 62946*(b*x + a)^n*b^11*c*d^2*n^7*x^8 + 2520*(b*x + a)^n*a^3*b^8*d^3*n^7*x^8 - 45360*(b*x + a)^n*a^2*b^9*d^3*n^6*x^9 + 269325*(b*x + a)^n*a*b^10*d^3*n^5*x^10 + 3416930*(b*x + a)^n*b^11*d^3*n^4*x^11 + 3*(b*x + a)^n*a*b^10*c^2*d*n^10*x^4 + 183*(b*x + a)^n*b^11*c^2*d*n^9*x^5 - 945*(b*x + a)^n*a^2*b^9*c*d^2*n^8*x^6 + 39762*(b*x + a)^n*a*b^10*c*d^2*n^7*x^7 - 720*(b*x + a)^n*a^4*b^7*d^3*n^7*x^7 + 568701*(b*x + a)^n*b^11*c*d^2*n^6*x^8 + 28980*(b*x + a)^n*a^3*b^8*d^3*n^6*x^8 - 224490*(b*x + a)^n*a^2*b^9*d^3*n^5*x^9 + 723680*(b*x + a)^n*a*b^10*d^3*n^4*x^10 + 8409500*(b*x + a)^n*b^11*d^3*n^3*x^11 + 171*(b*x + a)^n*a*b^10*c^2*d*n^9*x^4 + 4860*(b*x + a)^n*b^11*c^2*d*n^8*x^5 + 126*(b*x + a)^n*a^3*b^8*c*d^2*n^8*x^5 - 17514*(b*x + a)^n*a^2*b^9*c*d^2*n^7*x^6 + 290367*(b*x + a)^n*a*b^10*c*d^2*n^6*x^7 - 15120*(b*x + a)^n*a^4*b^7*d^3*n^6*x^7 + 3363066*(b*x + a)^n*b^11*c*d^2*n^5*x^8 + 176400*(b*x + a)^n*a^3*b^8*d^3*n^5*x^8 - 672840*(b*x + a)^n*a^2*b^9*d^3*n^4*x^9 + 1172700*(b*x + a)^n*a*b^10*d^3*n^3*x^10 + 12753576*(b*x + a)^n*b^11*d^3*n^2*x^11 + (b*x + a)^n*b^11*c^3*n^10*x^2 - 12*(b*x + a)^n*a^2*b^9*c^2*d*n^9*x^3 + 4176*(b*x + a)^n*a*b^10*c^2*d*n^8*x^4 + 73710*(b*x + a)^n*b^11*c^2*d*n^7*x^5 + 5040*(b*x + a)^n*a^3*b^8*c*d^2*n^7*x^5 - 173250*(b*x + a)^n*a^2*b^9*c*d^2*n^6*x^6 + 5040*(b*x + a)^n*a^5*b^6*d^3*n^6*x^6 + 1330497*(b*x + a)^n*a*b^10*c*d^2*n^5*x^7 - 126000*(b*x + a)^n*a^4*b^7*d^3*n^5*x^7 + 13114077*(b*x + a)^n*b^11*c*d^2*n^4*x^8 + 609210*(b*x + a)^n*a^3*b^8*d^3*n^4*x^8 - 1181240*(b*x + a)^n*a^2*b^9*d^3*n^3*x^9 + 1026576*(b*x + a)^n*a*b^10*d^3*n^2*x^10 + 10628640*(b*x + a)^n*b^11*d^3*n*x^11 + (b*x + a)^n*a*b^10*c^3*n^10*x + 64*(b*x + a)^n*b^11*c^3*n^9*x^2 - 648*(b*x + a)^n*a^2*b^9*c^2*d*n^8*x^3 + 57006*(b*x + a)^n*a*b^10*c^2*d*n^7*x^4 - 630*(b*x + a)^n*a^4*b^7*c*d^2*n^7*x^4 + 703719*(b*x + a)^n*b^11*c^2*d*n^6*x^5 + 79884*(b*x + a)^n*a^3*b^8*c*d^2*n^6*x^5 - 993069*(b*x + a)^n*a^2*b^9*c*d^2*n^5*x^6 + 75600*(b*x + a)^n*a^5*b^6*d^3*n^5*x^6 + 3800598*(b*x + a)^n*a*b^10*c*d^2*n^4*x^7 - 529200*(b*x + a)^n*a^4*b^7*d^3*n^4*x^7 + 33074574*(b*x + a)^n*b^11*c*d^2*n^3*x^8 + 1181880*(b*x + a)^n*a^3*b^8*d^3*n^3*x^8 - 1095840*(b*x + a)^n*a^2*b^9*d^3*n^2*x^9 + 362880*(b*x + a)^n*a*b^10*d^3*n*x^10 + 3628800*(b*x + a)^n*b^11*d^3*x^11 + 63*(b*x + a)^n*a*b^10*c^3*n^9*x + 1797*(b*x + a)^n*b^11*c^3*n^8*x^2 + 36*(b*x + a)^n*a^3*b^8*c^2*d*n^8*x^2 - 14760*(b*x + a)^n*a^2*b^9*c^2*d*n^7*x^3 + 475695*(b*x + a)^n*a*b^10*c^2*d*n^6*x^4 - 22680*(b*x + a)^n*a^4*b^7*c*d^2*n^6*x^4 + 4394079*(b*x + a)^n*b^11*c^2*d*n^5*x^5 + 640080*(b*x + a)^n*a^3*b^8*c*d^2*n^5*x^5 - 30240*(b*x + a)^n*a^6*b^5*d^3*n^5*x^5 - 3355065*(b*x + a)^n*a^2*b^9*c*d^2*n^4*x^6 + 428400*(b*x + a)^n*a^5*b^6*d^3*n^4*x^6 + 6470388*(b*x + a)^n*a*b^10*c*d^2*n^3*x^7 - 1169280*(b*x + a)^n*a^4*b^7*d^3*n^3*x^7 + 51177636*(b*x + a)^n*b^11*c*d^2*n^2*x^8 + 1176120*(b*x + a)^n*a^3*b^8*d^3*n^2*x^8 - 403200*(b*x + a)^n*a^2*b^9*d^3*n*x^9 - (b*x + a)^n*a^2*b^9*c^3*n^9 + 1734*(b*x + a)^n*a*b^10*c^3*n^8*x + 29076*(b*x + a)^n*b^11*c^3*n^7*x^2 + 1872*(b*x + a)^n*a^3*b^8*c^2*d*n^7*x^2 - 183744*(b*x + a)^n*a^2*b^9*c^2*d*n^6*x^3 + 2520*(b*x + a)^n*a^5*b^6*c*d^2*n^6*x^3 + 2491299*(b*x + a)^n*a*b^10*c^2*d*n^5*x^4 - 308700*(b*x + a)^n*a^4*b^7*c*d^2*n^5*x^4 + 18048210*(b*x + a)^n*b^11*c^2*d*n^4*x^5 + 2758014*(b*x + a)^n*a^3*b^8*c*d^2*n^4*x^5 - 302400*(b*x + a)^n*a^6*b^5*d^3*n^4*x^5 - 6473796*(b*x + a)^n*a^2*b^9*c*d^2*n^3*x^6 + 1134000*(b*x + a)^n*a^5*b^6*d^3*n^3*x^6 + 5884920*(b*x + a)^n*a*b^10*c*d^2*n^2*x^7 - 1270080*(b*x + a)^n*a^4*b^7*d^3*n^2*x^7 + 43332840*(b*x + a)^n*b^11*c*d^2*n*x^8 + 453600*(b*x + a)^n*a^3*b^8*d^3*n*x^8 - 63*(b*x + a)^n*a^2*b^9*c^3*n^8 + 27342*(b*x + a)^n*a*b^10*c^3*n^7*x - 72*(b*x + a)^n*a^4*b^7*c^2*d*n^7*x + 299271*(b*x + a)^n*b^11*c^3*n^6*x^2 + 40536*(b*x + a)^n*a^3*b^8*c^2*d*n^6*x^2 - 1351548*(b*x + a)^n*a^2*b^9*c^2*d*n^5*x^3 + 83160*(b*x + a)^n*a^5*b^6*c*d^2*n^5*x^3 + 8083014*(b*x + a)^n*a*b^10*c^2*d*n^4*x^4 - 1965600*(b*x + a)^n*a^4*b^7*c*d^2*n^4*x^4 + 151200*(b*x + a)^n*a^7*b^4*d^3*n^4*x^4 + 47746140*(b*x + a)^n*b^11*c^2*d*n^3*x^5 + 6340320*(b*x + a)^n*a^3*b^8*c*d^2*n^3*x^5 - 1058400*(b*x + a)^n*a^6*b^5*d^3*n^3*x^5 - 6449940*(b*x + a)^n*a^2*b^9*c*d^2*n^2*x^6 + 1380960*(b*x + a)^n*a^5*b^6*d^3*n^2*x^6 + 2138400*(b*x + a)^n*a*b^10*c*d^2*n*x^7 - 518400*(b*x + a)^n*a^4*b^7*d^3*n*x^7 + 14968800*(b*x + a)^n*b^11*c*d^2*x^8 - 1734*(b*x + a)^n*a^2*b^9*c^3*n^7 + 271929*(b*x + a)^n*a*b^10*c^3*n^6*x - 3672*(b*x + a)^n*a^4*b^7*c^2*d*n^6*x + 2039016*(b*x + a)^n*b^11*c^3*n^5*x^2 + 470160*(b*x + a)^n*a^3*b^8*c^2*d*n^5*x^2 - 7560*(b*x + a)^n*a^6*b^5*c*d^2*n^5*x^2 - 5910552*(b*x + a)^n*a^2*b^9*c^2*d*n^4*x^3 + 985320*(b*x + a)^n*a^5*b^6*c*d^2*n^4*x^3 + 15414084*(b*x + a)^n*a*b^10*c^2*d*n^3*x^4 - 5927670*(b*x + a)^n*a^4*b^7*c*d^2*n^3*x^4 + 907200*(b*x + a)^n*a^7*b^4*d^3*n^3*x^4 + 77043528*(b*x + a)^n*b^11*c^2*d*n^2*x^5 + 7141176*(b*x + a)^n*a^3*b^8*c*d^2*n^2*x^5 - 1512000*(b*x + a)^n*a^6*b^5*d^3*n^2*x^5 - 2494800*(b*x + a)^n*a^2*b^9*c*d^2*n*x^6 + 604800*(b*x + a)^n*a^5*b^6*d^3*n*x^6 - 27342*(b*x + a)^n*a^2*b^9*c^3*n^6 + 72*(b*x + a)^n*a^5*b^6*c^2*d*n^6 + 1767087*(b*x + a)^n*a*b^10*c^3*n^5*x - 77400*(b*x + a)^n*a^4*b^7*c^2*d*n^5*x + 9261503*(b*x + a)^n*b^11*c^3*n^4*x^2 + 3114324*(b*x + a)^n*a^3*b^8*c^2*d*n^4*x^2 - 234360*(b*x + a)^n*a^6*b^5*c*d^2*n^4*x^2 - 14600400*(b*x + a)^n*a^2*b^9*c^2*d*n^3*x^3 + 4906440*(b*x + a)^n*a^5*b^6*c*d^2*n^3*x^3 - 604800*(b*x + a)^n*a^8*b^3*d^3*n^3*x^3 + 15387192*(b*x + a)^n*a*b^10*c^2*d*n^2*x^4 - 7990920*(b*x + a)^n*a^4*b^7*c*d^2*n^2*x^4 + 1663200*(b*x + a)^n*a^7*b^4*d^3*n^2*x^4 + 67536288*(b*x + a)^n*b^11*c^2*d*n*x^5 + 2993760*(b*x + a)^n*a^3*b^8*c*d^2*n*x^5 - 725760*(b*x + a)^n*a^6*b^5*d^3*n*x^5 - 271929*(b*x + a)^n*a^2*b^9*c^3*n^5 + 3672*(b*x + a)^n*a^5*b^6*c^2*d*n^5 + 7494416*(b*x + a)^n*a*b^10*c^3*n^4*x - 862920*(b*x + a)^n*a^4*b^7*c^2*d*n^4*x + 15120*(b*x + a)^n*a^7*b^4*c*d^2*n^4*x + 27472724*(b*x + a)^n*b^11*c^3*n^3*x^2 + 11503008*(b*x + a)^n*a^3*b^8*c^2*d*n^3*x^2 - 2487240*(b*x + a)^n*a^6*b^5*c*d^2*n^3*x^2 - 17855136*(b*x + a)^n*a^2*b^9*c^2*d*n^2*x^3 + 8991360*(b*x + a)^n*a^5*b^6*c*d^2*n^2*x^3 - 1814400*(b*x + a)^n*a^8*b^3*d^3*n^2*x^3 + 5987520*(b*x + a)^n*a*b^10*c^2*d*n*x^4 - 3742200*(b*x + a)^n*a^4*b^7*c*d^2*n*x^4 + 907200*(b*x + a)^n*a^7*b^4*d^3*n*x^4 + 23950080*(b*x + a)^n*b^11*c^2*d*x^5 - 1767087*(b*x + a)^n*a^2*b^9*c^3*n^4 + 77400*(b*x + a)^n*a^5*b^6*c^2*d*n^4 + 19978308*(b*x + a)^n*a*b^10*c^3*n^3*x - 5365728*(b*x + a)^n*a^4*b^7*c^2*d*n^3*x + 453600*(b*x + a)^n*a^7*b^4*c*d^2*n^3*x + 50312628*(b*x + a)^n*b^11*c^3*n^2*x^2 + 20795184*(b*x + a)^n*a^3*b^8*c^2*d*n^2*x^2 - 9744840*(b*x + a)^n*a^6*b^5*c*d^2*n^2*x^2 + 1814400*(b*x + a)^n*a^9*b^2*d^3*n^2*x^2 - 7983360*(b*x + a)^n*a^2*b^9*c^2*d*n*x^3 + 4989600*(b*x + a)^n*a^5*b^6*c*d^2*n*x^3 - 1209600*(b*x + a)^n*a^8*b^3*d^3*n*x^3 - 7494416*(b*x + a)^n*a^2*b^9*c^3*n^3 + 862920*(b*x + a)^n*a^5*b^6*c^2*d*n^3 - 15120*(b*x + a)^n*a^8*b^3*c*d^2*n^3 + 30334320*(b*x + a)^n*a*b^10*c^3*n^2*x - 17640288*(b*x + a)^n*a^4*b^7*c^2*d*n^2*x + 4520880*(b*x + a)^n*a^7*b^4*c*d^2*n^2*x + 50292720*(b*x + a)^n*b^11*c^3*n*x^2 + 11975040*(b*x + a)^n*a^3*b^8*c^2*d*n*x^2 - 7484400*(b*x + a)^n*a^6*b^5*c*d^2*n*x^2 + 1814400*(b*x + a)^n*a^9*b^2*d^3*n*x^2 - 19978308*(b*x + a)^n*a^2*b^9*c^3*n^2 + 5365728*(b*x + a)^n*a^5*b^6*c^2*d*n^2 - 453600*(b*x + a)^n*a^8*b^3*c*d^2*n^2 + 19958400*(b*x + a)^n*a*b^10*c^3*n*x - 23950080*(b*x + a)^n*a^4*b^7*c^2*d*n*x + 14968800*(b*x + a)^n*a^7*b^4*c*d^2*n*x - 3628800*(b*x + a)^n*a^10*b*d^3*n*x + 19958400*(b*x + a)^n*b^11*c^3*x^2 - 30334320*(b*x + a)^n*a^2*b^9*c^3*n + 17640288*(b*x + a)^n*a^5*b^6*c^2*d*n - 4520880*(b*x + a)^n*a^8*b^3*c*d^2*n - 19958400*(b*x + a)^n*a^2*b^9*c^3 + 23950080*(b*x + a)^n*a^5*b^6*c^2*d - 14968800*(b*x + a)^n*a^8*b^3*c*d^2 + 3628800*(b*x + a)^n*a^11*d^3)/(b^11*n^11 + 66*b^11*n^10 + 1925*b^11*n^9 + 32670*b^11*n^8 + 357423*b^11*n^7 + 2637558*b^11*n^6 + 13339535*b^11*n^5 + 45995730*b^11*n^4 + 105258076*b^11*n^3 + 150917976*b^11*n^2 + 120543840*b^11*n + 39916800*b^11)","B",0
184,1,3874,0,0.665179," ","integrate((b*x+a)^n*(d*x^3+c)^3,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{n} b^{10} d^{3} n^{9} x^{10} + {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{9} x^{9} + 45 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{8} x^{10} + 36 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{8} x^{9} + 870 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{7} x^{10} + 3 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{9} x^{7} - 9 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{8} x^{8} + 546 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{7} x^{9} + 9450 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{6} x^{10} + 3 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{9} x^{6} + 144 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{8} x^{7} - 252 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{7} x^{8} + 4536 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{6} x^{9} + 63273 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{5} x^{10} + 126 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{8} x^{6} + 2952 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{7} x^{7} + 72 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n^{7} x^{7} - 2898 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{6} x^{8} + 22449 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{5} x^{9} + 269325 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{4} x^{10} + 3 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{9} x^{4} - 18 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{8} x^{5} + 2196 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{7} x^{6} + 33786 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{6} x^{7} + 1512 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n^{6} x^{7} - 17640 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{5} x^{8} + 67284 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{4} x^{9} + 723680 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{3} x^{10} + 3 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{9} x^{3} + 153 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{8} x^{4} - 666 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{7} x^{5} + 20610 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{6} x^{6} - 504 \, {\left(b x + a\right)}^{n} a^{4} b^{6} d^{3} n^{6} x^{6} + 236817 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{5} x^{7} + 12600 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n^{5} x^{7} - 60921 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{4} x^{8} + 118124 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{3} x^{9} + 1172700 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n^{2} x^{10} + 144 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{8} x^{3} + 3348 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{7} x^{4} + 90 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n^{7} x^{4} - 9846 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{6} x^{5} + 113157 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{5} x^{6} - 7560 \, {\left(b x + a\right)}^{n} a^{4} b^{6} d^{3} n^{5} x^{6} + 1048446 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{4} x^{7} + 52920 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n^{4} x^{7} - 118188 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{3} x^{8} + 109584 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n^{2} x^{9} + 1026576 \, {\left(b x + a\right)}^{n} b^{10} d^{3} n x^{10} + {\left(b x + a\right)}^{n} b^{10} c^{3} n^{9} x - 9 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{8} x^{2} + 2916 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{7} x^{3} + 41058 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{6} x^{4} + 2970 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n^{6} x^{4} - 74430 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{5} x^{5} + 3024 \, {\left(b x + a\right)}^{n} a^{5} b^{5} d^{3} n^{5} x^{5} + 369504 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{4} x^{6} - 42840 \, {\left(b x + a\right)}^{n} a^{4} b^{6} d^{3} n^{4} x^{6} + 2911668 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{3} x^{7} + 116928 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n^{3} x^{7} - 117612 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n^{2} x^{8} + 40320 \, {\left(b x + a\right)}^{n} a b^{9} d^{3} n x^{9} + 362880 \, {\left(b x + a\right)}^{n} b^{10} d^{3} x^{10} + {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{9} + 54 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{8} x - 414 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{7} x^{2} + 32310 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{6} x^{3} - 360 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c d^{2} n^{6} x^{3} + 309087 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{5} x^{4} + 37350 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n^{5} x^{4} - 306792 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{4} x^{5} + 30240 \, {\left(b x + a\right)}^{n} a^{5} b^{5} d^{3} n^{4} x^{5} + 694644 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{3} x^{6} - 113400 \, {\left(b x + a\right)}^{n} a^{4} b^{6} d^{3} n^{3} x^{6} + 4846824 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n^{2} x^{7} + 127008 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n^{2} x^{7} - 45360 \, {\left(b x + a\right)}^{n} a^{2} b^{8} d^{3} n x^{8} + 54 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{8} + 1266 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{7} x + 18 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n^{7} x - 7920 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{6} x^{2} + 212157 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{5} x^{3} - 10800 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c d^{2} n^{5} x^{3} + 1469817 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{4} x^{4} + 222750 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n^{4} x^{4} - 15120 \, {\left(b x + a\right)}^{n} a^{6} b^{4} d^{3} n^{4} x^{4} - 683064 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{3} x^{5} + 105840 \, {\left(b x + a\right)}^{n} a^{5} b^{5} d^{3} n^{3} x^{5} + 678960 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n^{2} x^{6} - 138096 \, {\left(b x + a\right)}^{n} a^{4} b^{6} d^{3} n^{2} x^{6} + 4332960 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} n x^{7} + 51840 \, {\left(b x + a\right)}^{n} a^{3} b^{7} d^{3} n x^{7} + 1266 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{7} + 16884 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{6} x + 810 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n^{6} x - 81090 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{5} x^{2} + 1080 \, {\left(b x + a\right)}^{n} a^{5} b^{5} c d^{2} n^{5} x^{2} + 833346 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{4} x^{3} - 117000 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c d^{2} n^{4} x^{3} + 4371522 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{3} x^{4} + 642960 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n^{3} x^{4} - 90720 \, {\left(b x + a\right)}^{n} a^{6} b^{4} d^{3} n^{3} x^{4} - 752544 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n^{2} x^{5} + 151200 \, {\left(b x + a\right)}^{n} a^{5} b^{5} d^{3} n^{2} x^{5} + 259200 \, {\left(b x + a\right)}^{n} a b^{9} c d^{2} n x^{6} - 60480 \, {\left(b x + a\right)}^{n} a^{4} b^{6} d^{3} n x^{6} + 1555200 \, {\left(b x + a\right)}^{n} b^{10} c d^{2} x^{7} + 16884 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{6} - 18 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d n^{6} + 140889 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{5} x + 15030 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n^{5} x - 474291 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{4} x^{2} + 30240 \, {\left(b x + a\right)}^{n} a^{5} b^{5} c d^{2} n^{4} x^{2} + 1871484 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{3} x^{3} - 540000 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c d^{2} n^{3} x^{3} + 60480 \, {\left(b x + a\right)}^{n} a^{7} b^{3} d^{3} n^{3} x^{3} + 7742412 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n^{2} x^{4} + 843480 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n^{2} x^{4} - 166320 \, {\left(b x + a\right)}^{n} a^{6} b^{4} d^{3} n^{2} x^{4} - 311040 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c d^{2} n x^{5} + 72576 \, {\left(b x + a\right)}^{n} a^{5} b^{5} d^{3} n x^{5} + 140889 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{5} - 810 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d n^{5} + 761166 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{4} x + 147150 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n^{4} x - 2160 \, {\left(b x + a\right)}^{n} a^{6} b^{4} c d^{2} n^{4} x - 1551456 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{3} x^{2} + 290520 \, {\left(b x + a\right)}^{n} a^{5} b^{5} c d^{2} n^{3} x^{2} + 2127960 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n^{2} x^{3} - 951840 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c d^{2} n^{2} x^{3} + 181440 \, {\left(b x + a\right)}^{n} a^{7} b^{3} d^{3} n^{2} x^{3} + 7291080 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d n x^{4} + 388800 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c d^{2} n x^{4} - 90720 \, {\left(b x + a\right)}^{n} a^{6} b^{4} d^{3} n x^{4} + 761166 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{4} - 15030 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d n^{4} + 2655764 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{3} x + 801432 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n^{3} x - 58320 \, {\left(b x + a\right)}^{n} a^{6} b^{4} c d^{2} n^{3} x - 2511540 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n^{2} x^{2} + 1038960 \, {\left(b x + a\right)}^{n} a^{5} b^{5} c d^{2} n^{2} x^{2} - 181440 \, {\left(b x + a\right)}^{n} a^{8} b^{2} d^{3} n^{2} x^{2} + 907200 \, {\left(b x + a\right)}^{n} a b^{9} c^{2} d n x^{3} - 518400 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c d^{2} n x^{3} + 120960 \, {\left(b x + a\right)}^{n} a^{7} b^{3} d^{3} n x^{3} + 2721600 \, {\left(b x + a\right)}^{n} b^{10} c^{2} d x^{4} + 2655764 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{3} - 147150 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d n^{3} + 2160 \, {\left(b x + a\right)}^{n} a^{7} b^{3} c d^{2} n^{3} + 5753736 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n^{2} x + 2301480 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n^{2} x - 522720 \, {\left(b x + a\right)}^{n} a^{6} b^{4} c d^{2} n^{2} x - 1360800 \, {\left(b x + a\right)}^{n} a^{2} b^{8} c^{2} d n x^{2} + 777600 \, {\left(b x + a\right)}^{n} a^{5} b^{5} c d^{2} n x^{2} - 181440 \, {\left(b x + a\right)}^{n} a^{8} b^{2} d^{3} n x^{2} + 5753736 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n^{2} - 801432 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d n^{2} + 58320 \, {\left(b x + a\right)}^{n} a^{7} b^{3} c d^{2} n^{2} + 6999840 \, {\left(b x + a\right)}^{n} b^{10} c^{3} n x + 2721600 \, {\left(b x + a\right)}^{n} a^{3} b^{7} c^{2} d n x - 1555200 \, {\left(b x + a\right)}^{n} a^{6} b^{4} c d^{2} n x + 362880 \, {\left(b x + a\right)}^{n} a^{9} b d^{3} n x + 6999840 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} n - 2301480 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d n + 522720 \, {\left(b x + a\right)}^{n} a^{7} b^{3} c d^{2} n + 3628800 \, {\left(b x + a\right)}^{n} b^{10} c^{3} x + 3628800 \, {\left(b x + a\right)}^{n} a b^{9} c^{3} - 2721600 \, {\left(b x + a\right)}^{n} a^{4} b^{6} c^{2} d + 1555200 \, {\left(b x + a\right)}^{n} a^{7} b^{3} c d^{2} - 362880 \, {\left(b x + a\right)}^{n} a^{10} d^{3}}{b^{10} n^{10} + 55 \, b^{10} n^{9} + 1320 \, b^{10} n^{8} + 18150 \, b^{10} n^{7} + 157773 \, b^{10} n^{6} + 902055 \, b^{10} n^{5} + 3416930 \, b^{10} n^{4} + 8409500 \, b^{10} n^{3} + 12753576 \, b^{10} n^{2} + 10628640 \, b^{10} n + 3628800 \, b^{10}}"," ",0,"((b*x + a)^n*b^10*d^3*n^9*x^10 + (b*x + a)^n*a*b^9*d^3*n^9*x^9 + 45*(b*x + a)^n*b^10*d^3*n^8*x^10 + 36*(b*x + a)^n*a*b^9*d^3*n^8*x^9 + 870*(b*x + a)^n*b^10*d^3*n^7*x^10 + 3*(b*x + a)^n*b^10*c*d^2*n^9*x^7 - 9*(b*x + a)^n*a^2*b^8*d^3*n^8*x^8 + 546*(b*x + a)^n*a*b^9*d^3*n^7*x^9 + 9450*(b*x + a)^n*b^10*d^3*n^6*x^10 + 3*(b*x + a)^n*a*b^9*c*d^2*n^9*x^6 + 144*(b*x + a)^n*b^10*c*d^2*n^8*x^7 - 252*(b*x + a)^n*a^2*b^8*d^3*n^7*x^8 + 4536*(b*x + a)^n*a*b^9*d^3*n^6*x^9 + 63273*(b*x + a)^n*b^10*d^3*n^5*x^10 + 126*(b*x + a)^n*a*b^9*c*d^2*n^8*x^6 + 2952*(b*x + a)^n*b^10*c*d^2*n^7*x^7 + 72*(b*x + a)^n*a^3*b^7*d^3*n^7*x^7 - 2898*(b*x + a)^n*a^2*b^8*d^3*n^6*x^8 + 22449*(b*x + a)^n*a*b^9*d^3*n^5*x^9 + 269325*(b*x + a)^n*b^10*d^3*n^4*x^10 + 3*(b*x + a)^n*b^10*c^2*d*n^9*x^4 - 18*(b*x + a)^n*a^2*b^8*c*d^2*n^8*x^5 + 2196*(b*x + a)^n*a*b^9*c*d^2*n^7*x^6 + 33786*(b*x + a)^n*b^10*c*d^2*n^6*x^7 + 1512*(b*x + a)^n*a^3*b^7*d^3*n^6*x^7 - 17640*(b*x + a)^n*a^2*b^8*d^3*n^5*x^8 + 67284*(b*x + a)^n*a*b^9*d^3*n^4*x^9 + 723680*(b*x + a)^n*b^10*d^3*n^3*x^10 + 3*(b*x + a)^n*a*b^9*c^2*d*n^9*x^3 + 153*(b*x + a)^n*b^10*c^2*d*n^8*x^4 - 666*(b*x + a)^n*a^2*b^8*c*d^2*n^7*x^5 + 20610*(b*x + a)^n*a*b^9*c*d^2*n^6*x^6 - 504*(b*x + a)^n*a^4*b^6*d^3*n^6*x^6 + 236817*(b*x + a)^n*b^10*c*d^2*n^5*x^7 + 12600*(b*x + a)^n*a^3*b^7*d^3*n^5*x^7 - 60921*(b*x + a)^n*a^2*b^8*d^3*n^4*x^8 + 118124*(b*x + a)^n*a*b^9*d^3*n^3*x^9 + 1172700*(b*x + a)^n*b^10*d^3*n^2*x^10 + 144*(b*x + a)^n*a*b^9*c^2*d*n^8*x^3 + 3348*(b*x + a)^n*b^10*c^2*d*n^7*x^4 + 90*(b*x + a)^n*a^3*b^7*c*d^2*n^7*x^4 - 9846*(b*x + a)^n*a^2*b^8*c*d^2*n^6*x^5 + 113157*(b*x + a)^n*a*b^9*c*d^2*n^5*x^6 - 7560*(b*x + a)^n*a^4*b^6*d^3*n^5*x^6 + 1048446*(b*x + a)^n*b^10*c*d^2*n^4*x^7 + 52920*(b*x + a)^n*a^3*b^7*d^3*n^4*x^7 - 118188*(b*x + a)^n*a^2*b^8*d^3*n^3*x^8 + 109584*(b*x + a)^n*a*b^9*d^3*n^2*x^9 + 1026576*(b*x + a)^n*b^10*d^3*n*x^10 + (b*x + a)^n*b^10*c^3*n^9*x - 9*(b*x + a)^n*a^2*b^8*c^2*d*n^8*x^2 + 2916*(b*x + a)^n*a*b^9*c^2*d*n^7*x^3 + 41058*(b*x + a)^n*b^10*c^2*d*n^6*x^4 + 2970*(b*x + a)^n*a^3*b^7*c*d^2*n^6*x^4 - 74430*(b*x + a)^n*a^2*b^8*c*d^2*n^5*x^5 + 3024*(b*x + a)^n*a^5*b^5*d^3*n^5*x^5 + 369504*(b*x + a)^n*a*b^9*c*d^2*n^4*x^6 - 42840*(b*x + a)^n*a^4*b^6*d^3*n^4*x^6 + 2911668*(b*x + a)^n*b^10*c*d^2*n^3*x^7 + 116928*(b*x + a)^n*a^3*b^7*d^3*n^3*x^7 - 117612*(b*x + a)^n*a^2*b^8*d^3*n^2*x^8 + 40320*(b*x + a)^n*a*b^9*d^3*n*x^9 + 362880*(b*x + a)^n*b^10*d^3*x^10 + (b*x + a)^n*a*b^9*c^3*n^9 + 54*(b*x + a)^n*b^10*c^3*n^8*x - 414*(b*x + a)^n*a^2*b^8*c^2*d*n^7*x^2 + 32310*(b*x + a)^n*a*b^9*c^2*d*n^6*x^3 - 360*(b*x + a)^n*a^4*b^6*c*d^2*n^6*x^3 + 309087*(b*x + a)^n*b^10*c^2*d*n^5*x^4 + 37350*(b*x + a)^n*a^3*b^7*c*d^2*n^5*x^4 - 306792*(b*x + a)^n*a^2*b^8*c*d^2*n^4*x^5 + 30240*(b*x + a)^n*a^5*b^5*d^3*n^4*x^5 + 694644*(b*x + a)^n*a*b^9*c*d^2*n^3*x^6 - 113400*(b*x + a)^n*a^4*b^6*d^3*n^3*x^6 + 4846824*(b*x + a)^n*b^10*c*d^2*n^2*x^7 + 127008*(b*x + a)^n*a^3*b^7*d^3*n^2*x^7 - 45360*(b*x + a)^n*a^2*b^8*d^3*n*x^8 + 54*(b*x + a)^n*a*b^9*c^3*n^8 + 1266*(b*x + a)^n*b^10*c^3*n^7*x + 18*(b*x + a)^n*a^3*b^7*c^2*d*n^7*x - 7920*(b*x + a)^n*a^2*b^8*c^2*d*n^6*x^2 + 212157*(b*x + a)^n*a*b^9*c^2*d*n^5*x^3 - 10800*(b*x + a)^n*a^4*b^6*c*d^2*n^5*x^3 + 1469817*(b*x + a)^n*b^10*c^2*d*n^4*x^4 + 222750*(b*x + a)^n*a^3*b^7*c*d^2*n^4*x^4 - 15120*(b*x + a)^n*a^6*b^4*d^3*n^4*x^4 - 683064*(b*x + a)^n*a^2*b^8*c*d^2*n^3*x^5 + 105840*(b*x + a)^n*a^5*b^5*d^3*n^3*x^5 + 678960*(b*x + a)^n*a*b^9*c*d^2*n^2*x^6 - 138096*(b*x + a)^n*a^4*b^6*d^3*n^2*x^6 + 4332960*(b*x + a)^n*b^10*c*d^2*n*x^7 + 51840*(b*x + a)^n*a^3*b^7*d^3*n*x^7 + 1266*(b*x + a)^n*a*b^9*c^3*n^7 + 16884*(b*x + a)^n*b^10*c^3*n^6*x + 810*(b*x + a)^n*a^3*b^7*c^2*d*n^6*x - 81090*(b*x + a)^n*a^2*b^8*c^2*d*n^5*x^2 + 1080*(b*x + a)^n*a^5*b^5*c*d^2*n^5*x^2 + 833346*(b*x + a)^n*a*b^9*c^2*d*n^4*x^3 - 117000*(b*x + a)^n*a^4*b^6*c*d^2*n^4*x^3 + 4371522*(b*x + a)^n*b^10*c^2*d*n^3*x^4 + 642960*(b*x + a)^n*a^3*b^7*c*d^2*n^3*x^4 - 90720*(b*x + a)^n*a^6*b^4*d^3*n^3*x^4 - 752544*(b*x + a)^n*a^2*b^8*c*d^2*n^2*x^5 + 151200*(b*x + a)^n*a^5*b^5*d^3*n^2*x^5 + 259200*(b*x + a)^n*a*b^9*c*d^2*n*x^6 - 60480*(b*x + a)^n*a^4*b^6*d^3*n*x^6 + 1555200*(b*x + a)^n*b^10*c*d^2*x^7 + 16884*(b*x + a)^n*a*b^9*c^3*n^6 - 18*(b*x + a)^n*a^4*b^6*c^2*d*n^6 + 140889*(b*x + a)^n*b^10*c^3*n^5*x + 15030*(b*x + a)^n*a^3*b^7*c^2*d*n^5*x - 474291*(b*x + a)^n*a^2*b^8*c^2*d*n^4*x^2 + 30240*(b*x + a)^n*a^5*b^5*c*d^2*n^4*x^2 + 1871484*(b*x + a)^n*a*b^9*c^2*d*n^3*x^3 - 540000*(b*x + a)^n*a^4*b^6*c*d^2*n^3*x^3 + 60480*(b*x + a)^n*a^7*b^3*d^3*n^3*x^3 + 7742412*(b*x + a)^n*b^10*c^2*d*n^2*x^4 + 843480*(b*x + a)^n*a^3*b^7*c*d^2*n^2*x^4 - 166320*(b*x + a)^n*a^6*b^4*d^3*n^2*x^4 - 311040*(b*x + a)^n*a^2*b^8*c*d^2*n*x^5 + 72576*(b*x + a)^n*a^5*b^5*d^3*n*x^5 + 140889*(b*x + a)^n*a*b^9*c^3*n^5 - 810*(b*x + a)^n*a^4*b^6*c^2*d*n^5 + 761166*(b*x + a)^n*b^10*c^3*n^4*x + 147150*(b*x + a)^n*a^3*b^7*c^2*d*n^4*x - 2160*(b*x + a)^n*a^6*b^4*c*d^2*n^4*x - 1551456*(b*x + a)^n*a^2*b^8*c^2*d*n^3*x^2 + 290520*(b*x + a)^n*a^5*b^5*c*d^2*n^3*x^2 + 2127960*(b*x + a)^n*a*b^9*c^2*d*n^2*x^3 - 951840*(b*x + a)^n*a^4*b^6*c*d^2*n^2*x^3 + 181440*(b*x + a)^n*a^7*b^3*d^3*n^2*x^3 + 7291080*(b*x + a)^n*b^10*c^2*d*n*x^4 + 388800*(b*x + a)^n*a^3*b^7*c*d^2*n*x^4 - 90720*(b*x + a)^n*a^6*b^4*d^3*n*x^4 + 761166*(b*x + a)^n*a*b^9*c^3*n^4 - 15030*(b*x + a)^n*a^4*b^6*c^2*d*n^4 + 2655764*(b*x + a)^n*b^10*c^3*n^3*x + 801432*(b*x + a)^n*a^3*b^7*c^2*d*n^3*x - 58320*(b*x + a)^n*a^6*b^4*c*d^2*n^3*x - 2511540*(b*x + a)^n*a^2*b^8*c^2*d*n^2*x^2 + 1038960*(b*x + a)^n*a^5*b^5*c*d^2*n^2*x^2 - 181440*(b*x + a)^n*a^8*b^2*d^3*n^2*x^2 + 907200*(b*x + a)^n*a*b^9*c^2*d*n*x^3 - 518400*(b*x + a)^n*a^4*b^6*c*d^2*n*x^3 + 120960*(b*x + a)^n*a^7*b^3*d^3*n*x^3 + 2721600*(b*x + a)^n*b^10*c^2*d*x^4 + 2655764*(b*x + a)^n*a*b^9*c^3*n^3 - 147150*(b*x + a)^n*a^4*b^6*c^2*d*n^3 + 2160*(b*x + a)^n*a^7*b^3*c*d^2*n^3 + 5753736*(b*x + a)^n*b^10*c^3*n^2*x + 2301480*(b*x + a)^n*a^3*b^7*c^2*d*n^2*x - 522720*(b*x + a)^n*a^6*b^4*c*d^2*n^2*x - 1360800*(b*x + a)^n*a^2*b^8*c^2*d*n*x^2 + 777600*(b*x + a)^n*a^5*b^5*c*d^2*n*x^2 - 181440*(b*x + a)^n*a^8*b^2*d^3*n*x^2 + 5753736*(b*x + a)^n*a*b^9*c^3*n^2 - 801432*(b*x + a)^n*a^4*b^6*c^2*d*n^2 + 58320*(b*x + a)^n*a^7*b^3*c*d^2*n^2 + 6999840*(b*x + a)^n*b^10*c^3*n*x + 2721600*(b*x + a)^n*a^3*b^7*c^2*d*n*x - 1555200*(b*x + a)^n*a^6*b^4*c*d^2*n*x + 362880*(b*x + a)^n*a^9*b*d^3*n*x + 6999840*(b*x + a)^n*a*b^9*c^3*n - 2301480*(b*x + a)^n*a^4*b^6*c^2*d*n + 522720*(b*x + a)^n*a^7*b^3*c*d^2*n + 3628800*(b*x + a)^n*b^10*c^3*x + 3628800*(b*x + a)^n*a*b^9*c^3 - 2721600*(b*x + a)^n*a^4*b^6*c^2*d + 1555200*(b*x + a)^n*a^7*b^3*c*d^2 - 362880*(b*x + a)^n*a^10*d^3)/(b^10*n^10 + 55*b^10*n^9 + 1320*b^10*n^8 + 18150*b^10*n^7 + 157773*b^10*n^6 + 902055*b^10*n^5 + 3416930*b^10*n^4 + 8409500*b^10*n^3 + 12753576*b^10*n^2 + 10628640*b^10*n + 3628800*b^10)","B",0
185,0,0,0,0.000000," ","integrate((b*x+a)^n*(d*x^3+c)^3/x,x, algorithm=""giac"")","\int \frac{{\left(d x^{3} + c\right)}^{3} {\left(b x + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((d*x^3 + c)^3*(b*x + a)^n/x, x)","F",0
186,0,0,0,0.000000," ","integrate(x^5*(f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n} x^{5}}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n*x^5/(b*x^3 + a), x)","F",0
187,0,0,0,0.000000," ","integrate(x^4*(f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n} x^{4}}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n*x^4/(b*x^3 + a), x)","F",0
188,0,0,0,0.000000," ","integrate(x^3*(f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n} x^{3}}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n*x^3/(b*x^3 + a), x)","F",0
189,0,0,0,0.000000," ","integrate(x^2*(f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n} x^{2}}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n*x^2/(b*x^3 + a), x)","F",0
190,0,0,0,0.000000," ","integrate(x*(f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n} x}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n*x/(b*x^3 + a), x)","F",0
191,0,0,0,0.000000," ","integrate((f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n}}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n/(b*x^3 + a), x)","F",0
192,0,0,0,0.000000," ","integrate((f*x+e)^n/x/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n}}{{\left(b x^{3} + a\right)} x}\,{d x}"," ",0,"integrate((f*x + e)^n/((b*x^3 + a)*x), x)","F",0
193,0,0,0,0.000000," ","integrate((f*x+e)^n/x^2/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n}}{{\left(b x^{3} + a\right)} x^{2}}\,{d x}"," ",0,"integrate((f*x + e)^n/((b*x^3 + a)*x^2), x)","F",0
194,0,0,0,0.000000," ","integrate(x^2*(d*x+c)^(1+n)/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{n + 1} x^{2}}{b x^{3} + a}\,{d x}"," ",0,"integrate((d*x + c)^(n + 1)*x^2/(b*x^3 + a), x)","F",0
195,0,0,0,0.000000," ","integrate(x^m*(f*x+e)^n/(b*x^3+a),x, algorithm=""giac"")","\int \frac{{\left(f x + e\right)}^{n} x^{m}}{b x^{3} + a}\,{d x}"," ",0,"integrate((f*x + e)^n*x^m/(b*x^3 + a), x)","F",0
196,0,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/(b*x+a),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{3} + c}}{b x + a}\,{d x}"," ",0,"integrate(sqrt(d*x^3 + c)/(b*x + a), x)","F",0
197,0,0,0,0.000000," ","integrate((e^3*x^3+d^3)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(e^{3} x^{3} + d^{3}\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((e^3*x^3 + d^3)^p/(e*x + d), x)","F",0
198,0,0,0,0.000000," ","integrate((-x^2-2*x+2)/(x^2+2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 2 \, x - 2}{\sqrt{x^{3} + 1} {\left(x^{2} + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 2*x - 2)/(sqrt(x^3 + 1)*(x^2 + 2)), x)","F",0
199,0,0,0,0.000000," ","integrate((-x^2+2*x+2)/(x^2+2)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 2 \, x - 2}{\sqrt{-x^{3} + 1} {\left(x^{2} + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 2*x - 2)/(sqrt(-x^3 + 1)*(x^2 + 2)), x)","F",0
200,0,0,0,0.000000," ","integrate((-x^2+2*x+2)/(x^2+2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(x^{2} + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(x^2 + 2)), x)","F",0
201,0,0,0,0.000000," ","integrate((-x^2-2*x+2)/(x^2+2)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 2 \, x - 2}{\sqrt{-x^{3} - 1} {\left(x^{2} + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 2*x - 2)/(sqrt(-x^3 - 1)*(x^2 + 2)), x)","F",0
202,0,0,0,0.000000," ","integrate((-x^2-2*x+2)/(d*x+x^2+d+2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 2 \, x - 2}{\sqrt{x^{3} + 1} {\left(d x + x^{2} + d + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 2*x - 2)/(sqrt(x^3 + 1)*(d*x + x^2 + d + 2)), x)","F",0
203,0,0,0,0.000000," ","integrate((-x^2+2*x+2)/(d*x+x^2-d+2)/(-x^3+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 2 \, x - 2}{\sqrt{-x^{3} + 1} {\left(d x + x^{2} - d + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 2*x - 2)/(sqrt(-x^3 + 1)*(d*x + x^2 - d + 2)), x)","F",0
204,0,0,0,0.000000," ","integrate((-x^2+2*x+2)/(d*x+x^2-d+2)/(x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 2 \, x - 2}{\sqrt{x^{3} - 1} {\left(d x + x^{2} - d + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 2*x - 2)/(sqrt(x^3 - 1)*(d*x + x^2 - d + 2)), x)","F",0
205,0,0,0,0.000000," ","integrate((-x^2-2*x+2)/(d*x+x^2+d+2)/(-x^3-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 2 \, x - 2}{\sqrt{-x^{3} - 1} {\left(d x + x^{2} + d + 2\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 2*x - 2)/(sqrt(-x^3 - 1)*(d*x + x^2 + d + 2)), x)","F",0
206,0,0,0,0.000000," ","integrate((e*x+d)^3*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a} {\left(e x + d\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)*(e*x + d)^3, x)","F",0
207,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a} {\left(e x + d\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)*(e*x + d)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a} {\left(e x + d\right)}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)*(e*x + d), x)","F",0
209,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + a}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a), x)","F",0
210,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/(e*x+d),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + a}}{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)/(e*x + d), x)","F",0
211,0,0,0,0.000000," ","integrate((c*x^4+a)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + a}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + a)/(e*x + d)^2, x)","F",0
212,0,0,0,0.000000," ","integrate((e*x+d)^3/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{3}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x + d)^3/sqrt(c*x^4 + a), x)","F",0
213,0,0,0,0.000000," ","integrate((e*x+d)^2/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2}}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x + d)^2/sqrt(c*x^4 + a), x)","F",0
214,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x + d}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate((e*x + d)/sqrt(c*x^4 + a), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(c*x^4 + a), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*(e*x + d)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} {\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*(e*x + d)^2), x)","F",0
218,0,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{4} + a} {\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^4 + a)*(e*x + d)^3), x)","F",0
219,0,0,0,0.000000," ","integrate((e*x+d)^3/(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{3}}{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^3/(c*x^4 + a)^(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate((e*x+d)^2/(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2}}{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^2/(c*x^4 + a)^(3/2), x)","F",0
221,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{e x + d}{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)/(c*x^4 + a)^(3/2), x)","F",0
222,0,0,0,0.000000," ","integrate(1/(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + a)^(-3/2), x)","F",0
223,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^4+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{4} + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^4 + a)^(3/2)*(e*x + d)), x)","F",0
224,0,0,0,0.000000," ","integrate(x^3*(d*x+c)^n/(b*x^4+a),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{n} x^{3}}{b x^{4} + a}\,{d x}"," ",0,"integrate((d*x + c)^n*x^3/(b*x^4 + a), x)","F",0
225,0,0,0,0.000000," ","integrate(x^3*(d*x+c)^(1+n)/(b*x^4+a),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{n + 1} x^{3}}{b x^{4} + a}\,{d x}"," ",0,"integrate((d*x + c)^(n + 1)*x^3/(b*x^4 + a), x)","F",0
226,0,0,0,0.000000," ","integrate(1/(e*x^2+d*x+c)/(b*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{4} + a} {\left(e x^{2} + d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^4 + a)*(e*x^2 + d*x + c)), x)","F",0
227,1,355,0,0.381907," ","integrate(x^m*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(b^{3} m^{3} x^{7} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 9 \, b^{3} m^{2} x^{7} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a b^{2} m^{3} x^{5} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 23 \, b^{3} m x^{7} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 33 \, a b^{2} m^{2} x^{5} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, b^{3} x^{7} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, a^{2} b m^{3} x^{3} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 93 \, a b^{2} m x^{5} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 39 \, a^{2} b m^{2} x^{3} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 63 \, a b^{2} x^{5} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} m^{3} x x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 141 \, a^{2} b m x^{3} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, a^{3} m^{2} x x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, a^{2} b x^{3} x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 71 \, a^{3} m x x^{m} \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, a^{3} x x^{m} \mathrm{sgn}\left(b x^{2} + a\right)\right)} c^{\frac{3}{2}}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"(b^3*m^3*x^7*x^m*sgn(b*x^2 + a) + 9*b^3*m^2*x^7*x^m*sgn(b*x^2 + a) + 3*a*b^2*m^3*x^5*x^m*sgn(b*x^2 + a) + 23*b^3*m*x^7*x^m*sgn(b*x^2 + a) + 33*a*b^2*m^2*x^5*x^m*sgn(b*x^2 + a) + 15*b^3*x^7*x^m*sgn(b*x^2 + a) + 3*a^2*b*m^3*x^3*x^m*sgn(b*x^2 + a) + 93*a*b^2*m*x^5*x^m*sgn(b*x^2 + a) + 39*a^2*b*m^2*x^3*x^m*sgn(b*x^2 + a) + 63*a*b^2*x^5*x^m*sgn(b*x^2 + a) + a^3*m^3*x*x^m*sgn(b*x^2 + a) + 141*a^2*b*m*x^3*x^m*sgn(b*x^2 + a) + 15*a^3*m^2*x*x^m*sgn(b*x^2 + a) + 105*a^2*b*x^3*x^m*sgn(b*x^2 + a) + 71*a^3*m*x*x^m*sgn(b*x^2 + a) + 105*a^3*x*x^m*sgn(b*x^2 + a))*c^(3/2)/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
228,1,72,0,0.299058," ","integrate(x^5*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{120} \, {\left(10 \, b^{3} x^{12} \mathrm{sgn}\left(b x^{2} + a\right) + 36 \, a b^{2} x^{10} \mathrm{sgn}\left(b x^{2} + a\right) + 45 \, a^{2} b x^{8} \mathrm{sgn}\left(b x^{2} + a\right) + 20 \, a^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right)\right)} c^{\frac{3}{2}}"," ",0,"1/120*(10*b^3*x^12*sgn(b*x^2 + a) + 36*a*b^2*x^10*sgn(b*x^2 + a) + 45*a^2*b*x^8*sgn(b*x^2 + a) + 20*a^3*x^6*sgn(b*x^2 + a))*c^(3/2)","A",0
229,1,72,0,0.287031," ","integrate(x^4*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{1155} \, {\left(105 \, b^{3} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 385 \, a b^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 495 \, a^{2} b x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 231 \, a^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right)\right)} c^{\frac{3}{2}}"," ",0,"1/1155*(105*b^3*x^11*sgn(b*x^2 + a) + 385*a*b^2*x^9*sgn(b*x^2 + a) + 495*a^2*b*x^7*sgn(b*x^2 + a) + 231*a^3*x^5*sgn(b*x^2 + a))*c^(3/2)","A",0
230,1,48,0,0.300396," ","integrate(x^3*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{40} \, {\left(4 \, b^{3} x^{10} + 15 \, a b^{2} x^{8} + 20 \, a^{2} b x^{6} + 10 \, a^{3} x^{4}\right)} c^{\frac{3}{2}} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/40*(4*b^3*x^10 + 15*a*b^2*x^8 + 20*a^2*b*x^6 + 10*a^3*x^4)*c^(3/2)*sgn(b*x^2 + a)","A",0
231,1,72,0,0.268087," ","integrate(x^2*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{315} \, {\left(35 \, b^{3} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 135 \, a b^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 189 \, a^{2} b x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, a^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)} c^{\frac{3}{2}}"," ",0,"1/315*(35*b^3*x^9*sgn(b*x^2 + a) + 135*a*b^2*x^7*sgn(b*x^2 + a) + 189*a^2*b*x^5*sgn(b*x^2 + a) + 105*a^3*x^3*sgn(b*x^2 + a))*c^(3/2)","A",0
232,1,25,0,0.247860," ","integrate(x*(c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(b x^{2} + a\right)}^{4} c^{\frac{3}{2}} \mathrm{sgn}\left(b x^{2} + a\right)}{8 \, b}"," ",0,"1/8*(b*x^2 + a)^4*c^(3/2)*sgn(b*x^2 + a)/b","A",0
233,1,46,0,0.327006," ","integrate((c*(b*x^2+a)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{35} \, {\left(5 \, b^{3} x^{7} + 21 \, a b^{2} x^{5} + 35 \, a^{2} b x^{3} + 35 \, a^{3} x\right)} c^{\frac{3}{2}} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/35*(5*b^3*x^7 + 21*a*b^2*x^5 + 35*a^2*b*x^3 + 35*a^3*x)*c^(3/2)*sgn(b*x^2 + a)","A",0
234,1,73,0,0.345924," ","integrate((c*(b*x^2+a)^2)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, b^{3} x^{6} \mathrm{sgn}\left(b x^{2} + a\right) + 9 \, a b^{2} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 18 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a^{3} \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right)\right)} c^{\frac{3}{2}}"," ",0,"1/12*(2*b^3*x^6*sgn(b*x^2 + a) + 9*a*b^2*x^4*sgn(b*x^2 + a) + 18*a^2*b*x^2*sgn(b*x^2 + a) + 6*a^3*log(x^2)*sgn(b*x^2 + a))*c^(3/2)","A",0
235,1,69,0,0.244483," ","integrate((c*(b*x^2+a)^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{5} \, {\left(b^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, a b^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, a^{2} b x \mathrm{sgn}\left(b x^{2} + a\right) - \frac{5 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{x}\right)} c^{\frac{3}{2}}"," ",0,"1/5*(b^3*x^5*sgn(b*x^2 + a) + 5*a*b^2*x^3*sgn(b*x^2 + a) + 15*a^2*b*x*sgn(b*x^2 + a) - 5*a^3*sgn(b*x^2 + a)/x)*c^(3/2)","A",0
236,1,91,0,0.294106," ","integrate((c*(b*x^2+a)^2)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(b^{3} x^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a b^{2} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a^{2} b \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) - \frac{2 \, {\left(3 \, a^{2} b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + a^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{x^{2}}\right)} c^{\frac{3}{2}}"," ",0,"1/4*(b^3*x^4*sgn(b*x^2 + a) + 6*a*b^2*x^2*sgn(b*x^2 + a) + 6*a^2*b*log(x^2)*sgn(b*x^2 + a) - 2*(3*a^2*b*x^2*sgn(b*x^2 + a) + a^3*sgn(b*x^2 + a))/x^2)*c^(3/2)","A",0
237,1,177,0,0.506927," ","integrate(x^2*(c*(b*x^2+a)^3)^(3/2),x, algorithm=""giac"")","\frac{1}{15360} \, {\left(\frac{315 \, a^{6} c \log\left({\left| -\sqrt{b c} x + \sqrt{b c x^{2} + a c} \right|}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c} b} + {\left(\frac{315 \, a^{5} \mathrm{sgn}\left(b x^{2} + a\right)}{b} + 2 \, {\left(2455 \, a^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, {\left(1429 \, a^{3} b \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, {\left(759 \, a^{2} b^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 8 \, {\left(10 \, b^{4} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 49 \, a b^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)} x^{2}\right)} x^{2}\right)} x^{2}\right)} x^{2}\right)} \sqrt{b c x^{2} + a c} x\right)} c"," ",0,"1/15360*(315*a^6*c*log(abs(-sqrt(b*c)*x + sqrt(b*c*x^2 + a*c)))*sgn(b*x^2 + a)/(sqrt(b*c)*b) + (315*a^5*sgn(b*x^2 + a)/b + 2*(2455*a^4*sgn(b*x^2 + a) + 4*(1429*a^3*b*sgn(b*x^2 + a) + 2*(759*a^2*b^2*sgn(b*x^2 + a) + 8*(10*b^4*x^2*sgn(b*x^2 + a) + 49*a*b^3*sgn(b*x^2 + a))*x^2)*x^2)*x^2)*x^2)*sqrt(b*c*x^2 + a*c)*x)*c","A",0
238,1,28,0,0.305830," ","integrate(x*(c*(b*x^2+a)^3)^(3/2),x, algorithm=""giac"")","\frac{{\left(b c x^{2} + a c\right)}^{\frac{11}{2}} \mathrm{sgn}\left(b x^{2} + a\right)}{11 \, b c^{4}}"," ",0,"1/11*(b*c*x^2 + a*c)^(11/2)*sgn(b*x^2 + a)/(b*c^4)","A",0
239,1,153,0,0.330320," ","integrate((c*(b*x^2+a)^3)^(3/2),x, algorithm=""giac"")","-\frac{1}{1280} \, {\left(\frac{315 \, a^{5} c \log\left({\left| -\sqrt{b c} x + \sqrt{b c x^{2} + a c} \right|}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c}} - {\left(965 \, a^{4} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, {\left(745 \, a^{3} b \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, {\left(171 \, a^{2} b^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, {\left(8 \, b^{4} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 41 \, a b^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)} x^{2}\right)} x^{2}\right)} x^{2}\right)} \sqrt{b c x^{2} + a c} x\right)} c"," ",0,"-1/1280*(315*a^5*c*log(abs(-sqrt(b*c)*x + sqrt(b*c*x^2 + a*c)))*sgn(b*x^2 + a)/sqrt(b*c) - (965*a^4*sgn(b*x^2 + a) + 2*(745*a^3*b*sgn(b*x^2 + a) + 4*(171*a^2*b^2*sgn(b*x^2 + a) + 2*(8*b^4*x^2*sgn(b*x^2 + a) + 41*a*b^3*sgn(b*x^2 + a))*x^2)*x^2)*x^2)*sqrt(b*c*x^2 + a*c)*x)*c","A",0
240,1,185,0,0.357216," ","integrate((c*(b*x^2+a)^3)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{315} \, {\left(\frac{315 \, a^{5} \arctan\left(\frac{\sqrt{b c x^{2} + a c}}{\sqrt{-a c}}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{-a c}} + \frac{315 \, \sqrt{b c x^{2} + a c} a^{4} c^{44} \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, {\left(b c x^{2} + a c\right)}^{\frac{3}{2}} a^{3} c^{43} \mathrm{sgn}\left(b x^{2} + a\right) + 63 \, {\left(b c x^{2} + a c\right)}^{\frac{5}{2}} a^{2} c^{42} \mathrm{sgn}\left(b x^{2} + a\right) + 45 \, {\left(b c x^{2} + a c\right)}^{\frac{7}{2}} a c^{41} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, {\left(b c x^{2} + a c\right)}^{\frac{9}{2}} c^{40} \mathrm{sgn}\left(b x^{2} + a\right)}{c^{45}}\right)} c^{2}"," ",0,"1/315*(315*a^5*arctan(sqrt(b*c*x^2 + a*c)/sqrt(-a*c))*sgn(b*x^2 + a)/sqrt(-a*c) + (315*sqrt(b*c*x^2 + a*c)*a^4*c^44*sgn(b*x^2 + a) + 105*(b*c*x^2 + a*c)^(3/2)*a^3*c^43*sgn(b*x^2 + a) + 63*(b*c*x^2 + a*c)^(5/2)*a^2*c^42*sgn(b*x^2 + a) + 45*(b*c*x^2 + a*c)^(7/2)*a*c^41*sgn(b*x^2 + a) + 35*(b*c*x^2 + a*c)^(9/2)*c^40*sgn(b*x^2 + a))/c^45)*c^2","A",0
241,1,185,0,0.544170," ","integrate((c*(b*x^2+a)^3)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{256} \, {\left(\frac{512 \, \sqrt{b c} a^{5} c \mathrm{sgn}\left(b x^{2} + a\right)}{{\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c}\right)}^{2} - a c} - 315 \, \sqrt{b c} a^{4} \log\left({\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c}\right)}^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, {\left(325 \, a^{3} b \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, {\left(105 \, a^{2} b^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, {\left(2 \, b^{4} x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 11 \, a b^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)} x^{2}\right)} x^{2}\right)} \sqrt{b c x^{2} + a c} x\right)} c"," ",0,"1/256*(512*sqrt(b*c)*a^5*c*sgn(b*x^2 + a)/((sqrt(b*c)*x - sqrt(b*c*x^2 + a*c))^2 - a*c) - 315*sqrt(b*c)*a^4*log((sqrt(b*c)*x - sqrt(b*c*x^2 + a*c))^2)*sgn(b*x^2 + a) + 2*(325*a^3*b*sgn(b*x^2 + a) + 2*(105*a^2*b^2*sgn(b*x^2 + a) + 4*(2*b^4*x^2*sgn(b*x^2 + a) + 11*a*b^3*sgn(b*x^2 + a))*x^2)*x^2)*sqrt(b*c*x^2 + a*c)*x)*c","A",0
242,1,204,0,0.394315," ","integrate((c*(b*x^2+a)^3)^(3/2)/x^3,x, algorithm=""giac"")","\frac{{\left(\frac{315 \, a^{4} b^{2} c \arctan\left(\frac{\sqrt{b c x^{2} + a c}}{\sqrt{-a c}}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{-a c}} - \frac{35 \, \sqrt{b c x^{2} + a c} a^{4} b \mathrm{sgn}\left(b x^{2} + a\right)}{x^{2}} + \frac{2 \, {\left(140 \, \sqrt{b c x^{2} + a c} a^{3} b^{2} c^{21} \mathrm{sgn}\left(b x^{2} + a\right) + 35 \, {\left(b c x^{2} + a c\right)}^{\frac{3}{2}} a^{2} b^{2} c^{20} \mathrm{sgn}\left(b x^{2} + a\right) + 14 \, {\left(b c x^{2} + a c\right)}^{\frac{5}{2}} a b^{2} c^{19} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, {\left(b c x^{2} + a c\right)}^{\frac{7}{2}} b^{2} c^{18} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{c^{21}}\right)} c}{70 \, b}"," ",0,"1/70*(315*a^4*b^2*c*arctan(sqrt(b*c*x^2 + a*c)/sqrt(-a*c))*sgn(b*x^2 + a)/sqrt(-a*c) - 35*sqrt(b*c*x^2 + a*c)*a^4*b*sgn(b*x^2 + a)/x^2 + 2*(140*sqrt(b*c*x^2 + a*c)*a^3*b^2*c^21*sgn(b*x^2 + a) + 35*(b*c*x^2 + a*c)^(3/2)*a^2*b^2*c^20*sgn(b*x^2 + a) + 14*(b*c*x^2 + a*c)^(5/2)*a*b^2*c^19*sgn(b*x^2 + a) + 5*(b*c*x^2 + a*c)^(7/2)*b^2*c^18*sgn(b*x^2 + a))/c^21)*c/b","A",0
243,1,71,0,0.458622," ","integrate(x^2*(c/(b*x^2+a))^(3/2),x, algorithm=""giac"")","-{\left(\frac{c x \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c x^{2} + a c} b} + \frac{c \log\left({\left| -\sqrt{b c} x + \sqrt{b c x^{2} + a c} \right|}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c} b}\right)} c"," ",0,"-(c*x*sgn(b*x^2 + a)/(sqrt(b*c*x^2 + a*c)*b) + c*log(abs(-sqrt(b*c)*x + sqrt(b*c*x^2 + a*c)))*sgn(b*x^2 + a)/(sqrt(b*c)*b))*c","A",0
244,1,28,0,0.391107," ","integrate(x*(c/(b*x^2+a))^(3/2),x, algorithm=""giac"")","-\frac{c^{2} \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c x^{2} + a c} b}"," ",0,"-c^2*sgn(b*x^2 + a)/(sqrt(b*c*x^2 + a*c)*b)","A",0
245,1,28,0,0.482700," ","integrate((c/(b*x^2+a))^(3/2),x, algorithm=""giac"")","\frac{c^{2} x \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c x^{2} + a c} a}"," ",0,"c^2*x*sgn(b*x^2 + a)/(sqrt(b*c*x^2 + a*c)*a)","A",0
246,1,59,0,0.246185," ","integrate((c/(b*x^2+a))^(3/2)/x,x, algorithm=""giac"")","c {\left(\frac{c \arctan\left(\frac{\sqrt{b c x^{2} + a c}}{\sqrt{-a c}}\right)}{\sqrt{-a c} a} + \frac{c}{\sqrt{b c x^{2} + a c} a}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"c*(c*arctan(sqrt(b*c*x^2 + a*c)/sqrt(-a*c))/(sqrt(-a*c)*a) + c/(sqrt(b*c*x^2 + a*c)*a))*sgn(b*x^2 + a)","A",0
247,1,81,0,0.343180," ","integrate((c/(b*x^2+a))^(3/2)/x^2,x, algorithm=""giac"")","-{\left(\frac{b c x \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{b c x^{2} + a c} a^{2}} - \frac{2 \, \sqrt{b c} c \mathrm{sgn}\left(b x^{2} + a\right)}{{\left({\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c}\right)}^{2} - a c\right)} a}\right)} c"," ",0,"-(b*c*x*sgn(b*x^2 + a)/(sqrt(b*c*x^2 + a*c)*a^2) - 2*sqrt(b*c)*c*sgn(b*x^2 + a)/(((sqrt(b*c)*x - sqrt(b*c*x^2 + a*c))^2 - a*c)*a))*c","A",0
248,1,103,0,0.327969," ","integrate((c/(b*x^2+a))^(3/2)/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, c {\left(\frac{3 \, b c \arctan\left(\frac{\sqrt{b c x^{2} + a c}}{\sqrt{-a c}}\right)}{\sqrt{-a c} a^{2}} + \frac{2 \, a b c^{2} - 3 \, {\left(b c x^{2} + a c\right)} b c}{{\left(\sqrt{b c x^{2} + a c} a c - {\left(b c x^{2} + a c\right)}^{\frac{3}{2}}\right)} a^{2}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"-1/2*c*(3*b*c*arctan(sqrt(b*c*x^2 + a*c)/sqrt(-a*c))/(sqrt(-a*c)*a^2) + (2*a*b*c^2 - 3*(b*c*x^2 + a*c)*b*c)/((sqrt(b*c*x^2 + a*c)*a*c - (b*c*x^2 + a*c)^(3/2))*a^2))*sgn(b*x^2 + a)","A",0
249,1,137,0,0.335871," ","integrate(x^7*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""giac"")","\frac{2 \, c^{\frac{3}{2}} {\left(\frac{19 \, {\left(77 \, {\left(b x^{2} + a\right)}^{\frac{15}{4}} - 315 \, {\left(b x^{2} + a\right)}^{\frac{11}{4}} a + 495 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} a^{2} - 385 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} a^{3}\right)} a}{b^{3}} + \frac{1155 \, {\left(b x^{2} + a\right)}^{\frac{19}{4}} - 5852 \, {\left(b x^{2} + a\right)}^{\frac{15}{4}} a + 11970 \, {\left(b x^{2} + a\right)}^{\frac{11}{4}} a^{2} - 12540 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} a^{3} + 7315 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} a^{4}}{b^{3}}\right)}}{21945 \, b}"," ",0,"2/21945*c^(3/2)*(19*(77*(b*x^2 + a)^(15/4) - 315*(b*x^2 + a)^(11/4)*a + 495*(b*x^2 + a)^(7/4)*a^2 - 385*(b*x^2 + a)^(3/4)*a^3)*a/b^3 + (1155*(b*x^2 + a)^(19/4) - 5852*(b*x^2 + a)^(15/4)*a + 11970*(b*x^2 + a)^(11/4)*a^2 - 12540*(b*x^2 + a)^(7/4)*a^3 + 7315*(b*x^2 + a)^(3/4)*a^4)/b^3)/b","A",0
250,1,109,0,0.241920," ","integrate(x^5*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""giac"")","\frac{2 \, c^{\frac{3}{2}} {\left(\frac{5 \, {\left(21 \, {\left(b x^{2} + a\right)}^{\frac{11}{4}} - 66 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} a + 77 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} a^{2}\right)} a}{b^{2}} + \frac{77 \, {\left(b x^{2} + a\right)}^{\frac{15}{4}} - 315 \, {\left(b x^{2} + a\right)}^{\frac{11}{4}} a + 495 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} a^{2} - 385 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} a^{3}}{b^{2}}\right)}}{1155 \, b}"," ",0,"2/1155*c^(3/2)*(5*(21*(b*x^2 + a)^(11/4) - 66*(b*x^2 + a)^(7/4)*a + 77*(b*x^2 + a)^(3/4)*a^2)*a/b^2 + (77*(b*x^2 + a)^(15/4) - 315*(b*x^2 + a)^(11/4)*a + 495*(b*x^2 + a)^(7/4)*a^2 - 385*(b*x^2 + a)^(3/4)*a^3)/b^2)/b","A",0
251,1,81,0,0.300687," ","integrate(x^3*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{11 \, {\left(3 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} - 7 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} a\right)} a}{b} + \frac{21 \, {\left(b x^{2} + a\right)}^{\frac{11}{4}} - 66 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} a + 77 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} a^{2}}{b}\right)} c^{\frac{3}{2}}}{231 \, b}"," ",0,"2/231*(11*(3*(b*x^2 + a)^(7/4) - 7*(b*x^2 + a)^(3/4)*a)*a/b + (21*(b*x^2 + a)^(11/4) - 66*(b*x^2 + a)^(7/4)*a + 77*(b*x^2 + a)^(3/4)*a^2)/b)*c^(3/2)/b","A",0
252,1,17,0,0.269560," ","integrate(x*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{4}} c^{\frac{3}{2}}}{7 \, b}"," ",0,"2/7*(b*x^2 + a)^(7/4)*c^(3/2)/b","A",0
253,1,190,0,0.406536," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(6 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{2} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) + 6 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{2} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right) - 3 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(\sqrt{2} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{2} + a} + \sqrt{-a}\right) + 3 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} \log\left(-\sqrt{2} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{2} + a} + \sqrt{-a}\right) - 8 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}}\right)} c^{\frac{3}{2}}"," ",0,"-1/12*(6*sqrt(2)*(-a)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^2 + a)^(1/4))/(-a)^(1/4)) + 6*sqrt(2)*(-a)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^2 + a)^(1/4))/(-a)^(1/4)) - 3*sqrt(2)*(-a)^(3/4)*log(sqrt(2)*(b*x^2 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^2 + a) + sqrt(-a)) + 3*sqrt(2)*(-a)^(3/4)*log(-sqrt(2)*(b*x^2 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^2 + a) + sqrt(-a)) - 8*(b*x^2 + a)^(3/4))*c^(3/2)","A",0
254,1,212,0,0.398197," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x^3,x, algorithm=""giac"")","\frac{{\left(\frac{6 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} + 2 \, {\left(b x^{2} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{1}{4}}} + \frac{6 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-a\right)^{\frac{1}{4}} - 2 \, {\left(b x^{2} + a\right)}^{\frac{1}{4}}\right)}}{2 \, \left(-a\right)^{\frac{1}{4}}}\right)}{\left(-a\right)^{\frac{1}{4}}} + \frac{3 \, \sqrt{2} \left(-a\right)^{\frac{3}{4}} b^{2} \log\left(\sqrt{2} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{2} + a} + \sqrt{-a}\right)}{a} + \frac{3 \, \sqrt{2} b^{2} \log\left(-\sqrt{2} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \left(-a\right)^{\frac{1}{4}} + \sqrt{b x^{2} + a} + \sqrt{-a}\right)}{\left(-a\right)^{\frac{1}{4}}} - \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} b}{x^{2}}\right)} c^{\frac{3}{2}}}{16 \, b}"," ",0,"1/16*(6*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) + 2*(b*x^2 + a)^(1/4))/(-a)^(1/4))/(-a)^(1/4) + 6*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-a)^(1/4) - 2*(b*x^2 + a)^(1/4))/(-a)^(1/4))/(-a)^(1/4) + 3*sqrt(2)*(-a)^(3/4)*b^2*log(sqrt(2)*(b*x^2 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^2 + a) + sqrt(-a))/a + 3*sqrt(2)*b^2*log(-sqrt(2)*(b*x^2 + a)^(1/4)*(-a)^(1/4) + sqrt(b*x^2 + a) + sqrt(-a))/(-a)^(1/4) - 8*(b*x^2 + a)^(3/4)*b/x^2)*c^(3/2)/b","A",0
255,0,0,0,0.000000," ","integrate(x^2*(c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""giac"")","\int \left(\sqrt{b x^{2} + a} c\right)^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((sqrt(b*x^2 + a)*c)^(3/2)*x^2, x)","F",0
256,0,0,0,0.000000," ","integrate((c*(b*x^2+a)^(1/2))^(3/2),x, algorithm=""giac"")","\int \left(\sqrt{b x^{2} + a} c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((sqrt(b*x^2 + a)*c)^(3/2), x)","F",0
257,0,0,0,0.000000," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{\left(\sqrt{b x^{2} + a} c\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((sqrt(b*x^2 + a)*c)^(3/2)/x^2, x)","F",0
258,0,0,0,0.000000," ","integrate((c*(b*x^2+a)^(1/2))^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{\left(\sqrt{b x^{2} + a} c\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((sqrt(b*x^2 + a)*c)^(3/2)/x^4, x)","F",0
259,1,61,0,0.286844," ","integrate(((b-x)*(-a+x))^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \arcsin\left(\frac{a + b - 2 \, x}{a - b}\right) \mathrm{sgn}\left(-a + b\right) - \frac{1}{4} \, \sqrt{-a b + a x + b x - x^{2}} {\left(a + b - 2 \, x\right)}"," ",0,"1/8*(a^2 - 2*a*b + b^2)*arcsin((a + b - 2*x)/(a - b))*sgn(-a + b) - 1/4*sqrt(-a*b + a*x + b*x - x^2)*(a + b - 2*x)","A",0
260,0,0,0,0.000000," ","integrate(((-x^2+1)*(x^2+3))^(1/2),x, algorithm=""giac"")","\int \sqrt{-{\left(x^{2} + 3\right)} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(-(x^2 + 3)*(x^2 - 1)), x)","F",0
261,1,22,0,0.425797," ","integrate(1/((b-x)*(-a+x))^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{a + b - 2 \, x}{a - b}\right) \mathrm{sgn}\left(-a + b\right)"," ",0,"arcsin((a + b - 2*x)/(a - b))*sgn(-a + b)","A",0
262,0,0,0,0.000000," ","integrate(1/((-x^2+1)*(x^2+3))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-{\left(x^{2} + 3\right)} {\left(x^{2} - 1\right)}}}\,{d x}"," ",0,"integrate(1/sqrt(-(x^2 + 3)*(x^2 - 1)), x)","F",0
263,1,243,0,0.725674," ","integrate(x^5*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{d} - \frac{5 \, b^{2} c d - a b d^{2}}{b^{2} d^{3}}\right)} + \frac{15 \, b^{2} c^{2} - 4 \, a b c d - 3 \, a^{2} d^{2}}{b^{2} d^{3}}\right)} + \frac{3 \, {\left(5 \, b^{3} c^{3} e - 3 \, a b^{2} c^{2} d e - a^{2} b c d^{2} e - a^{3} d^{3} e\right)} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -b c e - a d e - 2 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} \sqrt{b d} e^{\frac{1}{2}} \right|}\right)}{\sqrt{b d} b^{2} d^{3}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/96*(2*sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e)*(2*x^2*(4*x^2/d - (5*b^2*c*d - a*b*d^2)/(b^2*d^3)) + (15*b^2*c^2 - 4*a*b*c*d - 3*a^2*d^2)/(b^2*d^3)) + 3*(5*b^3*c^3*e - 3*a*b^2*c^2*d*e - a^2*b*c*d^2*e - a^3*d^3*e)*e^(-1/2)*log(abs(-b*c*e - a*d*e - 2*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*sqrt(b*d)*e^(1/2)))/(sqrt(b*d)*b^2*d^3))*sgn(d*x^2 + c)","A",0
264,1,185,0,0.816639," ","integrate(x^3*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, {\left(2 \, \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e} {\left(\frac{2 \, x^{2}}{d} - \frac{3 \, b c - a d}{b d^{2}}\right)} - \frac{{\left(3 \, b^{2} c^{2} e - 2 \, a b c d e - a^{2} d^{2} e\right)} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -b c e - a d e - 2 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} \sqrt{b d} e^{\frac{1}{2}} \right|}\right)}{\sqrt{b d} b d^{2}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/16*(2*sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e)*(2*x^2/d - (3*b*c - a*d)/(b*d^2)) - (3*b^2*c^2*e - 2*a*b*c*d*e - a^2*d^2*e)*e^(-1/2)*log(abs(-b*c*e - a*d*e - 2*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*sqrt(b*d)*e^(1/2)))/(sqrt(b*d)*b*d^2))*sgn(d*x^2 + c)","A",0
265,1,149,0,0.821393," ","integrate(x*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{{\left(b c e - a d e\right)} \sqrt{b d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{b d} b c e^{\frac{1}{2}} - \sqrt{b d} a d e^{\frac{1}{2}} - 2 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} b d \right|}\right)}{b d^{2}} + \frac{2 \, \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}}{d}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/4*((b*c*e - a*d*e)*sqrt(b*d)*e^(-1/2)*log(abs(-sqrt(b*d)*b*c*e^(1/2) - sqrt(b*d)*a*d*e^(1/2) - 2*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*b*d))/(b*d^2) + 2*sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e)/d)*sgn(d*x^2 + c)","A",0
266,-2,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Error: Bad Argument Type","F(-2)",0
267,1,269,0,0.675981," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{{\left(b c e - a d e\right)} \arctan\left(-\frac{\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}}{\sqrt{-a c e}}\right)}{\sqrt{-a c e} c} - \frac{{\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} b c e + {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a d e + 2 \, \sqrt{b d} a c e^{\frac{3}{2}}}{{\left(a c e - {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{2}\right)} c}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/2*((b*c*e - a*d*e)*arctan(-(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))/sqrt(-a*c*e))/(sqrt(-a*c*e)*c) - ((sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*b*c*e + (sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a*d*e + 2*sqrt(b*d)*a*c*e^(3/2))/((a*c*e - (sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^2)*c))*sgn(d*x^2 + c)","B",0
268,1,598,0,0.822879," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^5,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(\frac{{\left(b^{2} c^{2} e + 2 \, a b c d e - 3 \, a^{2} d^{2} e\right)} \arctan\left(-\frac{\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}}{\sqrt{-a c e}}\right)}{\sqrt{-a c e} a c^{2}} - \frac{{\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a b^{2} c^{3} e^{2} + 10 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a^{2} b c^{2} d e^{2} + 5 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a^{3} c d^{2} e^{2} + {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} b^{2} c^{2} e + 2 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} a b c d e - 3 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} a^{2} d^{2} e + 8 \, \sqrt{b d} a^{3} c^{2} d e^{\frac{5}{2}} + 8 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{2} \sqrt{b d} a b c^{2} e^{\frac{3}{2}}}{{\left(a c e - {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{2}\right)}^{2} a c^{2}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"-1/8*((b^2*c^2*e + 2*a*b*c*d*e - 3*a^2*d^2*e)*arctan(-(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))/sqrt(-a*c*e))/(sqrt(-a*c*e)*a*c^2) - ((sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a*b^2*c^3*e^2 + 10*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a^2*b*c^2*d*e^2 + 5*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a^3*c*d^2*e^2 + (sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*b^2*c^2*e + 2*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*a*b*c*d*e - 3*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*a^2*d^2*e + 8*sqrt(b*d)*a^3*c^2*d*e^(5/2) + 8*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^2*sqrt(b*d)*a*b*c^2*e^(3/2))/((a*c*e - (sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^2)^2*a*c^2))*sgn(d*x^2 + c)","B",0
269,1,1076,0,0.975670," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^7,x, algorithm=""giac"")","\frac{1}{48} \, {\left(\frac{3 \, {\left(b^{3} c^{3} e + a b^{2} c^{2} d e + 3 \, a^{2} b c d^{2} e - 5 \, a^{3} d^{3} e\right)} \arctan\left(-\frac{\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}}{\sqrt{-a c e}}\right)}{\sqrt{-a c e} a^{2} c^{3}} - \frac{3 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a^{2} b^{3} c^{5} e^{3} + 51 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a^{3} b^{2} c^{4} d e^{3} + 105 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a^{4} b c^{3} d^{2} e^{3} + 33 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)} a^{5} c^{2} d^{3} e^{3} + 8 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} a b^{3} c^{4} e^{2} + 72 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} a^{2} b^{2} c^{3} d e^{2} + 24 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} a^{3} b c^{2} d^{2} e^{2} - 40 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{3} a^{4} c d^{3} e^{2} - 3 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{5} b^{3} c^{3} e - 3 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{5} a b^{2} c^{2} d e - 9 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{5} a^{2} b c d^{2} e + 15 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{5} a^{3} d^{3} e + 16 \, \sqrt{b d} a^{4} b c^{4} d e^{\frac{7}{2}} + 48 \, \sqrt{b d} a^{5} c^{3} d^{2} e^{\frac{7}{2}} + 48 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{2} \sqrt{b d} a^{2} b^{2} c^{4} e^{\frac{5}{2}} + 144 \, {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{2} \sqrt{b d} a^{3} b c^{3} d e^{\frac{5}{2}}}{{\left(a c e - {\left(\sqrt{b d} x^{2} e^{\frac{1}{2}} - \sqrt{b d x^{4} e + b c x^{2} e + a d x^{2} e + a c e}\right)}^{2}\right)}^{3} a^{2} c^{3}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/48*(3*(b^3*c^3*e + a*b^2*c^2*d*e + 3*a^2*b*c*d^2*e - 5*a^3*d^3*e)*arctan(-(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))/sqrt(-a*c*e))/(sqrt(-a*c*e)*a^2*c^3) - (3*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a^2*b^3*c^5*e^3 + 51*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a^3*b^2*c^4*d*e^3 + 105*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a^4*b*c^3*d^2*e^3 + 33*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))*a^5*c^2*d^3*e^3 + 8*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*a*b^3*c^4*e^2 + 72*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*a^2*b^2*c^3*d*e^2 + 24*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*a^3*b*c^2*d^2*e^2 - 40*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^3*a^4*c*d^3*e^2 - 3*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^5*b^3*c^3*e - 3*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^5*a*b^2*c^2*d*e - 9*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^5*a^2*b*c*d^2*e + 15*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^5*a^3*d^3*e + 16*sqrt(b*d)*a^4*b*c^4*d*e^(7/2) + 48*sqrt(b*d)*a^5*c^3*d^2*e^(7/2) + 48*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^2*sqrt(b*d)*a^2*b^2*c^4*e^(5/2) + 144*(sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^2*sqrt(b*d)*a^3*b*c^3*d*e^(5/2))/((a*c*e - (sqrt(b*d)*x^2*e^(1/2) - sqrt(b*d*x^4*e + b*c*x^2*e + a*d*x^2*e + a*c*e))^2)^3*a^2*c^3))*sgn(d*x^2 + c)","B",0
270,0,0,0,0.000000," ","integrate(x^4*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}} x^{4}\,{d x}"," ",0,"integrate(sqrt((b*x^2 + a)*e/(d*x^2 + c))*x^4, x)","F",0
271,0,0,0,0.000000," ","integrate(x^2*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}} x^{2}\,{d x}"," ",0,"integrate(sqrt((b*x^2 + a)*e/(d*x^2 + c))*x^2, x)","F",0
272,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt((b*x^2 + a)*e/(d*x^2 + c)), x)","F",0
273,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt((b*x^2 + a)*e/(d*x^2 + c))/x^2, x)","F",0
274,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt((b*x^2 + a)*e/(d*x^2 + c))/x^4, x)","F",0
275,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt((b*x^2 + a)*e/(d*x^2 + c))/x^6, x)","F",0
276,-2,0,0,0.000000," ","integrate(x^5*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.84Unable to divide, perhaps due to rounding error%%%{%%%{2,[0,5,0]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-4,[0,4,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0,1]%%%}+%%%{%%%{2,[1,4,1]%%%},[0,0,0,2]%%%} / %%%{%%%{1,[0,2,2]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0,1]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
277,-2,0,0,0.000000," ","integrate(x^3*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.76Unable to divide, perhaps due to rounding error%%%{%%%{2,[0,4,0]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-4,[0,3,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0,1]%%%}+%%%{%%%{2,[1,3,1]%%%},[0,0,0,2]%%%} / %%%{%%%{1,[0,2,2]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0,1]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
278,-2,0,0,0.000000," ","integrate(x*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.67Unable to divide, perhaps due to rounding error%%%{%%%{2,[0,3,0]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-4,[0,2,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0,1]%%%}+%%%{%%%{2,[1,2,1]%%%},[0,0,0,2]%%%} / %%%{%%%{1,[0,2,2]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0,1]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
279,-2,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.52Error: Bad Argument Type","F(-2)",0
280,-2,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.55Unable to divide, perhaps due to rounding error%%%{%%%{2,[0,1,0]%%%},[6,0,0]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%%{2,[1,0,1]%%%},[4,2,0]%%%}+%%%{%%%{-4,[0,1,1]%%%},[4,1,1]%%%}+%%%{%%{[%%%{8,[0,0,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%%{-4,[1,0,2]%%%},[2,3,1]%%%}+%%%{%%%{2,[0,1,2]%%%},[2,2,2]%%%}+%%%{%%{[%%%{-4,[0,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%%{2,[1,0,3]%%%},[0,4,2]%%%} / %%%{%%%{1,[0,2,0]%%%},[6,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[4,2,0]%%%}+%%%{%%%{-2,[0,2,1]%%%},[4,1,1]%%%}+%%%{%%{[%%%{4,[0,1,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%%{-2,[1,1,2]%%%},[2,3,1]%%%}+%%%{%%%{1,[0,2,2]%%%},[2,2,2]%%%}+%%%{%%{[%%%{-2,[0,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,4,2]%%%} Error: Bad Argument Value","F(-2)",0
281,-2,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.56Unable to divide, perhaps due to rounding error%%%{%%%{2,[4,1,4]%%%},[2,7,0]%%%}+%%%{%%%{-8,[3,2,4]%%%},[2,6,1]%%%}+%%%{%%%{12,[2,3,4]%%%},[2,5,2]%%%}+%%%{%%%{-8,[1,4,4]%%%},[2,4,3]%%%}+%%%{%%%{2,[0,5,4]%%%},[2,3,4]%%%}+%%%{%%{[%%%{-4,[4,0,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,0]%%%}+%%%{%%{[%%%{16,[3,1,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,1]%%%}+%%%{%%{[%%%{-24,[2,2,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,2]%%%}+%%%{%%{[%%%{16,[1,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,3]%%%}+%%%{%%{[%%%{-4,[0,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,4]%%%}+%%%{%%%{2,[5,0,5]%%%},[0,9,0]%%%}+%%%{%%%{-8,[4,1,5]%%%},[0,8,1]%%%}+%%%{%%%{12,[3,2,5]%%%},[0,7,2]%%%}+%%%{%%%{-8,[2,3,5]%%%},[0,6,3]%%%}+%%%{%%%{2,[1,4,5]%%%},[0,5,4]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
282,-2,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^7,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x^2*d+c)]Evaluation time: 0.57Unable to divide, perhaps due to rounding error%%%{%%%{2,[5,1,5]%%%},[2,9,0]%%%}+%%%{%%%{-10,[4,2,5]%%%},[2,8,1]%%%}+%%%{%%%{20,[3,3,5]%%%},[2,7,2]%%%}+%%%{%%%{-20,[2,4,5]%%%},[2,6,3]%%%}+%%%{%%%{10,[1,5,5]%%%},[2,5,4]%%%}+%%%{%%%{-2,[0,6,5]%%%},[2,4,5]%%%}+%%%{%%{[%%%{-4,[5,0,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,10,0]%%%}+%%%{%%{[%%%{20,[4,1,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,9,1]%%%}+%%%{%%{[%%%{-40,[3,2,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,2]%%%}+%%%{%%{[%%%{40,[2,3,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,3]%%%}+%%%{%%{[%%%{-20,[1,4,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,4]%%%}+%%%{%%{[%%%{4,[0,5,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,5]%%%}+%%%{%%%{2,[6,0,6]%%%},[0,11,0]%%%}+%%%{%%%{-10,[5,1,6]%%%},[0,10,1]%%%}+%%%{%%%{20,[4,2,6]%%%},[0,9,2]%%%}+%%%{%%%{-20,[3,3,6]%%%},[0,8,3]%%%}+%%%{%%%{10,[2,4,6]%%%},[0,7,4]%%%}+%%%{%%%{-2,[1,5,6]%%%},[0,6,5]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
283,0,0,0,0.000000," ","integrate(x^4*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}} x^{4}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)*x^4, x)","F",0
284,0,0,0,0.000000," ","integrate(x^2*(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)*x^2, x)","F",0
285,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(3/2), x)","F",0
286,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)/x^2, x)","F",0
287,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)/x^4, x)","F",0
288,0,0,0,0.000000," ","integrate((e*(b*x^2+a)/(d*x^2+c))^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)/x^6, x)","F",0
289,1,18,0,0.284716," ","integrate(x*((-x^2+1)/(x^2+1))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{4} + 1} + \frac{1}{2} \, \arcsin\left(x^{2}\right)"," ",0,"1/2*sqrt(-x^4 + 1) + 1/2*arcsin(x^2)","A",0
290,1,30,0,0.352668," ","integrate(x*((-7*x^2+5)/(5*x^2+7))^(1/2),x, algorithm=""giac"")","\frac{37}{350} \, \sqrt{35} \arcsin\left(\frac{35}{37} \, x^{2} + \frac{12}{37}\right) + \frac{1}{10} \, \sqrt{-35 \, x^{4} - 24 \, x^{2} + 35}"," ",0,"37/350*sqrt(35)*arcsin(35/37*x^2 + 12/37) + 1/10*sqrt(-35*x^4 - 24*x^2 + 35)","A",0
291,1,22,0,0.290664," ","integrate(x^2*((-x^3+1)/(x^3+1))^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\sqrt{-x^{6} + 1} + \arcsin\left(x^{3}\right)\right)} \mathrm{sgn}\left(x^{3} + 1\right)"," ",0,"1/3*(sqrt(-x^6 + 1) + arcsin(x^3))*sgn(x^3 + 1)","A",0
292,0,0,0,0.000000," ","integrate(x^8*((-x^3+1)/(x^3+1))^(1/2),x, algorithm=""giac"")","\int x^{8} \sqrt{-\frac{x^{3} - 1}{x^{3} + 1}}\,{d x}"," ",0,"integrate(x^8*sqrt(-(x^3 - 1)/(x^3 + 1)), x)","F",0
293,1,47,0,0.366150," ","integrate(x^9*((-7*x^5+5)/(5*x^5+7))^(1/2),x, algorithm=""giac"")","\frac{1}{61250} \, {\left(35 \, \sqrt{-35 \, x^{10} - 24 \, x^{5} + 35} {\left(35 \, x^{5} - 86\right)} - 2257 \, \sqrt{35} \arcsin\left(\frac{35}{37} \, x^{5} + \frac{12}{37}\right)\right)} \mathrm{sgn}\left(5 \, x^{5} + 7\right)"," ",0,"1/61250*(35*sqrt(-35*x^10 - 24*x^5 + 35)*(35*x^5 - 86) - 2257*sqrt(35)*arcsin(35/37*x^5 + 12/37))*sgn(5*x^5 + 7)","A",0
294,1,40,0,0.420036," ","integrate((x^2/(x^2-1))^(1/2)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{x^{2} - 1}\right) \mathrm{sgn}\left(x^{2} - 1\right) \mathrm{sgn}\left(x\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} i \, \sqrt{2}\right) \mathrm{sgn}\left(x\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(x^2 - 1))*sgn(x^2 - 1)*sgn(x) + 1/2*sqrt(2)*arctan(1/2*I*sqrt(2))*sgn(x)","C",0
295,1,61,0,0.452725," ","integrate((x^2/(-1+a+(1+a)*x^2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{a x^{2} + x^{2} + a - 1}\right) \mathrm{sgn}\left(a x^{2} + x^{2} + a - 1\right) \mathrm{sgn}\left(x\right) - \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{a - 1}\right) \mathrm{sgn}\left(a - 1\right) \mathrm{sgn}\left(x\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*x^2 + x^2 + a - 1))*sgn(a*x^2 + x^2 + a - 1)*sgn(x) - 1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a - 1))*sgn(a - 1)*sgn(x)","A",0
296,-2,0,0,0.000000," ","integrate(x^5/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,1,0]%%%},[2,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1,0,1]%%%},[0,2]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2]%%%} Error: Bad Argument Value","F(-2)",0
297,-2,0,0,0.000000," ","integrate(x^3/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,1,0]%%%},[2,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1,0,1]%%%},[0,2]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2]%%%} Error: Bad Argument Value","F(-2)",0
298,-2,0,0,0.000000," ","integrate(x/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,1,0]%%%},[2,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1,0,1]%%%},[0,2]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2]%%%} Error: Bad Argument Value","F(-2)",0
299,-2,0,0,0.000000," ","integrate(1/x/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[2,1,2]%%%},[2,3,0]%%%}+%%%{%%%{-2,[1,2,2]%%%},[2,2,1]%%%}+%%%{%%%{1,[0,3,2]%%%},[2,1,2]%%%}+%%%{%%{[%%%{-2,[2,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,0]%%%}+%%%{%%{[%%%{4,[1,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,1]%%%}+%%%{%%{[%%%{-2,[0,2,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,2]%%%}+%%%{%%%{1,[3,0,3]%%%},[0,5,0]%%%}+%%%{%%%{-2,[2,1,3]%%%},[0,4,1]%%%}+%%%{%%%{1,[1,2,3]%%%},[0,3,2]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
300,-2,0,0,0.000000," ","integrate(1/x^3/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,1,0]%%%},[6,0,0]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%%{1,[1,0,1]%%%},[4,2,0]%%%}+%%%{%%%{-2,[0,1,1]%%%},[4,1,1]%%%}+%%%{%%{[%%%{4,[0,0,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%%{-2,[1,0,2]%%%},[2,3,1]%%%}+%%%{%%%{1,[0,1,2]%%%},[2,2,2]%%%}+%%%{%%{[%%%{-2,[0,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%%{1,[1,0,3]%%%},[0,4,2]%%%} / %%%{%%%{1,[0,2,0]%%%},[6,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[4,2,0]%%%}+%%%{%%%{-2,[0,2,1]%%%},[4,1,1]%%%}+%%%{%%{[%%%{4,[0,1,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%%{-2,[1,1,2]%%%},[2,3,1]%%%}+%%%{%%%{1,[0,2,2]%%%},[2,2,2]%%%}+%%%{%%{[%%%{-2,[0,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,4,2]%%%} Error: Bad Argument Value","F(-2)",0
301,-2,0,0,0.000000," ","integrate(1/x^5/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[4,1,4]%%%},[2,7,0]%%%}+%%%{%%%{-4,[3,2,4]%%%},[2,6,1]%%%}+%%%{%%%{6,[2,3,4]%%%},[2,5,2]%%%}+%%%{%%%{-4,[1,4,4]%%%},[2,4,3]%%%}+%%%{%%%{1,[0,5,4]%%%},[2,3,4]%%%}+%%%{%%{[%%%{-2,[4,0,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,0]%%%}+%%%{%%{[%%%{8,[3,1,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,1]%%%}+%%%{%%{[%%%{-12,[2,2,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,2]%%%}+%%%{%%{[%%%{8,[1,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,3]%%%}+%%%{%%{[%%%{-2,[0,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,4]%%%}+%%%{%%%{1,[5,0,5]%%%},[0,9,0]%%%}+%%%{%%%{-4,[4,1,5]%%%},[0,8,1]%%%}+%%%{%%%{6,[3,2,5]%%%},[0,7,2]%%%}+%%%{%%%{-4,[2,3,5]%%%},[0,6,3]%%%}+%%%{%%%{1,[1,4,5]%%%},[0,5,4]%%%} / %%%{%%%{1,[0,2,0]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-2,[0,1,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
302,0,0,0,0.000000," ","integrate(x^4/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}}\,{d x}"," ",0,"integrate(x^4/sqrt((b*x^2 + a)*e/(d*x^2 + c)), x)","F",0
303,0,0,0,0.000000," ","integrate(x^2/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}}\,{d x}"," ",0,"integrate(x^2/sqrt((b*x^2 + a)*e/(d*x^2 + c)), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}}}\,{d x}"," ",0,"integrate(1/sqrt((b*x^2 + a)*e/(d*x^2 + c)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/x^2/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt((b*x^2 + a)*e/(d*x^2 + c))*x^2), x)","F",0
306,0,0,0,0.000000," ","integrate(1/x^4/(e*(b*x^2+a)/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt((b*x^2 + a)*e/(d*x^2 + c))*x^4), x)","F",0
307,-2,0,0,0.000000," ","integrate(x^5/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{2,[1,2,2]%%%},[2,1,2,0]%%%}+%%%{%%%{-4,[2,1,2]%%%},[2,1,1,1]%%%}+%%%{%%%{2,[3,0,2]%%%},[2,1,0,2]%%%}+%%%{%%{[%%%{-4,[0,2,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,3,0]%%%}+%%%{%%{[%%%{8,[1,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,2,1]%%%}+%%%{%%{[%%%{-4,[2,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1,2]%%%}+%%%{%%%{2,[0,3,3]%%%},[0,1,4,0]%%%}+%%%{%%%{-4,[1,2,3]%%%},[0,1,3,1]%%%}+%%%{%%%{2,[2,1,3]%%%},[0,1,2,2]%%%} / %%%{%%%{1,[2,0,2]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[1,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,1,0]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
308,-2,0,0,0.000000," ","integrate(x^3/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{2,[1,2,2]%%%},[2,1,2,0]%%%}+%%%{%%%{-4,[2,1,2]%%%},[2,1,1,1]%%%}+%%%{%%%{2,[3,0,2]%%%},[2,1,0,2]%%%}+%%%{%%{[%%%{-4,[0,2,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,3,0]%%%}+%%%{%%{[%%%{8,[1,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,2,1]%%%}+%%%{%%{[%%%{-4,[2,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1,2]%%%}+%%%{%%%{2,[0,3,3]%%%},[0,1,4,0]%%%}+%%%{%%%{-4,[1,2,3]%%%},[0,1,3,1]%%%}+%%%{%%%{2,[2,1,3]%%%},[0,1,2,2]%%%} / %%%{%%%{1,[2,0,2]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[1,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,1,0]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
309,-2,0,0,0.000000," ","integrate(x/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{2,[1,2,2]%%%},[2,1,2,0]%%%}+%%%{%%%{-4,[2,1,2]%%%},[2,1,1,1]%%%}+%%%{%%%{2,[3,0,2]%%%},[2,1,0,2]%%%}+%%%{%%{[%%%{-4,[0,2,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,3,0]%%%}+%%%{%%{[%%%{8,[1,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,2,1]%%%}+%%%{%%{[%%%{-4,[2,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1,2]%%%}+%%%{%%%{2,[0,3,3]%%%},[0,1,4,0]%%%}+%%%{%%%{-4,[1,2,3]%%%},[0,1,3,1]%%%}+%%%{%%%{2,[2,1,3]%%%},[0,1,2,2]%%%} / %%%{%%%{1,[2,0,2]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[1,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,1,0]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
310,-2,0,0,0.000000," ","integrate(1/x/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{2,[1,2,2]%%%},[2,1,3,0]%%%}+%%%{%%%{-4,[2,1,2]%%%},[2,1,2,1]%%%}+%%%{%%%{2,[3,0,2]%%%},[2,1,1,2]%%%}+%%%{%%{[%%%{-4,[0,2,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,4,0]%%%}+%%%{%%{[%%%{8,[1,1,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,3,1]%%%}+%%%{%%{[%%%{-4,[2,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,2,2]%%%}+%%%{%%%{2,[0,3,3]%%%},[0,1,5,0]%%%}+%%%{%%%{-4,[1,2,3]%%%},[0,1,4,1]%%%}+%%%{%%%{2,[2,1,3]%%%},[0,1,3,2]%%%} / %%%{%%%{1,[2,0,0]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[1,0,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
311,-2,0,0,0.000000," ","integrate(1/x^3/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{2,[1,0,0]%%%},[6,1,0,0]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,1,0]%%%}+%%%{%%%{2,[0,1,1]%%%},[4,1,2,0]%%%}+%%%{%%%{-4,[1,0,1]%%%},[4,1,1,1]%%%}+%%%{%%{[%%%{8,[0,0,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,2,1]%%%}+%%%{%%%{-4,[0,1,2]%%%},[2,1,3,1]%%%}+%%%{%%%{2,[1,0,2]%%%},[2,1,2,2]%%%}+%%%{%%{[%%%{-4,[0,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,3,2]%%%}+%%%{%%%{2,[0,1,3]%%%},[0,1,4,2]%%%} / %%%{%%%{1,[2,0,0]%%%},[6,0,0,0]%%%}+%%%{%%{[%%%{-2,[1,0,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,0,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[4,0,2,0]%%%}+%%%{%%%{-2,[2,0,1]%%%},[4,0,1,1]%%%}+%%%{%%{[%%%{4,[1,0,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,0,2,1]%%%}+%%%{%%%{-2,[1,1,2]%%%},[2,0,3,1]%%%}+%%%{%%%{1,[2,0,2]%%%},[2,0,2,2]%%%}+%%%{%%{[%%%{-2,[1,0,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,3,2]%%%}+%%%{%%%{1,[1,1,3]%%%},[0,0,4,2]%%%} Error: Bad Argument Value","F(-2)",0
312,-2,0,0,0.000000," ","integrate(1/x^5/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep*d+c)]Unable to divide, perhaps due to rounding error%%%{%%%{2,[1,4,4]%%%},[2,1,7,0]%%%}+%%%{%%%{-8,[2,3,4]%%%},[2,1,6,1]%%%}+%%%{%%%{12,[3,2,4]%%%},[2,1,5,2]%%%}+%%%{%%%{-8,[4,1,4]%%%},[2,1,4,3]%%%}+%%%{%%%{2,[5,0,4]%%%},[2,1,3,4]%%%}+%%%{%%{[%%%{-4,[0,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,8,0]%%%}+%%%{%%{[%%%{16,[1,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,7,1]%%%}+%%%{%%{[%%%{-24,[2,2,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,6,2]%%%}+%%%{%%{[%%%{16,[3,1,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,5,3]%%%}+%%%{%%{[%%%{-4,[4,0,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,4,4]%%%}+%%%{%%%{2,[0,5,5]%%%},[0,1,9,0]%%%}+%%%{%%%{-8,[1,4,5]%%%},[0,1,8,1]%%%}+%%%{%%%{12,[2,3,5]%%%},[0,1,7,2]%%%}+%%%{%%%{-8,[3,2,5]%%%},[0,1,6,3]%%%}+%%%{%%%{2,[4,1,5]%%%},[0,1,5,4]%%%} / %%%{%%%{1,[2,0,0]%%%},[2,0,0,0]%%%}+%%%{%%{[%%%{-2,[1,0,0]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,1,0]%%%}+%%%{%%%{1,[1,1,1]%%%},[0,0,2,0]%%%} Error: Bad Argument Value","F(-2)",0
313,0,0,0,0.000000," ","integrate(x^4/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)*e/(d*x^2 + c))^(3/2), x)","F",0
314,0,0,0,0.000000," ","integrate(x^2/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)*e/(d*x^2 + c))^(3/2), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((b*x^2 + a)*e/(d*x^2 + c))^(-3/2), x)","F",0
316,0,0,0,0.000000," ","integrate(1/x^2/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)*x^2), x)","F",0
317,0,0,0,0.000000," ","integrate(1/x^4/(e*(b*x^2+a)/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(\frac{{\left(b x^{2} + a\right)} e}{d x^{2} + c}\right)^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/(((b*x^2 + a)*e/(d*x^2 + c))^(3/2)*x^4), x)","F",0
318,1,219,0,0.488715," ","integrate(x^5*(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{d} - \frac{4 \, a^{2} c d^{3} - a b d^{3}}{a^{2} d^{5}}\right)} + \frac{8 \, a^{2} c^{2} d^{2} - 10 \, a b c d^{2} - 3 \, b^{2} d^{2}}{a^{2} d^{5}}\right)} - \frac{3 \, {\left(8 \, a^{2} b c^{2} + 4 \, a b^{2} c + b^{3}\right)} \log\left({\left| -2 \, a c d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} \sqrt{a} {\left| d \right|} - b d \right|}\right)}{a^{\frac{5}{2}} d^{2} {\left| d \right|}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/96*(2*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*x^2*(4*x^2/d - (4*a^2*c*d^3 - a*b*d^3)/(a^2*d^5)) + (8*a^2*c^2*d^2 - 10*a*b*c*d^2 - 3*b^2*d^2)/(a^2*d^5)) - 3*(8*a^2*b*c^2 + 4*a*b^2*c + b^3)*log(abs(-2*a*c*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*sqrt(a)*abs(d) - b*d))/(a^(5/2)*d^2*abs(d)))*sgn(d*x^2 + c)","A",0
319,1,159,0,0.437687," ","integrate(x^3*(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, {\left(2 \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(\frac{2 \, x^{2}}{d} - \frac{2 \, a c d - b d}{a d^{3}}\right)} + \frac{{\left(4 \, a b c + b^{2}\right)} \log\left({\left| -2 \, a c d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} \sqrt{a} {\left| d \right|} - b d \right|}\right)}{a^{\frac{3}{2}} d {\left| d \right|}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/16*(2*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*x^2/d - (2*a*c*d - b*d)/(a*d^3)) + (4*a*b*c + b^2)*log(abs(-2*a*c*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*sqrt(a)*abs(d) - b*d))/(a^(3/2)*d*abs(d)))*sgn(d*x^2 + c)","A",0
320,1,127,0,0.511379," ","integrate(x*(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{b \log\left({\left| -8 \, a^{\frac{3}{2}} c d - 8 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a {\left| d \right|} - 4 \, \sqrt{a} b d \right|}\right)}{\sqrt{a} {\left| d \right|}} - \frac{2 \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{d}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"-1/4*(b*log(abs(-8*a^(3/2)*c*d - 8*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*abs(d) - 4*sqrt(a)*b*d))/(sqrt(a)*abs(d)) - 2*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)/d)*sgn(d*x^2 + c)","B",0
321,-2,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*x^2+c)]Error: Bad Argument Type","F(-2)",0
322,1,281,0,0.464755," ","integrate((a+b/(d*x^2+c))^(1/2)/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{b d \arctan\left(-\frac{\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{\sqrt{-a c^{2} - b c}}\right)}{\sqrt{-a c^{2} - b c} c} + \frac{2 \, a^{\frac{3}{2}} c^{2} {\left| d \right|} + 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a c d + 2 \, \sqrt{a} b c {\left| d \right|} + {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} b d}{{\left(a c^{2} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} + b c\right)} c}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"-1/2*(b*d*arctan(-(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))/sqrt(-a*c^2 - b*c))/(sqrt(-a*c^2 - b*c)*c) + (2*a^(3/2)*c^2*abs(d) + 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*c*d + 2*sqrt(a)*b*c*abs(d) + (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*b*d)/((a*c^2 - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2 + b*c)*c))*sgn(d*x^2 + c)","B",0
323,1,713,0,0.584267," ","integrate((a+b/(d*x^2+c))^(1/2)/x^5,x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{{\left(4 \, a b c d^{2} + 3 \, b^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{\sqrt{-a c^{2} - b c}}\right)}{{\left(a c^{3} + b c^{2}\right)} \sqrt{-a c^{2} - b c}} + \frac{8 \, a^{\frac{7}{2}} c^{5} d {\left| d \right|} + 16 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{3} c^{4} d^{2} + 8 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{5}{2}} c^{3} d {\left| d \right|} + 24 \, a^{\frac{5}{2}} b c^{4} d {\left| d \right|} + 36 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} b c^{3} d^{2} + 8 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} b c^{2} d {\left| d \right|} + 24 \, a^{\frac{3}{2}} b^{2} c^{3} d {\left| d \right|} - 4 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a b c d^{2} + 25 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b^{2} c^{2} d^{2} + 8 \, \sqrt{a} b^{3} c^{2} d {\left| d \right|} - 3 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} b^{2} d^{2} + 5 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} b^{3} c d^{2}}{{\left(a c^{3} + b c^{2}\right)} {\left(a c^{2} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} + b c\right)}^{2}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"1/8*((4*a*b*c*d^2 + 3*b^2*d^2)*arctan(-(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))/sqrt(-a*c^2 - b*c))/((a*c^3 + b*c^2)*sqrt(-a*c^2 - b*c)) + (8*a^(7/2)*c^5*d*abs(d) + 16*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^3*c^4*d^2 + 8*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(5/2)*c^3*d*abs(d) + 24*a^(5/2)*b*c^4*d*abs(d) + 36*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*b*c^3*d^2 + 8*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*b*c^2*d*abs(d) + 24*a^(3/2)*b^2*c^3*d*abs(d) - 4*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a*b*c*d^2 + 25*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b^2*c^2*d^2 + 8*sqrt(a)*b^3*c^2*d*abs(d) - 3*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*b^2*d^2 + 5*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*b^3*c*d^2)/((a*c^3 + b*c^2)*(a*c^2 - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2 + b*c)^2))*sgn(d*x^2 + c)","B",0
324,1,1414,0,0.771569," ","integrate((a+b/(d*x^2+c))^(1/2)/x^7,x, algorithm=""giac"")","-\frac{1}{48} \, {\left(\frac{3 \, {\left(8 \, a^{2} b c^{2} d^{3} + 12 \, a b^{2} c d^{3} + 5 \, b^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{\sqrt{-a c^{2} - b c}}\right)}{{\left(a^{2} c^{5} + 2 \, a b c^{4} + b^{2} c^{3}\right)} \sqrt{-a c^{2} - b c}} + \frac{64 \, a^{\frac{11}{2}} c^{8} d^{2} {\left| d \right|} + 192 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{5} c^{7} d^{3} + 192 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{9}{2}} c^{6} d^{2} {\left| d \right|} + 304 \, a^{\frac{9}{2}} b c^{7} d^{2} {\left| d \right|} + 64 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a^{4} c^{5} d^{3} + 744 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{4} b c^{6} d^{3} + 528 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{7}{2}} b c^{5} d^{2} {\left| d \right|} + 576 \, a^{\frac{7}{2}} b^{2} c^{6} d^{2} {\left| d \right|} + 64 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a^{3} b c^{4} d^{3} + 1116 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{3} b^{2} c^{5} d^{3} + 480 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{5}{2}} b^{2} c^{4} d^{2} {\left| d \right|} + 544 \, a^{\frac{5}{2}} b^{3} c^{5} d^{2} {\left| d \right|} + 24 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{5} a^{2} b c^{2} d^{3} - 96 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a^{2} b^{2} c^{3} d^{3} + 801 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} b^{3} c^{4} d^{3} + 144 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} b^{3} c^{3} d^{2} {\left| d \right|} + 256 \, a^{\frac{3}{2}} b^{4} c^{4} d^{2} {\left| d \right|} + 36 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{5} a b^{2} c d^{3} - 136 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a b^{3} c^{2} d^{3} + 270 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b^{4} c^{3} d^{3} + 48 \, \sqrt{a} b^{5} c^{3} d^{2} {\left| d \right|} + 15 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{5} b^{3} d^{3} - 40 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} b^{4} c d^{3} + 33 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} b^{5} c^{2} d^{3}}{{\left(a^{2} c^{5} + 2 \, a b c^{4} + b^{2} c^{3}\right)} {\left(a c^{2} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} + b c\right)}^{3}}\right)} \mathrm{sgn}\left(d x^{2} + c\right)"," ",0,"-1/48*(3*(8*a^2*b*c^2*d^3 + 12*a*b^2*c*d^3 + 5*b^3*d^3)*arctan(-(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))/sqrt(-a*c^2 - b*c))/((a^2*c^5 + 2*a*b*c^4 + b^2*c^3)*sqrt(-a*c^2 - b*c)) + (64*a^(11/2)*c^8*d^2*abs(d) + 192*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^5*c^7*d^3 + 192*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(9/2)*c^6*d^2*abs(d) + 304*a^(9/2)*b*c^7*d^2*abs(d) + 64*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a^4*c^5*d^3 + 744*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^4*b*c^6*d^3 + 528*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(7/2)*b*c^5*d^2*abs(d) + 576*a^(7/2)*b^2*c^6*d^2*abs(d) + 64*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a^3*b*c^4*d^3 + 1116*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^3*b^2*c^5*d^3 + 480*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(5/2)*b^2*c^4*d^2*abs(d) + 544*a^(5/2)*b^3*c^5*d^2*abs(d) + 24*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^5*a^2*b*c^2*d^3 - 96*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a^2*b^2*c^3*d^3 + 801*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*b^3*c^4*d^3 + 144*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*b^3*c^3*d^2*abs(d) + 256*a^(3/2)*b^4*c^4*d^2*abs(d) + 36*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^5*a*b^2*c*d^3 - 136*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a*b^3*c^2*d^3 + 270*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b^4*c^3*d^3 + 48*sqrt(a)*b^5*c^3*d^2*abs(d) + 15*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^5*b^3*d^3 - 40*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*b^4*c*d^3 + 33*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*b^5*c^2*d^3)/((a^2*c^5 + 2*a*b*c^4 + b^2*c^3)*(a*c^2 - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2 + b*c)^3))*sgn(d*x^2 + c)","B",0
325,0,0,0,0.000000," ","integrate(x^4*(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{d x^{2} + c}} x^{4}\,{d x}"," ",0,"integrate(sqrt(a + b/(d*x^2 + c))*x^4, x)","F",0
326,0,0,0,0.000000," ","integrate(x^2*(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{d x^{2} + c}} x^{2}\,{d x}"," ",0,"integrate(sqrt(a + b/(d*x^2 + c))*x^2, x)","F",0
327,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a + \frac{b}{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(a + b/(d*x^2 + c)), x)","F",0
328,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{d x^{2} + c}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a + b/(d*x^2 + c))/x^2, x)","F",0
329,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{d x^{2} + c}}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(a + b/(d*x^2 + c))/x^4, x)","F",0
330,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{a + \frac{b}{d x^{2} + c}}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(a + b/(d*x^2 + c))/x^6, x)","F",0
331,1,527,0,2.104399," ","integrate(x^5*(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(2 \, {\left(\frac{4 \, a x^{2} \mathrm{sgn}\left(d x^{2} + c\right)}{d} - \frac{4 \, a^{3} c d^{6} \mathrm{sgn}\left(d x^{2} + c\right) - 7 \, a^{2} b d^{6} \mathrm{sgn}\left(d x^{2} + c\right)}{a^{2} d^{8}}\right)} x^{2} + \frac{8 \, a^{3} c^{2} d^{5} \mathrm{sgn}\left(d x^{2} + c\right) - 46 \, a^{2} b c d^{5} \mathrm{sgn}\left(d x^{2} + c\right) + 3 \, a b^{2} d^{5} \mathrm{sgn}\left(d x^{2} + c\right)}{a^{2} d^{8}}\right)} - \frac{{\left(24 \, a^{\frac{5}{2}} b c^{2} \mathrm{sgn}\left(d x^{2} + c\right) - 12 \, a^{\frac{3}{2}} b^{2} c \mathrm{sgn}\left(d x^{2} + c\right) - \sqrt{a} b^{3} \mathrm{sgn}\left(d x^{2} + c\right)\right)} \log\left({\left| -2 \, a^{\frac{5}{2}} c^{3} d - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} c^{2} {\left| d \right|} - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} c d - a^{\frac{3}{2}} b c^{2} d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a {\left| d \right|} - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b c {\left| d \right|} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} \sqrt{a} b d \right|}\right)}{96 \, a^{2} d^{2} {\left| d \right|}}"," ",0,"1/48*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*(4*a*x^2*sgn(d*x^2 + c)/d - (4*a^3*c*d^6*sgn(d*x^2 + c) - 7*a^2*b*d^6*sgn(d*x^2 + c))/(a^2*d^8))*x^2 + (8*a^3*c^2*d^5*sgn(d*x^2 + c) - 46*a^2*b*c*d^5*sgn(d*x^2 + c) + 3*a*b^2*d^5*sgn(d*x^2 + c))/(a^2*d^8)) - 1/96*(24*a^(5/2)*b*c^2*sgn(d*x^2 + c) - 12*a^(3/2)*b^2*c*sgn(d*x^2 + c) - sqrt(a)*b^3*sgn(d*x^2 + c))*log(abs(-2*a^(5/2)*c^3*d - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*c^2*abs(d) - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*c*d - a^(3/2)*b*c^2*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a*abs(d) - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b*c*abs(d) - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*sqrt(a)*b*d))/(a^2*d^2*abs(d))","B",0
332,1,438,0,1.992284," ","integrate(x^3*(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(\frac{2 \, a x^{2} \mathrm{sgn}\left(d x^{2} + c\right)}{d} - \frac{2 \, a^{2} c d^{2} \mathrm{sgn}\left(d x^{2} + c\right) - 5 \, a b d^{2} \mathrm{sgn}\left(d x^{2} + c\right)}{a d^{4}}\right)} + \frac{{\left(4 \, a^{\frac{3}{2}} b c \mathrm{sgn}\left(d x^{2} + c\right) - \sqrt{a} b^{2} \mathrm{sgn}\left(d x^{2} + c\right)\right)} \log\left({\left| -2 \, a^{\frac{5}{2}} c^{3} d - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} c^{2} {\left| d \right|} - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} c d - a^{\frac{3}{2}} b c^{2} d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a {\left| d \right|} - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b c {\left| d \right|} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} \sqrt{a} b d \right|}\right)}{16 \, a d {\left| d \right|}}"," ",0,"1/8*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*a*x^2*sgn(d*x^2 + c)/d - (2*a^2*c*d^2*sgn(d*x^2 + c) - 5*a*b*d^2*sgn(d*x^2 + c))/(a*d^4)) + 1/16*(4*a^(3/2)*b*c*sgn(d*x^2 + c) - sqrt(a)*b^2*sgn(d*x^2 + c))*log(abs(-2*a^(5/2)*c^3*d - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*c^2*abs(d) - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*c*d - a^(3/2)*b*c^2*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a*abs(d) - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b*c*abs(d) - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*sqrt(a)*b*d))/(a*d*abs(d))","B",0
333,1,387,0,1.819528," ","integrate(x*(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{a} b \log\left({\left| -2 \, a^{\frac{5}{2}} c^{3} d - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} c^{2} {\left| d \right|} - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} c d - a^{\frac{3}{2}} b c^{2} d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a {\left| d \right|} - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b c {\left| d \right|} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} \sqrt{a} b d \right|}\right) \mathrm{sgn}\left(d x^{2} + c\right)}{4 \, {\left| d \right|}} - \frac{\sqrt{a} b {\left| d \right|} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(d x^{2} + c\right)}{4 \, d^{2}} + \frac{\sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} a \mathrm{sgn}\left(d x^{2} + c\right)}{2 \, d}"," ",0,"-1/4*sqrt(a)*b*log(abs(-2*a^(5/2)*c^3*d - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*c^2*abs(d) - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*c*d - a^(3/2)*b*c^2*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a*abs(d) - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b*c*abs(d) - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*sqrt(a)*b*d))*sgn(d*x^2 + c)/abs(d) - 1/4*sqrt(a)*b*abs(d)*log(abs(a))*sgn(d*x^2 + c)/d^2 + 1/2*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*a*sgn(d*x^2 + c)/d","B",0
334,-2,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*x^2+c)]Evaluation time: 0.71Error: Bad Argument Type","F(-2)",0
335,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x^3,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
336,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x^5,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
337,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x^7,x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
338,0,0,0,0.000000," ","integrate(x^4*(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int {\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}} x^{4}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(3/2)*x^4, x)","F",0
339,0,0,0,0.000000," ","integrate(x^2*(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int {\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(3/2)*x^2, x)","F",0
340,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int {\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(3/2)/x^2, x)","F",0
342,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}}{x^{4}}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(3/2)/x^4, x)","F",0
343,0,0,0,0.000000," ","integrate((a+b/(d*x^2+c))^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}}{x^{6}}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(3/2)/x^6, x)","F",0
344,1,274,0,0.566496," ","integrate(x^5/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{a d \mathrm{sgn}\left(d x^{2} + c\right)} - \frac{4 \, a^{2} c d^{3} \mathrm{sgn}\left(d x^{2} + c\right) + 5 \, a b d^{3} \mathrm{sgn}\left(d x^{2} + c\right)}{a^{3} d^{5}}\right)} + \frac{8 \, a^{2} c^{2} d^{2} \mathrm{sgn}\left(d x^{2} + c\right) + 26 \, a b c d^{2} \mathrm{sgn}\left(d x^{2} + c\right) + 15 \, b^{2} d^{2} \mathrm{sgn}\left(d x^{2} + c\right)}{a^{3} d^{5}}\right)} + \frac{{\left(8 \, a^{2} b c^{2} + 12 \, a b^{2} c + 5 \, b^{3}\right)} \log\left({\left| -2 \, a c d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} \sqrt{a} {\left| d \right|} - b d \right|}\right)}{32 \, a^{\frac{7}{2}} d^{2} {\left| d \right|} \mathrm{sgn}\left(d x^{2} + c\right)}"," ",0,"1/48*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*x^2*(4*x^2/(a*d*sgn(d*x^2 + c)) - (4*a^2*c*d^3*sgn(d*x^2 + c) + 5*a*b*d^3*sgn(d*x^2 + c))/(a^3*d^5)) + (8*a^2*c^2*d^2*sgn(d*x^2 + c) + 26*a*b*c*d^2*sgn(d*x^2 + c) + 15*b^2*d^2*sgn(d*x^2 + c))/(a^3*d^5)) + 1/32*(8*a^2*b*c^2 + 12*a*b^2*c + 5*b^3)*log(abs(-2*a*c*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*sqrt(a)*abs(d) - b*d))/(a^(7/2)*d^2*abs(d)*sgn(d*x^2 + c))","A",0
345,1,191,0,0.524082," ","integrate(x^3/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(\frac{2 \, x^{2}}{a d \mathrm{sgn}\left(d x^{2} + c\right)} - \frac{2 \, a c d \mathrm{sgn}\left(d x^{2} + c\right) + 3 \, b d \mathrm{sgn}\left(d x^{2} + c\right)}{a^{2} d^{3}}\right)} - \frac{{\left(4 \, a b c + 3 \, b^{2}\right)} \log\left({\left| -2 \, a c d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} \sqrt{a} {\left| d \right|} - b d \right|}\right)}{16 \, a^{\frac{5}{2}} d {\left| d \right|} \mathrm{sgn}\left(d x^{2} + c\right)}"," ",0,"1/8*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*x^2/(a*d*sgn(d*x^2 + c)) - (2*a*c*d*sgn(d*x^2 + c) + 3*b*d*sgn(d*x^2 + c))/(a^2*d^3)) - 1/16*(4*a*b*c + 3*b^2)*log(abs(-2*a*c*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*sqrt(a)*abs(d) - b*d))/(a^(5/2)*d*abs(d)*sgn(d*x^2 + c))","A",0
346,1,138,0,0.506973," ","integrate(x/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, a c d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} \sqrt{a} {\left| d \right|} - b d \right|}\right)}{4 \, a^{\frac{3}{2}} {\left| d \right|} \mathrm{sgn}\left(d x^{2} + c\right)} + \frac{\sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{2 \, a d \mathrm{sgn}\left(d x^{2} + c\right)}"," ",0,"1/4*b*log(abs(-2*a*c*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*sqrt(a)*abs(d) - b*d))/(a^(3/2)*abs(d)*sgn(d*x^2 + c)) + 1/2*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)/(a*d*sgn(d*x^2 + c))","B",0
347,-2,0,0,0.000000," ","integrate(1/x/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(c+d*t_nostep)]Error: Bad Argument Type","F(-2)",0
348,1,315,0,0.697157," ","integrate(1/x^3/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\frac{b d \arctan\left(-\frac{\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{\sqrt{-a c^{2} - b c}}\right)}{2 \, \sqrt{-a c^{2} - b c} {\left(a c \mathrm{sgn}\left(d x^{2} + c\right) + b \mathrm{sgn}\left(d x^{2} + c\right)\right)}} - \frac{2 \, a^{\frac{3}{2}} c^{2} {\left| d \right|} + 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a c d + 2 \, \sqrt{a} b c {\left| d \right|} + {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} b d}{2 \, {\left(a c^{2} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} + b c\right)} {\left(a c \mathrm{sgn}\left(d x^{2} + c\right) + b \mathrm{sgn}\left(d x^{2} + c\right)\right)}}"," ",0,"1/2*b*d*arctan(-(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))/sqrt(-a*c^2 - b*c))/(sqrt(-a*c^2 - b*c)*(a*c*sgn(d*x^2 + c) + b*sgn(d*x^2 + c))) - 1/2*(2*a^(3/2)*c^2*abs(d) + 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*c*d + 2*sqrt(a)*b*c*abs(d) + (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*b*d)/((a*c^2 - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2 + b*c)*(a*c*sgn(d*x^2 + c) + b*sgn(d*x^2 + c)))","B",0
349,1,815,0,10.391531," ","integrate(1/x^5/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, a b c d^{2} + b^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{\sqrt{-a c^{2} - b c}}\right)}{8 \, {\left(a^{2} c^{3} \mathrm{sgn}\left(d x^{2} + c\right) + 2 \, a b c^{2} \mathrm{sgn}\left(d x^{2} + c\right) + b^{2} c \mathrm{sgn}\left(d x^{2} + c\right)\right)} \sqrt{-a c^{2} - b c}} + \frac{8 \, a^{\frac{7}{2}} c^{5} d {\left| d \right|} + 16 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{3} c^{4} d^{2} + 8 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{5}{2}} c^{3} d {\left| d \right|} + 16 \, a^{\frac{5}{2}} b c^{4} d {\left| d \right|} + 28 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} b c^{3} d^{2} + 16 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} b c^{2} d {\left| d \right|} + 8 \, a^{\frac{3}{2}} b^{2} c^{3} d {\left| d \right|} + 4 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a b c d^{2} + 13 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b^{2} c^{2} d^{2} + 8 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} \sqrt{a} b^{2} c d {\left| d \right|} + {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} b^{2} d^{2} + {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} b^{3} c d^{2}}{8 \, {\left(a^{2} c^{3} \mathrm{sgn}\left(d x^{2} + c\right) + 2 \, a b c^{2} \mathrm{sgn}\left(d x^{2} + c\right) + b^{2} c \mathrm{sgn}\left(d x^{2} + c\right)\right)} {\left(a c^{2} - {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} + b c\right)}^{2}}"," ",0,"-1/8*(4*a*b*c*d^2 + b^2*d^2)*arctan(-(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))/sqrt(-a*c^2 - b*c))/((a^2*c^3*sgn(d*x^2 + c) + 2*a*b*c^2*sgn(d*x^2 + c) + b^2*c*sgn(d*x^2 + c))*sqrt(-a*c^2 - b*c)) + 1/8*(8*a^(7/2)*c^5*d*abs(d) + 16*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^3*c^4*d^2 + 8*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(5/2)*c^3*d*abs(d) + 16*a^(5/2)*b*c^4*d*abs(d) + 28*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*b*c^3*d^2 + 16*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*b*c^2*d*abs(d) + 8*a^(3/2)*b^2*c^3*d*abs(d) + 4*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a*b*c*d^2 + 13*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b^2*c^2*d^2 + 8*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*sqrt(a)*b^2*c*d*abs(d) + (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*b^2*d^2 + (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*b^3*c*d^2)/((a^2*c^3*sgn(d*x^2 + c) + 2*a*b*c^2*sgn(d*x^2 + c) + b^2*c*sgn(d*x^2 + c))*(a*c^2 - (sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2 + b*c)^2)","B",0
350,0,0,0,0.000000," ","integrate(x^4/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{a + \frac{b}{d x^{2} + c}}}\,{d x}"," ",0,"integrate(x^4/sqrt(a + b/(d*x^2 + c)), x)","F",0
351,0,0,0,0.000000," ","integrate(x^2/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{a + \frac{b}{d x^{2} + c}}}\,{d x}"," ",0,"integrate(x^2/sqrt(a + b/(d*x^2 + c)), x)","F",0
352,0,0,0,0.000000," ","integrate(1/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{d x^{2} + c}}}\,{d x}"," ",0,"integrate(1/sqrt(a + b/(d*x^2 + c)), x)","F",0
353,0,0,0,0.000000," ","integrate(1/x^2/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{d x^{2} + c}} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/(d*x^2 + c))*x^2), x)","F",0
354,0,0,0,0.000000," ","integrate(1/x^4/(a+b/(d*x^2+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a + \frac{b}{d x^{2} + c}} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(a + b/(d*x^2 + c))*x^4), x)","F",0
355,1,597,0,1.670382," ","integrate(x^5/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(2 \, x^{2} {\left(\frac{4 \, x^{2}}{a^{2} d \mathrm{sgn}\left(d x^{2} + c\right)} - \frac{4 \, a^{11} c d^{6} \mathrm{sgn}\left(d x^{2} + c\right) + 11 \, a^{10} b d^{6} \mathrm{sgn}\left(d x^{2} + c\right)}{a^{13} d^{8}}\right)} + \frac{8 \, a^{11} c^{2} d^{5} \mathrm{sgn}\left(d x^{2} + c\right) + 62 \, a^{10} b c d^{5} \mathrm{sgn}\left(d x^{2} + c\right) + 57 \, a^{9} b^{2} d^{5} \mathrm{sgn}\left(d x^{2} + c\right)}{a^{13} d^{8}}\right)} + \frac{{\left(24 \, a^{\frac{5}{2}} b c^{2} + 60 \, a^{\frac{3}{2}} b^{2} c + 35 \, \sqrt{a} b^{3}\right)} \log\left({\left| -2 \, a^{\frac{7}{2}} c^{3} d - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{3} c^{2} {\left| d \right|} - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{5}{2}} c d - 5 \, a^{\frac{5}{2}} b c^{2} d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a^{2} {\left| d \right|} - 10 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} b c {\left| d \right|} - 5 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} b d - 4 \, a^{\frac{3}{2}} b^{2} c d - 4 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b^{2} {\left| d \right|} - \sqrt{a} b^{3} d \right|}\right)}{96 \, a^{5} d^{2} {\left| d \right|} \mathrm{sgn}\left(d x^{2} + c\right)}"," ",0,"1/48*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*x^2*(4*x^2/(a^2*d*sgn(d*x^2 + c)) - (4*a^11*c*d^6*sgn(d*x^2 + c) + 11*a^10*b*d^6*sgn(d*x^2 + c))/(a^13*d^8)) + (8*a^11*c^2*d^5*sgn(d*x^2 + c) + 62*a^10*b*c*d^5*sgn(d*x^2 + c) + 57*a^9*b^2*d^5*sgn(d*x^2 + c))/(a^13*d^8)) + 1/96*(24*a^(5/2)*b*c^2 + 60*a^(3/2)*b^2*c + 35*sqrt(a)*b^3)*log(abs(-2*a^(7/2)*c^3*d - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^3*c^2*abs(d) - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(5/2)*c*d - 5*a^(5/2)*b*c^2*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a^2*abs(d) - 10*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*b*c*abs(d) - 5*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*b*d - 4*a^(3/2)*b^2*c*d - 4*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b^2*abs(d) - sqrt(a)*b^3*d))/(a^5*d^2*abs(d)*sgn(d*x^2 + c))","B",0
356,1,510,0,1.574346," ","integrate(x^3/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c} {\left(\frac{2 \, x^{2}}{a^{2} d \mathrm{sgn}\left(d x^{2} + c\right)} - \frac{2 \, a^{6} c d^{2} + 7 \, a^{5} b d^{2}}{a^{8} d^{4} \mathrm{sgn}\left(d x^{2} + c\right)}\right)} - \frac{{\left(4 \, a^{\frac{3}{2}} b c + 5 \, \sqrt{a} b^{2}\right)} \log\left({\left| -2 \, a^{\frac{7}{2}} c^{3} d - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{3} c^{2} {\left| d \right|} - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{5}{2}} c d - 5 \, a^{\frac{5}{2}} b c^{2} d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a^{2} {\left| d \right|} - 10 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} b c {\left| d \right|} - 5 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} b d - 4 \, a^{\frac{3}{2}} b^{2} c d - 4 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b^{2} {\left| d \right|} - \sqrt{a} b^{3} d \right|}\right)}{16 \, a^{4} d {\left| d \right|} \mathrm{sgn}\left(d x^{2} + c\right)}"," ",0,"1/8*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)*(2*x^2/(a^2*d*sgn(d*x^2 + c)) - (2*a^6*c*d^2 + 7*a^5*b*d^2)/(a^8*d^4*sgn(d*x^2 + c))) - 1/16*(4*a^(3/2)*b*c + 5*sqrt(a)*b^2)*log(abs(-2*a^(7/2)*c^3*d - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^3*c^2*abs(d) - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(5/2)*c*d - 5*a^(5/2)*b*c^2*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a^2*abs(d) - 10*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*b*c*abs(d) - 5*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*b*d - 4*a^(3/2)*b^2*c*d - 4*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b^2*abs(d) - sqrt(a)*b^3*d))/(a^4*d*abs(d)*sgn(d*x^2 + c))","B",0
357,1,449,0,1.547686," ","integrate(x/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, a^{\frac{7}{2}} c^{3} d - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{3} c^{2} {\left| d \right|} - 6 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{5}{2}} c d - 5 \, a^{\frac{5}{2}} b c^{2} d - 2 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{3} a^{2} {\left| d \right|} - 10 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a^{2} b c {\left| d \right|} - 5 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)}^{2} a^{\frac{3}{2}} b d - 4 \, a^{\frac{3}{2}} b^{2} c d - 4 \, {\left(\sqrt{a d^{2}} x^{2} - \sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}\right)} a b^{2} {\left| d \right|} - \sqrt{a} b^{3} d \right|}\right)}{4 \, a^{\frac{5}{2}} {\left| d \right|} \mathrm{sgn}\left(d x^{2} + c\right)} + \frac{\sqrt{a d^{2} x^{4} + 2 \, a c d x^{2} + b d x^{2} + a c^{2} + b c}}{2 \, a^{2} d \mathrm{sgn}\left(d x^{2} + c\right)}"," ",0,"1/4*b*log(abs(-2*a^(7/2)*c^3*d - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^3*c^2*abs(d) - 6*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(5/2)*c*d - 5*a^(5/2)*b*c^2*d - 2*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^3*a^2*abs(d) - 10*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a^2*b*c*abs(d) - 5*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))^2*a^(3/2)*b*d - 4*a^(3/2)*b^2*c*d - 4*(sqrt(a*d^2)*x^2 - sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c))*a*b^2*abs(d) - sqrt(a)*b^3*d))/(a^(5/2)*abs(d)*sgn(d*x^2 + c)) + 1/2*sqrt(a*d^2*x^4 + 2*a*c*d*x^2 + b*d*x^2 + a*c^2 + b*c)/(a^2*d*sgn(d*x^2 + c))","B",0
358,-2,0,0,0.000000," ","integrate(1/x/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(c+d*t_nostep)]Error: Bad Argument Type","F(-2)",0
359,0,0,0,0.000000," ","integrate(1/x^3/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
360,0,0,0,0.000000," ","integrate(1/x^5/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
361,0,0,0,0.000000," ","integrate(x^4/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/(a + b/(d*x^2 + c))^(3/2), x)","F",0
362,0,0,0,0.000000," ","integrate(x^2/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(a + b/(d*x^2 + c))^(3/2), x)","F",0
363,0,0,0,0.000000," ","integrate(1/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a + b/(d*x^2 + c))^(-3/2), x)","F",0
364,0,0,0,0.000000," ","integrate(1/x^2/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((a + b/(d*x^2 + c))^(3/2)*x^2), x)","F",0
365,0,0,0,0.000000," ","integrate(1/x^4/(a+b/(d*x^2+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a + \frac{b}{d x^{2} + c}\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((a + b/(d*x^2 + c))^(3/2)*x^4), x)","F",0
366,0,0,0,0.000000," ","integrate((a*x^23)^(1/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{23}}}{\sqrt{x^{5} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^23)/sqrt(x^5 + 1), x)","F",0
367,1,68,0,0.315410," ","integrate((a*x^13)^(1/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","\frac{a^{\frac{11}{2}} \log\left(-\sqrt{a x} a^{\frac{5}{2}} x^{2} + \sqrt{a^{6} x^{5} + a^{6}}\right)}{5 \, {\left| a \right|}^{5}} + \frac{\sqrt{a^{6} x^{5} + a^{6}} \sqrt{a x} x^{2}}{5 \, a^{2} {\left| a \right|}}"," ",0,"1/5*a^(11/2)*log(-sqrt(a*x)*a^(5/2)*x^2 + sqrt(a^6*x^5 + a^6))/abs(a)^5 + 1/5*sqrt(a^6*x^5 + a^6)*sqrt(a*x)*x^2/(a^2*abs(a))","A",0
368,1,58,0,0.190636," ","integrate((a*x^3)^(1/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","-\frac{2 \, a^{\frac{3}{2}} \log\left(-\sqrt{a x} a^{\frac{5}{2}} x^{2} + \sqrt{a^{6} x^{5} + a^{6}}\right) \mathrm{sgn}\left(x\right)}{5 \, {\left| a \right|}} + \frac{2 \, a^{\frac{3}{2}} \log\left(a^{2} {\left| a \right|}\right) \mathrm{sgn}\left(x\right)}{5 \, {\left| a \right|}}"," ",0,"-2/5*a^(3/2)*log(-sqrt(a*x)*a^(5/2)*x^2 + sqrt(a^6*x^5 + a^6))*sgn(x)/abs(a) + 2/5*a^(3/2)*log(a^2*abs(a))*sgn(x)/abs(a)","B",0
369,1,28,0,0.240190," ","integrate((a/x^7)^(1/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","-\frac{2 \, a^{4} {\left(\frac{\sqrt{a + \frac{a}{x^{5}}}}{a^{3}} - \frac{1}{a^{\frac{5}{2}}}\right)}}{5 \, {\left| a \right|}}"," ",0,"-2/5*a^4*(sqrt(a + a/x^5)/a^3 - 1/a^(5/2))/abs(a)","A",0
370,-2,0,0,0.000000," ","integrate((a/x^17)^(1/2)/(x^5+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
371,1,29,0,0.184691," ","integrate((a*x^6)^(1/2)/x/(-x^4+1),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(2 \, \arctan\left(x\right) \mathrm{sgn}\left(x\right) - \log\left({\left| x + 1 \right|}\right) \mathrm{sgn}\left(x\right) + \log\left({\left| x - 1 \right|}\right) \mathrm{sgn}\left(x\right)\right)} \sqrt{a}"," ",0,"-1/4*(2*arctan(x)*sgn(x) - log(abs(x + 1))*sgn(x) + log(abs(x - 1))*sgn(x))*sqrt(a)","A",0
372,1,29,0,0.196563," ","integrate((a*x^6)^(1/2)/(-x^5+x),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(2 \, \arctan\left(x\right) \mathrm{sgn}\left(x\right) - \log\left({\left| x + 1 \right|}\right) \mathrm{sgn}\left(x\right) + \log\left({\left| x - 1 \right|}\right) \mathrm{sgn}\left(x\right)\right)} \sqrt{a}"," ",0,"-1/4*(2*arctan(x)*sgn(x) - log(abs(x + 1))*sgn(x) + log(abs(x - 1))*sgn(x))*sqrt(a)","A",0
373,1,42,0,0.175047," ","integrate((a*x^6)^(3/2)/x/(-x^4+1),x, algorithm=""giac"")","-\frac{1}{20} \, {\left(4 \, x^{5} \mathrm{sgn}\left(x\right) + 20 \, x \mathrm{sgn}\left(x\right) - 10 \, \arctan\left(x\right) \mathrm{sgn}\left(x\right) - 5 \, \log\left({\left| x + 1 \right|}\right) \mathrm{sgn}\left(x\right) + 5 \, \log\left({\left| x - 1 \right|}\right) \mathrm{sgn}\left(x\right)\right)} a^{\frac{3}{2}}"," ",0,"-1/20*(4*x^5*sgn(x) + 20*x*sgn(x) - 10*arctan(x)*sgn(x) - 5*log(abs(x + 1))*sgn(x) + 5*log(abs(x - 1))*sgn(x))*a^(3/2)","A",0
374,1,48,0,0.182289," ","integrate(1/(-x^4+1)-(a*x^6)^(1/2)/x/(-x^4+1),x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, \arctan\left(x\right) \mathrm{sgn}\left(x\right) - \log\left({\left| x + 1 \right|}\right) \mathrm{sgn}\left(x\right) + \log\left({\left| x - 1 \right|}\right) \mathrm{sgn}\left(x\right)\right)} \sqrt{a} + \frac{1}{2} \, \arctan\left(x\right) + \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/4*(2*arctan(x)*sgn(x) - log(abs(x + 1))*sgn(x) + log(abs(x - 1))*sgn(x))*sqrt(a) + 1/2*arctan(x) + 1/4*log(abs(x + 1)) - 1/4*log(abs(x - 1))","A",0
375,1,48,0,0.193612," ","integrate(1/(-x^4+1)-(a*x^6)^(1/2)/(-x^5+x),x, algorithm=""giac"")","\frac{1}{4} \, {\left(2 \, \arctan\left(x\right) \mathrm{sgn}\left(x\right) - \log\left({\left| x + 1 \right|}\right) \mathrm{sgn}\left(x\right) + \log\left({\left| x - 1 \right|}\right) \mathrm{sgn}\left(x\right)\right)} \sqrt{a} + \frac{1}{2} \, \arctan\left(x\right) + \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/4*(2*arctan(x)*sgn(x) - log(abs(x + 1))*sgn(x) + log(abs(x - 1))*sgn(x))*sqrt(a) + 1/2*arctan(x) + 1/4*log(abs(x + 1)) - 1/4*log(abs(x - 1))","A",0
376,1,43,0,0.211952," ","integrate((a*x^3)^(1/2)/(-x^3+x),x, algorithm=""giac"")","-\frac{{\left(\frac{a^{2} \arctan\left(\frac{\sqrt{a x}}{\sqrt{-a}}\right)}{\sqrt{-a}} + a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{a x}}{\sqrt{a}}\right)\right)} \mathrm{sgn}\left(x\right)}{a}"," ",0,"-(a^2*arctan(sqrt(a*x)/sqrt(-a))/sqrt(-a) + a^(3/2)*arctan(sqrt(a*x)/sqrt(a)))*sgn(x)/a","A",0
377,1,27,0,0.193856," ","integrate((a*x^4)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\sqrt{x^{2} + 1} x + \log\left(-x + \sqrt{x^{2} + 1}\right)\right)} \sqrt{a}"," ",0,"1/2*(sqrt(x^2 + 1)*x + log(-x + sqrt(x^2 + 1)))*sqrt(a)","A",0
378,0,0,0,0.000000," ","integrate((a*x^3)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3}}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^3)/sqrt(x^2 + 1), x)","F",0
379,1,19,0,0.157750," ","integrate((a*x^2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","{\left(\sqrt{x^{2} + 1} \mathrm{sgn}\left(x\right) - \mathrm{sgn}\left(x\right)\right)} \sqrt{a}"," ",0,"(sqrt(x^2 + 1)*sgn(x) - sgn(x))*sqrt(a)","A",0
380,0,0,0,0.000000," ","integrate((a*x)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x)/sqrt(x^2 + 1), x)","F",0
381,0,0,0,0.000000," ","integrate((a/x)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(a/x)/sqrt(x^2 + 1), x)","F",0
382,1,30,0,0.212492," ","integrate((a/x^2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a} {\left(\log\left(\sqrt{x^{2} + 1} + 1\right) - \log\left(\sqrt{x^{2} + 1} - 1\right)\right)} \mathrm{sgn}\left(x\right)"," ",0,"-1/2*sqrt(a)*(log(sqrt(x^2 + 1) + 1) - log(sqrt(x^2 + 1) - 1))*sgn(x)","A",0
383,0,0,0,0.000000," ","integrate((a/x^3)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a}{x^{3}}}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(a/x^3)/sqrt(x^2 + 1), x)","F",0
384,1,22,0,0.178755," ","integrate((a/x^4)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a}}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 1}"," ",0,"2*sqrt(a)/((x - sqrt(x^2 + 1))^2 - 1)","A",0
385,1,12,0,0.167846," ","integrate((a*x^4)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + 1} \sqrt{a}"," ",0,"2/3*sqrt(x^3 + 1)*sqrt(a)","A",0
386,0,0,0,0.000000," ","integrate((a*x^3)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{3}}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^3)/sqrt(x^3 + 1), x)","F",0
387,0,0,0,0.000000," ","integrate((a*x^2)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2}}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^2)/sqrt(x^3 + 1), x)","F",0
388,1,35,0,0.189338," ","integrate((a*x)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{2 \, a^{\frac{5}{2}} \log\left(-\sqrt{a x} a^{\frac{3}{2}} x + \sqrt{a^{4} x^{3} + a^{4}}\right)}{3 \, {\left| a \right|}^{2}}"," ",0,"-2/3*a^(5/2)*log(-sqrt(a*x)*a^(3/2)*x + sqrt(a^4*x^3 + a^4))/abs(a)^2","B",0
389,0,0,0,0.000000," ","integrate((a/x)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(sqrt(a/x)/sqrt(x^3 + 1), x)","F",0
390,1,31,0,0.201481," ","integrate((a/x^2)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{a} {\left(\log\left(\sqrt{x^{3} + 1} + 1\right) - \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)\right)} \mathrm{sgn}\left(x\right)"," ",0,"-1/3*sqrt(a)*(log(sqrt(x^3 + 1) + 1) - log(abs(sqrt(x^3 + 1) - 1)))*sgn(x)","A",0
391,0,0,0,0.000000," ","integrate((a/x^3)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a}{x^{3}}}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(sqrt(a/x^3)/sqrt(x^3 + 1), x)","F",0
392,0,0,0,0.000000," ","integrate((a/x^4)^(1/2)/(x^3+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{a}{x^{4}}}}{\sqrt{x^{3} + 1}}\,{d x}"," ",0,"integrate(sqrt(a/x^4)/sqrt(x^3 + 1), x)","F",0
393,0,0,0,0.000000," ","integrate((a*x^(2*n))^(1/2)/(1+x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2 \, n}}}{\sqrt{x^{n} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^(2*n))/sqrt(x^n + 1), x)","F",0
394,0,0,0,0.000000," ","integrate((a*x^n)^(1/2)/(1+x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{n}}}{\sqrt{x^{n} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^n)/sqrt(x^n + 1), x)","F",0
395,0,0,0,0.000000," ","integrate((a*x^(1/2*n))^(1/2)/(1+x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{\frac{1}{2} \, n}}}{\sqrt{x^{n} + 1}}\,{d x}"," ",0,"integrate(sqrt(a*x^(1/2*n))/sqrt(x^n + 1), x)","F",0
396,0,0,0,0.000000," ","integrate((a*x^(2*n))^(1/2)/(1+x^n)^(1/2)+2*(a*x^(2*n))^(1/2)/(2+n)/(x^n)/(1+x^n)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x^{2 \, n}}}{\sqrt{x^{n} + 1}} + \frac{2 \, \sqrt{a x^{2 \, n}}}{{\left(n + 2\right)} \sqrt{x^{n} + 1} x^{n}}\,{d x}"," ",0,"integrate(sqrt(a*x^(2*n))/sqrt(x^n + 1) + 2*sqrt(a*x^(2*n))/((n + 2)*sqrt(x^n + 1)*x^n), x)","F",0
397,0,0,0,0.000000," ","integrate((a*x)^(1/2)/(e*x+d)^(1/2)/(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a x}}{\sqrt{e x + d} \sqrt{f x + e}}\,{d x}"," ",0,"integrate(sqrt(a*x)/(sqrt(e*x + d)*sqrt(f*x + e)), x)","F",0
398,1,20,0,0.207931," ","integrate((a*x^m)^r,x, algorithm=""giac"")","\frac{x e^{\left(m r \log\left(x\right) + r \log\left(a\right)\right)}}{m r + 1}"," ",0,"x*e^(m*r*log(x) + r*log(a))/(m*r + 1)","A",0
399,1,32,0,0.235524," ","integrate((a*x^m)^r*(b*x^n)^s,x, algorithm=""giac"")","\frac{x e^{\left(m r \log\left(x\right) + n s \log\left(x\right) + r \log\left(a\right) + s \log\left(b\right)\right)}}{m r + n s + 1}"," ",0,"x*e^(m*r*log(x) + n*s*log(x) + r*log(a) + s*log(b))/(m*r + n*s + 1)","A",0
400,1,44,0,0.244526," ","integrate((a*x^m)^r*(b*x^n)^s*(c*x^p)^t,x, algorithm=""giac"")","\frac{x e^{\left(m r \log\left(x\right) + n s \log\left(x\right) + p t \log\left(x\right) + r \log\left(a\right) + s \log\left(b\right) + t \log\left(c\right)\right)}}{m r + n s + p t + 1}"," ",0,"x*e^(m*r*log(x) + n*s*log(x) + p*t*log(x) + r*log(a) + s*log(b) + t*log(c))/(m*r + n*s + p*t + 1)","A",0
401,1,390,0,0.268484," ","integrate(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""giac"")","-\frac{2}{105} \, {\left({\left(3 \, {\left(b x + a\right)} {\left(\frac{5 \, {\left(a^{2} b^{9} - 2 \, a b^{9} c + b^{9} c^{2}\right)} {\left(b x + a\right)}}{a^{3} b^{12} - 3 \, a^{2} b^{12} c + 3 \, a b^{12} c^{2} - b^{12} c^{3}} - \frac{15 \, a^{3} b^{9} - 31 \, a^{2} b^{9} c + 17 \, a b^{9} c^{2} - b^{9} c^{3}}{a^{3} b^{12} - 3 \, a^{2} b^{12} c + 3 \, a b^{12} c^{2} - b^{12} c^{3}}\right)} + \frac{45 \, a^{4} b^{9} - 96 \, a^{3} b^{9} c + 53 \, a^{2} b^{9} c^{2} + 2 \, a b^{9} c^{3} - 4 \, b^{9} c^{4}}{a^{3} b^{12} - 3 \, a^{2} b^{12} c + 3 \, a b^{12} c^{2} - b^{12} c^{3}}\right)} {\left(b x + a\right)} - \frac{15 \, a^{5} b^{9} - 33 \, a^{4} b^{9} c + 17 \, a^{3} b^{9} c^{2} - 3 \, a^{2} b^{9} c^{3} + 12 \, a b^{9} c^{4} - 8 \, b^{9} c^{5}}{a^{3} b^{12} - 3 \, a^{2} b^{12} c + 3 \, a b^{12} c^{2} - b^{12} c^{3}}\right)} \sqrt{b x + c} + \frac{2 \, {\left(15 \, {\left(b x + a\right)}^{\frac{7}{2}} - 42 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2}\right)}}{105 \, {\left(a b^{3} - b^{3} c\right)}}"," ",0,"-2/105*((3*(b*x + a)*(5*(a^2*b^9 - 2*a*b^9*c + b^9*c^2)*(b*x + a)/(a^3*b^12 - 3*a^2*b^12*c + 3*a*b^12*c^2 - b^12*c^3) - (15*a^3*b^9 - 31*a^2*b^9*c + 17*a*b^9*c^2 - b^9*c^3)/(a^3*b^12 - 3*a^2*b^12*c + 3*a*b^12*c^2 - b^12*c^3)) + (45*a^4*b^9 - 96*a^3*b^9*c + 53*a^2*b^9*c^2 + 2*a*b^9*c^3 - 4*b^9*c^4)/(a^3*b^12 - 3*a^2*b^12*c + 3*a*b^12*c^2 - b^12*c^3))*(b*x + a) - (15*a^5*b^9 - 33*a^4*b^9*c + 17*a^3*b^9*c^2 - 3*a^2*b^9*c^3 + 12*a*b^9*c^4 - 8*b^9*c^5)/(a^3*b^12 - 3*a^2*b^12*c + 3*a*b^12*c^2 - b^12*c^3))*sqrt(b*x + c) + 2/105*(15*(b*x + a)^(7/2) - 42*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2)/(a*b^3 - b^3*c)","B",0
402,1,206,0,0.208240," ","integrate(x/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(b x + a\right)} {\left(\frac{3 \, {\left(a b^{2} - b^{2} c\right)} {\left(b x + a\right)}}{a^{2} b^{3} - 2 \, a b^{3} c + b^{3} c^{2}} - \frac{6 \, a^{2} b^{2} - 7 \, a b^{2} c + b^{2} c^{2}}{a^{2} b^{3} - 2 \, a b^{3} c + b^{3} c^{2}}\right)} + \frac{3 \, a^{3} b^{2} - 4 \, a^{2} b^{2} c - a b^{2} c^{2} + 2 \, b^{2} c^{3}}{a^{2} b^{3} - 2 \, a b^{3} c + b^{3} c^{2}}\right)} \sqrt{b x + c} - \frac{3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 5 \, {\left(b x + a\right)}^{\frac{3}{2}} a}{a b - b c}\right)}}{15 \, b}"," ",0,"-2/15*(((b*x + a)*(3*(a*b^2 - b^2*c)*(b*x + a)/(a^2*b^3 - 2*a*b^3*c + b^3*c^2) - (6*a^2*b^2 - 7*a*b^2*c + b^2*c^2)/(a^2*b^3 - 2*a*b^3*c + b^3*c^2)) + (3*a^3*b^2 - 4*a^2*b^2*c - a*b^2*c^2 + 2*b^2*c^3)/(a^2*b^3 - 2*a*b^3*c + b^3*c^2))*sqrt(b*x + c) - (3*(b*x + a)^(5/2) - 5*(b*x + a)^(3/2)*a)/(a*b - b*c))/b","B",0
403,1,75,0,0.208193," ","integrate(1/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{b x + c} {\left(\frac{{\left(b x + a\right)} b}{a b^{2} - b^{2} c} - \frac{a b - b c}{a b^{2} - b^{2} c}\right)} + \frac{2 \, {\left(b x + a\right)}^{\frac{3}{2}}}{3 \, {\left(a b - b c\right)}}"," ",0,"-2/3*sqrt(b*x + c)*((b*x + a)*b/(a*b^2 - b^2*c) - (a*b - b*c)/(a*b^2 - b^2*c)) + 2/3*(b*x + a)^(3/2)/(a*b - b*c)","A",0
404,1,1016,0,0.859395," ","integrate(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""giac"")","\frac{2 \, a \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} {\left(a - c\right)}} - \frac{2 \, {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} + 2 \, {\left(a c^{2} + \sqrt{a c} c^{2}\right)} {\left(a - c\right)}^{2} \mathrm{sgn}\left(-a + c\right) - 2 \, {\left(a c^{2} + \sqrt{a c} a c\right)} {\left(a - c\right)}^{2} + {\left(a^{2} c^{2} - 2 \, a c^{3} + c^{4} - {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} {\left| -a + c \right|} \mathrm{sgn}\left(-a + c\right) - {\left(a^{3} c - 2 \, a^{2} c^{2} + a c^{3} + {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} {\left| -a + c \right|} - {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} + {\left(a^{3} c - a^{2} c^{2} - a c^{3} + c^{4}\right)} \sqrt{a c}\right)} \mathrm{sgn}\left(-a + c\right) + {\left(a^{4} - a^{3} c - a^{2} c^{2} + a c^{3}\right)} \sqrt{a c}\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{2} - c^{2} + \sqrt{{\left(a^{2} - c^{2}\right)}^{2} - {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} {\left(a - c\right)}}}{a - c}}}\right)}{{\left(\sqrt{-a} a^{4} - a^{4} \sqrt{-c} - 4 \, \sqrt{-a} a^{3} c + 4 \, a^{3} \sqrt{-c} c + 6 \, \sqrt{-a} a^{2} c^{2} - 6 \, a^{2} \sqrt{-c} c^{2} - 4 \, \sqrt{-a} a c^{3} + 4 \, a \sqrt{-c} c^{3} + \sqrt{-a} c^{4} - \sqrt{-c} c^{4}\right)} {\left| -a + c \right|}} + \frac{2 \, {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} - 2 \, {\left(a c^{2} + \sqrt{a c} c^{2}\right)} {\left(a - c\right)}^{2} \mathrm{sgn}\left(-a + c\right) - 2 \, {\left(a c^{2} - \sqrt{a c} a c\right)} {\left(a - c\right)}^{2} + {\left(a^{2} c^{2} - 2 \, a c^{3} + c^{4} - {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} {\left| -a + c \right|} \mathrm{sgn}\left(-a + c\right) + {\left(a^{3} c - 2 \, a^{2} c^{2} + a c^{3} + {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} {\left| -a + c \right|} + {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} - {\left(a^{3} c - a^{2} c^{2} - a c^{3} + c^{4}\right)} \sqrt{a c}\right)} \mathrm{sgn}\left(-a + c\right) + {\left(a^{4} - a^{3} c - a^{2} c^{2} + a c^{3}\right)} \sqrt{a c}\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{2} - c^{2} - \sqrt{{\left(a^{2} - c^{2}\right)}^{2} - {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} {\left(a - c\right)}}}{a - c}}}\right)}{{\left(\sqrt{-a} a^{4} - a^{4} \sqrt{-c} - 4 \, \sqrt{-a} a^{3} c + 4 \, a^{3} \sqrt{-c} c + 6 \, \sqrt{-a} a^{2} c^{2} - 6 \, a^{2} \sqrt{-c} c^{2} - 4 \, \sqrt{-a} a c^{3} + 4 \, a \sqrt{-c} c^{3} + \sqrt{-a} c^{4} - \sqrt{-c} c^{4}\right)} {\left| -a + c \right|}} + \frac{2 \, \sqrt{b x + a}}{a - c} - \frac{2 \, \sqrt{b x + c}}{a - c}"," ",0,"2*a*arctan(sqrt(b*x + a)/sqrt(-a))/(sqrt(-a)*(a - c)) - 2*(a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 + 2*(a*c^2 + sqrt(a*c)*c^2)*(a - c)^2*sgn(-a + c) - 2*(a*c^2 + sqrt(a*c)*a*c)*(a - c)^2 + (a^2*c^2 - 2*a*c^3 + c^4 - (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*abs(-a + c)*sgn(-a + c) - (a^3*c - 2*a^2*c^2 + a*c^3 + (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*abs(-a + c) - (a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 + (a^3*c - a^2*c^2 - a*c^3 + c^4)*sqrt(a*c))*sgn(-a + c) + (a^4 - a^3*c - a^2*c^2 + a*c^3)*sqrt(a*c))*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^2 - c^2 + sqrt((a^2 - c^2)^2 - (a^3 - 3*a^2*c + 3*a*c^2 - c^3)*(a - c)))/(a - c)))/((sqrt(-a)*a^4 - a^4*sqrt(-c) - 4*sqrt(-a)*a^3*c + 4*a^3*sqrt(-c)*c + 6*sqrt(-a)*a^2*c^2 - 6*a^2*sqrt(-c)*c^2 - 4*sqrt(-a)*a*c^3 + 4*a*sqrt(-c)*c^3 + sqrt(-a)*c^4 - sqrt(-c)*c^4)*abs(-a + c)) + 2*(a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 - 2*(a*c^2 + sqrt(a*c)*c^2)*(a - c)^2*sgn(-a + c) - 2*(a*c^2 - sqrt(a*c)*a*c)*(a - c)^2 + (a^2*c^2 - 2*a*c^3 + c^4 - (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*abs(-a + c)*sgn(-a + c) + (a^3*c - 2*a^2*c^2 + a*c^3 + (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*abs(-a + c) + (a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 - (a^3*c - a^2*c^2 - a*c^3 + c^4)*sqrt(a*c))*sgn(-a + c) + (a^4 - a^3*c - a^2*c^2 + a*c^3)*sqrt(a*c))*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^2 - c^2 - sqrt((a^2 - c^2)^2 - (a^3 - 3*a^2*c + 3*a*c^2 - c^3)*(a - c)))/(a - c)))/((sqrt(-a)*a^4 - a^4*sqrt(-c) - 4*sqrt(-a)*a^3*c + 4*a^3*sqrt(-c)*c + 6*sqrt(-a)*a^2*c^2 - 6*a^2*sqrt(-c)*c^2 - 4*sqrt(-a)*a*c^3 + 4*a*sqrt(-c)*c^3 + sqrt(-a)*c^4 - sqrt(-c)*c^4)*abs(-a + c)) + 2*sqrt(b*x + a)/(a - c) - 2*sqrt(b*x + c)/(a - c)","B",0
405,1,1190,0,10.214232," ","integrate(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} {\left(a - c\right)}} + \frac{{\left(2 \, {\left(a c^{2} + \sqrt{a c} c^{2}\right)} {\left(a - c\right)}^{2} b \mathrm{sgn}\left(2 \, a - 2 \, c\right) + 2 \, {\left(a c^{2} + \sqrt{a c} a c\right)} {\left(a - c\right)}^{2} b + {\left(a^{2} c^{2} - 2 \, a c^{3} + c^{4} + {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} b {\left| a - c \right|} \mathrm{sgn}\left(2 \, a - 2 \, c\right) + {\left(a^{3} c - 2 \, a^{2} c^{2} + a c^{3} + {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} b {\left| a - c \right|} - {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} + {\left(a^{3} c - a^{2} c^{2} - a c^{3} + c^{4}\right)} \sqrt{a c}\right)} b \mathrm{sgn}\left(2 \, a - 2 \, c\right) - {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} + {\left(a^{4} - a^{3} c - a^{2} c^{2} + a c^{3}\right)} \sqrt{a c}\right)} b\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{2} - c^{2} + \sqrt{{\left(a^{2} - c^{2}\right)}^{2} - {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} {\left(a - c\right)}}}{a - c}}}\right)}{{\left(\sqrt{-a} a^{4} c - a^{4} \sqrt{-c} c - 4 \, \sqrt{-a} a^{3} c^{2} + 4 \, a^{3} \sqrt{-c} c^{2} + 6 \, \sqrt{-a} a^{2} c^{3} - 6 \, a^{2} \sqrt{-c} c^{3} - 4 \, \sqrt{-a} a c^{4} + 4 \, a \sqrt{-c} c^{4} + \sqrt{-a} c^{5} - \sqrt{-c} c^{5}\right)} {\left| a - c \right|}} - \frac{{\left(2 \, {\left(a c^{2} + \sqrt{a c} c^{2}\right)} {\left(a - c\right)}^{2} b \mathrm{sgn}\left(2 \, a - 2 \, c\right) - 2 \, {\left(a c^{2} + \sqrt{a c} a c\right)} {\left(a - c\right)}^{2} b + {\left(a^{2} c^{2} - 2 \, a c^{3} + c^{4} - {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} b {\left| a - c \right|} \mathrm{sgn}\left(2 \, a - 2 \, c\right) - {\left(a^{3} c - 2 \, a^{2} c^{2} + a c^{3} + {\left(a^{2} c - 2 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} b {\left| a - c \right|} - {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} - {\left(a^{3} c - a^{2} c^{2} - a c^{3} + c^{4}\right)} \sqrt{a c}\right)} b \mathrm{sgn}\left(2 \, a - 2 \, c\right) + {\left(a^{4} c - a^{3} c^{2} - a^{2} c^{3} + a c^{4} - {\left(a^{4} - a^{3} c - a^{2} c^{2} + a c^{3}\right)} \sqrt{a c}\right)} b\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{2} - c^{2} - \sqrt{{\left(a^{2} - c^{2}\right)}^{2} - {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} {\left(a - c\right)}}}{a - c}}}\right)}{{\left(\sqrt{-a} a^{4} c - a^{4} \sqrt{-c} c - 4 \, \sqrt{-a} a^{3} c^{2} + 4 \, a^{3} \sqrt{-c} c^{2} + 6 \, \sqrt{-a} a^{2} c^{3} - 6 \, a^{2} \sqrt{-c} c^{3} - 4 \, \sqrt{-a} a c^{4} + 4 \, a \sqrt{-c} c^{4} + \sqrt{-a} c^{5} - \sqrt{-c} c^{5}\right)} {\left| a - c \right|}} - \frac{2 \, {\left(b {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{3} - a b {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)} + b c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}\right)}}{{\left({\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{4} - 2 \, a {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} - 2 \, c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} + a^{2} - 2 \, a c + c^{2}\right)} {\left(a - c\right)}} - \frac{\sqrt{b x + a}}{{\left(a - c\right)} x}"," ",0,"b*arctan(sqrt(b*x + a)/sqrt(-a))/(sqrt(-a)*(a - c)) + (2*(a*c^2 + sqrt(a*c)*c^2)*(a - c)^2*b*sgn(2*a - 2*c) + 2*(a*c^2 + sqrt(a*c)*a*c)*(a - c)^2*b + (a^2*c^2 - 2*a*c^3 + c^4 + (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*b*abs(a - c)*sgn(2*a - 2*c) + (a^3*c - 2*a^2*c^2 + a*c^3 + (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*b*abs(a - c) - (a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 + (a^3*c - a^2*c^2 - a*c^3 + c^4)*sqrt(a*c))*b*sgn(2*a - 2*c) - (a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 + (a^4 - a^3*c - a^2*c^2 + a*c^3)*sqrt(a*c))*b)*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^2 - c^2 + sqrt((a^2 - c^2)^2 - (a^3 - 3*a^2*c + 3*a*c^2 - c^3)*(a - c)))/(a - c)))/((sqrt(-a)*a^4*c - a^4*sqrt(-c)*c - 4*sqrt(-a)*a^3*c^2 + 4*a^3*sqrt(-c)*c^2 + 6*sqrt(-a)*a^2*c^3 - 6*a^2*sqrt(-c)*c^3 - 4*sqrt(-a)*a*c^4 + 4*a*sqrt(-c)*c^4 + sqrt(-a)*c^5 - sqrt(-c)*c^5)*abs(a - c)) - (2*(a*c^2 + sqrt(a*c)*c^2)*(a - c)^2*b*sgn(2*a - 2*c) - 2*(a*c^2 + sqrt(a*c)*a*c)*(a - c)^2*b + (a^2*c^2 - 2*a*c^3 + c^4 - (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*b*abs(a - c)*sgn(2*a - 2*c) - (a^3*c - 2*a^2*c^2 + a*c^3 + (a^2*c - 2*a*c^2 + c^3)*sqrt(a*c))*b*abs(a - c) - (a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 - (a^3*c - a^2*c^2 - a*c^3 + c^4)*sqrt(a*c))*b*sgn(2*a - 2*c) + (a^4*c - a^3*c^2 - a^2*c^3 + a*c^4 - (a^4 - a^3*c - a^2*c^2 + a*c^3)*sqrt(a*c))*b)*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^2 - c^2 - sqrt((a^2 - c^2)^2 - (a^3 - 3*a^2*c + 3*a*c^2 - c^3)*(a - c)))/(a - c)))/((sqrt(-a)*a^4*c - a^4*sqrt(-c)*c - 4*sqrt(-a)*a^3*c^2 + 4*a^3*sqrt(-c)*c^2 + 6*sqrt(-a)*a^2*c^3 - 6*a^2*sqrt(-c)*c^3 - 4*sqrt(-a)*a*c^4 + 4*a*sqrt(-c)*c^4 + sqrt(-a)*c^5 - sqrt(-c)*c^5)*abs(a - c)) - 2*(b*(sqrt(b*x + a) - sqrt(b*x + c))^3 - a*b*(sqrt(b*x + a) - sqrt(b*x + c)) + b*c*(sqrt(b*x + a) - sqrt(b*x + c)))/(((sqrt(b*x + a) - sqrt(b*x + c))^4 - 2*a*(sqrt(b*x + a) - sqrt(b*x + c))^2 - 2*c*(sqrt(b*x + a) - sqrt(b*x + c))^2 + a^2 - 2*a*c + c^2)*(a - c)) - sqrt(b*x + a)/((a - c)*x)","B",0
406,1,797,0,0.389256," ","integrate(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{1}{96} \, {\left(2 \, {\left(4 \, {\left(b x + a\right)} {\left(\frac{6 \, {\left(a^{5} b^{9} - 5 \, a^{4} b^{9} c + 10 \, a^{3} b^{9} c^{2} - 10 \, a^{2} b^{9} c^{3} + 5 \, a b^{9} c^{4} - b^{9} c^{5}\right)} {\left(b x + a\right)}}{a^{7} b^{12} - 7 \, a^{6} b^{12} c + 21 \, a^{5} b^{12} c^{2} - 35 \, a^{4} b^{12} c^{3} + 35 \, a^{3} b^{12} c^{4} - 21 \, a^{2} b^{12} c^{5} + 7 \, a b^{12} c^{6} - b^{12} c^{7}} - \frac{17 \, a^{6} b^{9} - 86 \, a^{5} b^{9} c + 175 \, a^{4} b^{9} c^{2} - 180 \, a^{3} b^{9} c^{3} + 95 \, a^{2} b^{9} c^{4} - 22 \, a b^{9} c^{5} + b^{9} c^{6}}{a^{7} b^{12} - 7 \, a^{6} b^{12} c + 21 \, a^{5} b^{12} c^{2} - 35 \, a^{4} b^{12} c^{3} + 35 \, a^{3} b^{12} c^{4} - 21 \, a^{2} b^{12} c^{5} + 7 \, a b^{12} c^{6} - b^{12} c^{7}}\right)} + \frac{59 \, a^{7} b^{9} - 301 \, a^{6} b^{9} c + 615 \, a^{5} b^{9} c^{2} - 625 \, a^{4} b^{9} c^{3} + 305 \, a^{3} b^{9} c^{4} - 39 \, a^{2} b^{9} c^{5} - 19 \, a b^{9} c^{6} + 5 \, b^{9} c^{7}}{a^{7} b^{12} - 7 \, a^{6} b^{12} c + 21 \, a^{5} b^{12} c^{2} - 35 \, a^{4} b^{12} c^{3} + 35 \, a^{3} b^{12} c^{4} - 21 \, a^{2} b^{12} c^{5} + 7 \, a b^{12} c^{6} - b^{12} c^{7}}\right)} {\left(b x + a\right)} - \frac{3 \, {\left(5 \, a^{8} b^{9} - 24 \, a^{7} b^{9} c + 44 \, a^{6} b^{9} c^{2} - 40 \, a^{5} b^{9} c^{3} + 30 \, a^{4} b^{9} c^{4} - 40 \, a^{3} b^{9} c^{5} + 44 \, a^{2} b^{9} c^{6} - 24 \, a b^{9} c^{7} + 5 \, b^{9} c^{8}\right)}}{a^{7} b^{12} - 7 \, a^{6} b^{12} c + 21 \, a^{5} b^{12} c^{2} - 35 \, a^{4} b^{12} c^{3} + 35 \, a^{3} b^{12} c^{4} - 21 \, a^{2} b^{12} c^{5} + 7 \, a b^{12} c^{6} - b^{12} c^{7}}\right)} \sqrt{b x + a} \sqrt{b x + c} + \frac{3 \, {\left(b x + a\right)}^{4} - 10 \, {\left(b x + a\right)}^{3} a + 12 \, {\left(b x + a\right)}^{2} a^{2} - 6 \, {\left(b x + a\right)} a^{3} + 2 \, {\left(b x + a\right)}^{3} c - 6 \, {\left(b x + a\right)}^{2} a c + 6 \, {\left(b x + a\right)} a^{2} c}{6 \, {\left(a^{2} b^{3} - 2 \, a b^{3} c + b^{3} c^{2}\right)}} - \frac{{\left(5 \, a^{2} + 6 \, a c + 5 \, c^{2}\right)} \log\left({\left| -\sqrt{b x + a} + \sqrt{b x + c} \right|}\right)}{32 \, b^{3}}"," ",0,"-1/96*(2*(4*(b*x + a)*(6*(a^5*b^9 - 5*a^4*b^9*c + 10*a^3*b^9*c^2 - 10*a^2*b^9*c^3 + 5*a*b^9*c^4 - b^9*c^5)*(b*x + a)/(a^7*b^12 - 7*a^6*b^12*c + 21*a^5*b^12*c^2 - 35*a^4*b^12*c^3 + 35*a^3*b^12*c^4 - 21*a^2*b^12*c^5 + 7*a*b^12*c^6 - b^12*c^7) - (17*a^6*b^9 - 86*a^5*b^9*c + 175*a^4*b^9*c^2 - 180*a^3*b^9*c^3 + 95*a^2*b^9*c^4 - 22*a*b^9*c^5 + b^9*c^6)/(a^7*b^12 - 7*a^6*b^12*c + 21*a^5*b^12*c^2 - 35*a^4*b^12*c^3 + 35*a^3*b^12*c^4 - 21*a^2*b^12*c^5 + 7*a*b^12*c^6 - b^12*c^7)) + (59*a^7*b^9 - 301*a^6*b^9*c + 615*a^5*b^9*c^2 - 625*a^4*b^9*c^3 + 305*a^3*b^9*c^4 - 39*a^2*b^9*c^5 - 19*a*b^9*c^6 + 5*b^9*c^7)/(a^7*b^12 - 7*a^6*b^12*c + 21*a^5*b^12*c^2 - 35*a^4*b^12*c^3 + 35*a^3*b^12*c^4 - 21*a^2*b^12*c^5 + 7*a*b^12*c^6 - b^12*c^7))*(b*x + a) - 3*(5*a^8*b^9 - 24*a^7*b^9*c + 44*a^6*b^9*c^2 - 40*a^5*b^9*c^3 + 30*a^4*b^9*c^4 - 40*a^3*b^9*c^5 + 44*a^2*b^9*c^6 - 24*a*b^9*c^7 + 5*b^9*c^8)/(a^7*b^12 - 7*a^6*b^12*c + 21*a^5*b^12*c^2 - 35*a^4*b^12*c^3 + 35*a^3*b^12*c^4 - 21*a^2*b^12*c^5 + 7*a*b^12*c^6 - b^12*c^7))*sqrt(b*x + a)*sqrt(b*x + c) + 1/6*(3*(b*x + a)^4 - 10*(b*x + a)^3*a + 12*(b*x + a)^2*a^2 - 6*(b*x + a)*a^3 + 2*(b*x + a)^3*c - 6*(b*x + a)^2*a*c + 6*(b*x + a)*a^2*c)/(a^2*b^3 - 2*a*b^3*c + b^3*c^2) - 1/32*(5*a^2 + 6*a*c + 5*c^2)*log(abs(-sqrt(b*x + a) + sqrt(b*x + c)))/b^3","B",0
407,1,445,0,0.270951," ","integrate(x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(b x + a\right)} {\left(\frac{4 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{2} c + 3 \, a b^{2} c^{2} - b^{2} c^{3}\right)} {\left(b x + a\right)}}{a^{5} b^{3} - 5 \, a^{4} b^{3} c + 10 \, a^{3} b^{3} c^{2} - 10 \, a^{2} b^{3} c^{3} + 5 \, a b^{3} c^{4} - b^{3} c^{5}} - \frac{7 \, a^{4} b^{2} - 22 \, a^{3} b^{2} c + 24 \, a^{2} b^{2} c^{2} - 10 \, a b^{2} c^{3} + b^{2} c^{4}}{a^{5} b^{3} - 5 \, a^{4} b^{3} c + 10 \, a^{3} b^{3} c^{2} - 10 \, a^{2} b^{3} c^{3} + 5 \, a b^{3} c^{4} - b^{3} c^{5}}\right)} + \frac{3 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{2} c + 2 \, a^{3} b^{2} c^{2} + 2 \, a^{2} b^{2} c^{3} - 3 \, a b^{2} c^{4} + b^{2} c^{5}\right)}}{a^{5} b^{3} - 5 \, a^{4} b^{3} c + 10 \, a^{3} b^{3} c^{2} - 10 \, a^{2} b^{3} c^{3} + 5 \, a b^{3} c^{4} - b^{3} c^{5}}\right)} \sqrt{b x + a} \sqrt{b x + c} - \frac{3 \, {\left(a + c\right)} \log\left({\left| -\sqrt{b x + a} + \sqrt{b x + c} \right|}\right)}{b} - \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 6 \, {\left(b x + a\right)} a^{2} + 3 \, {\left(b x + a\right)}^{2} c - 6 \, {\left(b x + a\right)} a c\right)}}{a^{2} b - 2 \, a b c + b c^{2}}}{12 \, b}"," ",0,"-1/12*((2*(b*x + a)*(4*(a^3*b^2 - 3*a^2*b^2*c + 3*a*b^2*c^2 - b^2*c^3)*(b*x + a)/(a^5*b^3 - 5*a^4*b^3*c + 10*a^3*b^3*c^2 - 10*a^2*b^3*c^3 + 5*a*b^3*c^4 - b^3*c^5) - (7*a^4*b^2 - 22*a^3*b^2*c + 24*a^2*b^2*c^2 - 10*a*b^2*c^3 + b^2*c^4)/(a^5*b^3 - 5*a^4*b^3*c + 10*a^3*b^3*c^2 - 10*a^2*b^3*c^3 + 5*a*b^3*c^4 - b^3*c^5)) + 3*(a^5*b^2 - 3*a^4*b^2*c + 2*a^3*b^2*c^2 + 2*a^2*b^2*c^3 - 3*a*b^2*c^4 + b^2*c^5)/(a^5*b^3 - 5*a^4*b^3*c + 10*a^3*b^3*c^2 - 10*a^2*b^3*c^3 + 5*a*b^3*c^4 - b^3*c^5))*sqrt(b*x + a)*sqrt(b*x + c) - 3*(a + c)*log(abs(-sqrt(b*x + a) + sqrt(b*x + c)))/b - 2*(4*(b*x + a)^3 - 9*(b*x + a)^2*a + 6*(b*x + a)*a^2 + 3*(b*x + a)^2*c - 6*(b*x + a)*a*c)/(a^2*b - 2*a*b*c + b*c^2))/b","B",0
408,1,189,0,0.238354," ","integrate(1/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{b x + a} \sqrt{b x + c} {\left(\frac{2 \, {\left(a b - b c\right)} {\left(b x + a\right)}}{a^{3} b^{2} - 3 \, a^{2} b^{2} c + 3 \, a b^{2} c^{2} - b^{2} c^{3}} - \frac{a^{2} b - 2 \, a b c + b c^{2}}{a^{3} b^{2} - 3 \, a^{2} b^{2} c + 3 \, a b^{2} c^{2} - b^{2} c^{3}}\right)} + \frac{{\left(b x + a\right)}^{2} - {\left(b x + a\right)} a + {\left(b x + a\right)} c}{a^{2} b - 2 \, a b c + b c^{2}} - \frac{\log\left({\left| -\sqrt{b x + a} + \sqrt{b x + c} \right|}\right)}{2 \, b}"," ",0,"-1/2*sqrt(b*x + a)*sqrt(b*x + c)*(2*(a*b - b*c)*(b*x + a)/(a^3*b^2 - 3*a^2*b^2*c + 3*a*b^2*c^2 - b^2*c^3) - (a^2*b - 2*a*b*c + b*c^2)/(a^3*b^2 - 3*a^2*b^2*c + 3*a*b^2*c^2 - b^2*c^3)) + ((b*x + a)^2 - (b*x + a)*a + (b*x + a)*c)/(a^2*b - 2*a*b*c + b*c^2) - 1/2*log(abs(-sqrt(b*x + a) + sqrt(b*x + c)))/b","B",0
409,1,194,0,0.672682," ","integrate(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{4 \, a c \arctan\left(\frac{{\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} - a - c}{2 \, \sqrt{-a c}}\right)}{{\left(a^{2} - 2 \, a c + c^{2}\right)} \sqrt{-a c}} - \frac{2 \, {\left(a^{2} - 2 \, a c + c^{2}\right)} \sqrt{b x + a} \sqrt{b x + c}}{a^{4} - 4 \, a^{3} c + 6 \, a^{2} c^{2} - 4 \, a c^{3} + c^{4}} + \frac{{\left(a + c\right)} \log\left({\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2}\right)}{a^{2} - 2 \, a c + c^{2}} + \frac{{\left(a + c\right)} \log\left({\left| b x \right|}\right)}{a^{2} - 2 \, a c + c^{2}} + \frac{2 \, {\left(b x + a\right)}}{a^{2} - 2 \, a c + c^{2}}"," ",0,"4*a*c*arctan(1/2*((sqrt(b*x + a) - sqrt(b*x + c))^2 - a - c)/sqrt(-a*c))/((a^2 - 2*a*c + c^2)*sqrt(-a*c)) - 2*(a^2 - 2*a*c + c^2)*sqrt(b*x + a)*sqrt(b*x + c)/(a^4 - 4*a^3*c + 6*a^2*c^2 - 4*a*c^3 + c^4) + (a + c)*log((sqrt(b*x + a) - sqrt(b*x + c))^2)/(a^2 - 2*a*c + c^2) + (a + c)*log(abs(b*x))/(a^2 - 2*a*c + c^2) + 2*(b*x + a)/(a^2 - 2*a*c + c^2)","A",0
410,1,311,0,1.890209," ","integrate(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{2 \, b \log\left({\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2}\right)}{a^{2} - 2 \, a c + c^{2}} + \frac{2 \, b \log\left({\left| b x \right|}\right)}{a^{2} - 2 \, a c + c^{2}} + \frac{2 \, {\left(a b + b c\right)} \arctan\left(\frac{{\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} - a - c}{2 \, \sqrt{-a c}}\right)}{{\left(a^{2} - 2 \, a c + c^{2}\right)} \sqrt{-a c}} - \frac{4 \, {\left(a b {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} + b c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} - a^{2} b + 2 \, a b c - b c^{2}\right)}}{{\left({\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{4} - 2 \, a {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} - 2 \, c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} + a^{2} - 2 \, a c + c^{2}\right)} {\left(a^{2} - 2 \, a c + c^{2}\right)}} - \frac{2 \, {\left(b x + a\right)} b - a b + b c}{{\left(a^{2} - 2 \, a c + c^{2}\right)} b x}"," ",0,"2*b*log((sqrt(b*x + a) - sqrt(b*x + c))^2)/(a^2 - 2*a*c + c^2) + 2*b*log(abs(b*x))/(a^2 - 2*a*c + c^2) + 2*(a*b + b*c)*arctan(1/2*((sqrt(b*x + a) - sqrt(b*x + c))^2 - a - c)/sqrt(-a*c))/((a^2 - 2*a*c + c^2)*sqrt(-a*c)) - 4*(a*b*(sqrt(b*x + a) - sqrt(b*x + c))^2 + b*c*(sqrt(b*x + a) - sqrt(b*x + c))^2 - a^2*b + 2*a*b*c - b*c^2)/(((sqrt(b*x + a) - sqrt(b*x + c))^4 - 2*a*(sqrt(b*x + a) - sqrt(b*x + c))^2 - 2*c*(sqrt(b*x + a) - sqrt(b*x + c))^2 + a^2 - 2*a*c + c^2)*(a^2 - 2*a*c + c^2)) - (2*(b*x + a)*b - a*b + b*c)/((a^2 - 2*a*c + c^2)*b*x)","B",0
411,1,1447,0,0.806681," ","integrate(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""giac"")","-\frac{2}{315} \, {\left({\left({\left(5 \, {\left(b x + a\right)} {\left(\frac{28 \, {\left(a^{9} b^{12} - 9 \, a^{8} b^{12} c + 36 \, a^{7} b^{12} c^{2} - 84 \, a^{6} b^{12} c^{3} + 126 \, a^{5} b^{12} c^{4} - 126 \, a^{4} b^{12} c^{5} + 84 \, a^{3} b^{12} c^{6} - 36 \, a^{2} b^{12} c^{7} + 9 \, a b^{12} c^{8} - b^{12} c^{9}\right)} {\left(b x + a\right)}}{a^{12} b^{15} - 12 \, a^{11} b^{15} c + 66 \, a^{10} b^{15} c^{2} - 220 \, a^{9} b^{15} c^{3} + 495 \, a^{8} b^{15} c^{4} - 792 \, a^{7} b^{15} c^{5} + 924 \, a^{6} b^{15} c^{6} - 792 \, a^{5} b^{15} c^{7} + 495 \, a^{4} b^{15} c^{8} - 220 \, a^{3} b^{15} c^{9} + 66 \, a^{2} b^{15} c^{10} - 12 \, a b^{15} c^{11} + b^{15} c^{12}} - \frac{85 \, a^{10} b^{12} - 778 \, a^{9} b^{12} c + 3177 \, a^{8} b^{12} c^{2} - 7608 \, a^{7} b^{12} c^{3} + 11802 \, a^{6} b^{12} c^{4} - 12348 \, a^{5} b^{12} c^{5} + 8778 \, a^{4} b^{12} c^{6} - 4152 \, a^{3} b^{12} c^{7} + 1233 \, a^{2} b^{12} c^{8} - 202 \, a b^{12} c^{9} + 13 \, b^{12} c^{10}}{a^{12} b^{15} - 12 \, a^{11} b^{15} c + 66 \, a^{10} b^{15} c^{2} - 220 \, a^{9} b^{15} c^{3} + 495 \, a^{8} b^{15} c^{4} - 792 \, a^{7} b^{15} c^{5} + 924 \, a^{6} b^{15} c^{6} - 792 \, a^{5} b^{15} c^{7} + 495 \, a^{4} b^{15} c^{8} - 220 \, a^{3} b^{15} c^{9} + 66 \, a^{2} b^{15} c^{10} - 12 \, a b^{15} c^{11} + b^{15} c^{12}}\right)} + \frac{3 \, {\left(145 \, a^{11} b^{12} - 1361 \, a^{10} b^{12} c + 5719 \, a^{9} b^{12} c^{2} - 14151 \, a^{8} b^{12} c^{3} + 22794 \, a^{7} b^{12} c^{4} - 24906 \, a^{6} b^{12} c^{5} + 18606 \, a^{5} b^{12} c^{6} - 9294 \, a^{4} b^{12} c^{7} + 2901 \, a^{3} b^{12} c^{8} - 469 \, a^{2} b^{12} c^{9} + 11 \, a b^{12} c^{10} + 5 \, b^{12} c^{11}\right)}}{a^{12} b^{15} - 12 \, a^{11} b^{15} c + 66 \, a^{10} b^{15} c^{2} - 220 \, a^{9} b^{15} c^{3} + 495 \, a^{8} b^{15} c^{4} - 792 \, a^{7} b^{15} c^{5} + 924 \, a^{6} b^{15} c^{6} - 792 \, a^{5} b^{15} c^{7} + 495 \, a^{4} b^{15} c^{8} - 220 \, a^{3} b^{15} c^{9} + 66 \, a^{2} b^{15} c^{10} - 12 \, a b^{15} c^{11} + b^{15} c^{12}}\right)} {\left(b x + a\right)} - \frac{155 \, a^{12} b^{12} - 1536 \, a^{11} b^{12} c + 6855 \, a^{10} b^{12} c^{2} - 18170 \, a^{9} b^{12} c^{3} + 31770 \, a^{8} b^{12} c^{4} - 38520 \, a^{7} b^{12} c^{5} + 33222 \, a^{6} b^{12} c^{6} - 20700 \, a^{5} b^{12} c^{7} + 9495 \, a^{4} b^{12} c^{8} - 3320 \, a^{3} b^{12} c^{9} + 915 \, a^{2} b^{12} c^{10} - 186 \, a b^{12} c^{11} + 20 \, b^{12} c^{12}}{a^{12} b^{15} - 12 \, a^{11} b^{15} c + 66 \, a^{10} b^{15} c^{2} - 220 \, a^{9} b^{15} c^{3} + 495 \, a^{8} b^{15} c^{4} - 792 \, a^{7} b^{15} c^{5} + 924 \, a^{6} b^{15} c^{6} - 792 \, a^{5} b^{15} c^{7} + 495 \, a^{4} b^{15} c^{8} - 220 \, a^{3} b^{15} c^{9} + 66 \, a^{2} b^{15} c^{10} - 12 \, a b^{15} c^{11} + b^{15} c^{12}}\right)} {\left(b x + a\right)} + \frac{5 \, a^{13} b^{12} - 83 \, a^{12} b^{12} c + 543 \, a^{11} b^{12} c^{2} - 1925 \, a^{10} b^{12} c^{3} + 4070 \, a^{9} b^{12} c^{4} - 4950 \, a^{8} b^{12} c^{5} + 2046 \, a^{7} b^{12} c^{6} + 3894 \, a^{6} b^{12} c^{7} - 8415 \, a^{5} b^{12} c^{8} + 8305 \, a^{4} b^{12} c^{9} - 5005 \, a^{3} b^{12} c^{10} + 1887 \, a^{2} b^{12} c^{11} - 412 \, a b^{12} c^{12} + 40 \, b^{12} c^{13}}{a^{12} b^{15} - 12 \, a^{11} b^{15} c + 66 \, a^{10} b^{15} c^{2} - 220 \, a^{9} b^{15} c^{3} + 495 \, a^{8} b^{15} c^{4} - 792 \, a^{7} b^{15} c^{5} + 924 \, a^{6} b^{15} c^{6} - 792 \, a^{5} b^{15} c^{7} + 495 \, a^{4} b^{15} c^{8} - 220 \, a^{3} b^{15} c^{9} + 66 \, a^{2} b^{15} c^{10} - 12 \, a b^{15} c^{11} + b^{15} c^{12}}\right)} \sqrt{b x + c} + \frac{2 \, {\left(140 \, {\left(b x + a\right)}^{\frac{9}{2}} - 495 \, {\left(b x + a\right)}^{\frac{7}{2}} a + 630 \, {\left(b x + a\right)}^{\frac{5}{2}} a^{2} - 315 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} + 135 \, {\left(b x + a\right)}^{\frac{7}{2}} c - 378 \, {\left(b x + a\right)}^{\frac{5}{2}} a c + 315 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} c\right)}}{315 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{3} c + 3 \, a b^{3} c^{2} - b^{3} c^{3}\right)}}"," ",0,"-2/315*(((5*(b*x + a)*(28*(a^9*b^12 - 9*a^8*b^12*c + 36*a^7*b^12*c^2 - 84*a^6*b^12*c^3 + 126*a^5*b^12*c^4 - 126*a^4*b^12*c^5 + 84*a^3*b^12*c^6 - 36*a^2*b^12*c^7 + 9*a*b^12*c^8 - b^12*c^9)*(b*x + a)/(a^12*b^15 - 12*a^11*b^15*c + 66*a^10*b^15*c^2 - 220*a^9*b^15*c^3 + 495*a^8*b^15*c^4 - 792*a^7*b^15*c^5 + 924*a^6*b^15*c^6 - 792*a^5*b^15*c^7 + 495*a^4*b^15*c^8 - 220*a^3*b^15*c^9 + 66*a^2*b^15*c^10 - 12*a*b^15*c^11 + b^15*c^12) - (85*a^10*b^12 - 778*a^9*b^12*c + 3177*a^8*b^12*c^2 - 7608*a^7*b^12*c^3 + 11802*a^6*b^12*c^4 - 12348*a^5*b^12*c^5 + 8778*a^4*b^12*c^6 - 4152*a^3*b^12*c^7 + 1233*a^2*b^12*c^8 - 202*a*b^12*c^9 + 13*b^12*c^10)/(a^12*b^15 - 12*a^11*b^15*c + 66*a^10*b^15*c^2 - 220*a^9*b^15*c^3 + 495*a^8*b^15*c^4 - 792*a^7*b^15*c^5 + 924*a^6*b^15*c^6 - 792*a^5*b^15*c^7 + 495*a^4*b^15*c^8 - 220*a^3*b^15*c^9 + 66*a^2*b^15*c^10 - 12*a*b^15*c^11 + b^15*c^12)) + 3*(145*a^11*b^12 - 1361*a^10*b^12*c + 5719*a^9*b^12*c^2 - 14151*a^8*b^12*c^3 + 22794*a^7*b^12*c^4 - 24906*a^6*b^12*c^5 + 18606*a^5*b^12*c^6 - 9294*a^4*b^12*c^7 + 2901*a^3*b^12*c^8 - 469*a^2*b^12*c^9 + 11*a*b^12*c^10 + 5*b^12*c^11)/(a^12*b^15 - 12*a^11*b^15*c + 66*a^10*b^15*c^2 - 220*a^9*b^15*c^3 + 495*a^8*b^15*c^4 - 792*a^7*b^15*c^5 + 924*a^6*b^15*c^6 - 792*a^5*b^15*c^7 + 495*a^4*b^15*c^8 - 220*a^3*b^15*c^9 + 66*a^2*b^15*c^10 - 12*a*b^15*c^11 + b^15*c^12))*(b*x + a) - (155*a^12*b^12 - 1536*a^11*b^12*c + 6855*a^10*b^12*c^2 - 18170*a^9*b^12*c^3 + 31770*a^8*b^12*c^4 - 38520*a^7*b^12*c^5 + 33222*a^6*b^12*c^6 - 20700*a^5*b^12*c^7 + 9495*a^4*b^12*c^8 - 3320*a^3*b^12*c^9 + 915*a^2*b^12*c^10 - 186*a*b^12*c^11 + 20*b^12*c^12)/(a^12*b^15 - 12*a^11*b^15*c + 66*a^10*b^15*c^2 - 220*a^9*b^15*c^3 + 495*a^8*b^15*c^4 - 792*a^7*b^15*c^5 + 924*a^6*b^15*c^6 - 792*a^5*b^15*c^7 + 495*a^4*b^15*c^8 - 220*a^3*b^15*c^9 + 66*a^2*b^15*c^10 - 12*a*b^15*c^11 + b^15*c^12))*(b*x + a) + (5*a^13*b^12 - 83*a^12*b^12*c + 543*a^11*b^12*c^2 - 1925*a^10*b^12*c^3 + 4070*a^9*b^12*c^4 - 4950*a^8*b^12*c^5 + 2046*a^7*b^12*c^6 + 3894*a^6*b^12*c^7 - 8415*a^5*b^12*c^8 + 8305*a^4*b^12*c^9 - 5005*a^3*b^12*c^10 + 1887*a^2*b^12*c^11 - 412*a*b^12*c^12 + 40*b^12*c^13)/(a^12*b^15 - 12*a^11*b^15*c + 66*a^10*b^15*c^2 - 220*a^9*b^15*c^3 + 495*a^8*b^15*c^4 - 792*a^7*b^15*c^5 + 924*a^6*b^15*c^6 - 792*a^5*b^15*c^7 + 495*a^4*b^15*c^8 - 220*a^3*b^15*c^9 + 66*a^2*b^15*c^10 - 12*a*b^15*c^11 + b^15*c^12))*sqrt(b*x + c) + 2/315*(140*(b*x + a)^(9/2) - 495*(b*x + a)^(7/2)*a + 630*(b*x + a)^(5/2)*a^2 - 315*(b*x + a)^(3/2)*a^3 + 135*(b*x + a)^(7/2)*c - 378*(b*x + a)^(5/2)*a*c + 315*(b*x + a)^(3/2)*a^2*c)/(a^3*b^3 - 3*a^2*b^3*c + 3*a*b^3*c^2 - b^3*c^3)","B",0
412,1,866,0,0.377672," ","integrate(x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left({\left(b x + a\right)} {\left(\frac{20 \, {\left(a^{6} b^{3} - 6 \, a^{5} b^{3} c + 15 \, a^{4} b^{3} c^{2} - 20 \, a^{3} b^{3} c^{3} + 15 \, a^{2} b^{3} c^{4} - 6 \, a b^{3} c^{5} + b^{3} c^{6}\right)} {\left(b x + a\right)}}{a^{9} b^{4} - 9 \, a^{8} b^{4} c + 36 \, a^{7} b^{4} c^{2} - 84 \, a^{6} b^{4} c^{3} + 126 \, a^{5} b^{4} c^{4} - 126 \, a^{4} b^{4} c^{5} + 84 \, a^{3} b^{4} c^{6} - 36 \, a^{2} b^{4} c^{7} + 9 \, a b^{4} c^{8} - b^{4} c^{9}} - \frac{39 \, a^{7} b^{3} - 245 \, a^{6} b^{3} c + 651 \, a^{5} b^{3} c^{2} - 945 \, a^{4} b^{3} c^{3} + 805 \, a^{3} b^{3} c^{4} - 399 \, a^{2} b^{3} c^{5} + 105 \, a b^{3} c^{6} - 11 \, b^{3} c^{7}}{a^{9} b^{4} - 9 \, a^{8} b^{4} c + 36 \, a^{7} b^{4} c^{2} - 84 \, a^{6} b^{4} c^{3} + 126 \, a^{5} b^{4} c^{4} - 126 \, a^{4} b^{4} c^{5} + 84 \, a^{3} b^{4} c^{6} - 36 \, a^{2} b^{4} c^{7} + 9 \, a b^{4} c^{8} - b^{4} c^{9}}\right)} + \frac{3 \, {\left(6 \, a^{8} b^{3} - 41 \, a^{7} b^{3} c + 119 \, a^{6} b^{3} c^{2} - 189 \, a^{5} b^{3} c^{3} + 175 \, a^{4} b^{3} c^{4} - 91 \, a^{3} b^{3} c^{5} + 21 \, a^{2} b^{3} c^{6} + a b^{3} c^{7} - b^{3} c^{8}\right)}}{a^{9} b^{4} - 9 \, a^{8} b^{4} c + 36 \, a^{7} b^{4} c^{2} - 84 \, a^{6} b^{4} c^{3} + 126 \, a^{5} b^{4} c^{4} - 126 \, a^{4} b^{4} c^{5} + 84 \, a^{3} b^{4} c^{6} - 36 \, a^{2} b^{4} c^{7} + 9 \, a b^{4} c^{8} - b^{4} c^{9}}\right)} {\left(b x + a\right)} + \frac{a^{9} b^{3} - 2 \, a^{8} b^{3} c - 20 \, a^{7} b^{3} c^{2} + 112 \, a^{6} b^{3} c^{3} - 266 \, a^{5} b^{3} c^{4} + 364 \, a^{4} b^{3} c^{5} - 308 \, a^{3} b^{3} c^{6} + 160 \, a^{2} b^{3} c^{7} - 47 \, a b^{3} c^{8} + 6 \, b^{3} c^{9}}{a^{9} b^{4} - 9 \, a^{8} b^{4} c + 36 \, a^{7} b^{4} c^{2} - 84 \, a^{6} b^{4} c^{3} + 126 \, a^{5} b^{4} c^{4} - 126 \, a^{4} b^{4} c^{5} + 84 \, a^{3} b^{4} c^{6} - 36 \, a^{2} b^{4} c^{7} + 9 \, a b^{4} c^{8} - b^{4} c^{9}}\right)} \sqrt{b x + c} - \frac{20 \, {\left(b x + a\right)}^{\frac{7}{2}} - 49 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} + 21 \, {\left(b x + a\right)}^{\frac{5}{2}} c - 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a c}{a^{3} b - 3 \, a^{2} b c + 3 \, a b c^{2} - b c^{3}}\right)}}{35 \, b}"," ",0,"-2/35*((((b*x + a)*(20*(a^6*b^3 - 6*a^5*b^3*c + 15*a^4*b^3*c^2 - 20*a^3*b^3*c^3 + 15*a^2*b^3*c^4 - 6*a*b^3*c^5 + b^3*c^6)*(b*x + a)/(a^9*b^4 - 9*a^8*b^4*c + 36*a^7*b^4*c^2 - 84*a^6*b^4*c^3 + 126*a^5*b^4*c^4 - 126*a^4*b^4*c^5 + 84*a^3*b^4*c^6 - 36*a^2*b^4*c^7 + 9*a*b^4*c^8 - b^4*c^9) - (39*a^7*b^3 - 245*a^6*b^3*c + 651*a^5*b^3*c^2 - 945*a^4*b^3*c^3 + 805*a^3*b^3*c^4 - 399*a^2*b^3*c^5 + 105*a*b^3*c^6 - 11*b^3*c^7)/(a^9*b^4 - 9*a^8*b^4*c + 36*a^7*b^4*c^2 - 84*a^6*b^4*c^3 + 126*a^5*b^4*c^4 - 126*a^4*b^4*c^5 + 84*a^3*b^4*c^6 - 36*a^2*b^4*c^7 + 9*a*b^4*c^8 - b^4*c^9)) + 3*(6*a^8*b^3 - 41*a^7*b^3*c + 119*a^6*b^3*c^2 - 189*a^5*b^3*c^3 + 175*a^4*b^3*c^4 - 91*a^3*b^3*c^5 + 21*a^2*b^3*c^6 + a*b^3*c^7 - b^3*c^8)/(a^9*b^4 - 9*a^8*b^4*c + 36*a^7*b^4*c^2 - 84*a^6*b^4*c^3 + 126*a^5*b^4*c^4 - 126*a^4*b^4*c^5 + 84*a^3*b^4*c^6 - 36*a^2*b^4*c^7 + 9*a*b^4*c^8 - b^4*c^9))*(b*x + a) + (a^9*b^3 - 2*a^8*b^3*c - 20*a^7*b^3*c^2 + 112*a^6*b^3*c^3 - 266*a^5*b^3*c^4 + 364*a^4*b^3*c^5 - 308*a^3*b^3*c^6 + 160*a^2*b^3*c^7 - 47*a*b^3*c^8 + 6*b^3*c^9)/(a^9*b^4 - 9*a^8*b^4*c + 36*a^7*b^4*c^2 - 84*a^6*b^4*c^3 + 126*a^5*b^4*c^4 - 126*a^4*b^4*c^5 + 84*a^3*b^4*c^6 - 36*a^2*b^4*c^7 + 9*a*b^4*c^8 - b^4*c^9))*sqrt(b*x + c) - (20*(b*x + a)^(7/2) - 49*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2 + 21*(b*x + a)^(5/2)*c - 35*(b*x + a)^(3/2)*a*c)/(a^3*b - 3*a^2*b*c + 3*a*b*c^2 - b*c^3))/b","B",0
413,1,427,0,0.302371," ","integrate(1/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""giac"")","-\frac{2}{5} \, {\left({\left(b x + a\right)} {\left(\frac{4 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{2} c + 3 \, a b^{2} c^{2} - b^{2} c^{3}\right)} {\left(b x + a\right)}}{a^{6} b^{3} - 6 \, a^{5} b^{3} c + 15 \, a^{4} b^{3} c^{2} - 20 \, a^{3} b^{3} c^{3} + 15 \, a^{2} b^{3} c^{4} - 6 \, a b^{3} c^{5} + b^{3} c^{6}} - \frac{3 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{2} c + 6 \, a^{2} b^{2} c^{2} - 4 \, a b^{2} c^{3} + b^{2} c^{4}\right)}}{a^{6} b^{3} - 6 \, a^{5} b^{3} c + 15 \, a^{4} b^{3} c^{2} - 20 \, a^{3} b^{3} c^{3} + 15 \, a^{2} b^{3} c^{4} - 6 \, a b^{3} c^{5} + b^{3} c^{6}}\right)} - \frac{a^{5} b^{2} - 5 \, a^{4} b^{2} c + 10 \, a^{3} b^{2} c^{2} - 10 \, a^{2} b^{2} c^{3} + 5 \, a b^{2} c^{4} - b^{2} c^{5}}{a^{6} b^{3} - 6 \, a^{5} b^{3} c + 15 \, a^{4} b^{3} c^{2} - 20 \, a^{3} b^{3} c^{3} + 15 \, a^{2} b^{3} c^{4} - 6 \, a b^{3} c^{5} + b^{3} c^{6}}\right)} \sqrt{b x + c} + \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{\frac{5}{2}} - 5 \, {\left(b x + a\right)}^{\frac{3}{2}} a + 5 \, {\left(b x + a\right)}^{\frac{3}{2}} c\right)}}{5 \, {\left(a^{3} b - 3 \, a^{2} b c + 3 \, a b c^{2} - b c^{3}\right)}}"," ",0,"-2/5*((b*x + a)*(4*(a^3*b^2 - 3*a^2*b^2*c + 3*a*b^2*c^2 - b^2*c^3)*(b*x + a)/(a^6*b^3 - 6*a^5*b^3*c + 15*a^4*b^3*c^2 - 20*a^3*b^3*c^3 + 15*a^2*b^3*c^4 - 6*a*b^3*c^5 + b^3*c^6) - 3*(a^4*b^2 - 4*a^3*b^2*c + 6*a^2*b^2*c^2 - 4*a*b^2*c^3 + b^2*c^4)/(a^6*b^3 - 6*a^5*b^3*c + 15*a^4*b^3*c^2 - 20*a^3*b^3*c^3 + 15*a^2*b^3*c^4 - 6*a*b^3*c^5 + b^3*c^6)) - (a^5*b^2 - 5*a^4*b^2*c + 10*a^3*b^2*c^2 - 10*a^2*b^2*c^3 + 5*a*b^2*c^4 - b^2*c^5)/(a^6*b^3 - 6*a^5*b^3*c + 15*a^4*b^3*c^2 - 20*a^3*b^3*c^3 + 15*a^2*b^3*c^4 - 6*a*b^3*c^5 + b^3*c^6))*sqrt(b*x + c) + 2/5*(4*(b*x + a)^(5/2) - 5*(b*x + a)^(3/2)*a + 5*(b*x + a)^(3/2)*c)/(a^3*b - 3*a^2*b*c + 3*a*b*c^2 - b*c^3)","B",0
414,1,2652,0,2.909179," ","integrate(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{b x + c} {\left(\frac{4 \, {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} {\left(b x + a\right)}}{a^{6} - 6 \, a^{5} c + 15 \, a^{4} c^{2} - 20 \, a^{3} c^{3} + 15 \, a^{2} c^{4} - 6 \, a c^{5} + c^{6}} + \frac{5 \, a^{4} - 8 \, a^{3} c - 6 \, a^{2} c^{2} + 16 \, a c^{3} - 7 \, c^{4}}{a^{6} - 6 \, a^{5} c + 15 \, a^{4} c^{2} - 20 \, a^{3} c^{3} + 15 \, a^{2} c^{4} - 6 \, a c^{5} + c^{6}}\right)} + \frac{2 \, {\left(a^{2} + 3 \, a c\right)} \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{{\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} \sqrt{-a}} + \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{6} + 3 \, \sqrt{b x + a} a^{7} - 24 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{5} c - 9 \, \sqrt{b x + a} a^{6} c + 60 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{4} c^{2} - 9 \, \sqrt{b x + a} a^{5} c^{2} - 80 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{3} c^{3} + 75 \, \sqrt{b x + a} a^{4} c^{3} + 60 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} c^{4} - 135 \, \sqrt{b x + a} a^{3} c^{4} - 24 \, {\left(b x + a\right)}^{\frac{3}{2}} a c^{5} + 117 \, \sqrt{b x + a} a^{2} c^{5} + 4 \, {\left(b x + a\right)}^{\frac{3}{2}} c^{6} - 51 \, \sqrt{b x + a} a c^{6} + 9 \, \sqrt{b x + a} c^{7}\right)}}{3 \, {\left(a^{9} - 9 \, a^{8} c + 36 \, a^{7} c^{2} - 84 \, a^{6} c^{3} + 126 \, a^{5} c^{4} - 126 \, a^{4} c^{5} + 84 \, a^{3} c^{6} - 36 \, a^{2} c^{7} + 9 \, a c^{8} - c^{9}\right)}} - \frac{2 \, {\left(3 \, a^{9} c - 14 \, a^{8} c^{2} + 22 \, a^{7} c^{3} - 6 \, a^{6} c^{4} - 20 \, a^{5} c^{5} + 22 \, a^{4} c^{6} - 6 \, a^{3} c^{7} - 2 \, a^{2} c^{8} + a c^{9} - 2 \, {\left(3 \, a^{2} c^{2} + a c^{3} + {\left(3 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} \mathrm{sgn}\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right) - 2 \, {\left(3 \, a^{2} c^{2} + a c^{3} - {\left(3 \, a^{2} c + a c^{2}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} - {\left(3 \, a^{5} c^{2} - 11 \, a^{4} c^{3} + 14 \, a^{3} c^{4} - 6 \, a^{2} c^{5} - a c^{6} + c^{7} - {\left(3 \, a^{5} c - 11 \, a^{4} c^{2} + 14 \, a^{3} c^{3} - 6 \, a^{2} c^{4} - a c^{5} + c^{6}\right)} \sqrt{a c}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} \mathrm{sgn}\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right) - {\left(3 \, a^{6} c - 11 \, a^{5} c^{2} + 14 \, a^{4} c^{3} - 6 \, a^{3} c^{4} - a^{2} c^{5} + a c^{6} + {\left(3 \, a^{5} c - 11 \, a^{4} c^{2} + 14 \, a^{3} c^{3} - 6 \, a^{2} c^{4} - a c^{5} + c^{6}\right)} \sqrt{a c}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} + {\left(3 \, a^{9} c - 14 \, a^{8} c^{2} + 22 \, a^{7} c^{3} - 6 \, a^{6} c^{4} - 20 \, a^{5} c^{5} + 22 \, a^{4} c^{6} - 6 \, a^{3} c^{7} - 2 \, a^{2} c^{8} + a c^{9} - {\left(3 \, a^{8} c - 14 \, a^{7} c^{2} + 22 \, a^{6} c^{3} - 6 \, a^{5} c^{4} - 20 \, a^{4} c^{5} + 22 \, a^{3} c^{6} - 6 \, a^{2} c^{7} - 2 \, a c^{8} + c^{9}\right)} \sqrt{a c}\right)} \mathrm{sgn}\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right) + {\left(3 \, a^{9} - 14 \, a^{8} c + 22 \, a^{7} c^{2} - 6 \, a^{6} c^{3} - 20 \, a^{5} c^{4} + 22 \, a^{4} c^{5} - 6 \, a^{3} c^{6} - 2 \, a^{2} c^{7} + a c^{8}\right)} \sqrt{a c}\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4} + \sqrt{{\left(a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4}\right)}^{2} - {\left(a^{5} - 5 \, a^{4} c + 10 \, a^{3} c^{2} - 10 \, a^{2} c^{3} + 5 \, a c^{4} - c^{5}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}}{a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}}}}\right)}{{\left(\sqrt{-a} a^{8} - a^{8} \sqrt{-c} - 8 \, \sqrt{-a} a^{7} c + 8 \, a^{7} \sqrt{-c} c + 28 \, \sqrt{-a} a^{6} c^{2} - 28 \, a^{6} \sqrt{-c} c^{2} - 56 \, \sqrt{-a} a^{5} c^{3} + 56 \, a^{5} \sqrt{-c} c^{3} + 70 \, \sqrt{-a} a^{4} c^{4} - 70 \, a^{4} \sqrt{-c} c^{4} - 56 \, \sqrt{-a} a^{3} c^{5} + 56 \, a^{3} \sqrt{-c} c^{5} + 28 \, \sqrt{-a} a^{2} c^{6} - 28 \, a^{2} \sqrt{-c} c^{6} - 8 \, \sqrt{-a} a c^{7} + 8 \, a \sqrt{-c} c^{7} + \sqrt{-a} c^{8} - \sqrt{-c} c^{8}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|}} + \frac{2 \, {\left(3 \, a^{9} c - 14 \, a^{8} c^{2} + 22 \, a^{7} c^{3} - 6 \, a^{6} c^{4} - 20 \, a^{5} c^{5} + 22 \, a^{4} c^{6} - 6 \, a^{3} c^{7} - 2 \, a^{2} c^{8} + a c^{9} + 2 \, {\left(3 \, a^{2} c^{2} + a c^{3} + {\left(3 \, a c^{2} + c^{3}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} \mathrm{sgn}\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right) - 2 \, {\left(3 \, a^{2} c^{2} + a c^{3} + {\left(3 \, a^{2} c + a c^{2}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} - {\left(3 \, a^{5} c^{2} - 11 \, a^{4} c^{3} + 14 \, a^{3} c^{4} - 6 \, a^{2} c^{5} - a c^{6} + c^{7} - {\left(3 \, a^{5} c - 11 \, a^{4} c^{2} + 14 \, a^{3} c^{3} - 6 \, a^{2} c^{4} - a c^{5} + c^{6}\right)} \sqrt{a c}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} \mathrm{sgn}\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right) + {\left(3 \, a^{6} c - 11 \, a^{5} c^{2} + 14 \, a^{4} c^{3} - 6 \, a^{3} c^{4} - a^{2} c^{5} + a c^{6} + {\left(3 \, a^{5} c - 11 \, a^{4} c^{2} + 14 \, a^{3} c^{3} - 6 \, a^{2} c^{4} - a c^{5} + c^{6}\right)} \sqrt{a c}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} - {\left(3 \, a^{9} c - 14 \, a^{8} c^{2} + 22 \, a^{7} c^{3} - 6 \, a^{6} c^{4} - 20 \, a^{5} c^{5} + 22 \, a^{4} c^{6} - 6 \, a^{3} c^{7} - 2 \, a^{2} c^{8} + a c^{9} + {\left(3 \, a^{8} c - 14 \, a^{7} c^{2} + 22 \, a^{6} c^{3} - 6 \, a^{5} c^{4} - 20 \, a^{4} c^{5} + 22 \, a^{3} c^{6} - 6 \, a^{2} c^{7} - 2 \, a c^{8} + c^{9}\right)} \sqrt{a c}\right)} \mathrm{sgn}\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right) + {\left(3 \, a^{9} - 14 \, a^{8} c + 22 \, a^{7} c^{2} - 6 \, a^{6} c^{3} - 20 \, a^{5} c^{4} + 22 \, a^{4} c^{5} - 6 \, a^{3} c^{6} - 2 \, a^{2} c^{7} + a c^{8}\right)} \sqrt{a c}\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4} - \sqrt{{\left(a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4}\right)}^{2} - {\left(a^{5} - 5 \, a^{4} c + 10 \, a^{3} c^{2} - 10 \, a^{2} c^{3} + 5 \, a c^{4} - c^{5}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}}{a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}}}}\right)}{{\left(\sqrt{-a} a^{8} - a^{8} \sqrt{-c} - 8 \, \sqrt{-a} a^{7} c + 8 \, a^{7} \sqrt{-c} c + 28 \, \sqrt{-a} a^{6} c^{2} - 28 \, a^{6} \sqrt{-c} c^{2} - 56 \, \sqrt{-a} a^{5} c^{3} + 56 \, a^{5} \sqrt{-c} c^{3} + 70 \, \sqrt{-a} a^{4} c^{4} - 70 \, a^{4} \sqrt{-c} c^{4} - 56 \, \sqrt{-a} a^{3} c^{5} + 56 \, a^{3} \sqrt{-c} c^{5} + 28 \, \sqrt{-a} a^{2} c^{6} - 28 \, a^{2} \sqrt{-c} c^{6} - 8 \, \sqrt{-a} a c^{7} + 8 \, a \sqrt{-c} c^{7} + \sqrt{-a} c^{8} - \sqrt{-c} c^{8}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|}}"," ",0,"-2/3*sqrt(b*x + c)*(4*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)*(b*x + a)/(a^6 - 6*a^5*c + 15*a^4*c^2 - 20*a^3*c^3 + 15*a^2*c^4 - 6*a*c^5 + c^6) + (5*a^4 - 8*a^3*c - 6*a^2*c^2 + 16*a*c^3 - 7*c^4)/(a^6 - 6*a^5*c + 15*a^4*c^2 - 20*a^3*c^3 + 15*a^2*c^4 - 6*a*c^5 + c^6)) + 2*(a^2 + 3*a*c)*arctan(sqrt(b*x + a)/sqrt(-a))/((a^3 - 3*a^2*c + 3*a*c^2 - c^3)*sqrt(-a)) + 2/3*(4*(b*x + a)^(3/2)*a^6 + 3*sqrt(b*x + a)*a^7 - 24*(b*x + a)^(3/2)*a^5*c - 9*sqrt(b*x + a)*a^6*c + 60*(b*x + a)^(3/2)*a^4*c^2 - 9*sqrt(b*x + a)*a^5*c^2 - 80*(b*x + a)^(3/2)*a^3*c^3 + 75*sqrt(b*x + a)*a^4*c^3 + 60*(b*x + a)^(3/2)*a^2*c^4 - 135*sqrt(b*x + a)*a^3*c^4 - 24*(b*x + a)^(3/2)*a*c^5 + 117*sqrt(b*x + a)*a^2*c^5 + 4*(b*x + a)^(3/2)*c^6 - 51*sqrt(b*x + a)*a*c^6 + 9*sqrt(b*x + a)*c^7)/(a^9 - 9*a^8*c + 36*a^7*c^2 - 84*a^6*c^3 + 126*a^5*c^4 - 126*a^4*c^5 + 84*a^3*c^6 - 36*a^2*c^7 + 9*a*c^8 - c^9) - 2*(3*a^9*c - 14*a^8*c^2 + 22*a^7*c^3 - 6*a^6*c^4 - 20*a^5*c^5 + 22*a^4*c^6 - 6*a^3*c^7 - 2*a^2*c^8 + a*c^9 - 2*(3*a^2*c^2 + a*c^3 + (3*a*c^2 + c^3)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2*sgn(a^3 - 3*a^2*c + 3*a*c^2 - c^3) - 2*(3*a^2*c^2 + a*c^3 - (3*a^2*c + a*c^2)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2 - (3*a^5*c^2 - 11*a^4*c^3 + 14*a^3*c^4 - 6*a^2*c^5 - a*c^6 + c^7 - (3*a^5*c - 11*a^4*c^2 + 14*a^3*c^3 - 6*a^2*c^4 - a*c^5 + c^6)*sqrt(a*c))*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)*sgn(a^3 - 3*a^2*c + 3*a*c^2 - c^3) - (3*a^6*c - 11*a^5*c^2 + 14*a^4*c^3 - 6*a^3*c^4 - a^2*c^5 + a*c^6 + (3*a^5*c - 11*a^4*c^2 + 14*a^3*c^3 - 6*a^2*c^4 - a*c^5 + c^6)*sqrt(a*c))*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3) + (3*a^9*c - 14*a^8*c^2 + 22*a^7*c^3 - 6*a^6*c^4 - 20*a^5*c^5 + 22*a^4*c^6 - 6*a^3*c^7 - 2*a^2*c^8 + a*c^9 - (3*a^8*c - 14*a^7*c^2 + 22*a^6*c^3 - 6*a^5*c^4 - 20*a^4*c^5 + 22*a^3*c^6 - 6*a^2*c^7 - 2*a*c^8 + c^9)*sqrt(a*c))*sgn(a^3 - 3*a^2*c + 3*a*c^2 - c^3) + (3*a^9 - 14*a^8*c + 22*a^7*c^2 - 6*a^6*c^3 - 20*a^5*c^4 + 22*a^4*c^5 - 6*a^3*c^6 - 2*a^2*c^7 + a*c^8)*sqrt(a*c))*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^4 - 2*a^3*c + 2*a*c^3 - c^4 + sqrt((a^4 - 2*a^3*c + 2*a*c^3 - c^4)^2 - (a^5 - 5*a^4*c + 10*a^3*c^2 - 10*a^2*c^3 + 5*a*c^4 - c^5)*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/((sqrt(-a)*a^8 - a^8*sqrt(-c) - 8*sqrt(-a)*a^7*c + 8*a^7*sqrt(-c)*c + 28*sqrt(-a)*a^6*c^2 - 28*a^6*sqrt(-c)*c^2 - 56*sqrt(-a)*a^5*c^3 + 56*a^5*sqrt(-c)*c^3 + 70*sqrt(-a)*a^4*c^4 - 70*a^4*sqrt(-c)*c^4 - 56*sqrt(-a)*a^3*c^5 + 56*a^3*sqrt(-c)*c^5 + 28*sqrt(-a)*a^2*c^6 - 28*a^2*sqrt(-c)*c^6 - 8*sqrt(-a)*a*c^7 + 8*a*sqrt(-c)*c^7 + sqrt(-a)*c^8 - sqrt(-c)*c^8)*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)) + 2*(3*a^9*c - 14*a^8*c^2 + 22*a^7*c^3 - 6*a^6*c^4 - 20*a^5*c^5 + 22*a^4*c^6 - 6*a^3*c^7 - 2*a^2*c^8 + a*c^9 + 2*(3*a^2*c^2 + a*c^3 + (3*a*c^2 + c^3)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2*sgn(a^3 - 3*a^2*c + 3*a*c^2 - c^3) - 2*(3*a^2*c^2 + a*c^3 + (3*a^2*c + a*c^2)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2 - (3*a^5*c^2 - 11*a^4*c^3 + 14*a^3*c^4 - 6*a^2*c^5 - a*c^6 + c^7 - (3*a^5*c - 11*a^4*c^2 + 14*a^3*c^3 - 6*a^2*c^4 - a*c^5 + c^6)*sqrt(a*c))*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)*sgn(a^3 - 3*a^2*c + 3*a*c^2 - c^3) + (3*a^6*c - 11*a^5*c^2 + 14*a^4*c^3 - 6*a^3*c^4 - a^2*c^5 + a*c^6 + (3*a^5*c - 11*a^4*c^2 + 14*a^3*c^3 - 6*a^2*c^4 - a*c^5 + c^6)*sqrt(a*c))*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3) - (3*a^9*c - 14*a^8*c^2 + 22*a^7*c^3 - 6*a^6*c^4 - 20*a^5*c^5 + 22*a^4*c^6 - 6*a^3*c^7 - 2*a^2*c^8 + a*c^9 + (3*a^8*c - 14*a^7*c^2 + 22*a^6*c^3 - 6*a^5*c^4 - 20*a^4*c^5 + 22*a^3*c^6 - 6*a^2*c^7 - 2*a*c^8 + c^9)*sqrt(a*c))*sgn(a^3 - 3*a^2*c + 3*a*c^2 - c^3) + (3*a^9 - 14*a^8*c + 22*a^7*c^2 - 6*a^6*c^3 - 20*a^5*c^4 + 22*a^4*c^5 - 6*a^3*c^6 - 2*a^2*c^7 + a*c^8)*sqrt(a*c))*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^4 - 2*a^3*c + 2*a*c^3 - c^4 - sqrt((a^4 - 2*a^3*c + 2*a*c^3 - c^4)^2 - (a^5 - 5*a^4*c + 10*a^3*c^2 - 10*a^2*c^3 + 5*a*c^4 - c^5)*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/((sqrt(-a)*a^8 - a^8*sqrt(-c) - 8*sqrt(-a)*a^7*c + 8*a^7*sqrt(-c)*c + 28*sqrt(-a)*a^6*c^2 - 28*a^6*sqrt(-c)*c^2 - 56*sqrt(-a)*a^5*c^3 + 56*a^5*sqrt(-c)*c^3 + 70*sqrt(-a)*a^4*c^4 - 70*a^4*sqrt(-c)*c^4 - 56*sqrt(-a)*a^3*c^5 + 56*a^3*sqrt(-c)*c^5 + 28*sqrt(-a)*a^2*c^6 - 28*a^2*sqrt(-c)*c^6 - 8*sqrt(-a)*a*c^7 + 8*a*sqrt(-c)*c^7 + sqrt(-a)*c^8 - sqrt(-c)*c^8)*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3))","B",0
415,1,2594,0,39.981438," ","integrate(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x, algorithm=""giac"")","\frac{8 \, \sqrt{b x + a} b}{a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}} - \frac{8 \, \sqrt{b x + c} b}{a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}} + \frac{3 \, {\left(3 \, a b + b c\right)} \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{{\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} \sqrt{-a}} - \frac{3 \, {\left(2 \, {\left(a^{2} c^{2} + 3 \, a c^{3} + {\left(a c^{2} + 3 \, c^{3}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} b \mathrm{sgn}\left(-2 \, a^{3} + 6 \, a^{2} c - 6 \, a c^{2} + 2 \, c^{3}\right) - 2 \, {\left(a^{2} c^{2} + 3 \, a c^{3} - {\left(a^{2} c + 3 \, a c^{2}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} b + {\left(a^{5} c^{2} - a^{4} c^{3} - 6 \, a^{3} c^{4} + 14 \, a^{2} c^{5} - 11 \, a c^{6} + 3 \, c^{7} + {\left(a^{5} c - a^{4} c^{2} - 6 \, a^{3} c^{3} + 14 \, a^{2} c^{4} - 11 \, a c^{5} + 3 \, c^{6}\right)} \sqrt{a c}\right)} b {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} \mathrm{sgn}\left(-2 \, a^{3} + 6 \, a^{2} c - 6 \, a c^{2} + 2 \, c^{3}\right) - {\left(a^{6} c - a^{5} c^{2} - 6 \, a^{4} c^{3} + 14 \, a^{3} c^{4} - 11 \, a^{2} c^{5} + 3 \, a c^{6} + {\left(a^{5} c - a^{4} c^{2} - 6 \, a^{3} c^{3} + 14 \, a^{2} c^{4} - 11 \, a c^{5} + 3 \, c^{6}\right)} \sqrt{a c}\right)} b {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} - {\left(a^{9} c - 2 \, a^{8} c^{2} - 6 \, a^{7} c^{3} + 22 \, a^{6} c^{4} - 20 \, a^{5} c^{5} - 6 \, a^{4} c^{6} + 22 \, a^{3} c^{7} - 14 \, a^{2} c^{8} + 3 \, a c^{9} + {\left(a^{8} c - 2 \, a^{7} c^{2} - 6 \, a^{6} c^{3} + 22 \, a^{5} c^{4} - 20 \, a^{4} c^{5} - 6 \, a^{3} c^{6} + 22 \, a^{2} c^{7} - 14 \, a c^{8} + 3 \, c^{9}\right)} \sqrt{a c}\right)} b \mathrm{sgn}\left(-2 \, a^{3} + 6 \, a^{2} c - 6 \, a c^{2} + 2 \, c^{3}\right) + {\left(a^{9} c - 2 \, a^{8} c^{2} - 6 \, a^{7} c^{3} + 22 \, a^{6} c^{4} - 20 \, a^{5} c^{5} - 6 \, a^{4} c^{6} + 22 \, a^{3} c^{7} - 14 \, a^{2} c^{8} + 3 \, a c^{9} + {\left(a^{9} - 2 \, a^{8} c - 6 \, a^{7} c^{2} + 22 \, a^{6} c^{3} - 20 \, a^{5} c^{4} - 6 \, a^{4} c^{5} + 22 \, a^{3} c^{6} - 14 \, a^{2} c^{7} + 3 \, a c^{8}\right)} \sqrt{a c}\right)} b\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4} + \sqrt{{\left(a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4}\right)}^{2} - {\left(a^{5} - 5 \, a^{4} c + 10 \, a^{3} c^{2} - 10 \, a^{2} c^{3} + 5 \, a c^{4} - c^{5}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}}{a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}}}}\right)}{{\left(\sqrt{-a} a^{8} c - a^{8} \sqrt{-c} c - 8 \, \sqrt{-a} a^{7} c^{2} + 8 \, a^{7} \sqrt{-c} c^{2} + 28 \, \sqrt{-a} a^{6} c^{3} - 28 \, a^{6} \sqrt{-c} c^{3} - 56 \, \sqrt{-a} a^{5} c^{4} + 56 \, a^{5} \sqrt{-c} c^{4} + 70 \, \sqrt{-a} a^{4} c^{5} - 70 \, a^{4} \sqrt{-c} c^{5} - 56 \, \sqrt{-a} a^{3} c^{6} + 56 \, a^{3} \sqrt{-c} c^{6} + 28 \, \sqrt{-a} a^{2} c^{7} - 28 \, a^{2} \sqrt{-c} c^{7} - 8 \, \sqrt{-a} a c^{8} + 8 \, a \sqrt{-c} c^{8} + \sqrt{-a} c^{9} - \sqrt{-c} c^{9}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|}} - \frac{3 \, {\left(2 \, {\left(a^{2} c^{2} + 3 \, a c^{3} + {\left(a c^{2} + 3 \, c^{3}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} b \mathrm{sgn}\left(-2 \, a^{3} + 6 \, a^{2} c - 6 \, a c^{2} + 2 \, c^{3}\right) + 2 \, {\left(a^{2} c^{2} + 3 \, a c^{3} + {\left(a^{2} c + 3 \, a c^{2}\right)} \sqrt{a c}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}^{2} b - {\left(a^{5} c^{2} - a^{4} c^{3} - 6 \, a^{3} c^{4} + 14 \, a^{2} c^{5} - 11 \, a c^{6} + 3 \, c^{7} + {\left(a^{5} c - a^{4} c^{2} - 6 \, a^{3} c^{3} + 14 \, a^{2} c^{4} - 11 \, a c^{5} + 3 \, c^{6}\right)} \sqrt{a c}\right)} b {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} \mathrm{sgn}\left(-2 \, a^{3} + 6 \, a^{2} c - 6 \, a c^{2} + 2 \, c^{3}\right) - {\left(a^{6} c - a^{5} c^{2} - 6 \, a^{4} c^{3} + 14 \, a^{3} c^{4} - 11 \, a^{2} c^{5} + 3 \, a c^{6} + {\left(a^{5} c - a^{4} c^{2} - 6 \, a^{3} c^{3} + 14 \, a^{2} c^{4} - 11 \, a c^{5} + 3 \, c^{6}\right)} \sqrt{a c}\right)} b {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|} - {\left(a^{9} c - 2 \, a^{8} c^{2} - 6 \, a^{7} c^{3} + 22 \, a^{6} c^{4} - 20 \, a^{5} c^{5} - 6 \, a^{4} c^{6} + 22 \, a^{3} c^{7} - 14 \, a^{2} c^{8} + 3 \, a c^{9} + {\left(a^{8} c - 2 \, a^{7} c^{2} - 6 \, a^{6} c^{3} + 22 \, a^{5} c^{4} - 20 \, a^{4} c^{5} - 6 \, a^{3} c^{6} + 22 \, a^{2} c^{7} - 14 \, a c^{8} + 3 \, c^{9}\right)} \sqrt{a c}\right)} b \mathrm{sgn}\left(-2 \, a^{3} + 6 \, a^{2} c - 6 \, a c^{2} + 2 \, c^{3}\right) - {\left(a^{9} c - 2 \, a^{8} c^{2} - 6 \, a^{7} c^{3} + 22 \, a^{6} c^{4} - 20 \, a^{5} c^{5} - 6 \, a^{4} c^{6} + 22 \, a^{3} c^{7} - 14 \, a^{2} c^{8} + 3 \, a c^{9} - {\left(a^{9} - 2 \, a^{8} c - 6 \, a^{7} c^{2} + 22 \, a^{6} c^{3} - 20 \, a^{5} c^{4} - 6 \, a^{4} c^{5} + 22 \, a^{3} c^{6} - 14 \, a^{2} c^{7} + 3 \, a c^{8}\right)} \sqrt{a c}\right)} b\right)} \arctan\left(-\frac{\sqrt{b x + a} - \sqrt{b x + c}}{\sqrt{-\frac{a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4} - \sqrt{{\left(a^{4} - 2 \, a^{3} c + 2 \, a c^{3} - c^{4}\right)}^{2} - {\left(a^{5} - 5 \, a^{4} c + 10 \, a^{3} c^{2} - 10 \, a^{2} c^{3} + 5 \, a c^{4} - c^{5}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}}}{a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}}}}\right)}{{\left(\sqrt{-a} a^{8} c - a^{8} \sqrt{-c} c - 8 \, \sqrt{-a} a^{7} c^{2} + 8 \, a^{7} \sqrt{-c} c^{2} + 28 \, \sqrt{-a} a^{6} c^{3} - 28 \, a^{6} \sqrt{-c} c^{3} - 56 \, \sqrt{-a} a^{5} c^{4} + 56 \, a^{5} \sqrt{-c} c^{4} + 70 \, \sqrt{-a} a^{4} c^{5} - 70 \, a^{4} \sqrt{-c} c^{5} - 56 \, \sqrt{-a} a^{3} c^{6} + 56 \, a^{3} \sqrt{-c} c^{6} + 28 \, \sqrt{-a} a^{2} c^{7} - 28 \, a^{2} \sqrt{-c} c^{7} - 8 \, \sqrt{-a} a c^{8} + 8 \, a \sqrt{-c} c^{8} + \sqrt{-a} c^{9} - \sqrt{-c} c^{9}\right)} {\left| -a^{3} + 3 \, a^{2} c - 3 \, a c^{2} + c^{3} \right|}} - \frac{2 \, {\left(3 \, a b {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{3} + b c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{3} - 3 \, a^{2} b {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)} + 2 \, a b c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)} + b c^{2} {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}\right)}}{{\left({\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{4} - 2 \, a {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} - 2 \, c {\left(\sqrt{b x + a} - \sqrt{b x + c}\right)}^{2} + a^{2} - 2 \, a c + c^{2}\right)} {\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)}} - \frac{\sqrt{b x + a} a b + 3 \, \sqrt{b x + a} b c}{{\left(a^{3} - 3 \, a^{2} c + 3 \, a c^{2} - c^{3}\right)} b x}"," ",0,"8*sqrt(b*x + a)*b/(a^3 - 3*a^2*c + 3*a*c^2 - c^3) - 8*sqrt(b*x + c)*b/(a^3 - 3*a^2*c + 3*a*c^2 - c^3) + 3*(3*a*b + b*c)*arctan(sqrt(b*x + a)/sqrt(-a))/((a^3 - 3*a^2*c + 3*a*c^2 - c^3)*sqrt(-a)) - 3*(2*(a^2*c^2 + 3*a*c^3 + (a*c^2 + 3*c^3)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2*b*sgn(-2*a^3 + 6*a^2*c - 6*a*c^2 + 2*c^3) - 2*(a^2*c^2 + 3*a*c^3 - (a^2*c + 3*a*c^2)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2*b + (a^5*c^2 - a^4*c^3 - 6*a^3*c^4 + 14*a^2*c^5 - 11*a*c^6 + 3*c^7 + (a^5*c - a^4*c^2 - 6*a^3*c^3 + 14*a^2*c^4 - 11*a*c^5 + 3*c^6)*sqrt(a*c))*b*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)*sgn(-2*a^3 + 6*a^2*c - 6*a*c^2 + 2*c^3) - (a^6*c - a^5*c^2 - 6*a^4*c^3 + 14*a^3*c^4 - 11*a^2*c^5 + 3*a*c^6 + (a^5*c - a^4*c^2 - 6*a^3*c^3 + 14*a^2*c^4 - 11*a*c^5 + 3*c^6)*sqrt(a*c))*b*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3) - (a^9*c - 2*a^8*c^2 - 6*a^7*c^3 + 22*a^6*c^4 - 20*a^5*c^5 - 6*a^4*c^6 + 22*a^3*c^7 - 14*a^2*c^8 + 3*a*c^9 + (a^8*c - 2*a^7*c^2 - 6*a^6*c^3 + 22*a^5*c^4 - 20*a^4*c^5 - 6*a^3*c^6 + 22*a^2*c^7 - 14*a*c^8 + 3*c^9)*sqrt(a*c))*b*sgn(-2*a^3 + 6*a^2*c - 6*a*c^2 + 2*c^3) + (a^9*c - 2*a^8*c^2 - 6*a^7*c^3 + 22*a^6*c^4 - 20*a^5*c^5 - 6*a^4*c^6 + 22*a^3*c^7 - 14*a^2*c^8 + 3*a*c^9 + (a^9 - 2*a^8*c - 6*a^7*c^2 + 22*a^6*c^3 - 20*a^5*c^4 - 6*a^4*c^5 + 22*a^3*c^6 - 14*a^2*c^7 + 3*a*c^8)*sqrt(a*c))*b)*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^4 - 2*a^3*c + 2*a*c^3 - c^4 + sqrt((a^4 - 2*a^3*c + 2*a*c^3 - c^4)^2 - (a^5 - 5*a^4*c + 10*a^3*c^2 - 10*a^2*c^3 + 5*a*c^4 - c^5)*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/((sqrt(-a)*a^8*c - a^8*sqrt(-c)*c - 8*sqrt(-a)*a^7*c^2 + 8*a^7*sqrt(-c)*c^2 + 28*sqrt(-a)*a^6*c^3 - 28*a^6*sqrt(-c)*c^3 - 56*sqrt(-a)*a^5*c^4 + 56*a^5*sqrt(-c)*c^4 + 70*sqrt(-a)*a^4*c^5 - 70*a^4*sqrt(-c)*c^5 - 56*sqrt(-a)*a^3*c^6 + 56*a^3*sqrt(-c)*c^6 + 28*sqrt(-a)*a^2*c^7 - 28*a^2*sqrt(-c)*c^7 - 8*sqrt(-a)*a*c^8 + 8*a*sqrt(-c)*c^8 + sqrt(-a)*c^9 - sqrt(-c)*c^9)*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)) - 3*(2*(a^2*c^2 + 3*a*c^3 + (a*c^2 + 3*c^3)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2*b*sgn(-2*a^3 + 6*a^2*c - 6*a*c^2 + 2*c^3) + 2*(a^2*c^2 + 3*a*c^3 + (a^2*c + 3*a*c^2)*sqrt(a*c))*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)^2*b - (a^5*c^2 - a^4*c^3 - 6*a^3*c^4 + 14*a^2*c^5 - 11*a*c^6 + 3*c^7 + (a^5*c - a^4*c^2 - 6*a^3*c^3 + 14*a^2*c^4 - 11*a*c^5 + 3*c^6)*sqrt(a*c))*b*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)*sgn(-2*a^3 + 6*a^2*c - 6*a*c^2 + 2*c^3) - (a^6*c - a^5*c^2 - 6*a^4*c^3 + 14*a^3*c^4 - 11*a^2*c^5 + 3*a*c^6 + (a^5*c - a^4*c^2 - 6*a^3*c^3 + 14*a^2*c^4 - 11*a*c^5 + 3*c^6)*sqrt(a*c))*b*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3) - (a^9*c - 2*a^8*c^2 - 6*a^7*c^3 + 22*a^6*c^4 - 20*a^5*c^5 - 6*a^4*c^6 + 22*a^3*c^7 - 14*a^2*c^8 + 3*a*c^9 + (a^8*c - 2*a^7*c^2 - 6*a^6*c^3 + 22*a^5*c^4 - 20*a^4*c^5 - 6*a^3*c^6 + 22*a^2*c^7 - 14*a*c^8 + 3*c^9)*sqrt(a*c))*b*sgn(-2*a^3 + 6*a^2*c - 6*a*c^2 + 2*c^3) - (a^9*c - 2*a^8*c^2 - 6*a^7*c^3 + 22*a^6*c^4 - 20*a^5*c^5 - 6*a^4*c^6 + 22*a^3*c^7 - 14*a^2*c^8 + 3*a*c^9 - (a^9 - 2*a^8*c - 6*a^7*c^2 + 22*a^6*c^3 - 20*a^5*c^4 - 6*a^4*c^5 + 22*a^3*c^6 - 14*a^2*c^7 + 3*a*c^8)*sqrt(a*c))*b)*arctan(-(sqrt(b*x + a) - sqrt(b*x + c))/sqrt(-(a^4 - 2*a^3*c + 2*a*c^3 - c^4 - sqrt((a^4 - 2*a^3*c + 2*a*c^3 - c^4)^2 - (a^5 - 5*a^4*c + 10*a^3*c^2 - 10*a^2*c^3 + 5*a*c^4 - c^5)*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/(a^3 - 3*a^2*c + 3*a*c^2 - c^3)))/((sqrt(-a)*a^8*c - a^8*sqrt(-c)*c - 8*sqrt(-a)*a^7*c^2 + 8*a^7*sqrt(-c)*c^2 + 28*sqrt(-a)*a^6*c^3 - 28*a^6*sqrt(-c)*c^3 - 56*sqrt(-a)*a^5*c^4 + 56*a^5*sqrt(-c)*c^4 + 70*sqrt(-a)*a^4*c^5 - 70*a^4*sqrt(-c)*c^5 - 56*sqrt(-a)*a^3*c^6 + 56*a^3*sqrt(-c)*c^6 + 28*sqrt(-a)*a^2*c^7 - 28*a^2*sqrt(-c)*c^7 - 8*sqrt(-a)*a*c^8 + 8*a*sqrt(-c)*c^8 + sqrt(-a)*c^9 - sqrt(-c)*c^9)*abs(-a^3 + 3*a^2*c - 3*a*c^2 + c^3)) - 2*(3*a*b*(sqrt(b*x + a) - sqrt(b*x + c))^3 + b*c*(sqrt(b*x + a) - sqrt(b*x + c))^3 - 3*a^2*b*(sqrt(b*x + a) - sqrt(b*x + c)) + 2*a*b*c*(sqrt(b*x + a) - sqrt(b*x + c)) + b*c^2*(sqrt(b*x + a) - sqrt(b*x + c)))/(((sqrt(b*x + a) - sqrt(b*x + c))^4 - 2*a*(sqrt(b*x + a) - sqrt(b*x + c))^2 - 2*c*(sqrt(b*x + a) - sqrt(b*x + c))^2 + a^2 - 2*a*c + c^2)*(a^3 - 3*a^2*c + 3*a*c^2 - c^3)) - (sqrt(b*x + a)*a*b + 3*sqrt(b*x + a)*b*c)/((a^3 - 3*a^2*c + 3*a*c^2 - c^3)*b*x)","B",0
416,1,13,0,0.229530," ","integrate(1/(x^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{2}{3} \, x^{\frac{3}{2}}"," ",0,"2/3*(x + 1)^(3/2) - 2/3*x^(3/2)","A",0
417,1,13,0,0.192608," ","integrate(1/((-1+x)^(1/2)+x^(1/2)),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(x - 1\right)}^{\frac{3}{2}} + \frac{2}{3} \, x^{\frac{3}{2}}"," ",0,"-2/3*(x - 1)^(3/2) + 2/3*x^(3/2)","A",0
418,1,15,0,0.190152," ","integrate(1/((-1+x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{1}{3} \, {\left(x - 1\right)}^{\frac{3}{2}}"," ",0,"1/3*(x + 1)^(3/2) - 1/3*(x - 1)^(3/2)","A",0
419,1,77,0,0.222790," ","integrate(x^3*((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{4} + \frac{1}{60} \, {\left({\left(2 \, {\left(3 \, {\left(4 \, x - 17\right)} {\left(x + 1\right)} + 133\right)} {\left(x + 1\right)} - 295\right)} {\left(x + 1\right)} + 195\right)} \sqrt{x + 1} \sqrt{-x + 1} + \frac{1}{12} \, {\left({\left(2 \, {\left(3 \, x - 10\right)} {\left(x + 1\right)} + 43\right)} {\left(x + 1\right)} - 39\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"1/2*x^4 + 1/60*((2*(3*(4*x - 17)*(x + 1) + 133)*(x + 1) - 295)*(x + 1) + 195)*sqrt(x + 1)*sqrt(-x + 1) + 1/12*((2*(3*x - 10)*(x + 1) + 43)*(x + 1) - 39)*sqrt(x + 1)*sqrt(-x + 1)","B",0
420,1,76,0,0.232219," ","integrate(x^2*((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""giac"")","\frac{2}{3} \, x^{3} + \frac{1}{12} \, {\left({\left(2 \, {\left(3 \, x - 10\right)} {\left(x + 1\right)} + 43\right)} {\left(x + 1\right)} - 39\right)} \sqrt{x + 1} \sqrt{-x + 1} + \frac{1}{3} \, {\left({\left(2 \, x - 5\right)} {\left(x + 1\right)} + 9\right)} \sqrt{x + 1} \sqrt{-x + 1} + \frac{1}{2} \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 1}\right)"," ",0,"2/3*x^3 + 1/12*((2*(3*x - 10)*(x + 1) + 43)*(x + 1) - 39)*sqrt(x + 1)*sqrt(-x + 1) + 1/3*((2*x - 5)*(x + 1) + 9)*sqrt(x + 1)*sqrt(-x + 1) + 1/2*arcsin(1/2*sqrt(2)*sqrt(x + 1))","B",0
421,1,51,0,0.250251," ","integrate(x*((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""giac"")","{\left(x + 1\right)}^{2} + \frac{1}{3} \, {\left({\left(2 \, x - 5\right)} {\left(x + 1\right)} + 9\right)} \sqrt{x + 1} \sqrt{-x + 1} + \sqrt{x + 1} {\left(x - 2\right)} \sqrt{-x + 1} - 2 \, x - 2"," ",0,"(x + 1)^2 + 1/3*((2*x - 5)*(x + 1) + 9)*sqrt(x + 1)*sqrt(-x + 1) + sqrt(x + 1)*(x - 2)*sqrt(-x + 1) - 2*x - 2","B",0
422,1,48,0,0.204120," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""giac"")","\sqrt{x + 1} {\left(x - 2\right)} \sqrt{-x + 1} + 2 \, x + 2 \, \sqrt{x + 1} \sqrt{-x + 1} + 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 1}\right) + 2"," ",0,"sqrt(x + 1)*(x - 2)*sqrt(-x + 1) + 2*x + 2*sqrt(x + 1)*sqrt(-x + 1) + 2*arcsin(1/2*sqrt(2)*sqrt(x + 1)) + 2","B",0
423,-2,0,0,0.000000," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2/x,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-93.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-17.8804557086]2*ln(abs(sqrt(x+1)-1))+2*ln(sqrt(x+1)+1)+2*sqrt(x+1)*sqrt(-x+1)-2*ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))+2*ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))","F(-2)",0
424,1,149,0,0.263912," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2/x^2,x, algorithm=""giac"")","-2 \, \pi - \frac{8 \, {\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{x + 1}} - \frac{\sqrt{x + 1}}{\sqrt{2} - \sqrt{-x + 1}}\right)}}{{\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{x + 1}} - \frac{\sqrt{x + 1}}{\sqrt{2} - \sqrt{-x + 1}}\right)}^{2} - 4} - \frac{2}{x} - 4 \, \arctan\left(\frac{\sqrt{x + 1} {\left(\frac{{\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{2}}{x + 1} - 1\right)}}{2 \, {\left(\sqrt{2} - \sqrt{-x + 1}\right)}}\right)"," ",0,"-2*pi - 8*((sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) - sqrt(x + 1)/(sqrt(2) - sqrt(-x + 1)))/(((sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) - sqrt(x + 1)/(sqrt(2) - sqrt(-x + 1)))^2 - 4) - 2/x - 4*arctan(1/2*sqrt(x + 1)*((sqrt(2) - sqrt(-x + 1))^2/(x + 1) - 1)/(sqrt(2) - sqrt(-x + 1)))","B",0
425,-2,0,0,0.000000," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))^2/x^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-93.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-17.8804557086]-(4*(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1))^3+16*(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))/((2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1))^2-4)^2+ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))-ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))-1/x^2","F(-2)",0
426,1,451,0,0.430477," ","integrate(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""giac"")","-\frac{2}{105} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left({\left(3 \, {\left(b x + a\right)} {\left(\frac{5 \, {\left(b^{17} c^{5} {\left| b \right|} - 2 \, b^{16} c^{6} {\left| b \right|} + b^{15} c^{7} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{23} c^{5} - 3 \, b^{22} c^{6} + 3 \, b^{21} c^{7} - b^{20} c^{8}} + \frac{a b^{18} c^{4} {\left| b \right|} - 17 \, a b^{17} c^{5} {\left| b \right|} + 31 \, a b^{16} c^{6} {\left| b \right|} - 15 \, a b^{15} c^{7} {\left| b \right|}}{b^{23} c^{5} - 3 \, b^{22} c^{6} + 3 \, b^{21} c^{7} - b^{20} c^{8}}\right)} - \frac{4 \, a^{2} b^{19} c^{3} {\left| b \right|} - 2 \, a^{2} b^{18} c^{4} {\left| b \right|} - 53 \, a^{2} b^{17} c^{5} {\left| b \right|} + 96 \, a^{2} b^{16} c^{6} {\left| b \right|} - 45 \, a^{2} b^{15} c^{7} {\left| b \right|}}{b^{23} c^{5} - 3 \, b^{22} c^{6} + 3 \, b^{21} c^{7} - b^{20} c^{8}}\right)} {\left(b x + a\right)} + \frac{8 \, a^{3} b^{20} c^{2} {\left| b \right|} - 12 \, a^{3} b^{19} c^{3} {\left| b \right|} + 3 \, a^{3} b^{18} c^{4} {\left| b \right|} - 17 \, a^{3} b^{17} c^{5} {\left| b \right|} + 33 \, a^{3} b^{16} c^{6} {\left| b \right|} - 15 \, a^{3} b^{15} c^{7} {\left| b \right|}}{b^{23} c^{5} - 3 \, b^{22} c^{6} + 3 \, b^{21} c^{7} - b^{20} c^{8}}\right)} + \frac{2 \, {\left(15 \, {\left(b x + a\right)}^{\frac{7}{2}} - 42 \, {\left(b x + a\right)}^{\frac{5}{2}} a + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2}\right)}}{105 \, {\left(b^{4} - b^{3} c\right)}}"," ",0,"-2/105*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*((3*(b*x + a)*(5*(b^17*c^5*abs(b) - 2*b^16*c^6*abs(b) + b^15*c^7*abs(b))*(b*x + a)/(b^23*c^5 - 3*b^22*c^6 + 3*b^21*c^7 - b^20*c^8) + (a*b^18*c^4*abs(b) - 17*a*b^17*c^5*abs(b) + 31*a*b^16*c^6*abs(b) - 15*a*b^15*c^7*abs(b))/(b^23*c^5 - 3*b^22*c^6 + 3*b^21*c^7 - b^20*c^8)) - (4*a^2*b^19*c^3*abs(b) - 2*a^2*b^18*c^4*abs(b) - 53*a^2*b^17*c^5*abs(b) + 96*a^2*b^16*c^6*abs(b) - 45*a^2*b^15*c^7*abs(b))/(b^23*c^5 - 3*b^22*c^6 + 3*b^21*c^7 - b^20*c^8))*(b*x + a) + (8*a^3*b^20*c^2*abs(b) - 12*a^3*b^19*c^3*abs(b) + 3*a^3*b^18*c^4*abs(b) - 17*a^3*b^17*c^5*abs(b) + 33*a^3*b^16*c^6*abs(b) - 15*a^3*b^15*c^7*abs(b))/(b^23*c^5 - 3*b^22*c^6 + 3*b^21*c^7 - b^20*c^8)) + 2/105*(15*(b*x + a)^(7/2) - 42*(b*x + a)^(5/2)*a + 35*(b*x + a)^(3/2)*a^2)/(b^4 - b^3*c)","B",0
427,1,255,0,0.390238," ","integrate(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""giac"")","-\frac{2}{15} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left({\left(b x + a\right)} {\left(\frac{3 \, {\left(b^{9} c^{3} {\left| b \right|} - b^{8} c^{4} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{14} c^{3} - 2 \, b^{13} c^{4} + b^{12} c^{5}} + \frac{a b^{10} c^{2} {\left| b \right|} - 7 \, a b^{9} c^{3} {\left| b \right|} + 6 \, a b^{8} c^{4} {\left| b \right|}}{b^{14} c^{3} - 2 \, b^{13} c^{4} + b^{12} c^{5}}\right)} - \frac{2 \, a^{2} b^{11} c {\left| b \right|} - a^{2} b^{10} c^{2} {\left| b \right|} - 4 \, a^{2} b^{9} c^{3} {\left| b \right|} + 3 \, a^{2} b^{8} c^{4} {\left| b \right|}}{b^{14} c^{3} - 2 \, b^{13} c^{4} + b^{12} c^{5}}\right)} + \frac{2 \, {\left(3 \, {\left(b x + a\right)}^{\frac{5}{2}} - 5 \, {\left(b x + a\right)}^{\frac{3}{2}} a\right)}}{15 \, {\left(b^{3} - b^{2} c\right)}}"," ",0,"-2/15*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*((b*x + a)*(3*(b^9*c^3*abs(b) - b^8*c^4*abs(b))*(b*x + a)/(b^14*c^3 - 2*b^13*c^4 + b^12*c^5) + (a*b^10*c^2*abs(b) - 7*a*b^9*c^3*abs(b) + 6*a*b^8*c^4*abs(b))/(b^14*c^3 - 2*b^13*c^4 + b^12*c^5)) - (2*a^2*b^11*c*abs(b) - a^2*b^10*c^2*abs(b) - 4*a^2*b^9*c^3*abs(b) + 3*a^2*b^8*c^4*abs(b))/(b^14*c^3 - 2*b^13*c^4 + b^12*c^5)) + 2/15*(3*(b*x + a)^(5/2) - 5*(b*x + a)^(3/2)*a)/(b^3 - b^2*c)","B",0
428,1,107,0,0.315866," ","integrate(x/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, {\left({\left(\frac{{\left(b x + a\right)} b^{2} c {\left| b \right|}}{b^{5} c - b^{4} c^{2}} + \frac{a b^{3} {\left| b \right|} - a b^{2} c {\left| b \right|}}{b^{5} c - b^{4} c^{2}}\right)} \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} - \frac{{\left(b x + a\right)}^{\frac{3}{2}}}{b - c}\right)}}{3 \, b}"," ",0,"-2/3*(((b*x + a)*b^2*c*abs(b)/(b^5*c - b^4*c^2) + (a*b^3*abs(b) - a*b^2*c*abs(b))/(b^5*c - b^4*c^2))*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c) - (b*x + a)^(3/2)/(b - c))/b","B",0
429,1,1093,0,0.997860," ","integrate(1/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left| b \right|}}{b^{3} - b^{2} c} + \frac{2 \, a \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} {\left(b - c\right)}} + \frac{2 \, \sqrt{b x + a}}{b - c} - \frac{2 \, {\left(2 \, {\left(a b^{3} c - a b^{2} c^{2}\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b - c\right) + 2 \, {\left(a b^{3} - a b^{2} c\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{5} - 3 \, a^{2} b^{4} c + 3 \, a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3}\right)} \sqrt{-a b c} {\left| a b^{2} - a b c \right|} {\left| b \right|} \mathrm{sgn}\left(b - c\right) + {\left(a^{2} b^{6} - 3 \, a^{2} b^{5} c + 3 \, a^{2} b^{4} c^{2} - a^{2} b^{3} c^{3}\right)} \sqrt{-a} {\left| a b^{2} - a b c \right|} {\left| b \right|} + {\left(a^{3} b^{7} c - 2 \, a^{3} b^{6} c^{2} + 2 \, a^{3} b^{4} c^{4} - a^{3} b^{3} c^{5}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b - c\right) + {\left(a^{3} b^{7} - 2 \, a^{3} b^{6} c + 2 \, a^{3} b^{4} c^{3} - a^{3} b^{3} c^{4}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{3} - a b c^{2} + \sqrt{{\left(a b^{3} - a b c^{2}\right)}^{2} - {\left(a^{2} b^{5} - 3 \, a^{2} b^{4} c + 3 \, a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3}\right)} {\left(b - c\right)}}}{b - c}}}\right)}{{\left(b^{8} - 5 \, b^{7} c + 10 \, b^{6} c^{2} - 10 \, b^{5} c^{3} + 5 \, b^{4} c^{4} - b^{3} c^{5}\right)} a^{2} {\left| a b^{2} - a b c \right|}} + \frac{2 \, {\left(2 \, {\left(a b^{3} c - a b^{2} c^{2}\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b - c\right) + 2 \, {\left(a b^{3} - a b^{2} c\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{5} - 3 \, a^{2} b^{4} c + 3 \, a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3}\right)} \sqrt{-a b c} {\left| a b^{2} - a b c \right|} {\left| b \right|} \mathrm{sgn}\left(b - c\right) + {\left(a^{2} b^{6} - 3 \, a^{2} b^{5} c + 3 \, a^{2} b^{4} c^{2} - a^{2} b^{3} c^{3}\right)} \sqrt{-a} {\left| a b^{2} - a b c \right|} {\left| b \right|} + {\left(a^{3} b^{7} c - 2 \, a^{3} b^{6} c^{2} + 2 \, a^{3} b^{4} c^{4} - a^{3} b^{3} c^{5}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b - c\right) + {\left(a^{3} b^{7} - 2 \, a^{3} b^{6} c + 2 \, a^{3} b^{4} c^{3} - a^{3} b^{3} c^{4}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{3} - a b c^{2} - \sqrt{{\left(a b^{3} - a b c^{2}\right)}^{2} - {\left(a^{2} b^{5} - 3 \, a^{2} b^{4} c + 3 \, a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3}\right)} {\left(b - c\right)}}}{b - c}}}\right)}{{\left(b^{8} - 5 \, b^{7} c + 10 \, b^{6} c^{2} - 10 \, b^{5} c^{3} + 5 \, b^{4} c^{4} - b^{3} c^{5}\right)} a^{2} {\left| a b^{2} - a b c \right|}}"," ",0,"-2*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*abs(b)/(b^3 - b^2*c) + 2*a*arctan(sqrt(b*x + a)/sqrt(-a))/(sqrt(-a)*(b - c)) + 2*sqrt(b*x + a)/(b - c) - 2*(2*(a*b^3*c - a*b^2*c^2)*(a*b^2 - a*b*c)^2*sqrt(-a)*abs(b)*sgn(b - c) + 2*(a*b^3 - a*b^2*c)*(a*b^2 - a*b*c)^2*sqrt(-a*b*c)*abs(b) + (a^2*b^5 - 3*a^2*b^4*c + 3*a^2*b^3*c^2 - a^2*b^2*c^3)*sqrt(-a*b*c)*abs(a*b^2 - a*b*c)*abs(b)*sgn(b - c) + (a^2*b^6 - 3*a^2*b^5*c + 3*a^2*b^4*c^2 - a^2*b^3*c^3)*sqrt(-a)*abs(a*b^2 - a*b*c)*abs(b) + (a^3*b^7*c - 2*a^3*b^6*c^2 + 2*a^3*b^4*c^4 - a^3*b^3*c^5)*sqrt(-a)*abs(b)*sgn(b - c) + (a^3*b^7 - 2*a^3*b^6*c + 2*a^3*b^4*c^3 - a^3*b^3*c^4)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^3 - a*b*c^2 + sqrt((a*b^3 - a*b*c^2)^2 - (a^2*b^5 - 3*a^2*b^4*c + 3*a^2*b^3*c^2 - a^2*b^2*c^3)*(b - c)))/(b - c)))/((b^8 - 5*b^7*c + 10*b^6*c^2 - 10*b^5*c^3 + 5*b^4*c^4 - b^3*c^5)*a^2*abs(a*b^2 - a*b*c)) + 2*(2*(a*b^3*c - a*b^2*c^2)*(a*b^2 - a*b*c)^2*sqrt(-a)*abs(b)*sgn(b - c) + 2*(a*b^3 - a*b^2*c)*(a*b^2 - a*b*c)^2*sqrt(-a*b*c)*abs(b) + (a^2*b^5 - 3*a^2*b^4*c + 3*a^2*b^3*c^2 - a^2*b^2*c^3)*sqrt(-a*b*c)*abs(a*b^2 - a*b*c)*abs(b)*sgn(b - c) + (a^2*b^6 - 3*a^2*b^5*c + 3*a^2*b^4*c^2 - a^2*b^3*c^3)*sqrt(-a)*abs(a*b^2 - a*b*c)*abs(b) + (a^3*b^7*c - 2*a^3*b^6*c^2 + 2*a^3*b^4*c^4 - a^3*b^3*c^5)*sqrt(-a)*abs(b)*sgn(b - c) + (a^3*b^7 - 2*a^3*b^6*c + 2*a^3*b^4*c^3 - a^3*b^3*c^4)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^3 - a*b*c^2 - sqrt((a*b^3 - a*b*c^2)^2 - (a^2*b^5 - 3*a^2*b^4*c + 3*a^2*b^3*c^2 - a^2*b^2*c^3)*(b - c)))/(b - c)))/((b^8 - 5*b^7*c + 10*b^6*c^2 - 10*b^5*c^3 + 5*b^4*c^4 - b^3*c^5)*a^2*abs(a*b^2 - a*b*c))","B",0
430,1,1402,0,12.671369," ","integrate(1/x/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a} {\left(b - c\right)}} - \frac{2 \, {\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a b^{2} c {\left| b \right|} - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a b c^{2} {\left| b \right|} + {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{3} c {\left| b \right|}\right)}}{{\left(a^{2} b^{4} - 2 \, a^{2} b^{3} c + a^{2} b^{2} c^{2} - 2 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a b^{2} - 2 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a b c + {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4}\right)} {\left(b - c\right)}} - \frac{\sqrt{b x + a}}{{\left(b - c\right)} x} + \frac{{\left(2 \, {\left(a b^{3} c^{2} - a b^{2} c^{3}\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + 2 \, {\left(a b^{3} c - a b^{2} c^{2}\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{5} c - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{2} b^{3} c^{3} - a^{2} b^{2} c^{4}\right)} \sqrt{-a b c} {\left| -a b^{2} + a b c \right|} {\left| b \right|} \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + {\left(a^{2} b^{6} c - 3 \, a^{2} b^{5} c^{2} + 3 \, a^{2} b^{4} c^{3} - a^{2} b^{3} c^{4}\right)} \sqrt{-a} {\left| -a b^{2} + a b c \right|} {\left| b \right|} + {\left(a^{3} b^{7} c^{2} - 2 \, a^{3} b^{6} c^{3} + 2 \, a^{3} b^{4} c^{5} - a^{3} b^{3} c^{6}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + {\left(a^{3} b^{7} c - 2 \, a^{3} b^{6} c^{2} + 2 \, a^{3} b^{4} c^{4} - a^{3} b^{3} c^{5}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{3} - a b c^{2} + \sqrt{{\left(a b^{3} - a b c^{2}\right)}^{2} - {\left(a^{2} b^{5} - 3 \, a^{2} b^{4} c + 3 \, a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3}\right)} {\left(b - c\right)}}}{b - c}}}\right)}{{\left(b^{8} - 5 \, b^{7} c + 10 \, b^{6} c^{2} - 10 \, b^{5} c^{3} + 5 \, b^{4} c^{4} - b^{3} c^{5}\right)} a^{3} {\left| -a b^{2} + a b c \right|}} - \frac{{\left(2 \, {\left(a b^{3} c^{2} - a b^{2} c^{3}\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + 2 \, {\left(a b^{3} c - a b^{2} c^{2}\right)} {\left(a b^{2} - a b c\right)}^{2} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{5} c - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{2} b^{3} c^{3} - a^{2} b^{2} c^{4}\right)} \sqrt{-a b c} {\left| -a b^{2} + a b c \right|} {\left| b \right|} \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + {\left(a^{2} b^{6} c - 3 \, a^{2} b^{5} c^{2} + 3 \, a^{2} b^{4} c^{3} - a^{2} b^{3} c^{4}\right)} \sqrt{-a} {\left| -a b^{2} + a b c \right|} {\left| b \right|} + {\left(a^{3} b^{7} c^{2} - 2 \, a^{3} b^{6} c^{3} + 2 \, a^{3} b^{4} c^{5} - a^{3} b^{3} c^{6}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + {\left(a^{3} b^{7} c - 2 \, a^{3} b^{6} c^{2} + 2 \, a^{3} b^{4} c^{4} - a^{3} b^{3} c^{5}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{3} - a b c^{2} - \sqrt{{\left(a b^{3} - a b c^{2}\right)}^{2} - {\left(a^{2} b^{5} - 3 \, a^{2} b^{4} c + 3 \, a^{2} b^{3} c^{2} - a^{2} b^{2} c^{3}\right)} {\left(b - c\right)}}}{b - c}}}\right)}{{\left(b^{8} - 5 \, b^{7} c + 10 \, b^{6} c^{2} - 10 \, b^{5} c^{3} + 5 \, b^{4} c^{4} - b^{3} c^{5}\right)} a^{3} {\left| -a b^{2} + a b c \right|}}"," ",0,"b*arctan(sqrt(b*x + a)/sqrt(-a))/(sqrt(-a)*(b - c)) - 2*((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a*b^2*c*abs(b) - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a*b*c^2*abs(b) + (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^3*c*abs(b))/((a^2*b^4 - 2*a^2*b^3*c + a^2*b^2*c^2 - 2*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*b^2 - 2*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*b*c + (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4)*(b - c)) - sqrt(b*x + a)/((b - c)*x) + (2*(a*b^3*c^2 - a*b^2*c^3)*(a*b^2 - a*b*c)^2*sqrt(-a)*abs(b)*sgn(-2*b + 2*c) + 2*(a*b^3*c - a*b^2*c^2)*(a*b^2 - a*b*c)^2*sqrt(-a*b*c)*abs(b) + (a^2*b^5*c - 3*a^2*b^4*c^2 + 3*a^2*b^3*c^3 - a^2*b^2*c^4)*sqrt(-a*b*c)*abs(-a*b^2 + a*b*c)*abs(b)*sgn(-2*b + 2*c) + (a^2*b^6*c - 3*a^2*b^5*c^2 + 3*a^2*b^4*c^3 - a^2*b^3*c^4)*sqrt(-a)*abs(-a*b^2 + a*b*c)*abs(b) + (a^3*b^7*c^2 - 2*a^3*b^6*c^3 + 2*a^3*b^4*c^5 - a^3*b^3*c^6)*sqrt(-a)*abs(b)*sgn(-2*b + 2*c) + (a^3*b^7*c - 2*a^3*b^6*c^2 + 2*a^3*b^4*c^4 - a^3*b^3*c^5)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^3 - a*b*c^2 + sqrt((a*b^3 - a*b*c^2)^2 - (a^2*b^5 - 3*a^2*b^4*c + 3*a^2*b^3*c^2 - a^2*b^2*c^3)*(b - c)))/(b - c)))/((b^8 - 5*b^7*c + 10*b^6*c^2 - 10*b^5*c^3 + 5*b^4*c^4 - b^3*c^5)*a^3*abs(-a*b^2 + a*b*c)) - (2*(a*b^3*c^2 - a*b^2*c^3)*(a*b^2 - a*b*c)^2*sqrt(-a)*abs(b)*sgn(-2*b + 2*c) + 2*(a*b^3*c - a*b^2*c^2)*(a*b^2 - a*b*c)^2*sqrt(-a*b*c)*abs(b) + (a^2*b^5*c - 3*a^2*b^4*c^2 + 3*a^2*b^3*c^3 - a^2*b^2*c^4)*sqrt(-a*b*c)*abs(-a*b^2 + a*b*c)*abs(b)*sgn(-2*b + 2*c) + (a^2*b^6*c - 3*a^2*b^5*c^2 + 3*a^2*b^4*c^3 - a^2*b^3*c^4)*sqrt(-a)*abs(-a*b^2 + a*b*c)*abs(b) + (a^3*b^7*c^2 - 2*a^3*b^6*c^3 + 2*a^3*b^4*c^5 - a^3*b^3*c^6)*sqrt(-a)*abs(b)*sgn(-2*b + 2*c) + (a^3*b^7*c - 2*a^3*b^6*c^2 + 2*a^3*b^4*c^4 - a^3*b^3*c^5)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^3 - a*b*c^2 - sqrt((a*b^3 - a*b*c^2)^2 - (a^2*b^5 - 3*a^2*b^4*c + 3*a^2*b^3*c^2 - a^2*b^2*c^3)*(b - c)))/(b - c)))/((b^8 - 5*b^7*c + 10*b^6*c^2 - 10*b^5*c^3 + 5*b^4*c^4 - b^3*c^5)*a^3*abs(-a*b^2 + a*b*c))","B",0
431,1,1895,0,37.260723," ","integrate(1/x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x, algorithm=""giac"")","-\frac{b^{2} \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{4 \, {\left(a b - a c\right)} \sqrt{-a}} - \frac{{\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a^{3} b^{6} c^{2} {\left| b \right|} - 3 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a^{3} b^{5} c^{3} {\left| b \right|} + 3 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a^{3} b^{4} c^{4} {\left| b \right|} - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a^{3} b^{3} c^{5} {\left| b \right|} + 7 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{3} a^{2} b^{4} c^{2} {\left| b \right|} - 10 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{3} a^{2} b^{3} c^{3} {\left| b \right|} + 3 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{3} a^{2} b^{2} c^{4} {\left| b \right|} + 7 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{5} a b^{2} c^{2} {\left| b \right|} - 3 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{5} a b c^{3} {\left| b \right|} + {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{7} c^{2} {\left| b \right|}}{2 \, {\left(a^{2} b^{4} - 2 \, a^{2} b^{3} c + a^{2} b^{2} c^{2} - 2 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a b^{2} - 2 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a b c + {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4}\right)}^{2} {\left(a b - a c\right)}} - \frac{{\left(b x + a\right)}^{\frac{3}{2}} b^{2} + \sqrt{b x + a} a b^{2}}{4 \, {\left(a b - a c\right)} b^{2} x^{2}} - \frac{{\left(2 \, {\left(a b^{3} c^{3} - a b^{2} c^{4}\right)} {\left(a^{2} b^{2} - a^{2} b c\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(8 \, a b - 8 \, a c\right) + 2 \, {\left(a b^{3} c^{2} - a b^{2} c^{3}\right)} {\left(a^{2} b^{2} - a^{2} b c\right)}^{2} \sqrt{-a b c} {\left| b \right|} + {\left(a^{3} b^{5} c^{2} - 3 \, a^{3} b^{4} c^{3} + 3 \, a^{3} b^{3} c^{4} - a^{3} b^{2} c^{5}\right)} \sqrt{-a b c} {\left| a^{2} b^{2} - a^{2} b c \right|} {\left| b \right|} \mathrm{sgn}\left(8 \, a b - 8 \, a c\right) + {\left(a^{3} b^{6} c^{2} - 3 \, a^{3} b^{5} c^{3} + 3 \, a^{3} b^{4} c^{4} - a^{3} b^{3} c^{5}\right)} \sqrt{-a} {\left| a^{2} b^{2} - a^{2} b c \right|} {\left| b \right|} + {\left(a^{5} b^{7} c^{3} - 2 \, a^{5} b^{6} c^{4} + 2 \, a^{5} b^{4} c^{6} - a^{5} b^{3} c^{7}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(8 \, a b - 8 \, a c\right) + {\left(a^{5} b^{7} c^{2} - 2 \, a^{5} b^{6} c^{3} + 2 \, a^{5} b^{4} c^{5} - a^{5} b^{3} c^{6}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a^{2} b^{3} - a^{2} b c^{2} + \sqrt{{\left(a^{2} b^{3} - a^{2} b c^{2}\right)}^{2} - {\left(a^{3} b^{5} - 3 \, a^{3} b^{4} c + 3 \, a^{3} b^{3} c^{2} - a^{3} b^{2} c^{3}\right)} {\left(a b - a c\right)}}}{a b - a c}}}\right)}{4 \, {\left(b^{8} - 5 \, b^{7} c + 10 \, b^{6} c^{2} - 10 \, b^{5} c^{3} + 5 \, b^{4} c^{4} - b^{3} c^{5}\right)} a^{5} {\left| a^{2} b^{2} - a^{2} b c \right|}} + \frac{{\left(2 \, {\left(a b^{3} c^{3} - a b^{2} c^{4}\right)} {\left(a^{2} b^{2} - a^{2} b c\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(8 \, a b - 8 \, a c\right) + 2 \, {\left(a b^{3} c^{2} - a b^{2} c^{3}\right)} {\left(a^{2} b^{2} - a^{2} b c\right)}^{2} \sqrt{-a b c} {\left| b \right|} + {\left(a^{3} b^{5} c^{2} - 3 \, a^{3} b^{4} c^{3} + 3 \, a^{3} b^{3} c^{4} - a^{3} b^{2} c^{5}\right)} \sqrt{-a b c} {\left| a^{2} b^{2} - a^{2} b c \right|} {\left| b \right|} \mathrm{sgn}\left(8 \, a b - 8 \, a c\right) + {\left(a^{3} b^{6} c^{2} - 3 \, a^{3} b^{5} c^{3} + 3 \, a^{3} b^{4} c^{4} - a^{3} b^{3} c^{5}\right)} \sqrt{-a} {\left| a^{2} b^{2} - a^{2} b c \right|} {\left| b \right|} + {\left(a^{5} b^{7} c^{3} - 2 \, a^{5} b^{6} c^{4} + 2 \, a^{5} b^{4} c^{6} - a^{5} b^{3} c^{7}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(8 \, a b - 8 \, a c\right) + {\left(a^{5} b^{7} c^{2} - 2 \, a^{5} b^{6} c^{3} + 2 \, a^{5} b^{4} c^{5} - a^{5} b^{3} c^{6}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a^{2} b^{3} - a^{2} b c^{2} - \sqrt{{\left(a^{2} b^{3} - a^{2} b c^{2}\right)}^{2} - {\left(a^{3} b^{5} - 3 \, a^{3} b^{4} c + 3 \, a^{3} b^{3} c^{2} - a^{3} b^{2} c^{3}\right)} {\left(a b - a c\right)}}}{a b - a c}}}\right)}{4 \, {\left(b^{8} - 5 \, b^{7} c + 10 \, b^{6} c^{2} - 10 \, b^{5} c^{3} + 5 \, b^{4} c^{4} - b^{3} c^{5}\right)} a^{5} {\left| a^{2} b^{2} - a^{2} b c \right|}}"," ",0,"-1/4*b^2*arctan(sqrt(b*x + a)/sqrt(-a))/((a*b - a*c)*sqrt(-a)) - 1/2*((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a^3*b^6*c^2*abs(b) - 3*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a^3*b^5*c^3*abs(b) + 3*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a^3*b^4*c^4*abs(b) - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a^3*b^3*c^5*abs(b) + 7*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^3*a^2*b^4*c^2*abs(b) - 10*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^3*a^2*b^3*c^3*abs(b) + 3*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^3*a^2*b^2*c^4*abs(b) + 7*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^5*a*b^2*c^2*abs(b) - 3*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^5*a*b*c^3*abs(b) + (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^7*c^2*abs(b))/((a^2*b^4 - 2*a^2*b^3*c + a^2*b^2*c^2 - 2*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*b^2 - 2*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*b*c + (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4)^2*(a*b - a*c)) - 1/4*((b*x + a)^(3/2)*b^2 + sqrt(b*x + a)*a*b^2)/((a*b - a*c)*b^2*x^2) - 1/4*(2*(a*b^3*c^3 - a*b^2*c^4)*(a^2*b^2 - a^2*b*c)^2*sqrt(-a)*abs(b)*sgn(8*a*b - 8*a*c) + 2*(a*b^3*c^2 - a*b^2*c^3)*(a^2*b^2 - a^2*b*c)^2*sqrt(-a*b*c)*abs(b) + (a^3*b^5*c^2 - 3*a^3*b^4*c^3 + 3*a^3*b^3*c^4 - a^3*b^2*c^5)*sqrt(-a*b*c)*abs(a^2*b^2 - a^2*b*c)*abs(b)*sgn(8*a*b - 8*a*c) + (a^3*b^6*c^2 - 3*a^3*b^5*c^3 + 3*a^3*b^4*c^4 - a^3*b^3*c^5)*sqrt(-a)*abs(a^2*b^2 - a^2*b*c)*abs(b) + (a^5*b^7*c^3 - 2*a^5*b^6*c^4 + 2*a^5*b^4*c^6 - a^5*b^3*c^7)*sqrt(-a)*abs(b)*sgn(8*a*b - 8*a*c) + (a^5*b^7*c^2 - 2*a^5*b^6*c^3 + 2*a^5*b^4*c^5 - a^5*b^3*c^6)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a^2*b^3 - a^2*b*c^2 + sqrt((a^2*b^3 - a^2*b*c^2)^2 - (a^3*b^5 - 3*a^3*b^4*c + 3*a^3*b^3*c^2 - a^3*b^2*c^3)*(a*b - a*c)))/(a*b - a*c)))/((b^8 - 5*b^7*c + 10*b^6*c^2 - 10*b^5*c^3 + 5*b^4*c^4 - b^3*c^5)*a^5*abs(a^2*b^2 - a^2*b*c)) + 1/4*(2*(a*b^3*c^3 - a*b^2*c^4)*(a^2*b^2 - a^2*b*c)^2*sqrt(-a)*abs(b)*sgn(8*a*b - 8*a*c) + 2*(a*b^3*c^2 - a*b^2*c^3)*(a^2*b^2 - a^2*b*c)^2*sqrt(-a*b*c)*abs(b) + (a^3*b^5*c^2 - 3*a^3*b^4*c^3 + 3*a^3*b^3*c^4 - a^3*b^2*c^5)*sqrt(-a*b*c)*abs(a^2*b^2 - a^2*b*c)*abs(b)*sgn(8*a*b - 8*a*c) + (a^3*b^6*c^2 - 3*a^3*b^5*c^3 + 3*a^3*b^4*c^4 - a^3*b^3*c^5)*sqrt(-a)*abs(a^2*b^2 - a^2*b*c)*abs(b) + (a^5*b^7*c^3 - 2*a^5*b^6*c^4 + 2*a^5*b^4*c^6 - a^5*b^3*c^7)*sqrt(-a)*abs(b)*sgn(8*a*b - 8*a*c) + (a^5*b^7*c^2 - 2*a^5*b^6*c^3 + 2*a^5*b^4*c^5 - a^5*b^3*c^6)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a^2*b^3 - a^2*b*c^2 - sqrt((a^2*b^3 - a^2*b*c^2)^2 - (a^3*b^5 - 3*a^3*b^4*c + 3*a^3*b^3*c^2 - a^3*b^2*c^3)*(a*b - a*c)))/(a*b - a*c)))/((b^8 - 5*b^7*c + 10*b^6*c^2 - 10*b^5*c^3 + 5*b^4*c^4 - b^3*c^5)*a^5*abs(a^2*b^2 - a^2*b*c))","B",0
432,1,511,0,3.471790," ","integrate(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left(2 \, {\left(b x + a\right)} {\left(\frac{4 \, {\left(b^{11} c^{4} {\left| b \right|} - 3 \, b^{10} c^{5} {\left| b \right|} + 3 \, b^{9} c^{6} {\left| b \right|} - b^{8} c^{7} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{17} c^{4} - 5 \, b^{16} c^{5} + 10 \, b^{15} c^{6} - 10 \, b^{14} c^{7} + 5 \, b^{13} c^{8} - b^{12} c^{9}} + \frac{a b^{12} c^{3} {\left| b \right|} - 10 \, a b^{11} c^{4} {\left| b \right|} + 24 \, a b^{10} c^{5} {\left| b \right|} - 22 \, a b^{9} c^{6} {\left| b \right|} + 7 \, a b^{8} c^{7} {\left| b \right|}}{b^{17} c^{4} - 5 \, b^{16} c^{5} + 10 \, b^{15} c^{6} - 10 \, b^{14} c^{7} + 5 \, b^{13} c^{8} - b^{12} c^{9}}\right)} - \frac{3 \, {\left(a^{2} b^{13} c^{2} {\left| b \right|} - 3 \, a^{2} b^{12} c^{3} {\left| b \right|} + 2 \, a^{2} b^{11} c^{4} {\left| b \right|} + 2 \, a^{2} b^{10} c^{5} {\left| b \right|} - 3 \, a^{2} b^{9} c^{6} {\left| b \right|} + a^{2} b^{8} c^{7} {\left| b \right|}\right)}}{b^{17} c^{4} - 5 \, b^{16} c^{5} + 10 \, b^{15} c^{6} - 10 \, b^{14} c^{7} + 5 \, b^{13} c^{8} - b^{12} c^{9}}\right)} \sqrt{b x + a} + \frac{{\left(b x + a\right)}^{3} b - 3 \, {\left(b x + a\right)} a^{2} b + {\left(b x + a\right)}^{3} c - 3 \, {\left(b x + a\right)}^{2} a c + 3 \, {\left(b x + a\right)} a^{2} c}{3 \, {\left(b^{5} - 2 \, b^{4} c + b^{3} c^{2}\right)}} + \frac{{\left(a^{3} b {\left| b \right|} + a^{3} c {\left| b \right|}\right)} \log\left({\left| -\sqrt{b c} \sqrt{b x + a} + \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} \right|}\right)}{4 \, \sqrt{b c} b^{3} c^{2}}"," ",0,"-1/12*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*(2*(b*x + a)*(4*(b^11*c^4*abs(b) - 3*b^10*c^5*abs(b) + 3*b^9*c^6*abs(b) - b^8*c^7*abs(b))*(b*x + a)/(b^17*c^4 - 5*b^16*c^5 + 10*b^15*c^6 - 10*b^14*c^7 + 5*b^13*c^8 - b^12*c^9) + (a*b^12*c^3*abs(b) - 10*a*b^11*c^4*abs(b) + 24*a*b^10*c^5*abs(b) - 22*a*b^9*c^6*abs(b) + 7*a*b^8*c^7*abs(b))/(b^17*c^4 - 5*b^16*c^5 + 10*b^15*c^6 - 10*b^14*c^7 + 5*b^13*c^8 - b^12*c^9)) - 3*(a^2*b^13*c^2*abs(b) - 3*a^2*b^12*c^3*abs(b) + 2*a^2*b^11*c^4*abs(b) + 2*a^2*b^10*c^5*abs(b) - 3*a^2*b^9*c^6*abs(b) + a^2*b^8*c^7*abs(b))/(b^17*c^4 - 5*b^16*c^5 + 10*b^15*c^6 - 10*b^14*c^7 + 5*b^13*c^8 - b^12*c^9))*sqrt(b*x + a) + 1/3*((b*x + a)^3*b - 3*(b*x + a)*a^2*b + (b*x + a)^3*c - 3*(b*x + a)^2*a*c + 3*(b*x + a)*a^2*c)/(b^5 - 2*b^4*c + b^3*c^2) + 1/4*(a^3*b*abs(b) + a^3*c*abs(b))*log(abs(-sqrt(b*c)*sqrt(b*x + a) + sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)))/(sqrt(b*c)*b^3*c^2)","B",0
433,1,272,0,3.276799," ","integrate(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} \sqrt{b x + a} {\left(\frac{2 \, {\left(b^{4} c^{2} {\left| b \right|} - b^{3} c^{3} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{9} c^{2} - 3 \, b^{8} c^{3} + 3 \, b^{7} c^{4} - b^{6} c^{5}} + \frac{a b^{5} c {\left| b \right|} - 2 \, a b^{4} c^{2} {\left| b \right|} + a b^{3} c^{3} {\left| b \right|}}{b^{9} c^{2} - 3 \, b^{8} c^{3} + 3 \, b^{7} c^{4} - b^{6} c^{5}}\right)} - \frac{a^{2} {\left| b \right|} \log\left({\left| -\sqrt{b c} \sqrt{b x + a} + \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} \right|}\right)}{2 \, \sqrt{b c} b^{2} c} + \frac{{\left(b x + a\right)}^{2} b + 2 \, {\left(b x + a\right)} a b + {\left(b x + a\right)}^{2} c - 2 \, {\left(b x + a\right)} a c}{2 \, {\left(b^{4} - 2 \, b^{3} c + b^{2} c^{2}\right)}}"," ",0,"-1/2*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*sqrt(b*x + a)*(2*(b^4*c^2*abs(b) - b^3*c^3*abs(b))*(b*x + a)/(b^9*c^2 - 3*b^8*c^3 + 3*b^7*c^4 - b^6*c^5) + (a*b^5*c*abs(b) - 2*a*b^4*c^2*abs(b) + a*b^3*c^3*abs(b))/(b^9*c^2 - 3*b^8*c^3 + 3*b^7*c^4 - b^6*c^5)) - 1/2*a^2*abs(b)*log(abs(-sqrt(b*c)*sqrt(b*x + a) + sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)))/(sqrt(b*c)*b^2*c) + 1/2*((b*x + a)^2*b + 2*(b*x + a)*a*b + (b*x + a)^2*c - 2*(b*x + a)*a*c)/(b^4 - 2*b^3*c + b^2*c^2)","B",0
434,1,306,0,3.525980," ","integrate(x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""giac"")","\frac{\frac{\sqrt{b c} a {\left(b + c\right)} {\left| b \right|} \log\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2}\right)}{b^{3} c - 2 \, b^{2} c^{2} + b c^{3}} - \frac{4 \, \sqrt{b c} a {\left| b \right|} \arctan\left(\frac{a b^{2} + a b c - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2}}{2 \, \sqrt{-b c} a b}\right)}{{\left(b^{2} - 2 \, b c + c^{2}\right)} \sqrt{-b c}} + \frac{2 \, a b \log\left({\left| b x \right|}\right)}{b^{2} - 2 \, b c + c^{2}} - \frac{2 \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left(b^{2} {\left| b \right|} - 2 \, b c {\left| b \right|} + c^{2} {\left| b \right|}\right)} \sqrt{b x + a}}{b^{5} - 4 \, b^{4} c + 6 \, b^{3} c^{2} - 4 \, b^{2} c^{3} + b c^{4}} + \frac{{\left(b x + a\right)} b + {\left(b x + a\right)} c}{b^{2} - 2 \, b c + c^{2}}}{b}"," ",0,"(sqrt(b*c)*a*(b + c)*abs(b)*log((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2)/(b^3*c - 2*b^2*c^2 + b*c^3) - 4*sqrt(b*c)*a*abs(b)*arctan(1/2*(a*b^2 + a*b*c - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2)/(sqrt(-b*c)*a*b))/((b^2 - 2*b*c + c^2)*sqrt(-b*c)) + 2*a*b*log(abs(b*x))/(b^2 - 2*b*c + c^2) - 2*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*(b^2*abs(b) - 2*b*c*abs(b) + c^2*abs(b))*sqrt(b*x + a)/(b^5 - 4*b^4*c + 6*b^3*c^2 - 4*b^2*c^3 + b*c^4) + ((b*x + a)*b + (b*x + a)*c)/(b^2 - 2*b*c + c^2))/b","B",0
435,1,438,0,4.496702," ","integrate(1/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{b c} {\left| b \right|} \log\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2}\right)}{b^{3} - 2 \, b^{2} c + b c^{2}} - \frac{2 \, \sqrt{b c} {\left(b + c\right)} {\left| b \right|} \arctan\left(\frac{a b^{2} + a b c - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2}}{2 \, \sqrt{-b c} a b}\right)}{{\left(b^{2} - 2 \, b c + c^{2}\right)} \sqrt{-b c} b} + \frac{{\left(b + c\right)} \log\left({\left| b x \right|}\right)}{b^{2} - 2 \, b c + c^{2}} - \frac{4 \, {\left(\sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a {\left(b + c\right)} {\left| b \right|} - {\left(b^{3} - 2 \, b^{2} c + b c^{2}\right)} \sqrt{b c} a^{2} {\left| b \right|}\right)}}{{\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4} - 2 \, {\left(b^{2} + b c\right)} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a + {\left(b^{4} - 2 \, b^{3} c + b^{2} c^{2}\right)} a^{2}\right)} {\left(b^{2} - 2 \, b c + c^{2}\right)}} - \frac{{\left(b x + a\right)} b + a b + {\left(b x + a\right)} c - a c}{{\left(b^{2} - 2 \, b c + c^{2}\right)} b x}"," ",0,"2*sqrt(b*c)*abs(b)*log((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2)/(b^3 - 2*b^2*c + b*c^2) - 2*sqrt(b*c)*(b + c)*abs(b)*arctan(1/2*(a*b^2 + a*b*c - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2)/(sqrt(-b*c)*a*b))/((b^2 - 2*b*c + c^2)*sqrt(-b*c)*b) + (b + c)*log(abs(b*x))/(b^2 - 2*b*c + c^2) - 4*(sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*(b + c)*abs(b) - (b^3 - 2*b^2*c + b*c^2)*sqrt(b*c)*a^2*abs(b))/(((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4 - 2*(b^2 + b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a + (b^4 - 2*b^3*c + b^2*c^2)*a^2)*(b^2 - 2*b*c + c^2)) - ((b*x + a)*b + a*b + (b*x + a)*c - a*c)/((b^2 - 2*b*c + c^2)*b*x)","B",0
436,1,532,0,12.251195," ","integrate(1/x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""giac"")","\frac{\sqrt{b c} {\left| b \right|} \arctan\left(\frac{a b^{2} + a b c - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2}}{2 \, \sqrt{-b c} a b}\right)}{2 \, \sqrt{-b c} a b} - \frac{{\left(b^{2} + 6 \, b c + c^{2}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{6} {\left| b \right|} - {\left(3 \, b^{4} + 5 \, b^{3} c + 5 \, b^{2} c^{2} + 3 \, b c^{3}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4} a {\left| b \right|} + {\left(3 \, b^{6} - 4 \, b^{5} c + 2 \, b^{4} c^{2} - 4 \, b^{3} c^{3} + 3 \, b^{2} c^{4}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a^{2} {\left| b \right|} - {\left(b^{8} - 3 \, b^{7} c + 2 \, b^{6} c^{2} + 2 \, b^{5} c^{3} - 3 \, b^{4} c^{4} + b^{3} c^{5}\right)} \sqrt{b c} a^{3} {\left| b \right|}}{{\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4} - 2 \, {\left(b^{2} + b c\right)} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a + {\left(b^{4} - 2 \, b^{3} c + b^{2} c^{2}\right)} a^{2}\right)}^{2} {\left(b^{2} - 2 \, b c + c^{2}\right)}} - \frac{{\left(b x + a\right)} b^{2} + {\left(b x + a\right)} b c - a b c}{{\left(b^{2} - 2 \, b c + c^{2}\right)} b^{2} x^{2}}"," ",0,"1/2*sqrt(b*c)*abs(b)*arctan(1/2*(a*b^2 + a*b*c - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2)/(sqrt(-b*c)*a*b))/(sqrt(-b*c)*a*b) - ((b^2 + 6*b*c + c^2)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^6*abs(b) - (3*b^4 + 5*b^3*c + 5*b^2*c^2 + 3*b*c^3)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4*a*abs(b) + (3*b^6 - 4*b^5*c + 2*b^4*c^2 - 4*b^3*c^3 + 3*b^2*c^4)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a^2*abs(b) - (b^8 - 3*b^7*c + 2*b^6*c^2 + 2*b^5*c^3 - 3*b^4*c^4 + b^3*c^5)*sqrt(b*c)*a^3*abs(b))/(((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4 - 2*(b^2 + b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a + (b^4 - 2*b^3*c + b^2*c^2)*a^2)^2*(b^2 - 2*b*c + c^2)) - ((b*x + a)*b^2 + (b*x + a)*b*c - a*b*c)/((b^2 - 2*b*c + c^2)*b^2*x^2)","B",0
437,1,802,0,16.937099," ","integrate(1/x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x, algorithm=""giac"")","-\frac{\sqrt{b c} {\left(b + c\right)} {\left| b \right|} \arctan\left(\frac{a b^{2} + a b c - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2}}{2 \, \sqrt{-b c} a b}\right)}{4 \, \sqrt{-b c} a^{2} b} + \frac{3 \, {\left(b^{3} - b^{2} c - b c^{2} + c^{3}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{10} {\left| b \right|} - 3 \, {\left(5 \, b^{5} + 22 \, b^{3} c^{2} + 5 \, b c^{4}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{8} a {\left| b \right|} + 2 \, {\left(15 \, b^{7} - b^{6} c + 18 \, b^{5} c^{2} + 18 \, b^{4} c^{3} - b^{3} c^{4} + 15 \, b^{2} c^{5}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{6} a^{2} {\left| b \right|} - 6 \, {\left(5 \, b^{9} - 6 \, b^{8} c - 5 \, b^{7} c^{2} + 12 \, b^{6} c^{3} - 5 \, b^{5} c^{4} - 6 \, b^{4} c^{5} + 5 \, b^{3} c^{6}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4} a^{3} {\left| b \right|} + 3 \, {\left(5 \, b^{11} - 17 \, b^{10} c + 21 \, b^{9} c^{2} - 9 \, b^{8} c^{3} - 9 \, b^{7} c^{4} + 21 \, b^{6} c^{5} - 17 \, b^{5} c^{6} + 5 \, b^{4} c^{7}\right)} \sqrt{b c} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a^{4} {\left| b \right|} - {\left(3 \, b^{13} - 20 \, b^{12} c + 60 \, b^{11} c^{2} - 108 \, b^{10} c^{3} + 130 \, b^{9} c^{4} - 108 \, b^{8} c^{5} + 60 \, b^{7} c^{6} - 20 \, b^{6} c^{7} + 3 \, b^{5} c^{8}\right)} \sqrt{b c} a^{5} {\left| b \right|}}{6 \, {\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4} - 2 \, {\left(b^{2} + b c\right)} {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a + {\left(b^{4} - 2 \, b^{3} c + b^{2} c^{2}\right)} a^{2}\right)}^{3} {\left(b^{2} - 2 \, b c + c^{2}\right)} a} - \frac{3 \, {\left(b x + a\right)} b^{3} + a b^{3} + 3 \, {\left(b x + a\right)} b^{2} c - 3 \, a b^{2} c}{6 \, {\left(b^{2} - 2 \, b c + c^{2}\right)} b^{3} x^{3}}"," ",0,"-1/4*sqrt(b*c)*(b + c)*abs(b)*arctan(1/2*(a*b^2 + a*b*c - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2)/(sqrt(-b*c)*a*b))/(sqrt(-b*c)*a^2*b) + 1/6*(3*(b^3 - b^2*c - b*c^2 + c^3)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^10*abs(b) - 3*(5*b^5 + 22*b^3*c^2 + 5*b*c^4)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^8*a*abs(b) + 2*(15*b^7 - b^6*c + 18*b^5*c^2 + 18*b^4*c^3 - b^3*c^4 + 15*b^2*c^5)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^6*a^2*abs(b) - 6*(5*b^9 - 6*b^8*c - 5*b^7*c^2 + 12*b^6*c^3 - 5*b^5*c^4 - 6*b^4*c^5 + 5*b^3*c^6)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4*a^3*abs(b) + 3*(5*b^11 - 17*b^10*c + 21*b^9*c^2 - 9*b^8*c^3 - 9*b^7*c^4 + 21*b^6*c^5 - 17*b^5*c^6 + 5*b^4*c^7)*sqrt(b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a^4*abs(b) - (3*b^13 - 20*b^12*c + 60*b^11*c^2 - 108*b^10*c^3 + 130*b^9*c^4 - 108*b^8*c^5 + 60*b^7*c^6 - 20*b^6*c^7 + 3*b^5*c^8)*sqrt(b*c)*a^5*abs(b))/(((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4 - 2*(b^2 + b*c)*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a + (b^4 - 2*b^3*c + b^2*c^2)*a^2)^3*(b^2 - 2*b*c + c^2)*a) - 1/6*(3*(b*x + a)*b^3 + a*b^3 + 3*(b*x + a)*b^2*c - 3*a*b^2*c)/((b^2 - 2*b*c + c^2)*b^3*x^3)","B",0
438,1,932,0,5.576834," ","integrate(x^4/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""giac"")","-\frac{2}{35} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left({\left({\left(b x + a\right)} {\left(\frac{5 \, {\left(3 \, b^{22} c^{5} {\left| b \right|} - 17 \, b^{21} c^{6} {\left| b \right|} + 39 \, b^{20} c^{7} {\left| b \right|} - 45 \, b^{19} c^{8} {\left| b \right|} + 25 \, b^{18} c^{9} {\left| b \right|} - 3 \, b^{17} c^{10} {\left| b \right|} - 3 \, b^{16} c^{11} {\left| b \right|} + b^{15} c^{12} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{29} c^{5} - 9 \, b^{28} c^{6} + 36 \, b^{27} c^{7} - 84 \, b^{26} c^{8} + 126 \, b^{25} c^{9} - 126 \, b^{24} c^{10} + 84 \, b^{23} c^{11} - 36 \, b^{22} c^{12} + 9 \, b^{21} c^{13} - b^{20} c^{14}} + \frac{3 \, a b^{23} c^{4} {\left| b \right|} - 34 \, a b^{22} c^{5} {\left| b \right|} + 126 \, a b^{21} c^{6} {\left| b \right|} - 210 \, a b^{20} c^{7} {\left| b \right|} + 140 \, a b^{19} c^{8} {\left| b \right|} + 42 \, a b^{18} c^{9} {\left| b \right|} - 126 \, a b^{17} c^{10} {\left| b \right|} + 74 \, a b^{16} c^{11} {\left| b \right|} - 15 \, a b^{15} c^{12} {\left| b \right|}}{b^{29} c^{5} - 9 \, b^{28} c^{6} + 36 \, b^{27} c^{7} - 84 \, b^{26} c^{8} + 126 \, b^{25} c^{9} - 126 \, b^{24} c^{10} + 84 \, b^{23} c^{11} - 36 \, b^{22} c^{12} + 9 \, b^{21} c^{13} - b^{20} c^{14}}\right)} - \frac{4 \, a^{2} b^{24} c^{3} {\left| b \right|} - 26 \, a^{2} b^{23} c^{4} {\left| b \right|} + 85 \, a^{2} b^{22} c^{5} {\left| b \right|} - 203 \, a^{2} b^{21} c^{6} {\left| b \right|} + 385 \, a^{2} b^{20} c^{7} {\left| b \right|} - 539 \, a^{2} b^{19} c^{8} {\left| b \right|} + 511 \, a^{2} b^{18} c^{9} {\left| b \right|} - 305 \, a^{2} b^{17} c^{10} {\left| b \right|} + 103 \, a^{2} b^{16} c^{11} {\left| b \right|} - 15 \, a^{2} b^{15} c^{12} {\left| b \right|}}{b^{29} c^{5} - 9 \, b^{28} c^{6} + 36 \, b^{27} c^{7} - 84 \, b^{26} c^{8} + 126 \, b^{25} c^{9} - 126 \, b^{24} c^{10} + 84 \, b^{23} c^{11} - 36 \, b^{22} c^{12} + 9 \, b^{21} c^{13} - b^{20} c^{14}}\right)} {\left(b x + a\right)} + \frac{8 \, a^{3} b^{25} c^{2} {\left| b \right|} - 60 \, a^{3} b^{24} c^{3} {\left| b \right|} + 187 \, a^{3} b^{23} c^{4} {\left| b \right|} - 296 \, a^{3} b^{22} c^{5} {\left| b \right|} + 196 \, a^{3} b^{21} c^{6} {\left| b \right|} + 112 \, a^{3} b^{20} c^{7} {\left| b \right|} - 350 \, a^{3} b^{19} c^{8} {\left| b \right|} + 328 \, a^{3} b^{18} c^{9} {\left| b \right|} - 164 \, a^{3} b^{17} c^{10} {\left| b \right|} + 44 \, a^{3} b^{16} c^{11} {\left| b \right|} - 5 \, a^{3} b^{15} c^{12} {\left| b \right|}}{b^{29} c^{5} - 9 \, b^{28} c^{6} + 36 \, b^{27} c^{7} - 84 \, b^{26} c^{8} + 126 \, b^{25} c^{9} - 126 \, b^{24} c^{10} + 84 \, b^{23} c^{11} - 36 \, b^{22} c^{12} + 9 \, b^{21} c^{13} - b^{20} c^{14}}\right)} + \frac{2 \, {\left(5 \, {\left(b x + a\right)}^{\frac{7}{2}} b + 14 \, {\left(b x + a\right)}^{\frac{5}{2}} a b - 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} b + 15 \, {\left(b x + a\right)}^{\frac{7}{2}} c - 42 \, {\left(b x + a\right)}^{\frac{5}{2}} a c + 35 \, {\left(b x + a\right)}^{\frac{3}{2}} a^{2} c\right)}}{35 \, {\left(b^{6} - 3 \, b^{5} c + 3 \, b^{4} c^{2} - b^{3} c^{3}\right)}}"," ",0,"-2/35*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*(((b*x + a)*(5*(3*b^22*c^5*abs(b) - 17*b^21*c^6*abs(b) + 39*b^20*c^7*abs(b) - 45*b^19*c^8*abs(b) + 25*b^18*c^9*abs(b) - 3*b^17*c^10*abs(b) - 3*b^16*c^11*abs(b) + b^15*c^12*abs(b))*(b*x + a)/(b^29*c^5 - 9*b^28*c^6 + 36*b^27*c^7 - 84*b^26*c^8 + 126*b^25*c^9 - 126*b^24*c^10 + 84*b^23*c^11 - 36*b^22*c^12 + 9*b^21*c^13 - b^20*c^14) + (3*a*b^23*c^4*abs(b) - 34*a*b^22*c^5*abs(b) + 126*a*b^21*c^6*abs(b) - 210*a*b^20*c^7*abs(b) + 140*a*b^19*c^8*abs(b) + 42*a*b^18*c^9*abs(b) - 126*a*b^17*c^10*abs(b) + 74*a*b^16*c^11*abs(b) - 15*a*b^15*c^12*abs(b))/(b^29*c^5 - 9*b^28*c^6 + 36*b^27*c^7 - 84*b^26*c^8 + 126*b^25*c^9 - 126*b^24*c^10 + 84*b^23*c^11 - 36*b^22*c^12 + 9*b^21*c^13 - b^20*c^14)) - (4*a^2*b^24*c^3*abs(b) - 26*a^2*b^23*c^4*abs(b) + 85*a^2*b^22*c^5*abs(b) - 203*a^2*b^21*c^6*abs(b) + 385*a^2*b^20*c^7*abs(b) - 539*a^2*b^19*c^8*abs(b) + 511*a^2*b^18*c^9*abs(b) - 305*a^2*b^17*c^10*abs(b) + 103*a^2*b^16*c^11*abs(b) - 15*a^2*b^15*c^12*abs(b))/(b^29*c^5 - 9*b^28*c^6 + 36*b^27*c^7 - 84*b^26*c^8 + 126*b^25*c^9 - 126*b^24*c^10 + 84*b^23*c^11 - 36*b^22*c^12 + 9*b^21*c^13 - b^20*c^14))*(b*x + a) + (8*a^3*b^25*c^2*abs(b) - 60*a^3*b^24*c^3*abs(b) + 187*a^3*b^23*c^4*abs(b) - 296*a^3*b^22*c^5*abs(b) + 196*a^3*b^21*c^6*abs(b) + 112*a^3*b^20*c^7*abs(b) - 350*a^3*b^19*c^8*abs(b) + 328*a^3*b^18*c^9*abs(b) - 164*a^3*b^17*c^10*abs(b) + 44*a^3*b^16*c^11*abs(b) - 5*a^3*b^15*c^12*abs(b))/(b^29*c^5 - 9*b^28*c^6 + 36*b^27*c^7 - 84*b^26*c^8 + 126*b^25*c^9 - 126*b^24*c^10 + 84*b^23*c^11 - 36*b^22*c^12 + 9*b^21*c^13 - b^20*c^14)) + 2/35*(5*(b*x + a)^(7/2)*b + 14*(b*x + a)^(5/2)*a*b - 35*(b*x + a)^(3/2)*a^2*b + 15*(b*x + a)^(7/2)*c - 42*(b*x + a)^(5/2)*a*c + 35*(b*x + a)^(3/2)*a^2*c)/(b^6 - 3*b^5*c + 3*b^4*c^2 - b^3*c^3)","B",0
439,1,480,0,5.226399," ","integrate(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""giac"")","-\frac{2}{5} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left({\left(b x + a\right)} {\left(\frac{{\left(3 \, b^{12} c^{3} {\left| b \right|} - 8 \, b^{11} c^{4} {\left| b \right|} + 6 \, b^{10} c^{5} {\left| b \right|} - b^{8} c^{7} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{18} c^{3} - 6 \, b^{17} c^{4} + 15 \, b^{16} c^{5} - 20 \, b^{15} c^{6} + 15 \, b^{14} c^{7} - 6 \, b^{13} c^{8} + b^{12} c^{9}} + \frac{a b^{13} c^{2} {\left| b \right|} - 2 \, a b^{12} c^{3} {\left| b \right|} - 2 \, a b^{11} c^{4} {\left| b \right|} + 8 \, a b^{10} c^{5} {\left| b \right|} - 7 \, a b^{9} c^{6} {\left| b \right|} + 2 \, a b^{8} c^{7} {\left| b \right|}}{b^{18} c^{3} - 6 \, b^{17} c^{4} + 15 \, b^{16} c^{5} - 20 \, b^{15} c^{6} + 15 \, b^{14} c^{7} - 6 \, b^{13} c^{8} + b^{12} c^{9}}\right)} - \frac{2 \, a^{2} b^{14} c {\left| b \right|} - 11 \, a^{2} b^{13} c^{2} {\left| b \right|} + 25 \, a^{2} b^{12} c^{3} {\left| b \right|} - 30 \, a^{2} b^{11} c^{4} {\left| b \right|} + 20 \, a^{2} b^{10} c^{5} {\left| b \right|} - 7 \, a^{2} b^{9} c^{6} {\left| b \right|} + a^{2} b^{8} c^{7} {\left| b \right|}}{b^{18} c^{3} - 6 \, b^{17} c^{4} + 15 \, b^{16} c^{5} - 20 \, b^{15} c^{6} + 15 \, b^{14} c^{7} - 6 \, b^{13} c^{8} + b^{12} c^{9}}\right)} + \frac{2 \, {\left({\left(b x + a\right)}^{\frac{5}{2}} b + 5 \, {\left(b x + a\right)}^{\frac{3}{2}} a b + 3 \, {\left(b x + a\right)}^{\frac{5}{2}} c - 5 \, {\left(b x + a\right)}^{\frac{3}{2}} a c\right)}}{5 \, {\left(b^{5} - 3 \, b^{4} c + 3 \, b^{3} c^{2} - b^{2} c^{3}\right)}}"," ",0,"-2/5*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*((b*x + a)*((3*b^12*c^3*abs(b) - 8*b^11*c^4*abs(b) + 6*b^10*c^5*abs(b) - b^8*c^7*abs(b))*(b*x + a)/(b^18*c^3 - 6*b^17*c^4 + 15*b^16*c^5 - 20*b^15*c^6 + 15*b^14*c^7 - 6*b^13*c^8 + b^12*c^9) + (a*b^13*c^2*abs(b) - 2*a*b^12*c^3*abs(b) - 2*a*b^11*c^4*abs(b) + 8*a*b^10*c^5*abs(b) - 7*a*b^9*c^6*abs(b) + 2*a*b^8*c^7*abs(b))/(b^18*c^3 - 6*b^17*c^4 + 15*b^16*c^5 - 20*b^15*c^6 + 15*b^14*c^7 - 6*b^13*c^8 + b^12*c^9)) - (2*a^2*b^14*c*abs(b) - 11*a^2*b^13*c^2*abs(b) + 25*a^2*b^12*c^3*abs(b) - 30*a^2*b^11*c^4*abs(b) + 20*a^2*b^10*c^5*abs(b) - 7*a^2*b^9*c^6*abs(b) + a^2*b^8*c^7*abs(b))/(b^18*c^3 - 6*b^17*c^4 + 15*b^16*c^5 - 20*b^15*c^6 + 15*b^14*c^7 - 6*b^13*c^8 + b^12*c^9)) + 2/5*((b*x + a)^(5/2)*b + 5*(b*x + a)^(3/2)*a*b + 3*(b*x + a)^(5/2)*c - 5*(b*x + a)^(3/2)*a*c)/(b^5 - 3*b^4*c + 3*b^3*c^2 - b^2*c^3)","B",0
440,1,2374,0,10.122345," ","integrate(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left(\frac{{\left(3 \, b^{7} c {\left| b \right|} - 8 \, b^{6} c^{2} {\left| b \right|} + 6 \, b^{5} c^{3} {\left| b \right|} - b^{3} c^{5} {\left| b \right|}\right)} {\left(b x + a\right)}}{b^{12} c - 6 \, b^{11} c^{2} + 15 \, b^{10} c^{3} - 20 \, b^{9} c^{4} + 15 \, b^{8} c^{5} - 6 \, b^{7} c^{6} + b^{6} c^{7}} + \frac{3 \, a b^{8} {\left| b \right|} + a b^{7} c {\left| b \right|} - 22 \, a b^{6} c^{2} {\left| b \right|} + 30 \, a b^{5} c^{3} {\left| b \right|} - 13 \, a b^{4} c^{4} {\left| b \right|} + a b^{3} c^{5} {\left| b \right|}}{b^{12} c - 6 \, b^{11} c^{2} + 15 \, b^{10} c^{3} - 20 \, b^{9} c^{4} + 15 \, b^{8} c^{5} - 6 \, b^{7} c^{6} + b^{6} c^{7}}\right)} + \frac{8 \, a^{2} \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{{\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)} \sqrt{-a}} + \frac{2 \, {\left({\left(b x + a\right)}^{\frac{3}{2}} b^{9} + 12 \, \sqrt{b x + a} a b^{9} - 3 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{8} c - 72 \, \sqrt{b x + a} a b^{8} c - 3 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{7} c^{2} + 180 \, \sqrt{b x + a} a b^{7} c^{2} + 25 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{6} c^{3} - 240 \, \sqrt{b x + a} a b^{6} c^{3} - 45 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{5} c^{4} + 180 \, \sqrt{b x + a} a b^{5} c^{4} + 39 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{4} c^{5} - 72 \, \sqrt{b x + a} a b^{4} c^{5} - 17 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{3} c^{6} + 12 \, \sqrt{b x + a} a b^{3} c^{6} + 3 \, {\left(b x + a\right)}^{\frac{3}{2}} b^{2} c^{7}\right)}}{3 \, {\left(b^{12} - 9 \, b^{11} c + 36 \, b^{10} c^{2} - 84 \, b^{9} c^{3} + 126 \, b^{8} c^{4} - 126 \, b^{7} c^{5} + 84 \, b^{6} c^{6} - 36 \, b^{5} c^{7} + 9 \, b^{4} c^{8} - b^{3} c^{9}\right)}} - \frac{8 \, {\left(2 \, {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} {\left(a b^{3} c - a b^{2} c^{2}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + 2 \, {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} {\left(a b^{3} - a b^{2} c\right)} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{7} - 5 \, a^{2} b^{6} c + 10 \, a^{2} b^{5} c^{2} - 10 \, a^{2} b^{4} c^{3} + 5 \, a^{2} b^{3} c^{4} - a^{2} b^{2} c^{5}\right)} \sqrt{-a b c} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{2} b^{8} - 5 \, a^{2} b^{7} c + 10 \, a^{2} b^{6} c^{2} - 10 \, a^{2} b^{5} c^{3} + 5 \, a^{2} b^{4} c^{4} - a^{2} b^{3} c^{5}\right)} \sqrt{-a} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} + {\left(a^{3} b^{11} c - 6 \, a^{3} b^{10} c^{2} + 14 \, a^{3} b^{9} c^{3} - 14 \, a^{3} b^{8} c^{4} + 14 \, a^{3} b^{6} c^{6} - 14 \, a^{3} b^{5} c^{7} + 6 \, a^{3} b^{4} c^{8} - a^{3} b^{3} c^{9}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{3} b^{11} - 6 \, a^{3} b^{10} c + 14 \, a^{3} b^{9} c^{2} - 14 \, a^{3} b^{8} c^{3} + 14 \, a^{3} b^{6} c^{5} - 14 \, a^{3} b^{5} c^{6} + 6 \, a^{3} b^{4} c^{7} - a^{3} b^{3} c^{8}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4} + \sqrt{{\left(a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4}\right)}^{2} - {\left(a^{2} b^{7} - 5 \, a^{2} b^{6} c + 10 \, a^{2} b^{5} c^{2} - 10 \, a^{2} b^{4} c^{3} + 5 \, a^{2} b^{3} c^{4} - a^{2} b^{2} c^{5}\right)} {\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)}}}{b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}}}}\right)}{{\left(b^{12} - 9 \, b^{11} c + 36 \, b^{10} c^{2} - 84 \, b^{9} c^{3} + 126 \, b^{8} c^{4} - 126 \, b^{7} c^{5} + 84 \, b^{6} c^{6} - 36 \, b^{5} c^{7} + 9 \, b^{4} c^{8} - b^{3} c^{9}\right)} a {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|}} + \frac{8 \, {\left(2 \, {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} {\left(a b^{3} c - a b^{2} c^{2}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + 2 \, {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} {\left(a b^{3} - a b^{2} c\right)} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{7} - 5 \, a^{2} b^{6} c + 10 \, a^{2} b^{5} c^{2} - 10 \, a^{2} b^{4} c^{3} + 5 \, a^{2} b^{3} c^{4} - a^{2} b^{2} c^{5}\right)} \sqrt{-a b c} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{2} b^{8} - 5 \, a^{2} b^{7} c + 10 \, a^{2} b^{6} c^{2} - 10 \, a^{2} b^{5} c^{3} + 5 \, a^{2} b^{4} c^{4} - a^{2} b^{3} c^{5}\right)} \sqrt{-a} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} + {\left(a^{3} b^{11} c - 6 \, a^{3} b^{10} c^{2} + 14 \, a^{3} b^{9} c^{3} - 14 \, a^{3} b^{8} c^{4} + 14 \, a^{3} b^{6} c^{6} - 14 \, a^{3} b^{5} c^{7} + 6 \, a^{3} b^{4} c^{8} - a^{3} b^{3} c^{9}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{3} b^{11} - 6 \, a^{3} b^{10} c + 14 \, a^{3} b^{9} c^{2} - 14 \, a^{3} b^{8} c^{3} + 14 \, a^{3} b^{6} c^{5} - 14 \, a^{3} b^{5} c^{6} + 6 \, a^{3} b^{4} c^{7} - a^{3} b^{3} c^{8}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4} - \sqrt{{\left(a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4}\right)}^{2} - {\left(a^{2} b^{7} - 5 \, a^{2} b^{6} c + 10 \, a^{2} b^{5} c^{2} - 10 \, a^{2} b^{4} c^{3} + 5 \, a^{2} b^{3} c^{4} - a^{2} b^{2} c^{5}\right)} {\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)}}}{b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}}}}\right)}{{\left(b^{12} - 9 \, b^{11} c + 36 \, b^{10} c^{2} - 84 \, b^{9} c^{3} + 126 \, b^{8} c^{4} - 126 \, b^{7} c^{5} + 84 \, b^{6} c^{6} - 36 \, b^{5} c^{7} + 9 \, b^{4} c^{8} - b^{3} c^{9}\right)} a {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|}}"," ",0,"-2/3*sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*((3*b^7*c*abs(b) - 8*b^6*c^2*abs(b) + 6*b^5*c^3*abs(b) - b^3*c^5*abs(b))*(b*x + a)/(b^12*c - 6*b^11*c^2 + 15*b^10*c^3 - 20*b^9*c^4 + 15*b^8*c^5 - 6*b^7*c^6 + b^6*c^7) + (3*a*b^8*abs(b) + a*b^7*c*abs(b) - 22*a*b^6*c^2*abs(b) + 30*a*b^5*c^3*abs(b) - 13*a*b^4*c^4*abs(b) + a*b^3*c^5*abs(b))/(b^12*c - 6*b^11*c^2 + 15*b^10*c^3 - 20*b^9*c^4 + 15*b^8*c^5 - 6*b^7*c^6 + b^6*c^7)) + 8*a^2*arctan(sqrt(b*x + a)/sqrt(-a))/((b^3 - 3*b^2*c + 3*b*c^2 - c^3)*sqrt(-a)) + 2/3*((b*x + a)^(3/2)*b^9 + 12*sqrt(b*x + a)*a*b^9 - 3*(b*x + a)^(3/2)*b^8*c - 72*sqrt(b*x + a)*a*b^8*c - 3*(b*x + a)^(3/2)*b^7*c^2 + 180*sqrt(b*x + a)*a*b^7*c^2 + 25*(b*x + a)^(3/2)*b^6*c^3 - 240*sqrt(b*x + a)*a*b^6*c^3 - 45*(b*x + a)^(3/2)*b^5*c^4 + 180*sqrt(b*x + a)*a*b^5*c^4 + 39*(b*x + a)^(3/2)*b^4*c^5 - 72*sqrt(b*x + a)*a*b^4*c^5 - 17*(b*x + a)^(3/2)*b^3*c^6 + 12*sqrt(b*x + a)*a*b^3*c^6 + 3*(b*x + a)^(3/2)*b^2*c^7)/(b^12 - 9*b^11*c + 36*b^10*c^2 - 84*b^9*c^3 + 126*b^8*c^4 - 126*b^7*c^5 + 84*b^6*c^6 - 36*b^5*c^7 + 9*b^4*c^8 - b^3*c^9) - 8*(2*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*(a*b^3*c - a*b^2*c^2)*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + 2*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*(a*b^3 - a*b^2*c)*sqrt(-a*b*c)*abs(b) + (a^2*b^7 - 5*a^2*b^6*c + 10*a^2*b^5*c^2 - 10*a^2*b^4*c^3 + 5*a^2*b^3*c^4 - a^2*b^2*c^5)*sqrt(-a*b*c)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^2*b^8 - 5*a^2*b^7*c + 10*a^2*b^6*c^2 - 10*a^2*b^5*c^3 + 5*a^2*b^4*c^4 - a^2*b^3*c^5)*sqrt(-a)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b) + (a^3*b^11*c - 6*a^3*b^10*c^2 + 14*a^3*b^9*c^3 - 14*a^3*b^8*c^4 + 14*a^3*b^6*c^6 - 14*a^3*b^5*c^7 + 6*a^3*b^4*c^8 - a^3*b^3*c^9)*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^3*b^11 - 6*a^3*b^10*c + 14*a^3*b^9*c^2 - 14*a^3*b^8*c^3 + 14*a^3*b^6*c^5 - 14*a^3*b^5*c^6 + 6*a^3*b^4*c^7 - a^3*b^3*c^8)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4 + sqrt((a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4)^2 - (a^2*b^7 - 5*a^2*b^6*c + 10*a^2*b^5*c^2 - 10*a^2*b^4*c^3 + 5*a^2*b^3*c^4 - a^2*b^2*c^5)*(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/((b^12 - 9*b^11*c + 36*b^10*c^2 - 84*b^9*c^3 + 126*b^8*c^4 - 126*b^7*c^5 + 84*b^6*c^6 - 36*b^5*c^7 + 9*b^4*c^8 - b^3*c^9)*a*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)) + 8*(2*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*(a*b^3*c - a*b^2*c^2)*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + 2*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*(a*b^3 - a*b^2*c)*sqrt(-a*b*c)*abs(b) + (a^2*b^7 - 5*a^2*b^6*c + 10*a^2*b^5*c^2 - 10*a^2*b^4*c^3 + 5*a^2*b^3*c^4 - a^2*b^2*c^5)*sqrt(-a*b*c)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^2*b^8 - 5*a^2*b^7*c + 10*a^2*b^6*c^2 - 10*a^2*b^5*c^3 + 5*a^2*b^4*c^4 - a^2*b^3*c^5)*sqrt(-a)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b) + (a^3*b^11*c - 6*a^3*b^10*c^2 + 14*a^3*b^9*c^3 - 14*a^3*b^8*c^4 + 14*a^3*b^6*c^6 - 14*a^3*b^5*c^7 + 6*a^3*b^4*c^8 - a^3*b^3*c^9)*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^3*b^11 - 6*a^3*b^10*c + 14*a^3*b^9*c^2 - 14*a^3*b^8*c^3 + 14*a^3*b^6*c^5 - 14*a^3*b^5*c^6 + 6*a^3*b^4*c^7 - a^3*b^3*c^8)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4 - sqrt((a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4)^2 - (a^2*b^7 - 5*a^2*b^6*c + 10*a^2*b^5*c^2 - 10*a^2*b^4*c^3 + 5*a^2*b^3*c^4 - a^2*b^2*c^5)*(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/((b^12 - 9*b^11*c + 36*b^10*c^2 - 84*b^9*c^3 + 126*b^8*c^4 - 126*b^7*c^5 + 84*b^6*c^6 - 36*b^5*c^7 + 9*b^4*c^8 - b^3*c^9)*a*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3))","B",0
441,1,2318,0,78.697761," ","integrate(x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{\sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c} {\left(3 \, b {\left| b \right|} + c {\left| b \right|}\right)}}{b^{4} - 3 \, b^{3} c + 3 \, b^{2} c^{2} - b c^{3}} + \frac{2 \, \sqrt{b x + a} a b}{{\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)} x} - \frac{3 \, {\left(a b^{2} + a b c\right)} \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{{\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)} \sqrt{-a}} - \frac{\sqrt{b x + a} b^{2} + 3 \, \sqrt{b x + a} b c}{b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}} + \frac{4 \, {\left({\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a^{2} b^{3} c {\left| b \right|} - {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)} a^{2} b^{2} c^{2} {\left| b \right|} + {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{3} a b c {\left| b \right|}\right)}}{{\left(a^{2} b^{4} - 2 \, a^{2} b^{3} c + a^{2} b^{2} c^{2} - 2 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a b^{2} - 2 \, {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{2} a b c + {\left(\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}\right)}^{4}\right)} {\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)}} + \frac{3 \, {\left(2 \, {\left(a b^{4} c - a b^{2} c^{3}\right)} {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + 2 \, {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} {\left(a b^{4} - a b^{2} c^{2}\right)} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{8} - 4 \, a^{2} b^{7} c + 5 \, a^{2} b^{6} c^{2} - 5 \, a^{2} b^{4} c^{4} + 4 \, a^{2} b^{3} c^{5} - a^{2} b^{2} c^{6}\right)} \sqrt{-a b c} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{2} b^{9} - 4 \, a^{2} b^{8} c + 5 \, a^{2} b^{7} c^{2} - 5 \, a^{2} b^{5} c^{4} + 4 \, a^{2} b^{4} c^{5} - a^{2} b^{3} c^{6}\right)} \sqrt{-a} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} + {\left(a^{3} b^{12} c - 5 \, a^{3} b^{11} c^{2} + 8 \, a^{3} b^{10} c^{3} - 14 \, a^{3} b^{8} c^{5} + 14 \, a^{3} b^{7} c^{6} - 8 \, a^{3} b^{5} c^{8} + 5 \, a^{3} b^{4} c^{9} - a^{3} b^{3} c^{10}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{3} b^{12} - 5 \, a^{3} b^{11} c + 8 \, a^{3} b^{10} c^{2} - 14 \, a^{3} b^{8} c^{4} + 14 \, a^{3} b^{7} c^{5} - 8 \, a^{3} b^{5} c^{7} + 5 \, a^{3} b^{4} c^{8} - a^{3} b^{3} c^{9}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4} + \sqrt{{\left(a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4}\right)}^{2} - {\left(a^{2} b^{7} - 5 \, a^{2} b^{6} c + 10 \, a^{2} b^{5} c^{2} - 10 \, a^{2} b^{4} c^{3} + 5 \, a^{2} b^{3} c^{4} - a^{2} b^{2} c^{5}\right)} {\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)}}}{b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}}}}\right)}{{\left(b^{11} - 9 \, b^{10} c + 36 \, b^{9} c^{2} - 84 \, b^{8} c^{3} + 126 \, b^{7} c^{4} - 126 \, b^{6} c^{5} + 84 \, b^{5} c^{6} - 36 \, b^{4} c^{7} + 9 \, b^{3} c^{8} - b^{2} c^{9}\right)} a^{2} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|}} - \frac{3 \, {\left(2 \, {\left(a b^{4} c - a b^{2} c^{3}\right)} {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + 2 \, {\left(a b^{4} - 3 \, a b^{3} c + 3 \, a b^{2} c^{2} - a b c^{3}\right)}^{2} {\left(a b^{4} - a b^{2} c^{2}\right)} \sqrt{-a b c} {\left| b \right|} + {\left(a^{2} b^{8} - 4 \, a^{2} b^{7} c + 5 \, a^{2} b^{6} c^{2} - 5 \, a^{2} b^{4} c^{4} + 4 \, a^{2} b^{3} c^{5} - a^{2} b^{2} c^{6}\right)} \sqrt{-a b c} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{2} b^{9} - 4 \, a^{2} b^{8} c + 5 \, a^{2} b^{7} c^{2} - 5 \, a^{2} b^{5} c^{4} + 4 \, a^{2} b^{4} c^{5} - a^{2} b^{3} c^{6}\right)} \sqrt{-a} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|} {\left| b \right|} + {\left(a^{3} b^{12} c - 5 \, a^{3} b^{11} c^{2} + 8 \, a^{3} b^{10} c^{3} - 14 \, a^{3} b^{8} c^{5} + 14 \, a^{3} b^{7} c^{6} - 8 \, a^{3} b^{5} c^{8} + 5 \, a^{3} b^{4} c^{9} - a^{3} b^{3} c^{10}\right)} \sqrt{-a} {\left| b \right|} \mathrm{sgn}\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right) + {\left(a^{3} b^{12} - 5 \, a^{3} b^{11} c + 8 \, a^{3} b^{10} c^{2} - 14 \, a^{3} b^{8} c^{4} + 14 \, a^{3} b^{7} c^{5} - 8 \, a^{3} b^{5} c^{7} + 5 \, a^{3} b^{4} c^{8} - a^{3} b^{3} c^{9}\right)} \sqrt{-a b c} {\left| b \right|}\right)} \arctan\left(-\frac{\sqrt{b c} \sqrt{b x + a} - \sqrt{a b^{2} + {\left(b x + a\right)} b c - a b c}}{\sqrt{-\frac{a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4} - \sqrt{{\left(a b^{5} - 2 \, a b^{4} c + 2 \, a b^{2} c^{3} - a b c^{4}\right)}^{2} - {\left(a^{2} b^{7} - 5 \, a^{2} b^{6} c + 10 \, a^{2} b^{5} c^{2} - 10 \, a^{2} b^{4} c^{3} + 5 \, a^{2} b^{3} c^{4} - a^{2} b^{2} c^{5}\right)} {\left(b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}\right)}}}{b^{3} - 3 \, b^{2} c + 3 \, b c^{2} - c^{3}}}}\right)}{{\left(b^{11} - 9 \, b^{10} c + 36 \, b^{9} c^{2} - 84 \, b^{8} c^{3} + 126 \, b^{7} c^{4} - 126 \, b^{6} c^{5} + 84 \, b^{5} c^{6} - 36 \, b^{4} c^{7} + 9 \, b^{3} c^{8} - b^{2} c^{9}\right)} a^{2} {\left| -a b^{4} + 3 \, a b^{3} c - 3 \, a b^{2} c^{2} + a b c^{3} \right|}}\right)}}{b}"," ",0,"-2*(sqrt(a*b^2 + (b*x + a)*b*c - a*b*c)*(3*b*abs(b) + c*abs(b))/(b^4 - 3*b^3*c + 3*b^2*c^2 - b*c^3) + 2*sqrt(b*x + a)*a*b/((b^3 - 3*b^2*c + 3*b*c^2 - c^3)*x) - 3*(a*b^2 + a*b*c)*arctan(sqrt(b*x + a)/sqrt(-a))/((b^3 - 3*b^2*c + 3*b*c^2 - c^3)*sqrt(-a)) - (sqrt(b*x + a)*b^2 + 3*sqrt(b*x + a)*b*c)/(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + 4*((sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a^2*b^3*c*abs(b) - (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))*a^2*b^2*c^2*abs(b) + (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^3*a*b*c*abs(b))/((a^2*b^4 - 2*a^2*b^3*c + a^2*b^2*c^2 - 2*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*b^2 - 2*(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^2*a*b*c + (sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))^4)*(b^3 - 3*b^2*c + 3*b*c^2 - c^3)) + 3*(2*(a*b^4*c - a*b^2*c^3)*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + 2*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*(a*b^4 - a*b^2*c^2)*sqrt(-a*b*c)*abs(b) + (a^2*b^8 - 4*a^2*b^7*c + 5*a^2*b^6*c^2 - 5*a^2*b^4*c^4 + 4*a^2*b^3*c^5 - a^2*b^2*c^6)*sqrt(-a*b*c)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^2*b^9 - 4*a^2*b^8*c + 5*a^2*b^7*c^2 - 5*a^2*b^5*c^4 + 4*a^2*b^4*c^5 - a^2*b^3*c^6)*sqrt(-a)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b) + (a^3*b^12*c - 5*a^3*b^11*c^2 + 8*a^3*b^10*c^3 - 14*a^3*b^8*c^5 + 14*a^3*b^7*c^6 - 8*a^3*b^5*c^8 + 5*a^3*b^4*c^9 - a^3*b^3*c^10)*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^3*b^12 - 5*a^3*b^11*c + 8*a^3*b^10*c^2 - 14*a^3*b^8*c^4 + 14*a^3*b^7*c^5 - 8*a^3*b^5*c^7 + 5*a^3*b^4*c^8 - a^3*b^3*c^9)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4 + sqrt((a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4)^2 - (a^2*b^7 - 5*a^2*b^6*c + 10*a^2*b^5*c^2 - 10*a^2*b^4*c^3 + 5*a^2*b^3*c^4 - a^2*b^2*c^5)*(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/((b^11 - 9*b^10*c + 36*b^9*c^2 - 84*b^8*c^3 + 126*b^7*c^4 - 126*b^6*c^5 + 84*b^5*c^6 - 36*b^4*c^7 + 9*b^3*c^8 - b^2*c^9)*a^2*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)) - 3*(2*(a*b^4*c - a*b^2*c^3)*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + 2*(a*b^4 - 3*a*b^3*c + 3*a*b^2*c^2 - a*b*c^3)^2*(a*b^4 - a*b^2*c^2)*sqrt(-a*b*c)*abs(b) + (a^2*b^8 - 4*a^2*b^7*c + 5*a^2*b^6*c^2 - 5*a^2*b^4*c^4 + 4*a^2*b^3*c^5 - a^2*b^2*c^6)*sqrt(-a*b*c)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^2*b^9 - 4*a^2*b^8*c + 5*a^2*b^7*c^2 - 5*a^2*b^5*c^4 + 4*a^2*b^4*c^5 - a^2*b^3*c^6)*sqrt(-a)*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)*abs(b) + (a^3*b^12*c - 5*a^3*b^11*c^2 + 8*a^3*b^10*c^3 - 14*a^3*b^8*c^5 + 14*a^3*b^7*c^6 - 8*a^3*b^5*c^8 + 5*a^3*b^4*c^9 - a^3*b^3*c^10)*sqrt(-a)*abs(b)*sgn(b^3 - 3*b^2*c + 3*b*c^2 - c^3) + (a^3*b^12 - 5*a^3*b^11*c + 8*a^3*b^10*c^2 - 14*a^3*b^8*c^4 + 14*a^3*b^7*c^5 - 8*a^3*b^5*c^7 + 5*a^3*b^4*c^8 - a^3*b^3*c^9)*sqrt(-a*b*c)*abs(b))*arctan(-(sqrt(b*c)*sqrt(b*x + a) - sqrt(a*b^2 + (b*x + a)*b*c - a*b*c))/sqrt(-(a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4 - sqrt((a*b^5 - 2*a*b^4*c + 2*a*b^2*c^3 - a*b*c^4)^2 - (a^2*b^7 - 5*a^2*b^6*c + 10*a^2*b^5*c^2 - 10*a^2*b^4*c^3 + 5*a^2*b^3*c^4 - a^2*b^2*c^5)*(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/(b^3 - 3*b^2*c + 3*b*c^2 - c^3)))/((b^11 - 9*b^10*c + 36*b^9*c^2 - 84*b^8*c^3 + 126*b^7*c^4 - 126*b^6*c^5 + 84*b^5*c^6 - 36*b^4*c^7 + 9*b^3*c^8 - b^2*c^9)*a^2*abs(-a*b^4 + 3*a*b^3*c - 3*a*b^2*c^2 + a*b*c^3)))/b","B",0
442,-1,0,0,0.000000," ","integrate(1/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,1,54,0,0.613281," ","integrate((1-x)^(1/2)*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(x - 1\right)}^{2} + \frac{1}{2} \, {\left(x + 2\right)} \sqrt{x + 1} \sqrt{-x + 1} - \sqrt{x + 1} \sqrt{-x + 1} - \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{-x + 1}\right)"," ",0,"-1/2*(x - 1)^2 + 1/2*(x + 2)*sqrt(x + 1)*sqrt(-x + 1) - sqrt(x + 1)*sqrt(-x + 1) - arcsin(1/2*sqrt(2)*sqrt(-x + 1))","B",0
444,1,77,0,0.538537," ","integrate(x^3*(-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, x^{4} - \frac{1}{60} \, {\left({\left(2 \, {\left(3 \, {\left(4 \, x - 17\right)} {\left(x + 1\right)} + 133\right)} {\left(x + 1\right)} - 295\right)} {\left(x + 1\right)} + 195\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{1}{12} \, {\left({\left(2 \, {\left(3 \, x - 10\right)} {\left(x + 1\right)} + 43\right)} {\left(x + 1\right)} - 39\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"-1/2*x^4 - 1/60*((2*(3*(4*x - 17)*(x + 1) + 133)*(x + 1) - 295)*(x + 1) + 195)*sqrt(x + 1)*sqrt(-x + 1) - 1/12*((2*(3*x - 10)*(x + 1) + 43)*(x + 1) - 39)*sqrt(x + 1)*sqrt(-x + 1)","B",0
445,1,76,0,0.469220," ","integrate(x^2*(-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","-\frac{2}{3} \, x^{3} - \frac{1}{12} \, {\left({\left(2 \, {\left(3 \, x - 10\right)} {\left(x + 1\right)} + 43\right)} {\left(x + 1\right)} - 39\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{1}{3} \, {\left({\left(2 \, x - 5\right)} {\left(x + 1\right)} + 9\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{1}{2} \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 1}\right)"," ",0,"-2/3*x^3 - 1/12*((2*(3*x - 10)*(x + 1) + 43)*(x + 1) - 39)*sqrt(x + 1)*sqrt(-x + 1) - 1/3*((2*x - 5)*(x + 1) + 9)*sqrt(x + 1)*sqrt(-x + 1) - 1/2*arcsin(1/2*sqrt(2)*sqrt(x + 1))","B",0
446,1,54,0,0.391104," ","integrate(x*(-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","-{\left(x + 1\right)}^{2} - \frac{1}{3} \, {\left({\left(2 \, x - 5\right)} {\left(x + 1\right)} + 9\right)} \sqrt{x + 1} \sqrt{-x + 1} - \sqrt{x + 1} {\left(x - 2\right)} \sqrt{-x + 1} + 2 \, x + 2"," ",0,"-(x + 1)^2 - 1/3*((2*x - 5)*(x + 1) + 9)*sqrt(x + 1)*sqrt(-x + 1) - sqrt(x + 1)*(x - 2)*sqrt(-x + 1) + 2*x + 2","B",0
447,1,49,0,0.368372," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","-\sqrt{x + 1} {\left(x - 2\right)} \sqrt{-x + 1} - 2 \, x - 2 \, \sqrt{x + 1} \sqrt{-x + 1} - 2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 1}\right) - 2"," ",0,"-sqrt(x + 1)*(x - 2)*sqrt(-x + 1) - 2*x - 2*sqrt(x + 1)*sqrt(-x + 1) - 2*arcsin(1/2*sqrt(2)*sqrt(x + 1)) - 2","B",0
448,-2,0,0,0.000000," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-93.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-17.8804557086]-2*ln(abs(sqrt(x+1)-1))-2*ln(sqrt(x+1)+1)-2*sqrt(x+1)*sqrt(-x+1)+2*ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))-2*ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))","F(-2)",0
449,1,149,0,0.461311," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x^2,x, algorithm=""giac"")","2 \, \pi + \frac{8 \, {\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{x + 1}} - \frac{\sqrt{x + 1}}{\sqrt{2} - \sqrt{-x + 1}}\right)}}{{\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{x + 1}} - \frac{\sqrt{x + 1}}{\sqrt{2} - \sqrt{-x + 1}}\right)}^{2} - 4} + \frac{2}{x} + 4 \, \arctan\left(\frac{\sqrt{x + 1} {\left(\frac{{\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{2}}{x + 1} - 1\right)}}{2 \, {\left(\sqrt{2} - \sqrt{-x + 1}\right)}}\right)"," ",0,"2*pi + 8*((sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) - sqrt(x + 1)/(sqrt(2) - sqrt(-x + 1)))/(((sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) - sqrt(x + 1)/(sqrt(2) - sqrt(-x + 1)))^2 - 4) + 2/x + 4*arctan(1/2*sqrt(x + 1)*((sqrt(2) - sqrt(-x + 1))^2/(x + 1) - 1)/(sqrt(2) - sqrt(-x + 1)))","B",0
450,-2,0,0,0.000000," ","integrate((-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-93.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-17.8804557086](4*(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1))^3+16*(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))/((2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1))^2-4)^2-ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))+ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))+1/x^2","F(-2)",0
451,-2,0,0,0.000000," ","integrate(((1-x)^(1/2)+(1+x)^(1/2))/(-(1-x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-93.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-17.8804557086]ln(abs(sqrt(x+1)-1))+ln(sqrt(x+1)+1)+sqrt(x+1)*sqrt(-x+1)-ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))+ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))","F(-2)",0
452,1,41,0,0.380980," ","integrate((-(-1+x)^(1/2)+(1+x)^(1/2))/((-1+x)^(1/2)+(1+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x + 1\right)}^{2} - \frac{1}{2} \, \sqrt{x + 1} \sqrt{x - 1} x - x - \log\left(\sqrt{x + 1} - \sqrt{x - 1}\right) - 1"," ",0,"1/2*(x + 1)^2 - 1/2*sqrt(x + 1)*sqrt(x - 1)*x - x - log(sqrt(x + 1) - sqrt(x - 1)) - 1","A",0
453,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a} f + d\right)}^{n}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a)*f + d)^n, x)","F",0
454,1,163,0,0.450324," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""giac"")","-\frac{3}{2} \, a d^{2} f {\left| f \right|} e^{\left(-1\right)} \log\left({\left| -x e + \sqrt{a f^{2} + x^{2} e^{2}} \right|}\right) + \frac{3}{2} \, a f^{2} x^{2} e + 3 \, a d f^{2} x + x^{4} e^{3} + 2 \, d x^{3} e^{2} + \frac{3}{2} \, d^{2} x^{2} e + d^{3} x + \frac{1}{2} \, {\left(4 \, a d f {\left| f \right|} e^{\left(-1\right)} + {\left(2 \, {\left(\frac{x {\left| f \right|} e^{2}}{f} + \frac{2 \, d {\left| f \right|} e}{f}\right)} x + \frac{{\left(2 \, a f^{4} {\left| f \right|} e^{4} + 3 \, d^{2} f^{2} {\left| f \right|} e^{4}\right)} e^{\left(-4\right)}}{f^{3}}\right)} x\right)} \sqrt{a f^{2} + x^{2} e^{2}}"," ",0,"-3/2*a*d^2*f*abs(f)*e^(-1)*log(abs(-x*e + sqrt(a*f^2 + x^2*e^2))) + 3/2*a*f^2*x^2*e + 3*a*d*f^2*x + x^4*e^3 + 2*d*x^3*e^2 + 3/2*d^2*x^2*e + d^3*x + 1/2*(4*a*d*f*abs(f)*e^(-1) + (2*(x*abs(f)*e^2/f + 2*d*abs(f)*e/f)*x + (2*a*f^4*abs(f)*e^4 + 3*d^2*f^2*abs(f)*e^4)*e^(-4)/f^3)*x)*sqrt(a*f^2 + x^2*e^2)","A",0
455,1,103,0,0.521430," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""giac"")","-a d f {\left| f \right|} e^{\left(-1\right)} \log\left({\left| -x e + \sqrt{a f^{2} + x^{2} e^{2}} \right|}\right) + a f^{2} x + \frac{2}{3} \, x^{3} e^{2} + d x^{2} e + d^{2} x + \frac{1}{3} \, {\left(2 \, a f {\left| f \right|} e^{\left(-1\right)} + {\left(\frac{2 \, x {\left| f \right|} e}{f} + \frac{3 \, d {\left| f \right|}}{f}\right)} x\right)} \sqrt{a f^{2} + x^{2} e^{2}}"," ",0,"-a*d*f*abs(f)*e^(-1)*log(abs(-x*e + sqrt(a*f^2 + x^2*e^2))) + a*f^2*x + 2/3*x^3*e^2 + d*x^2*e + d^2*x + 1/3*(2*a*f*abs(f)*e^(-1) + (2*x*abs(f)*e/f + 3*d*abs(f)/f)*x)*sqrt(a*f^2 + x^2*e^2)","A",0
456,1,65,0,0.345401," ","integrate(d+e*x+f*(a+e^2*x^2/f^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} e + d x - \frac{{\left(a f^{2} e^{\left(-1\right)} \log\left({\left| -x e + \sqrt{a f^{2} + x^{2} e^{2}} \right|}\right) - \sqrt{a f^{2} + x^{2} e^{2}} x\right)} {\left| f \right|}}{2 \, f}"," ",0,"1/2*x^2*e + d*x - 1/2*(a*f^2*e^(-1)*log(abs(-x*e + sqrt(a*f^2 + x^2*e^2))) - sqrt(a*f^2 + x^2*e^2)*x)*abs(f)/f","A",0
457,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2)),x, algorithm=""giac"")","\left[\mathit{undef}, +\infty, 1\right]"," ",0,"[undef, +Infinity, 1]","F",0
458,-1,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""giac"")","\int {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a} f + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a)*f + d)^(5/2), x)","F",0
461,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""giac"")","\int {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a} f + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a)*f + d)^(3/2), x)","F",0
462,0,0,0,0.000000," ","integrate((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a} f + d}\,{d x}"," ",0,"integrate(sqrt(e*x + sqrt(e^2*x^2/f^2 + a)*f + d), x)","F",0
463,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a} f + d}}\,{d x}"," ",0,"integrate(1/sqrt(e*x + sqrt(e^2*x^2/f^2 + a)*f + d), x)","F",0
464,-2,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [-49,85.3561567818,-64,-30]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [0,61.7937478349,0,0]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [56,62.4600259969,-13,46]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [-6,25.8388736797,81,18]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [63,31.8503101398,2,62]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [0,10.4309062702,0,0]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [65,39.1803401988,28,-44]Warning, choosing root of [1,0,%%%{-2,[1,2,0,0]%%%}+%%%{-2,[0,1,0,0]%%%}+%%%{-2,[0,0,2,1]%%%},0,%%%{1,[2,4,0,0]%%%}+%%%{-2,[1,3,0,0]%%%}+%%%{2,[1,2,2,1]%%%}+%%%{1,[0,2,0,0]%%%}+%%%{-2,[0,1,2,1]%%%}+%%%{1,[0,0,4,2]%%%}] at parameters values [91,88.2886286299,-21,88]Evaluation time: 0.64Done","F(-2)",0
465,-1,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,0,0,0,0.000000," ","integrate((x-(x^2-4)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{x - \sqrt{x^{2} - 4}}\,{d x}"," ",0,"integrate(sqrt(x - sqrt(x^2 - 4)), x)","F",0
467,0,0,0,0.000000," ","integrate((a*x+b*(c+a^2*x^2/b^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{a x + \sqrt{\frac{a^{2} x^{2}}{b^{2}} + c} b}\,{d x}"," ",0,"integrate(sqrt(a*x + sqrt(a^2*x^2/b^2 + c)*b), x)","F",0
468,0,0,0,0.000000," ","integrate((1+(-x^2+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{-x^{2} + 1} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(-x^2 + 1) + 1), x)","F",0
469,0,0,0,0.000000," ","integrate(((x^2+1)^(1/2)+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{x^{2} + 1} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 1) + 1), x)","F",0
470,0,0,0,0.000000," ","integrate((5+(x^2+25)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{x^{2} + 25} + 5}\,{d x}"," ",0,"integrate(sqrt(sqrt(x^2 + 25) + 5), x)","F",0
471,0,0,0,0.000000," ","integrate((a+b*(1/b^2*a^2+c*x^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{c x^{2} + \frac{a^{2}}{b^{2}}} b + a}\,{d x}"," ",0,"integrate(sqrt(sqrt(c*x^2 + a^2/b^2)*b + a), x)","F",0
472,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(e x + \sqrt{b x + \frac{e^{2} x^{2}}{f^{2}} + a} f + d\right)}^{n}\,{d x}"," ",0,"integrate((e*x + sqrt(b*x + e^2*x^2/f^2 + a)*f + d)^n, x)","F",0
473,1,373,0,0.369670," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""giac"")","b f^{2} x^{3} e + \frac{3}{2} \, b d f^{2} x^{2} + \frac{3}{2} \, a f^{2} x^{2} e + 3 \, a d f^{2} x + x^{4} e^{3} + 2 \, d x^{3} e^{2} + \frac{3}{2} \, d^{2} x^{2} e + d^{3} x + \frac{3}{32} \, {\left(b^{4} f^{7} {\left| f \right|} - 4 \, b^{3} d f^{5} {\left| f \right|} e - 4 \, a b^{2} f^{5} {\left| f \right|} e^{2} + 4 \, b^{2} d^{2} f^{3} {\left| f \right|} e^{2} + 16 \, a b d f^{3} {\left| f \right|} e^{3} - 16 \, a d^{2} f {\left| f \right|} e^{4}\right)} e^{\left(-5\right)} \log\left({\left| -b f^{2} - 2 \, {\left(x e - \sqrt{b f^{2} x + a f^{2} + x^{2} e^{2}}\right)} e \right|}\right) + \frac{1}{16} \, \sqrt{b f^{2} x + a f^{2} + x^{2} e^{2}} {\left(2 \, {\left(4 \, {\left(\frac{2 \, x {\left| f \right|} e^{2}}{f} + \frac{{\left(b f^{4} {\left| f \right|} e^{6} + 4 \, d f^{2} {\left| f \right|} e^{7}\right)} e^{\left(-6\right)}}{f^{3}}\right)} x - \frac{{\left(b^{2} f^{6} {\left| f \right|} e^{4} - 4 \, b d f^{4} {\left| f \right|} e^{5} - 8 \, a f^{4} {\left| f \right|} e^{6} - 12 \, d^{2} f^{2} {\left| f \right|} e^{6}\right)} e^{\left(-6\right)}}{f^{3}}\right)} x + \frac{{\left(3 \, b^{3} f^{8} {\left| f \right|} e^{2} - 12 \, b^{2} d f^{6} {\left| f \right|} e^{3} - 8 \, a b f^{6} {\left| f \right|} e^{4} + 12 \, b d^{2} f^{4} {\left| f \right|} e^{4} + 32 \, a d f^{4} {\left| f \right|} e^{5}\right)} e^{\left(-6\right)}}{f^{3}}\right)}"," ",0,"b*f^2*x^3*e + 3/2*b*d*f^2*x^2 + 3/2*a*f^2*x^2*e + 3*a*d*f^2*x + x^4*e^3 + 2*d*x^3*e^2 + 3/2*d^2*x^2*e + d^3*x + 3/32*(b^4*f^7*abs(f) - 4*b^3*d*f^5*abs(f)*e - 4*a*b^2*f^5*abs(f)*e^2 + 4*b^2*d^2*f^3*abs(f)*e^2 + 16*a*b*d*f^3*abs(f)*e^3 - 16*a*d^2*f*abs(f)*e^4)*e^(-5)*log(abs(-b*f^2 - 2*(x*e - sqrt(b*f^2*x + a*f^2 + x^2*e^2))*e)) + 1/16*sqrt(b*f^2*x + a*f^2 + x^2*e^2)*(2*(4*(2*x*abs(f)*e^2/f + (b*f^4*abs(f)*e^6 + 4*d*f^2*abs(f)*e^7)*e^(-6)/f^3)*x - (b^2*f^6*abs(f)*e^4 - 4*b*d*f^4*abs(f)*e^5 - 8*a*f^4*abs(f)*e^6 - 12*d^2*f^2*abs(f)*e^6)*e^(-6)/f^3)*x + (3*b^3*f^8*abs(f)*e^2 - 12*b^2*d*f^6*abs(f)*e^3 - 8*a*b*f^6*abs(f)*e^4 + 12*b*d^2*f^4*abs(f)*e^4 + 32*a*d*f^4*abs(f)*e^5)*e^(-6)/f^3)","A",0
474,1,224,0,0.295881," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""giac"")","\frac{1}{2} \, b f^{2} x^{2} + a f^{2} x + \frac{2}{3} \, x^{3} e^{2} + d x^{2} e + d^{2} x - \frac{1}{8} \, {\left(b^{3} f^{5} {\left| f \right|} - 2 \, b^{2} d f^{3} {\left| f \right|} e - 4 \, a b f^{3} {\left| f \right|} e^{2} + 8 \, a d f {\left| f \right|} e^{3}\right)} e^{\left(-4\right)} \log\left({\left| -b f^{2} - 2 \, {\left(x e - \sqrt{b f^{2} x + a f^{2} + x^{2} e^{2}}\right)} e \right|}\right) + \frac{1}{12} \, \sqrt{b f^{2} x + a f^{2} + x^{2} e^{2}} {\left(2 \, {\left(\frac{4 \, x {\left| f \right|} e}{f} + \frac{{\left(b f^{3} {\left| f \right|} e^{3} + 6 \, d f {\left| f \right|} e^{4}\right)} e^{\left(-4\right)}}{f^{2}}\right)} x - \frac{{\left(3 \, b^{2} f^{5} {\left| f \right|} e - 6 \, b d f^{3} {\left| f \right|} e^{2} - 8 \, a f^{3} {\left| f \right|} e^{3}\right)} e^{\left(-4\right)}}{f^{2}}\right)}"," ",0,"1/2*b*f^2*x^2 + a*f^2*x + 2/3*x^3*e^2 + d*x^2*e + d^2*x - 1/8*(b^3*f^5*abs(f) - 2*b^2*d*f^3*abs(f)*e - 4*a*b*f^3*abs(f)*e^2 + 8*a*d*f*abs(f)*e^3)*e^(-4)*log(abs(-b*f^2 - 2*(x*e - sqrt(b*f^2*x + a*f^2 + x^2*e^2))*e)) + 1/12*sqrt(b*f^2*x + a*f^2 + x^2*e^2)*(2*(4*x*abs(f)*e/f + (b*f^3*abs(f)*e^3 + 6*d*f*abs(f)*e^4)*e^(-4)/f^2)*x - (3*b^2*f^5*abs(f)*e - 6*b*d*f^3*abs(f)*e^2 - 8*a*f^3*abs(f)*e^3)*e^(-4)/f^2)","A",0
475,1,111,0,0.217174," ","integrate(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} e + d x + \frac{{\left({\left(b^{2} f^{4} - 4 \, a f^{2} e^{2}\right)} e^{\left(-3\right)} \log\left({\left| -b f^{2} - 2 \, {\left(x e - \sqrt{b f^{2} x + a f^{2} + x^{2} e^{2}}\right)} e \right|}\right) + 2 \, \sqrt{b f^{2} x + a f^{2} + x^{2} e^{2}} {\left(b f^{2} e^{\left(-2\right)} + 2 \, x\right)}\right)} {\left| f \right|}}{8 \, f}"," ",0,"1/2*x^2*e + d*x + 1/8*((b^2*f^4 - 4*a*f^2*e^2)*e^(-3)*log(abs(-b*f^2 - 2*(x*e - sqrt(b*f^2*x + a*f^2 + x^2*e^2))*e)) + 2*sqrt(b*f^2*x + a*f^2 + x^2*e^2)*(b*f^2*e^(-2) + 2*x))*abs(f)/f","A",0
476,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2)),x, algorithm=""giac"")","\left[\mathit{undef}, +\infty, 1\right]"," ",0,"[undef, +Infinity, 1]","F",0
477,-1,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""giac"")","\int {\left(e x + \sqrt{b x + \frac{e^{2} x^{2}}{f^{2}} + a} f + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((e*x + sqrt(b*x + e^2*x^2/f^2 + a)*f + d)^(5/2), x)","F",0
480,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""giac"")","\int {\left(e x + \sqrt{b x + \frac{e^{2} x^{2}}{f^{2}} + a} f + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*x + sqrt(b*x + e^2*x^2/f^2 + a)*f + d)^(3/2), x)","F",0
481,0,0,0,0.000000," ","integrate((d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + \sqrt{b x + \frac{e^{2} x^{2}}{f^{2}} + a} f + d}\,{d x}"," ",0,"integrate(sqrt(e*x + sqrt(b*x + e^2*x^2/f^2 + a)*f + d), x)","F",0
482,0,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e x + \sqrt{b x + \frac{e^{2} x^{2}}{f^{2}} + a} f + d}}\,{d x}"," ",0,"integrate(1/sqrt(e*x + sqrt(b*x + e^2*x^2/f^2 + a)*f + d), x)","F",0
483,-2,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{-2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{-2,[0,1,3,1,0]%%%}+%%%{2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [-49,-86,61.7937478349,-30,70]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{-2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{-2,[0,1,3,1,0]%%%}+%%%{2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [0,0,71.707969239,0,0]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{-2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{-2,[0,1,3,1,0]%%%}+%%%{2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [-9,-13,47.3295757947,24,49]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{-2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{-2,[0,1,3,1,0]%%%}+%%%{2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [81,18,54.7579903365,-33,-70]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{-2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{2,[0,1,3,1,0]%%%}+%%%{-2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [62,-37,8.05231268331,-23,65]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{-2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{2,[0,1,3,1,0]%%%}+%%%{-2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [0,0,64.3995612673,0,0]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{-2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{2,[0,1,3,1,0]%%%}+%%%{-2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [-22,93,94.1262030317,31,-21]Warning, choosing root of [1,0,%%%{-2,[1,0,2,0,0]%%%}+%%%{2,[0,1,2,1,0]%%%}+%%%{-2,[0,0,1,0,0]%%%}+%%%{-2,[0,0,0,2,1]%%%},0,%%%{1,[2,0,4,0,0]%%%}+%%%{-2,[1,1,4,1,0]%%%}+%%%{-2,[1,0,3,0,0]%%%}+%%%{2,[1,0,2,2,1]%%%}+%%%{1,[0,2,4,2,0]%%%}+%%%{2,[0,1,3,1,0]%%%}+%%%{-2,[0,1,2,3,1]%%%}+%%%{1,[0,0,2,0,0]%%%}+%%%{-2,[0,0,1,2,1]%%%}+%%%{1,[0,0,0,4,2]%%%}] at parameters values [-66,66,6.82230772497,-23,79]Evaluation time: 1.2Done","F(-2)",0
484,-1,0,0,0.000000," ","integrate(1/(d+e*x+f*(a+b*x+e^2*x^2/f^2)^(1/2))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,0,0,0,0.000000," ","integrate((x^2+a)^2*(x+(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)}^{2} {\left(x + \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)^2*(x + sqrt(x^2 + a))^n, x)","F",0
486,0,0,0,0.000000," ","integrate((x^2+a)*(x+(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)} {\left(x + \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)*(x + sqrt(x^2 + a))^n, x)","F",0
487,0,0,0,0.000000," ","integrate((x+(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x + \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + a))^n, x)","F",0
488,0,0,0,0.000000," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a),x, algorithm=""giac"")","\int \frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{x^{2} + a}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + a))^n/(x^2 + a), x)","F",0
489,0,0,0,0.000000," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{{\left(x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + a))^n/(x^2 + a)^2, x)","F",0
490,0,0,0,0.000000," ","integrate((x^2+a)^2*(x-(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)}^{2} {\left(x - \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)^2*(x - sqrt(x^2 + a))^n, x)","F",0
491,0,0,0,0.000000," ","integrate((x^2+a)*(x-(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)} {\left(x - \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)*(x - sqrt(x^2 + a))^n, x)","F",0
492,0,0,0,0.000000," ","integrate((x-(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x - \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + a))^n, x)","F",0
493,0,0,0,0.000000," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a),x, algorithm=""giac"")","\int \frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{x^{2} + a}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + a))^n/(x^2 + a), x)","F",0
494,0,0,0,0.000000," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{{\left(x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + a))^n/(x^2 + a)^2, x)","F",0
495,0,0,0,0.000000," ","integrate((x^2+a)^(5/2)*(x+(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)}^{\frac{5}{2}} {\left(x + \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)^(5/2)*(x + sqrt(x^2 + a))^n, x)","F",0
496,0,0,0,0.000000," ","integrate((x^2+a)^(3/2)*(x+(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)}^{\frac{3}{2}} {\left(x + \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)^(3/2)*(x + sqrt(x^2 + a))^n, x)","F",0
497,0,0,0,0.000000," ","integrate((x^2+a)^(1/2)*(x+(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int \sqrt{x^{2} + a} {\left(x + \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(x^2 + a)*(x + sqrt(x^2 + a))^n, x)","F",0
498,0,0,0,0.000000," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{\sqrt{x^{2} + a}}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + a))^n/sqrt(x^2 + a), x)","F",0
499,0,0,0,0.000000," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{{\left(x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + a))^n/(x^2 + a)^(3/2), x)","F",0
500,0,0,0,0.000000," ","integrate((x+(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(x + \sqrt{x^{2} + a}\right)}^{n}}{{\left(x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((x + sqrt(x^2 + a))^n/(x^2 + a)^(5/2), x)","F",0
501,0,0,0,0.000000," ","integrate((x^2+a)^(5/2)*(x-(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)}^{\frac{5}{2}} {\left(x - \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)^(5/2)*(x - sqrt(x^2 + a))^n, x)","F",0
502,0,0,0,0.000000," ","integrate((x^2+a)^(3/2)*(x-(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int {\left(x^{2} + a\right)}^{\frac{3}{2}} {\left(x - \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate((x^2 + a)^(3/2)*(x - sqrt(x^2 + a))^n, x)","F",0
503,0,0,0,0.000000," ","integrate((x^2+a)^(1/2)*(x-(x^2+a)^(1/2))^n,x, algorithm=""giac"")","\int \sqrt{x^{2} + a} {\left(x - \sqrt{x^{2} + a}\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(x^2 + a)*(x - sqrt(x^2 + a))^n, x)","F",0
504,0,0,0,0.000000," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{\sqrt{x^{2} + a}}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + a))^n/sqrt(x^2 + a), x)","F",0
505,0,0,0,0.000000," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{{\left(x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + a))^n/(x^2 + a)^(3/2), x)","F",0
506,0,0,0,0.000000," ","integrate((x-(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(x - \sqrt{x^{2} + a}\right)}^{n}}{{\left(x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((x - sqrt(x^2 + a))^n/(x^2 + a)^(5/2), x)","F",0
507,0,0,0,0.000000," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)^2*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}\right)}^{2} {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}\,{d x}"," ",0,"integrate((e^2*x^2/f^2 + a + 2*d*e*x/f^2)^2*(e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n, x)","F",0
508,0,0,0,0.000000," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}\right)} {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}\,{d x}"," ",0,"integrate((e^2*x^2/f^2 + a + 2*d*e*x/f^2)*(e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n, x)","F",0
509,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n, x)","F",0
510,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2),x, algorithm=""giac"")","\int \frac{{\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}}{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n/(e^2*x^2/f^2 + a + 2*d*e*x/f^2), x)","F",0
511,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}}{{\left(\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n/(e^2*x^2/f^2 + a + 2*d*e*x/f^2)^2, x)","F",0
512,0,0,0,0.000000," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(e x + f \sqrt{\frac{a f^{2} + {\left(e x + 2 \, d\right)} e x}{f^{2}}} + d\right)}^{n}\,{d x}"," ",0,"integrate((e*x + f*sqrt((a*f^2 + (e*x + 2*d)*e*x)/f^2) + d)^n, x)","F",0
513,0,0,0,0.000000," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2),x, algorithm=""giac"")","\int \frac{{\left(e x + f \sqrt{\frac{a f^{2} + {\left(e x + 2 \, d\right)} e x}{f^{2}}} + d\right)}^{n}}{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}}\,{d x}"," ",0,"integrate((e*x + f*sqrt((a*f^2 + (e*x + 2*d)*e*x)/f^2) + d)^n/(e^2*x^2/f^2 + a + 2*d*e*x/f^2), x)","F",0
514,0,0,0,0.000000," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)^(3/2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int {\left(\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}\right)}^{\frac{3}{2}} {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}\,{d x}"," ",0,"integrate((e^2*x^2/f^2 + a + 2*d*e*x/f^2)^(3/2)*(e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n, x)","F",0
515,0,0,0,0.000000," ","integrate((a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*(e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n, x)","F",0
516,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}}{\sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n/sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2), x)","F",0
517,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a+2*d*e*x/f^2+e^2*x^2/f^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}}{{\left(\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n/(e^2*x^2/f^2 + a + 2*d*e*x/f^2)^(3/2), x)","F",0
518,0,0,0,0.000000," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n/((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + f \sqrt{\frac{a f^{2} + {\left(e x + 2 \, d\right)} e x}{f^{2}}} + d\right)}^{n}}{\sqrt{\frac{a f^{2} + {\left(e x + 2 \, d\right)} e x}{f^{2}}}}\,{d x}"," ",0,"integrate((e*x + f*sqrt((a*f^2 + (e*x + 2*d)*e*x)/f^2) + d)^n/sqrt((a*f^2 + (e*x + 2*d)*e*x)/f^2), x)","F",0
519,0,0,0,0.000000," ","integrate((a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(1/2)*(d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n,x, algorithm=""giac"")","\int \sqrt{\frac{e^{2} g x^{2}}{f^{2}} + a g + \frac{2 \, d e g x}{f^{2}}} {\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(e^2*g*x^2/f^2 + a*g + 2*d*e*g*x/f^2)*(e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n, x)","F",0
520,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}}{\sqrt{\frac{e^{2} g x^{2}}{f^{2}} + a g + \frac{2 \, d e g x}{f^{2}}}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n/sqrt(e^2*g*x^2/f^2 + a*g + 2*d*e*g*x/f^2), x)","F",0
521,0,0,0,0.000000," ","integrate((d+e*x+f*(a+2*d*e*x/f^2+e^2*x^2/f^2)^(1/2))^n/(a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + \sqrt{\frac{e^{2} x^{2}}{f^{2}} + a + \frac{2 \, d e x}{f^{2}}} f + d\right)}^{n}}{{\left(\frac{e^{2} g x^{2}}{f^{2}} + a g + \frac{2 \, d e g x}{f^{2}}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + sqrt(e^2*x^2/f^2 + a + 2*d*e*x/f^2)*f + d)^n/(e^2*g*x^2/f^2 + a*g + 2*d*e*g*x/f^2)^(3/2), x)","F",0
522,0,0,0,0.000000," ","integrate((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n/((a*f^2*g+e*g*x*(e*x+2*d))/f^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + f \sqrt{\frac{a f^{2} + {\left(e x + 2 \, d\right)} e x}{f^{2}}} + d\right)}^{n}}{\sqrt{\frac{a f^{2} g + {\left(e x + 2 \, d\right)} e g x}{f^{2}}}}\,{d x}"," ",0,"integrate((e*x + f*sqrt((a*f^2 + (e*x + 2*d)*e*x)/f^2) + d)^n/sqrt((a*f^2*g + (e*x + 2*d)*e*g*x)/f^2), x)","F",0
523,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-2,0,0,0.000000," ","integrate((-2*f*x^2+e)/(4*f^2*x^4+4*d*f*x^2+4*e*f*x^2+e^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueDone","F(-2)",0
525,-2,0,0,0.000000," ","integrate((-2*f*x^2+e)/(4*f^2*x^4-4*d*f*x^2+4*e*f*x^2+e^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueDone","F(-2)",0
526,0,0,0,0.000000," ","integrate((-4*f*x^3+e)/(4*f^2*x^6+4*e*f*x^3+4*d*f*x^2+e^2),x, algorithm=""giac"")","\int -\frac{4 \, f x^{3} - e}{4 \, f^{2} x^{6} + 4 \, e f x^{3} + 4 \, d f x^{2} + e^{2}}\,{d x}"," ",0,"integrate(-(4*f*x^3 - e)/(4*f^2*x^6 + 4*e*f*x^3 + 4*d*f*x^2 + e^2), x)","F",0
527,0,0,0,0.000000," ","integrate((-4*f*x^3+e)/(4*f^2*x^6+4*e*f*x^3-4*d*f*x^2+e^2),x, algorithm=""giac"")","\int -\frac{4 \, f x^{3} - e}{4 \, f^{2} x^{6} + 4 \, e f x^{3} - 4 \, d f x^{2} + e^{2}}\,{d x}"," ",0,"integrate(-(4*f*x^3 - e)/(4*f^2*x^6 + 4*e*f*x^3 - 4*d*f*x^2 + e^2), x)","F",0
528,0,0,0,0.000000," ","integrate((e-2*f*(-1+n)*x^n)/(e^2+4*d*f*x^2+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""giac"")","\int -\frac{2 \, f {\left(n - 1\right)} x^{n} - e}{4 \, d f x^{2} + 4 \, f^{2} x^{2 \, n} + 4 \, e f x^{n} + e^{2}}\,{d x}"," ",0,"integrate(-(2*f*(n - 1)*x^n - e)/(4*d*f*x^2 + 4*f^2*x^(2*n) + 4*e*f*x^n + e^2), x)","F",0
529,0,0,0,0.000000," ","integrate((e-2*f*(-1+n)*x^n)/(e^2-4*d*f*x^2+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""giac"")","\int \frac{2 \, f {\left(n - 1\right)} x^{n} - e}{4 \, d f x^{2} - 4 \, f^{2} x^{2 \, n} - 4 \, e f x^{n} - e^{2}}\,{d x}"," ",0,"integrate((2*f*(n - 1)*x^n - e)/(4*d*f*x^2 - 4*f^2*x^(2*n) - 4*e*f*x^n - e^2), x)","F",0
530,1,38,0,10.575538," ","integrate(x/(4*d*f*x^4+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{{\left(2 \, d f x^{2} + 2 \, f^{2} x^{2} + f e\right)} e^{\left(-1\right)}}{\sqrt{d f}}\right) e^{\left(-1\right)}}{4 \, \sqrt{d f}}"," ",0,"1/4*arctan((2*d*f*x^2 + 2*f^2*x^2 + f*e)*e^(-1)/sqrt(d*f))*e^(-1)/sqrt(d*f)","A",0
531,1,41,0,10.052561," ","integrate(x/(-4*d*f*x^4+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{2 \, d f x^{2} - 2 \, f^{2} x^{2} - f e}{\sqrt{-d f e^{2}}}\right)}{4 \, \sqrt{-d f e^{2}}}"," ",0,"-1/4*arctan((2*d*f*x^2 - 2*f^2*x^2 - f*e)/sqrt(-d*f*e^2))/sqrt(-d*f*e^2)","A",0
532,0,0,0,0.000000," ","integrate(x^2*(2*f*x^2+3*e)/(4*d*f*x^6+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""giac"")","\int \frac{{\left(2 \, f x^{2} + 3 \, e\right)} x^{2}}{4 \, d f x^{6} + 4 \, f^{2} x^{4} + 4 \, e f x^{2} + e^{2}}\,{d x}"," ",0,"integrate((2*f*x^2 + 3*e)*x^2/(4*d*f*x^6 + 4*f^2*x^4 + 4*e*f*x^2 + e^2), x)","F",0
533,0,0,0,0.000000," ","integrate(x^2*(2*f*x^2+3*e)/(-4*d*f*x^6+4*f^2*x^4+4*e*f*x^2+e^2),x, algorithm=""giac"")","\int -\frac{{\left(2 \, f x^{2} + 3 \, e\right)} x^{2}}{4 \, d f x^{6} - 4 \, f^{2} x^{4} - 4 \, e f x^{2} - e^{2}}\,{d x}"," ",0,"integrate(-(2*f*x^2 + 3*e)*x^2/(4*d*f*x^6 - 4*f^2*x^4 - 4*e*f*x^2 - e^2), x)","F",0
534,0,0,0,0.000000," ","integrate(x^m*(e*(1+m)+2*f*(-1+m)*x^2)/(e^2+4*e*f*x^2+4*f^2*x^4+4*d*f*x^(2+2*m)),x, algorithm=""giac"")","\int \frac{{\left(2 \, f {\left(m - 1\right)} x^{2} + e {\left(m + 1\right)}\right)} x^{m}}{4 \, f^{2} x^{4} + 4 \, e f x^{2} + 4 \, d f x^{2 \, m + 2} + e^{2}}\,{d x}"," ",0,"integrate((2*f*(m - 1)*x^2 + e*(m + 1))*x^m/(4*f^2*x^4 + 4*e*f*x^2 + 4*d*f*x^(2*m + 2) + e^2), x)","F",0
535,0,0,0,0.000000," ","integrate(x^m*(e*(1+m)+2*f*(-1+m)*x^2)/(e^2+4*e*f*x^2+4*f^2*x^4-4*d*f*x^(2+2*m)),x, algorithm=""giac"")","\int \frac{{\left(2 \, f {\left(m - 1\right)} x^{2} + e {\left(m + 1\right)}\right)} x^{m}}{4 \, f^{2} x^{4} + 4 \, e f x^{2} - 4 \, d f x^{2 \, m + 2} + e^{2}}\,{d x}"," ",0,"integrate((2*f*(m - 1)*x^2 + e*(m + 1))*x^m/(4*f^2*x^4 + 4*e*f*x^2 - 4*d*f*x^(2*m + 2) + e^2), x)","F",0
536,0,0,0,0.000000," ","integrate(x*(-2*f*x^3+2*e)/(4*f^2*x^6+4*d*f*x^4+4*e*f*x^3+e^2),x, algorithm=""giac"")","\int -\frac{2 \, {\left(f x^{3} - e\right)} x}{4 \, f^{2} x^{6} + 4 \, d f x^{4} + 4 \, e f x^{3} + e^{2}}\,{d x}"," ",0,"integrate(-2*(f*x^3 - e)*x/(4*f^2*x^6 + 4*d*f*x^4 + 4*e*f*x^3 + e^2), x)","F",0
537,0,0,0,0.000000," ","integrate(x*(-2*f*x^3+2*e)/(4*f^2*x^6-4*d*f*x^4+4*e*f*x^3+e^2),x, algorithm=""giac"")","\int -\frac{2 \, {\left(f x^{3} - e\right)} x}{4 \, f^{2} x^{6} - 4 \, d f x^{4} + 4 \, e f x^{3} + e^{2}}\,{d x}"," ",0,"integrate(-2*(f*x^3 - e)*x/(4*f^2*x^6 - 4*d*f*x^4 + 4*e*f*x^3 + e^2), x)","F",0
538,1,38,0,10.127719," ","integrate(x^2/(4*d*f*x^6+4*f^2*x^6+4*e*f*x^3+e^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{{\left(2 \, d f x^{3} + 2 \, f^{2} x^{3} + f e\right)} e^{\left(-1\right)}}{\sqrt{d f}}\right) e^{\left(-1\right)}}{6 \, \sqrt{d f}}"," ",0,"1/6*arctan((2*d*f*x^3 + 2*f^2*x^3 + f*e)*e^(-1)/sqrt(d*f))*e^(-1)/sqrt(d*f)","A",0
539,1,41,0,9.217034," ","integrate(x^2/(-4*d*f*x^6+4*f^2*x^6+4*e*f*x^3+e^2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{2 \, d f x^{3} - 2 \, f^{2} x^{3} - f e}{\sqrt{-d f e^{2}}}\right)}{6 \, \sqrt{-d f e^{2}}}"," ",0,"-1/6*arctan((2*d*f*x^3 - 2*f^2*x^3 - f*e)/sqrt(-d*f*e^2))/sqrt(-d*f*e^2)","A",0
540,0,0,0,0.000000," ","integrate(x^m*(e*(1+m)+2*f*(-2+m)*x^3)/(e^2+4*e*f*x^3+4*f^2*x^6+4*d*f*x^(2+2*m)),x, algorithm=""giac"")","\int \frac{{\left(2 \, f {\left(m - 2\right)} x^{3} + e {\left(m + 1\right)}\right)} x^{m}}{4 \, f^{2} x^{6} + 4 \, e f x^{3} + 4 \, d f x^{2 \, m + 2} + e^{2}}\,{d x}"," ",0,"integrate((2*f*(m - 2)*x^3 + e*(m + 1))*x^m/(4*f^2*x^6 + 4*e*f*x^3 + 4*d*f*x^(2*m + 2) + e^2), x)","F",0
541,0,0,0,0.000000," ","integrate(x^m*(e*(1+m)+2*f*(-2+m)*x^3)/(e^2+4*e*f*x^3+4*f^2*x^6-4*d*f*x^(2+2*m)),x, algorithm=""giac"")","\int \frac{{\left(2 \, f {\left(m - 2\right)} x^{3} + e {\left(m + 1\right)}\right)} x^{m}}{4 \, f^{2} x^{6} + 4 \, e f x^{3} - 4 \, d f x^{2 \, m + 2} + e^{2}}\,{d x}"," ",0,"integrate((2*f*(m - 2)*x^3 + e*(m + 1))*x^m/(4*f^2*x^6 + 4*e*f*x^3 - 4*d*f*x^(2*m + 2) + e^2), x)","F",0
542,0,0,0,0.000000," ","integrate(x^m*(e*(1+m)+2*f*(1+m-n)*x^n)/(e^2+4*d*f*x^(2+2*m)+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(2 \, f {\left(m - n + 1\right)} x^{n} + e {\left(m + 1\right)}\right)} x^{m}}{4 \, d f x^{2 \, m + 2} + 4 \, f^{2} x^{2 \, n} + 4 \, e f x^{n} + e^{2}}\,{d x}"," ",0,"integrate((2*f*(m - n + 1)*x^n + e*(m + 1))*x^m/(4*d*f*x^(2*m + 2) + 4*f^2*x^(2*n) + 4*e*f*x^n + e^2), x)","F",0
543,0,0,0,0.000000," ","integrate(x^m*(e*(1+m)+2*f*(1+m-n)*x^n)/(e^2-4*d*f*x^(2+2*m)+4*e*f*x^n+4*f^2*x^(2*n)),x, algorithm=""giac"")","\int -\frac{{\left(2 \, f {\left(m - n + 1\right)} x^{n} + e {\left(m + 1\right)}\right)} x^{m}}{4 \, d f x^{2 \, m + 2} - 4 \, f^{2} x^{2 \, n} - 4 \, e f x^{n} - e^{2}}\,{d x}"," ",0,"integrate(-(2*f*(m - n + 1)*x^n + e*(m + 1))*x^m/(4*d*f*x^(2*m + 2) - 4*f^2*x^(2*n) - 4*e*f*x^n - e^2), x)","F",0
544,1,155,0,0.349697," ","integrate(x^5/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","\frac{{\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left({\left| \sqrt{b x^{2} + a} c + d \right|}\right)}{b^{3} c^{5}} + \frac{3 \, {\left(b x^{2} + a\right)}^{2} b^{9} c^{3} - 12 \, {\left(b x^{2} + a\right)} a b^{9} c^{3} - 4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{9} c^{2} d + 24 \, \sqrt{b x^{2} + a} a b^{9} c^{2} d + 6 \, {\left(b x^{2} + a\right)} b^{9} c d^{2} - 12 \, \sqrt{b x^{2} + a} b^{9} d^{3}}{12 \, b^{12} c^{4}}"," ",0,"(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(abs(sqrt(b*x^2 + a)*c + d))/(b^3*c^5) + 1/12*(3*(b*x^2 + a)^2*b^9*c^3 - 12*(b*x^2 + a)*a*b^9*c^3 - 4*(b*x^2 + a)^(3/2)*b^9*c^2*d + 24*sqrt(b*x^2 + a)*a*b^9*c^2*d + 6*(b*x^2 + a)*b^9*c*d^2 - 12*sqrt(b*x^2 + a)*b^9*d^3)/(b^12*c^4)","A",0
545,1,72,0,0.404527," ","integrate(x^3/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a c^{2} - d^{2}\right)} \log\left({\left| \sqrt{b x^{2} + a} c + d \right|}\right)}{b c^{3}} - \frac{{\left(b x^{2} + a\right)} b c - 2 \, \sqrt{b x^{2} + a} b d}{b^{2} c^{2}}}{2 \, b}"," ",0,"-1/2*(2*(a*c^2 - d^2)*log(abs(sqrt(b*x^2 + a)*c + d))/(b*c^3) - ((b*x^2 + a)*b*c - 2*sqrt(b*x^2 + a)*b*d)/(b^2*c^2))/b","A",0
546,1,22,0,0.323146," ","integrate(x/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","\frac{\log\left({\left| \sqrt{b x^{2} + a} c + d \right|}\right)}{b c}"," ",0,"log(abs(sqrt(b*x^2 + a)*c + d))/(b*c)","A",0
547,1,94,0,0.335542," ","integrate(1/x/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","-\frac{c^{2} \log\left({\left| \sqrt{b x^{2} + a} c + d \right|}\right)}{a c^{3} - c d^{2}} + \frac{c \log\left(b x^{2}\right)}{2 \, {\left(a c^{2} - d^{2}\right)}} - \frac{d \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{{\left(a c^{2} - d^{2}\right)} \sqrt{-a}}"," ",0,"-c^2*log(abs(sqrt(b*x^2 + a)*c + d))/(a*c^3 - c*d^2) + 1/2*c*log(b*x^2)/(a*c^2 - d^2) - d*arctan(sqrt(b*x^2 + a)/sqrt(-a))/((a*c^2 - d^2)*sqrt(-a))","A",0
548,1,210,0,0.372376," ","integrate(1/x^3/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","\frac{b c^{4} \log\left({\left| \sqrt{b x^{2} + a} c + d \right|}\right)}{a^{2} c^{5} - 2 \, a c^{3} d^{2} + c d^{4}} - \frac{b c^{3} \log\left(-b x^{2}\right)}{2 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)}} + \frac{{\left(3 \, a b c^{2} d - b d^{3}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, {\left(a^{3} c^{4} - 2 \, a^{2} c^{2} d^{2} + a d^{4}\right)} \sqrt{-a}} - \frac{a^{2} b c^{3} - a b c d^{2} - {\left(a b c^{2} d - b d^{3}\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a c^{2} - d^{2}\right)}^{2} a b x^{2}}"," ",0,"b*c^4*log(abs(sqrt(b*x^2 + a)*c + d))/(a^2*c^5 - 2*a*c^3*d^2 + c*d^4) - 1/2*b*c^3*log(-b*x^2)/(a^2*c^4 - 2*a*c^2*d^2 + d^4) + 1/2*(3*a*b*c^2*d - b*d^3)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/((a^3*c^4 - 2*a^2*c^2*d^2 + a*d^4)*sqrt(-a)) - 1/2*(a^2*b*c^3 - a*b*c*d^2 - (a*b*c^2*d - b*d^3)*sqrt(b*x^2 + a))/((a*c^2 - d^2)^2*a*b*x^2)","A",0
549,-2,0,0,0.000000," ","integrate(x^2/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
550,1,107,0,0.364120," ","integrate(1/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b c x}{\sqrt{a b c^{2} - b d^{2}}}\right)}{\sqrt{a b c^{2} - b d^{2}}} + \frac{\arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} c^{2} + a c^{2} - 2 \, d^{2}}{2 \, \sqrt{a c^{2} - d^{2}} d}\right)}{\sqrt{a c^{2} - d^{2}} \sqrt{b}}"," ",0,"arctan(b*c*x/sqrt(a*b*c^2 - b*d^2))/sqrt(a*b*c^2 - b*d^2) + arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*c^2 + a*c^2 - 2*d^2)/(sqrt(a*c^2 - d^2)*d))/(sqrt(a*c^2 - d^2)*sqrt(b))","A",0
551,1,211,0,0.460627," ","integrate(1/x^2/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x, algorithm=""giac"")","-b^{\frac{3}{2}} d {\left(\frac{c^{2} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} c^{2} + a c^{2} - 2 \, d^{2}}{2 \, \sqrt{a c^{2} - d^{2}} d}\right)}{{\left(a b c^{2} - b d^{2}\right)} \sqrt{a c^{2} - d^{2}} d} + \frac{2}{{\left(a b c^{2} - b d^{2}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}}\right)} - \frac{b c^{2} \arctan\left(\frac{b c x}{\sqrt{a b c^{2} - b d^{2}}}\right)}{\sqrt{a b c^{2} - b d^{2}} {\left(a c^{2} - d^{2}\right)}} - \frac{c}{{\left(a c^{2} - d^{2}\right)} x}"," ",0,"-b^(3/2)*d*(c^2*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*c^2 + a*c^2 - 2*d^2)/(sqrt(a*c^2 - d^2)*d))/((a*b*c^2 - b*d^2)*sqrt(a*c^2 - d^2)*d) + 2/((a*b*c^2 - b*d^2)*((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a))) - b*c^2*arctan(b*c*x/sqrt(a*b*c^2 - b*d^2))/(sqrt(a*b*c^2 - b*d^2)*(a*c^2 - d^2)) - c/((a*c^2 - d^2)*x)","A",0
552,1,156,0,0.391026," ","integrate(x^8/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\frac{2 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)} \log\left({\left| \sqrt{b x^{3} + a} c + d \right|}\right)}{3 \, b^{3} c^{5}} + \frac{3 \, {\left(b x^{3} + a\right)}^{2} b^{9} c^{3} - 12 \, {\left(b x^{3} + a\right)} a b^{9} c^{3} - 4 \, {\left(b x^{3} + a\right)}^{\frac{3}{2}} b^{9} c^{2} d + 24 \, \sqrt{b x^{3} + a} a b^{9} c^{2} d + 6 \, {\left(b x^{3} + a\right)} b^{9} c d^{2} - 12 \, \sqrt{b x^{3} + a} b^{9} d^{3}}{18 \, b^{12} c^{4}}"," ",0,"2/3*(a^2*c^4 - 2*a*c^2*d^2 + d^4)*log(abs(sqrt(b*x^3 + a)*c + d))/(b^3*c^5) + 1/18*(3*(b*x^3 + a)^2*b^9*c^3 - 12*(b*x^3 + a)*a*b^9*c^3 - 4*(b*x^3 + a)^(3/2)*b^9*c^2*d + 24*sqrt(b*x^3 + a)*a*b^9*c^2*d + 6*(b*x^3 + a)*b^9*c*d^2 - 12*sqrt(b*x^3 + a)*b^9*d^3)/(b^12*c^4)","A",0
553,1,72,0,0.330924," ","integrate(x^5/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a c^{2} - d^{2}\right)} \log\left({\left| \sqrt{b x^{3} + a} c + d \right|}\right)}{b c^{3}} - \frac{{\left(b x^{3} + a\right)} b c - 2 \, \sqrt{b x^{3} + a} b d}{b^{2} c^{2}}}{3 \, b}"," ",0,"-1/3*(2*(a*c^2 - d^2)*log(abs(sqrt(b*x^3 + a)*c + d))/(b*c^3) - ((b*x^3 + a)*b*c - 2*sqrt(b*x^3 + a)*b*d)/(b^2*c^2))/b","A",0
554,1,23,0,0.320389," ","integrate(x^2/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\frac{2 \, \log\left({\left| \sqrt{b x^{3} + a} c + d \right|}\right)}{3 \, b c}"," ",0,"2/3*log(abs(sqrt(b*x^3 + a)*c + d))/(b*c)","A",0
555,1,94,0,0.353561," ","integrate(1/x/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, c^{2} \log\left({\left| \sqrt{b x^{3} + a} c + d \right|}\right)}{3 \, {\left(a c^{3} - c d^{2}\right)}} + \frac{c \log\left(b x^{3}\right)}{3 \, {\left(a c^{2} - d^{2}\right)}} - \frac{2 \, d \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{3 \, {\left(a c^{2} - d^{2}\right)} \sqrt{-a}}"," ",0,"-2/3*c^2*log(abs(sqrt(b*x^3 + a)*c + d))/(a*c^3 - c*d^2) + 1/3*c*log(b*x^3)/(a*c^2 - d^2) - 2/3*d*arctan(sqrt(b*x^3 + a)/sqrt(-a))/((a*c^2 - d^2)*sqrt(-a))","A",0
556,1,211,0,0.344526," ","integrate(1/x^4/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\frac{2 \, b c^{4} \log\left({\left| \sqrt{b x^{3} + a} c + d \right|}\right)}{3 \, {\left(a^{2} c^{5} - 2 \, a c^{3} d^{2} + c d^{4}\right)}} - \frac{b c^{3} \log\left(-b x^{3}\right)}{3 \, {\left(a^{2} c^{4} - 2 \, a c^{2} d^{2} + d^{4}\right)}} + \frac{{\left(3 \, a b c^{2} d - b d^{3}\right)} \arctan\left(\frac{\sqrt{b x^{3} + a}}{\sqrt{-a}}\right)}{3 \, {\left(a^{3} c^{4} - 2 \, a^{2} c^{2} d^{2} + a d^{4}\right)} \sqrt{-a}} - \frac{a^{2} b c^{3} - a b c d^{2} - {\left(a b c^{2} d - b d^{3}\right)} \sqrt{b x^{3} + a}}{3 \, {\left(a c^{2} - d^{2}\right)}^{2} a b x^{3}}"," ",0,"2/3*b*c^4*log(abs(sqrt(b*x^3 + a)*c + d))/(a^2*c^5 - 2*a*c^3*d^2 + c*d^4) - 1/3*b*c^3*log(-b*x^3)/(a^2*c^4 - 2*a*c^2*d^2 + d^4) + 1/3*(3*a*b*c^2*d - b*d^3)*arctan(sqrt(b*x^3 + a)/sqrt(-a))/((a^3*c^4 - 2*a^2*c^2*d^2 + a*d^4)*sqrt(-a)) - 1/3*(a^2*b*c^3 - a*b*c*d^2 - (a*b*c^2*d - b*d^3)*sqrt(b*x^3 + a))/((a*c^2 - d^2)^2*a*b*x^3)","A",0
557,0,0,0,0.000000," ","integrate(x^3/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\int \frac{x^{3}}{b c x^{3} + a c + \sqrt{b x^{3} + a} d}\,{d x}"," ",0,"integrate(x^3/(b*c*x^3 + a*c + sqrt(b*x^3 + a)*d), x)","F",0
558,0,0,0,0.000000," ","integrate(x/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\int \frac{x}{b c x^{3} + a c + \sqrt{b x^{3} + a} d}\,{d x}"," ",0,"integrate(x/(b*c*x^3 + a*c + sqrt(b*x^3 + a)*d), x)","F",0
559,0,0,0,0.000000," ","integrate(1/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\int \frac{1}{b c x^{3} + a c + \sqrt{b x^{3} + a} d}\,{d x}"," ",0,"integrate(1/(b*c*x^3 + a*c + sqrt(b*x^3 + a)*d), x)","F",0
560,0,0,0,0.000000," ","integrate(1/x^2/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\int \frac{1}{{\left(b c x^{3} + a c + \sqrt{b x^{3} + a} d\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*c*x^3 + a*c + sqrt(b*x^3 + a)*d)*x^2), x)","F",0
561,0,0,0,0.000000," ","integrate(1/x^3/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x, algorithm=""giac"")","\int \frac{1}{{\left(b c x^{3} + a c + \sqrt{b x^{3} + a} d\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((b*c*x^3 + a*c + sqrt(b*x^3 + a)*d)*x^3), x)","F",0
562,0,0,0,0.000000," ","integrate(1/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x, algorithm=""giac"")","\int \frac{1}{b c x^{n} + a c + \sqrt{b x^{n} + a} d}\,{d x}"," ",0,"integrate(1/(b*c*x^n + a*c + sqrt(b*x^n + a)*d), x)","F",0
563,0,0,0,0.000000," ","integrate(x^m/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x, algorithm=""giac"")","\int \frac{x^{m}}{b c x^{n} + a c + \sqrt{b x^{n} + a} d}\,{d x}"," ",0,"integrate(x^m/(b*c*x^n + a*c + sqrt(b*x^n + a)*d), x)","F",0
564,1,26,0,0.370190," ","integrate(x^(-1+n)/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x, algorithm=""giac"")","\frac{2 \, \log\left({\left| \sqrt{b x^{n} + a} c + d \right|}\right)}{b c n}"," ",0,"2*log(abs(sqrt(b*x^n + a)*c + d))/(b*c*n)","A",0
565,1,6,0,0.317833," ","integrate(1/(4*x^(3/2)+x^(1/2)),x, algorithm=""giac"")","\arctan\left(2 \, \sqrt{x}\right)"," ",0,"arctan(2*sqrt(x))","A",0
566,1,22,0,0.345090," ","integrate(1/(-x^(5/2)+x^(1/2)),x, algorithm=""giac"")","\arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left({\left| \sqrt{x} - 1 \right|}\right)"," ",0,"arctan(sqrt(x)) + 1/2*log(sqrt(x) + 1) - 1/2*log(abs(sqrt(x) - 1))","B",0
567,1,20,0,0.339885," ","integrate(1/(-x^(1/4)+x^(1/2)),x, algorithm=""giac"")","2 \, \sqrt{x} + 4 \, x^{\frac{1}{4}} + 4 \, \log\left({\left| x^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2*sqrt(x) + 4*x^(1/4) + 4*log(abs(x^(1/4) - 1))","A",0
568,1,24,0,0.326495," ","integrate(1/(x^(1/3)+x^(1/2)),x, algorithm=""giac"")","2 \, \sqrt{x} - 3 \, x^{\frac{1}{3}} + 6 \, x^{\frac{1}{6}} - 6 \, \log\left(x^{\frac{1}{6}} + 1\right)"," ",0,"2*sqrt(x) - 3*x^(1/3) + 6*x^(1/6) - 6*log(x^(1/6) + 1)","A",0
569,1,19,0,0.343810," ","integrate(1/(x^(1/4)+x^(1/2)),x, algorithm=""giac"")","2 \, \sqrt{x} - 4 \, x^{\frac{1}{4}} + 4 \, \log\left(x^{\frac{1}{4}} + 1\right)"," ",0,"2*sqrt(x) - 4*x^(1/4) + 4*log(x^(1/4) + 1)","A",0
570,1,15,0,0.427205," ","integrate(1/(-x^(1/3)+x^(2/3)),x, algorithm=""giac"")","3 \, x^{\frac{1}{3}} + 3 \, \log\left({\left| x^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"3*x^(1/3) + 3*log(abs(x^(1/3) - 1))","A",0
571,1,45,0,0.334554," ","integrate(1/(1/x^(1/4)+x^(1/2)),x, algorithm=""giac"")","-\frac{4}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{\frac{1}{4}} - 1\right)}\right) + 2 \, \sqrt{x} - \frac{2}{3} \, \log\left(\sqrt{x} - x^{\frac{1}{4}} + 1\right) + \frac{4}{3} \, \log\left(x^{\frac{1}{4}} + 1\right)"," ",0,"-4/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^(1/4) - 1)) + 2*sqrt(x) - 2/3*log(sqrt(x) - x^(1/4) + 1) + 4/3*log(x^(1/4) + 1)","A",0
572,1,49,0,0.320867," ","integrate(1/(x^(1/4)+x^(1/3)),x, algorithm=""giac"")","\frac{3}{2} \, x^{\frac{2}{3}} - \frac{12}{7} \, x^{\frac{7}{12}} + 2 \, \sqrt{x} - \frac{12}{5} \, x^{\frac{5}{12}} + 3 \, x^{\frac{1}{3}} - 4 \, x^{\frac{1}{4}} + 6 \, x^{\frac{1}{6}} - 12 \, x^{\frac{1}{12}} + 12 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"3/2*x^(2/3) - 12/7*x^(7/12) + 2*sqrt(x) - 12/5*x^(5/12) + 3*x^(1/3) - 4*x^(1/4) + 6*x^(1/6) - 12*x^(1/12) + 12*log(x^(1/12) + 1)","A",0
573,1,82,0,0.355964," ","integrate(1/(1/x^(1/3)+1/x^(1/4)),x, algorithm=""giac"")","\frac{4}{5} \, x^{\frac{5}{4}} - \frac{6}{7} \, x^{\frac{7}{6}} + \frac{12}{13} \, x^{\frac{13}{12}} - x + \frac{12}{11} \, x^{\frac{11}{12}} - \frac{6}{5} \, x^{\frac{5}{6}} + \frac{4}{3} \, x^{\frac{3}{4}} - \frac{3}{2} \, x^{\frac{2}{3}} + \frac{12}{7} \, x^{\frac{7}{12}} - 2 \, \sqrt{x} + \frac{12}{5} \, x^{\frac{5}{12}} - 3 \, x^{\frac{1}{3}} + 4 \, x^{\frac{1}{4}} - 6 \, x^{\frac{1}{6}} + 12 \, x^{\frac{1}{12}} - 12 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"4/5*x^(5/4) - 6/7*x^(7/6) + 12/13*x^(13/12) - x + 12/11*x^(11/12) - 6/5*x^(5/6) + 4/3*x^(3/4) - 3/2*x^(2/3) + 12/7*x^(7/12) - 2*sqrt(x) + 12/5*x^(5/12) - 3*x^(1/3) + 4*x^(1/4) - 6*x^(1/6) + 12*x^(1/12) - 12*log(x^(1/12) + 1)","A",0
574,1,139,0,1.117644," ","integrate(1/(-1/x^(1/3)+x^(1/2)),x, algorithm=""giac"")","\frac{3}{5} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(-\frac{\sqrt{5} - 4 \, x^{\frac{1}{6}} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{3}{5} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{\sqrt{5} + 4 \, x^{\frac{1}{6}} + 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) + \frac{3}{10} \, \sqrt{5} \log\left(\frac{1}{2} \, x^{\frac{1}{6}} {\left(\sqrt{5} + 1\right)} + x^{\frac{1}{3}} + 1\right) - \frac{3}{10} \, \sqrt{5} \log\left(-\frac{1}{2} \, x^{\frac{1}{6}} {\left(\sqrt{5} - 1\right)} + x^{\frac{1}{3}} + 1\right) + 2 \, \sqrt{x} - \frac{3}{10} \, \log\left(x^{\frac{2}{3}} + \sqrt{x} + x^{\frac{1}{3}} + x^{\frac{1}{6}} + 1\right) + \frac{6}{5} \, \log\left({\left| x^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"3/5*sqrt(-2*sqrt(5) + 10)*arctan(-(sqrt(5) - 4*x^(1/6) - 1)/sqrt(2*sqrt(5) + 10)) - 3/5*sqrt(2*sqrt(5) + 10)*arctan((sqrt(5) + 4*x^(1/6) + 1)/sqrt(-2*sqrt(5) + 10)) + 3/10*sqrt(5)*log(1/2*x^(1/6)*(sqrt(5) + 1) + x^(1/3) + 1) - 3/10*sqrt(5)*log(-1/2*x^(1/6)*(sqrt(5) - 1) + x^(1/3) + 1) + 2*sqrt(x) - 3/10*log(x^(2/3) + sqrt(x) + x^(1/3) + x^(1/6) + 1) + 6/5*log(abs(x^(1/6) - 1))","A",0
575,1,6,0,0.286024," ","integrate(x^(1/2)/(x^2+x),x, algorithm=""giac"")","2 \, \arctan\left(\sqrt{x}\right)"," ",0,"2*arctan(sqrt(x))","A",0
576,1,15,0,0.386306," ","integrate(x/(x+4*x^(1/2)),x, algorithm=""giac"")","x - 8 \, \sqrt{x} + 32 \, \log\left(\sqrt{x} + 4\right)"," ",0,"x - 8*sqrt(x) + 32*log(sqrt(x) + 4)","A",0
577,1,83,0,0.437774," ","integrate(x^(1/2)/(x^(1/3)+x),x, algorithm=""giac"")","-\frac{3}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, x^{\frac{1}{6}}\right)}\right) - \frac{3}{2} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, x^{\frac{1}{6}}\right)}\right) + \frac{3}{4} \, \sqrt{2} \log\left(\sqrt{2} x^{\frac{1}{6}} + x^{\frac{1}{3}} + 1\right) - \frac{3}{4} \, \sqrt{2} \log\left(-\sqrt{2} x^{\frac{1}{6}} + x^{\frac{1}{3}} + 1\right) + 2 \, \sqrt{x}"," ",0,"-3/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*x^(1/6))) - 3/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*x^(1/6))) + 3/4*sqrt(2)*log(sqrt(2)*x^(1/6) + x^(1/3) + 1) - 3/4*sqrt(2)*log(-sqrt(2)*x^(1/6) + x^(1/3) + 1) + 2*sqrt(x)","A",0
578,1,60,0,0.340390," ","integrate(x^(1/3)/(x^(1/4)+x^(1/2)),x, algorithm=""giac"")","4 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{\frac{1}{12}} - 1\right)}\right) + \frac{6}{5} \, x^{\frac{5}{6}} - \frac{12}{7} \, x^{\frac{7}{12}} + 3 \, x^{\frac{1}{3}} - 12 \, x^{\frac{1}{12}} - 2 \, \log\left(x^{\frac{1}{6}} - x^{\frac{1}{12}} + 1\right) + 4 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^(1/12) - 1)) + 6/5*x^(5/6) - 12/7*x^(7/12) + 3*x^(1/3) - 12*x^(1/12) - 2*log(x^(1/6) - x^(1/12) + 1) + 4*log(x^(1/12) + 1)","A",0
579,1,75,0,0.463910," ","integrate(x^(1/2)/(x^(1/4)+x^(1/3)),x, algorithm=""giac"")","\frac{6}{7} \, x^{\frac{7}{6}} - \frac{12}{13} \, x^{\frac{13}{12}} + x - \frac{12}{11} \, x^{\frac{11}{12}} + \frac{6}{5} \, x^{\frac{5}{6}} - \frac{4}{3} \, x^{\frac{3}{4}} + \frac{3}{2} \, x^{\frac{2}{3}} - \frac{12}{7} \, x^{\frac{7}{12}} + 2 \, \sqrt{x} - \frac{12}{5} \, x^{\frac{5}{12}} + 3 \, x^{\frac{1}{3}} - 4 \, x^{\frac{1}{4}} + 6 \, x^{\frac{1}{6}} - 12 \, x^{\frac{1}{12}} + 12 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"6/7*x^(7/6) - 12/13*x^(13/12) + x - 12/11*x^(11/12) + 6/5*x^(5/6) - 4/3*x^(3/4) + 3/2*x^(2/3) - 12/7*x^(7/12) + 2*sqrt(x) - 12/5*x^(5/12) + 3*x^(1/3) - 4*x^(1/4) + 6*x^(1/6) - 12*x^(1/12) + 12*log(x^(1/12) + 1)","A",0
580,1,140,0,1.204399," ","integrate(x^(1/2)/(-1/x^(1/3)+x^(1/2)),x, algorithm=""giac"")","-\frac{3}{5} \, \sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{\sqrt{5} - 4 \, x^{\frac{1}{6}} - 1}{\sqrt{2 \, \sqrt{5} + 10}}\right) - \frac{3}{5} \, \sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{\sqrt{5} + 4 \, x^{\frac{1}{6}} + 1}{\sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{3}{10} \, \sqrt{5} \log\left(\frac{1}{2} \, x^{\frac{1}{6}} {\left(\sqrt{5} + 1\right)} + x^{\frac{1}{3}} + 1\right) + \frac{3}{10} \, \sqrt{5} \log\left(-\frac{1}{2} \, x^{\frac{1}{6}} {\left(\sqrt{5} - 1\right)} + x^{\frac{1}{3}} + 1\right) + x + 6 \, x^{\frac{1}{6}} - \frac{3}{10} \, \log\left(x^{\frac{2}{3}} + \sqrt{x} + x^{\frac{1}{3}} + x^{\frac{1}{6}} + 1\right) + \frac{6}{5} \, \log\left({\left| x^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"-3/5*sqrt(2*sqrt(5) + 10)*arctan(-(sqrt(5) - 4*x^(1/6) - 1)/sqrt(2*sqrt(5) + 10)) - 3/5*sqrt(-2*sqrt(5) + 10)*arctan((sqrt(5) + 4*x^(1/6) + 1)/sqrt(-2*sqrt(5) + 10)) - 3/10*sqrt(5)*log(1/2*x^(1/6)*(sqrt(5) + 1) + x^(1/3) + 1) + 3/10*sqrt(5)*log(-1/2*x^(1/6)*(sqrt(5) - 1) + x^(1/3) + 1) + x + 6*x^(1/6) - 3/10*log(x^(2/3) + sqrt(x) + x^(1/3) + x^(1/6) + 1) + 6/5*log(abs(x^(1/6) - 1))","A",0
581,-2,0,0,0.000000," ","integrate(x^m*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
582,1,76,0,0.375704," ","integrate(x^2*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{-a b} a^{2} {\left| b \right|} \mathrm{sgn}\left(x\right)}{5 \, b^{4}} - \frac{2 \, {\left(\sqrt{-a b} a^{2} - \frac{{\left({\left(b x - a\right)} b + a b\right)}^{2} \sqrt{-{\left(b x - a\right)} b - a b}}{b^{2}}\right)} {\left| b \right|} \mathrm{sgn}\left(x\right)}{5 \, b^{4}}"," ",0,"2/5*sqrt(-a*b)*a^2*abs(b)*sgn(x)/b^4 - 2/5*(sqrt(-a*b)*a^2 - ((b*x - a)*b + a*b)^2*sqrt(-(b*x - a)*b - a*b)/b^2)*abs(b)*sgn(x)/b^4","B",0
583,1,56,0,0.492309," ","integrate(x*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{-a b} a {\left| b \right|} \mathrm{sgn}\left(x\right)}{3 \, b^{3}} - \frac{2 \, {\left(\sqrt{-a b} a + \frac{{\left(-{\left(b x - a\right)} b - a b\right)}^{\frac{3}{2}}}{b}\right)} {\left| b \right|} \mathrm{sgn}\left(x\right)}{3 \, b^{3}}"," ",0,"2/3*sqrt(-a*b)*a*abs(b)*sgn(x)/b^3 - 2/3*(sqrt(-a*b)*a + (-(b*x - a)*b - a*b)^(3/2)/b)*abs(b)*sgn(x)/b^3","B",0
584,1,51,0,0.399956," ","integrate((b-a/x)^(1/2)/(-b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\sqrt{-{\left(b x - a\right)} b - a b} - \sqrt{-a b}\right)} {\left| b \right|} \mathrm{sgn}\left(x\right)}{b^{2}} + \frac{2 \, \sqrt{-a b} {\left| b \right|} \mathrm{sgn}\left(x\right)}{b^{2}}"," ",0,"2*(sqrt(-(b*x - a)*b - a*b) - sqrt(-a*b))*abs(b)*sgn(x)/b^2 + 2*sqrt(-a*b)*abs(b)*sgn(x)/b^2","B",0
585,1,42,0,0.431466," ","integrate((b-a/x)^(1/2)/x/(-b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{b^{3}}{\sqrt{-{\left(b x - a\right)} b - a b}} - \frac{b^{3}}{\sqrt{-a b}}\right)} {\left| b \right|} \mathrm{sgn}\left(x\right)}{b^{3}}"," ",0,"2*(b^3/sqrt(-(b*x - a)*b - a*b) - b^3/sqrt(-a*b))*abs(b)*sgn(x)/b^3","B",0
586,1,60,0,0.506287," ","integrate((b-a/x)^(1/2)/x^2/(-b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{b^{5}}{{\left({\left(b x - a\right)} b + a b\right)} \sqrt{-{\left(b x - a\right)} b - a b}} - \frac{b^{4}}{\sqrt{-a b} a}\right)} {\left| b \right|} \mathrm{sgn}\left(x\right)}{3 \, b^{3}}"," ",0,"2/3*(b^5/(((b*x - a)*b + a*b)*sqrt(-(b*x - a)*b - a*b)) - b^4/(sqrt(-a*b)*a))*abs(b)*sgn(x)/b^3","B",0
587,0,0,0,0.000000," ","integrate((a+b/x)^m*(d*x+c)^n,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{n} {\left(a + \frac{b}{x}\right)}^{m}\,{d x}"," ",0,"integrate((d*x + c)^n*(a + b/x)^m, x)","F",0
588,0,0,0,0.000000," ","integrate((a+b/x)^m*(d*x+c)^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} {\left(a + \frac{b}{x}\right)}^{m}\,{d x}"," ",0,"integrate((d*x + c)^2*(a + b/x)^m, x)","F",0
589,0,0,0,0.000000," ","integrate((a+b/x)^m*(d*x+c),x, algorithm=""giac"")","\int {\left(d x + c\right)} {\left(a + \frac{b}{x}\right)}^{m}\,{d x}"," ",0,"integrate((d*x + c)*(a + b/x)^m, x)","F",0
590,0,0,0,0.000000," ","integrate((a+b/x)^m,x, algorithm=""giac"")","\int {\left(a + \frac{b}{x}\right)}^{m}\,{d x}"," ",0,"integrate((a + b/x)^m, x)","F",0
591,0,0,0,0.000000," ","integrate((a+b/x)^m/(d*x+c),x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{m}}{d x + c}\,{d x}"," ",0,"integrate((a + b/x)^m/(d*x + c), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b/x)^m/(d*x+c)^2,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{m}}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate((a + b/x)^m/(d*x + c)^2, x)","F",0
593,0,0,0,0.000000," ","integrate((a+b/x)^m/(d*x+c)^3,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{m}}{{\left(d x + c\right)}^{3}}\,{d x}"," ",0,"integrate((a + b/x)^m/(d*x + c)^3, x)","F",0
594,0,0,0,0.000000," ","integrate((a+b/x)^m/(d*x+c)^4,x, algorithm=""giac"")","\int \frac{{\left(a + \frac{b}{x}\right)}^{m}}{{\left(d x + c\right)}^{4}}\,{d x}"," ",0,"integrate((a + b/x)^m/(d*x + c)^4, x)","F",0
595,0,0,0,0.000000," ","integrate(x^m*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b - \frac{a}{x^{2}}} x^{m}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(b - a/x^2)*x^m/sqrt(-b*x^2 + a), x)","F",0
596,1,15,0,0.327783," ","integrate(x^2*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{i \, b x^{2} - i \, a}{2 \, b}"," ",0,"-1/2*(I*b*x^2 - I*a)/b","C",0
597,0,0,0,0.000000," ","integrate(x*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b - \frac{a}{x^{2}}} x}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(b - a/x^2)*x/sqrt(-b*x^2 + a), x)","F",0
598,-2,0,0,0.000000," ","integrate((b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Sign error %%%{b,2%%%}Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
599,0,0,0,0.000000," ","integrate((b-a/x^2)^(1/2)/x/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b - \frac{a}{x^{2}}}}{\sqrt{-b x^{2} + a} x}\,{d x}"," ",0,"integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x), x)","F",0
600,1,5,0,0.365952," ","integrate((b-a/x^2)^(1/2)/x^2/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{i}{2 \, x^{2}}"," ",0,"1/2*I/x^2","C",0
601,0,0,0,0.000000," ","integrate((d*x+c)^(3/2)/(a+b/x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{\frac{3}{2}}}{\sqrt{a + \frac{b}{x^{2}}}}\,{d x}"," ",0,"integrate((d*x + c)^(3/2)/sqrt(a + b/x^2), x)","F",0
602,1,11,0,0.318515," ","integrate((x^3-1)/(x^4-4*x)^(2/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{4} - 4 \, x\right)}^{\frac{1}{3}}"," ",0,"3/4*(x^4 - 4*x)^(1/3)","A",0
603,1,13,0,0.325797," ","integrate((-x^2+2)*(-x^3+6*x)^(1/4),x, algorithm=""giac"")","\frac{4}{15} \, {\left(-x^{3} + 6 \, x\right)}^{\frac{5}{4}}"," ",0,"4/15*(-x^3 + 6*x)^(5/4)","A",0
604,1,11,0,0.397916," ","integrate((x^4+1)*(x^5+5*x)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(x^{5} + 5 \, x\right)}^{\frac{3}{2}}"," ",0,"2/15*(x^5 + 5*x)^(3/2)","A",0
605,1,11,0,0.404658," ","integrate((5*x^4+2)*(x^5+2*x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x^{5} + 2 \, x\right)}^{\frac{3}{2}}"," ",0,"2/3*(x^5 + 2*x)^(3/2)","A",0
606,1,11,0,0.358596," ","integrate((3*x^2+x)/(2*x^3+x^2)^(1/2),x, algorithm=""giac"")","\sqrt{2 \, x^{3} + x^{2}}"," ",0,"sqrt(2*x^3 + x^2)","A",0
607,1,33,0,0.481868," ","integrate((2+(1-5*x)^(1/3))/(3+(1-5*x)^(1/3)),x, algorithm=""giac"")","x + \frac{3}{10} \, {\left(-5 \, x + 1\right)}^{\frac{2}{3}} - \frac{9}{5} \, {\left(-5 \, x + 1\right)}^{\frac{1}{3}} + \frac{27}{5} \, \log\left({\left(-5 \, x + 1\right)}^{\frac{1}{3}} + 3\right) - \frac{1}{5}"," ",0,"x + 3/10*(-5*x + 1)^(2/3) - 9/5*(-5*x + 1)^(1/3) + 27/5*log((-5*x + 1)^(1/3) + 3) - 1/5","A",0
608,1,16,0,0.307123," ","integrate((1+x^(1/2))/(-1+x^(1/2)),x, algorithm=""giac"")","x + 4 \, \sqrt{x} + 4 \, \log\left({\left| \sqrt{x} - 1 \right|}\right)"," ",0,"x + 4*sqrt(x) + 4*log(abs(sqrt(x) - 1))","A",0
609,1,26,0,0.332842," ","integrate((1-(2+3*x)^(1/2))/(1+(2+3*x)^(1/2)),x, algorithm=""giac"")","-x + \frac{4}{3} \, \sqrt{3 \, x + 2} - \frac{4}{3} \, \log\left(\sqrt{3 \, x + 2} + 1\right) - \frac{2}{3}"," ",0,"-x + 4/3*sqrt(3*x + 2) - 4/3*log(sqrt(3*x + 2) + 1) - 2/3","A",0
610,1,38,0,0.361374," ","integrate((-1+(b*x+a)^(1/2))/(1+(b*x+a)^(1/2)),x, algorithm=""giac"")","\frac{4 \, \log\left(\sqrt{b x + a} + 1\right)}{b} + \frac{{\left(b x + a\right)} b - 4 \, \sqrt{b x + a} b}{b^{2}}"," ",0,"4*log(sqrt(b*x + a) + 1)/b + ((b*x + a)*b - 4*sqrt(b*x + a)*b)/b^2","A",0
611,0,0,0,0.000000," ","integrate((a+b*n*x^(-1+n))/(a*x+b*x^n),x, algorithm=""giac"")","\int \frac{b n x^{n - 1} + a}{a x + b x^{n}}\,{d x}"," ",0,"integrate((b*n*x^(n - 1) + a)/(a*x + b*x^n), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*n*x^(-1+n))/(x^n)/(b+a*x^(1-n)),x, algorithm=""giac"")","\int \frac{b n x^{n - 1} + a}{{\left(a x^{-n + 1} + b\right)} x^{n}}\,{d x}"," ",0,"integrate((b*n*x^(n - 1) + a)/((a*x^(-n + 1) + b)*x^n), x)","F",0
613,-1,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(2*a*d+(a*e*n+b*d*m+3*a*e+3*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+4*a*f+4*b*e+4*c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+5*a*g+5*b*f+5*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+6*b*g+6*c*f)*x^4+c*g*(7+2*m+3*n)*x^5),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(a*d+(a*e*n+b*d*m+2*a*e+2*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+3*a*f+3*b*e+3*c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+4*a*g+4*b*f+4*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+5*b*g+5*c*f)*x^4+c*g*(6+2*m+3*n)*x^5),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(b*d+a*e+b*d*m+a*e*n+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+2*a*f+2*b*e+2*c*d)*x+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+3*a*g+3*b*f+3*c*e)*x^2+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+4*b*g+4*c*f)*x^3+c*g*(5+2*m+3*n)*x^4),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-a*d+(a*e*n+b*d*m)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+a*f+b*e+c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+2*a*g+2*b*f+2*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+3*b*g+3*c*f)*x^4+c*g*(4+2*m+3*n)*x^5)/x^2,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
617,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x^4+c*g*(3+2*m+3*n)*x^5)/x^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,1,151,0,0.407380," ","integrate(x^3*(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{252 \, b^{2} d^{2} x^{5} + 315 \, b^{2} c d x^{4} + 315 \, a^{2} d x^{4} + \frac{144 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} a b c}{d^{3}} + \frac{16 \, {\left(35 \, {\left(d x + c\right)}^{\frac{9}{2}} - 180 \, {\left(d x + c\right)}^{\frac{7}{2}} c + 378 \, {\left(d x + c\right)}^{\frac{5}{2}} c^{2} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{3} + 315 \, \sqrt{d x + c} c^{4}\right)} a b}{d^{3}}}{1260 \, d}"," ",0,"1/1260*(252*b^2*d^2*x^5 + 315*b^2*c*d*x^4 + 315*a^2*d*x^4 + 144*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*a*b*c/d^3 + 16*(35*(d*x + c)^(9/2) - 180*(d*x + c)^(7/2)*c + 378*(d*x + c)^(5/2)*c^2 - 420*(d*x + c)^(3/2)*c^3 + 315*sqrt(d*x + c)*c^4)*a*b/d^3)/d","A",0
619,1,127,0,0.427877," ","integrate(x^2*(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{105 \, b^{2} d^{2} x^{4} + 140 \, b^{2} c d x^{3} + 140 \, a^{2} d x^{3} + \frac{112 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} a b c}{d^{2}} + \frac{48 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)} a b}{d^{2}}}{420 \, d}"," ",0,"1/420*(105*b^2*d^2*x^4 + 140*b^2*c*d*x^3 + 140*a^2*d*x^3 + 112*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*a*b*c/d^2 + 48*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)*a*b/d^2)/d","A",0
620,1,131,0,0.511946," ","integrate(x*(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{10 \, b^{2} d^{2} x^{3} + \frac{40 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} a b c}{d} + \frac{15 \, {\left({\left(d x + c\right)}^{2} - 2 \, {\left(d x + c\right)} c\right)} b^{2} c}{d} + \frac{15 \, {\left({\left(d x + c\right)}^{2} - 2 \, {\left(d x + c\right)} c\right)} a^{2}}{d} + \frac{8 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)} a b}{d}}{30 \, d}"," ",0,"1/30*(10*b^2*d^2*x^3 + 40*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*a*b*c/d + 15*((d*x + c)^2 - 2*(d*x + c)*c)*b^2*c/d + 15*((d*x + c)^2 - 2*(d*x + c)*c)*a^2/d + 8*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)*a*b/d)/d","A",0
621,1,82,0,0.357151," ","integrate((a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{6 \, {\left(d x + c\right)} b^{2} c + 24 \, \sqrt{d x + c} a b c + 6 \, {\left(d x + c\right)} a^{2} + 8 \, {\left({\left(d x + c\right)}^{\frac{3}{2}} - 3 \, \sqrt{d x + c} c\right)} a b + 3 \, {\left({\left(d x + c\right)}^{2} - 2 \, {\left(d x + c\right)} c\right)} b^{2}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*b^2*c + 24*sqrt(d*x + c)*a*b*c + 6*(d*x + c)*a^2 + 8*((d*x + c)^(3/2) - 3*sqrt(d*x + c)*c)*a*b + 3*((d*x + c)^2 - 2*(d*x + c)*c)*b^2)/d","B",0
622,1,59,0,0.423826," ","integrate((a+b*(d*x+c)^(1/2))^2/x,x, algorithm=""giac"")","\frac{4 \, a b c \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + {\left(d x + c\right)} b^{2} + 4 \, \sqrt{d x + c} a b + {\left(b^{2} c + a^{2}\right)} \log\left(d x\right)"," ",0,"4*a*b*c*arctan(sqrt(d*x + c)/sqrt(-c))/sqrt(-c) + (d*x + c)*b^2 + 4*sqrt(d*x + c)*a*b + (b^2*c + a^2)*log(d*x)","A",0
623,1,80,0,0.437481," ","integrate((a+b*(d*x+c)^(1/2))^2/x^2,x, algorithm=""giac"")","\frac{b^{2} d^{2} \log\left(d x\right) + \frac{2 \, a b d^{2} \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{b^{2} c d^{2} + 2 \, \sqrt{d x + c} a b d^{2} + a^{2} d^{2}}{d x}}{d}"," ",0,"(b^2*d^2*log(d*x) + 2*a*b*d^2*arctan(sqrt(d*x + c)/sqrt(-c))/sqrt(-c) - (b^2*c*d^2 + 2*sqrt(d*x + c)*a*b*d^2 + a^2*d^2)/(d*x))/d","A",0
624,1,105,0,0.362659," ","integrate((a+b*(d*x+c)^(1/2))^2/x^3,x, algorithm=""giac"")","-\frac{\frac{a b d^{3} \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c} + \frac{2 \, {\left(d x + c\right)} b^{2} c d^{3} - b^{2} c^{2} d^{3} + {\left(d x + c\right)}^{\frac{3}{2}} a b d^{3} + \sqrt{d x + c} a b c d^{3} + a^{2} c d^{3}}{c d^{2} x^{2}}}{2 \, d}"," ",0,"-1/2*(a*b*d^3*arctan(sqrt(d*x + c)/sqrt(-c))/(sqrt(-c)*c) + (2*(d*x + c)*b^2*c*d^3 - b^2*c^2*d^3 + (d*x + c)^(3/2)*a*b*d^3 + sqrt(d*x + c)*a*b*c*d^3 + a^2*c*d^3)/(c*d^2*x^2))/d","A",0
625,1,915,0,0.630281," ","integrate(x^3*(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{17 \, {\left(15015 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{6} c^{3} - 45045 \, \sqrt{\sqrt{d x + c} b + a} a b^{6} c^{3} - 19305 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} b^{4} c^{2} + 81081 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a b^{4} c^{2} - 135135 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} b^{4} c^{2} + 135135 \, \sqrt{\sqrt{d x + c} b + a} a^{3} b^{4} c^{2} + 12285 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} b^{2} c - 75075 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a b^{2} c + 193050 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{2} b^{2} c - 270270 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{3} b^{2} c + 225225 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{4} b^{2} c - 135135 \, \sqrt{\sqrt{d x + c} b + a} a^{5} b^{2} c - 3003 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{15}{2}} + 24255 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{13}{2}} a - 85995 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} a^{2} + 175175 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a^{3} - 225225 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{4} + 189189 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{5} - 105105 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{6} + 45045 \, \sqrt{\sqrt{d x + c} b + a} a^{7}\right)} a}{b^{7} d^{3}} + \frac{153153 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} b^{6} c^{3} - 510510 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a b^{6} c^{3} + 765765 \, \sqrt{\sqrt{d x + c} b + a} a^{2} b^{6} c^{3} - 255255 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} b^{4} c^{2} + 1312740 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a b^{4} c^{2} - 2756754 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{2} b^{4} c^{2} + 3063060 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{3} b^{4} c^{2} - 2297295 \, \sqrt{\sqrt{d x + c} b + a} a^{4} b^{4} c^{2} + 176715 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{13}{2}} b^{2} c - 1253070 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} a b^{2} c + 3828825 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a^{2} b^{2} c - 6563700 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{3} b^{2} c + 6891885 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{4} b^{2} c - 4594590 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{5} b^{2} c + 2297295 \, \sqrt{\sqrt{d x + c} b + a} a^{6} b^{2} c - 45045 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{17}{2}} + 408408 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{15}{2}} a - 1649340 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{13}{2}} a^{2} + 3898440 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} a^{3} - 5955950 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a^{4} + 6126120 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{5} - 4288284 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{6} + 2042040 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{7} - 765765 \, \sqrt{\sqrt{d x + c} b + a} a^{8}}{b^{7} d^{3}}\right)}}{765765 \, b d}"," ",0,"-4/765765*(17*(15015*(sqrt(d*x + c)*b + a)^(3/2)*b^6*c^3 - 45045*sqrt(sqrt(d*x + c)*b + a)*a*b^6*c^3 - 19305*(sqrt(d*x + c)*b + a)^(7/2)*b^4*c^2 + 81081*(sqrt(d*x + c)*b + a)^(5/2)*a*b^4*c^2 - 135135*(sqrt(d*x + c)*b + a)^(3/2)*a^2*b^4*c^2 + 135135*sqrt(sqrt(d*x + c)*b + a)*a^3*b^4*c^2 + 12285*(sqrt(d*x + c)*b + a)^(11/2)*b^2*c - 75075*(sqrt(d*x + c)*b + a)^(9/2)*a*b^2*c + 193050*(sqrt(d*x + c)*b + a)^(7/2)*a^2*b^2*c - 270270*(sqrt(d*x + c)*b + a)^(5/2)*a^3*b^2*c + 225225*(sqrt(d*x + c)*b + a)^(3/2)*a^4*b^2*c - 135135*sqrt(sqrt(d*x + c)*b + a)*a^5*b^2*c - 3003*(sqrt(d*x + c)*b + a)^(15/2) + 24255*(sqrt(d*x + c)*b + a)^(13/2)*a - 85995*(sqrt(d*x + c)*b + a)^(11/2)*a^2 + 175175*(sqrt(d*x + c)*b + a)^(9/2)*a^3 - 225225*(sqrt(d*x + c)*b + a)^(7/2)*a^4 + 189189*(sqrt(d*x + c)*b + a)^(5/2)*a^5 - 105105*(sqrt(d*x + c)*b + a)^(3/2)*a^6 + 45045*sqrt(sqrt(d*x + c)*b + a)*a^7)*a/(b^7*d^3) + (153153*(sqrt(d*x + c)*b + a)^(5/2)*b^6*c^3 - 510510*(sqrt(d*x + c)*b + a)^(3/2)*a*b^6*c^3 + 765765*sqrt(sqrt(d*x + c)*b + a)*a^2*b^6*c^3 - 255255*(sqrt(d*x + c)*b + a)^(9/2)*b^4*c^2 + 1312740*(sqrt(d*x + c)*b + a)^(7/2)*a*b^4*c^2 - 2756754*(sqrt(d*x + c)*b + a)^(5/2)*a^2*b^4*c^2 + 3063060*(sqrt(d*x + c)*b + a)^(3/2)*a^3*b^4*c^2 - 2297295*sqrt(sqrt(d*x + c)*b + a)*a^4*b^4*c^2 + 176715*(sqrt(d*x + c)*b + a)^(13/2)*b^2*c - 1253070*(sqrt(d*x + c)*b + a)^(11/2)*a*b^2*c + 3828825*(sqrt(d*x + c)*b + a)^(9/2)*a^2*b^2*c - 6563700*(sqrt(d*x + c)*b + a)^(7/2)*a^3*b^2*c + 6891885*(sqrt(d*x + c)*b + a)^(5/2)*a^4*b^2*c - 4594590*(sqrt(d*x + c)*b + a)^(3/2)*a^5*b^2*c + 2297295*sqrt(sqrt(d*x + c)*b + a)*a^6*b^2*c - 45045*(sqrt(d*x + c)*b + a)^(17/2) + 408408*(sqrt(d*x + c)*b + a)^(15/2)*a - 1649340*(sqrt(d*x + c)*b + a)^(13/2)*a^2 + 3898440*(sqrt(d*x + c)*b + a)^(11/2)*a^3 - 5955950*(sqrt(d*x + c)*b + a)^(9/2)*a^4 + 6126120*(sqrt(d*x + c)*b + a)^(7/2)*a^5 - 4288284*(sqrt(d*x + c)*b + a)^(5/2)*a^6 + 2042040*(sqrt(d*x + c)*b + a)^(3/2)*a^7 - 765765*sqrt(sqrt(d*x + c)*b + a)*a^8)/(b^7*d^3))/(b*d)","B",0
626,1,549,0,0.462885," ","integrate(x^2*(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{13 \, {\left(1155 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{4} c^{2} - 3465 \, \sqrt{\sqrt{d x + c} b + a} a b^{4} c^{2} - 990 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} b^{2} c + 4158 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a b^{2} c - 6930 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} b^{2} c + 6930 \, \sqrt{\sqrt{d x + c} b + a} a^{3} b^{2} c + 315 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} - 1925 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a + 4950 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{2} - 6930 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{3} + 5775 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{4} - 3465 \, \sqrt{\sqrt{d x + c} b + a} a^{5}\right)} a}{b^{5} d^{2}} + \frac{9009 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} b^{4} c^{2} - 30030 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a b^{4} c^{2} + 45045 \, \sqrt{\sqrt{d x + c} b + a} a^{2} b^{4} c^{2} - 10010 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} b^{2} c + 51480 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a b^{2} c - 108108 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{2} b^{2} c + 120120 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{3} b^{2} c - 90090 \, \sqrt{\sqrt{d x + c} b + a} a^{4} b^{2} c + 3465 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{13}{2}} - 24570 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} a + 75075 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a^{2} - 128700 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{3} + 135135 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{4} - 90090 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{5} + 45045 \, \sqrt{\sqrt{d x + c} b + a} a^{6}}{b^{5} d^{2}}\right)}}{45045 \, b d}"," ",0,"4/45045*(13*(1155*(sqrt(d*x + c)*b + a)^(3/2)*b^4*c^2 - 3465*sqrt(sqrt(d*x + c)*b + a)*a*b^4*c^2 - 990*(sqrt(d*x + c)*b + a)^(7/2)*b^2*c + 4158*(sqrt(d*x + c)*b + a)^(5/2)*a*b^2*c - 6930*(sqrt(d*x + c)*b + a)^(3/2)*a^2*b^2*c + 6930*sqrt(sqrt(d*x + c)*b + a)*a^3*b^2*c + 315*(sqrt(d*x + c)*b + a)^(11/2) - 1925*(sqrt(d*x + c)*b + a)^(9/2)*a + 4950*(sqrt(d*x + c)*b + a)^(7/2)*a^2 - 6930*(sqrt(d*x + c)*b + a)^(5/2)*a^3 + 5775*(sqrt(d*x + c)*b + a)^(3/2)*a^4 - 3465*sqrt(sqrt(d*x + c)*b + a)*a^5)*a/(b^5*d^2) + (9009*(sqrt(d*x + c)*b + a)^(5/2)*b^4*c^2 - 30030*(sqrt(d*x + c)*b + a)^(3/2)*a*b^4*c^2 + 45045*sqrt(sqrt(d*x + c)*b + a)*a^2*b^4*c^2 - 10010*(sqrt(d*x + c)*b + a)^(9/2)*b^2*c + 51480*(sqrt(d*x + c)*b + a)^(7/2)*a*b^2*c - 108108*(sqrt(d*x + c)*b + a)^(5/2)*a^2*b^2*c + 120120*(sqrt(d*x + c)*b + a)^(3/2)*a^3*b^2*c - 90090*sqrt(sqrt(d*x + c)*b + a)*a^4*b^2*c + 3465*(sqrt(d*x + c)*b + a)^(13/2) - 24570*(sqrt(d*x + c)*b + a)^(11/2)*a + 75075*(sqrt(d*x + c)*b + a)^(9/2)*a^2 - 128700*(sqrt(d*x + c)*b + a)^(7/2)*a^3 + 135135*(sqrt(d*x + c)*b + a)^(5/2)*a^4 - 90090*(sqrt(d*x + c)*b + a)^(3/2)*a^5 + 45045*sqrt(sqrt(d*x + c)*b + a)*a^6)/(b^5*d^2))/(b*d)","B",0
627,1,279,0,0.367634," ","integrate(x*(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{3 \, {\left(35 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{2} c - 105 \, \sqrt{\sqrt{d x + c} b + a} a b^{2} c - 15 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} + 63 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a - 105 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} + 105 \, \sqrt{\sqrt{d x + c} b + a} a^{3}\right)} a}{b^{3} d} + \frac{63 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} b^{2} c - 210 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a b^{2} c + 315 \, \sqrt{\sqrt{d x + c} b + a} a^{2} b^{2} c - 35 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} + 180 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a - 378 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{2} + 420 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{3} - 315 \, \sqrt{\sqrt{d x + c} b + a} a^{4}}{b^{3} d}\right)}}{315 \, b d}"," ",0,"-4/315*(3*(35*(sqrt(d*x + c)*b + a)^(3/2)*b^2*c - 105*sqrt(sqrt(d*x + c)*b + a)*a*b^2*c - 15*(sqrt(d*x + c)*b + a)^(7/2) + 63*(sqrt(d*x + c)*b + a)^(5/2)*a - 105*(sqrt(d*x + c)*b + a)^(3/2)*a^2 + 105*sqrt(sqrt(d*x + c)*b + a)*a^3)*a/(b^3*d) + (63*(sqrt(d*x + c)*b + a)^(5/2)*b^2*c - 210*(sqrt(d*x + c)*b + a)^(3/2)*a*b^2*c + 315*sqrt(sqrt(d*x + c)*b + a)*a^2*b^2*c - 35*(sqrt(d*x + c)*b + a)^(9/2) + 180*(sqrt(d*x + c)*b + a)^(7/2)*a - 378*(sqrt(d*x + c)*b + a)^(5/2)*a^2 + 420*(sqrt(d*x + c)*b + a)^(3/2)*a^3 - 315*sqrt(sqrt(d*x + c)*b + a)*a^4)/(b^3*d))/(b*d)","B",0
628,1,99,0,0.355881," ","integrate((a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(\frac{5 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{d x + c} b + a} a\right)} a}{b} + \frac{3 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} - 10 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{\sqrt{d x + c} b + a} a^{2}}{b}\right)}}{15 \, b d}"," ",0,"4/15*(5*((sqrt(d*x + c)*b + a)^(3/2) - 3*sqrt(sqrt(d*x + c)*b + a)*a)*a/b + (3*(sqrt(d*x + c)*b + a)^(5/2) - 10*(sqrt(d*x + c)*b + a)^(3/2)*a + 15*sqrt(sqrt(d*x + c)*b + a)*a^2)/b)/(b*d)","B",0
629,1,150,0,0.494027," ","integrate((a+b*(d*x+c)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, {\left(2 \, \sqrt{\sqrt{d x + c} b + a} b - \frac{{\left(b^{3} c - a^{2} b\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-a + \sqrt{b^{2} c}}}\right)}{{\left(b \sqrt{c} + a\right)} \sqrt{b \sqrt{c} - a}} + \frac{{\left(b^{3} c - a^{2} b\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-a - \sqrt{b^{2} c}}}\right)}{{\left(b \sqrt{c} - a\right)} \sqrt{-b \sqrt{c} - a}}\right)}}{b}"," ",0,"2*(2*sqrt(sqrt(d*x + c)*b + a)*b - (b^3*c - a^2*b)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-a + sqrt(b^2*c)))/((b*sqrt(c) + a)*sqrt(b*sqrt(c) - a)) + (b^3*c - a^2*b)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-a - sqrt(b^2*c)))/((b*sqrt(c) - a)*sqrt(-b*sqrt(c) - a)))/b","A",0
630,1,232,0,0.656404," ","integrate((a+b*(d*x+c)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{\sqrt{d x + c} b + a} b^{3} d^{2}}{b^{2} c - {\left(\sqrt{d x + c} b + a\right)}^{2} + 2 \, {\left(\sqrt{d x + c} b + a\right)} a - a^{2}} - \frac{{\left(b^{3} c d^{2} {\left| b \right|} + a b^{3} \sqrt{c} d^{2}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-a + \sqrt{b^{2} c}}}\right)}{{\left(b c^{\frac{3}{2}} + a c\right)} \sqrt{b \sqrt{c} - a} {\left| b \right|}} + \frac{{\left(b^{3} c d^{2} {\left| b \right|} - a b^{3} \sqrt{c} d^{2}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-a - \sqrt{b^{2} c}}}\right)}{{\left(b c^{\frac{3}{2}} - a c\right)} \sqrt{-b \sqrt{c} - a} {\left| b \right|}}}{2 \, b d}"," ",0,"1/2*(2*sqrt(sqrt(d*x + c)*b + a)*b^3*d^2/(b^2*c - (sqrt(d*x + c)*b + a)^2 + 2*(sqrt(d*x + c)*b + a)*a - a^2) - (b^3*c*d^2*abs(b) + a*b^3*sqrt(c)*d^2)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-a + sqrt(b^2*c)))/((b*c^(3/2) + a*c)*sqrt(b*sqrt(c) - a)*abs(b)) + (b^3*c*d^2*abs(b) - a*b^3*sqrt(c)*d^2)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-a - sqrt(b^2*c)))/((b*c^(3/2) - a*c)*sqrt(-b*sqrt(c) - a)*abs(b)))/(b*d)","B",0
631,1,895,0,1.102588," ","integrate((a+b*(d*x+c)^(1/2))^(1/2)/x^3,x, algorithm=""giac"")","\frac{\frac{{\left({\left(b^{3} c^{2} - a^{2} b c\right)}^{2} a b^{3} \sqrt{c} d^{3} - {\left(3 \, b^{7} c^{3} - 4 \, a^{2} b^{5} c^{2} + a^{4} b^{3} c\right)} d^{3} {\left| b^{3} c^{2} - a^{2} b c \right|} + {\left(3 \, a b^{9} c^{\frac{9}{2}} - 8 \, a^{3} b^{7} c^{\frac{7}{2}} + 7 \, a^{5} b^{5} c^{\frac{5}{2}} - 2 \, a^{7} b^{3} c^{\frac{3}{2}}\right)} d^{3}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-\frac{a b^{2} c^{2} - a^{3} c + \sqrt{{\left(a b^{2} c^{2} - a^{3} c\right)}^{2} + {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} {\left(b^{2} c^{2} - a^{2} c\right)}}}{b^{2} c^{2} - a^{2} c}}}\right)}{{\left(b^{5} c^{\frac{9}{2}} - a b^{4} c^{4} - 2 \, a^{2} b^{3} c^{\frac{7}{2}} + 2 \, a^{3} b^{2} c^{3} + a^{4} b c^{\frac{5}{2}} - a^{5} c^{2}\right)} \sqrt{-b \sqrt{c} - a} {\left| b^{3} c^{2} - a^{2} b c \right|}} + \frac{{\left({\left(b^{3} c^{2} - a^{2} b c\right)}^{2} a b^{3} d^{3} + {\left(3 \, b^{7} c^{\frac{5}{2}} - 4 \, a^{2} b^{5} c^{\frac{3}{2}} + a^{4} b^{3} \sqrt{c}\right)} d^{3} {\left| b^{3} c^{2} - a^{2} b c \right|} + {\left(3 \, a b^{9} c^{4} - 8 \, a^{3} b^{7} c^{3} + 7 \, a^{5} b^{5} c^{2} - 2 \, a^{7} b^{3} c\right)} d^{3}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-\frac{a b^{2} c^{2} - a^{3} c - \sqrt{{\left(a b^{2} c^{2} - a^{3} c\right)}^{2} + {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} {\left(b^{2} c^{2} - a^{2} c\right)}}}{b^{2} c^{2} - a^{2} c}}}\right)}{{\left(b^{5} c^{4} + a b^{4} c^{\frac{7}{2}} - 2 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{\frac{5}{2}} + a^{4} b c^{2} + a^{5} c^{\frac{3}{2}}\right)} \sqrt{b \sqrt{c} - a} {\left| b^{3} c^{2} - a^{2} b c \right|}} - \frac{2 \, {\left(3 \, \sqrt{\sqrt{d x + c} b + a} b^{7} c^{2} d^{3} + {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} b^{5} c d^{3} - {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a b^{5} c d^{3} - 4 \, \sqrt{\sqrt{d x + c} b + a} a^{2} b^{5} c d^{3} - {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a b^{3} d^{3} + 3 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{2} b^{3} d^{3} - 3 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{3} b^{3} d^{3} + \sqrt{\sqrt{d x + c} b + a} a^{4} b^{3} d^{3}\right)}}{{\left(b^{2} c^{2} - a^{2} c\right)} {\left(b^{2} c - {\left(\sqrt{d x + c} b + a\right)}^{2} + 2 \, {\left(\sqrt{d x + c} b + a\right)} a - a^{2}\right)}^{2}}}{16 \, b d}"," ",0,"1/16*(((b^3*c^2 - a^2*b*c)^2*a*b^3*sqrt(c)*d^3 - (3*b^7*c^3 - 4*a^2*b^5*c^2 + a^4*b^3*c)*d^3*abs(b^3*c^2 - a^2*b*c) + (3*a*b^9*c^(9/2) - 8*a^3*b^7*c^(7/2) + 7*a^5*b^5*c^(5/2) - 2*a^7*b^3*c^(3/2))*d^3)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-(a*b^2*c^2 - a^3*c + sqrt((a*b^2*c^2 - a^3*c)^2 + (b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*(b^2*c^2 - a^2*c)))/(b^2*c^2 - a^2*c)))/((b^5*c^(9/2) - a*b^4*c^4 - 2*a^2*b^3*c^(7/2) + 2*a^3*b^2*c^3 + a^4*b*c^(5/2) - a^5*c^2)*sqrt(-b*sqrt(c) - a)*abs(b^3*c^2 - a^2*b*c)) + ((b^3*c^2 - a^2*b*c)^2*a*b^3*d^3 + (3*b^7*c^(5/2) - 4*a^2*b^5*c^(3/2) + a^4*b^3*sqrt(c))*d^3*abs(b^3*c^2 - a^2*b*c) + (3*a*b^9*c^4 - 8*a^3*b^7*c^3 + 7*a^5*b^5*c^2 - 2*a^7*b^3*c)*d^3)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-(a*b^2*c^2 - a^3*c - sqrt((a*b^2*c^2 - a^3*c)^2 + (b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*(b^2*c^2 - a^2*c)))/(b^2*c^2 - a^2*c)))/((b^5*c^4 + a*b^4*c^(7/2) - 2*a^2*b^3*c^3 - 2*a^3*b^2*c^(5/2) + a^4*b*c^2 + a^5*c^(3/2))*sqrt(b*sqrt(c) - a)*abs(b^3*c^2 - a^2*b*c)) - 2*(3*sqrt(sqrt(d*x + c)*b + a)*b^7*c^2*d^3 + (sqrt(d*x + c)*b + a)^(5/2)*b^5*c*d^3 - (sqrt(d*x + c)*b + a)^(3/2)*a*b^5*c*d^3 - 4*sqrt(sqrt(d*x + c)*b + a)*a^2*b^5*c*d^3 - (sqrt(d*x + c)*b + a)^(7/2)*a*b^3*d^3 + 3*(sqrt(d*x + c)*b + a)^(5/2)*a^2*b^3*d^3 - 3*(sqrt(d*x + c)*b + a)^(3/2)*a^3*b^3*d^3 + sqrt(sqrt(d*x + c)*b + a)*a^4*b^3*d^3)/((b^2*c^2 - a^2*c)*(b^2*c - (sqrt(d*x + c)*b + a)^2 + 2*(sqrt(d*x + c)*b + a)*a - a^2)^2))/(b*d)","B",0
632,1,341,0,0.373823," ","integrate(x^3/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","\frac{2 \, {\left(a b^{6} c^{3} - 3 \, a^{3} b^{4} c^{2} + 3 \, a^{5} b^{2} c - a^{7}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{8} d^{4}} + \frac{60 \, {\left(d x + c\right)}^{\frac{7}{2}} b^{6} d^{24} - 252 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{6} c d^{24} + 420 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{6} c^{2} d^{24} - 420 \, \sqrt{d x + c} b^{6} c^{3} d^{24} - 70 \, {\left(d x + c\right)}^{3} a b^{5} d^{24} + 315 \, {\left(d x + c\right)}^{2} a b^{5} c d^{24} - 630 \, {\left(d x + c\right)} a b^{5} c^{2} d^{24} + 84 \, {\left(d x + c\right)}^{\frac{5}{2}} a^{2} b^{4} d^{24} - 420 \, {\left(d x + c\right)}^{\frac{3}{2}} a^{2} b^{4} c d^{24} + 1260 \, \sqrt{d x + c} a^{2} b^{4} c^{2} d^{24} - 105 \, {\left(d x + c\right)}^{2} a^{3} b^{3} d^{24} + 630 \, {\left(d x + c\right)} a^{3} b^{3} c d^{24} + 140 \, {\left(d x + c\right)}^{\frac{3}{2}} a^{4} b^{2} d^{24} - 1260 \, \sqrt{d x + c} a^{4} b^{2} c d^{24} - 210 \, {\left(d x + c\right)} a^{5} b d^{24} + 420 \, \sqrt{d x + c} a^{6} d^{24}}{210 \, b^{7} d^{28}}"," ",0,"2*(a*b^6*c^3 - 3*a^3*b^4*c^2 + 3*a^5*b^2*c - a^7)*log(abs(sqrt(d*x + c)*b + a))/(b^8*d^4) + 1/210*(60*(d*x + c)^(7/2)*b^6*d^24 - 252*(d*x + c)^(5/2)*b^6*c*d^24 + 420*(d*x + c)^(3/2)*b^6*c^2*d^24 - 420*sqrt(d*x + c)*b^6*c^3*d^24 - 70*(d*x + c)^3*a*b^5*d^24 + 315*(d*x + c)^2*a*b^5*c*d^24 - 630*(d*x + c)*a*b^5*c^2*d^24 + 84*(d*x + c)^(5/2)*a^2*b^4*d^24 - 420*(d*x + c)^(3/2)*a^2*b^4*c*d^24 + 1260*sqrt(d*x + c)*a^2*b^4*c^2*d^24 - 105*(d*x + c)^2*a^3*b^3*d^24 + 630*(d*x + c)*a^3*b^3*c*d^24 + 140*(d*x + c)^(3/2)*a^4*b^2*d^24 - 1260*sqrt(d*x + c)*a^4*b^2*c*d^24 - 210*(d*x + c)*a^5*b*d^24 + 420*sqrt(d*x + c)*a^6*d^24)/(b^7*d^28)","A",0
633,1,198,0,0.410947," ","integrate(x^2/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, {\left(a b^{4} c^{2} - 2 \, a^{3} b^{2} c + a^{5}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{6} d^{3}} + \frac{12 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4} d^{12} - 40 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{4} c d^{12} + 60 \, \sqrt{d x + c} b^{4} c^{2} d^{12} - 15 \, {\left(d x + c\right)}^{2} a b^{3} d^{12} + 60 \, {\left(d x + c\right)} a b^{3} c d^{12} + 20 \, {\left(d x + c\right)}^{\frac{3}{2}} a^{2} b^{2} d^{12} - 120 \, \sqrt{d x + c} a^{2} b^{2} c d^{12} - 30 \, {\left(d x + c\right)} a^{3} b d^{12} + 60 \, \sqrt{d x + c} a^{4} d^{12}}{30 \, b^{5} d^{15}}"," ",0,"-2*(a*b^4*c^2 - 2*a^3*b^2*c + a^5)*log(abs(sqrt(d*x + c)*b + a))/(b^6*d^3) + 1/30*(12*(d*x + c)^(5/2)*b^4*d^12 - 40*(d*x + c)^(3/2)*b^4*c*d^12 + 60*sqrt(d*x + c)*b^4*c^2*d^12 - 15*(d*x + c)^2*a*b^3*d^12 + 60*(d*x + c)*a*b^3*c*d^12 + 20*(d*x + c)^(3/2)*a^2*b^2*d^12 - 120*sqrt(d*x + c)*a^2*b^2*c*d^12 - 30*(d*x + c)*a^3*b*d^12 + 60*sqrt(d*x + c)*a^4*d^12)/(b^5*d^15)","A",0
634,1,105,0,0.332359," ","integrate(x/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","\frac{\frac{6 \, {\left(a b^{2} c - a^{3}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{4} d} + \frac{2 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d^{2} - 6 \, \sqrt{d x + c} b^{2} c d^{2} - 3 \, {\left(d x + c\right)} a b d^{2} + 6 \, \sqrt{d x + c} a^{2} d^{2}}{b^{3} d^{3}}}{3 \, d}"," ",0,"1/3*(6*(a*b^2*c - a^3)*log(abs(sqrt(d*x + c)*b + a))/(b^4*d) + (2*(d*x + c)^(3/2)*b^2*d^2 - 6*sqrt(d*x + c)*b^2*c*d^2 - 3*(d*x + c)*a*b*d^2 + 6*sqrt(d*x + c)*a^2*d^2)/(b^3*d^3))/d","A",0
635,1,38,0,0.350570," ","integrate(1/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, a \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{2} d} + \frac{2 \, \sqrt{d x + c}}{b d}"," ",0,"-2*a*log(abs(sqrt(d*x + c)*b + a))/(b^2*d) + 2*sqrt(d*x + c)/(b*d)","A",0
636,1,88,0,0.343081," ","integrate(1/x/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","\frac{2 \, a b \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{3} c - a^{2} b} + \frac{2 \, b c \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{{\left(b^{2} c - a^{2}\right)} \sqrt{-c}} - \frac{a \log\left(d x\right)}{b^{2} c - a^{2}}"," ",0,"2*a*b*log(abs(sqrt(d*x + c)*b + a))/(b^3*c - a^2*b) + 2*b*c*arctan(sqrt(d*x + c)/sqrt(-c))/((b^2*c - a^2)*sqrt(-c)) - a*log(d*x)/(b^2*c - a^2)","A",0
637,1,191,0,0.456277," ","integrate(1/x^2/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, a b^{3} d \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{5} c^{2} - 2 \, a^{2} b^{3} c + a^{4} b} + \frac{a b^{2} d \log\left(-d x\right)}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}} - \frac{{\left(b^{3} c d + a^{2} b d\right)} \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{{\left(b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}\right)} \sqrt{-c}} + \frac{a b^{2} c d - a^{3} d - {\left(b^{3} c d - a^{2} b d\right)} \sqrt{d x + c}}{{\left(b^{2} c - a^{2}\right)}^{2} d x}"," ",0,"-2*a*b^3*d*log(abs(sqrt(d*x + c)*b + a))/(b^5*c^2 - 2*a^2*b^3*c + a^4*b) + a*b^2*d*log(-d*x)/(b^4*c^2 - 2*a^2*b^2*c + a^4) - (b^3*c*d + a^2*b*d)*arctan(sqrt(d*x + c)/sqrt(-c))/((b^4*c^2 - 2*a^2*b^2*c + a^4)*sqrt(-c)) + (a*b^2*c*d - a^3*d - (b^3*c*d - a^2*b*d)*sqrt(d*x + c))/((b^2*c - a^2)^2*d*x)","A",0
638,1,375,0,0.458473," ","integrate(1/x^3/(a+b*(d*x+c)^(1/2)),x, algorithm=""giac"")","\frac{2 \, a b^{5} d^{2} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{7} c^{3} - 3 \, a^{2} b^{5} c^{2} + 3 \, a^{4} b^{3} c - a^{6} b} - \frac{a b^{4} d^{2} \log\left(d x\right)}{b^{6} c^{3} - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{4} b^{2} c - a^{6}} + \frac{{\left(3 \, b^{5} c^{2} d^{2} + 6 \, a^{2} b^{3} c d^{2} - a^{4} b d^{2}\right)} \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{4 \, {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} \sqrt{-c}} + \frac{6 \, a b^{4} c^{3} d^{2} - 8 \, a^{3} b^{2} c^{2} d^{2} + 2 \, a^{5} c d^{2} + {\left(3 \, b^{5} c^{2} d^{2} - 2 \, a^{2} b^{3} c d^{2} - a^{4} b d^{2}\right)} {\left(d x + c\right)}^{\frac{3}{2}} - 4 \, {\left(a b^{4} c^{2} d^{2} - a^{3} b^{2} c d^{2}\right)} {\left(d x + c\right)} - {\left(5 \, b^{5} c^{3} d^{2} - 6 \, a^{2} b^{3} c^{2} d^{2} + a^{4} b c d^{2}\right)} \sqrt{d x + c}}{4 \, {\left(b^{2} c - a^{2}\right)}^{3} c d^{2} x^{2}}"," ",0,"2*a*b^5*d^2*log(abs(sqrt(d*x + c)*b + a))/(b^7*c^3 - 3*a^2*b^5*c^2 + 3*a^4*b^3*c - a^6*b) - a*b^4*d^2*log(d*x)/(b^6*c^3 - 3*a^2*b^4*c^2 + 3*a^4*b^2*c - a^6) + 1/4*(3*b^5*c^2*d^2 + 6*a^2*b^3*c*d^2 - a^4*b*d^2)*arctan(sqrt(d*x + c)/sqrt(-c))/((b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*sqrt(-c)) + 1/4*(6*a*b^4*c^3*d^2 - 8*a^3*b^2*c^2*d^2 + 2*a^5*c*d^2 + (3*b^5*c^2*d^2 - 2*a^2*b^3*c*d^2 - a^4*b*d^2)*(d*x + c)^(3/2) - 4*(a*b^4*c^2*d^2 - a^3*b^2*c*d^2)*(d*x + c) - (5*b^5*c^3*d^2 - 6*a^2*b^3*c^2*d^2 + a^4*b*c*d^2)*sqrt(d*x + c))/((b^2*c - a^2)^3*c*d^2*x^2)","A",0
639,1,324,0,0.483702," ","integrate(x^3/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(b^{6} c^{3} - 9 \, a^{2} b^{4} c^{2} + 15 \, a^{4} b^{2} c - 7 \, a^{6}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{8} d^{4}} - \frac{2 \, {\left(a b^{6} c^{3} - 3 \, a^{3} b^{4} c^{2} + 3 \, a^{5} b^{2} c - a^{7}\right)}}{{\left(\sqrt{d x + c} b + a\right)} b^{8} d^{4}} + \frac{10 \, {\left(d x + c\right)}^{3} b^{10} d^{20} - 45 \, {\left(d x + c\right)}^{2} b^{10} c d^{20} + 90 \, {\left(d x + c\right)} b^{10} c^{2} d^{20} - 24 \, {\left(d x + c\right)}^{\frac{5}{2}} a b^{9} d^{20} + 120 \, {\left(d x + c\right)}^{\frac{3}{2}} a b^{9} c d^{20} - 360 \, \sqrt{d x + c} a b^{9} c^{2} d^{20} + 45 \, {\left(d x + c\right)}^{2} a^{2} b^{8} d^{20} - 270 \, {\left(d x + c\right)} a^{2} b^{8} c d^{20} - 80 \, {\left(d x + c\right)}^{\frac{3}{2}} a^{3} b^{7} d^{20} + 720 \, \sqrt{d x + c} a^{3} b^{7} c d^{20} + 150 \, {\left(d x + c\right)} a^{4} b^{6} d^{20} - 360 \, \sqrt{d x + c} a^{5} b^{5} d^{20}}{30 \, b^{12} d^{24}}"," ",0,"-2*(b^6*c^3 - 9*a^2*b^4*c^2 + 15*a^4*b^2*c - 7*a^6)*log(abs(sqrt(d*x + c)*b + a))/(b^8*d^4) - 2*(a*b^6*c^3 - 3*a^3*b^4*c^2 + 3*a^5*b^2*c - a^7)/((sqrt(d*x + c)*b + a)*b^8*d^4) + 1/30*(10*(d*x + c)^3*b^10*d^20 - 45*(d*x + c)^2*b^10*c*d^20 + 90*(d*x + c)*b^10*c^2*d^20 - 24*(d*x + c)^(5/2)*a*b^9*d^20 + 120*(d*x + c)^(3/2)*a*b^9*c*d^20 - 360*sqrt(d*x + c)*a*b^9*c^2*d^20 + 45*(d*x + c)^2*a^2*b^8*d^20 - 270*(d*x + c)*a^2*b^8*c*d^20 - 80*(d*x + c)^(3/2)*a^3*b^7*d^20 + 720*sqrt(d*x + c)*a^3*b^7*c*d^20 + 150*(d*x + c)*a^4*b^6*d^20 - 360*sqrt(d*x + c)*a^5*b^5*d^20)/(b^12*d^24)","A",0
640,1,191,0,0.372392," ","integrate(x^2/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{2 \, {\left(b^{4} c^{2} - 6 \, a^{2} b^{2} c + 5 \, a^{4}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{6} d^{3}} + \frac{2 \, {\left(a b^{4} c^{2} - 2 \, a^{3} b^{2} c + a^{5}\right)}}{{\left(\sqrt{d x + c} b + a\right)} b^{6} d^{3}} + \frac{3 \, {\left(d x + c\right)}^{2} b^{6} d^{9} - 12 \, {\left(d x + c\right)} b^{6} c d^{9} - 8 \, {\left(d x + c\right)}^{\frac{3}{2}} a b^{5} d^{9} + 48 \, \sqrt{d x + c} a b^{5} c d^{9} + 18 \, {\left(d x + c\right)} a^{2} b^{4} d^{9} - 48 \, \sqrt{d x + c} a^{3} b^{3} d^{9}}{6 \, b^{8} d^{12}}"," ",0,"2*(b^4*c^2 - 6*a^2*b^2*c + 5*a^4)*log(abs(sqrt(d*x + c)*b + a))/(b^6*d^3) + 2*(a*b^4*c^2 - 2*a^3*b^2*c + a^5)/((sqrt(d*x + c)*b + a)*b^6*d^3) + 1/6*(3*(d*x + c)^2*b^6*d^9 - 12*(d*x + c)*b^6*c*d^9 - 8*(d*x + c)^(3/2)*a*b^5*d^9 + 48*sqrt(d*x + c)*a*b^5*c*d^9 + 18*(d*x + c)*a^2*b^4*d^9 - 48*sqrt(d*x + c)*a^3*b^3*d^9)/(b^8*d^12)","A",0
641,1,102,0,0.405511," ","integrate(x/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(b^{2} c - 3 \, a^{2}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{4} d} - \frac{{\left(d x + c\right)} b^{2} d - 4 \, \sqrt{d x + c} a b d}{b^{4} d^{2}} + \frac{2 \, {\left(a b^{2} c - a^{3}\right)}}{{\left(\sqrt{d x + c} b + a\right)} b^{4} d}}{d}"," ",0,"-(2*(b^2*c - 3*a^2)*log(abs(sqrt(d*x + c)*b + a))/(b^4*d) - ((d*x + c)*b^2*d - 4*sqrt(d*x + c)*a*b*d)/(b^4*d^2) + 2*(a*b^2*c - a^3)/((sqrt(d*x + c)*b + a)*b^4*d))/d","A",0
642,1,44,0,0.335015," ","integrate(1/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{2 \, \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{2} d} + \frac{2 \, a}{{\left(\sqrt{d x + c} b + a\right)} b^{2} d}"," ",0,"2*log(abs(sqrt(d*x + c)*b + a))/(b^2*d) + 2*a/((sqrt(d*x + c)*b + a)*b^2*d)","A",0
643,1,174,0,0.409953," ","integrate(1/x/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{4 \, a b c \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{{\left(b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}\right)} \sqrt{-c}} + \frac{{\left(b^{2} c + a^{2}\right)} \log\left(-d x\right)}{b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}} - \frac{2 \, {\left(b^{3} c + a^{2} b\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{5} c^{2} - 2 \, a^{2} b^{3} c + a^{4} b} - \frac{2 \, {\left(a b^{2} c - a^{3}\right)}}{{\left(b^{2} c - a^{2}\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}}"," ",0,"-4*a*b*c*arctan(sqrt(d*x + c)/sqrt(-c))/((b^4*c^2 - 2*a^2*b^2*c + a^4)*sqrt(-c)) + (b^2*c + a^2)*log(-d*x)/(b^4*c^2 - 2*a^2*b^2*c + a^4) - 2*(b^3*c + a^2*b)*log(abs(sqrt(d*x + c)*b + a))/(b^5*c^2 - 2*a^2*b^3*c + a^4*b) - 2*(a*b^2*c - a^3)/((b^2*c - a^2)^2*(sqrt(d*x + c)*b + a))","A",0
644,1,311,0,0.412528," ","integrate(1/x^2/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","-\frac{{\left(b^{4} c d + 3 \, a^{2} b^{2} d\right)} \log\left(-d x\right)}{b^{6} c^{3} - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{4} b^{2} c - a^{6}} + \frac{2 \, {\left(b^{5} c d + 3 \, a^{2} b^{3} d\right)} \log\left({\left| -\sqrt{d x + c} b - a \right|}\right)}{b^{7} c^{3} - 3 \, a^{2} b^{5} c^{2} + 3 \, a^{4} b^{3} c - a^{6} b} + \frac{2 \, {\left(3 \, a b^{3} c d + a^{3} b d\right)} \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{{\left(b^{6} c^{3} - 3 \, a^{2} b^{4} c^{2} + 3 \, a^{4} b^{2} c - a^{6}\right)} \sqrt{-c}} - \frac{\sqrt{d x + c} b^{3} c d - 4 \, {\left(d x + c\right)} a b^{2} d + 3 \, a b^{2} c d - \sqrt{d x + c} a^{2} b d + a^{3} d}{{\left(b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}\right)} {\left({\left(d x + c\right)}^{\frac{3}{2}} b - \sqrt{d x + c} b c + {\left(d x + c\right)} a - a c\right)}}"," ",0,"-(b^4*c*d + 3*a^2*b^2*d)*log(-d*x)/(b^6*c^3 - 3*a^2*b^4*c^2 + 3*a^4*b^2*c - a^6) + 2*(b^5*c*d + 3*a^2*b^3*d)*log(abs(-sqrt(d*x + c)*b - a))/(b^7*c^3 - 3*a^2*b^5*c^2 + 3*a^4*b^3*c - a^6*b) + 2*(3*a*b^3*c*d + a^3*b*d)*arctan(sqrt(d*x + c)/sqrt(-c))/((b^6*c^3 - 3*a^2*b^4*c^2 + 3*a^4*b^2*c - a^6)*sqrt(-c)) - (sqrt(d*x + c)*b^3*c*d - 4*(d*x + c)*a*b^2*d + 3*a*b^2*c*d - sqrt(d*x + c)*a^2*b*d + a^3*d)/((b^4*c^2 - 2*a^2*b^2*c + a^4)*((d*x + c)^(3/2)*b - sqrt(d*x + c)*b*c + (d*x + c)*a - a*c))","A",0
645,1,521,0,0.504826," ","integrate(1/x^3/(a+b*(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\frac{{\left(b^{6} c d^{2} + 5 \, a^{2} b^{4} d^{2}\right)} \log\left(-d x\right)}{b^{8} c^{4} - 4 \, a^{2} b^{6} c^{3} + 6 \, a^{4} b^{4} c^{2} - 4 \, a^{6} b^{2} c + a^{8}} - \frac{2 \, {\left(b^{7} c d^{2} + 5 \, a^{2} b^{5} d^{2}\right)} \log\left({\left| \sqrt{d x + c} b + a \right|}\right)}{b^{9} c^{4} - 4 \, a^{2} b^{7} c^{3} + 6 \, a^{4} b^{5} c^{2} - 4 \, a^{6} b^{3} c + a^{8} b} - \frac{{\left(15 \, a b^{5} c^{2} d^{2} + 10 \, a^{3} b^{3} c d^{2} - a^{5} b d^{2}\right)} \arctan\left(\frac{\sqrt{d x + c}}{\sqrt{-c}}\right)}{2 \, {\left(b^{8} c^{5} - 4 \, a^{2} b^{6} c^{4} + 6 \, a^{4} b^{4} c^{3} - 4 \, a^{6} b^{2} c^{2} + a^{8} c\right)} \sqrt{-c}} - \frac{7 \, a b^{6} c^{4} d^{2} - a^{3} b^{4} c^{3} d^{2} - 7 \, a^{5} b^{2} c^{2} d^{2} + a^{7} c d^{2} + {\left(11 \, a b^{6} c^{2} d^{2} - 10 \, a^{3} b^{4} c d^{2} - a^{5} b^{2} d^{2}\right)} {\left(d x + c\right)}^{2} - {\left(2 \, b^{7} c^{3} d^{2} - 3 \, a^{2} b^{5} c^{2} d^{2} + a^{6} b d^{2}\right)} {\left(d x + c\right)}^{\frac{3}{2}} - {\left(19 \, a b^{6} c^{3} d^{2} - 14 \, a^{3} b^{4} c^{2} d^{2} - 5 \, a^{5} b^{2} c d^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(b^{7} c^{4} d^{2} - 2 \, a^{2} b^{5} c^{3} d^{2} + a^{4} b^{3} c^{2} d^{2}\right)} \sqrt{d x + c}}{2 \, {\left(b^{2} c - a^{2}\right)}^{4} {\left(\sqrt{d x + c} b + a\right)} c d^{2} x^{2}}"," ",0,"(b^6*c*d^2 + 5*a^2*b^4*d^2)*log(-d*x)/(b^8*c^4 - 4*a^2*b^6*c^3 + 6*a^4*b^4*c^2 - 4*a^6*b^2*c + a^8) - 2*(b^7*c*d^2 + 5*a^2*b^5*d^2)*log(abs(sqrt(d*x + c)*b + a))/(b^9*c^4 - 4*a^2*b^7*c^3 + 6*a^4*b^5*c^2 - 4*a^6*b^3*c + a^8*b) - 1/2*(15*a*b^5*c^2*d^2 + 10*a^3*b^3*c*d^2 - a^5*b*d^2)*arctan(sqrt(d*x + c)/sqrt(-c))/((b^8*c^5 - 4*a^2*b^6*c^4 + 6*a^4*b^4*c^3 - 4*a^6*b^2*c^2 + a^8*c)*sqrt(-c)) - 1/2*(7*a*b^6*c^4*d^2 - a^3*b^4*c^3*d^2 - 7*a^5*b^2*c^2*d^2 + a^7*c*d^2 + (11*a*b^6*c^2*d^2 - 10*a^3*b^4*c*d^2 - a^5*b^2*d^2)*(d*x + c)^2 - (2*b^7*c^3*d^2 - 3*a^2*b^5*c^2*d^2 + a^6*b*d^2)*(d*x + c)^(3/2) - (19*a*b^6*c^3*d^2 - 14*a^3*b^4*c^2*d^2 - 5*a^5*b^2*c*d^2)*(d*x + c) + 3*(b^7*c^4*d^2 - 2*a^2*b^5*c^3*d^2 + a^4*b^3*c^2*d^2)*sqrt(d*x + c))/((b^2*c - a^2)^4*(sqrt(d*x + c)*b + a)*c*d^2*x^2)","A",0
646,1,409,0,0.417306," ","integrate(x^3/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(15015 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{6} c^{3} - 45045 \, \sqrt{\sqrt{d x + c} b + a} a b^{6} c^{3} - 19305 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} b^{4} c^{2} + 81081 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a b^{4} c^{2} - 135135 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} b^{4} c^{2} + 135135 \, \sqrt{\sqrt{d x + c} b + a} a^{3} b^{4} c^{2} + 12285 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} b^{2} c - 75075 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a b^{2} c + 193050 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{2} b^{2} c - 270270 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{3} b^{2} c + 225225 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{4} b^{2} c - 135135 \, \sqrt{\sqrt{d x + c} b + a} a^{5} b^{2} c - 3003 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{15}{2}} + 24255 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{13}{2}} a - 85995 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} a^{2} + 175175 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a^{3} - 225225 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{4} + 189189 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{5} - 105105 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{6} + 45045 \, \sqrt{\sqrt{d x + c} b + a} a^{7}\right)}}{45045 \, b^{8} d^{4}}"," ",0,"-4/45045*(15015*(sqrt(d*x + c)*b + a)^(3/2)*b^6*c^3 - 45045*sqrt(sqrt(d*x + c)*b + a)*a*b^6*c^3 - 19305*(sqrt(d*x + c)*b + a)^(7/2)*b^4*c^2 + 81081*(sqrt(d*x + c)*b + a)^(5/2)*a*b^4*c^2 - 135135*(sqrt(d*x + c)*b + a)^(3/2)*a^2*b^4*c^2 + 135135*sqrt(sqrt(d*x + c)*b + a)*a^3*b^4*c^2 + 12285*(sqrt(d*x + c)*b + a)^(11/2)*b^2*c - 75075*(sqrt(d*x + c)*b + a)^(9/2)*a*b^2*c + 193050*(sqrt(d*x + c)*b + a)^(7/2)*a^2*b^2*c - 270270*(sqrt(d*x + c)*b + a)^(5/2)*a^3*b^2*c + 225225*(sqrt(d*x + c)*b + a)^(3/2)*a^4*b^2*c - 135135*sqrt(sqrt(d*x + c)*b + a)*a^5*b^2*c - 3003*(sqrt(d*x + c)*b + a)^(15/2) + 24255*(sqrt(d*x + c)*b + a)^(13/2)*a - 85995*(sqrt(d*x + c)*b + a)^(11/2)*a^2 + 175175*(sqrt(d*x + c)*b + a)^(9/2)*a^3 - 225225*(sqrt(d*x + c)*b + a)^(7/2)*a^4 + 189189*(sqrt(d*x + c)*b + a)^(5/2)*a^5 - 105105*(sqrt(d*x + c)*b + a)^(3/2)*a^6 + 45045*sqrt(sqrt(d*x + c)*b + a)*a^7)/(b^8*d^4)","A",0
647,1,238,0,0.325495," ","integrate(x^2/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(1155 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{4} c^{2} - 3465 \, \sqrt{\sqrt{d x + c} b + a} a b^{4} c^{2} - 990 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} b^{2} c + 4158 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a b^{2} c - 6930 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} b^{2} c + 6930 \, \sqrt{\sqrt{d x + c} b + a} a^{3} b^{2} c + 315 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{11}{2}} - 1925 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{9}{2}} a + 4950 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{2} - 6930 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{3} + 5775 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{4} - 3465 \, \sqrt{\sqrt{d x + c} b + a} a^{5}\right)}}{3465 \, b^{6} d^{3}}"," ",0,"4/3465*(1155*(sqrt(d*x + c)*b + a)^(3/2)*b^4*c^2 - 3465*sqrt(sqrt(d*x + c)*b + a)*a*b^4*c^2 - 990*(sqrt(d*x + c)*b + a)^(7/2)*b^2*c + 4158*(sqrt(d*x + c)*b + a)^(5/2)*a*b^2*c - 6930*(sqrt(d*x + c)*b + a)^(3/2)*a^2*b^2*c + 6930*sqrt(sqrt(d*x + c)*b + a)*a^3*b^2*c + 315*(sqrt(d*x + c)*b + a)^(11/2) - 1925*(sqrt(d*x + c)*b + a)^(9/2)*a + 4950*(sqrt(d*x + c)*b + a)^(7/2)*a^2 - 6930*(sqrt(d*x + c)*b + a)^(5/2)*a^3 + 5775*(sqrt(d*x + c)*b + a)^(3/2)*a^4 - 3465*sqrt(sqrt(d*x + c)*b + a)*a^5)/(b^6*d^3)","A",0
648,1,115,0,0.366089," ","integrate(x/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(35 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{2} c - 105 \, \sqrt{\sqrt{d x + c} b + a} a b^{2} c - 15 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} + 63 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a - 105 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} + 105 \, \sqrt{\sqrt{d x + c} b + a} a^{3}\right)}}{105 \, b^{4} d^{2}}"," ",0,"-4/105*(35*(sqrt(d*x + c)*b + a)^(3/2)*b^2*c - 105*sqrt(sqrt(d*x + c)*b + a)*a*b^2*c - 15*(sqrt(d*x + c)*b + a)^(7/2) + 63*(sqrt(d*x + c)*b + a)^(5/2)*a - 105*(sqrt(d*x + c)*b + a)^(3/2)*a^2 + 105*sqrt(sqrt(d*x + c)*b + a)*a^3)/(b^4*d^2)","A",0
649,1,38,0,0.438096," ","integrate(1/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{d x + c} b + a} a\right)}}{3 \, b^{2} d}"," ",0,"4/3*((sqrt(d*x + c)*b + a)^(3/2) - 3*sqrt(sqrt(d*x + c)*b + a)*a)/(b^2*d)","A",0
650,1,140,0,0.502207," ","integrate(1/x/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(b^{2} \sqrt{c} {\left| b \right|} + a b^{2}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-a + \sqrt{b^{2} c}}}\right)}{{\left(b \sqrt{c} + a\right)} \sqrt{b \sqrt{c} - a}} + \frac{{\left(b^{2} \sqrt{c} {\left| b \right|} - a b^{2}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-a - \sqrt{b^{2} c}}}\right)}{{\left(b \sqrt{c} - a\right)} \sqrt{-b \sqrt{c} - a}}\right)}}{b^{2}}"," ",0,"2*((b^2*sqrt(c)*abs(b) + a*b^2)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-a + sqrt(b^2*c)))/((b*sqrt(c) + a)*sqrt(b*sqrt(c) - a)) + (b^2*sqrt(c)*abs(b) - a*b^2)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-a - sqrt(b^2*c)))/((b*sqrt(c) - a)*sqrt(-b*sqrt(c) - a)))/b^2","A",0
651,1,654,0,0.756599," ","integrate(1/x^2/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(b^{3} c - a^{2} b\right)}^{2} b^{4} c^{\frac{3}{2}} d^{2} - 2 \, {\left(a b^{6} c^{2} - a^{3} b^{4} c\right)} d^{2} {\left| -b^{3} c + a^{2} b \right|} + {\left(a^{2} b^{8} c^{\frac{5}{2}} - 2 \, a^{4} b^{6} c^{\frac{3}{2}} + a^{6} b^{4} \sqrt{c}\right)} d^{2}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-\frac{a b^{2} c - a^{3} + \sqrt{{\left(a b^{2} c - a^{3}\right)}^{2} + {\left(b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}\right)} {\left(b^{2} c - a^{2}\right)}}}{b^{2} c - a^{2}}}}\right)}{{\left(b^{5} c^{\frac{7}{2}} + a b^{4} c^{3} - 2 \, a^{2} b^{3} c^{\frac{5}{2}} - 2 \, a^{3} b^{2} c^{2} + a^{4} b c^{\frac{3}{2}} + a^{5} c\right)} \sqrt{b \sqrt{c} - a} {\left| -b^{3} c + a^{2} b \right|}} + \frac{{\left({\left(b^{3} c - a^{2} b\right)}^{2} b^{4} c^{\frac{3}{2}} d^{2} + 2 \, {\left(a b^{6} c^{2} - a^{3} b^{4} c\right)} d^{2} {\left| -b^{3} c + a^{2} b \right|} + {\left(a^{2} b^{8} c^{\frac{5}{2}} - 2 \, a^{4} b^{6} c^{\frac{3}{2}} + a^{6} b^{4} \sqrt{c}\right)} d^{2}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-\frac{a b^{2} c - a^{3} - \sqrt{{\left(a b^{2} c - a^{3}\right)}^{2} + {\left(b^{4} c^{2} - 2 \, a^{2} b^{2} c + a^{4}\right)} {\left(b^{2} c - a^{2}\right)}}}{b^{2} c - a^{2}}}}\right)}{{\left(b^{5} c^{\frac{7}{2}} - a b^{4} c^{3} - 2 \, a^{2} b^{3} c^{\frac{5}{2}} + 2 \, a^{3} b^{2} c^{2} + a^{4} b c^{\frac{3}{2}} - a^{5} c\right)} \sqrt{-b \sqrt{c} - a} {\left| -b^{3} c + a^{2} b \right|}} + \frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{4} d^{2} - 2 \, \sqrt{\sqrt{d x + c} b + a} a b^{4} d^{2}\right)}}{{\left(b^{2} c - {\left(\sqrt{d x + c} b + a\right)}^{2} + 2 \, {\left(\sqrt{d x + c} b + a\right)} a - a^{2}\right)} {\left(b^{2} c - a^{2}\right)}}}{2 \, b^{2} d}"," ",0,"1/2*(((b^3*c - a^2*b)^2*b^4*c^(3/2)*d^2 - 2*(a*b^6*c^2 - a^3*b^4*c)*d^2*abs(-b^3*c + a^2*b) + (a^2*b^8*c^(5/2) - 2*a^4*b^6*c^(3/2) + a^6*b^4*sqrt(c))*d^2)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-(a*b^2*c - a^3 + sqrt((a*b^2*c - a^3)^2 + (b^4*c^2 - 2*a^2*b^2*c + a^4)*(b^2*c - a^2)))/(b^2*c - a^2)))/((b^5*c^(7/2) + a*b^4*c^3 - 2*a^2*b^3*c^(5/2) - 2*a^3*b^2*c^2 + a^4*b*c^(3/2) + a^5*c)*sqrt(b*sqrt(c) - a)*abs(-b^3*c + a^2*b)) + ((b^3*c - a^2*b)^2*b^4*c^(3/2)*d^2 + 2*(a*b^6*c^2 - a^3*b^4*c)*d^2*abs(-b^3*c + a^2*b) + (a^2*b^8*c^(5/2) - 2*a^4*b^6*c^(3/2) + a^6*b^4*sqrt(c))*d^2)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-(a*b^2*c - a^3 - sqrt((a*b^2*c - a^3)^2 + (b^4*c^2 - 2*a^2*b^2*c + a^4)*(b^2*c - a^2)))/(b^2*c - a^2)))/((b^5*c^(7/2) - a*b^4*c^3 - 2*a^2*b^3*c^(5/2) + 2*a^3*b^2*c^2 + a^4*b*c^(3/2) - a^5*c)*sqrt(-b*sqrt(c) - a)*abs(-b^3*c + a^2*b)) + 2*((sqrt(d*x + c)*b + a)^(3/2)*b^4*d^2 - 2*sqrt(sqrt(d*x + c)*b + a)*a*b^4*d^2)/((b^2*c - (sqrt(d*x + c)*b + a)^2 + 2*(sqrt(d*x + c)*b + a)*a - a^2)*(b^2*c - a^2)))/(b^2*d)","B",0
652,1,1303,0,1.271473," ","integrate(1/x^3/(a+b*(d*x+c)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left({\left(b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} + a^{4} b c\right)}^{2} {\left(5 \, b^{6} c + a^{2} b^{4}\right)} d^{3} - {\left(13 \, a b^{10} c^{\frac{7}{2}} - 27 \, a^{3} b^{8} c^{\frac{5}{2}} + 15 \, a^{5} b^{6} c^{\frac{3}{2}} - a^{7} b^{4} \sqrt{c}\right)} d^{3} {\left| b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} + a^{4} b c \right|} + 2 \, {\left(4 \, a^{2} b^{14} c^{6} - 17 \, a^{4} b^{12} c^{5} + 28 \, a^{6} b^{10} c^{4} - 22 \, a^{8} b^{8} c^{3} + 8 \, a^{10} b^{6} c^{2} - a^{12} b^{4} c\right)} d^{3}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-\frac{a b^{4} c^{3} - 2 \, a^{3} b^{2} c^{2} + a^{5} c + \sqrt{{\left(a b^{4} c^{3} - 2 \, a^{3} b^{2} c^{2} + a^{5} c\right)}^{2} + {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)}}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}}}\right)}{{\left(b^{9} c^{6} - a b^{8} c^{\frac{11}{2}} - 4 \, a^{2} b^{7} c^{5} + 4 \, a^{3} b^{6} c^{\frac{9}{2}} + 6 \, a^{4} b^{5} c^{4} - 6 \, a^{5} b^{4} c^{\frac{7}{2}} - 4 \, a^{6} b^{3} c^{3} + 4 \, a^{7} b^{2} c^{\frac{5}{2}} + a^{8} b c^{2} - a^{9} c^{\frac{3}{2}}\right)} \sqrt{-b \sqrt{c} - a} {\left| b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} + a^{4} b c \right|}} + \frac{{\left({\left(b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} + a^{4} b c\right)}^{2} {\left(5 \, b^{6} c + a^{2} b^{4}\right)} d^{3} + {\left(13 \, a b^{10} c^{\frac{7}{2}} - 27 \, a^{3} b^{8} c^{\frac{5}{2}} + 15 \, a^{5} b^{6} c^{\frac{3}{2}} - a^{7} b^{4} \sqrt{c}\right)} d^{3} {\left| b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} + a^{4} b c \right|} + 2 \, {\left(4 \, a^{2} b^{14} c^{6} - 17 \, a^{4} b^{12} c^{5} + 28 \, a^{6} b^{10} c^{4} - 22 \, a^{8} b^{8} c^{3} + 8 \, a^{10} b^{6} c^{2} - a^{12} b^{4} c\right)} d^{3}\right)} \arctan\left(\frac{\sqrt{\sqrt{d x + c} b + a}}{\sqrt{-\frac{a b^{4} c^{3} - 2 \, a^{3} b^{2} c^{2} + a^{5} c - \sqrt{{\left(a b^{4} c^{3} - 2 \, a^{3} b^{2} c^{2} + a^{5} c\right)}^{2} + {\left(b^{6} c^{4} - 3 \, a^{2} b^{4} c^{3} + 3 \, a^{4} b^{2} c^{2} - a^{6} c\right)} {\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)}}}{b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c}}}\right)}{{\left(b^{9} c^{6} + a b^{8} c^{\frac{11}{2}} - 4 \, a^{2} b^{7} c^{5} - 4 \, a^{3} b^{6} c^{\frac{9}{2}} + 6 \, a^{4} b^{5} c^{4} + 6 \, a^{5} b^{4} c^{\frac{7}{2}} - 4 \, a^{6} b^{3} c^{3} - 4 \, a^{7} b^{2} c^{\frac{5}{2}} + a^{8} b c^{2} + a^{9} c^{\frac{3}{2}}\right)} \sqrt{b \sqrt{c} - a} {\left| b^{5} c^{3} - 2 \, a^{2} b^{3} c^{2} + a^{4} b c \right|}} - \frac{2 \, {\left(9 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} b^{8} c^{2} d^{3} - 19 \, \sqrt{\sqrt{d x + c} b + a} a b^{8} c^{2} d^{3} - 5 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} b^{6} c d^{3} + 21 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a b^{6} c d^{3} - 30 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{2} b^{6} c d^{3} + 18 \, \sqrt{\sqrt{d x + c} b + a} a^{3} b^{6} c d^{3} - {\left(\sqrt{d x + c} b + a\right)}^{\frac{7}{2}} a^{2} b^{4} d^{3} + 3 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{5}{2}} a^{3} b^{4} d^{3} - 3 \, {\left(\sqrt{d x + c} b + a\right)}^{\frac{3}{2}} a^{4} b^{4} d^{3} + \sqrt{\sqrt{d x + c} b + a} a^{5} b^{4} d^{3}\right)}}{{\left(b^{4} c^{3} - 2 \, a^{2} b^{2} c^{2} + a^{4} c\right)} {\left(b^{2} c - {\left(\sqrt{d x + c} b + a\right)}^{2} + 2 \, {\left(\sqrt{d x + c} b + a\right)} a - a^{2}\right)}^{2}}}{16 \, b^{2} d}"," ",0,"1/16*(((b^5*c^3 - 2*a^2*b^3*c^2 + a^4*b*c)^2*(5*b^6*c + a^2*b^4)*d^3 - (13*a*b^10*c^(7/2) - 27*a^3*b^8*c^(5/2) + 15*a^5*b^6*c^(3/2) - a^7*b^4*sqrt(c))*d^3*abs(b^5*c^3 - 2*a^2*b^3*c^2 + a^4*b*c) + 2*(4*a^2*b^14*c^6 - 17*a^4*b^12*c^5 + 28*a^6*b^10*c^4 - 22*a^8*b^8*c^3 + 8*a^10*b^6*c^2 - a^12*b^4*c)*d^3)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-(a*b^4*c^3 - 2*a^3*b^2*c^2 + a^5*c + sqrt((a*b^4*c^3 - 2*a^3*b^2*c^2 + a^5*c)^2 + (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)))/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)))/((b^9*c^6 - a*b^8*c^(11/2) - 4*a^2*b^7*c^5 + 4*a^3*b^6*c^(9/2) + 6*a^4*b^5*c^4 - 6*a^5*b^4*c^(7/2) - 4*a^6*b^3*c^3 + 4*a^7*b^2*c^(5/2) + a^8*b*c^2 - a^9*c^(3/2))*sqrt(-b*sqrt(c) - a)*abs(b^5*c^3 - 2*a^2*b^3*c^2 + a^4*b*c)) + ((b^5*c^3 - 2*a^2*b^3*c^2 + a^4*b*c)^2*(5*b^6*c + a^2*b^4)*d^3 + (13*a*b^10*c^(7/2) - 27*a^3*b^8*c^(5/2) + 15*a^5*b^6*c^(3/2) - a^7*b^4*sqrt(c))*d^3*abs(b^5*c^3 - 2*a^2*b^3*c^2 + a^4*b*c) + 2*(4*a^2*b^14*c^6 - 17*a^4*b^12*c^5 + 28*a^6*b^10*c^4 - 22*a^8*b^8*c^3 + 8*a^10*b^6*c^2 - a^12*b^4*c)*d^3)*arctan(sqrt(sqrt(d*x + c)*b + a)/sqrt(-(a*b^4*c^3 - 2*a^3*b^2*c^2 + a^5*c - sqrt((a*b^4*c^3 - 2*a^3*b^2*c^2 + a^5*c)^2 + (b^6*c^4 - 3*a^2*b^4*c^3 + 3*a^4*b^2*c^2 - a^6*c)*(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)))/(b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)))/((b^9*c^6 + a*b^8*c^(11/2) - 4*a^2*b^7*c^5 - 4*a^3*b^6*c^(9/2) + 6*a^4*b^5*c^4 + 6*a^5*b^4*c^(7/2) - 4*a^6*b^3*c^3 - 4*a^7*b^2*c^(5/2) + a^8*b*c^2 + a^9*c^(3/2))*sqrt(b*sqrt(c) - a)*abs(b^5*c^3 - 2*a^2*b^3*c^2 + a^4*b*c)) - 2*(9*(sqrt(d*x + c)*b + a)^(3/2)*b^8*c^2*d^3 - 19*sqrt(sqrt(d*x + c)*b + a)*a*b^8*c^2*d^3 - 5*(sqrt(d*x + c)*b + a)^(7/2)*b^6*c*d^3 + 21*(sqrt(d*x + c)*b + a)^(5/2)*a*b^6*c*d^3 - 30*(sqrt(d*x + c)*b + a)^(3/2)*a^2*b^6*c*d^3 + 18*sqrt(sqrt(d*x + c)*b + a)*a^3*b^6*c*d^3 - (sqrt(d*x + c)*b + a)^(7/2)*a^2*b^4*d^3 + 3*(sqrt(d*x + c)*b + a)^(5/2)*a^3*b^4*d^3 - 3*(sqrt(d*x + c)*b + a)^(3/2)*a^4*b^4*d^3 + sqrt(sqrt(d*x + c)*b + a)*a^5*b^4*d^3)/((b^4*c^3 - 2*a^2*b^2*c^2 + a^4*c)*(b^2*c - (sqrt(d*x + c)*b + a)^2 + 2*(sqrt(d*x + c)*b + a)*a - a^2)^2))/(b^2*d)","B",0
653,1,5699,0,0.967703," ","integrate(x^3*(a+b*(d*x+c)^(1/2))^p,x, algorithm=""giac"")","-\frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p^{7} - {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p^{7} + 34 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p^{6} - 35 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p^{6} - 3 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{7} + 9 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{7} - 9 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p^{7} + 3 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p^{7} + 478 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p^{5} - 511 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p^{5} - 96 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{6} + 297 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{6} - 306 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p^{6} + 105 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p^{6} + 3 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{7} - 15 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{7} + 30 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{7} - 30 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{7} + 15 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p^{7} - 3 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p^{7} + 3580 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p^{4} - 4025 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p^{4} - 1254 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{5} + 4023 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{5} - 4302 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p^{5} + 1533 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p^{5} + 90 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{6} - 465 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{6} + 960 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{6} - 990 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{6} + 510 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p^{6} - 105 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p^{6} - {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{7} + 7 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{7} - 21 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{7} + 35 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{7} - 35 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{7} + 21 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{7} - 7 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p^{7} + {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p^{7} + 15289 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p^{3} - 18424 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p^{3} - 8592 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{4} + 28755 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{4} - 32220 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p^{4} + 12075 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p^{4} + 1098 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{5} - 5865 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{5} + 12540 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{5} - 13410 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{5} + 7170 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p^{5} - 1533 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p^{5} - 28 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{6} + 203 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{6} - 630 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{6} + 1085 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{6} - 1120 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{6} + 693 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{6} - 238 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p^{6} + 35 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p^{6} + 36706 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p^{2} - 48860 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p^{2} - 32979 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{3} + 115776 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{3} - 137601 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p^{3} + 55272 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p^{3} + 7020 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{4} - 38715 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{4} + 85920 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{4} - 95850 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{4} + 53700 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p^{4} - 12075 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p^{4} - 322 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{5} + 2401 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{5} - 7686 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{5} + 13685 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{5} - 14630 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{5} + 9387 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{5} - 3346 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p^{5} + 511 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p^{5} + 44712 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} p - 69264 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} p - 69936 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{2} + 258228 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{2} - 330354 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p^{2} + 146580 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p^{2} + 25227 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{3} - 143160 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{3} + 329790 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{3} - 385920 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{3} + 229335 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p^{3} - 55272 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p^{3} - 1960 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{4} + 14945 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{4} - 49140 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{4} + 90335 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{4} - 100240 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{4} + 67095 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{4} - 25060 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p^{4} + 4025 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p^{4} + 20160 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{6} c^{3} - 40320 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{6} c^{3} - 74628 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p + 288432 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p - 402408 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} p + 207792 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} p + 50490 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{2} - 293460 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{2} + 699360 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{2} - 860760 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{2} + 550590 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p^{2} - 146580 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p^{2} - 6769 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{3} + 52528 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{3} - 176589 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{3} + 334040 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{3} - 384755 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{3} + 270144 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{3} - 107023 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p^{3} + 18424 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p^{3} - 30240 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} + 120960 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} - 181440 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{4} c^{2} + 120960 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{4} c^{2} + 51432 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p - 304560 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p + 746280 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p - 961440 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p + 670680 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c p - 207792 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c p - 13132 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{2} + 103292 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{2} - 353430 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{2} + 684740 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{2} - 815920 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{2} + 602532 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{2} - 256942 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p^{2} + 48860 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p^{2} + 20160 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c - 120960 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c + 302400 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c - 403200 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c + 302400 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} b^{2} c - 120960 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} b^{2} c - 13068 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} p + 103824 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a p - 360024 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p + 710640 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p - 870660 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p + 673008 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p - 312984 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} p + 69264 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7} p - 5040 \, {\left(\sqrt{d x + c} b + a\right)}^{8} {\left(\sqrt{d x + c} b + a\right)}^{p} + 40320 \, {\left(\sqrt{d x + c} b + a\right)}^{7} {\left(\sqrt{d x + c} b + a\right)}^{p} a - 141120 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} + 282240 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} - 352800 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} + 282240 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} - 141120 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{6} + 40320 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{7}\right)}}{{\left(b^{6} d^{3} p^{8} + 36 \, b^{6} d^{3} p^{7} + 546 \, b^{6} d^{3} p^{6} + 4536 \, b^{6} d^{3} p^{5} + 22449 \, b^{6} d^{3} p^{4} + 67284 \, b^{6} d^{3} p^{3} + 118124 \, b^{6} d^{3} p^{2} + 109584 \, b^{6} d^{3} p + 40320 \, b^{6} d^{3}\right)} b^{2} d}"," ",0,"-2*((sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p^7 - (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p^7 + 34*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p^6 - 35*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p^6 - 3*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^7 + 9*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^7 - 9*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p^7 + 3*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p^7 + 478*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p^5 - 511*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p^5 - 96*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^6 + 297*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^6 - 306*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p^6 + 105*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p^6 + 3*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p^7 - 15*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^7 + 30*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^7 - 30*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^7 + 15*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p^7 - 3*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p^7 + 3580*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p^4 - 4025*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p^4 - 1254*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^5 + 4023*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^5 - 4302*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p^5 + 1533*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p^5 + 90*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p^6 - 465*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^6 + 960*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^6 - 990*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^6 + 510*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p^6 - 105*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p^6 - (sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p^7 + 7*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p^7 - 21*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p^7 + 35*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p^7 - 35*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p^7 + 21*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p^7 - 7*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p^7 + (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p^7 + 15289*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p^3 - 18424*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p^3 - 8592*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^4 + 28755*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^4 - 32220*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p^4 + 12075*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p^4 + 1098*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p^5 - 5865*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^5 + 12540*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^5 - 13410*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^5 + 7170*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p^5 - 1533*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p^5 - 28*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p^6 + 203*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p^6 - 630*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p^6 + 1085*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p^6 - 1120*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p^6 + 693*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p^6 - 238*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p^6 + 35*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p^6 + 36706*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p^2 - 48860*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p^2 - 32979*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^3 + 115776*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^3 - 137601*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p^3 + 55272*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p^3 + 7020*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p^4 - 38715*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^4 + 85920*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^4 - 95850*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^4 + 53700*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p^4 - 12075*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p^4 - 322*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p^5 + 2401*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p^5 - 7686*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p^5 + 13685*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p^5 - 14630*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p^5 + 9387*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p^5 - 3346*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p^5 + 511*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p^5 + 44712*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3*p - 69264*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3*p - 69936*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^2 + 258228*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^2 - 330354*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p^2 + 146580*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p^2 + 25227*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p^3 - 143160*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^3 + 329790*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^3 - 385920*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^3 + 229335*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p^3 - 55272*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p^3 - 1960*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p^4 + 14945*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p^4 - 49140*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p^4 + 90335*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p^4 - 100240*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p^4 + 67095*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p^4 - 25060*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p^4 + 4025*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p^4 + 20160*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^6*c^3 - 40320*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^6*c^3 - 74628*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p + 288432*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p - 402408*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2*p + 207792*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2*p + 50490*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p^2 - 293460*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^2 + 699360*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^2 - 860760*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^2 + 550590*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p^2 - 146580*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p^2 - 6769*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p^3 + 52528*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p^3 - 176589*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p^3 + 334040*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p^3 - 384755*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p^3 + 270144*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p^3 - 107023*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p^3 + 18424*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p^3 - 30240*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^4*c^2 + 120960*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2 - 181440*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^4*c^2 + 120960*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^4*c^2 + 51432*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c*p - 304560*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p + 746280*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p - 961440*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p + 670680*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c*p - 207792*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c*p - 13132*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p^2 + 103292*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p^2 - 353430*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p^2 + 684740*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p^2 - 815920*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p^2 + 602532*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p^2 - 256942*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p^2 + 48860*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p^2 + 20160*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*b^2*c - 120960*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*b^2*c + 302400*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c - 403200*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c + 302400*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*b^2*c - 120960*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*b^2*c - 13068*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p*p + 103824*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a*p - 360024*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2*p + 710640*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3*p - 870660*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4*p + 673008*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5*p - 312984*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6*p + 69264*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7*p - 5040*(sqrt(d*x + c)*b + a)^8*(sqrt(d*x + c)*b + a)^p + 40320*(sqrt(d*x + c)*b + a)^7*(sqrt(d*x + c)*b + a)^p*a - 141120*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*a^2 + 282240*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a^3 - 352800*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^4 + 282240*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^5 - 141120*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^6 + 40320*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^7)/((b^6*d^3*p^8 + 36*b^6*d^3*p^7 + 546*b^6*d^3*p^6 + 4536*b^6*d^3*p^5 + 22449*b^6*d^3*p^4 + 67284*b^6*d^3*p^3 + 118124*b^6*d^3*p^2 + 109584*b^6*d^3*p + 40320*b^6*d^3)*b^2*d)","B",0
654,1,2511,0,0.587108," ","integrate(x^2*(a+b*(d*x+c)^(1/2))^p,x, algorithm=""giac"")","\frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{5} - {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{5} + 19 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{4} - 20 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{4} - 2 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{5} + 6 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{5} - 6 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{5} + 2 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{5} + 137 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{3} - 155 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{3} - 34 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{4} + 108 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{4} - 114 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{4} + 40 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{4} + {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{5} - 5 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{5} + 10 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{5} - 10 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{5} + 5 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{5} - {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{5} + 461 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p^{2} - 580 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p^{2} - 214 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{3} + 726 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{3} - 822 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{3} + 310 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{3} + 15 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{4} - 80 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{4} + 170 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{4} - 180 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{4} + 95 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{4} - 20 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{4} + 702 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} p - 1044 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} p - 614 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{2} + 2232 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{2} - 2766 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p^{2} + 1160 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p^{2} + 85 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{3} - 475 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{3} + 1070 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{3} - 1210 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{3} + 685 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{3} - 155 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{3} + 360 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{4} c^{2} - 720 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{4} c^{2} - 792 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p + 3048 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p - 4212 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c p + 2088 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c p + 225 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{2} - 1300 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{2} + 3070 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{2} - 3720 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{2} + 2305 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p^{2} - 580 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p^{2} - 360 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c + 1440 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c - 2160 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} b^{2} c + 1440 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} b^{2} c + 274 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} p - 1620 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a p + 3960 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p - 5080 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p + 3510 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} p - 1044 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5} p + 120 \, {\left(\sqrt{d x + c} b + a\right)}^{6} {\left(\sqrt{d x + c} b + a\right)}^{p} - 720 \, {\left(\sqrt{d x + c} b + a\right)}^{5} {\left(\sqrt{d x + c} b + a\right)}^{p} a + 1800 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} - 2400 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} + 1800 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{4} - 720 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{5}\right)}}{{\left(b^{4} d^{2} p^{6} + 21 \, b^{4} d^{2} p^{5} + 175 \, b^{4} d^{2} p^{4} + 735 \, b^{4} d^{2} p^{3} + 1624 \, b^{4} d^{2} p^{2} + 1764 \, b^{4} d^{2} p + 720 \, b^{4} d^{2}\right)} b^{2} d}"," ",0,"2*((sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^5 - (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^5 + 19*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^4 - 20*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^4 - 2*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^2*c*p^5 + 6*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^5 - 6*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^5 + 2*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^5 + 137*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^3 - 155*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^3 - 34*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^2*c*p^4 + 108*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^4 - 114*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^4 + 40*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^4 + (sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*p^5 - 5*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*p^5 + 10*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*p^5 - 10*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*p^5 + 5*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*p^5 - (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*p^5 + 461*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p^2 - 580*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p^2 - 214*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^2*c*p^3 + 726*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^3 - 822*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^3 + 310*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^3 + 15*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*p^4 - 80*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*p^4 + 170*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*p^4 - 180*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*p^4 + 95*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*p^4 - 20*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*p^4 + 702*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^4*c^2*p - 1044*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2*p - 614*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^2*c*p^2 + 2232*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^2 - 2766*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p^2 + 1160*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p^2 + 85*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*p^3 - 475*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*p^3 + 1070*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*p^3 - 1210*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*p^3 + 685*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*p^3 - 155*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*p^3 + 360*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^4*c^2 - 720*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^4*c^2 - 792*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^2*c*p + 3048*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p - 4212*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c*p + 2088*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c*p + 225*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*p^2 - 1300*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*p^2 + 3070*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*p^2 - 3720*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*p^2 + 2305*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*p^2 - 580*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*p^2 - 360*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*b^2*c + 1440*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*b^2*c - 2160*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*b^2*c + 1440*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*b^2*c + 274*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p*p - 1620*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a*p + 3960*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2*p - 5080*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3*p + 3510*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4*p - 1044*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5*p + 120*(sqrt(d*x + c)*b + a)^6*(sqrt(d*x + c)*b + a)^p - 720*(sqrt(d*x + c)*b + a)^5*(sqrt(d*x + c)*b + a)^p*a + 1800*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*a^2 - 2400*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a^3 + 1800*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^4 - 720*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^5)/((b^4*d^2*p^6 + 21*b^4*d^2*p^5 + 175*b^4*d^2*p^4 + 735*b^4*d^2*p^3 + 1624*b^4*d^2*p^2 + 1764*b^4*d^2*p + 720*b^4*d^2)*b^2*d)","B",0
655,1,806,0,0.443831," ","integrate(x*(a+b*(d*x+c)^(1/2))^p,x, algorithm=""giac"")","-\frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{3} - {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{3} + 8 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p^{2} - 9 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p^{2} - {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{3} + 3 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{3} - 3 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{3} + {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{3} + 19 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c p - 26 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c p - 6 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} p^{2} + 21 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a p^{2} - 24 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p^{2} + 9 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p^{2} + 12 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} b^{2} c - 24 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a b^{2} c - 11 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} p + 42 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a p - 57 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} p + 26 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3} p - 6 \, {\left(\sqrt{d x + c} b + a\right)}^{4} {\left(\sqrt{d x + c} b + a\right)}^{p} + 24 \, {\left(\sqrt{d x + c} b + a\right)}^{3} {\left(\sqrt{d x + c} b + a\right)}^{p} a - 36 \, {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{2} + 24 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a^{3}\right)}}{{\left(b^{2} p^{4} + 10 \, b^{2} p^{3} + 35 \, b^{2} p^{2} + 50 \, b^{2} p + 24 \, b^{2}\right)} b^{2} d^{2}}"," ",0,"-2*((sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^2*c*p^3 - (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^3 + 8*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^2*c*p^2 - 9*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p^2 - (sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*p^3 + 3*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*p^3 - 3*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*p^3 + (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*p^3 + 19*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^2*c*p - 26*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^2*c*p - 6*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*p^2 + 21*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*p^2 - 24*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*p^2 + 9*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*p^2 + 12*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*b^2*c - 24*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*b^2*c - 11*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p*p + 42*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a*p - 57*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2*p + 26*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3*p - 6*(sqrt(d*x + c)*b + a)^4*(sqrt(d*x + c)*b + a)^p + 24*(sqrt(d*x + c)*b + a)^3*(sqrt(d*x + c)*b + a)^p*a - 36*(sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*a^2 + 24*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a^3)/((b^2*p^4 + 10*b^2*p^3 + 35*b^2*p^2 + 50*b^2*p + 24*b^2)*b^2*d^2)","B",0
656,1,129,0,0.438633," ","integrate((a+b*(d*x+c)^(1/2))^p,x, algorithm=""giac"")","\frac{2 \, {\left({\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} p - {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a p + {\left(\sqrt{d x + c} b + a\right)}^{2} {\left(\sqrt{d x + c} b + a\right)}^{p} - 2 \, {\left(\sqrt{d x + c} b + a\right)} {\left(\sqrt{d x + c} b + a\right)}^{p} a\right)}}{{\left(p^{2} + 3 \, p + 2\right)} b^{2} d}"," ",0,"2*((sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p*p - (sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a*p + (sqrt(d*x + c)*b + a)^2*(sqrt(d*x + c)*b + a)^p - 2*(sqrt(d*x + c)*b + a)*(sqrt(d*x + c)*b + a)^p*a)/((p^2 + 3*p + 2)*b^2*d)","B",0
657,0,0,0,0.000000," ","integrate((a+b*(d*x+c)^(1/2))^p/x,x, algorithm=""giac"")","\int \frac{{\left(\sqrt{d x + c} b + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((sqrt(d*x + c)*b + a)^p/x, x)","F",0
658,0,0,0,0.000000," ","integrate((a+b*(c*x)^n)^(5/2)/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x\right)^{n} b + a\right)}^{\frac{5}{2}}}{x}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^(5/2)/x, x)","F",0
659,0,0,0,0.000000," ","integrate((a+b*(c*x)^n)^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x\right)^{n} b + a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(((c*x)^n*b + a)^(3/2)/x, x)","F",0
660,0,0,0,0.000000," ","integrate((a+b*(c*x)^n)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x\right)^{n} b + a}}{x}\,{d x}"," ",0,"integrate(sqrt((c*x)^n*b + a)/x, x)","F",0
661,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x)^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\left(c x\right)^{n} b + a} x}\,{d x}"," ",0,"integrate(1/(sqrt((c*x)^n*b + a)*x), x)","F",0
662,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x)^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x\right)^{n} b + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/(((c*x)^n*b + a)^(3/2)*x), x)","F",0
663,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x)^n)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x\right)^{n} b + a\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(1/(((c*x)^n*b + a)^(5/2)*x), x)","F",0
664,0,0,0,0.000000," ","integrate((-a+b*(c*x)^n)^(5/2)/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x\right)^{n} b - a\right)}^{\frac{5}{2}}}{x}\,{d x}"," ",0,"integrate(((c*x)^n*b - a)^(5/2)/x, x)","F",0
665,0,0,0,0.000000," ","integrate((-a+b*(c*x)^n)^(3/2)/x,x, algorithm=""giac"")","\int \frac{{\left(\left(c x\right)^{n} b - a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(((c*x)^n*b - a)^(3/2)/x, x)","F",0
666,0,0,0,0.000000," ","integrate((-a+b*(c*x)^n)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{\left(c x\right)^{n} b - a}}{x}\,{d x}"," ",0,"integrate(sqrt((c*x)^n*b - a)/x, x)","F",0
667,0,0,0,0.000000," ","integrate(1/x/(-a+b*(c*x)^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\left(c x\right)^{n} b - a} x}\,{d x}"," ",0,"integrate(1/(sqrt((c*x)^n*b - a)*x), x)","F",0
668,0,0,0,0.000000," ","integrate(1/x/(-a+b*(c*x)^n)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x\right)^{n} b - a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/(((c*x)^n*b - a)^(3/2)*x), x)","F",0
669,0,0,0,0.000000," ","integrate(1/x/(-a+b*(c*x)^n)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\left(c x\right)^{n} b - a\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(1/(((c*x)^n*b - a)^(5/2)*x), x)","F",0
670,1,21,0,0.407332," ","integrate(1/x/(b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{b x + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}"," ",0,"2*arctan(sqrt(b*x + a)/sqrt(-a))/sqrt(-a)","A",0
671,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*x)^m)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\left(c x\right)^{m} b + a} x}\,{d x}"," ",0,"integrate(1/(sqrt((c*x)^m*b + a)*x), x)","F",0
672,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*(d*x)^m)^n)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\left(\left(d x\right)^{m} c\right)^{n} b + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(((d*x)^m*c)^n*b + a)*x), x)","F",0
673,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*(d*(e*x)^m)^n)^p)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\left(\left(\left(e x\right)^{m} d\right)^{n} c\right)^{p} b + a} x}\,{d x}"," ",0,"integrate(1/(sqrt((((e*x)^m*d)^n*c)^p*b + a)*x), x)","F",0
674,0,0,0,0.000000," ","integrate(1/x/(a+b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\left(\left(\left(\left(f x\right)^{m} e\right)^{n} d\right)^{p} c\right)^{q} b + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(((((f*x)^m*e)^n*d)^p*c)^q*b + a)*x), x)","F",0
675,1,77,0,0.391145," ","integrate((x^2-1)^3*(-1+1/x^2)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, x^{2} \mathrm{sgn}\left(x\right) - 19 \, \mathrm{sgn}\left(x\right)\right)} x^{2} + 87 \, \mathrm{sgn}\left(x\right)\right)} \sqrt{-x^{2} + 1} x + \frac{35}{16} \, \arcsin\left(x\right) \mathrm{sgn}\left(x\right) - \frac{x \mathrm{sgn}\left(x\right)}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)} \mathrm{sgn}\left(x\right)}{2 \, x}"," ",0,"1/48*(2*(4*x^2*sgn(x) - 19*sgn(x))*x^2 + 87*sgn(x))*sqrt(-x^2 + 1)*x + 35/16*arcsin(x)*sgn(x) - 1/2*x*sgn(x)/(sqrt(-x^2 + 1) - 1) + 1/2*(sqrt(-x^2 + 1) - 1)*sgn(x)/x","A",0
676,1,67,0,0.425345," ","integrate((x^2-1)^2*(-1+1/x^2)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, x^{2} \mathrm{sgn}\left(x\right) - 9 \, \mathrm{sgn}\left(x\right)\right)} \sqrt{-x^{2} + 1} x - \frac{15}{8} \, \arcsin\left(x\right) \mathrm{sgn}\left(x\right) + \frac{x \mathrm{sgn}\left(x\right)}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} - \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)} \mathrm{sgn}\left(x\right)}{2 \, x}"," ",0,"1/8*(2*x^2*sgn(x) - 9*sgn(x))*sqrt(-x^2 + 1)*x - 15/8*arcsin(x)*sgn(x) + 1/2*x*sgn(x)/(sqrt(-x^2 + 1) - 1) - 1/2*(sqrt(-x^2 + 1) - 1)*sgn(x)/x","A",0
677,1,57,0,0.383958," ","integrate((x^2-1)*(-1+1/x^2)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x \mathrm{sgn}\left(x\right) + \frac{3}{2} \, \arcsin\left(x\right) \mathrm{sgn}\left(x\right) - \frac{x \mathrm{sgn}\left(x\right)}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)} \mathrm{sgn}\left(x\right)}{2 \, x}"," ",0,"1/2*sqrt(-x^2 + 1)*x*sgn(x) + 3/2*arcsin(x)*sgn(x) - 1/2*x*sgn(x)/(sqrt(-x^2 + 1) - 1) + 1/2*(sqrt(-x^2 + 1) - 1)*sgn(x)/x","A",0
678,1,37,0,0.399563," ","integrate((-1+1/x^2)^(1/2)/x/(x^2-1),x, algorithm=""giac"")","-\frac{x \mathrm{sgn}\left(x\right)}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)} \mathrm{sgn}\left(x\right)}{2 \, x}"," ",0,"-1/2*x*sgn(x)/(sqrt(-x^2 + 1) - 1) + 1/2*(sqrt(-x^2 + 1) - 1)*sgn(x)/x","B",0
679,1,58,0,0.381996," ","integrate((-1+1/x^2)^(1/2)/x/(x^2-1)^2,x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} + 1} x \mathrm{sgn}\left(x\right)}{x^{2} - 1} + \frac{x \mathrm{sgn}\left(x\right)}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} - \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)} \mathrm{sgn}\left(x\right)}{2 \, x}"," ",0,"-sqrt(-x^2 + 1)*x*sgn(x)/(x^2 - 1) + 1/2*x*sgn(x)/(sqrt(-x^2 + 1) - 1) - 1/2*(sqrt(-x^2 + 1) - 1)*sgn(x)/x","B",0
680,1,68,0,0.435933," ","integrate((-1+1/x^2)^(1/2)/x/(x^2-1)^3,x, algorithm=""giac"")","-\frac{x \mathrm{sgn}\left(x\right)}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)} \mathrm{sgn}\left(x\right)}{2 \, x} - \frac{{\left(5 \, x^{2} \mathrm{sgn}\left(x\right) - 6 \, \mathrm{sgn}\left(x\right)\right)} x}{3 \, {\left(x^{2} - 1\right)} \sqrt{-x^{2} + 1}}"," ",0,"-1/2*x*sgn(x)/(sqrt(-x^2 + 1) - 1) + 1/2*(sqrt(-x^2 + 1) - 1)*sgn(x)/x - 1/3*(5*x^2*sgn(x) - 6*sgn(x))*x/((x^2 - 1)*sqrt(-x^2 + 1))","B",0
681,1,11,0,0.336967," ","integrate(x*(1+1/x^2)^(1/2)/(x^2+1)^2,x, algorithm=""giac"")","\frac{x \mathrm{sgn}\left(x\right)}{\sqrt{x^{2} + 1}}"," ",0,"x*sgn(x)/sqrt(x^2 + 1)","A",0
682,1,20,0,0.333199," ","integrate(1/x/(x^2+1)/(1+1/x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{x^{2} - \sqrt{x^{4} + x^{2}} + 1} - 1"," ",0,"1/(x^2 - sqrt(x^4 + x^2) + 1) - 1","B",0
683,1,16,0,0.339137," ","integrate(x/(a+b*x^2+(b*x^2+a)^(1/2)),x, algorithm=""giac"")","\frac{\log\left(\sqrt{b x^{2} + a} + 1\right)}{b}"," ",0,"log(sqrt(b*x^2 + a) + 1)/b","A",0
684,1,16,0,0.467957," ","integrate(x/(x^2-(x^2)^(1/3)),x, algorithm=""giac"")","\frac{3}{4} \, \log\left({\left| \left(x \mathrm{sgn}\left(x\right)\right)^{\frac{1}{3}} x \mathrm{sgn}\left(x\right) - 1 \right|}\right)"," ",0,"3/4*log(abs((x*sgn(x))^(1/3)*x*sgn(x) - 1))","A",0
685,1,29,0,0.345481," ","integrate(x*(x^2+1)^3*(x^4+2*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{10} \, {\left(x^{4} + 2 \, x^{2} + 2\right)}^{\frac{5}{2}} - \frac{1}{6} \, {\left(x^{4} + 2 \, x^{2} + 2\right)}^{\frac{3}{2}}"," ",0,"1/10*(x^4 + 2*x^2 + 2)^(5/2) - 1/6*(x^4 + 2*x^2 + 2)^(3/2)","A",0
686,1,138,0,0.367782," ","integrate(x^5*(x^9+1)^2*(-x^3+1)^(1/2),x, algorithm=""giac"")","\frac{2}{51} \, {\left(x^{3} - 1\right)}^{8} \sqrt{-x^{3} + 1} + \frac{14}{45} \, {\left(x^{3} - 1\right)}^{7} \sqrt{-x^{3} + 1} + \frac{14}{13} \, {\left(x^{3} - 1\right)}^{6} \sqrt{-x^{3} + 1} + \frac{74}{33} \, {\left(x^{3} - 1\right)}^{5} \sqrt{-x^{3} + 1} + \frac{86}{27} \, {\left(x^{3} - 1\right)}^{4} \sqrt{-x^{3} + 1} + \frac{22}{7} \, {\left(x^{3} - 1\right)}^{3} \sqrt{-x^{3} + 1} + \frac{32}{15} \, {\left(x^{3} - 1\right)}^{2} \sqrt{-x^{3} + 1} - \frac{8}{9} \, {\left(-x^{3} + 1\right)}^{\frac{3}{2}}"," ",0,"2/51*(x^3 - 1)^8*sqrt(-x^3 + 1) + 14/45*(x^3 - 1)^7*sqrt(-x^3 + 1) + 14/13*(x^3 - 1)^6*sqrt(-x^3 + 1) + 74/33*(x^3 - 1)^5*sqrt(-x^3 + 1) + 86/27*(x^3 - 1)^4*sqrt(-x^3 + 1) + 22/7*(x^3 - 1)^3*sqrt(-x^3 + 1) + 32/15*(x^3 - 1)^2*sqrt(-x^3 + 1) - 8/9*(-x^3 + 1)^(3/2)","A",0
687,1,41,0,0.354566," ","integrate(x/(b*x^2+a)^(3/2)+x/(x^2+1)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a + b}}\right)}{\sqrt{-a + b}} - \frac{1}{\sqrt{b x^{2} + a} b}"," ",0,"arctan(sqrt(b*x^2 + a)/sqrt(-a + b))/sqrt(-a + b) - 1/(sqrt(b*x^2 + a)*b)","A",0
688,1,41,0,0.380947," ","integrate(x*(b*x^2+x^2+a+1)/(x^2+1)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a + b}}\right)}{\sqrt{-a + b}} - \frac{1}{\sqrt{b x^{2} + a} b}"," ",0,"arctan(sqrt(b*x^2 + a)/sqrt(-a + b))/sqrt(-a + b) - 1/(sqrt(b*x^2 + a)*b)","A",0
689,1,55,0,0.346595," ","integrate(x/(b*x^2+a)^(5/2)+x/(b*x^2+a)^(3/2)+x/(x^2+1)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a + b}}\right)}{\sqrt{-a + b}} - \frac{1}{\sqrt{b x^{2} + a} b} - \frac{1}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b}"," ",0,"arctan(sqrt(b*x^2 + a)/sqrt(-a + b))/sqrt(-a + b) - 1/(sqrt(b*x^2 + a)*b) - 1/3/((b*x^2 + a)^(3/2)*b)","A",0
690,1,52,0,0.458688," ","integrate(x*(b^2*x^4+b*x^4+2*a*b*x^2+a*x^2+b*x^2+a^2+x^2+a+1)/(x^2+1)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a + b}}\right)}{\sqrt{-a + b}} - \frac{3 \, b x^{2} + 3 \, a + 1}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b}"," ",0,"arctan(sqrt(b*x^2 + a)/sqrt(-a + b))/sqrt(-a + b) - 1/3*(3*b*x^2 + 3*a + 1)/((b*x^2 + a)^(3/2)*b)","A",0
691,1,27,0,0.367792," ","integrate(1/(x+x^(1/2))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x + \sqrt{x}} + \log\left(-2 \, \sqrt{x + \sqrt{x}} + 2 \, \sqrt{x} + 1\right)"," ",0,"2*sqrt(x + sqrt(x)) + log(-2*sqrt(x + sqrt(x)) + 2*sqrt(x) + 1)","A",0
692,1,43,0,0.452371," ","integrate((x+x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, \sqrt{x} {\left(4 \, \sqrt{x} + 1\right)} - 3\right)} \sqrt{x + \sqrt{x}} - \frac{1}{8} \, \log\left(-2 \, \sqrt{x + \sqrt{x}} + 2 \, \sqrt{x} + 1\right)"," ",0,"1/12*(2*sqrt(x)*(4*sqrt(x) + 1) - 3)*sqrt(x + sqrt(x)) - 1/8*log(-2*sqrt(x + sqrt(x)) + 2*sqrt(x) + 1)","A",0
693,1,16,0,0.307306," ","integrate((-x)^(1/2)*(x+(-x)^(1/2)),x, algorithm=""giac"")","\frac{2}{5} \, \sqrt{-x} x^{2} - \frac{1}{2} \, x^{2}"," ",0,"2/5*sqrt(-x)*x^2 - 1/2*x^2","A",0
694,1,55,0,0.485058," ","integrate((5+x^(1/4))/(-6+x),x, algorithm=""giac"")","-2 \cdot 6^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 6^{\frac{3}{4}} x^{\frac{1}{4}}\right) - 6^{\frac{1}{4}} \log\left(6^{\frac{1}{4}} + x^{\frac{1}{4}}\right) + 6^{\frac{1}{4}} \log\left({\left| -6^{\frac{1}{4}} + x^{\frac{1}{4}} \right|}\right) + 4 \, x^{\frac{1}{4}} + 5 \, \log\left({\left| x - 6 \right|}\right)"," ",0,"-2*6^(1/4)*arctan(1/6*6^(3/4)*x^(1/4)) - 6^(1/4)*log(6^(1/4) + x^(1/4)) + 6^(1/4)*log(abs(-6^(1/4) + x^(1/4))) + 4*x^(1/4) + 5*log(abs(x - 6))","A",0
695,1,12,0,0.305674," ","integrate(1/(4-x+(4-x)^(1/2)),x, algorithm=""giac"")","-2 \, \log\left(\sqrt{-x + 4} + 1\right)"," ",0,"-2*log(sqrt(-x + 4) + 1)","A",0
696,1,50,0,0.328180," ","integrate(1/(1+x-(2+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{x + 2} - 1 \right|}}{{\left| \sqrt{5} + 2 \, \sqrt{x + 2} - 1 \right|}}\right) + \log\left({\left| x - \sqrt{x + 2} + 1 \right|}\right)"," ",0,"1/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(x + 2) - 1)/abs(sqrt(5) + 2*sqrt(x + 2) - 1)) + log(abs(x - sqrt(x + 2) + 1))","A",0
697,1,30,0,0.373252," ","integrate(1/(4+x+(1+x)^(1/2)),x, algorithm=""giac"")","-\frac{2}{11} \, \sqrt{11} \arctan\left(\frac{1}{11} \, \sqrt{11} {\left(2 \, \sqrt{x + 1} + 1\right)}\right) + \log\left(x + \sqrt{x + 1} + 4\right)"," ",0,"-2/11*sqrt(11)*arctan(1/11*sqrt(11)*(2*sqrt(x + 1) + 1)) + log(x + sqrt(x + 1) + 4)","A",0
698,1,49,0,0.364139," ","integrate(1/(x-(1+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{x + 1} - 1 \right|}}{{\left| \sqrt{5} + 2 \, \sqrt{x + 1} - 1 \right|}}\right) + \log\left({\left| x - \sqrt{x + 1} \right|}\right)"," ",0,"1/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(x + 1) - 1)/abs(sqrt(5) + 2*sqrt(x + 1) - 1)) + log(abs(x - sqrt(x + 1)))","A",0
699,1,22,0,0.387479," ","integrate(1/(x-(2+x)^(1/2)),x, algorithm=""giac"")","\frac{2}{3} \, \log\left(\sqrt{x + 2} + 1\right) + \frac{4}{3} \, \log\left({\left| \sqrt{x + 2} - 2 \right|}\right)"," ",0,"2/3*log(sqrt(x + 2) + 1) + 4/3*log(abs(sqrt(x + 2) - 2))","A",0
700,1,54,0,0.353451," ","integrate(1/(x-(1-x)^(1/2)),x, algorithm=""giac"")","-\frac{1}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{-x + 1} + 1 \right|}}{\sqrt{5} + 2 \, \sqrt{-x + 1} + 1}\right) + \log\left({\left| -x + \sqrt{-x + 1} \right|}\right)"," ",0,"-1/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(-x + 1) + 1)/(sqrt(5) + 2*sqrt(-x + 1) + 1)) + log(abs(-x + sqrt(-x + 1)))","A",0
701,1,45,0,0.403942," ","integrate((1+x+x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, \sqrt{x} {\left(4 \, \sqrt{x} + 1\right)} + 5\right)} \sqrt{x + \sqrt{x} + 1} + \frac{3}{8} \, \log\left(2 \, \sqrt{x + \sqrt{x} + 1} - 2 \, \sqrt{x} - 1\right)"," ",0,"1/12*(2*sqrt(x)*(4*sqrt(x) + 1) + 5)*sqrt(x + sqrt(x) + 1) + 3/8*log(2*sqrt(x + sqrt(x) + 1) - 2*sqrt(x) - 1)","A",0
702,1,55,0,0.407570," ","integrate((1+x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, \sqrt{x + 1} {\left(4 \, \sqrt{x + 1} + 1\right)} - 3\right)} \sqrt{x + \sqrt{x + 1} + 1} - \frac{1}{8} \, \log\left(-2 \, \sqrt{x + \sqrt{x + 1} + 1} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"1/12*(2*sqrt(x + 1)*(4*sqrt(x + 1) + 1) - 3)*sqrt(x + sqrt(x + 1) + 1) - 1/8*log(-2*sqrt(x + sqrt(x + 1) + 1) + 2*sqrt(x + 1) + 1)","A",0
703,1,53,0,0.396485," ","integrate((x+(-1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, \sqrt{x - 1} {\left(4 \, \sqrt{x - 1} + 1\right)} + 5\right)} \sqrt{x + \sqrt{x - 1}} + \frac{3}{8} \, \log\left(2 \, \sqrt{x + \sqrt{x - 1}} - 2 \, \sqrt{x - 1} - 1\right)"," ",0,"1/12*(2*sqrt(x - 1)*(4*sqrt(x - 1) + 1) + 5)*sqrt(x + sqrt(x - 1)) + 3/8*log(2*sqrt(x + sqrt(x - 1)) - 2*sqrt(x - 1) - 1)","A",0
704,1,67,0,0.446551," ","integrate((2*x+(-1+2*x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(2 \, \sqrt{2 \, x - 1} {\left(4 \, \sqrt{2 \, x - 1} + 1\right)} + 5\right)} \sqrt{2 \, x + \sqrt{2 \, x - 1}} + \frac{3}{16} \, \log\left(2 \, \sqrt{2 \, x + \sqrt{2 \, x - 1}} - 2 \, \sqrt{2 \, x - 1} - 1\right)"," ",0,"1/24*(2*sqrt(2*x - 1)*(4*sqrt(2*x - 1) + 1) + 5)*sqrt(2*x + sqrt(2*x - 1)) + 3/16*log(2*sqrt(2*x + sqrt(2*x - 1)) - 2*sqrt(2*x - 1) - 1)","A",0
705,1,88,0,0.471113," ","integrate((3*x+(-7+8*x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{216} \, \sqrt{2} {\left(3 \, \sqrt{2} {\left(\sqrt{8 \, x - 7} {\left(3 \, \sqrt{8 \, x - 7} + 2\right)} + 13\right)} \sqrt{3 \, x + \sqrt{8 \, x - 7}} + 47 \, \sqrt{3} \log\left(-\sqrt{3} {\left(\sqrt{3} \sqrt{8 \, x - 7} - 2 \, \sqrt{2} \sqrt{3 \, x + \sqrt{8 \, x - 7}}\right)} - 4\right)\right)}"," ",0,"1/216*sqrt(2)*(3*sqrt(2)*(sqrt(8*x - 7)*(3*sqrt(8*x - 7) + 2) + 13)*sqrt(3*x + sqrt(8*x - 7)) + 47*sqrt(3)*log(-sqrt(3)*(sqrt(3)*sqrt(8*x - 7) - 2*sqrt(2)*sqrt(3*x + sqrt(8*x - 7))) - 4))","A",0
706,1,33,0,0.428133," ","integrate(1/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x + \sqrt{x + 1}} + \log\left(-2 \, \sqrt{x + \sqrt{x + 1}} + 2 \, \sqrt{x + 1} + 1\right)"," ",0,"2*sqrt(x + sqrt(x + 1)) + log(-2*sqrt(x + sqrt(x + 1)) + 2*sqrt(x + 1) + 1)","A",0
707,1,49,0,0.376429," ","integrate((1+x)/(4+x+(-9+6*x)^(1/2)),x, algorithm=""giac"")","4 \, \sqrt{6} \arctan\left(\frac{1}{12} \, \sqrt{6} {\left(\sqrt{6 \, x - 9} + 3\right)}\right) + x - 2 \, \sqrt{6 \, x - 9} + 3 \, \log\left(6 \, x + 6 \, \sqrt{6 \, x - 9} + 24\right) - \frac{3}{2}"," ",0,"4*sqrt(6)*arctan(1/12*sqrt(6)*(sqrt(6*x - 9) + 3)) + x - 2*sqrt(6*x - 9) + 3*log(6*x + 6*sqrt(6*x - 9) + 24) - 3/2","A",0
708,1,51,0,0.327613," ","integrate((12-x)/(4+x+(-9+6*x)^(1/2)),x, algorithm=""giac"")","-\frac{21}{2} \, \sqrt{6} \arctan\left(\frac{1}{12} \, \sqrt{6} {\left(\sqrt{6 \, x - 9} + 3\right)}\right) - x + 2 \, \sqrt{6 \, x - 9} + 10 \, \log\left(6 \, x + 6 \, \sqrt{6 \, x - 9} + 24\right) + \frac{3}{2}"," ",0,"-21/2*sqrt(6)*arctan(1/12*sqrt(6)*(sqrt(6*x - 9) + 3)) - x + 2*sqrt(6*x - 9) + 10*log(6*x + 6*sqrt(6*x - 9) + 24) + 3/2","A",0
709,1,46,0,0.309038," ","integrate((x^3-1)/(x^2+1)/x^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, x^{\frac{3}{2}} - \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{x}\right)}\right) - \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{x}\right)}\right)"," ",0,"2/3*x^(3/2) - sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(x))) - sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(x)))","A",0
710,1,25,0,0.374423," ","integrate(1/2/(-1+x)^(1/2)/(x-(-1+x)^(1/2))^(1/2),x, algorithm=""giac"")","-\log\left(2 \, \sqrt{x - \sqrt{x - 1}} - 2 \, \sqrt{x - 1} + 1\right)"," ",0,"-log(2*sqrt(x - sqrt(x - 1)) - 2*sqrt(x - 1) + 1)","A",0
711,1,30,0,0.340298," ","integrate((1+x^(7/2))/(-x^2+1),x, algorithm=""giac"")","-\frac{2}{5} \, x^{\frac{5}{2}} - 2 \, \sqrt{x} + \arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(x + 1\right) - \log\left({\left| \sqrt{x} - 1 \right|}\right)"," ",0,"-2/5*x^(5/2) - 2*sqrt(x) + arctan(sqrt(x)) + 1/2*log(x + 1) - log(abs(sqrt(x) - 1))","A",0
712,1,89,0,0.389804," ","integrate((4+2*x)/((-1+2*x)^(1/3)+(-1+2*x)^(1/2)),x, algorithm=""giac"")","\frac{1}{3} \, {\left(2 \, x - 1\right)}^{\frac{3}{2}} - \frac{3}{8} \, {\left(2 \, x - 1\right)}^{\frac{4}{3}} + \frac{3}{7} \, {\left(2 \, x - 1\right)}^{\frac{7}{6}} - x + \frac{3}{5} \, {\left(2 \, x - 1\right)}^{\frac{5}{6}} - \frac{3}{4} \, {\left(2 \, x - 1\right)}^{\frac{2}{3}} + 6 \, \sqrt{2 \, x - 1} - 9 \, {\left(2 \, x - 1\right)}^{\frac{1}{3}} + 18 \, {\left(2 \, x - 1\right)}^{\frac{1}{6}} - 18 \, \log\left({\left(2 \, x - 1\right)}^{\frac{1}{6}} + 1\right) + \frac{1}{2}"," ",0,"1/3*(2*x - 1)^(3/2) - 3/8*(2*x - 1)^(4/3) + 3/7*(2*x - 1)^(7/6) - x + 3/5*(2*x - 1)^(5/6) - 3/4*(2*x - 1)^(2/3) + 6*sqrt(2*x - 1) - 9*(2*x - 1)^(1/3) + 18*(2*x - 1)^(1/6) - 18*log((2*x - 1)^(1/6) + 1) + 1/2","A",0
713,1,82,0,3.457237," ","integrate(1/(2+(1+x^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(15 \, {\left(\sqrt{\sqrt{x} + 1} + 2\right)}^{\frac{7}{2}} - 126 \, {\left(\sqrt{\sqrt{x} + 1} + 2\right)}^{\frac{5}{2}} + 385 \, {\left(\sqrt{\sqrt{x} + 1} + 2\right)}^{\frac{3}{2}} - 630 \, \sqrt{\sqrt{\sqrt{x} + 1} + 2}\right)}}{105 \, \mathrm{sgn}\left(4 \, {\left(\sqrt{x} + 1\right)}^{2} - 8 \, \sqrt{x} - 7\right) \mathrm{sgn}\left(4 \, x - 3\right)}"," ",0,"8/105*(15*(sqrt(sqrt(x) + 1) + 2)^(7/2) - 126*(sqrt(sqrt(x) + 1) + 2)^(5/2) + 385*(sqrt(sqrt(x) + 1) + 2)^(3/2) - 630*sqrt(sqrt(sqrt(x) + 1) + 2))/(sgn(4*(sqrt(x) + 1)^2 - 8*sqrt(x) - 7)*sgn(4*x - 3))","A",0
714,1,268,0,7.652840," ","integrate((2+(4+x^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8}{315} \, {\left({\left(35 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{9}{2}} - 360 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{7}{2}} + 1512 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{5}{2}} - 3360 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{3}{2}} + 5040 \, \sqrt{\sqrt{\sqrt{x} + 4} + 2}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x} + 4\right)}^{2} - 32 \, \sqrt{x} - 79\right) + 18 \, {\left(5 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{7}{2}} - 42 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{5}{2}} + 140 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{3}{2}} - 280 \, \sqrt{\sqrt{\sqrt{x} + 4} + 2}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x} + 4\right)}^{2} - 32 \, \sqrt{x} - 79\right) - 84 \, {\left(3 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{5}{2}} - 20 \, {\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{3}{2}} + 60 \, \sqrt{\sqrt{\sqrt{x} + 4} + 2}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x} + 4\right)}^{2} - 32 \, \sqrt{x} - 79\right) - 840 \, {\left({\left(\sqrt{\sqrt{x} + 4} + 2\right)}^{\frac{3}{2}} - 6 \, \sqrt{\sqrt{\sqrt{x} + 4} + 2}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x} + 4\right)}^{2} - 32 \, \sqrt{x} - 79\right)\right)} \mathrm{sgn}\left(4 \, x - 15\right)"," ",0,"8/315*((35*(sqrt(sqrt(x) + 4) + 2)^(9/2) - 360*(sqrt(sqrt(x) + 4) + 2)^(7/2) + 1512*(sqrt(sqrt(x) + 4) + 2)^(5/2) - 3360*(sqrt(sqrt(x) + 4) + 2)^(3/2) + 5040*sqrt(sqrt(sqrt(x) + 4) + 2))*sgn(4*(sqrt(x) + 4)^2 - 32*sqrt(x) - 79) + 18*(5*(sqrt(sqrt(x) + 4) + 2)^(7/2) - 42*(sqrt(sqrt(x) + 4) + 2)^(5/2) + 140*(sqrt(sqrt(x) + 4) + 2)^(3/2) - 280*sqrt(sqrt(sqrt(x) + 4) + 2))*sgn(4*(sqrt(x) + 4)^2 - 32*sqrt(x) - 79) - 84*(3*(sqrt(sqrt(x) + 4) + 2)^(5/2) - 20*(sqrt(sqrt(x) + 4) + 2)^(3/2) + 60*sqrt(sqrt(sqrt(x) + 4) + 2))*sgn(4*(sqrt(x) + 4)^2 - 32*sqrt(x) - 79) - 840*((sqrt(sqrt(x) + 4) + 2)^(3/2) - 6*sqrt(sqrt(sqrt(x) + 4) + 2))*sgn(4*(sqrt(x) + 4)^2 - 32*sqrt(x) - 79))*sgn(4*x - 15)","B",0
715,1,474,0,7.170375," ","integrate((2-(4+(-9+5*x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","-\frac{8}{1575} \, {\left({\left(35 \, {\left(\sqrt{\sqrt{5 \, x - 9} + 4} - 2\right)}^{4} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2} + 360 \, {\left(\sqrt{\sqrt{5 \, x - 9} + 4} - 2\right)}^{3} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2} + 1512 \, {\left(\sqrt{\sqrt{5 \, x - 9} + 4} - 2\right)}^{2} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2} - 3360 \, {\left(-\sqrt{\sqrt{5 \, x - 9} + 4} + 2\right)}^{\frac{3}{2}} + 5040 \, \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2}\right)} \mathrm{sgn}\left(-4 \, {\left(\sqrt{5 \, x - 9} + 4\right)}^{2} + 32 \, \sqrt{5 \, x - 9} + 79\right) - 18 \, {\left(5 \, {\left(\sqrt{\sqrt{5 \, x - 9} + 4} - 2\right)}^{3} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2} + 42 \, {\left(\sqrt{\sqrt{5 \, x - 9} + 4} - 2\right)}^{2} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2} - 140 \, {\left(-\sqrt{\sqrt{5 \, x - 9} + 4} + 2\right)}^{\frac{3}{2}} + 280 \, \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2}\right)} \mathrm{sgn}\left(-4 \, {\left(\sqrt{5 \, x - 9} + 4\right)}^{2} + 32 \, \sqrt{5 \, x - 9} + 79\right) - 84 \, {\left(3 \, {\left(\sqrt{\sqrt{5 \, x - 9} + 4} - 2\right)}^{2} \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2} - 20 \, {\left(-\sqrt{\sqrt{5 \, x - 9} + 4} + 2\right)}^{\frac{3}{2}} + 60 \, \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2}\right)} \mathrm{sgn}\left(-4 \, {\left(\sqrt{5 \, x - 9} + 4\right)}^{2} + 32 \, \sqrt{5 \, x - 9} + 79\right) - 840 \, {\left({\left(-\sqrt{\sqrt{5 \, x - 9} + 4} + 2\right)}^{\frac{3}{2}} - 6 \, \sqrt{-\sqrt{\sqrt{5 \, x - 9} + 4} + 2}\right)} \mathrm{sgn}\left(-4 \, {\left(\sqrt{5 \, x - 9} + 4\right)}^{2} + 32 \, \sqrt{5 \, x - 9} + 79\right)\right)} \mathrm{sgn}\left(20 \, x - 51\right)"," ",0,"-8/1575*((35*(sqrt(sqrt(5*x - 9) + 4) - 2)^4*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2) + 360*(sqrt(sqrt(5*x - 9) + 4) - 2)^3*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2) + 1512*(sqrt(sqrt(5*x - 9) + 4) - 2)^2*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2) - 3360*(-sqrt(sqrt(5*x - 9) + 4) + 2)^(3/2) + 5040*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2))*sgn(-4*(sqrt(5*x - 9) + 4)^2 + 32*sqrt(5*x - 9) + 79) - 18*(5*(sqrt(sqrt(5*x - 9) + 4) - 2)^3*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2) + 42*(sqrt(sqrt(5*x - 9) + 4) - 2)^2*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2) - 140*(-sqrt(sqrt(5*x - 9) + 4) + 2)^(3/2) + 280*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2))*sgn(-4*(sqrt(5*x - 9) + 4)^2 + 32*sqrt(5*x - 9) + 79) - 84*(3*(sqrt(sqrt(5*x - 9) + 4) - 2)^2*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2) - 20*(-sqrt(sqrt(5*x - 9) + 4) + 2)^(3/2) + 60*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2))*sgn(-4*(sqrt(5*x - 9) + 4)^2 + 32*sqrt(5*x - 9) + 79) - 840*((-sqrt(sqrt(5*x - 9) + 4) + 2)^(3/2) - 6*sqrt(-sqrt(sqrt(5*x - 9) + 4) + 2))*sgn(-4*(sqrt(5*x - 9) + 4)^2 + 32*sqrt(5*x - 9) + 79))*sgn(20*x - 51)","B",0
716,1,82,0,3.180275," ","integrate(1/(2+(1+x^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8 \, {\left(15 \, {\left(\sqrt{\sqrt{x} + 1} + 2\right)}^{\frac{7}{2}} - 126 \, {\left(\sqrt{\sqrt{x} + 1} + 2\right)}^{\frac{5}{2}} + 385 \, {\left(\sqrt{\sqrt{x} + 1} + 2\right)}^{\frac{3}{2}} - 630 \, \sqrt{\sqrt{\sqrt{x} + 1} + 2}\right)}}{105 \, \mathrm{sgn}\left(4 \, {\left(\sqrt{x} + 1\right)}^{2} - 8 \, \sqrt{x} - 7\right) \mathrm{sgn}\left(4 \, x - 3\right)}"," ",0,"8/105*(15*(sqrt(sqrt(x) + 1) + 2)^(7/2) - 126*(sqrt(sqrt(x) + 1) + 2)^(5/2) + 385*(sqrt(sqrt(x) + 1) + 2)^(3/2) - 630*sqrt(sqrt(sqrt(x) + 1) + 2))/(sgn(4*(sqrt(x) + 1)^2 - 8*sqrt(x) - 7)*sgn(4*x - 3))","A",0
717,-1,0,0,0.000000," ","integrate((1+(1+(1+x^(1/2))^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,1,271,0,51.245648," ","integrate((2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{4}{255255} \, {\left(15015 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{17}{2}} - 238238 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{15}{2}} + 1472625 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{13}{2}} - 4408950 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{11}{2}} + 6466460 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{9}{2}} - 4375800 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{7}{2}} + 1735734 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{5}{2}} - 340340 \, {\left(\sqrt{\sqrt{2 \, \sqrt{x} - 1} + 3} + 2\right)}^{\frac{3}{2}}\right)} \mathrm{sgn}\left(131072 \, x^{23} + 6029312 \, x^{22} + 131596288 \, x^{21} + 1823539200 \, x^{20} + 18092523520 \, x^{19} + 137313009664 \, x^{18} + 830934196224 \, x^{17} + 4121209913344 \, x^{16} + 17059018985472 \, x^{15} + 59571270234112 \, x^{14} + 176317166240256 \, x^{13} + 442104199109632 \, x^{12} + 934792487842816 \, x^{11} + 1653389259996160 \, x^{10} + 2419262240692992 \, x^{9} + 2886578907966976 \, x^{8} + 2756595188687360 \, x^{7} + 2055315711024768 \, x^{6} + 1156127428771360 \, x^{5} + 466803251648192 \, x^{4} + 125285938081152 \, x^{3} + 19649836876032 \, x^{2} + 1399854182400 \, x + 14929920000\right)"," ",0,"4/255255*(15015*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(17/2) - 238238*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(15/2) + 1472625*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(13/2) - 4408950*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(11/2) + 6466460*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(9/2) - 4375800*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(7/2) + 1735734*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(5/2) - 340340*(sqrt(sqrt(2*sqrt(x) - 1) + 3) + 2)^(3/2))*sgn(131072*x^23 + 6029312*x^22 + 131596288*x^21 + 1823539200*x^20 + 18092523520*x^19 + 137313009664*x^18 + 830934196224*x^17 + 4121209913344*x^16 + 17059018985472*x^15 + 59571270234112*x^14 + 176317166240256*x^13 + 442104199109632*x^12 + 934792487842816*x^11 + 1653389259996160*x^10 + 2419262240692992*x^9 + 2886578907966976*x^8 + 2756595188687360*x^7 + 2055315711024768*x^6 + 1156127428771360*x^5 + 466803251648192*x^4 + 125285938081152*x^3 + 19649836876032*x^2 + 1399854182400*x + 14929920000)","A",0
719,1,859,0,15.543626," ","integrate(x*(1+(1+(-1+x)^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\frac{8}{765765} \, {\left(7 \, {\left(6435 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{17}{2}} - 58344 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{15}{2}} + 235620 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{13}{2}} - 556920 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{11}{2}} + 850850 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{9}{2}} - 875160 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{7}{2}} + 612612 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} - 291720 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} + 109395 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) + 119 \, {\left(429 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{15}{2}} - 3465 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{13}{2}} + 12285 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{11}{2}} - 25025 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{9}{2}} + 32175 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{7}{2}} - 27027 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} + 15015 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} - 6435 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) - 765 \, {\left(231 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{13}{2}} - 1638 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{11}{2}} + 5005 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{9}{2}} - 8580 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{7}{2}} + 9009 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} - 6006 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} + 3003 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) - 3315 \, {\left(63 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{11}{2}} - 385 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{9}{2}} + 990 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{7}{2}} - 1386 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} + 1155 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} - 693 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) + 9724 \, {\left(35 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{9}{2}} - 180 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{7}{2}} + 378 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} - 420 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} + 315 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) + 87516 \, {\left(5 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{7}{2}} - 21 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} + 35 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} - 35 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) - 102102 \, {\left(3 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{5}{2}} - 10 \, {\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} + 15 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right) - 510510 \, {\left({\left(\sqrt{\sqrt{x - 1} + 1} + 1\right)}^{\frac{3}{2}} - 3 \, \sqrt{\sqrt{\sqrt{x - 1} + 1} + 1}\right)} \mathrm{sgn}\left(4 \, {\left(\sqrt{x - 1} + 1\right)}^{2} - 8 \, \sqrt{x - 1} - 7\right)\right)} \mathrm{sgn}\left(4 \, x - 7\right)"," ",0,"8/765765*(7*(6435*(sqrt(sqrt(x - 1) + 1) + 1)^(17/2) - 58344*(sqrt(sqrt(x - 1) + 1) + 1)^(15/2) + 235620*(sqrt(sqrt(x - 1) + 1) + 1)^(13/2) - 556920*(sqrt(sqrt(x - 1) + 1) + 1)^(11/2) + 850850*(sqrt(sqrt(x - 1) + 1) + 1)^(9/2) - 875160*(sqrt(sqrt(x - 1) + 1) + 1)^(7/2) + 612612*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) - 291720*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) + 109395*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) + 119*(429*(sqrt(sqrt(x - 1) + 1) + 1)^(15/2) - 3465*(sqrt(sqrt(x - 1) + 1) + 1)^(13/2) + 12285*(sqrt(sqrt(x - 1) + 1) + 1)^(11/2) - 25025*(sqrt(sqrt(x - 1) + 1) + 1)^(9/2) + 32175*(sqrt(sqrt(x - 1) + 1) + 1)^(7/2) - 27027*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) + 15015*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) - 6435*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) - 765*(231*(sqrt(sqrt(x - 1) + 1) + 1)^(13/2) - 1638*(sqrt(sqrt(x - 1) + 1) + 1)^(11/2) + 5005*(sqrt(sqrt(x - 1) + 1) + 1)^(9/2) - 8580*(sqrt(sqrt(x - 1) + 1) + 1)^(7/2) + 9009*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) - 6006*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) + 3003*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) - 3315*(63*(sqrt(sqrt(x - 1) + 1) + 1)^(11/2) - 385*(sqrt(sqrt(x - 1) + 1) + 1)^(9/2) + 990*(sqrt(sqrt(x - 1) + 1) + 1)^(7/2) - 1386*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) + 1155*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) - 693*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) + 9724*(35*(sqrt(sqrt(x - 1) + 1) + 1)^(9/2) - 180*(sqrt(sqrt(x - 1) + 1) + 1)^(7/2) + 378*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) - 420*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) + 315*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) + 87516*(5*(sqrt(sqrt(x - 1) + 1) + 1)^(7/2) - 21*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) + 35*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) - 35*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) - 102102*(3*(sqrt(sqrt(x - 1) + 1) + 1)^(5/2) - 10*(sqrt(sqrt(x - 1) + 1) + 1)^(3/2) + 15*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7) - 510510*((sqrt(sqrt(x - 1) + 1) + 1)^(3/2) - 3*sqrt(sqrt(sqrt(x - 1) + 1) + 1))*sgn(4*(sqrt(x - 1) + 1)^2 - 8*sqrt(x - 1) - 7))*sgn(4*x - 7)","B",0
720,1,25,0,0.318334," ","integrate(1/(-1+x)^(1/2)/(x-(-1+x)^(1/2))^(1/2),x, algorithm=""giac"")","-2 \, \log\left(2 \, \sqrt{x - \sqrt{x - 1}} - 2 \, \sqrt{x - 1} + 1\right)"," ",0,"-2*log(2*sqrt(x - sqrt(x - 1)) - 2*sqrt(x - 1) + 1)","A",0
721,1,49,0,0.304341," ","integrate(1/(1+x+(-1+2*x)^(1/2))^(1/2),x, algorithm=""giac"")","\sqrt{2} {\left(\sqrt{2 \, x + 2 \, \sqrt{2 \, x - 1} + 2} + \log\left(\sqrt{2 \, x + 2 \, \sqrt{2 \, x - 1} + 2} - \sqrt{2 \, x - 1} - 1\right)\right)}"," ",0,"sqrt(2)*(sqrt(2*x + 2*sqrt(2*x - 1) + 2) + log(sqrt(2*x + 2*sqrt(2*x - 1) + 2) - sqrt(2*x - 1) - 1))","A",0
722,1,61,0,0.324173," ","integrate((p*x+q)/(a*x+b)^(1/2)/(f+(a*x+b)^(1/2)),x, algorithm=""giac"")","\frac{2 \, {\left(f^{2} p - b p + a q\right)} \log\left({\left| f + \sqrt{a x + b} \right|}\right)}{a^{2}} - \frac{2 \, \sqrt{a x + b} a^{2} f p - {\left(a x + b\right)} a^{2} p}{a^{4}}"," ",0,"2*(f^2*p - b*p + a*q)*log(abs(f + sqrt(a*x + b)))/a^2 - (2*sqrt(a*x + b)*a^2*f*p - (a*x + b)*a^2*p)/a^4","A",0
723,1,44,0,0.346163," ","integrate((1-x-x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(2 \, \sqrt{x} {\left(4 \, \sqrt{x} + 1\right)} - 11\right)} \sqrt{-x - \sqrt{x} + 1} - \frac{5}{8} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} {\left(2 \, \sqrt{x} + 1\right)}\right)"," ",0,"1/12*(2*sqrt(x)*(4*sqrt(x) + 1) - 11)*sqrt(-x - sqrt(x) + 1) - 5/8*arcsin(1/5*sqrt(5)*(2*sqrt(x) + 1))","A",0
724,1,15,0,0.392274," ","integrate((9+x+6*x^(1/2))/(x+4*x^(1/2)),x, algorithm=""giac"")","x + 4 \, \sqrt{x} + 2 \, \log\left(\sqrt{x} + 4\right)"," ",0,"x + 4*sqrt(x) + 2*log(sqrt(x) + 4)","A",0
725,1,50,0,0.353230," ","integrate((6-8*x^(7/2))/(5-9*x^(1/2)),x, algorithm=""giac"")","\frac{2}{9} \, x^{4} + \frac{80}{567} \, x^{\frac{7}{2}} + \frac{200}{2187} \, x^{3} + \frac{400}{6561} \, x^{\frac{5}{2}} + \frac{2500}{59049} \, x^{2} + \frac{50000}{1594323} \, x^{\frac{3}{2}} + \frac{125000}{4782969} \, x - \frac{56145628}{43046721} \, \sqrt{x} - \frac{280728140}{387420489} \, \log\left({\left| 9 \, \sqrt{x} - 5 \right|}\right)"," ",0,"2/9*x^4 + 80/567*x^(7/2) + 200/2187*x^3 + 400/6561*x^(5/2) + 2500/59049*x^2 + 50000/1594323*x^(3/2) + 125000/4782969*x - 56145628/43046721*sqrt(x) - 280728140/387420489*log(abs(9*sqrt(x) - 5))","A",0
726,1,171,0,1.710521," ","integrate((x^3+1)*(1+x)^(1/2)/(x^2+1),x, algorithm=""giac"")","\frac{2}{5} \, {\left(x + 1\right)}^{\frac{5}{2}} - \frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} + \sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{2} \, \sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right) - \frac{1}{2} \, \sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right) - 2 \, \sqrt{x + 1}"," ",0,"2/5*(x + 1)^(5/2) - 2/3*(x + 1)^(3/2) + sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + 1/2*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1) - 1/2*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1) - 2*sqrt(x + 1)","B",0
727,1,81,0,1.240115," ","integrate((-1+x-x^(1/2))^(1/2)/(-1+x)/x^(1/2),x, algorithm=""giac"")","-2 \, \arctan\left(\sqrt{x - \sqrt{x} - 1} - \sqrt{x} + 1\right) - \log\left(-\sqrt{x - \sqrt{x} - 1} + \sqrt{x} + 2\right) + \log\left(-\sqrt{x - \sqrt{x} - 1} + \sqrt{x}\right) - 2 \, \log\left({\left| 2 \, \sqrt{x - \sqrt{x} - 1} - 2 \, \sqrt{x} + 1 \right|}\right)"," ",0,"-2*arctan(sqrt(x - sqrt(x) - 1) - sqrt(x) + 1) - log(-sqrt(x - sqrt(x) - 1) + sqrt(x) + 2) + log(-sqrt(x - sqrt(x) - 1) + sqrt(x)) - 2*log(abs(2*sqrt(x - sqrt(x) - 1) - 2*sqrt(x) + 1))","A",0
728,1,65,0,1.162792," ","integrate((1+2*(1+x)^(1/2))/x/(1+x)^(1/2)/(x+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} - 1\right) - 3 \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) + 3 \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right)"," ",0,"2*arctan(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) - 1) - 3*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) + 3*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)))","A",0
729,1,14,0,0.252495," ","integrate(1/x^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","-2 \, \log\left(\sqrt{x + 1} - \sqrt{x}\right)"," ",0,"-2*log(sqrt(x + 1) - sqrt(x))","B",0
730,1,22,0,0.402064," ","integrate((x/(1+x))^(1/2)/x,x, algorithm=""giac"")","-\log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + x} - 1 \right|}\right) \mathrm{sgn}\left(x + 1\right)"," ",0,"-log(abs(-2*x + 2*sqrt(x^2 + x) - 1))*sgn(x + 1)","B",0
731,1,22,0,0.385339," ","integrate(x^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\sqrt{x + 1} \sqrt{x} + \log\left(\sqrt{x + 1} - \sqrt{x}\right)"," ",0,"sqrt(x + 1)*sqrt(x) + log(sqrt(x + 1) - sqrt(x))","A",0
732,1,35,0,0.438842," ","integrate((x/(1+x))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + x} - 1 \right|}\right) \mathrm{sgn}\left(x + 1\right) + \sqrt{x^{2} + x} \mathrm{sgn}\left(x + 1\right)"," ",0,"1/2*log(abs(-2*x + 2*sqrt(x^2 + x) - 1))*sgn(x + 1) + sqrt(x^2 + x)*sgn(x + 1)","B",0
733,1,42,0,0.333910," ","integrate((-1+x)^(1/2)/x^2/(1+x)^(1/2),x, algorithm=""giac"")","-\frac{8}{{\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{4} + 4} - 2 \, \arctan\left(\frac{1}{2} \, {\left(\sqrt{x + 1} - \sqrt{x - 1}\right)}^{2}\right)"," ",0,"-8/((sqrt(x + 1) - sqrt(x - 1))^4 + 4) - 2*arctan(1/2*(sqrt(x + 1) - sqrt(x - 1))^2)","A",0
734,1,51,0,0.410072," ","integrate(((-1+x)/(1+x))^(1/2)/x^2,x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\pi - 2\right)} \mathrm{sgn}\left(x + 1\right) + 2 \, \arctan\left(-x + \sqrt{x^{2} - 1}\right) \mathrm{sgn}\left(x + 1\right) - \frac{2 \, \mathrm{sgn}\left(x + 1\right)}{{\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 1}"," ",0,"-1/2*(pi - 2)*sgn(x + 1) + 2*arctan(-x + sqrt(x^2 - 1))*sgn(x + 1) - 2*sgn(x + 1)/((x - sqrt(x^2 - 1))^2 + 1)","A",0
735,1,47,0,0.329883," ","integrate(x^3*(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, {\left({\left(2 \, {\left(3 \, x - 10\right)} {\left(x + 1\right)} + 43\right)} {\left(x + 1\right)} - 39\right)} \sqrt{x + 1} \sqrt{x - 1} - \frac{3}{4} \, \log\left(\sqrt{x + 1} - \sqrt{x - 1}\right)"," ",0,"1/24*((2*(3*x - 10)*(x + 1) + 43)*(x + 1) - 39)*sqrt(x + 1)*sqrt(x - 1) - 3/4*log(sqrt(x + 1) - sqrt(x - 1))","A",0
736,1,62,0,0.340630," ","integrate(x^3*((-1+x)/(1+x))^(1/2),x, algorithm=""giac"")","-\frac{3}{8} \, \log\left({\left| -x + \sqrt{x^{2} - 1} \right|}\right) \mathrm{sgn}\left(x + 1\right) + \frac{1}{24} \, {\left({\left(2 \, {\left(3 \, x \mathrm{sgn}\left(x + 1\right) - 4 \, \mathrm{sgn}\left(x + 1\right)\right)} x + 9 \, \mathrm{sgn}\left(x + 1\right)\right)} x - 16 \, \mathrm{sgn}\left(x + 1\right)\right)} \sqrt{x^{2} - 1}"," ",0,"-3/8*log(abs(-x + sqrt(x^2 - 1)))*sgn(x + 1) + 1/24*((2*(3*x*sgn(x + 1) - 4*sgn(x + 1))*x + 9*sgn(x + 1))*x - 16*sgn(x + 1))*sqrt(x^2 - 1)","A",0
737,1,20,0,0.301009," ","integrate((-x/(1+x))^(1/2)/x,x, algorithm=""giac"")","-\frac{1}{2} \, \pi \mathrm{sgn}\left(x + 1\right) - \arcsin\left(2 \, x + 1\right) \mathrm{sgn}\left(x + 1\right)"," ",0,"-1/2*pi*sgn(x + 1) - arcsin(2*x + 1)*sgn(x + 1)","A",0
738,1,16,0,0.312366," ","integrate(((1-x)/(1+x))^(1/2)/(-1+x),x, algorithm=""giac"")","-\frac{1}{2} \, \pi \mathrm{sgn}\left(x + 1\right) - \arcsin\left(x\right) \mathrm{sgn}\left(x + 1\right)"," ",0,"-1/2*pi*sgn(x + 1) - arcsin(x)*sgn(x + 1)","A",0
739,1,41,0,0.497233," ","integrate(((b*x+a)/(-b*x+c))^(1/2)/(b*x+a),x, algorithm=""giac"")","-\frac{\arcsin\left(-\frac{2 \, b x + a - c}{a + c}\right) \mathrm{sgn}\left(-a b - b c\right) \mathrm{sgn}\left(b x - c\right)}{{\left| b \right|}}"," ",0,"-arcsin(-(2*b*x + a - c)/(a + c))*sgn(-a*b - b*c)*sgn(b*x - c)/abs(b)","A",0
740,1,74,0,0.493497," ","integrate(((b*x+a)/(d*x+c))^(1/2)/(b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{b d} \log\left({\left| -2 \, {\left(\sqrt{b d} x - \sqrt{b d x^{2} + b c x + a d x + a c}\right)} b d - \sqrt{b d} b c - \sqrt{b d} a d \right|}\right) \mathrm{sgn}\left(d x + c\right)}{b d}"," ",0,"-sqrt(b*d)*log(abs(-2*(sqrt(b*d)*x - sqrt(b*d*x^2 + b*c*x + a*d*x + a*c))*b*d - sqrt(b*d)*b*c - sqrt(b*d)*a*d))*sgn(d*x + c)/(b*d)","B",0
741,1,36,0,0.353668," ","integrate((-x/(1+x))^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \pi \mathrm{sgn}\left(x + 1\right) + \frac{1}{2} \, \arcsin\left(2 \, x + 1\right) \mathrm{sgn}\left(x + 1\right) + \sqrt{-x^{2} - x} \mathrm{sgn}\left(x + 1\right)"," ",0,"1/4*pi*sgn(x + 1) + 1/2*arcsin(2*x + 1)*sgn(x + 1) + sqrt(-x^2 - x)*sgn(x + 1)","A",0
742,1,29,0,0.396334," ","integrate(((1-x)/(1+x))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \pi \mathrm{sgn}\left(x + 1\right) + \arcsin\left(x\right) \mathrm{sgn}\left(x + 1\right) + \sqrt{-x^{2} + 1} \mathrm{sgn}\left(x + 1\right)"," ",0,"1/2*pi*sgn(x + 1) + arcsin(x)*sgn(x + 1) + sqrt(-x^2 + 1)*sgn(x + 1)","A",0
743,1,36,0,0.445507," ","integrate(((a+x)/(a-x))^(1/2),x, algorithm=""giac"")","a \arcsin\left(\frac{x}{a}\right) \mathrm{sgn}\left(a - x\right) \mathrm{sgn}\left(a\right) - \sqrt{a^{2} - x^{2}} \mathrm{sgn}\left(a - x\right)"," ",0,"a*arcsin(x/a)*sgn(a - x)*sgn(a) - sqrt(a^2 - x^2)*sgn(a - x)","A",0
744,1,40,0,0.310239," ","integrate(((-a+x)/(a+x))^(1/2),x, algorithm=""giac"")","a \log\left({\left| -x + \sqrt{-a^{2} + x^{2}} \right|}\right) \mathrm{sgn}\left(a + x\right) + \sqrt{-a^{2} + x^{2}} \mathrm{sgn}\left(a + x\right)"," ",0,"a*log(abs(-x + sqrt(-a^2 + x^2)))*sgn(a + x) + sqrt(-a^2 + x^2)*sgn(a + x)","A",0
745,1,119,0,0.569657," ","integrate(((b*x+a)/(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b d x^{2} + b c x + a d x + a c} \mathrm{sgn}\left(d x + c\right)}{d} + \frac{{\left(b c \mathrm{sgn}\left(d x + c\right) - a d \mathrm{sgn}\left(d x + c\right)\right)} \sqrt{b d} \log\left({\left| -2 \, {\left(\sqrt{b d} x - \sqrt{b d x^{2} + b c x + a d x + a c}\right)} b d - \sqrt{b d} b c - \sqrt{b d} a d \right|}\right)}{2 \, b d^{2}}"," ",0,"sqrt(b*d*x^2 + b*c*x + a*d*x + a*c)*sgn(d*x + c)/d + 1/2*(b*c*sgn(d*x + c) - a*d*sgn(d*x + c))*sqrt(b*d)*log(abs(-2*(sqrt(b*d)*x - sqrt(b*d*x^2 + b*c*x + a*d*x + a*c))*b*d - sqrt(b*d)*b*c - sqrt(b*d)*a*d))/(b*d^2)","A",0
746,1,74,0,0.398475," ","integrate(((-1+x)/(5+3*x))^(1/2),x, algorithm=""giac"")","-\frac{8}{9} \, \sqrt{3} \log\left(2\right) \mathrm{sgn}\left(3 \, x + 5\right) + \frac{4}{9} \, \sqrt{3} \log\left({\left| -\sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 2 \, x - 5}\right)} - 1 \right|}\right) \mathrm{sgn}\left(3 \, x + 5\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 2 \, x - 5} \mathrm{sgn}\left(3 \, x + 5\right)"," ",0,"-8/9*sqrt(3)*log(2)*sgn(3*x + 5) + 4/9*sqrt(3)*log(abs(-sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2*x - 5)) - 1))*sgn(3*x + 5) + 1/3*sqrt(3*x^2 + 2*x - 5)*sgn(3*x + 5)","B",0
747,1,114,0,0.404450," ","integrate(((-1+5*x)/(1+7*x))^(1/2)/x^2,x, algorithm=""giac"")","{\left(\sqrt{35} - 12 \, \arctan\left(\frac{1}{7} \, \sqrt{35}\right)\right)} \mathrm{sgn}\left(7 \, x + 1\right) + 12 \, \arctan\left(-\sqrt{35} x + \sqrt{35 \, x^{2} - 2 \, x - 1}\right) \mathrm{sgn}\left(7 \, x + 1\right) - \frac{2 \, {\left({\left(\sqrt{35} x - \sqrt{35 \, x^{2} - 2 \, x - 1}\right)} \mathrm{sgn}\left(7 \, x + 1\right) + \sqrt{35} \mathrm{sgn}\left(7 \, x + 1\right)\right)}}{{\left(\sqrt{35} x - \sqrt{35 \, x^{2} - 2 \, x - 1}\right)}^{2} + 1}"," ",0,"(sqrt(35) - 12*arctan(1/7*sqrt(35)))*sgn(7*x + 1) + 12*arctan(-sqrt(35)*x + sqrt(35*x^2 - 2*x - 1))*sgn(7*x + 1) - 2*((sqrt(35)*x - sqrt(35*x^2 - 2*x - 1))*sgn(7*x + 1) + sqrt(35)*sgn(7*x + 1))/((sqrt(35)*x - sqrt(35*x^2 - 2*x - 1))^2 + 1)","B",0
748,1,29,0,0.415354," ","integrate(x/(1+x)/((1-x)/(1+x))^(1/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{-\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{-\frac{x - 1}{x + 1}}}}"," ",0,"-2/(sqrt(-(x - 1)/(x + 1)) + 1/sqrt(-(x - 1)/(x + 1)))","A",0
749,1,29,0,0.259271," ","integrate(x/(1+x)/(-1+2/(1+x))^(1/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{-\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{-\frac{x - 1}{x + 1}}}}"," ",0,"-2/(sqrt(-(x - 1)/(x + 1)) + 1/sqrt(-(x - 1)/(x + 1)))","A",0
750,1,107,0,0.297604," ","integrate(x/(1+x)/((2+x)/(3+x))^(1/2),x, algorithm=""giac"")","-\sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sqrt{\frac{x + 2}{x + 3}} \right|}}{2 \, {\left(\sqrt{2} + 2 \, \sqrt{\frac{x + 2}{x + 3}}\right)}}\right) - \frac{\sqrt{\frac{x + 2}{x + 3}}}{\frac{x + 2}{x + 3} - 1} - \frac{1}{2} \, \log\left(\sqrt{\frac{x + 2}{x + 3}} + 1\right) + \frac{1}{2} \, \log\left({\left| \sqrt{\frac{x + 2}{x + 3}} - 1 \right|}\right)"," ",0,"-sqrt(2)*log(1/2*abs(-2*sqrt(2) + 4*sqrt((x + 2)/(x + 3)))/(sqrt(2) + 2*sqrt((x + 2)/(x + 3)))) - sqrt((x + 2)/(x + 3))/((x + 2)/(x + 3) - 1) - 1/2*log(sqrt((x + 2)/(x + 3)) + 1) + 1/2*log(abs(sqrt((x + 2)/(x + 3)) - 1))","B",0
751,1,23,0,0.292731," ","integrate((1+1/x)^(1/2)/(1+x)^2,x, algorithm=""giac"")","\frac{2 \, \mathrm{sgn}\left(x\right)}{x - \sqrt{x^{2} + x} + 1} - 2 \, \mathrm{sgn}\left(x\right)"," ",0,"2*sgn(x)/(x - sqrt(x^2 + x) + 1) - 2*sgn(x)","B",0
752,0,0,0,0.000000," ","integrate((1+1/x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{1}{x} + 1}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(1/x + 1)/sqrt(-x^2 + 1), x)","F",0
753,1,287,0,0.516993," ","integrate(1/(x+(-x^2-2*x+3)^(1/2)),x, algorithm=""giac"")","-\frac{1}{28} \, \sqrt{7} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{7} + 2 \right|}}{{\left| 4 \, x + 2 \, \sqrt{7} + 2 \right|}}\right) + \frac{1}{28} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + \frac{6 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + 4 \right|}}{{\left| 2 \, \sqrt{7} + \frac{6 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + 4 \right|}}\right) - \frac{1}{28} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + \frac{2 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} - 4 \right|}}{{\left| 2 \, \sqrt{7} + \frac{2 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} - 4 \right|}}\right) + \frac{1}{2} \, \arcsin\left(\frac{1}{2} \, x + \frac{1}{2}\right) + \frac{1}{4} \, \log\left({\left| 2 \, x^{2} + 2 \, x - 3 \right|}\right) + \frac{1}{4} \, \log\left({\left| \frac{4 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + \frac{3 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{2}}{{\left(x + 1\right)}^{2}} - 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| -\frac{4 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + \frac{{\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{2}}{{\left(x + 1\right)}^{2}} - 3 \right|}\right)"," ",0,"-1/28*sqrt(7)*log(abs(4*x - 2*sqrt(7) + 2)/abs(4*x + 2*sqrt(7) + 2)) + 1/28*sqrt(7)*log(abs(-2*sqrt(7) + 6*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 4)/abs(2*sqrt(7) + 6*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 4)) - 1/28*sqrt(7)*log(abs(-2*sqrt(7) + 2*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) - 4)/abs(2*sqrt(7) + 2*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) - 4)) + 1/2*arcsin(1/2*x + 1/2) + 1/4*log(abs(2*x^2 + 2*x - 3)) + 1/4*log(abs(4*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 3*(sqrt(-x^2 - 2*x + 3) - 2)^2/(x + 1)^2 - 1)) - 1/4*log(abs(-4*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + (sqrt(-x^2 - 2*x + 3) - 2)^2/(x + 1)^2 - 3))","B",0
754,1,350,0,0.477167," ","integrate(1/(x+(-x^2-2*x+3)^(1/2))^2,x, algorithm=""giac"")","-\frac{2}{49} \, \sqrt{7} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{7} + 2 \right|}}{{\left| 4 \, x + 2 \, \sqrt{7} + 2 \right|}}\right) + \frac{2}{49} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + \frac{6 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + 4 \right|}}{{\left| 2 \, \sqrt{7} + \frac{6 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + 4 \right|}}\right) - \frac{2}{49} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + \frac{2 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} - 4 \right|}}{{\left| 2 \, \sqrt{7} + \frac{2 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} - 4 \right|}}\right) - \frac{8 \, x - 3}{14 \, {\left(2 \, x^{2} + 2 \, x - 3\right)}} - \frac{8 \, {\left(\frac{5 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + \frac{26 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{11 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{3}}{{\left(x + 1\right)}^{3}} - 6\right)}}{21 \, {\left(\frac{8 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + \frac{26 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{8 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{3}}{{\left(x + 1\right)}^{3}} - \frac{3 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{4}}{{\left(x + 1\right)}^{4}} - 3\right)}}"," ",0,"-2/49*sqrt(7)*log(abs(4*x - 2*sqrt(7) + 2)/abs(4*x + 2*sqrt(7) + 2)) + 2/49*sqrt(7)*log(abs(-2*sqrt(7) + 6*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 4)/abs(2*sqrt(7) + 6*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 4)) - 2/49*sqrt(7)*log(abs(-2*sqrt(7) + 2*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) - 4)/abs(2*sqrt(7) + 2*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) - 4)) - 1/14*(8*x - 3)/(2*x^2 + 2*x - 3) - 8/21*(5*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 26*(sqrt(-x^2 - 2*x + 3) - 2)^2/(x + 1)^2 + 11*(sqrt(-x^2 - 2*x + 3) - 2)^3/(x + 1)^3 - 6)/(8*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 26*(sqrt(-x^2 - 2*x + 3) - 2)^2/(x + 1)^2 + 8*(sqrt(-x^2 - 2*x + 3) - 2)^3/(x + 1)^3 - 3*(sqrt(-x^2 - 2*x + 3) - 2)^4/(x + 1)^4 - 3)","B",0
755,1,452,0,0.558523," ","integrate(1/(x+(-x^2-2*x+3)^(1/2))^3,x, algorithm=""giac"")","-\frac{3}{343} \, \sqrt{7} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{7} + 2 \right|}}{{\left| 4 \, x + 2 \, \sqrt{7} + 2 \right|}}\right) + \frac{3}{343} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + \frac{6 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + 4 \right|}}{{\left| 2 \, \sqrt{7} + \frac{6 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + 4 \right|}}\right) - \frac{3}{343} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + \frac{2 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} - 4 \right|}}{{\left| 2 \, \sqrt{7} + \frac{2 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} - 4 \right|}}\right) - \frac{48 \, x^{3} - 26 \, x^{2} - 300 \, x + 279}{196 \, {\left(2 \, x^{2} + 2 \, x - 3\right)}^{2}} + \frac{4 \, {\left(\frac{231 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + \frac{3286 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{2}}{{\left(x + 1\right)}^{2}} - \frac{4441 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{3}}{{\left(x + 1\right)}^{3}} - \frac{18906 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{4}}{{\left(x + 1\right)}^{4}} - \frac{12487 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{5}}{{\left(x + 1\right)}^{5}} + \frac{946 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{6}}{{\left(x + 1\right)}^{6}} + \frac{1977 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{7}}{{\left(x + 1\right)}^{7}} - 414\right)}}{441 \, {\left(\frac{8 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}}{x + 1} + \frac{26 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{2}}{{\left(x + 1\right)}^{2}} + \frac{8 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{3}}{{\left(x + 1\right)}^{3}} - \frac{3 \, {\left(\sqrt{-x^{2} - 2 \, x + 3} - 2\right)}^{4}}{{\left(x + 1\right)}^{4}} - 3\right)}^{2}}"," ",0,"-3/343*sqrt(7)*log(abs(4*x - 2*sqrt(7) + 2)/abs(4*x + 2*sqrt(7) + 2)) + 3/343*sqrt(7)*log(abs(-2*sqrt(7) + 6*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 4)/abs(2*sqrt(7) + 6*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 4)) - 3/343*sqrt(7)*log(abs(-2*sqrt(7) + 2*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) - 4)/abs(2*sqrt(7) + 2*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) - 4)) - 1/196*(48*x^3 - 26*x^2 - 300*x + 279)/(2*x^2 + 2*x - 3)^2 + 4/441*(231*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 3286*(sqrt(-x^2 - 2*x + 3) - 2)^2/(x + 1)^2 - 4441*(sqrt(-x^2 - 2*x + 3) - 2)^3/(x + 1)^3 - 18906*(sqrt(-x^2 - 2*x + 3) - 2)^4/(x + 1)^4 - 12487*(sqrt(-x^2 - 2*x + 3) - 2)^5/(x + 1)^5 + 946*(sqrt(-x^2 - 2*x + 3) - 2)^6/(x + 1)^6 + 1977*(sqrt(-x^2 - 2*x + 3) - 2)^7/(x + 1)^7 - 414)/(8*(sqrt(-x^2 - 2*x + 3) - 2)/(x + 1) + 26*(sqrt(-x^2 - 2*x + 3) - 2)^2/(x + 1)^2 + 8*(sqrt(-x^2 - 2*x + 3) - 2)^3/(x + 1)^3 - 3*(sqrt(-x^2 - 2*x + 3) - 2)^4/(x + 1)^4 - 3)^2","A",0
756,1,81,0,0.370277," ","integrate(1/(x+(x^2-2*x-3)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{x^{2} - 2 \, x - 3} - \frac{3}{4} \, \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{5}{4} \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} + 1 \right|}\right) + \frac{3}{4} \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} \right|}\right) - \frac{3}{4} \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} - 3 \right|}\right)"," ",0,"1/2*x - 1/2*sqrt(x^2 - 2*x - 3) - 3/4*log(abs(2*x + 3)) - 5/4*log(abs(-x + sqrt(x^2 - 2*x - 3) + 1)) + 3/4*log(abs(-x + sqrt(x^2 - 2*x - 3))) - 3/4*log(abs(-x + sqrt(x^2 - 2*x - 3) - 3))","A",0
757,1,143,0,0.512345," ","integrate(1/(x+(x^2-2*x-3)^(1/2))^2,x, algorithm=""giac"")","\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{x^{2} - 2 \, x - 3} - \frac{3 \, {\left(5 \, x - 5 \, \sqrt{x^{2} - 2 \, x - 3} + 3\right)}}{4 \, {\left({\left(x - \sqrt{x^{2} - 2 \, x - 3}\right)}^{2} + 3 \, x - 3 \, \sqrt{x^{2} - 2 \, x - 3}\right)}} - \frac{9}{4 \, {\left(2 \, x + 3\right)}} - 2 \, \log\left({\left| 2 \, x + 3 \right|}\right) - 2 \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} + 1 \right|}\right) + 2 \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} \right|}\right) - 2 \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} - 3 \right|}\right)"," ",0,"1/2*x - 1/2*sqrt(x^2 - 2*x - 3) - 3/4*(5*x - 5*sqrt(x^2 - 2*x - 3) + 3)/((x - sqrt(x^2 - 2*x - 3))^2 + 3*x - 3*sqrt(x^2 - 2*x - 3)) - 9/4/(2*x + 3) - 2*log(abs(2*x + 3)) - 2*log(abs(-x + sqrt(x^2 - 2*x - 3) + 1)) + 2*log(abs(-x + sqrt(x^2 - 2*x - 3))) - 2*log(abs(-x + sqrt(x^2 - 2*x - 3) - 3))","B",0
758,1,184,0,0.422652," ","integrate(1/(x+(x^2-2*x-3)^(1/2))^3,x, algorithm=""giac"")","\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{x^{2} - 2 \, x - 3} - \frac{104 \, {\left(x - \sqrt{x^{2} - 2 \, x - 3}\right)}^{3} + 315 \, {\left(x - \sqrt{x^{2} - 2 \, x - 3}\right)}^{2} + 162 \, x - 162 \, \sqrt{x^{2} - 2 \, x - 3} + 27}{8 \, {\left({\left(x - \sqrt{x^{2} - 2 \, x - 3}\right)}^{2} + 3 \, x - 3 \, \sqrt{x^{2} - 2 \, x - 3}\right)}^{2}} - \frac{9 \, {\left(16 \, x + 21\right)}}{8 \, {\left(2 \, x + 3\right)}^{2}} - 3 \, \log\left({\left| 2 \, x + 3 \right|}\right) - 3 \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} + 1 \right|}\right) + 3 \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} \right|}\right) - 3 \, \log\left({\left| -x + \sqrt{x^{2} - 2 \, x - 3} - 3 \right|}\right)"," ",0,"1/2*x - 1/2*sqrt(x^2 - 2*x - 3) - 1/8*(104*(x - sqrt(x^2 - 2*x - 3))^3 + 315*(x - sqrt(x^2 - 2*x - 3))^2 + 162*x - 162*sqrt(x^2 - 2*x - 3) + 27)/((x - sqrt(x^2 - 2*x - 3))^2 + 3*x - 3*sqrt(x^2 - 2*x - 3))^2 - 9/8*(16*x + 21)/(2*x + 3)^2 - 3*log(abs(2*x + 3)) - 3*log(abs(-x + sqrt(x^2 - 2*x - 3) + 1)) + 3*log(abs(-x + sqrt(x^2 - 2*x - 3))) - 3*log(abs(-x + sqrt(x^2 - 2*x - 3) - 3))","B",0
759,1,197,0,0.452831," ","integrate(1/(x+(-x^2-4*x-3)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} {\left(x + 1\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) + \frac{1}{2} \, \arcsin\left(x + 2\right) + \frac{1}{4} \, \log\left(2 \, x^{2} + 4 \, x + 3\right) + \frac{1}{4} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) - \frac{1}{4} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"-1/2*sqrt(2)*arctan(sqrt(2)*(x + 1)) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/2*arcsin(x + 2) + 1/4*log(2*x^2 + 4*x + 3) + 1/4*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) - 1/4*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","B",0
760,1,263,0,0.462578," ","integrate(1/(x+(-x^2-4*x-3)^(1/2))^2,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\sqrt{2} {\left(x + 1\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) + \frac{x + 3}{2 \, {\left(2 \, x^{2} + 4 \, x + 3\right)}} - \frac{\frac{10 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{7 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} - \frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{3}}{{\left(x + 2\right)}^{3}} + 3}{3 \, {\left(\frac{8 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{14 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + \frac{8 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{3}}{{\left(x + 2\right)}^{3}} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{4}}{{\left(x + 2\right)}^{4}} + 3\right)}}"," ",0,"1/4*sqrt(2)*arctan(sqrt(2)*(x + 1)) - 1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 1/4*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/2*(x + 3)/(2*x^2 + 4*x + 3) - 1/3*(10*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 7*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 - 2*(sqrt(-x^2 - 4*x - 3) - 1)^3/(x + 2)^3 + 3)/(8*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 14*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 8*(sqrt(-x^2 - 4*x - 3) - 1)^3/(x + 2)^3 + 3*(sqrt(-x^2 - 4*x - 3) - 1)^4/(x + 2)^4 + 3)","B",0
761,1,367,0,0.452751," ","integrate(1/(x+(-x^2-4*x-3)^(1/2))^3,x, algorithm=""giac"")","-\frac{3}{8} \, \sqrt{2} \arctan\left(\sqrt{2} {\left(x + 1\right)}\right) + \frac{3}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{3}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) - \frac{6 \, x^{3} + 16 \, x^{2} + 15 \, x + 9}{4 \, {\left(2 \, x^{2} + 4 \, x + 3\right)}^{2}} + \frac{\frac{618 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{1547 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + \frac{2362 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{3}}{{\left(x + 2\right)}^{3}} + \frac{2223 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{4}}{{\left(x + 2\right)}^{4}} + \frac{1174 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{5}}{{\left(x + 2\right)}^{5}} + \frac{377 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{6}}{{\left(x + 2\right)}^{6}} + \frac{6 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{7}}{{\left(x + 2\right)}^{7}} + 117}{18 \, {\left(\frac{8 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{14 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + \frac{8 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{3}}{{\left(x + 2\right)}^{3}} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{4}}{{\left(x + 2\right)}^{4}} + 3\right)}^{2}}"," ",0,"-3/8*sqrt(2)*arctan(sqrt(2)*(x + 1)) + 3/8*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 3/8*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 1/4*(6*x^3 + 16*x^2 + 15*x + 9)/(2*x^2 + 4*x + 3)^2 + 1/18*(618*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1547*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 2362*(sqrt(-x^2 - 4*x - 3) - 1)^3/(x + 2)^3 + 2223*(sqrt(-x^2 - 4*x - 3) - 1)^4/(x + 2)^4 + 1174*(sqrt(-x^2 - 4*x - 3) - 1)^5/(x + 2)^5 + 377*(sqrt(-x^2 - 4*x - 3) - 1)^6/(x + 2)^6 + 6*(sqrt(-x^2 - 4*x - 3) - 1)^7/(x + 2)^7 + 117)/(8*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 14*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 8*(sqrt(-x^2 - 4*x - 3) - 1)^3/(x + 2)^3 + 3*(sqrt(-x^2 - 4*x - 3) - 1)^4/(x + 2)^4 + 3)^2","B",0
762,1,58,0,0.328880," ","integrate(x^3*(1+x)^3*(1+2*x)*(-x^4-2*x^3-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{4} + 2 \, x^{3} + x^{2} - 1\right)}^{2} \sqrt{-x^{4} - 2 \, x^{3} - x^{2} + 1} - \frac{1}{3} \, {\left(-x^{4} - 2 \, x^{3} - x^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/5*(x^4 + 2*x^3 + x^2 - 1)^2*sqrt(-x^4 - 2*x^3 - x^2 + 1) - 1/3*(-x^4 - 2*x^3 - x^2 + 1)^(3/2)","A",0
763,1,58,0,0.386912," ","integrate((1+2*x)*(x^2+x)^3*(1-(x^2+x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{4} + 2 \, x^{3} + x^{2} - 1\right)}^{2} \sqrt{-x^{4} - 2 \, x^{3} - x^{2} + 1} - \frac{1}{3} \, {\left(-x^{4} - 2 \, x^{3} - x^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/5*(x^4 + 2*x^3 + x^2 - 1)^2*sqrt(-x^4 - 2*x^3 - x^2 + 1) - 1/3*(-x^4 - 2*x^3 - x^2 + 1)^(3/2)","A",0
764,0,0,0,0.000000," ","integrate((-x^4+4*x^3-8*x^2+8*x)^(3/2),x, algorithm=""giac"")","\int {\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-x^4 + 4*x^3 - 8*x^2 + 8*x)^(3/2), x)","F",0
765,0,0,0,0.000000," ","integrate((-x^4+4*x^3-8*x^2+8*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}\,{d x}"," ",0,"integrate(sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x), x)","F",0
766,0,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+8*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + 4*x^3 - 8*x^2 + 8*x), x)","F",0
767,0,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+8*x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-x^4 + 4*x^3 - 8*x^2 + 8*x)^(-3/2), x)","F",0
768,0,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+8*x)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-x^4 + 4*x^3 - 8*x^2 + 8*x)^(-5/2), x)","F",0
769,0,0,0,0.000000," ","integrate(((2-x)*x*(x^2-2*x+4))^(3/2),x, algorithm=""giac"")","\int \left(-{\left(x^{2} - 2 \, x + 4\right)} {\left(x - 2\right)} x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-(x^2 - 2*x + 4)*(x - 2)*x)^(3/2), x)","F",0
770,0,0,0,0.000000," ","integrate(((2-x)*x*(x^2-2*x+4))^(1/2),x, algorithm=""giac"")","\int \sqrt{-{\left(x^{2} - 2 \, x + 4\right)} {\left(x - 2\right)} x}\,{d x}"," ",0,"integrate(sqrt(-(x^2 - 2*x + 4)*(x - 2)*x), x)","F",0
771,0,0,0,0.000000," ","integrate(1/((2-x)*x*(x^2-2*x+4))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-{\left(x^{2} - 2 \, x + 4\right)} {\left(x - 2\right)} x}}\,{d x}"," ",0,"integrate(1/sqrt(-(x^2 - 2*x + 4)*(x - 2)*x), x)","F",0
772,0,0,0,0.000000," ","integrate(1/((2-x)*x*(x^2-2*x+4))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\left(-{\left(x^{2} - 2 \, x + 4\right)} {\left(x - 2\right)} x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-(x^2 - 2*x + 4)*(x - 2)*x)^(-3/2), x)","F",0
773,0,0,0,0.000000," ","integrate(1/((2-x)*x*(x^2-2*x+4))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\left(-{\left(x^{2} - 2 \, x + 4\right)} {\left(x - 2\right)} x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-(x^2 - 2*x + 4)*(x - 2)*x)^(-5/2), x)","F",0
774,0,0,0,0.000000," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(3/2),x, algorithm=""giac"")","\int {\left(d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c)^(3/2), x)","F",0
775,0,0,0,0.000000," ","integrate((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2),x, algorithm=""giac"")","\int \sqrt{d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c}\,{d x}"," ",0,"integrate(sqrt(d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c), x)","F",0
776,0,0,0,0.000000," ","integrate(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c}}\,{d x}"," ",0,"integrate(1/sqrt(d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c), x)","F",0
777,0,0,0,0.000000," ","integrate(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(d^{2} x^{4} + 4 \, c d x^{3} + 4 \, c^{2} x^{2} + 4 \, a c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d^2*x^4 + 4*c*d*x^3 + 4*c^2*x^2 + 4*a*c)^(-3/2), x)","F",0
778,-1,0,0,0.000000," ","integrate((8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,0,0,0,0.000000," ","integrate(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{8 \, e^{3} x^{4} + 8 \, d e^{2} x^{3} - d^{3} x + 8 \, a e^{2}}}\,{d x}"," ",0,"integrate(1/sqrt(8*e^3*x^4 + 8*d*e^2*x^3 - d^3*x + 8*a*e^2), x)","F",0
780,-1,0,0,0.000000," ","integrate(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
781,-1,0,0,0.000000," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
782,0,0,0,0.000000," ","integrate((-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}\,{d x}"," ",0,"integrate(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
783,0,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}}\,{d x}"," ",0,"integrate(1/sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
784,0,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-x^4 + 4*x^3 - 8*x^2 + a + 8*x)^(-3/2), x)","F",0
785,-1,0,0,0.000000," ","integrate(1/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
786,-1,0,0,0.000000," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
787,0,0,0,0.000000," ","integrate(x*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x\,{d x}"," ",0,"integrate(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x, x)","F",0
788,0,0,0,0.000000," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}}\,{d x}"," ",0,"integrate(x/sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
789,0,0,0,0.000000," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)^(3/2), x)","F",0
790,-1,0,0,0.000000," ","integrate(x/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
791,-1,0,0,0.000000," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
792,0,0,0,0.000000," ","integrate(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x} x^{2}\,{d x}"," ",0,"integrate(sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)*x^2, x)","F",0
793,0,0,0,0.000000," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x}}\,{d x}"," ",0,"integrate(x^2/sqrt(-x^4 + 4*x^3 - 8*x^2 + a + 8*x), x)","F",0
794,0,0,0,0.000000," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(-x^{4} + 4 \, x^{3} - 8 \, x^{2} + a + 8 \, x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(-x^4 + 4*x^3 - 8*x^2 + a + 8*x)^(3/2), x)","F",0
795,-1,0,0,0.000000," ","integrate(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
796,0,0,0,0.000000," ","integrate(1/(8*x^4-x^3+8*x+8)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{8 \, x^{4} - x^{3} + 8 \, x + 8}}\,{d x}"," ",0,"integrate(1/sqrt(8*x^4 - x^3 + 8*x + 8), x)","F",0
797,0,0,0,0.000000," ","integrate(1/(8*x^4-x^3+8*x+8)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(8 \, x^{4} - x^{3} + 8 \, x + 8\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((8*x^4 - x^3 + 8*x + 8)^(-3/2), x)","F",0
798,0,0,0,0.000000," ","integrate(1/(4*x^4+4*x^2+4*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, x^{4} + 4 \, x^{2} + 4 \, x + 1}}\,{d x}"," ",0,"integrate(1/sqrt(4*x^4 + 4*x^2 + 4*x + 1), x)","F",0
799,0,0,0,0.000000," ","integrate(1/(4*x^4+4*x^2+4*x+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(4 \, x^{4} + 4 \, x^{2} + 4 \, x + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((4*x^4 + 4*x^2 + 4*x + 1)^(-3/2), x)","F",0
800,0,0,0,0.000000," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8}}\,{d x}"," ",0,"integrate(1/sqrt(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8), x)","F",0
801,0,0,0,0.000000," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^(-3/2), x)","F",0
802,0,0,0,0.000000," ","integrate(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(8 \, x^{4} - 15 \, x^{3} + 8 \, x^{2} + 24 \, x + 8\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^(-5/2), x)","F",0
803,0,0,0,0.000000," ","integrate(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9}}\,{d x}"," ",0,"integrate(1/sqrt(3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9), x)","F",0
804,0,0,0,0.000000," ","integrate(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{4} + 15 \, x^{3} - 44 \, x^{2} - 6 \, x + 9\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^4 + 15*x^3 - 44*x^2 - 6*x + 9)^(-3/2), x)","F",0
805,-2,0,0,0.000000," ","integrate((2*(3-x)^(1/2)+3/(1+x)^(1/2))^2/x,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-8,0,%%%{4,[2]%%%}+%%%{-8,[1]%%%}+%%%{4,[0]%%%}] at parameters values [-91.616423693]Warning, choosing root of [1,0,-8,0,%%%{4,[2]%%%}+%%%{-8,[1]%%%}+%%%{4,[0]%%%}] at parameters values [-15.8804557086]-9*ln(abs(-x-1))+21*ln(abs(x))+4*(-x+3)+36*ln(abs(-4*sqrt(3)+6*(2*sqrt(-x+3)/(-2*sqrt(x+1)+4)-1/2*(-2*sqrt(x+1)+4)/sqrt(-x+3)))/abs(4*sqrt(3)+6*(2*sqrt(-x+3)/(-2*sqrt(x+1)+4)-1/2*(-2*sqrt(x+1)+4)/sqrt(-x+3))))/sqrt(3)-24*(-1/2*pi-atan(sqrt(-x+3)*((-1/2*(-2*sqrt(x+1)+4)/sqrt(-x+3))^2-1)/(-2*sqrt(x+1)+4)))","F(-2)",0
806,1,89,0,0.419589," ","integrate((x^2+x-1)/((x^2+1)^(1/2)+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{2} + 1} {\left(x + 2\right)} - x - \frac{2}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 1} - \frac{1}{x} + \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1}\right) - \log\left({\left| x \right|}\right) - \log\left({\left| -x + \sqrt{x^{2} + 1} + 1 \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + 1} - 1 \right|}\right)"," ",0,"1/2*sqrt(x^2 + 1)*(x + 2) - x - 2/((x - sqrt(x^2 + 1))^2 - 1) - 1/x + 1/2*log(-x + sqrt(x^2 + 1)) - log(abs(x)) - log(abs(-x + sqrt(x^2 + 1) + 1)) + log(abs(-x + sqrt(x^2 + 1) - 1))","A",0
807,1,80,0,0.438895," ","integrate((x^2+x-1)/(1+x+(x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{6} \, x^{3} + \frac{1}{2} \, x^{2} - \frac{1}{12} \, {\left({\left(2 \, x + 3\right)} x - 4\right)} \sqrt{x^{2} + 1} + \frac{1}{4} \, \log\left(-x + \sqrt{x^{2} + 1}\right) - \frac{1}{2} \, \log\left({\left| x \right|}\right) - \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} + 1} + 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} + 1} - 1 \right|}\right)"," ",0,"1/6*x^3 + 1/2*x^2 - 1/12*((2*x + 3)*x - 4)*sqrt(x^2 + 1) + 1/4*log(-x + sqrt(x^2 + 1)) - 1/2*log(abs(x)) - 1/2*log(abs(-x + sqrt(x^2 + 1) + 1)) + 1/2*log(abs(-x + sqrt(x^2 + 1) - 1))","A",0
808,1,12,0,0.395504," ","integrate((x+2*(-1+x)^(1/2))/x/(-1+x)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x - 1} + 2 \, \log\left(x\right)"," ",0,"2*sqrt(x - 1) + 2*log(x)","A",0
809,1,43,0,0.430332," ","integrate((a+b*x^(2/3)+c*x^(1/2))^2,x, algorithm=""giac"")","\frac{3}{7} \, b^{2} x^{\frac{7}{3}} + \frac{12}{13} \, b c x^{\frac{13}{6}} + \frac{1}{2} \, c^{2} x^{2} + \frac{6}{5} \, a b x^{\frac{5}{3}} + \frac{4}{3} \, a c x^{\frac{3}{2}} + a^{2} x"," ",0,"3/7*b^2*x^(7/3) + 12/13*b*c*x^(13/6) + 1/2*c^2*x^2 + 6/5*a*b*x^(5/3) + 4/3*a*c*x^(3/2) + a^2*x","A",0
810,1,84,0,0.344514," ","integrate((a+b*x^(2/3)+c*x^(1/2))^3,x, algorithm=""giac"")","\frac{1}{3} \, b^{3} x^{3} + \frac{18}{17} \, b^{2} c x^{\frac{17}{6}} + \frac{9}{8} \, b c^{2} x^{\frac{8}{3}} + \frac{2}{5} \, c^{3} x^{\frac{5}{2}} + \frac{9}{7} \, a b^{2} x^{\frac{7}{3}} + \frac{36}{13} \, a b c x^{\frac{13}{6}} + \frac{3}{2} \, a c^{2} x^{2} + \frac{9}{5} \, a^{2} b x^{\frac{5}{3}} + 2 \, a^{2} c x^{\frac{3}{2}} + a^{3} x"," ",0,"1/3*b^3*x^3 + 18/17*b^2*c*x^(17/6) + 9/8*b*c^2*x^(8/3) + 2/5*c^3*x^(5/2) + 9/7*a*b^2*x^(7/3) + 36/13*a*b*c*x^(13/6) + 3/2*a*c^2*x^2 + 9/5*a^2*b*x^(5/3) + 2*a^2*c*x^(3/2) + a^3*x","A",0
811,-2,0,0,0.000000," ","integrate((x^2-1)/x^3/(a-b+b/x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%}+%%%{-2,[0,1,1]%%%}+%%%{2,[0,0,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{2,[1,3,1]%%%}+%%%{4,[1,2,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{-2,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-2,[0,3,2]%%%}+%%%{-1,[0,2,2]%%%}+%%%{2,[0,1,2]%%%}+%%%{1,[0,0,2]%%%}] at parameters values [86,-97,-82]Sign error (%%%{b,0%%%}+%%%{-2*sqrt(a-b)*sqrt(b),1/2%%%}+%%%{2*(a-b),1%%%}+%%%{-(a*sqrt(a-b)*sqrt(b)-b*sqrt(a-b)*sqrt(b))/b,3/2%%%}+%%%{-(-a^2*sqrt(a-b)*sqrt(b)+2*a*b*sqrt(a-b)*sqrt(b)-b^2*sqrt(a-b)*sqrt(b))/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
812,-2,0,0,0.000000," ","integrate((x^2-1)/x^3/(a+b*(-1+1/x^2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%}+%%%{-2,[0,1,1]%%%}+%%%{2,[0,0,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{2,[1,3,1]%%%}+%%%{4,[1,2,1]%%%}+%%%{-2,[1,1,1]%%%}+%%%{-2,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-2,[0,3,2]%%%}+%%%{-1,[0,2,2]%%%}+%%%{2,[0,1,2]%%%}+%%%{1,[0,0,2]%%%}] at parameters values [86,-97,-82]Sign error (%%%{b,0%%%}+%%%{-2*sqrt(a-b)*sqrt(b),1/2%%%}+%%%{2*(a-b),1%%%}+%%%{-(a*sqrt(a-b)*sqrt(b)-b*sqrt(a-b)*sqrt(b))/b,3/2%%%}+%%%{-(-a^2*sqrt(a-b)*sqrt(b)+2*a*b*sqrt(a-b)*sqrt(b)-b^2*sqrt(a-b)*sqrt(b))/(4*b^2),5/2%%%}+%%%{undef,7/2%%%})Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
813,1,123,0,0.435780," ","integrate((1+x)/(x^2+4)/(x^2+9)^(1/2),x, algorithm=""giac"")","-\frac{1}{10} \, \sqrt{5} \arctan\left(\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{5} - \frac{1}{2} \, \sqrt{x^{2} + 9}\right) - \frac{1}{10} \, \sqrt{5} \arctan\left(-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{5} + \frac{1}{2} \, \sqrt{x^{2} + 9}\right) + \frac{1}{10} \, \sqrt{5} \log\left({\left(x - \sqrt{x^{2} + 9}\right)}^{2} + 2 \, \sqrt{5} {\left(x - \sqrt{x^{2} + 9}\right)} + 9\right) - \frac{1}{10} \, \sqrt{5} \log\left({\left(x - \sqrt{x^{2} + 9}\right)}^{2} - 2 \, \sqrt{5} {\left(x - \sqrt{x^{2} + 9}\right)} + 9\right)"," ",0,"-1/10*sqrt(5)*arctan(1/2*x - 1/2*sqrt(5) - 1/2*sqrt(x^2 + 9)) - 1/10*sqrt(5)*arctan(-1/2*x - 1/2*sqrt(5) + 1/2*sqrt(x^2 + 9)) + 1/10*sqrt(5)*log((x - sqrt(x^2 + 9))^2 + 2*sqrt(5)*(x - sqrt(x^2 + 9)) + 9) - 1/10*sqrt(5)*log((x - sqrt(x^2 + 9))^2 - 2*sqrt(5)*(x - sqrt(x^2 + 9)) + 9)","B",0
814,1,18,0,0.328608," ","integrate(x*(1+(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{1}{3} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} - \frac{1}{2}"," ",0,"1/2*x^2 - 1/3*(-x^2 + 1)^(3/2) - 1/2","A",0
815,1,54,0,0.450767," ","integrate(x*(1+(1-x)^(1/2)*(1+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x + 1\right)}^{2} + \frac{1}{6} \, {\left({\left(2 \, x - 5\right)} {\left(x + 1\right)} + 9\right)} \sqrt{x + 1} \sqrt{-x + 1} + \frac{1}{2} \, \sqrt{x + 1} {\left(x - 2\right)} \sqrt{-x + 1} - x - 1"," ",0,"1/2*(x + 1)^2 + 1/6*((2*x - 5)*(x + 1) + 9)*sqrt(x + 1)*sqrt(-x + 1) + 1/2*sqrt(x + 1)*(x - 2)*sqrt(-x + 1) - x - 1","B",0
816,1,39,0,0.384518," ","integrate(x*(1+1/(2+x)^(1/2)/(3+x)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x + 3\right)}^{2} + \sqrt{x + 3} \sqrt{x + 2} - 3 \, x + 5 \, \log\left(\sqrt{x + 3} - \sqrt{x + 2}\right) - 9"," ",0,"1/2*(x + 3)^2 + sqrt(x + 3)*sqrt(x + 2) - 3*x + 5*log(sqrt(x + 3) - sqrt(x + 2)) - 9","A",0
817,1,31,0,0.399163," ","integrate((x-(x^6)^(1/2))/x/(-x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\mathrm{sgn}\left(x\right) + 1\right)} \arctan\left(x\right) - \frac{1}{4} \, {\left(\mathrm{sgn}\left(x\right) - 1\right)} \log\left({\left| x + 1 \right|}\right) + \frac{1}{4} \, {\left(\mathrm{sgn}\left(x\right) - 1\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*(sgn(x) + 1)*arctan(x) - 1/4*(sgn(x) - 1)*log(abs(x + 1)) + 1/4*(sgn(x) - 1)*log(abs(x - 1))","A",0
818,1,31,0,0.389927," ","integrate((1-(x^6)^(1/2)/x)/(-x^4+1),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\mathrm{sgn}\left(x\right) + 1\right)} \arctan\left(x\right) - \frac{1}{4} \, {\left(\mathrm{sgn}\left(x\right) - 1\right)} \log\left({\left| x + 1 \right|}\right) + \frac{1}{4} \, {\left(\mathrm{sgn}\left(x\right) - 1\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*(sgn(x) + 1)*arctan(x) - 1/4*(sgn(x) - 1)*log(abs(x + 1)) + 1/4*(sgn(x) - 1)*log(abs(x - 1))","A",0
819,1,31,0,0.362797," ","integrate((x-(x^6)^(1/2))/(-x^5+x),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\mathrm{sgn}\left(x\right) + 1\right)} \arctan\left(x\right) - \frac{1}{4} \, {\left(\mathrm{sgn}\left(x\right) - 1\right)} \log\left({\left| x + 1 \right|}\right) + \frac{1}{4} \, {\left(\mathrm{sgn}\left(x\right) - 1\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*(sgn(x) + 1)*arctan(x) - 1/4*(sgn(x) - 1)*log(abs(x + 1)) + 1/4*(sgn(x) - 1)*log(abs(x - 1))","A",0
820,1,12,0,0.369563," ","integrate(x/(x+(x^6)^(1/2)),x, algorithm=""giac"")","\frac{\arctan\left(x \sqrt{\mathrm{sgn}\left(x\right)}\right)}{\sqrt{\mathrm{sgn}\left(x\right)}}"," ",0,"arctan(x*sqrt(sgn(x)))/sqrt(sgn(x))","A",0
821,1,6,0,0.319247," ","integrate((x^(1/2)-(x^3)^(1/2))/(-x^3+x),x, algorithm=""giac"")","2 \, \arctan\left(\sqrt{x}\right)"," ",0,"2*arctan(sqrt(x))","A",0
822,1,6,0,0.318328," ","integrate(1/(x^(1/2)+(x^3)^(1/2)),x, algorithm=""giac"")","2 \, \arctan\left(\sqrt{x}\right)"," ",0,"2*arctan(sqrt(x))","A",0
823,1,8,0,0.413779," ","integrate(1/((-1+x)^(1/2)+((-1+x)^3)^(1/2)),x, algorithm=""giac"")","2 \, \arctan\left(\sqrt{x - 1}\right)"," ",0,"2*arctan(sqrt(x - 1))","A",0
824,1,54,0,0.442542," ","integrate(-3/(4+5*x)^2+(-5-4*x)/(4+5*x)^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\frac{8}{5 \, x + 4} + \frac{9}{{\left(5 \, x + 4\right)}^{2}} - 1}}{5 \, \mathrm{sgn}\left(\frac{1}{5 \, x + 4}\right)} + \frac{3}{5 \, {\left(5 \, x + 4\right)}} - \frac{1}{5} i \, \mathrm{sgn}\left(\frac{1}{5 \, x + 4}\right)"," ",0,"1/5*sqrt(8/(5*x + 4) + 9/(5*x + 4)^2 - 1)/sgn(1/(5*x + 4)) + 3/5/(5*x + 4) - 1/5*I*sgn(1/(5*x + 4))","C",0
825,1,54,0,0.588782," ","integrate((-5-4*x-3*(-x^2+1)^(1/2))/(4+5*x)^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\frac{8}{5 \, x + 4} + \frac{9}{{\left(5 \, x + 4\right)}^{2}} - 1}}{5 \, \mathrm{sgn}\left(\frac{1}{5 \, x + 4}\right)} + \frac{3}{5 \, {\left(5 \, x + 4\right)}} - \frac{1}{5} i \, \mathrm{sgn}\left(\frac{1}{5 \, x + 4}\right)"," ",0,"1/5*sqrt(8/(5*x + 4) + 9/(5*x + 4)^2 - 1)/sgn(1/(5*x + 4)) + 3/5/(5*x + 4) - 1/5*I*sgn(1/(5*x + 4))","C",0
826,1,68,0,0.500012," ","integrate(1/(-3*x^2+3+(-5-4*x)*(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - 4}{4 \, {\left(\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 2\right)}} + \frac{3}{5 \, {\left(5 \, x + 4\right)}}"," ",0,"1/4*(5*(sqrt(-x^2 + 1) - 1)/x - 4)/(5*(sqrt(-x^2 + 1) - 1)/x - 2*(sqrt(-x^2 + 1) - 1)^2/x^2 - 2) + 3/5/(5*x + 4)","B",0
827,1,68,0,0.366292," ","integrate(1/(3-3*x^2-5*(-x^2+1)^(1/2)-4*x*(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - 4}{4 \, {\left(\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 2\right)}} + \frac{3}{5 \, {\left(5 \, x + 4\right)}}"," ",0,"1/4*(5*(sqrt(-x^2 + 1) - 1)/x - 4)/(5*(sqrt(-x^2 + 1) - 1)/x - 2*(sqrt(-x^2 + 1) - 1)^2/x^2 - 2) + 3/5/(5*x + 4)","B",0
828,1,68,0,0.615673," ","integrate((-1+(-x^2+1)^(1/2))/(2+x-2*(-x^2+1)^(1/2))^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - 4}{4 \, {\left(\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 2\right)}} + \frac{3}{5 \, {\left(5 \, x + 4\right)}}"," ",0,"1/4*(5*(sqrt(-x^2 + 1) - 1)/x - 4)/(5*(sqrt(-x^2 + 1) - 1)/x - 2*(sqrt(-x^2 + 1) - 1)^2/x^2 - 2) + 3/5/(5*x + 4)","B",0
829,0,0,0,0.000000," ","integrate((a+b*x^(-1+n))/(c*x+d*x^n),x, algorithm=""giac"")","\int \frac{b x^{n - 1} + a}{c x + d x^{n}}\,{d x}"," ",0,"integrate((b*x^(n - 1) + a)/(c*x + d*x^n), x)","F",0
830,1,57,0,0.455556," ","integrate((2*x^2+1)^(1/2)/(1+(2*x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 1}\right) + x - \frac{\sqrt{2}}{{\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} - 1} - \frac{1}{2 \, x}"," ",0,"1/2*sqrt(2)*log(-sqrt(2)*x + sqrt(2*x^2 + 1)) + x - sqrt(2)/((sqrt(2)*x - sqrt(2*x^2 + 1))^2 - 1) - 1/2/x","A",0
831,1,133,0,0.567473," ","integrate((4*x^2-1)^(1/2)/(x+(4*x^2-1)^(1/2)),x, algorithm=""giac"")","\frac{1}{18} \, \sqrt{3} \log\left(\frac{{\left| 6 \, x - 2 \, \sqrt{3} \right|}}{{\left| 6 \, x + 2 \, \sqrt{3} \right|}}\right) - \frac{1}{18} \, \sqrt{3} \log\left(-\frac{{\left| -12 \, x - 4 \, \sqrt{3} + 6 \, \sqrt{4 \, x^{2} - 1} + \frac{6}{2 \, x - \sqrt{4 \, x^{2} - 1}} \right|}}{2 \, {\left(6 \, x - 2 \, \sqrt{3} - 3 \, \sqrt{4 \, x^{2} - 1} - \frac{3}{2 \, x - \sqrt{4 \, x^{2} - 1}}\right)}}\right) + \frac{4}{3} \, x - \frac{1}{3} \, \sqrt{4 \, x^{2} - 1}"," ",0,"1/18*sqrt(3)*log(abs(6*x - 2*sqrt(3))/abs(6*x + 2*sqrt(3))) - 1/18*sqrt(3)*log(-1/2*abs(-12*x - 4*sqrt(3) + 6*sqrt(4*x^2 - 1) + 6/(2*x - sqrt(4*x^2 - 1)))/(6*x - 2*sqrt(3) - 3*sqrt(4*x^2 - 1) - 3/(2*x - sqrt(4*x^2 - 1)))) + 4/3*x - 1/3*sqrt(4*x^2 - 1)","B",0
832,1,536,0,0.491783," ","integrate((c*x^2+b*x+a)/(e*x+d)^3/(x^2-1)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, a d^{2} + c d^{2} - 3 \, b d e + a e^{2} + 2 \, c e^{2}\right)} \arctan\left(-\frac{{\left(x - \sqrt{x^{2} - 1}\right)} e + d}{\sqrt{-d^{2} + e^{2}}}\right)}{{\left(d^{4} - 2 \, d^{2} e^{2} + e^{4}\right)} \sqrt{-d^{2} + e^{2}}} + \frac{2 \, c d^{4} {\left(x - \sqrt{x^{2} - 1}\right)}^{3} e + 2 \, c d^{5} {\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 2 \, b d^{4} {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e - 2 \, a d^{2} {\left(x - \sqrt{x^{2} - 1}\right)}^{3} e^{3} - 5 \, c d^{2} {\left(x - \sqrt{x^{2} - 1}\right)}^{3} e^{3} - 6 \, a d^{3} {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e^{2} - 7 \, c d^{3} {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e^{2} + 2 \, c d^{4} {\left(x - \sqrt{x^{2} - 1}\right)} e + 3 \, b d {\left(x - \sqrt{x^{2} - 1}\right)}^{3} e^{4} + 5 \, b d^{2} {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e^{3} + 4 \, b d^{3} {\left(x - \sqrt{x^{2} - 1}\right)} e^{2} - a {\left(x - \sqrt{x^{2} - 1}\right)}^{3} e^{5} - 3 \, a d {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e^{4} - 4 \, c d {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e^{4} - 10 \, a d^{2} {\left(x - \sqrt{x^{2} - 1}\right)} e^{3} - 11 \, c d^{2} {\left(x - \sqrt{x^{2} - 1}\right)} e^{3} + c d^{3} e^{2} + 2 \, b {\left(x - \sqrt{x^{2} - 1}\right)}^{2} e^{5} + 5 \, b d {\left(x - \sqrt{x^{2} - 1}\right)} e^{4} + b d^{2} e^{3} + a {\left(x - \sqrt{x^{2} - 1}\right)} e^{5} - 3 \, a d e^{4} - 4 \, c d e^{4} + 2 \, b e^{5}}{{\left(d^{4} e^{2} - 2 \, d^{2} e^{4} + e^{6}\right)} {\left({\left(x - \sqrt{x^{2} - 1}\right)}^{2} e + 2 \, d {\left(x - \sqrt{x^{2} - 1}\right)} + e\right)}^{2}}"," ",0,"(2*a*d^2 + c*d^2 - 3*b*d*e + a*e^2 + 2*c*e^2)*arctan(-((x - sqrt(x^2 - 1))*e + d)/sqrt(-d^2 + e^2))/((d^4 - 2*d^2*e^2 + e^4)*sqrt(-d^2 + e^2)) + (2*c*d^4*(x - sqrt(x^2 - 1))^3*e + 2*c*d^5*(x - sqrt(x^2 - 1))^2 + 2*b*d^4*(x - sqrt(x^2 - 1))^2*e - 2*a*d^2*(x - sqrt(x^2 - 1))^3*e^3 - 5*c*d^2*(x - sqrt(x^2 - 1))^3*e^3 - 6*a*d^3*(x - sqrt(x^2 - 1))^2*e^2 - 7*c*d^3*(x - sqrt(x^2 - 1))^2*e^2 + 2*c*d^4*(x - sqrt(x^2 - 1))*e + 3*b*d*(x - sqrt(x^2 - 1))^3*e^4 + 5*b*d^2*(x - sqrt(x^2 - 1))^2*e^3 + 4*b*d^3*(x - sqrt(x^2 - 1))*e^2 - a*(x - sqrt(x^2 - 1))^3*e^5 - 3*a*d*(x - sqrt(x^2 - 1))^2*e^4 - 4*c*d*(x - sqrt(x^2 - 1))^2*e^4 - 10*a*d^2*(x - sqrt(x^2 - 1))*e^3 - 11*c*d^2*(x - sqrt(x^2 - 1))*e^3 + c*d^3*e^2 + 2*b*(x - sqrt(x^2 - 1))^2*e^5 + 5*b*d*(x - sqrt(x^2 - 1))*e^4 + b*d^2*e^3 + a*(x - sqrt(x^2 - 1))*e^5 - 3*a*d*e^4 - 4*c*d*e^4 + 2*b*e^5)/((d^4*e^2 - 2*d^2*e^4 + e^6)*((x - sqrt(x^2 - 1))^2*e + 2*d*(x - sqrt(x^2 - 1)) + e)^2)","B",0
833,1,34,0,0.381747," ","integrate((2*x^8+1)/x/(x^8+1)^(3/2),x, algorithm=""giac"")","-\frac{1}{4 \, \sqrt{x^{8} + 1}} - \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"-1/4/sqrt(x^8 + 1) - 1/8*log(sqrt(x^8 + 1) + 1) + 1/8*log(sqrt(x^8 + 1) - 1)","A",0
834,1,34,0,0.495032," ","integrate((2*x^8+1)*(x^8+1)^(1/2)/(x^17+2*x^9+x),x, algorithm=""giac"")","-\frac{1}{4 \, \sqrt{x^{8} + 1}} - \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} + 1\right) + \frac{1}{8} \, \log\left(\sqrt{x^{8} + 1} - 1\right)"," ",0,"-1/4/sqrt(x^8 + 1) - 1/8*log(sqrt(x^8 + 1) + 1) + 1/8*log(sqrt(x^8 + 1) - 1)","A",0
835,1,18,0,0.340436," ","integrate(1-9*x^2+x/(-9*x^2+1)^(1/2),x, algorithm=""giac"")","-3 \, x^{3} + x - \frac{1}{9} \, \sqrt{-9 \, x^{2} + 1}"," ",0,"-3*x^3 + x - 1/9*sqrt(-9*x^2 + 1)","A",0
836,1,18,0,0.566693," ","integrate((x+(-9*x^2+1)^(3/2))/(-9*x^2+1)^(1/2),x, algorithm=""giac"")","-3 \, x^{3} + x - \frac{1}{9} \, \sqrt{-9 \, x^{2} + 1}"," ",0,"-3*x^3 + x - 1/9*sqrt(-9*x^2 + 1)","A",0
837,1,11,0,0.370988," ","integrate((x-3*x^(1/2))^(2/3)*(-3+2*x^(1/2))/x^(1/2),x, algorithm=""giac"")","\frac{6}{5} \, {\left(x - 3 \, \sqrt{x}\right)}^{\frac{5}{3}}"," ",0,"6/5*(x - 3*sqrt(x))^(5/3)","A",0
838,1,11,0,0.325839," ","integrate((9+2*x-9*x^(1/2))/(x-3*x^(1/2))^(1/3),x, algorithm=""giac"")","\frac{6}{5} \, {\left(x - 3 \, \sqrt{x}\right)}^{\frac{5}{3}}"," ",0,"6/5*(x - 3*sqrt(x))^(5/3)","A",0
839,1,6,0,0.364190," ","integrate(1/(-9*x^2+4)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \arcsin\left(\frac{3}{2} \, x\right)"," ",0,"1/3*arcsin(3/2*x)","A",0
840,1,12,0,0.366035," ","integrate(1/(2-3*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, \arcsin\left(\frac{1}{2} \, \sqrt{3 \, x + 2}\right)"," ",0,"2/3*arcsin(1/2*sqrt(3*x + 2))","A",0
841,1,6,0,0.394657," ","integrate(1/((2-3*x)*(2+3*x))^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \arcsin\left(\frac{3}{2} \, x\right)"," ",0,"1/3*arcsin(3/2*x)","A",0
842,1,6,0,0.419513," ","integrate(1/(-x^2-2*x+15)^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{1}{4} \, x + \frac{1}{4}\right)"," ",0,"arcsin(1/4*x + 1/4)","A",0
843,1,13,0,0.326037," ","integrate(1/(3-x)^(1/2)/(5+x)^(1/2),x, algorithm=""giac"")","2 \, \arcsin\left(\frac{1}{4} \, \sqrt{2} \sqrt{x + 5}\right)"," ",0,"2*arcsin(1/4*sqrt(2)*sqrt(x + 5))","B",0
844,1,6,0,0.345198," ","integrate(1/((3-x)*(5+x))^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{1}{4} \, x + \frac{1}{4}\right)"," ",0,"arcsin(1/4*x + 1/4)","A",0
845,1,4,0,0.342329," ","integrate(1/(-x^2-8*x-15)^(1/2),x, algorithm=""giac"")","\arcsin\left(x + 4\right)"," ",0,"arcsin(x + 4)","A",0
846,1,13,0,0.315925," ","integrate(1/(-3-x)^(1/2)/(5+x)^(1/2),x, algorithm=""giac"")","2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{x + 5}\right)"," ",0,"2*arcsin(1/2*sqrt(2)*sqrt(x + 5))","B",0
847,1,4,0,0.387793," ","integrate(1/((-3-x)*(5+x))^(1/2),x, algorithm=""giac"")","\arcsin\left(x + 4\right)"," ",0,"arcsin(x + 4)","A",0
848,1,7,0,0.360605," ","integrate(1-x^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, x^{\frac{3}{2}} + x"," ",0,"-2/3*x^(3/2) + x","A",0
849,1,7,0,0.332220," ","integrate((1-x)/(1+x^(1/2)),x, algorithm=""giac"")","-\frac{2}{3} \, x^{\frac{3}{2}} + x"," ",0,"-2/3*x^(3/2) + x","A",0
850,1,10,0,0.421774," ","integrate((1/(-x^2+1))^(1/2),x, algorithm=""giac"")","-\arcsin\left(x\right) \mathrm{sgn}\left(x^{2} - 1\right)"," ",0,"-arcsin(x)*sgn(x^2 - 1)","A",0
851,1,10,0,0.337371," ","integrate(((x^2+1)/(-x^4+1))^(1/2),x, algorithm=""giac"")","-\arcsin\left(x\right) \mathrm{sgn}\left(x^{2} - 1\right)"," ",0,"-arcsin(x)*sgn(x^2 - 1)","A",0
852,1,15,0,0.359731," ","integrate((1/(x^2-1))^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x + \sqrt{x^{2} - 1} \right|}\right)"," ",0,"-log(abs(-x + sqrt(x^2 - 1)))","A",0
853,1,21,0,0.316638," ","integrate(((x^2+1)/(x^4-1))^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x + \sqrt{x^{2} - 1} \right|}\right) \mathrm{sgn}\left(x^{2} - 1\right)"," ",0,"-log(abs(-x + sqrt(x^2 - 1)))*sgn(x^2 - 1)","A",0
854,1,9,0,0.334422," ","integrate(1/(1-x)^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{-x + 1}"," ",0,"-2*sqrt(-x + 1)","A",0
855,1,15,0,0.321273," ","integrate((1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} - 2 \, \sqrt{-x + 1}"," ",0,"2*sqrt(2) - 2*sqrt(-x + 1)","A",0
856,1,7,0,0.341254," ","integrate(1/(1+x)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x + 1}"," ",0,"2*sqrt(x + 1)","A",0
857,1,13,0,0.425726," ","integrate((1-x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{2} + 2 \, \sqrt{x + 1}"," ",0,"-2*sqrt(2) + 2*sqrt(x + 1)","A",0
858,1,9,0,0.345010," ","integrate((1-x)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(-x + 1\right)}^{\frac{3}{2}}"," ",0,"-2/3*(-x + 1)^(3/2)","A",0
859,1,15,0,0.334270," ","integrate((-x^2+1)^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(-x + 1\right)}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{2}"," ",0,"-2/3*(-x + 1)^(3/2) + 4/3*sqrt(2)","A",0
860,1,7,0,0.318325," ","integrate((1+x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}}"," ",0,"2/3*(x + 1)^(3/2)","A",0
861,1,13,0,0.334488," ","integrate((-x^2+1)^(1/2)/(1-x)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{2}"," ",0,"2/3*(x + 1)^(3/2) - 4/3*sqrt(2)","A",0
862,1,39,0,0.351567," ","integrate((2+3*x)^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} {\left(\sqrt{3 \, x + 3} \sqrt{3 \, x + 2} + \log\left(\sqrt{3 \, x + 3} - \sqrt{3 \, x + 2}\right)\right)}"," ",0,"1/3*sqrt(3)*(sqrt(3*x + 3)*sqrt(3*x + 2) + log(sqrt(3*x + 3) - sqrt(3*x + 2)))","A",0
863,0,0,0,0.000000," ","integrate((1-x)^(1/2)*(2+3*x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{3 \, x + 2} \sqrt{-x + 1}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(3*x + 2)*sqrt(-x + 1)/sqrt(-x^2 + 1), x)","F",0
864,-2,0,0,0.000000," ","integrate((1+x)^(3/2)/(1-x)^(3/2)/x,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-93.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}] at parameters values [-17.8804557086]2*(-1/2*pi-atan(sqrt(x+1)*((-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1))^2-1)/(-2*sqrt(-x+1)+2*sqrt(2))))-ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))+ln(abs(2*sqrt(x+1)/(-2*sqrt(-x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+1)+2*sqrt(2))/sqrt(x+1)))+4*sqrt(x+1)*sqrt(-x+1)/(-x+1)","F(-2)",0
865,1,44,0,0.395015," ","integrate((1+x)^3/x/(-x^2+1)^(3/2),x, algorithm=""giac"")","\frac{8}{\frac{\sqrt{-x^{2} + 1} - 1}{x} + 1} - \arcsin\left(x\right) + \log\left(-\frac{\sqrt{-x^{2} + 1} - 1}{{\left| x \right|}}\right)"," ",0,"8/((sqrt(-x^2 + 1) - 1)/x + 1) - arcsin(x) + log(-(sqrt(-x^2 + 1) - 1)/abs(x))","A",0
866,-2,0,0,0.000000," ","integrate((a*x+1)^(3/2)/x/(-a*x+1)^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [70,22]Warning, choosing root of [1,0,-4,0,%%%{4,[2,2]%%%}] at parameters values [42,56]2*(-1/2*pi-atan(sqrt(a*x+1)*((-1/2*(-2*sqrt(-a*x+1)+2*sqrt(2))/sqrt(a*x+1))^2-1)/(-2*sqrt(-a*x+1)+2*sqrt(2))))-ln(abs(2*sqrt(a*x+1)/(-2*sqrt(-a*x+1)+2*sqrt(2))+2-1/2*(-2*sqrt(-a*x+1)+2*sqrt(2))/sqrt(a*x+1)))+ln(abs(2*sqrt(a*x+1)/(-2*sqrt(-a*x+1)+2*sqrt(2))-2-1/2*(-2*sqrt(-a*x+1)+2*sqrt(2))/sqrt(a*x+1)))+4*sqrt(a*x+1)*sqrt(-a*x+1)/(-a*x+1)","F(-2)",0
867,1,87,0,0.543328," ","integrate((a*x+1)^3/x/(-a^2*x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{a \arcsin\left(a x\right) \mathrm{sgn}\left(a\right)}{{\left| a \right|}} - \frac{a \log\left(\frac{{\left| -2 \, \sqrt{-a^{2} x^{2} + 1} {\left| a \right|} - 2 \, a \right|}}{2 \, a^{2} {\left| x \right|}}\right)}{{\left| a \right|}} + \frac{8 \, a}{{\left(\frac{\sqrt{-a^{2} x^{2} + 1} {\left| a \right|} + a}{a^{2} x} - 1\right)} {\left| a \right|}}"," ",0,"-a*arcsin(a*x)*sgn(a)/abs(a) - a*log(1/2*abs(-2*sqrt(-a^2*x^2 + 1)*abs(a) - 2*a)/(a^2*abs(x)))/abs(a) + 8*a/(((sqrt(-a^2*x^2 + 1)*abs(a) + a)/(a^2*x) - 1)*abs(a))","B",0
868,1,2,0,0.344369," ","integrate(1/(-x^2+1)^(1/2),x, algorithm=""giac"")","\arcsin\left(x\right)"," ",0,"arcsin(x)","A",0
869,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(-x^4 + 1), x)","F",0
870,1,14,0,0.427795," ","integrate(1/(x^2+1)^(1/2),x, algorithm=""giac"")","-\log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-log(-x + sqrt(x^2 + 1))","B",0
871,0,0,0,0.000000," ","integrate((-x^2+1)^(1/2)/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 1}}{\sqrt{-x^{4} + 1}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 1)/sqrt(-x^4 + 1), x)","F",0
872,1,17,0,0.357459," ","integrate((-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x + \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"1/2*sqrt(-x^2 + 1)*x + 1/2*arcsin(x)","A",0
873,0,0,0,0.000000," ","integrate((-x^4+1)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} + 1}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-x^4 + 1)/sqrt(x^2 + 1), x)","F",0
874,1,25,0,0.372243," ","integrate((x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{2} + 1} x - \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"1/2*sqrt(x^2 + 1)*x - 1/2*log(-x + sqrt(x^2 + 1))","A",0
875,0,0,0,0.000000," ","integrate((-x^4+1)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{4} + 1}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-x^4 + 1)/sqrt(-x^2 + 1), x)","F",0
876,0,0,0,0.000000," ","integrate(((c*x^2+a+b)/d)^m,x, algorithm=""giac"")","\int \left(\frac{c x^{2} + a + b}{d}\right)^{m}\,{d x}"," ",0,"integrate(((c*x^2 + a + b)/d)^m, x)","F",0
877,1,30,0,0.336297," ","integrate(1/(x-(x^2+1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} - \frac{1}{2} \, \sqrt{x^{2} + 1} x + \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-1/2*x^2 - 1/2*sqrt(x^2 + 1)*x + 1/2*log(-x + sqrt(x^2 + 1))","A",0
878,1,140,0,0.437670," ","integrate(1/(x-(-x^2+1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) - \frac{1}{2} \, \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right) + \frac{1}{4} \, \log\left({\left| x + \frac{1}{2} \, \sqrt{2} \right|}\right) + \frac{1}{4} \, \log\left({\left| x - \frac{1}{2} \, \sqrt{2} \right|}\right) - \frac{1}{4} \, \log\left({\left| -\frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| -\frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} - 2 \right|}\right)"," ",0,"-1/4*pi*sgn(x) - 1/2*arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)) + 1/4*log(abs(x + 1/2*sqrt(2))) + 1/4*log(abs(x - 1/2*sqrt(2))) - 1/4*log(abs(-x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x + 2)) + 1/4*log(abs(-x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x - 2))","B",0
879,1,88,0,0.409004," ","integrate(1/(x-(2*x^2+1)^(1/2)),x, algorithm=""giac"")","\sqrt{2} \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 1}\right) + \frac{1}{2} \, \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} + 2 \, \sqrt{2} + 3\right) - \frac{1}{2} \, \log\left({\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} - 2 \, \sqrt{2} + 3\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"sqrt(2)*log(-sqrt(2)*x + sqrt(2*x^2 + 1)) + 1/2*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 + 2*sqrt(2) + 3) - 1/2*log((sqrt(2)*x - sqrt(2*x^2 + 1))^2 - 2*sqrt(2) + 3) - 1/2*log(x^2 + 1)","B",0
880,1,117,0,0.440907," ","integrate((2*x-x^3+x^2*(-x^2+2)^(1/2))/(2*x^2-2),x, algorithm=""giac"")","-\frac{1}{4} \, x^{2} + \frac{1}{4} \, \sqrt{-x^{2} + 2} x + \frac{1}{4} \, \log\left({\left| x^{2} - 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| \frac{x}{\sqrt{2} - \sqrt{-x^{2} + 2}} - \frac{\sqrt{2} - \sqrt{-x^{2} + 2}}{x} + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| \frac{x}{\sqrt{2} - \sqrt{-x^{2} + 2}} - \frac{\sqrt{2} - \sqrt{-x^{2} + 2}}{x} - 2 \right|}\right)"," ",0,"-1/4*x^2 + 1/4*sqrt(-x^2 + 2)*x + 1/4*log(abs(x^2 - 1)) - 1/4*log(abs(x/(sqrt(2) - sqrt(-x^2 + 2)) - (sqrt(2) - sqrt(-x^2 + 2))/x + 2)) + 1/4*log(abs(x/(sqrt(2) - sqrt(-x^2 + 2)) - (sqrt(2) - sqrt(-x^2 + 2))/x - 2))","B",0
881,1,117,0,0.514494," ","integrate(x*(-x^2+2)^(1/2)/(x-(-x^2+2)^(1/2)),x, algorithm=""giac"")","-\frac{1}{4} \, x^{2} + \frac{1}{4} \, \sqrt{-x^{2} + 2} x + \frac{1}{4} \, \log\left({\left| x^{2} - 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| \frac{x}{\sqrt{2} - \sqrt{-x^{2} + 2}} - \frac{\sqrt{2} - \sqrt{-x^{2} + 2}}{x} + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| \frac{x}{\sqrt{2} - \sqrt{-x^{2} + 2}} - \frac{\sqrt{2} - \sqrt{-x^{2} + 2}}{x} - 2 \right|}\right)"," ",0,"-1/4*x^2 + 1/4*sqrt(-x^2 + 2)*x + 1/4*log(abs(x^2 - 1)) - 1/4*log(abs(x/(sqrt(2) - sqrt(-x^2 + 2)) - (sqrt(2) - sqrt(-x^2 + 2))/x + 2)) + 1/4*log(abs(x/(sqrt(2) - sqrt(-x^2 + 2)) - (sqrt(2) - sqrt(-x^2 + 2))/x - 2))","B",0
882,1,50,0,0.425882," ","integrate(x/(-x+(-x^2+2*x)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right) - \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*x - 1/2*sqrt(-x^2 + 2*x) - 1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2)) - 1/2*log(abs(x - 1))","A",0
883,1,50,0,0.483547," ","integrate((x+(-x^2+2*x)^(1/2))/(2-2*x),x, algorithm=""giac"")","-\frac{1}{2} \, x - \frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right) - \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*x - 1/2*sqrt(-x^2 + 2*x) - 1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2)) - 1/2*log(abs(x - 1))","A",0
884,-2,0,0,0.000000," ","integrate((x+(2-x)^(1/2)*x^(1/2))/(2-2*x),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}+%%%{-8,[1]%%%}+%%%{4,[0]%%%}] at parameters values [-92.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}+%%%{-8,[1]%%%}+%%%{4,[0]%%%}] at parameters values [-16.8804557086]-1/2*(x+ln(abs(x-1))+sqrt(x)*sqrt(-x+2)-ln(abs(2*sqrt(x)/(-2*sqrt(-x+2)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+2)+2*sqrt(2))/sqrt(x)))+ln(abs(2*sqrt(x)/(-2*sqrt(-x+2)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+2)+2*sqrt(2))/sqrt(x))))","F(-2)",0
885,-2,0,0,0.000000," ","integrate(x^(1/2)/((2-x)^(1/2)-x^(1/2)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}+%%%{-8,[1]%%%}+%%%{4,[0]%%%}] at parameters values [-92.616423693]Warning, choosing root of [1,0,-4,0,%%%{4,[2]%%%}+%%%{-8,[1]%%%}+%%%{4,[0]%%%}] at parameters values [-16.8804557086]2*(-x/4-1/4*ln(abs(x-1))-1/4*sqrt(x)*sqrt(-x+2)+1/4*ln(abs(2*sqrt(x)/(-2*sqrt(-x+2)+2*sqrt(2))+2-1/2*(-2*sqrt(-x+2)+2*sqrt(2))/sqrt(x)))-1/4*ln(abs(2*sqrt(x)/(-2*sqrt(-x+2)+2*sqrt(2))-2-1/2*(-2*sqrt(-x+2)+2*sqrt(2))/sqrt(x))))","F(-2)",0
886,0,0,0,0.000000," ","integrate(1/((1+x)*(x^2-1))^(2/3),x, algorithm=""giac"")","\int \frac{1}{\left({\left(x^{2} - 1\right)} {\left(x + 1\right)}\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(((x^2 - 1)*(x + 1))^(-2/3), x)","F",0
887,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x*(x^2+1))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{{\left(x^{2} + 1\right)} x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt((x^2 + 1)*x)*(x^2 + 1)), x)","F",0
888,0,0,0,0.000000," ","integrate((x^2-1)/(x^2+1)/(x^3+x)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} - 1}{\sqrt{x^{3} + x} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x^2 - 1)/(sqrt(x^3 + x)*(x^2 + 1)), x)","F",0
889,0,0,0,0.000000," ","integrate(((x^2-1)^2/x/(x^2+1))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{{\left(x^{2} - 1\right)}^{2}}{{\left(x^{2} + 1\right)} x}}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt((x^2 - 1)^2/((x^2 + 1)*x))/(x^2 + 1), x)","F",0
890,0,0,0,0.000000," ","integrate(((x^2-1)^2/(x^3+x))^(1/2)/(x^2+1),x, algorithm=""giac"")","\int \frac{\sqrt{\frac{{\left(x^{2} - 1\right)}^{2}}{x^{3} + x}}}{x^{2} + 1}\,{d x}"," ",0,"integrate(sqrt((x^2 - 1)^2/(x^3 + x))/(x^2 + 1), x)","F",0
891,-2,0,0,0.000000," ","integrate(1/(a+b/x^2)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [sign(t_nostep)]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-22,93,91]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [31,-21,88]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [76,-66,66]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [5,-23,79]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-88,9,6]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-69,-8,31]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [2,90.2102860468,-92]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-17,26.2119182013,64]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [89,29.4664394325,-51]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [22,45.1969879479,76]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-63,68.7323710029,13]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [43,85.9758855961,12]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [72,95.2558838762,11]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-9,91.3720739307,81]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [15,23.9552401127,-50]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [93,60.8246789905,-18]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-88,63.3562821955,93]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-11,92.3620133325,-60]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-88,51.1034068516,72]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-90,71.1075269701,48]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-47,53.5483433446,-60]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [70,89.9395644632,-32]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-74,8.0407431256,-16]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [85,16.2654368887,-14]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-77,83.0705981795,31]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [76,41.5291932677,-48]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-47,25.6140411007,23]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [32,76.6146142203,-62]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [66,99.6590219955,-30]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-50,17.713730142,-44]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [45,14.5515509131,62]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [44,88.8429926978,11]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-19,42.8964279308,-92]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [67,19.2648137459,-22]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [9,87.7979063494,94]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [95,98.9582961812,-92]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [52,79.2538507222,22]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-43,16.7638230952,21]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [71,61.8959259251,-83]Warning, choosing root of [1,0,%%%{-2,[1,0,2]%%%}+%%%{-4,[0,1,0]%%%},0,%%%{1,[2,0,4]%%%}] at parameters values [-30,23.6526960679,40]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[2,0,0]%%%}+%%%{2,[1,1,2]%%%}+%%%{-2,[1,1,0]%%%}+%%%{1,[0,2,4]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [0,56.2346625305,0]Warning, choosing root of [1,0,%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[2,0,0]%%%}+%%%{2,[1,1,2]%%%}+%%%{-2,[1,1,0]%%%}+%%%{1,[0,2,4]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-43,9.82222589385,18]Warning, choosing root of [1,0,%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[2,0,0]%%%}+%%%{2,[1,1,2]%%%}+%%%{-2,[1,1,0]%%%}+%%%{1,[0,2,4]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [95,6.65142845921,-60]Warning, choosing root of [1,0,%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[2,0,0]%%%}+%%%{2,[1,1,2]%%%}+%%%{-2,[1,1,0]%%%}+%%%{1,[0,2,4]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [65,77.8863785956,-16]Warning, choosing root of [1,0,%%%{-2,[1,0,0]%%%}+%%%{-2,[0,1,2]%%%}+%%%{-2,[0,1,0]%%%},0,%%%{1,[2,0,0]%%%}+%%%{2,[1,1,2]%%%}+%%%{-2,[1,1,0]%%%}+%%%{1,[0,2,4]%%%}+%%%{-2,[0,2,2]%%%}+%%%{1,[0,2,0]%%%}] at parameters values [-81,85.3390313801,-19]gen.cc:simplify/tmp.type!=_EXT Error: Bad Argument ValueEvaluation time: 21.47Done","F(-2)",0
892,1,46,0,0.359111," ","integrate((x^4-2*x^2)^(1/2)/(x^2-1)/(x^2+2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\arctan\left(i \, \sqrt{2}\right) - 2 \, \arctan\left(\frac{1}{2} i \, \sqrt{2}\right)\right)} \mathrm{sgn}\left(x\right) + \frac{2}{3} \, \arctan\left(\frac{1}{2} \, \sqrt{x^{2} - 2}\right) \mathrm{sgn}\left(x\right) - \frac{1}{3} \, \arctan\left(\sqrt{x^{2} - 2}\right) \mathrm{sgn}\left(x\right)"," ",0,"1/3*(arctan(I*sqrt(2)) - 2*arctan(1/2*I*sqrt(2)))*sgn(x) + 2/3*arctan(1/2*sqrt(x^2 - 2))*sgn(x) - 1/3*arctan(sqrt(x^2 - 2))*sgn(x)","C",0
893,1,18,0,0.340056," ","integrate((1-1/(x^2-1)^2)^(1/2)/(-x^2+2),x, algorithm=""giac"")","-\arctan\left(\sqrt{x^{2} - 2}\right) \mathrm{sgn}\left(x^{3} - x\right)"," ",0,"-arctan(sqrt(x^2 - 2))*sgn(x^3 - x)","A",0
894,1,39,0,0.413822," ","integrate(((x^4-2*x^2)/(x^2-1)^2)^(1/2)/(x^2+2),x, algorithm=""giac"")","\frac{2}{3} \, \arctan\left(\frac{1}{2} \, \sqrt{x^{2} - 2}\right) \mathrm{sgn}\left(x^{3} - x\right) - \frac{1}{3} \, \arctan\left(\sqrt{x^{2} - 2}\right) \mathrm{sgn}\left(x^{3} - x\right)"," ",0,"2/3*arctan(1/2*sqrt(x^2 - 2))*sgn(x^3 - x) - 1/3*arctan(sqrt(x^2 - 2))*sgn(x^3 - x)","A",0
895,1,86,0,0.468945," ","integrate((1+2*x/(x^2+1))^(5/2),x, algorithm=""giac"")","{\left(\sqrt{2} + 5 \, \log\left(\sqrt{2} + 1\right)\right)} \mathrm{sgn}\left(x + 1\right) - 5 \, \log\left(-x + \sqrt{x^{2} + 1}\right) \mathrm{sgn}\left(x + 1\right) + \frac{{\left({\left({\left(3 \, x \mathrm{sgn}\left(x + 1\right) - 8 \, \mathrm{sgn}\left(x + 1\right)\right)} x - 18 \, \mathrm{sgn}\left(x + 1\right)\right)} x - 12 \, \mathrm{sgn}\left(x + 1\right)\right)} x - 17 \, \mathrm{sgn}\left(x + 1\right)}{3 \, {\left(x^{2} + 1\right)}^{\frac{3}{2}}}"," ",0,"(sqrt(2) + 5*log(sqrt(2) + 1))*sgn(x + 1) - 5*log(-x + sqrt(x^2 + 1))*sgn(x + 1) + 1/3*((((3*x*sgn(x + 1) - 8*sgn(x + 1))*x - 18*sgn(x + 1))*x - 12*sgn(x + 1))*x - 17*sgn(x + 1))/(x^2 + 1)^(3/2)","A",0
896,1,67,0,0.372028," ","integrate((1+2*x/(x^2+1))^(3/2),x, algorithm=""giac"")","-{\left(\sqrt{2} - 3 \, \log\left(\sqrt{2} + 1\right)\right)} \mathrm{sgn}\left(x + 1\right) - 3 \, \log\left(-x + \sqrt{x^{2} + 1}\right) \mathrm{sgn}\left(x + 1\right) + \frac{{\left(x \mathrm{sgn}\left(x + 1\right) - 2 \, \mathrm{sgn}\left(x + 1\right)\right)} x - \mathrm{sgn}\left(x + 1\right)}{\sqrt{x^{2} + 1}}"," ",0,"-(sqrt(2) - 3*log(sqrt(2) + 1))*sgn(x + 1) - 3*log(-x + sqrt(x^2 + 1))*sgn(x + 1) + ((x*sgn(x + 1) - 2*sgn(x + 1))*x - sgn(x + 1))/sqrt(x^2 + 1)","A",0
897,1,49,0,0.480466," ","integrate((1+2*x/(x^2+1))^(1/2),x, algorithm=""giac"")","-{\left(\sqrt{2} - \log\left(\sqrt{2} + 1\right)\right)} \mathrm{sgn}\left(x + 1\right) - \log\left(-x + \sqrt{x^{2} + 1}\right) \mathrm{sgn}\left(x + 1\right) + \sqrt{x^{2} + 1} \mathrm{sgn}\left(x + 1\right)"," ",0,"-(sqrt(2) - log(sqrt(2) + 1))*sgn(x + 1) - log(-x + sqrt(x^2 + 1))*sgn(x + 1) + sqrt(x^2 + 1)*sgn(x + 1)","A",0
898,1,88,0,0.570603," ","integrate(1/(1+2*x/(x^2+1))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{2} + 2 \, \sqrt{x^{2} + 1} - 2 \right|}}{{\left| -2 \, x + 2 \, \sqrt{2} + 2 \, \sqrt{x^{2} + 1} - 2 \right|}}\right)}{\mathrm{sgn}\left(x + 1\right)} + \frac{\log\left(-x + \sqrt{x^{2} + 1}\right)}{\mathrm{sgn}\left(x + 1\right)} + \frac{\sqrt{x^{2} + 1}}{\mathrm{sgn}\left(x + 1\right)}"," ",0,"sqrt(2)*log(abs(-2*x - 2*sqrt(2) + 2*sqrt(x^2 + 1) - 2)/abs(-2*x + 2*sqrt(2) + 2*sqrt(x^2 + 1) - 2))/sgn(x + 1) + log(-x + sqrt(x^2 + 1))/sgn(x + 1) + sqrt(x^2 + 1)/sgn(x + 1)","A",0
899,0,0,0,0.000000," ","integrate(1/(1+2*x/(x^2+1))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\frac{2 \, x}{x^{2} + 1} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*x/(x^2 + 1) + 1)^(-3/2), x)","F",0
900,1,30,0,0.390528," ","integrate((1+2*x/(x^2+1))^(1/2)/(x^2+1),x, algorithm=""giac"")","\sqrt{2} \mathrm{sgn}\left(x + 1\right) + \frac{x \mathrm{sgn}\left(x + 1\right) - \mathrm{sgn}\left(x + 1\right)}{\sqrt{x^{2} + 1}}"," ",0,"sqrt(2)*sgn(x + 1) + (x*sgn(x + 1) - sgn(x + 1))/sqrt(x^2 + 1)","A",0
901,0,0,0,0.000000," ","integrate(F(x)*(-x^2+x)^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{2} + x} F\left(x\right)\,{d x}"," ",0,"integrate(sqrt(-x^2 + x)*F(x), x)","F",0
902,0,0,0,0.000000," ","integrate(F(x)/(-x^2+x)^(1/2),x, algorithm=""giac"")","\int \frac{F\left(x\right)}{\sqrt{-x^{2} + x}}\,{d x}"," ",0,"integrate(F(x)/sqrt(-x^2 + x), x)","F",0
903,0,0,0,0.000000," ","integrate(F(x)*(1-x)^(1/2)*x^(1/2),x, algorithm=""giac"")","\int \sqrt{x} \sqrt{-x + 1} F\left(x\right)\,{d x}"," ",0,"integrate(sqrt(x)*sqrt(-x + 1)*F(x), x)","F",0
904,0,0,0,0.000000," ","integrate(F(x)/(1-x)^(1/2)/x^(1/2),x, algorithm=""giac"")","\int \frac{F\left(x\right)}{\sqrt{x} \sqrt{-x + 1}}\,{d x}"," ",0,"integrate(F(x)/(sqrt(x)*sqrt(-x + 1)), x)","F",0
905,0,0,0,0.000000," ","integrate(F((b*x+a)/x),x, algorithm=""giac"")","\int F\left(\frac{b x + a}{x}\right)\,{d x}"," ",0,"integrate(F((b*x + a)/x), x)","F",0
906,0,0,0,0.000000," ","integrate(F((b*x^2+a)/x^2),x, algorithm=""giac"")","\int F\left(\frac{b x^{2} + a}{x^{2}}\right)\,{d x}"," ",0,"integrate(F((b*x^2 + a)/x^2), x)","F",0
907,0,0,0,0.000000," ","integrate(F(x/(b*x+a)),x, algorithm=""giac"")","\int F\left(\frac{x}{b x + a}\right)\,{d x}"," ",0,"integrate(F(x/(b*x + a)), x)","F",0
908,0,0,0,0.000000," ","integrate(F(x^2/(b*x^2+a)),x, algorithm=""giac"")","\int F\left(\frac{x^{2}}{b x^{2} + a}\right)\,{d x}"," ",0,"integrate(F(x^2/(b*x^2 + a)), x)","F",0
909,0,0,0,0.000000," ","integrate(F(x^2/(b*x+a)^2),x, algorithm=""giac"")","\int F\left(\frac{x^{2}}{{\left(b x + a\right)}^{2}}\right)\,{d x}"," ",0,"integrate(F(x^2/(b*x + a)^2), x)","F",0
910,0,0,0,0.000000," ","integrate(F(x^4/(b*x^2+a)^2),x, algorithm=""giac"")","\int F\left(\frac{x^{4}}{{\left(b x^{2} + a\right)}^{2}}\right)\,{d x}"," ",0,"integrate(F(x^4/(b*x^2 + a)^2), x)","F",0
911,0,0,0,0.000000," ","integrate((b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + \sqrt{b^{2} x^{4} + a}}}{\sqrt{b^{2} x^{4} + a}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + sqrt(b^2*x^4 + a))/sqrt(b^2*x^4 + a), x)","F",0
912,0,0,0,0.000000," ","integrate((-b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} + \sqrt{b^{2} x^{4} + a}}}{\sqrt{b^{2} x^{4} + a}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + sqrt(b^2*x^4 + a))/sqrt(b^2*x^4 + a), x)","F",0
913,0,0,0,0.000000," ","integrate((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)/(4*x^4+3)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{2} + \sqrt{4 \, x^{4} + 3}}}{\sqrt{4 \, x^{4} + 3} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(2*x^2 + sqrt(4*x^4 + 3))/(sqrt(4*x^4 + 3)*(d*x + c)), x)","F",0
914,0,0,0,0.000000," ","integrate((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)^2/(4*x^4+3)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{2} + \sqrt{4 \, x^{4} + 3}}}{\sqrt{4 \, x^{4} + 3} {\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(2*x^2 + sqrt(4*x^4 + 3))/(sqrt(4*x^4 + 3)*(d*x + c)^2), x)","F",0
915,1,27,0,0.396762," ","integrate((-4+x)/(1+x^(1/3))/x^(1/2),x, algorithm=""giac"")","\frac{6}{7} \, x^{\frac{7}{6}} - \frac{6}{5} \, x^{\frac{5}{6}} + 2 \, \sqrt{x} - 30 \, x^{\frac{1}{6}} + 30 \, \arctan\left(x^{\frac{1}{6}}\right)"," ",0,"6/7*x^(7/6) - 6/5*x^(5/6) + 2*sqrt(x) - 30*x^(1/6) + 30*arctan(x^(1/6))","A",0
916,1,20,0,0.350194," ","integrate((1+x^(1/2))/(x^(5/6)+x^(7/6)),x, algorithm=""giac"")","3 \, x^{\frac{1}{3}} + 6 \, \arctan\left(x^{\frac{1}{6}}\right) - 3 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"3*x^(1/3) + 6*arctan(x^(1/6)) - 3*log(x^(1/3) + 1)","A",0
917,1,30,0,0.338707," ","integrate((1+x^(1/2))/(1+x^(1/3))/x^(1/2),x, algorithm=""giac"")","\frac{3}{2} \, x^{\frac{2}{3}} - 3 \, x^{\frac{1}{3}} + 6 \, x^{\frac{1}{6}} - 6 \, \arctan\left(x^{\frac{1}{6}}\right) + 3 \, \log\left(x^{\frac{1}{3}} + 1\right)"," ",0,"3/2*x^(2/3) - 3*x^(1/3) + 6*x^(1/6) - 6*arctan(x^(1/6)) + 3*log(x^(1/3) + 1)","A",0
918,1,44,0,0.351033," ","integrate((2+b/x^2)^(1/2)/(2*x^2+b),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{2 \, x^{2} + b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}} - \frac{\arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{-b}}"," ",0,"arctan(sqrt(2*x^2 + b)/sqrt(-b))*sgn(x)/sqrt(-b) - arctan(sqrt(b)/sqrt(-b))*sgn(x)/sqrt(-b)","B",0
919,1,40,0,0.415787," ","integrate((2-b/x^2)^(1/2)/(2*x^2-b),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{2 \, x^{2} - b}}{\sqrt{b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{b}} - \frac{\arctan\left(\frac{\sqrt{-b}}{\sqrt{b}}\right) \mathrm{sgn}\left(x\right)}{\sqrt{b}}"," ",0,"arctan(sqrt(2*x^2 - b)/sqrt(b))*sgn(x)/sqrt(b) - arctan(sqrt(-b)/sqrt(b))*sgn(x)/sqrt(b)","B",0
920,-2,0,0,0.000000," ","integrate((a+c/x^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
921,-2,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Error: Bad Argument Type","F(-2)",0
922,1,11,0,0.511268," ","integrate((x^(1/6)+(x^3)^(1/5))/x^(1/2),x, algorithm=""giac"")","\frac{10}{11} \, x^{\frac{11}{10}} + \frac{3}{2} \, x^{\frac{2}{3}}"," ",0,"10/11*x^(11/10) + 3/2*x^(2/3)","A",0
923,1,22,0,0.614464," ","integrate((2+x)/(-x^2+4*x)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 4 \, x} + 4 \, \arcsin\left(\frac{1}{2} \, x - 1\right)"," ",0,"-sqrt(-x^2 + 4*x) + 4*arcsin(1/2*x - 1)","A",0
924,1,11,0,0.427239," ","integrate((3+x)/(x^2+6*x)^(1/3),x, algorithm=""giac"")","\frac{3}{4} \, {\left(x^{2} + 6 \, x\right)}^{\frac{2}{3}}"," ",0,"3/4*(x^2 + 6*x)^(2/3)","A",0
925,1,27,0,0.521547," ","integrate((4+x)/(-x^2+6*x)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} + 6 \, x} {\left(7 \, x - 12\right)}}{9 \, {\left(x^{2} - 6 \, x\right)}}"," ",0,"-1/9*sqrt(-x^2 + 6*x)*(7*x - 12)/(x^2 - 6*x)","A",0
926,1,17,0,0.589437," ","integrate(1/(1+x)/(x^2+2*x)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(-x + \sqrt{x^{2} + 2 \, x} - 1\right)"," ",0,"2*arctan(-x + sqrt(x^2 + 2*x) - 1)","A",0
927,1,17,0,0.616060," ","integrate(1/(1+2*x)/(x^2+x)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(-2 \, x + 2 \, \sqrt{x^{2} + x} - 1\right)"," ",0,"2*arctan(-2*x + 2*sqrt(x^2 + x) - 1)","A",0
928,1,13,0,0.596517," ","integrate((-1+x)/(-x^2+2*x)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 2 \, x}"," ",0,"-sqrt(-x^2 + 2*x)","A",0
929,1,53,0,0.504928," ","integrate((-x^2+x)^(1/2)/(1+x),x, algorithm=""giac"")","2 \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} {\left(\frac{3 \, {\left(2 \, \sqrt{-x^{2} + x} - 1\right)}}{2 \, x - 1} - 1\right)}\right) + \sqrt{-x^{2} + x} + \frac{3}{2} \, \arcsin\left(2 \, x - 1\right)"," ",0,"2*sqrt(2)*arctan(1/4*sqrt(2)*(3*(2*sqrt(-x^2 + x) - 1)/(2*x - 1) - 1)) + sqrt(-x^2 + x) + 3/2*arcsin(2*x - 1)","A",0
930,1,45,0,4.566178," ","integrate((x^(1/4)+x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{x + x^{\frac{1}{4}}} x^{\frac{1}{4}} {\left(2 \, x^{\frac{3}{4}} + 1\right)} - \frac{1}{6} \, \log\left(\sqrt{\frac{1}{x^{\frac{3}{4}}} + 1} + 1\right) + \frac{1}{6} \, \log\left({\left| \sqrt{\frac{1}{x^{\frac{3}{4}}} + 1} - 1 \right|}\right)"," ",0,"1/3*sqrt(x + x^(1/4))*x^(1/4)*(2*x^(3/4) + 1) - 1/6*log(sqrt(1/x^(3/4) + 1) + 1) + 1/6*log(abs(sqrt(1/x^(3/4) + 1) - 1))","A",0
931,1,33,0,0.395229," ","integrate((x+x^(3/2))^(1/2),x, algorithm=""giac"")","\frac{4}{105} \, {\left(15 \, {\left(\sqrt{x} + 1\right)}^{\frac{7}{2}} - 42 \, {\left(\sqrt{x} + 1\right)}^{\frac{5}{2}} + 35 \, {\left(\sqrt{x} + 1\right)}^{\frac{3}{2}} - 8\right)} \mathrm{sgn}\left(x\right)"," ",0,"4/105*(15*(sqrt(x) + 1)^(7/2) - 42*(sqrt(x) + 1)^(5/2) + 35*(sqrt(x) + 1)^(3/2) - 8)*sgn(x)","A",0
932,1,51,0,0.383167," ","integrate(x*(x+x^(3/2))^(1/2),x, algorithm=""giac"")","\frac{4}{3465} \, {\left(315 \, {\left(\sqrt{x} + 1\right)}^{\frac{11}{2}} - 1540 \, {\left(\sqrt{x} + 1\right)}^{\frac{9}{2}} + 2970 \, {\left(\sqrt{x} + 1\right)}^{\frac{7}{2}} - 2772 \, {\left(\sqrt{x} + 1\right)}^{\frac{5}{2}} + 1155 \, {\left(\sqrt{x} + 1\right)}^{\frac{3}{2}} - 128\right)} \mathrm{sgn}\left(x\right)"," ",0,"4/3465*(315*(sqrt(x) + 1)^(11/2) - 1540*(sqrt(x) + 1)^(9/2) + 2970*(sqrt(x) + 1)^(7/2) - 2772*(sqrt(x) + 1)^(5/2) + 1155*(sqrt(x) + 1)^(3/2) - 128)*sgn(x)","A",0
933,1,18,0,0.479664," ","integrate((-x^2+1)*(1/(-x^2+2))^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{2} + 2} x \mathrm{sgn}\left(x^{2} - 2\right)"," ",0,"-1/2*sqrt(-x^2 + 2)*x*sgn(x^2 - 2)","A",0
934,1,60,0,0.430104," ","integrate((-x^4+x^3+x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(15 \, \arcsin\left(\frac{1}{5} \, \sqrt{5}\right) + 22\right)} \mathrm{sgn}\left(x\right) + \frac{5}{16} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} {\left(2 \, x - 1\right)}\right) \mathrm{sgn}\left(x\right) + \frac{1}{24} \, {\left(2 \, {\left(4 \, x \mathrm{sgn}\left(x\right) - \mathrm{sgn}\left(x\right)\right)} x - 11 \, \mathrm{sgn}\left(x\right)\right)} \sqrt{-x^{2} + x + 1}"," ",0,"1/48*(15*arcsin(1/5*sqrt(5)) + 22)*sgn(x) + 5/16*arcsin(1/5*sqrt(5)*(2*x - 1))*sgn(x) + 1/24*(2*(4*x*sgn(x) - sgn(x))*x - 11*sgn(x))*sqrt(-x^2 + x + 1)","A",0
935,1,14,0,0.424302," ","integrate(1/((a^2+x^2)^3)^(1/2),x, algorithm=""giac"")","\frac{x}{\sqrt{a^{2} + x^{2}} a^{2}}"," ",0,"x/(sqrt(a^2 + x^2)*a^2)","A",0
936,1,33,0,0.391113," ","integrate(x^(1/2)/(1+x+x^(1/2)),x, algorithm=""giac"")","-\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} + 1\right)}\right) + 2 \, \sqrt{x} - \log\left(x + \sqrt{x} + 1\right)"," ",0,"-2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*sqrt(x) + 1)) + 2*sqrt(x) - log(x + sqrt(x) + 1)","A",0
937,1,25,0,0.362852," ","integrate(x/(1+x+x^(1/2)),x, algorithm=""giac"")","\frac{4}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} + 1\right)}\right) + x - 2 \, \sqrt{x}"," ",0,"4/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*sqrt(x) + 1)) + x - 2*sqrt(x)","A",0
938,1,45,0,0.426584," ","integrate(1/x^(1/2)/(1+x+x^(1/2))^(7/2),x, algorithm=""giac"")","\frac{4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, \sqrt{x} {\left(2 \, \sqrt{x} + 5\right)} + 35\right)} \sqrt{x} + 65\right)} \sqrt{x} + 355\right)} \sqrt{x} + 203\right)}}{405 \, {\left(x + \sqrt{x} + 1\right)}^{\frac{5}{2}}}"," ",0,"4/405*(2*(8*(2*(4*sqrt(x)*(2*sqrt(x) + 5) + 35)*sqrt(x) + 65)*sqrt(x) + 355)*sqrt(x) + 203)/(x + sqrt(x) + 1)^(5/2)","A",0
939,1,79,0,0.432455," ","integrate((-1+x)/((x^2+1)^(1/2)+1),x, algorithm=""giac"")","\sqrt{x^{2} + 1} - \frac{2}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 1} - \frac{1}{x} + \log\left(-x + \sqrt{x^{2} + 1}\right) - \log\left({\left| x \right|}\right) - \log\left({\left| -x + \sqrt{x^{2} + 1} + 1 \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + 1} - 1 \right|}\right)"," ",0,"sqrt(x^2 + 1) - 2/((x - sqrt(x^2 + 1))^2 - 1) - 1/x + log(-x + sqrt(x^2 + 1)) - log(abs(x)) - log(abs(-x + sqrt(x^2 + 1) + 1)) + log(abs(-x + sqrt(x^2 + 1) - 1))","A",0
940,1,13,0,0.360178," ","integrate(1/(1+x)^(2/3)/(x^2-1)^(2/3),x, algorithm=""giac"")","\frac{3}{2} \, {\left(-\frac{2}{x + 1} + 1\right)}^{\frac{1}{3}}"," ",0,"3/2*(-2/(x + 1) + 1)^(1/3)","A",0
941,0,0,0,0.000000," ","integrate((-x^6+1)^(2/3)+(-x^6+1)^(2/3)/x^6,x, algorithm=""giac"")","\int {\left(-x^{6} + 1\right)}^{\frac{2}{3}} + \frac{{\left(-x^{6} + 1\right)}^{\frac{2}{3}}}{x^{6}}\,{d x}"," ",0,"integrate((-x^6 + 1)^(2/3) + (-x^6 + 1)^(2/3)/x^6, x)","F",0
942,0,0,0,0.000000," ","integrate(1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b {\left(2 \, m - n\right)} x^{n} + 2 \, a m\right)} x^{m - 1}}{2 \, {\left(b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/2*(b*(2*m - n)*x^n + 2*a*m)*x^(m - 1)/(b*x^n + a)^(3/2), x)","F",0
943,1,37,0,0.336566," ","integrate((-2*x^3+x)/(2+3*x)^(1/2),x, algorithm=""giac"")","-\frac{4}{567} \, {\left(3 \, x + 2\right)}^{\frac{7}{2}} + \frac{8}{135} \, {\left(3 \, x + 2\right)}^{\frac{5}{2}} - \frac{10}{81} \, {\left(3 \, x + 2\right)}^{\frac{3}{2}} - \frac{4}{81} \, \sqrt{3 \, x + 2}"," ",0,"-4/567*(3*x + 2)^(7/2) + 8/135*(3*x + 2)^(5/2) - 10/81*(3*x + 2)^(3/2) - 4/81*sqrt(3*x + 2)","A",0
944,1,25,0,0.320561," ","integrate(1/((1+x)^(1/4)+(1+x)^(1/2)),x, algorithm=""giac"")","2 \, \sqrt{x + 1} - 4 \, {\left(x + 1\right)}^{\frac{1}{4}} + 4 \, \log\left({\left(x + 1\right)}^{\frac{1}{4}} + 1\right)"," ",0,"2*sqrt(x + 1) - 4*(x + 1)^(1/4) + 4*log((x + 1)^(1/4) + 1)","A",0
945,1,9,0,0.364974," ","integrate((1+2*x)/(x^2+x)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x^{2} + x}"," ",0,"2*sqrt(x^2 + x)","A",0
946,1,4,0,0.332006," ","integrate(1/2/(1+x)/x^(1/2),x, algorithm=""giac"")","\arctan\left(\sqrt{x}\right)"," ",0,"arctan(sqrt(x))","A",0
947,1,25,0,0.414297," ","integrate(1/x/(-x^2+6*x)^(1/2),x, algorithm=""giac"")","\frac{2}{3 \, {\left(\frac{\sqrt{-x^{2} + 6 \, x} - 3}{x - 3} - 1\right)}}"," ",0,"2/3/((sqrt(-x^2 + 6*x) - 3)/(x - 3) - 1)","A",0
948,1,11,0,0.348572," ","integrate(x^(1/2)*(1+x^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + \frac{2}{3} \, x^{\frac{3}{2}}"," ",0,"1/2*x^2 + 2/3*x^(3/2)","A",0
949,1,11,0,0.365952," ","integrate((1-x^(1/2))/x^(1/3),x, algorithm=""giac"")","-\frac{6}{7} \, x^{\frac{7}{6}} + \frac{3}{2} \, x^{\frac{2}{3}}"," ",0,"-6/7*x^(7/6) + 3/2*x^(2/3)","A",0
950,1,27,0,0.379760," ","integrate(x^(1/2)/(1+x^(1/3)),x, algorithm=""giac"")","\frac{6}{7} \, x^{\frac{7}{6}} - \frac{6}{5} \, x^{\frac{5}{6}} + 2 \, \sqrt{x} - 6 \, x^{\frac{1}{6}} + 6 \, \arctan\left(x^{\frac{1}{6}}\right)"," ",0,"6/7*x^(7/6) - 6/5*x^(5/6) + 2*sqrt(x) - 6*x^(1/6) + 6*arctan(x^(1/6))","A",0
951,1,64,0,0.631616," ","integrate((1+x^(1/2))^(1/3)/x,x, algorithm=""giac"")","-2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + 6 \, {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} - \log\left({\left(\sqrt{x} + 1\right)}^{\frac{2}{3}} + {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} + 1\right) + 2 \, \log\left({\left| {\left(\sqrt{x} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-2*sqrt(3)*arctan(1/3*sqrt(3)*(2*(sqrt(x) + 1)^(1/3) + 1)) + 6*(sqrt(x) + 1)^(1/3) - log((sqrt(x) + 1)^(2/3) + (sqrt(x) + 1)^(1/3) + 1) + 2*log(abs((sqrt(x) + 1)^(1/3) - 1))","A",0
952,1,7,0,0.330727," ","integrate(1-x^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, x^{\frac{3}{2}} + x"," ",0,"-2/3*x^(3/2) + x","A",0
953,1,7,0,0.347420," ","integrate(1-x^(1/4),x, algorithm=""giac"")","-\frac{4}{5} \, x^{\frac{5}{4}} + x"," ",0,"-4/5*x^(5/4) + x","A",0
954,1,7,0,0.354492," ","integrate((1-x^(1/2))/(1+x^(1/4)),x, algorithm=""giac"")","-\frac{4}{5} \, x^{\frac{5}{4}} + x"," ",0,"-4/5*x^(5/4) + x","A",0
955,1,68,0,0.721234," ","integrate(1/((b*x+a)*(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b d} \log\left({\left| -2 \, {\left(\sqrt{b d} x - \sqrt{b d x^{2} + b c x + a d x + a c}\right)} b d - \sqrt{b d} b c - \sqrt{b d} a d \right|}\right)}{b d}"," ",0,"-sqrt(b*d)*log(abs(-2*(sqrt(b*d)*x - sqrt(b*d*x^2 + b*c*x + a*d*x + a*c))*b*d - sqrt(b*d)*b*c - sqrt(b*d)*a*d))/(b*d)","A",0
956,1,59,0,0.740078," ","integrate(1/((b*x+a)*(-d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| b c - a d + 2 \, \sqrt{-b d} {\left(\sqrt{-b d} x - \sqrt{-b d x^{2} + b c x - a d x + a c}\right)} \right|}\right)}{\sqrt{-b d}}"," ",0,"-log(abs(b*c - a*d + 2*sqrt(-b*d)*(sqrt(-b*d)*x - sqrt(-b*d*x^2 + b*c*x - a*d*x + a*c))))/sqrt(-b*d)","A",0
957,1,22,0,0.392295," ","integrate(1/(-x^2+1)/x^(1/2),x, algorithm=""giac"")","\arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left({\left| \sqrt{x} - 1 \right|}\right)"," ",0,"arctan(sqrt(x)) + 1/2*log(sqrt(x) + 1) - 1/2*log(abs(sqrt(x) - 1))","B",0
958,1,22,0,0.303462," ","integrate(x^(1/2)/(-x^3+x),x, algorithm=""giac"")","\arctan\left(\sqrt{x}\right) + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left({\left| \sqrt{x} - 1 \right|}\right)"," ",0,"arctan(sqrt(x)) + 1/2*log(sqrt(x) + 1) - 1/2*log(abs(sqrt(x) - 1))","B",0
959,1,80,0,0.427754," ","integrate(x/(2+x^2-3^(1/2)+x*(1+3^(1/2))),x, algorithm=""giac"")","-\frac{{\left(\sqrt{3} + 1\right)} \log\left(\frac{{\left| 2 \, x + \sqrt{3} - \sqrt{6 \, \sqrt{3} - 4} + 1 \right|}}{{\left| 2 \, x + \sqrt{3} + \sqrt{6 \, \sqrt{3} - 4} + 1 \right|}}\right)}{2 \, \sqrt{6 \, \sqrt{3} - 4}} + \frac{1}{2} \, \log\left({\left| x^{2} + x {\left(\sqrt{3} + 1\right)} - \sqrt{3} + 2 \right|}\right)"," ",0,"-1/2*(sqrt(3) + 1)*log(abs(2*x + sqrt(3) - sqrt(6*sqrt(3) - 4) + 1)/abs(2*x + sqrt(3) + sqrt(6*sqrt(3) - 4) + 1))/sqrt(6*sqrt(3) - 4) + 1/2*log(abs(x^2 + x*(sqrt(3) + 1) - sqrt(3) + 2))","A",0
960,1,48,0,0.383293," ","integrate((x^3+x^2)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x + 1\right)}^{\frac{5}{2}} - 10 \, {\left(x + 1\right)}^{\frac{3}{2}} + 15 \, \sqrt{x + 1}\right)} \mathrm{sgn}\left(x\right) + \frac{2}{3} \, {\left({\left(x + 1\right)}^{\frac{3}{2}} - 3 \, \sqrt{x + 1}\right)} \mathrm{sgn}\left(x\right) + \frac{4}{15} \, \mathrm{sgn}\left(x\right)"," ",0,"2/15*(3*(x + 1)^(5/2) - 10*(x + 1)^(3/2) + 15*sqrt(x + 1))*sgn(x) + 2/3*((x + 1)^(3/2) - 3*sqrt(x + 1))*sgn(x) + 4/15*sgn(x)","A",0
961,1,17,0,0.464924," ","integrate(1/(1+x)/(x^2+2*x)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(-x + \sqrt{x^{2} + 2 \, x} - 1\right)"," ",0,"2*arctan(-x + sqrt(x^2 + 2*x) - 1)","A",0
962,1,51,0,0.386382," ","integrate(x^(1/2)*(1-x-x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, {\left(4 \, \sqrt{x} {\left(6 \, \sqrt{x} + 1\right)} - 17\right)} \sqrt{x} + 67\right)} \sqrt{-x - \sqrt{x} + 1} + \frac{45}{64} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} {\left(2 \, \sqrt{x} + 1\right)}\right)"," ",0,"1/96*(2*(4*sqrt(x)*(6*sqrt(x) + 1) - 17)*sqrt(x) + 67)*sqrt(-x - sqrt(x) + 1) + 45/64*arcsin(1/5*sqrt(5)*(2*sqrt(x) + 1))","A",0
963,1,23,0,0.323502," ","integrate((1+(-3+x)^(1/2))^(1/3),x, algorithm=""giac"")","\frac{6}{7} \, {\left(\sqrt{x - 3} + 1\right)}^{\frac{7}{3}} - \frac{3}{2} \, {\left(\sqrt{x - 3} + 1\right)}^{\frac{4}{3}}"," ",0,"6/7*(sqrt(x - 3) + 1)^(7/3) - 3/2*(sqrt(x - 3) + 1)^(4/3)","A",0
964,1,27,0,0.340918," ","integrate(1/(3+(-1+2*x)^(1/2))^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(\sqrt{2 \, x - 1} + 3\right)}^{\frac{3}{2}} - 6 \, \sqrt{\sqrt{2 \, x - 1} + 3}"," ",0,"2/3*(sqrt(2*x - 1) + 3)^(3/2) - 6*sqrt(sqrt(2*x - 1) + 3)","A",0
965,1,29,0,0.408224," ","integrate((1-x)^(1/2)/(1+x^(1/2)),x, algorithm=""giac"")","\sqrt{x} \sqrt{-x + 1} - 2 \, \sqrt{-x + 1} + \arcsin\left(\sqrt{-x + 1}\right)"," ",0,"sqrt(x)*sqrt(-x + 1) - 2*sqrt(-x + 1) + arcsin(sqrt(-x + 1))","A",0
966,1,32,0,0.402342," ","integrate((1-x)^(1/2)/(1-x^(1/2)),x, algorithm=""giac"")","-\sqrt{x} \sqrt{-x + 1} - 2 \, \sqrt{-x + 1} - \arcsin\left(\sqrt{-x + 1}\right)"," ",0,"-sqrt(x)*sqrt(-x + 1) - 2*sqrt(-x + 1) - arcsin(sqrt(-x + 1))","A",0
967,1,15,0,0.340847," ","integrate(x/(x-(x^2+1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{3} \, x^{3} - \frac{1}{3} \, {\left(x^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"-1/3*x^3 - 1/3*(x^2 + 1)^(3/2)","A",0
968,1,105,0,0.572385," ","integrate(x/(x-(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{2} \right|}}{{\left| 4 \, x + 2 \, \sqrt{2} \right|}}\right) - \frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} + \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 6 \right|}}{{\left| 4 \, \sqrt{2} + \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 6 \right|}}\right) + \frac{1}{2} \, x + \frac{1}{2} \, \sqrt{-x^{2} + 1}"," ",0,"1/8*sqrt(2)*log(abs(4*x - 2*sqrt(2))/abs(4*x + 2*sqrt(2))) - 1/8*sqrt(2)*log(abs(-4*sqrt(2) + 2*(sqrt(-x^2 + 1) - 1)^2/x^2 - 6)/abs(4*sqrt(2) + 2*(sqrt(-x^2 + 1) - 1)^2/x^2 - 6)) + 1/2*x + 1/2*sqrt(-x^2 + 1)","B",0
969,1,63,0,0.463718," ","integrate(x/(x-(2*x^2+1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, \pi - x - \sqrt{2 \, x^{2} + 1} + \arctan\left(x\right) + \arctan\left(-\frac{{\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}^{2} + 1}{2 \, {\left(\sqrt{2} x - \sqrt{2 \, x^{2} + 1}\right)}}\right)"," ",0,"-1/2*pi - x - sqrt(2*x^2 + 1) + arctan(x) + arctan(-1/2*((sqrt(2)*x - sqrt(2*x^2 + 1))^2 + 1)/(sqrt(2)*x - sqrt(2*x^2 + 1)))","B",0
970,1,50,0,0.441930," ","integrate(x^(1/2)*(x+x^(1/2))^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, {\left(2 \, {\left(4 \, \sqrt{x} {\left(6 \, \sqrt{x} + 1\right)} - 5\right)} \sqrt{x} + 15\right)} \sqrt{x + \sqrt{x}} + \frac{5}{64} \, \log\left(-2 \, \sqrt{x + \sqrt{x}} + 2 \, \sqrt{x} + 1\right)"," ",0,"1/96*(2*(4*sqrt(x)*(6*sqrt(x) + 1) - 5)*sqrt(x) + 15)*sqrt(x + sqrt(x)) + 5/64*log(-2*sqrt(x + sqrt(x)) + 2*sqrt(x) + 1)","A",0
971,1,55,0,0.464103," ","integrate((1+x^(1/3))/(1+x^(1/2)),x, algorithm=""giac"")","2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{\frac{1}{6}} - 1\right)}\right) + \frac{6}{5} \, x^{\frac{5}{6}} + 2 \, \sqrt{x} - 3 \, x^{\frac{1}{3}} - \log\left(x^{\frac{1}{3}} - x^{\frac{1}{6}} + 1\right) - 4 \, \log\left(x^{\frac{1}{6}} + 1\right)"," ",0,"2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^(1/6) - 1)) + 6/5*x^(5/6) + 2*sqrt(x) - 3*x^(1/3) - log(x^(1/3) - x^(1/6) + 1) - 4*log(x^(1/6) + 1)","A",0
972,1,80,0,0.430675," ","integrate((1+x^(1/3))/(1+x^(1/4)),x, algorithm=""giac"")","-4 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{\frac{1}{12}} - 1\right)}\right) + \frac{12}{13} \, x^{\frac{13}{12}} - \frac{6}{5} \, x^{\frac{5}{6}} + \frac{4}{3} \, x^{\frac{3}{4}} + \frac{12}{7} \, x^{\frac{7}{12}} - 2 \, \sqrt{x} - 3 \, x^{\frac{1}{3}} + 4 \, x^{\frac{1}{4}} + 12 \, x^{\frac{1}{12}} - 2 \, \log\left(x^{\frac{1}{6}} - x^{\frac{1}{12}} + 1\right) - 8 \, \log\left(x^{\frac{1}{12}} + 1\right)"," ",0,"-4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^(1/12) - 1)) + 12/13*x^(13/12) - 6/5*x^(5/6) + 4/3*x^(3/4) + 12/7*x^(7/12) - 2*sqrt(x) - 3*x^(1/3) + 4*x^(1/4) + 12*x^(1/12) - 2*log(x^(1/6) - x^(1/12) + 1) - 8*log(x^(1/12) + 1)","A",0
973,1,4,0,0.332971," ","integrate(x^2/(-1+x^2+(-x^2+1)^(1/2)),x, algorithm=""giac"")","x + \arcsin\left(x\right)"," ",0,"x + arcsin(x)","A",0
974,1,31,0,0.389915," ","integrate(((1+x)/x)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + x} - 1 \right|}\right) \mathrm{sgn}\left(x\right) + \sqrt{x^{2} + x} \mathrm{sgn}\left(x\right)"," ",0,"-1/2*log(abs(-2*x + 2*sqrt(x^2 + x) - 1))*sgn(x) + sqrt(x^2 + x)*sgn(x)","A",0
975,1,28,0,0.395931," ","integrate(((1-x)/x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) + \frac{1}{2} \, \arcsin\left(2 \, x - 1\right) \mathrm{sgn}\left(x\right) + \sqrt{-x^{2} + x} \mathrm{sgn}\left(x\right)"," ",0,"1/4*pi*sgn(x) + 1/2*arcsin(2*x - 1)*sgn(x) + sqrt(-x^2 + x)*sgn(x)","A",0
976,1,35,0,0.379959," ","integrate(((-1+x)/x)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x} + 1 \right|}\right) \mathrm{sgn}\left(x\right) + \sqrt{x^{2} - x} \mathrm{sgn}\left(x\right)"," ",0,"1/2*log(abs(-2*x + 2*sqrt(x^2 - x) + 1))*sgn(x) + sqrt(x^2 - x)*sgn(x)","A",0
977,1,38,0,0.379817," ","integrate(((1+x)/x)^(1/2)/x,x, algorithm=""giac"")","-\log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + x} - 1 \right|}\right) \mathrm{sgn}\left(x\right) + \frac{2 \, \mathrm{sgn}\left(x\right)}{x - \sqrt{x^{2} + x}}"," ",0,"-log(abs(-2*x + 2*sqrt(x^2 + x) - 1))*sgn(x) + 2*sgn(x)/(x - sqrt(x^2 + x))","A",0
978,1,35,0,0.385675," ","integrate((x/(1+x))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + x} - 1 \right|}\right) \mathrm{sgn}\left(x + 1\right) + \sqrt{x^{2} + x} \mathrm{sgn}\left(x + 1\right)"," ",0,"1/2*log(abs(-2*x + 2*sqrt(x^2 + x) - 1))*sgn(x + 1) + sqrt(x^2 + x)*sgn(x + 1)","B",0
979,1,35,0,0.458830," ","integrate(1/((-1-x)/x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) - \frac{\arcsin\left(2 \, x + 1\right)}{2 \, \mathrm{sgn}\left(x\right)} - \frac{\sqrt{-x^{2} - x}}{\mathrm{sgn}\left(x\right)}"," ",0,"1/4*pi*sgn(x) - 1/2*arcsin(2*x + 1)/sgn(x) - sqrt(-x^2 - x)/sgn(x)","A",0
980,1,25,0,0.385527," ","integrate(((4-x)*x)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 4 \, x} {\left(x - 2\right)} + 2 \, \arcsin\left(\frac{1}{2} \, x - 1\right)"," ",0,"1/2*sqrt(-x^2 + 4*x)*(x - 2) + 2*arcsin(1/2*x - 1)","A",0
981,1,6,0,0.388238," ","integrate(1/((1-x)*x)^(1/2),x, algorithm=""giac"")","\arcsin\left(2 \, x - 1\right)"," ",0,"arcsin(2*x - 1)","A",0
982,1,16,0,0.328461," ","integrate(x/(x*(2+x))^(3/2),x, algorithm=""giac"")","\frac{2}{x - \sqrt{{\left(x + 2\right)} x} + 2}"," ",0,"2/(x - sqrt((x + 2)*x) + 2)","A",0
983,1,73,0,0.534285," ","integrate((1+1/x)^(1/2)/(-x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{\sqrt{2} - 1}{\sqrt{2} + 1}\right) \mathrm{sgn}\left(x\right) - \frac{1}{2} \, \sqrt{2} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{2} + 2 \, \sqrt{x^{2} + x} + 2 \right|}}{{\left| -2 \, x + 2 \, \sqrt{2} + 2 \, \sqrt{x^{2} + x} + 2 \right|}}\right) \mathrm{sgn}\left(x\right)"," ",0,"1/2*sqrt(2)*log((sqrt(2) - 1)/(sqrt(2) + 1))*sgn(x) - 1/2*sqrt(2)*log(abs(-2*x - 2*sqrt(2) + 2*sqrt(x^2 + x) + 2)/abs(-2*x + 2*sqrt(2) + 2*sqrt(x^2 + x) + 2))*sgn(x)","B",0
984,1,13,0,0.361484," ","integrate(1/(1-x^2+5^(1/2)+x^2*5^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(\frac{2 \, x}{\sqrt{5} + 1}\right)"," ",0,"1/2*arctan(2*x/(sqrt(5) + 1))","A",0
985,1,35,0,0.466231," ","integrate(1/(b*x^2+a*x)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b)","A",0
986,1,35,0,0.414636," ","integrate(1/(x*(b*x+a))^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b)","A",0
987,1,35,0,0.422448," ","integrate(1/((a/x+b)*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b)","A",0
988,1,35,0,0.496878," ","integrate(1/((a/x^2+b/x)*x^3)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b)","A",0
989,1,35,0,0.559992," ","integrate(1/((b*x^3+a*x^2)/x)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b)","A",0
990,1,35,0,0.474316," ","integrate(1/((b*x^4+a*x^3)/x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b)","A",0
991,1,50,0,0.496189," ","integrate(1/(b*c*x^2+a*c*x)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b c} \log\left({\left| -2 \, {\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c x}\right)} b - \sqrt{b c} a \right|}\right)}{b c}"," ",0,"-sqrt(b*c)*log(abs(-2*(sqrt(b*c)*x - sqrt(b*c*x^2 + a*c*x))*b - sqrt(b*c)*a))/(b*c)","A",0
992,1,50,0,0.569994," ","integrate(1/(c*(b*x^2+a*x))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b c} \log\left({\left| -2 \, {\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c x}\right)} b - \sqrt{b c} a \right|}\right)}{b c}"," ",0,"-sqrt(b*c)*log(abs(-2*(sqrt(b*c)*x - sqrt(b*c*x^2 + a*c*x))*b - sqrt(b*c)*a))/(b*c)","A",0
993,1,50,0,0.490647," ","integrate(1/(c*x*(b*x+a))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b c} \log\left({\left| -2 \, {\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c x}\right)} b - \sqrt{b c} a \right|}\right)}{b c}"," ",0,"-sqrt(b*c)*log(abs(-2*(sqrt(b*c)*x - sqrt(b*c*x^2 + a*c*x))*b - sqrt(b*c)*a))/(b*c)","A",0
994,1,50,0,0.515063," ","integrate(1/(c*(a/x+b)*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b c} \log\left({\left| -2 \, {\left(\sqrt{b c} x - \sqrt{b c x^{2} + a c x}\right)} b - \sqrt{b c} a \right|}\right)}{b c}"," ",0,"-sqrt(b*c)*log(abs(-2*(sqrt(b*c)*x - sqrt(b*c*x^2 + a*c*x))*b - sqrt(b*c)*a))/(b*c)","A",0
995,0,0,0,0.000000," ","integrate((1-x^2+x*(x^2-1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{-x^{2} + \sqrt{x^{2} - 1} x + 1}\,{d x}"," ",0,"integrate(sqrt(-x^2 + sqrt(x^2 - 1)*x + 1), x)","F",0
996,0,0,0,0.000000," ","integrate((-x+x^(1/2)*(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x + 1} \sqrt{x} - x}}{\sqrt{x + 1}}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + 1)*sqrt(x) - x)/sqrt(x + 1), x)","F",0
997,1,218,0,0.861606," ","integrate((-x-2*(x^2+1)^(1/2))/(x+x^3+(x^2+1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2 \, \sqrt{5} + 2} \arctan\left(-\frac{x - \sqrt{x^{2} + 1} + \frac{1}{x - \sqrt{x^{2} + 1}}}{\sqrt{2 \, \sqrt{5} - 2}}\right) - \frac{1}{2} \, \sqrt{2 \, \sqrt{5} + 2} \arctan\left(\frac{x}{\sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(-x + \sqrt{x^{2} + 1} + \sqrt{2 \, \sqrt{5} + 2} - \frac{1}{x - \sqrt{x^{2} + 1}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| x + \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| x - \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}} \right|}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| -x + \sqrt{x^{2} + 1} - \sqrt{2 \, \sqrt{5} + 2} - \frac{1}{x - \sqrt{x^{2} + 1}} \right|}\right)"," ",0,"-1/2*sqrt(2*sqrt(5) + 2)*arctan(-(x - sqrt(x^2 + 1) + 1/(x - sqrt(x^2 + 1)))/sqrt(2*sqrt(5) - 2)) - 1/2*sqrt(2*sqrt(5) + 2)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) + 1/4*sqrt(2*sqrt(5) - 2)*log(-x + sqrt(x^2 + 1) + sqrt(2*sqrt(5) + 2) - 1/(x - sqrt(x^2 + 1))) - 1/4*sqrt(2*sqrt(5) - 2)*log(abs(x + sqrt(1/2*sqrt(5) - 1/2))) + 1/4*sqrt(2*sqrt(5) - 2)*log(abs(x - sqrt(1/2*sqrt(5) - 1/2))) - 1/4*sqrt(2*sqrt(5) - 2)*log(abs(-x + sqrt(x^2 + 1) - sqrt(2*sqrt(5) + 2) - 1/(x - sqrt(x^2 + 1))))","B",0
998,1,444,0,0.719921," ","integrate((1+2*x)/(x^2+1)/(x^2+2*x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(256 \, {\left(\sqrt{5} {\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)} - 2 \, x + \sqrt{5} \sqrt{\sqrt{5} - 2} + \sqrt{5} + 2 \, \sqrt{x^{2} + 2 \, x + 2} - 2 \, \sqrt{\sqrt{5} - 2} - 2\right)}^{2} + 256 \, {\left(\sqrt{5} {\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)} - 2 \, x - \sqrt{5} + 2 \, \sqrt{x^{2} + 2 \, x + 2} + \sqrt{\sqrt{5} - 2} + 2\right)}^{2}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(256 \, {\left(\sqrt{5} {\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)} - 2 \, x - \sqrt{5} \sqrt{\sqrt{5} - 2} + \sqrt{5} + 2 \, \sqrt{x^{2} + 2 \, x + 2} + 2 \, \sqrt{\sqrt{5} - 2} - 2\right)}^{2} + 256 \, {\left(\sqrt{5} {\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)} - 2 \, x - \sqrt{5} + 2 \, \sqrt{x^{2} + 2 \, x + 2} - \sqrt{\sqrt{5} - 2} + 2\right)}^{2}\right) + \frac{{\left(\pi + 4 \, \arctan\left(\frac{1}{2} \, {\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)} {\left(2 \, \sqrt{5} \sqrt{\sqrt{5} - 2} + \sqrt{5} + 4 \, \sqrt{\sqrt{5} - 2} + 3\right)} + \frac{3}{2} \, \sqrt{5} \sqrt{\sqrt{5} - 2} + \frac{1}{2} \, \sqrt{5} + \frac{7}{2} \, \sqrt{\sqrt{5} - 2} + \frac{3}{2}\right)\right)} \sqrt{2 \, \sqrt{5} - 2}}{4 \, {\left(\sqrt{5} - 1\right)}} - \frac{{\left(\pi + 4 \, \arctan\left(-\frac{1}{2} \, {\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)} {\left(2 \, \sqrt{5} \sqrt{\sqrt{5} - 2} - \sqrt{5} + 4 \, \sqrt{\sqrt{5} - 2} - 3\right)} - \frac{3}{2} \, \sqrt{5} \sqrt{\sqrt{5} - 2} + \frac{1}{2} \, \sqrt{5} - \frac{7}{2} \, \sqrt{\sqrt{5} - 2} + \frac{3}{2}\right)\right)} \sqrt{2 \, \sqrt{5} - 2}}{4 \, {\left(\sqrt{5} - 1\right)}}"," ",0,"1/4*sqrt(2*sqrt(5) - 2)*log(256*(sqrt(5)*(x - sqrt(x^2 + 2*x + 2)) - 2*x + sqrt(5)*sqrt(sqrt(5) - 2) + sqrt(5) + 2*sqrt(x^2 + 2*x + 2) - 2*sqrt(sqrt(5) - 2) - 2)^2 + 256*(sqrt(5)*(x - sqrt(x^2 + 2*x + 2)) - 2*x - sqrt(5) + 2*sqrt(x^2 + 2*x + 2) + sqrt(sqrt(5) - 2) + 2)^2) - 1/4*sqrt(2*sqrt(5) - 2)*log(256*(sqrt(5)*(x - sqrt(x^2 + 2*x + 2)) - 2*x - sqrt(5)*sqrt(sqrt(5) - 2) + sqrt(5) + 2*sqrt(x^2 + 2*x + 2) + 2*sqrt(sqrt(5) - 2) - 2)^2 + 256*(sqrt(5)*(x - sqrt(x^2 + 2*x + 2)) - 2*x - sqrt(5) + 2*sqrt(x^2 + 2*x + 2) - sqrt(sqrt(5) - 2) + 2)^2) + 1/4*(pi + 4*arctan(1/2*(x - sqrt(x^2 + 2*x + 2))*(2*sqrt(5)*sqrt(sqrt(5) - 2) + sqrt(5) + 4*sqrt(sqrt(5) - 2) + 3) + 3/2*sqrt(5)*sqrt(sqrt(5) - 2) + 1/2*sqrt(5) + 7/2*sqrt(sqrt(5) - 2) + 3/2))*sqrt(2*sqrt(5) - 2)/(sqrt(5) - 1) - 1/4*(pi + 4*arctan(-1/2*(x - sqrt(x^2 + 2*x + 2))*(2*sqrt(5)*sqrt(sqrt(5) - 2) - sqrt(5) + 4*sqrt(sqrt(5) - 2) - 3) - 3/2*sqrt(5)*sqrt(sqrt(5) - 2) + 1/2*sqrt(5) - 7/2*sqrt(sqrt(5) - 2) + 3/2))*sqrt(2*sqrt(5) - 2)/(sqrt(5) - 1)","B",0
999,0,0,0,0.000000," ","integrate(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{4} + 1\right)} \sqrt{-x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)*sqrt(-x^2 + sqrt(x^4 + 1))), x)","F",0
1000,0,0,0,0.000000," ","integrate(1/(b*x^4+a)/(c*x^2+d*(b*x^4+a)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)} \sqrt{c x^{2} + \sqrt{b x^{4} + a} d}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)*sqrt(c*x^2 + sqrt(b*x^4 + a)*d)), x)","F",0
1001,0,0,0,0.000000," ","integrate(1/(b*x^4+a)/(-c*x^2+d*(b*x^4+a)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{4} + a\right)} \sqrt{-c x^{2} + \sqrt{b x^{4} + a} d}}\,{d x}"," ",0,"integrate(1/((b*x^4 + a)*sqrt(-c*x^2 + sqrt(b*x^4 + a)*d)), x)","F",0
1002,0,0,0,0.000000," ","integrate(x/(b*d^4*x^4+4*b*c*d^3*x^3+6*b*c^2*d^2*x^2+4*b*c^3*d*x+b*c^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a}}\,{d x}"," ",0,"integrate(x/sqrt(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a), x)","F",0
1003,0,0,0,0.000000," ","integrate(1/(b*d^4*x^4+4*b*c*d^3*x^3+6*b*c^2*d^2*x^2+4*b*c^3*d*x+b*c^4+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*d^4*x^4 + 4*b*c*d^3*x^3 + 6*b*c^2*d^2*x^2 + 4*b*c^3*d*x + b*c^4 + a), x)","F",0
1004,0,0,0,0.000000," ","integrate((-c*x^4+a)/(c*d*x^4+a*e*x^2+a*d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int -\frac{c x^{4} - a}{{\left(c d x^{4} + a e x^{2} + a d\right)} \sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate(-(c*x^4 - a)/((c*d*x^4 + a*e*x^2 + a*d)*sqrt(c*x^4 + b*x^2 + a)), x)","F",0
1005,0,0,0,0.000000," ","integrate((-c*x^4+a)/(c*d*x^4+a*e*x^2+a*d)/(c*x^4-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int -\frac{c x^{4} - a}{{\left(c d x^{4} + a e x^{2} + a d\right)} \sqrt{c x^{4} - b x^{2} + a}}\,{d x}"," ",0,"integrate(-(c*x^4 - a)/((c*d*x^4 + a*e*x^2 + a*d)*sqrt(c*x^4 - b*x^2 + a)), x)","F",0
1006,1,164,0,0.591420," ","integrate(1/(x^3+8)/(x^2-2*x+5)^(1/2),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - \sqrt{x^{2} - 2 \, x + 5}\right)}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - \sqrt{x^{2} - 2 \, x + 5} - 2\right)}\right) + \frac{1}{156} \, \sqrt{13} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{13} + 2 \, \sqrt{x^{2} - 2 \, x + 5} - 4 \right|}}{{\left| -2 \, x + 2 \, \sqrt{13} + 2 \, \sqrt{x^{2} - 2 \, x + 5} - 4 \right|}}\right) + \frac{1}{24} \, \log\left({\left(x - \sqrt{x^{2} - 2 \, x + 5}\right)}^{2} - 4 \, x + 4 \, \sqrt{x^{2} - 2 \, x + 5} + 7\right) - \frac{1}{24} \, \log\left({\left(x - \sqrt{x^{2} - 2 \, x + 5}\right)}^{2} + 3\right)"," ",0,"-1/12*sqrt(3)*arctan(-1/3*sqrt(3)*(x - sqrt(x^2 - 2*x + 5))) + 1/12*sqrt(3)*arctan(-1/3*sqrt(3)*(x - sqrt(x^2 - 2*x + 5) - 2)) + 1/156*sqrt(13)*log(abs(-2*x - 2*sqrt(13) + 2*sqrt(x^2 - 2*x + 5) - 4)/abs(-2*x + 2*sqrt(13) + 2*sqrt(x^2 - 2*x + 5) - 4)) + 1/24*log((x - sqrt(x^2 - 2*x + 5))^2 - 4*x + 4*sqrt(x^2 - 2*x + 5) + 7) - 1/24*log((x - sqrt(x^2 - 2*x + 5))^2 + 3)","B",0
1007,1,15,0,0.438032," ","integrate((x^2/(x^2+1))^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} + 1} \mathrm{sgn}\left(x\right) - \mathrm{sgn}\left(x\right)"," ",0,"sqrt(x^2 + 1)*sgn(x) - sgn(x)","A",0
1008,0,0,0,0.000000," ","integrate((x^n/(1+x^n))^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{x^{n}}{x^{n} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^n/(x^n + 1)), x)","F",0
1009,0,0,0,0.000000," ","integrate((-e*f*x^2+e*f)/(a*d*x^2+b*d*x+a*d)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int -\frac{e f x^{2} - e f}{\sqrt{a x^{4} + b x^{3} + c x^{2} + b x + a} {\left(a d x^{2} + b d x + a d\right)}}\,{d x}"," ",0,"integrate(-(e*f*x^2 - e*f)/(sqrt(a*x^4 + b*x^3 + c*x^2 + b*x + a)*(a*d*x^2 + b*d*x + a*d)), x)","F",0
1010,0,0,0,0.000000," ","integrate((-e*f*x^2+e*f)/(-a*d*x^2+b*d*x-a*d)/(-a*x^4+b*x^3+c*x^2+b*x-a)^(1/2),x, algorithm=""giac"")","\int \frac{e f x^{2} - e f}{\sqrt{-a x^{4} + b x^{3} + c x^{2} + b x - a} {\left(a d x^{2} - b d x + a d\right)}}\,{d x}"," ",0,"integrate((e*f*x^2 - e*f)/(sqrt(-a*x^4 + b*x^3 + c*x^2 + b*x - a)*(a*d*x^2 - b*d*x + a*d)), x)","F",0
1011,0,0,0,0.000000," ","integrate((a*x^2+b*x*(-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, algorithm=""giac"")","\int \frac{\sqrt{a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} x}\,{d x}"," ",0,"integrate(sqrt(a*x^2 + sqrt(a^2*x^2/b^2 - a/b^2)*b*x)/(sqrt(a^2*x^2/b^2 - a/b^2)*x), x)","F",0
1012,0,0,0,0.000000," ","integrate((-a*x^2+b*x*(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, algorithm=""giac"")","\int \frac{\sqrt{-a x^{2} + \sqrt{\frac{a^{2} x^{2}}{b^{2}} + \frac{a}{b^{2}}} b x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} + \frac{a}{b^{2}}} x}\,{d x}"," ",0,"integrate(sqrt(-a*x^2 + sqrt(a^2*x^2/b^2 + a/b^2)*b*x)/(sqrt(a^2*x^2/b^2 + a/b^2)*x), x)","F",0
1013,0,0,0,0.000000," ","integrate((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, algorithm=""giac"")","\int \frac{\sqrt{{\left(a x + \sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} b\right)} x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} - \frac{a}{b^{2}}} x}\,{d x}"," ",0,"integrate(sqrt((a*x + sqrt(a^2*x^2/b^2 - a/b^2)*b)*x)/(sqrt(a^2*x^2/b^2 - a/b^2)*x), x)","F",0
1014,0,0,0,0.000000," ","integrate((x*(b*(a/b^2+a^2*x^2/b^2)^(1/2)-a*x))^(1/2)/x/(a/b^2+a^2*x^2/b^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-{\left(a x - \sqrt{\frac{a^{2} x^{2}}{b^{2}} + \frac{a}{b^{2}}} b\right)} x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}} + \frac{a}{b^{2}}} x}\,{d x}"," ",0,"integrate(sqrt(-(a*x - sqrt(a^2*x^2/b^2 + a/b^2)*b)*x)/(sqrt(a^2*x^2/b^2 + a/b^2)*x), x)","F",0
1015,1,58,0,0.621595," ","integrate((-(-4+x)^(1/2)+x*(-4+x)^(1/2)-4*(-1+x)^(1/2)+x*(-1+x)^(1/2))/(x^2-5*x+4)/(1+(-4+x)^(1/2)+(-1+x)^(1/2)),x, algorithm=""giac"")","-\log\left(\sqrt{x - 1} - \sqrt{x - 4} + 1\right) - \log\left(\sqrt{x - 1} - \sqrt{x - 4}\right) + \log\left(\sqrt{x - 1} + 2\right) + \log\left({\left| -\sqrt{x - 1} + \sqrt{x - 4} - 3 \right|}\right)"," ",0,"-log(sqrt(x - 1) - sqrt(x - 4) + 1) - log(sqrt(x - 1) - sqrt(x - 4)) + log(sqrt(x - 1) + 2) + log(abs(-sqrt(x - 1) + sqrt(x - 4) - 3))","B",0
1016,0,0,0,0.000000," ","integrate(1/x/(x^2+3*x+3)/(x^3+3*x^2+3*x+3)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{1}{3}} {\left(x^{2} + 3 \, x + 3\right)} x}\,{d x}"," ",0,"integrate(1/((x^3 + 3*x^2 + 3*x + 3)^(1/3)*(x^2 + 3*x + 3)*x), x)","F",0
1017,0,0,0,0.000000," ","integrate((-x^2+1)/(x^2-x+1)/(-x^3+1)^(2/3),x, algorithm=""giac"")","\int -\frac{x^{2} - 1}{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} {\left(x^{2} - x + 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 1)/((-x^3 + 1)^(2/3)*(x^2 - x + 1)), x)","F",0
1018,0,0,0,0.000000," ","integrate(x^2/(x^4+1)/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{4} + 1\right)} \sqrt{x^{4} - 1}}\,{d x}"," ",0,"integrate(x^2/((x^4 + 1)*sqrt(x^4 - 1)), x)","F",0
1019,0,0,0,0.000000," ","integrate((-c*x^4+a)/(c*d*x^2+a*e)/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int -\frac{c x^{4} - a}{\sqrt{c x^{4} + b x^{2} + a} {\left(c d x^{2} + a e\right)} {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"integrate(-(c*x^4 - a)/(sqrt(c*x^4 + b*x^2 + a)*(c*d*x^2 + a*e)*(e*x^2 + d)), x)","F",0
1020,1,1,0,0.352274," ","integrate(x+(-x^2+1)/(1+x),x, algorithm=""giac"")","x"," ",0,"x","A",0
1021,1,193,0,0.416999," ","integrate(1/(1/x+(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \pi \mathrm{sgn}\left(x\right) - \frac{1}{6} \, \sqrt{3} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{3} x {\left(\frac{\sqrt{-x^{2} + 1} - 1}{x} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{3 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} - \frac{1}{6} \, \sqrt{3} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(\frac{\sqrt{3} x {\left(\frac{\sqrt{-x^{2} + 1} - 1}{x} - \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 1\right)}}{3 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)"," ",0,"1/2*pi*sgn(x) - 1/6*sqrt(3)*(pi*sgn(x) + 2*arctan(-1/3*sqrt(3)*x*((sqrt(-x^2 + 1) - 1)/x + (sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))) - 1/6*sqrt(3)*(pi*sgn(x) + 2*arctan(1/3*sqrt(3)*x*((sqrt(-x^2 + 1) - 1)/x - (sqrt(-x^2 + 1) - 1)^2/x^2 + 1)/(sqrt(-x^2 + 1) - 1))) + 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))","B",0
1022,1,193,0,0.582858," ","integrate(x*(-x^2+1)^(1/2)/(x-x^3+(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \pi \mathrm{sgn}\left(x\right) - \frac{1}{6} \, \sqrt{3} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{3} x {\left(\frac{\sqrt{-x^{2} + 1} - 1}{x} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{3 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} - \frac{1}{6} \, \sqrt{3} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(\frac{\sqrt{3} x {\left(\frac{\sqrt{-x^{2} + 1} - 1}{x} - \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 1\right)}}{3 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)"," ",0,"1/2*pi*sgn(x) - 1/6*sqrt(3)*(pi*sgn(x) + 2*arctan(-1/3*sqrt(3)*x*((sqrt(-x^2 + 1) - 1)/x + (sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))) - 1/6*sqrt(3)*(pi*sgn(x) + 2*arctan(1/3*sqrt(3)*x*((sqrt(-x^2 + 1) - 1)/x - (sqrt(-x^2 + 1) - 1)^2/x^2 + 1)/(sqrt(-x^2 + 1) - 1))) + 1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))","B",0
1023,1,81,0,0.456630," ","integrate((-x^4+1)^n/((x^3+x^2+x+1)^n),x, algorithm=""giac"")","\frac{\frac{x e^{\left(n \log\left(x^{3} + x^{2} + x + 1\right) + n \log\left(-x + 1\right)\right)}}{{\left(x^{3} + x^{2} + x + 1\right)}^{n}} - \frac{e^{\left(n \log\left(x^{3} + x^{2} + x + 1\right) + n \log\left(-x + 1\right)\right)}}{{\left(x^{3} + x^{2} + x + 1\right)}^{n}}}{n + 1}"," ",0,"(x*e^(n*log(x^3 + x^2 + x + 1) + n*log(-x + 1))/(x^3 + x^2 + x + 1)^n - e^(n*log(x^3 + x^2 + x + 1) + n*log(-x + 1))/(x^3 + x^2 + x + 1)^n)/(n + 1)","B",0
1024,0,0,0,0.000000," ","integrate(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{5308416 \, c^{4} x^{4} + 576000 \, b^{2} c^{2} x^{2} + 576000 \, b^{3} c x - 44375 \, b^{4}}}\,{d x}"," ",0,"integrate(x/sqrt(5308416*c^4*x^4 + 576000*b^2*c^2*x^2 + 576000*b^3*c*x - 44375*b^4), x)","F",0
1025,0,0,0,0.000000," ","integrate((1+4*x)/(64*x^4+64*x^3+64*x^2+120*x+9)^(1/2),x, algorithm=""giac"")","\int \frac{4 \, x + 1}{\sqrt{64 \, x^{4} + 64 \, x^{3} + 64 \, x^{2} + 120 \, x + 9}}\,{d x}"," ",0,"integrate((4*x + 1)/sqrt(64*x^4 + 64*x^3 + 64*x^2 + 120*x + 9), x)","F",0
