1,1,54,0,1.018101," ","integrate(arcsin(x)*log(x),x, algorithm=""fricas"")","x \arcsin\left(x\right) \log\left(x\right) - x \arcsin\left(x\right) + \sqrt{-x^{2} + 1} {\left(\log\left(x\right) - 2\right)} + \frac{1}{2} \, \log\left(\sqrt{-x^{2} + 1} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{-x^{2} + 1} - 1\right)"," ",0,"x*arcsin(x)*log(x) - x*arcsin(x) + sqrt(-x^2 + 1)*(log(x) - 2) + 1/2*log(sqrt(-x^2 + 1) + 1) - 1/2*log(sqrt(-x^2 + 1) - 1)","A",0
2,1,15,0,1.031657," ","integrate(x*arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 1} \arcsin\left(x\right) + x"," ",0,"-sqrt(-x^2 + 1)*arcsin(x) + x","A",0
3,1,49,0,88.462638," ","integrate(-arcsin(x^(1/2)-(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{8} \, {\left(8 \, x + 3\right)} \arcsin\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{8} \, \sqrt{2 \, \sqrt{x + 1} \sqrt{x} - 2 \, x} {\left(3 \, \sqrt{x + 1} + \sqrt{x}\right)}"," ",0,"1/8*(8*x + 3)*arcsin(sqrt(x + 1) - sqrt(x)) + 1/8*sqrt(2*sqrt(x + 1)*sqrt(x) - 2*x)*(3*sqrt(x + 1) + sqrt(x))","A",0
4,1,402,0,1.014350," ","integrate(log(1+x*(x^2+1)^(1/2)),x, algorithm=""fricas"")","-\sqrt{2} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{4} \, \sqrt{2} \sqrt{4 \, x^{4} + 4 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} + 1\right)} - 2 \, {\left(2 \, x^{3} + \sqrt{5} x + x\right)} \sqrt{x^{2} + 1} + 1} {\left(\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + 1}\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{2} \, \sqrt{2} \sqrt{x^{2} + 1} \sqrt{\sqrt{5} + 1}\right) - \sqrt{2} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{8} \, \sqrt{4 \, x^{2} + 2 \, \sqrt{5} + 2} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{4} \, {\left(\sqrt{5} \sqrt{2} x - \sqrt{2} x\right)} \sqrt{\sqrt{5} + 1}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(4 \, x^{2} - 4 \, \sqrt{x^{2} + 1} x + {\left(\sqrt{5} \sqrt{2} x - \sqrt{x^{2} + 1} {\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} + \sqrt{2} x\right)} \sqrt{\sqrt{5} - 1} + 4\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(4 \, x^{2} - 4 \, \sqrt{x^{2} + 1} x - {\left(\sqrt{5} \sqrt{2} x - \sqrt{x^{2} + 1} {\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} + \sqrt{2} x\right)} \sqrt{\sqrt{5} - 1} + 4\right) + x \log\left(\sqrt{x^{2} + 1} x + 1\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(2 \, x + \sqrt{2} \sqrt{\sqrt{5} - 1}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(2 \, x - \sqrt{2} \sqrt{\sqrt{5} - 1}\right) - 2 \, x"," ",0,"-sqrt(2)*sqrt(sqrt(5) + 1)*arctan(1/4*sqrt(2)*sqrt(4*x^4 + 4*x^2 + sqrt(5)*(2*x^2 + 1) - 2*(2*x^3 + sqrt(5)*x + x)*sqrt(x^2 + 1) + 1)*(sqrt(2)*x + sqrt(2)*sqrt(x^2 + 1))*sqrt(sqrt(5) + 1) - 1/2*sqrt(2)*sqrt(x^2 + 1)*sqrt(sqrt(5) + 1)) - sqrt(2)*sqrt(sqrt(5) + 1)*arctan(1/8*sqrt(4*x^2 + 2*sqrt(5) + 2)*(sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 1) - 1/4*(sqrt(5)*sqrt(2)*x - sqrt(2)*x)*sqrt(sqrt(5) + 1)) + 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(4*x^2 - 4*sqrt(x^2 + 1)*x + (sqrt(5)*sqrt(2)*x - sqrt(x^2 + 1)*(sqrt(5)*sqrt(2) + sqrt(2)) + sqrt(2)*x)*sqrt(sqrt(5) - 1) + 4) - 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(4*x^2 - 4*sqrt(x^2 + 1)*x - (sqrt(5)*sqrt(2)*x - sqrt(x^2 + 1)*(sqrt(5)*sqrt(2) + sqrt(2)) + sqrt(2)*x)*sqrt(sqrt(5) - 1) + 4) + x*log(sqrt(x^2 + 1)*x + 1) + 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(2*x + sqrt(2)*sqrt(sqrt(5) - 1)) - 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(2*x - sqrt(2)*sqrt(sqrt(5) - 1)) - 2*x","B",0
5,1,33,0,1.014129," ","integrate(cos(x)^2/(1+cos(x)^2+cos(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \arctan\left(\frac{2 \, \sqrt{\cos\left(x\right)^{4} + \cos\left(x\right)^{2} + 1} \cos\left(x\right)^{3} \sin\left(x\right)}{2 \, \cos\left(x\right)^{6} - 1}\right)"," ",0,"1/6*arctan(2*sqrt(cos(x)^4 + cos(x)^2 + 1)*cos(x)^3*sin(x)/(2*cos(x)^6 - 1))","A",0
6,1,88,0,1.171387," ","integrate((1+tan(x)^4)^(1/2)*tan(x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{3 \, \tan\left(x\right)^{4} - 2 \, \tan\left(x\right)^{2} + 2 \, \sqrt{\tan\left(x\right)^{4} + 1} {\left(\sqrt{2} \tan\left(x\right)^{2} - \sqrt{2}\right)} + 3}{\tan\left(x\right)^{4} + 2 \, \tan\left(x\right)^{2} + 1}\right) + \frac{1}{2} \, \sqrt{\tan\left(x\right)^{4} + 1} + \frac{1}{2} \, \log\left(-\tan\left(x\right)^{2} + \sqrt{\tan\left(x\right)^{4} + 1}\right)"," ",0,"1/4*sqrt(2)*log((3*tan(x)^4 - 2*tan(x)^2 + 2*sqrt(tan(x)^4 + 1)*(sqrt(2)*tan(x)^2 - sqrt(2)) + 3)/(tan(x)^4 + 2*tan(x)^2 + 1)) + 1/2*sqrt(tan(x)^4 + 1) + 1/2*log(-tan(x)^2 + sqrt(tan(x)^4 + 1))","B",0
7,1,30,0,0.935776," ","integrate(tan(x)/(1+sec(x)^3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(2 \, \sqrt{\frac{\cos\left(x\right)^{3} + 1}{\cos\left(x\right)^{3}}} \cos\left(x\right)^{3} - 2 \, \cos\left(x\right)^{3} - 1\right)"," ",0,"1/3*log(2*sqrt((cos(x)^3 + 1)/cos(x)^3)*cos(x)^3 - 2*cos(x)^3 - 1)","B",0
8,-1,0,0,0.000000," ","integrate((2+2*tan(x)+tan(x)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,32,0,1.296874," ","integrate(arctan((-1+sec(x))^(1/2))*sin(x),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(2 \, \cos\left(x\right) - 1\right)} \arctan\left(\sqrt{\sec\left(x\right) - 1}\right) + \frac{1}{2} \, \sqrt{-\frac{\cos\left(x\right) - 1}{\cos\left(x\right)}} \cos\left(x\right)"," ",0,"-1/2*(2*cos(x) - 1)*arctan(sqrt(sec(x) - 1)) + 1/2*sqrt(-(cos(x) - 1)/cos(x))*cos(x)","A",0
10,1,28,0,1.083753," ","integrate(exp(arcsin(x))*x^3/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{10} \, {\left(x^{3} - 3 \, {\left(x^{2} + 1\right)} \sqrt{-x^{2} + 1} + 3 \, x\right)} e^{\arcsin\left(x\right)}"," ",0,"1/10*(x^3 - 3*(x^2 + 1)*sqrt(-x^2 + 1) + 3*x)*e^arcsin(x)","A",0
11,1,43,0,0.992522," ","integrate(x*log(x^2+1)*log(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} + 1} {\left(\log\left(x^{2} + 1\right) - 2\right)} \log\left(x + \sqrt{x^{2} + 1}\right) - x \log\left(x^{2} + 1\right) + 4 \, x - 2 \, \arctan\left(x\right)"," ",0,"sqrt(x^2 + 1)*(log(x^2 + 1) - 2)*log(x + sqrt(x^2 + 1)) - x*log(x^2 + 1) + 4*x - 2*arctan(x)","A",0
12,1,191,0,0.954994," ","integrate(arctan(x+(-x^2+1)^(1/2)),x, algorithm=""fricas"")","x \arctan\left(x + \sqrt{-x^{2} + 1}\right) - \frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{8} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \sqrt{-x^{2} + 1} x + \sqrt{3}}{3 \, {\left(2 \, x^{2} - 1\right)}}\right) - \frac{1}{8} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \sqrt{-x^{2} + 1} x - \sqrt{3}}{3 \, {\left(2 \, x^{2} - 1\right)}}\right) + \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{2} + 1} x}{x^{2} - 1}\right) - \frac{1}{8} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{16} \, \log\left(-x^{4} + x^{2} + 2 \, \sqrt{-x^{2} + 1} x + 1\right) + \frac{1}{16} \, \log\left(-x^{4} + x^{2} - 2 \, \sqrt{-x^{2} + 1} x + 1\right)"," ",0,"x*arctan(x + sqrt(-x^2 + 1)) - 1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/8*sqrt(3)*arctan(1/3*(4*sqrt(3)*sqrt(-x^2 + 1)*x + sqrt(3))/(2*x^2 - 1)) - 1/8*sqrt(3)*arctan(1/3*(4*sqrt(3)*sqrt(-x^2 + 1)*x - sqrt(3))/(2*x^2 - 1)) + 1/2*arctan(sqrt(-x^2 + 1)*x/(x^2 - 1)) - 1/8*log(x^4 - x^2 + 1) - 1/16*log(-x^4 + x^2 + 2*sqrt(-x^2 + 1)*x + 1) + 1/16*log(-x^4 + x^2 - 2*sqrt(-x^2 + 1)*x + 1)","A",0
13,1,200,0,1.017777," ","integrate(x*arctan(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \sqrt{-x^{2} + 1} \arctan\left(x + \sqrt{-x^{2} + 1}\right) - \frac{1}{8} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \sqrt{-x^{2} + 1} x + \sqrt{3}}{3 \, {\left(2 \, x^{2} - 1\right)}}\right) - \frac{1}{8} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} \sqrt{-x^{2} + 1} x - \sqrt{3}}{3 \, {\left(2 \, x^{2} - 1\right)}}\right) + \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{2} + 1} x}{x^{2} - 1}\right) + \frac{1}{8} \, \log\left(x^{4} - x^{2} + 1\right) + \frac{1}{16} \, \log\left(-x^{4} + x^{2} + 2 \, \sqrt{-x^{2} + 1} x + 1\right) - \frac{1}{16} \, \log\left(-x^{4} + x^{2} - 2 \, \sqrt{-x^{2} + 1} x + 1\right)"," ",0,"-1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - sqrt(-x^2 + 1)*arctan(x + sqrt(-x^2 + 1)) - 1/8*sqrt(3)*arctan(1/3*(4*sqrt(3)*sqrt(-x^2 + 1)*x + sqrt(3))/(2*x^2 - 1)) - 1/8*sqrt(3)*arctan(1/3*(4*sqrt(3)*sqrt(-x^2 + 1)*x - sqrt(3))/(2*x^2 - 1)) + 1/2*arctan(sqrt(-x^2 + 1)*x/(x^2 - 1)) + 1/8*log(x^4 - x^2 + 1) + 1/16*log(-x^4 + x^2 + 2*sqrt(-x^2 + 1)*x + 1) - 1/16*log(-x^4 + x^2 - 2*sqrt(-x^2 + 1)*x + 1)","A",0
14,1,63,0,1.039191," ","integrate(arcsin(x)/(1+(-x^2+1)^(1/2)),x, algorithm=""fricas"")","\frac{x \arcsin\left(x\right)^{2} - 2 \, x \log\left(x\right) - x \log\left(\sqrt{-x^{2} + 1} + 1\right) + x \log\left(\sqrt{-x^{2} + 1} - 1\right) + 2 \, \sqrt{-x^{2} + 1} \arcsin\left(x\right) - 2 \, \arcsin\left(x\right)}{2 \, x}"," ",0,"1/2*(x*arcsin(x)^2 - 2*x*log(x) - x*log(sqrt(-x^2 + 1) + 1) + x*log(sqrt(-x^2 + 1) - 1) + 2*sqrt(-x^2 + 1)*arcsin(x) - 2*arcsin(x))/x","A",0
15,1,62,0,1.001945," ","integrate(log(x+(x^2+1)^(1/2))/(-x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-x^{2} + 1} x \log\left(x + \sqrt{x^{2} + 1}\right) - {\left(x^{2} - 1\right)} \arctan\left(\frac{\sqrt{x^{2} + 1} \sqrt{-x^{2} + 1} - 1}{x^{2}}\right)}{x^{2} - 1}"," ",0,"-(sqrt(-x^2 + 1)*x*log(x + sqrt(x^2 + 1)) - (x^2 - 1)*arctan((sqrt(x^2 + 1)*sqrt(-x^2 + 1) - 1)/x^2))/(x^2 - 1)","B",0
16,1,56,0,0.908013," ","integrate(arcsin(x)/(x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{x^{2} + 1} x \arcsin\left(x\right) + {\left(x^{2} + 1\right)} \arctan\left(\frac{\sqrt{x^{2} + 1} \sqrt{-x^{2} + 1} x^{2}}{x^{4} - 1}\right)}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(2*sqrt(x^2 + 1)*x*arcsin(x) + (x^2 + 1)*arctan(sqrt(x^2 + 1)*sqrt(-x^2 + 1)*x^2/(x^4 - 1)))/(x^2 + 1)","B",0
17,1,58,0,1.188566," ","integrate(log(x+(x^2-1)^(1/2))/(x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{x^{2} + 1} x \log\left(x + \sqrt{x^{2} - 1}\right) + {\left(x^{2} + 1\right)} \log\left(-x^{2} + \sqrt{x^{2} + 1} \sqrt{x^{2} - 1}\right)}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(2*sqrt(x^2 + 1)*x*log(x + sqrt(x^2 - 1)) + (x^2 + 1)*log(-x^2 + sqrt(x^2 + 1)*sqrt(x^2 - 1)))/(x^2 + 1)","B",0
18,1,32,0,0.866148," ","integrate(log(x)/x^2/(x^2-1)^(1/2),x, algorithm=""fricas"")","\frac{x \log\left(-x + \sqrt{x^{2} - 1}\right) + \sqrt{x^{2} - 1} {\left(\log\left(x\right) + 1\right)} + x}{x}"," ",0,"(x*log(-x + sqrt(x^2 - 1)) + sqrt(x^2 - 1)*(log(x) + 1) + x)/x","A",0
19,1,34,0,0.900313," ","integrate((x^3+1)^(1/2)/x,x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{x^{3} + 1} - \frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} - 1\right)"," ",0,"2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(sqrt(x^3 + 1) - 1)","A",0
20,1,22,0,0.733451," ","integrate(x*log(x+(x^2-1)^(1/2))/(x^2-1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} - 1} \log\left(x + \sqrt{x^{2} - 1}\right) - x"," ",0,"sqrt(x^2 - 1)*log(x + sqrt(x^2 - 1)) - x","A",0
21,1,138,0,1.482021," ","integrate(x^3*arcsin(x)/(-x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{-x^{4} + 1} {\left(x^{2} - 1\right)} \arcsin\left(x\right) + 2 \, \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} x + {\left(x^{2} - 1\right)} \log\left(\frac{x^{3} + \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} - x}{x^{3} - x}\right) - {\left(x^{2} - 1\right)} \log\left(-\frac{x^{3} - \sqrt{-x^{4} + 1} \sqrt{-x^{2} + 1} - x}{x^{3} - x}\right)}{8 \, {\left(x^{2} - 1\right)}}"," ",0,"-1/8*(4*sqrt(-x^4 + 1)*(x^2 - 1)*arcsin(x) + 2*sqrt(-x^4 + 1)*sqrt(-x^2 + 1)*x + (x^2 - 1)*log((x^3 + sqrt(-x^4 + 1)*sqrt(-x^2 + 1) - x)/(x^3 - x)) - (x^2 - 1)*log(-(x^3 - sqrt(-x^4 + 1)*sqrt(-x^2 + 1) - x)/(x^3 - x)))/(x^2 - 1)","B",0
22,1,110,0,1.041747," ","integrate(x^3*arcsec(x)/(x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(x^{2} - 1\right)} \log\left(\frac{x^{2} + \sqrt{x^{4} - 1} \sqrt{x^{2} - 1} - 1}{x^{2} - 1}\right) - {\left(x^{2} - 1\right)} \log\left(-\frac{x^{2} - \sqrt{x^{4} - 1} \sqrt{x^{2} - 1} - 1}{x^{2} - 1}\right) + 2 \, \sqrt{x^{4} - 1} {\left({\left(x^{2} - 1\right)} \operatorname{arcsec}\left(x\right) - \sqrt{x^{2} - 1}\right)}}{4 \, {\left(x^{2} - 1\right)}}"," ",0,"1/4*((x^2 - 1)*log((x^2 + sqrt(x^4 - 1)*sqrt(x^2 - 1) - 1)/(x^2 - 1)) - (x^2 - 1)*log(-(x^2 - sqrt(x^4 - 1)*sqrt(x^2 - 1) - 1)/(x^2 - 1)) + 2*sqrt(x^4 - 1)*((x^2 - 1)*arcsec(x) - sqrt(x^2 - 1)))/(x^2 - 1)","B",0
23,1,48,0,1.093775," ","integrate(x*arctan(x)*log(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} + 1} \arctan\left(x\right) \log\left(x + \sqrt{x^{2} + 1}\right) - x \arctan\left(x\right) - \frac{1}{2} \, \log\left(x + \sqrt{x^{2} + 1}\right)^{2} + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"sqrt(x^2 + 1)*arctan(x)*log(x + sqrt(x^2 + 1)) - x*arctan(x) - 1/2*log(x + sqrt(x^2 + 1))^2 + 1/2*log(x^2 + 1)","A",0
24,1,35,0,0.915666," ","integrate(x*log(1+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-{\left(\sqrt{-x^{2} + 1} + 1\right)} \log\left(\sqrt{-x^{2} + 1} + 1\right) + \sqrt{-x^{2} + 1}"," ",0,"-(sqrt(-x^2 + 1) + 1)*log(sqrt(-x^2 + 1) + 1) + sqrt(-x^2 + 1)","A",0
25,1,22,0,0.717644," ","integrate(x*log(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} + 1} \log\left(x + \sqrt{x^{2} + 1}\right) - x"," ",0,"sqrt(x^2 + 1)*log(x + sqrt(x^2 + 1)) - x","A",0
26,1,115,0,0.731679," ","integrate(x*log(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 1} \log\left(x + \sqrt{-x^{2} + 1}\right) + \frac{1}{4} \, \sqrt{2} \log\left(\frac{6 \, x^{2} - 2 \, \sqrt{2} {\left(2 \, x^{2} - 3\right)} + 2 \, \sqrt{-x^{2} + 1} {\left(3 \, \sqrt{2} - 4\right)} - 9}{2 \, x^{2} - 1}\right) + \frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, x^{2} + 2 \, \sqrt{2} x + 1}{2 \, x^{2} - 1}\right) + \sqrt{-x^{2} + 1}"," ",0,"-sqrt(-x^2 + 1)*log(x + sqrt(-x^2 + 1)) + 1/4*sqrt(2)*log((6*x^2 - 2*sqrt(2)*(2*x^2 - 3) + 2*sqrt(-x^2 + 1)*(3*sqrt(2) - 4) - 9)/(2*x^2 - 1)) + 1/4*sqrt(2)*log((2*x^2 + 2*sqrt(2)*x + 1)/(2*x^2 - 1)) + sqrt(-x^2 + 1)","A",0
27,1,39,0,0.903721," ","integrate(log(x)/x^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, x \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - \sqrt{-x^{2} + 1} {\left(\log\left(x\right) + 1\right)}}{x}"," ",0,"(2*x*arctan((sqrt(-x^2 + 1) - 1)/x) - sqrt(-x^2 + 1)*(log(x) + 1))/x","A",0
28,1,23,0,1.011541," ","integrate(x*arctan(x)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} + 1} \arctan\left(x\right) + \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"sqrt(x^2 + 1)*arctan(x) + log(-x + sqrt(x^2 + 1))","A",0
29,1,81,0,1.027785," ","integrate(arctan(x)/x^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} x \log\left(\frac{x^{2} - 2 \, \sqrt{2} \sqrt{-x^{2} + 1} - 3}{x^{2} + 1}\right) - x \log\left(\sqrt{-x^{2} + 1} + 1\right) + x \log\left(\sqrt{-x^{2} + 1} - 1\right) - 2 \, \sqrt{-x^{2} + 1} \arctan\left(x\right)}{2 \, x}"," ",0,"1/2*(sqrt(2)*x*log((x^2 - 2*sqrt(2)*sqrt(-x^2 + 1) - 3)/(x^2 + 1)) - x*log(sqrt(-x^2 + 1) + 1) + x*log(sqrt(-x^2 + 1) - 1) - 2*sqrt(-x^2 + 1)*arctan(x))/x","A",0
30,1,69,0,1.095284," ","integrate(x*arctan(x)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(3 \, x^{2} - 1\right)} \sqrt{-x^{2} + 1}}{4 \, {\left(x^{3} - x\right)}}\right) - \sqrt{-x^{2} + 1} \arctan\left(x\right) + \arctan\left(\frac{\sqrt{-x^{2} + 1} x}{x^{2} - 1}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/4*sqrt(2)*(3*x^2 - 1)*sqrt(-x^2 + 1)/(x^3 - x)) - sqrt(-x^2 + 1)*arctan(x) + arctan(sqrt(-x^2 + 1)*x/(x^2 - 1))","A",0
31,1,47,0,1.131614," ","integrate(arctan(x)/x^2/(x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{x \log\left(-x + \sqrt{x^{2} + 1} + 1\right) - x \log\left(-x + \sqrt{x^{2} + 1} - 1\right) + \sqrt{x^{2} + 1} \arctan\left(x\right)}{x}"," ",0,"-(x*log(-x + sqrt(x^2 + 1) + 1) - x*log(-x + sqrt(x^2 + 1) - 1) + sqrt(x^2 + 1)*arctan(x))/x","A",0
32,1,22,0,1.065661," ","integrate(arcsin(x)/x^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{x \log\left(x\right) - \sqrt{-x^{2} + 1} \arcsin\left(x\right)}{x}"," ",0,"(x*log(x) - sqrt(-x^2 + 1)*arcsin(x))/x","A",0
33,1,27,0,0.864880," ","integrate(x*log(x)/(x^2-1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} - 1} {\left(\log\left(x\right) - 1\right)} + 2 \, \arctan\left(-x + \sqrt{x^{2} - 1}\right)"," ",0,"sqrt(x^2 - 1)*(log(x) - 1) + 2*arctan(-x + sqrt(x^2 - 1))","A",0
34,1,33,0,1.096021," ","integrate(log(x)/x^2/(x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{x \log\left(-x + \sqrt{x^{2} + 1}\right) + \sqrt{x^{2} + 1} {\left(\log\left(x\right) + 1\right)} + x}{x}"," ",0,"-(x*log(-x + sqrt(x^2 + 1)) + sqrt(x^2 + 1)*(log(x) + 1) + x)/x","A",0
35,1,15,0,0.704952," ","integrate(x*arcsec(x)/(x^2-1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} - 1} \operatorname{arcsec}\left(x\right) - \log\left(x\right)"," ",0,"sqrt(x^2 - 1)*arcsec(x) - log(x)","A",0
36,1,41,0,0.694343," ","integrate(x*log(x)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} + 1} {\left(\log\left(x\right) - 1\right)} + \log\left(-x + \sqrt{x^{2} + 1} + 1\right) - \log\left(-x + \sqrt{x^{2} + 1} - 1\right)"," ",0,"sqrt(x^2 + 1)*(log(x) - 1) + log(-x + sqrt(x^2 + 1) + 1) - log(-x + sqrt(x^2 + 1) - 1)","A",0
37,1,29,0,1.000668," ","integrate(sin(x)/(1+sin(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{\cos\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2}{\cos\left(x\right)^{2} - 2}\right)"," ",0,"1/4*sqrt(2)*log(-(cos(x)^2 - 2*sqrt(2)*cos(x) + 2)/(cos(x)^2 - 2))","B",0
38,1,42,0,0.754332," ","integrate((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{x^{4} + 2 \, \sqrt{2} \sqrt{x^{4} + 1} x + 2 \, x^{2} + 1}{x^{4} - 2 \, x^{2} + 1}\right)"," ",0,"1/4*sqrt(2)*log((x^4 + 2*sqrt(2)*sqrt(x^4 + 1)*x + 2*x^2 + 1)/(x^4 - 2*x^2 + 1))","B",0
39,1,18,0,1.036996," ","integrate((-x^2+1)/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x}{\sqrt{x^{4} + 1}}\right)"," ",0,"1/2*sqrt(2)*arctan(sqrt(2)*x/sqrt(x^4 + 1))","A",0
40,1,93,0,1.093574," ","integrate(log(sin(x))/(1+sin(x)),x, algorithm=""fricas"")","-\frac{4 \, {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)} \arctan\left(-\frac{\cos\left(x\right) + \sin\left(x\right) + 1}{\cos\left(x\right) - \sin\left(x\right) + 1}\right) + 4 \, x \cos\left(x\right) + {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 2 \, {\left(\cos\left(x\right) - \sin\left(x\right) + 1\right)} \log\left(\sin\left(x\right)\right) + 4 \, x \sin\left(x\right) + 4 \, x}{2 \, {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)}}"," ",0,"-1/2*(4*(cos(x) + sin(x) + 1)*arctan(-(cos(x) + sin(x) + 1)/(cos(x) - sin(x) + 1)) + 4*x*cos(x) + (cos(x) + sin(x) + 1)*log(1/2*cos(x) + 1/2) - (cos(x) + sin(x) + 1)*log(-1/2*cos(x) + 1/2) + 2*(cos(x) - sin(x) + 1)*log(sin(x)) + 4*x*sin(x) + 4*x)/(cos(x) + sin(x) + 1)","B",0
41,1,146,0,1.007338," ","integrate(log(sin(x))*(1+sin(x))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)} \log\left(\frac{\cos\left(x\right)^{2} - {\left(\cos\left(x\right) - 1\right)} \sin\left(x\right) + 2 \, {\left(\cos\left(x\right) - \sin\left(x\right) + 1\right)} \sqrt{\sin\left(x\right) + 1} + 2 \, \cos\left(x\right) + 1}{2 \, {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)}}\right) - {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)} \log\left(\frac{\cos\left(x\right)^{2} - {\left(\cos\left(x\right) - 1\right)} \sin\left(x\right) - 2 \, {\left(\cos\left(x\right) - \sin\left(x\right) + 1\right)} \sqrt{\sin\left(x\right) + 1} + 2 \, \cos\left(x\right) + 1}{2 \, {\left(\cos\left(x\right) + \sin\left(x\right) + 1\right)}}\right) + 2 \, {\left({\left(\cos\left(x\right) - \sin\left(x\right) + 1\right)} \log\left(\sin\left(x\right)\right) - 2 \, \cos\left(x\right) + 2 \, \sin\left(x\right) - 2\right)} \sqrt{\sin\left(x\right) + 1}}{\cos\left(x\right) + \sin\left(x\right) + 1}"," ",0,"-((cos(x) + sin(x) + 1)*log(1/2*(cos(x)^2 - (cos(x) - 1)*sin(x) + 2*(cos(x) - sin(x) + 1)*sqrt(sin(x) + 1) + 2*cos(x) + 1)/(cos(x) + sin(x) + 1)) - (cos(x) + sin(x) + 1)*log(1/2*(cos(x)^2 - (cos(x) - 1)*sin(x) - 2*(cos(x) - sin(x) + 1)*sqrt(sin(x) + 1) + 2*cos(x) + 1)/(cos(x) + sin(x) + 1)) + 2*((cos(x) - sin(x) + 1)*log(sin(x)) - 2*cos(x) + 2*sin(x) - 2)*sqrt(sin(x) + 1))/(cos(x) + sin(x) + 1)","B",0
42,1,54,0,1.181953," ","integrate(sec(x)/(-1+sec(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, {\left(2 \, \sqrt{2} \sqrt{-\frac{\cos\left(x\right)^{4} - 1}{\cos\left(x\right)^{4}}} \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{2} + 3\right)} \sin\left(x\right)\right)}}{{\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}\right)"," ",0,"1/4*sqrt(2)*log(-2*(2*sqrt(2)*sqrt(-(cos(x)^4 - 1)/cos(x)^4)*cos(x)^2 - (cos(x)^2 + 3)*sin(x))/((cos(x)^2 - 1)*sin(x)))","B",0
43,1,186,0,0.952685," ","integrate(tan(x)/(1+tan(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{1}{32} \, \sqrt{2} \log\left(\frac{577 \, \tan\left(x\right)^{16} - 1912 \, \tan\left(x\right)^{14} + 4124 \, \tan\left(x\right)^{12} - 6216 \, \tan\left(x\right)^{10} + 7110 \, \tan\left(x\right)^{8} - 6216 \, \tan\left(x\right)^{6} + 4124 \, \tan\left(x\right)^{4} - 1912 \, \tan\left(x\right)^{2} + 8 \, {\left(51 \, \sqrt{2} \tan\left(x\right)^{14} - 169 \, \sqrt{2} \tan\left(x\right)^{12} + 339 \, \sqrt{2} \tan\left(x\right)^{10} - 465 \, \sqrt{2} \tan\left(x\right)^{8} + 465 \, \sqrt{2} \tan\left(x\right)^{6} - 339 \, \sqrt{2} \tan\left(x\right)^{4} + 169 \, \sqrt{2} \tan\left(x\right)^{2} - 51 \, \sqrt{2}\right)} \sqrt{\tan\left(x\right)^{4} + 1} + 577}{\tan\left(x\right)^{16} + 8 \, \tan\left(x\right)^{14} + 28 \, \tan\left(x\right)^{12} + 56 \, \tan\left(x\right)^{10} + 70 \, \tan\left(x\right)^{8} + 56 \, \tan\left(x\right)^{6} + 28 \, \tan\left(x\right)^{4} + 8 \, \tan\left(x\right)^{2} + 1}\right)"," ",0,"1/32*sqrt(2)*log((577*tan(x)^16 - 1912*tan(x)^14 + 4124*tan(x)^12 - 6216*tan(x)^10 + 7110*tan(x)^8 - 6216*tan(x)^6 + 4124*tan(x)^4 - 1912*tan(x)^2 + 8*(51*sqrt(2)*tan(x)^14 - 169*sqrt(2)*tan(x)^12 + 339*sqrt(2)*tan(x)^10 - 465*sqrt(2)*tan(x)^8 + 465*sqrt(2)*tan(x)^6 - 339*sqrt(2)*tan(x)^4 + 169*sqrt(2)*tan(x)^2 - 51*sqrt(2))*sqrt(tan(x)^4 + 1) + 577)/(tan(x)^16 + 8*tan(x)^14 + 28*tan(x)^12 + 56*tan(x)^10 + 70*tan(x)^8 + 56*tan(x)^6 + 28*tan(x)^4 + 8*tan(x)^2 + 1))","B",0
44,1,63,0,1.243711," ","integrate(sin(x)/(1-sin(x)^6)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{7 \, \cos\left(x\right)^{5} - 24 \, \cos\left(x\right)^{3} - 4 \, \sqrt{\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2}} {\left(\sqrt{3} \cos\left(x\right)^{2} - 2 \, \sqrt{3}\right)} + 24 \, \cos\left(x\right)}{\cos\left(x\right)^{5}}\right)"," ",0,"1/12*sqrt(3)*log((7*cos(x)^5 - 24*cos(x)^3 - 4*sqrt(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2)*(sqrt(3)*cos(x)^2 - 2*sqrt(3)) + 24*cos(x))/cos(x)^5)","B",0
45,-1,0,0,0.000000," ","integrate((-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,1,52,0,1.122924," ","integrate(x*arctan(x)^2*log(x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x^{2} + 3\right)} \arctan\left(x\right)^{2} + 3 \, x \arctan\left(x\right) + \frac{1}{2} \, {\left({\left(x^{2} + 1\right)} \arctan\left(x\right)^{2} - 2 \, x \arctan\left(x\right) - 3\right)} \log\left(x^{2} + 1\right) + \frac{1}{4} \, \log\left(x^{2} + 1\right)^{2}"," ",0,"-1/2*(x^2 + 3)*arctan(x)^2 + 3*x*arctan(x) + 1/2*((x^2 + 1)*arctan(x)^2 - 2*x*arctan(x) - 3)*log(x^2 + 1) + 1/4*log(x^2 + 1)^2","A",0
47,1,287,0,1.299984," ","integrate(arctan(x*(x^2+1)^(1/2)),x, algorithm=""fricas"")","x \arctan\left(\sqrt{x^{2} + 1} x\right) - \frac{1}{4} \, \sqrt{3} \log\left(32 \, x^{4} + 80 \, x^{2} + 32 \, \sqrt{3} {\left(x^{3} + x\right)} - 16 \, {\left(2 \, x^{3} + \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 32\right) + \frac{1}{4} \, \sqrt{3} \log\left(32 \, x^{4} + 80 \, x^{2} - 32 \, \sqrt{3} {\left(x^{3} + x\right)} - 16 \, {\left(2 \, x^{3} - \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 32\right) + \arctan\left(2 \, \sqrt{2 \, x^{4} + 5 \, x^{2} + 2 \, \sqrt{3} {\left(x^{3} + x\right)} - {\left(2 \, x^{3} + \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 2} {\left(x + \sqrt{x^{2} + 1}\right)} + \sqrt{3} - 2 \, \sqrt{x^{2} + 1}\right) + \arctan\left(2 \, \sqrt{2 \, x^{4} + 5 \, x^{2} - 2 \, \sqrt{3} {\left(x^{3} + x\right)} - {\left(2 \, x^{3} - \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 2} {\left(x + \sqrt{x^{2} + 1}\right)} - \sqrt{3} - 2 \, \sqrt{x^{2} + 1}\right)"," ",0,"x*arctan(sqrt(x^2 + 1)*x) - 1/4*sqrt(3)*log(32*x^4 + 80*x^2 + 32*sqrt(3)*(x^3 + x) - 16*(2*x^3 + sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 32) + 1/4*sqrt(3)*log(32*x^4 + 80*x^2 - 32*sqrt(3)*(x^3 + x) - 16*(2*x^3 - sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 32) + arctan(2*sqrt(2*x^4 + 5*x^2 + 2*sqrt(3)*(x^3 + x) - (2*x^3 + sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 2)*(x + sqrt(x^2 + 1)) + sqrt(3) - 2*sqrt(x^2 + 1)) + arctan(2*sqrt(2*x^4 + 5*x^2 - 2*sqrt(3)*(x^3 + x) - (2*x^3 - sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 2)*(x + sqrt(x^2 + 1)) - sqrt(3) - 2*sqrt(x^2 + 1))","B",0
48,1,22,0,1.714313," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""fricas"")","{\left(x + 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{2} \, \sqrt{x}"," ",0,"(x + 1)*arctan(sqrt(x + 1) - sqrt(x)) + 1/2*sqrt(x)","A",0
49,1,60,0,1.471094," ","integrate(arcsin(x/(-x^2+1)^(1/2)),x, algorithm=""fricas"")","-x \arcsin\left(\frac{\sqrt{-x^{2} + 1} x}{x^{2} - 1}\right) + \arctan\left(\frac{x^{2} + \sqrt{-x^{2} + 1} \sqrt{\frac{2 \, x^{2} - 1}{x^{2} - 1}} - 1}{x^{2}}\right)"," ",0,"-x*arcsin(sqrt(-x^2 + 1)*x/(x^2 - 1)) + arctan((x^2 + sqrt(-x^2 + 1)*sqrt((2*x^2 - 1)/(x^2 - 1)) - 1)/x^2)","B",0
50,1,164,0,1.196813," ","integrate(arctan(x*(-x^2+1)^(1/2)),x, algorithm=""fricas"")","x \arctan\left(\sqrt{-x^{2} + 1} x\right) + \sqrt{2} \sqrt{\sqrt{5} + 1} \arctan\left(-\frac{1}{2} \, \sqrt{2} \sqrt{-x^{2} + 1} \sqrt{\sqrt{5} + 1} + \frac{1}{8} \, \sqrt{2} \sqrt{-16 \, x^{2} + 8 \, \sqrt{5} + 8} \sqrt{\sqrt{5} + 1}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left({\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{\sqrt{5} - 1} + 4 \, \sqrt{-x^{2} + 1}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(-{\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{\sqrt{5} - 1} + 4 \, \sqrt{-x^{2} + 1}\right)"," ",0,"x*arctan(sqrt(-x^2 + 1)*x) + sqrt(2)*sqrt(sqrt(5) + 1)*arctan(-1/2*sqrt(2)*sqrt(-x^2 + 1)*sqrt(sqrt(5) + 1) + 1/8*sqrt(2)*sqrt(-16*x^2 + 8*sqrt(5) + 8)*sqrt(sqrt(5) + 1)) + 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log((sqrt(5)*sqrt(2) + sqrt(2))*sqrt(sqrt(5) - 1) + 4*sqrt(-x^2 + 1)) - 1/4*sqrt(2)*sqrt(sqrt(5) - 1)*log(-(sqrt(5)*sqrt(2) + sqrt(2))*sqrt(sqrt(5) - 1) + 4*sqrt(-x^2 + 1))","B",0
