1,1,272,0,1.152055," ","integrate(arcsin(x)*log(x),x, algorithm=""giac"")","x \arcsin\left(x\right) \log\left(x\right) + \sqrt{-x^{2} + 1} \log\left(x\right) - \frac{2 \, x \arcsin\left(x\right)}{{\left(\sqrt{-x^{2} + 1} + 1\right)} {\left(\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1\right)}} + \frac{x^{2} \log\left(\sqrt{-x^{2} + 1} + 1\right)}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2} {\left(\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1\right)}} + \frac{\log\left(\sqrt{-x^{2} + 1} + 1\right)}{\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1} - \frac{x^{2} \log\left({\left| x \right|}\right)}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2} {\left(\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1\right)}} - \frac{\log\left({\left| x \right|}\right)}{\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1} + \frac{2 \, x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2} {\left(\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1\right)}} - \frac{2}{\frac{x^{2}}{{\left(\sqrt{-x^{2} + 1} + 1\right)}^{2}} + 1}"," ",0,"x*arcsin(x)*log(x) + sqrt(-x^2 + 1)*log(x) - 2*x*arcsin(x)/((sqrt(-x^2 + 1) + 1)*(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1)) + x^2*log(sqrt(-x^2 + 1) + 1)/((sqrt(-x^2 + 1) + 1)^2*(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1)) + log(sqrt(-x^2 + 1) + 1)/(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1) - x^2*log(abs(x))/((sqrt(-x^2 + 1) + 1)^2*(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1)) - log(abs(x))/(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1) + 2*x^2/((sqrt(-x^2 + 1) + 1)^2*(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1)) - 2/(x^2/(sqrt(-x^2 + 1) + 1)^2 + 1)","B",0
2,1,15,0,0.851626," ","integrate(x*arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 1} \arcsin\left(x\right) + x"," ",0,"-sqrt(-x^2 + 1)*arcsin(x) + x","A",0
3,0,0,0,0.000000," ","integrate(-arcsin(x^(1/2)-(1+x)^(1/2)),x, algorithm=""giac"")","\int -\arcsin\left(-\sqrt{x + 1} + \sqrt{x}\right)\,{d x}"," ",0,"integrate(-arcsin(-sqrt(x + 1) + sqrt(x)), x)","F",0
4,1,235,0,1.245291," ","integrate(log(1+x*(x^2+1)^(1/2)),x, algorithm=""giac"")","x \log\left(\sqrt{x^{2} + 1} x + 1\right) + \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) - 2 \, x"," ",0,"x*log(sqrt(x^2 + 1)*x + 1) + 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)))) - 2*x","B",0
5,0,0,0,0.000000," ","integrate(cos(x)^2/(1+cos(x)^2+cos(x)^4)^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(x\right)^{2}}{\sqrt{\cos\left(x\right)^{4} + \cos\left(x\right)^{2} + 1}}\,{d x}"," ",0,"integrate(cos(x)^2/sqrt(cos(x)^4 + cos(x)^2 + 1), x)","F",0
6,1,79,0,1.201612," ","integrate((1+tan(x)^4)^(1/2)*tan(x),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{\tan\left(x\right)^{2} + \sqrt{2} - \sqrt{\tan\left(x\right)^{4} + 1} + 1}{\tan\left(x\right)^{2} - \sqrt{2} - \sqrt{\tan\left(x\right)^{4} + 1} + 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,"1/2*sqrt(2)*log(-(tan(x)^2 + sqrt(2) - sqrt(tan(x)^4 + 1) + 1)/(tan(x)^2 - sqrt(2) - sqrt(tan(x)^4 + 1) + 1)) + 1/2*sqrt(tan(x)^4 + 1) + 1/2*log(-tan(x)^2 + sqrt(tan(x)^4 + 1))","A",0
7,1,28,0,1.229433," ","integrate(tan(x)/(1+sec(x)^3)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(\sqrt{\frac{1}{\cos\left(x\right)^{3}} + 1} + 1\right) + \frac{1}{3} \, \log\left({\left| \sqrt{\frac{1}{\cos\left(x\right)^{3}} + 1} - 1 \right|}\right)"," ",0,"-1/3*log(sqrt(1/cos(x)^3 + 1) + 1) + 1/3*log(abs(sqrt(1/cos(x)^3 + 1) - 1))","B",0
8,1,495,0,1.436016," ","integrate((2+2*tan(x)+tan(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(256 \, {\left(\sqrt{5} {\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right)\right)} + \sqrt{5} \sqrt{\sqrt{5} - 2} - \sqrt{5} - 2 \, \sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - 2 \, \sqrt{\sqrt{5} - 2} + 2 \, \tan\left(x\right) + 2\right)}^{2} + 256 \, {\left(\sqrt{5} {\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right)\right)} + \sqrt{5} - 2 \, \sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} + \sqrt{\sqrt{5} - 2} + 2 \, \tan\left(x\right) - 2\right)}^{2}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(256 \, {\left(\sqrt{5} {\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right)\right)} - \sqrt{5} \sqrt{\sqrt{5} - 2} - \sqrt{5} - 2 \, \sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} + 2 \, \sqrt{\sqrt{5} - 2} + 2 \, \tan\left(x\right) + 2\right)}^{2} + 256 \, {\left(\sqrt{5} {\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right)\right)} + \sqrt{5} - 2 \, \sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \sqrt{\sqrt{5} - 2} + 2 \, \tan\left(x\right) - 2\right)}^{2}\right) + \frac{{\left(\pi + 4 \, \arctan\left(-\frac{1}{2} \, {\left(2 \, \sqrt{5} \sqrt{\sqrt{5} - 2} + \sqrt{5} + 4 \, \sqrt{\sqrt{5} - 2} + 3\right)} {\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right)\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(2 \, \sqrt{5} \sqrt{\sqrt{5} - 2} - \sqrt{5} + 4 \, \sqrt{\sqrt{5} - 2} - 3\right)} {\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right)\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)}} - \log\left(\sqrt{\tan\left(x\right)^{2} + 2 \, \tan\left(x\right) + 2} - \tan\left(x\right) - 1\right)"," ",0,"-1/4*sqrt(2*sqrt(5) - 2)*log(256*(sqrt(5)*(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x)) + sqrt(5)*sqrt(sqrt(5) - 2) - sqrt(5) - 2*sqrt(tan(x)^2 + 2*tan(x) + 2) - 2*sqrt(sqrt(5) - 2) + 2*tan(x) + 2)^2 + 256*(sqrt(5)*(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x)) + sqrt(5) - 2*sqrt(tan(x)^2 + 2*tan(x) + 2) + sqrt(sqrt(5) - 2) + 2*tan(x) - 2)^2) + 1/4*sqrt(2*sqrt(5) - 2)*log(256*(sqrt(5)*(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x)) - sqrt(5)*sqrt(sqrt(5) - 2) - sqrt(5) - 2*sqrt(tan(x)^2 + 2*tan(x) + 2) + 2*sqrt(sqrt(5) - 2) + 2*tan(x) + 2)^2 + 256*(sqrt(5)*(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x)) + sqrt(5) - 2*sqrt(tan(x)^2 + 2*tan(x) + 2) - sqrt(sqrt(5) - 2) + 2*tan(x) - 2)^2) + 1/4*(pi + 4*arctan(-1/2*(2*sqrt(5)*sqrt(sqrt(5) - 2) + sqrt(5) + 4*sqrt(sqrt(5) - 2) + 3)*(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x)) + 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*(2*sqrt(5)*sqrt(sqrt(5) - 2) - sqrt(5) + 4*sqrt(sqrt(5) - 2) - 3)*(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x)) - 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) - log(sqrt(tan(x)^2 + 2*tan(x) + 2) - tan(x) - 1)","B",0
9,0,0,0,0.000000," ","integrate(arctan((-1+sec(x))^(1/2))*sin(x),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
10,1,46,0,1.472093," ","integrate(exp(arcsin(x))*x^3/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{10} \, {\left(x^{2} - 1\right)} x e^{\arcsin\left(x\right)} + \frac{3}{10} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} e^{\arcsin\left(x\right)} + \frac{2}{5} \, x e^{\arcsin\left(x\right)} - \frac{3}{5} \, \sqrt{-x^{2} + 1} e^{\arcsin\left(x\right)}"," ",0,"1/10*(x^2 - 1)*x*e^arcsin(x) + 3/10*(-x^2 + 1)^(3/2)*e^arcsin(x) + 2/5*x*e^arcsin(x) - 3/5*sqrt(-x^2 + 1)*e^arcsin(x)","A",0
11,0,0,0,0.000000," ","integrate(x*log(x^2+1)*log(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x \log\left(x^{2} + 1\right) \log\left(x + \sqrt{x^{2} + 1}\right)}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(x*log(x^2 + 1)*log(x + sqrt(x^2 + 1))/sqrt(x^2 + 1), x)","F",0
12,1,364,0,1.467187," ","integrate(arctan(x+(-x^2+1)^(1/2)),x, algorithm=""giac"")","x \arctan\left(x + \sqrt{-x^{2} + 1}\right) - \frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) + \frac{1}{8} \, \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}{8} \, \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}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\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}{8} \, \log\left(x^{4} - x^{2} + 1\right) + \frac{1}{8} \, \log\left({\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}^{2} + \frac{2 \, x}{\sqrt{-x^{2} + 1} - 1} - \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} + 4\right) - \frac{1}{8} \, \log\left({\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}^{2} - \frac{2 \, x}{\sqrt{-x^{2} + 1} - 1} + \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} + 4\right)"," ",0,"x*arctan(x + sqrt(-x^2 + 1)) - 1/4*pi*sgn(x) + 1/8*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))) + 1/8*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))) - 1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/2*arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)) - 1/8*log(x^4 - x^2 + 1) + 1/8*log((x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)^2 + 2*x/(sqrt(-x^2 + 1) - 1) - 2*(sqrt(-x^2 + 1) - 1)/x + 4) - 1/8*log((x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)^2 - 2*x/(sqrt(-x^2 + 1) - 1) + 2*(sqrt(-x^2 + 1) - 1)/x + 4)","B",0
13,1,373,0,1.568257," ","integrate(x*arctan(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) + \frac{1}{8} \, \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}{8} \, \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}{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}{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}{8} \, \log\left(x^{4} - x^{2} + 1\right) - \frac{1}{8} \, \log\left({\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}^{2} + \frac{2 \, x}{\sqrt{-x^{2} + 1} - 1} - \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} + 4\right) + \frac{1}{8} \, \log\left({\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}^{2} - \frac{2 \, x}{\sqrt{-x^{2} + 1} - 1} + \frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} + 4\right)"," ",0,"-1/4*pi*sgn(x) + 1/8*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))) + 1/8*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))) - 1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - sqrt(-x^2 + 1)*arctan(x + sqrt(-x^2 + 1)) - 1/2*arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)) + 1/8*log(x^4 - x^2 + 1) - 1/8*log((x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)^2 + 2*x/(sqrt(-x^2 + 1) - 1) - 2*(sqrt(-x^2 + 1) - 1)/x + 4) + 1/8*log((x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)^2 - 2*x/(sqrt(-x^2 + 1) - 1) + 2*(sqrt(-x^2 + 1) - 1)/x + 4)","B",0
14,1,57,0,1.295338," ","integrate(arcsin(x)/(1+(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, \arcsin\left(x\right)^{2} - \frac{x \arcsin\left(x\right)}{\sqrt{-x^{2} + 1} + 1} - 2 \, \log\left(2\right) + \log\left(2 \, \sqrt{-x^{2} + 1} + 2\right) - 2 \, \log\left(\sqrt{-x^{2} + 1} + 1\right)"," ",0,"1/2*arcsin(x)^2 - x*arcsin(x)/(sqrt(-x^2 + 1) + 1) - 2*log(2) + log(2*sqrt(-x^2 + 1) + 2) - 2*log(sqrt(-x^2 + 1) + 1)","A",0
15,1,36,0,1.382733," ","integrate(log(x+(x^2+1)^(1/2))/(-x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} + 1} x \log\left(x + \sqrt{x^{2} + 1}\right)}{x^{2} - 1} - \frac{1}{2} \, \arcsin\left(x^{2}\right)"," ",0,"-sqrt(-x^2 + 1)*x*log(x + sqrt(x^2 + 1))/(x^2 - 1) - 1/2*arcsin(x^2)","A",0
16,1,18,0,1.056607," ","integrate(arcsin(x)/(x^2+1)^(3/2),x, algorithm=""giac"")","\frac{x \arcsin\left(x\right)}{\sqrt{x^{2} + 1}} - \frac{1}{2} \, \arcsin\left(x^{2}\right)"," ",0,"x*arcsin(x)/sqrt(x^2 + 1) - 1/2*arcsin(x^2)","A",0
17,1,36,0,1.118589," ","integrate(log(x+(x^2-1)^(1/2))/(x^2+1)^(3/2),x, algorithm=""giac"")","\frac{x \log\left(x + \sqrt{x^{2} - 1}\right)}{\sqrt{x^{2} + 1}} + \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} - 1}\right)"," ",0,"x*log(x + sqrt(x^2 - 1))/sqrt(x^2 + 1) + 1/2*log(x^2 - sqrt(x^4 - 1))","A",0
18,1,62,0,1.160997," ","integrate(log(x)/x^2/(x^2-1)^(1/2),x, algorithm=""giac"")","\frac{2 \, \log\left(x\right)}{{\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 1} + \frac{2}{{\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 1} + \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} - 1}\right)}^{2}\right) - \log\left({\left| x \right|}\right)"," ",0,"2*log(x)/((x - sqrt(x^2 - 1))^2 + 1) + 2/((x - sqrt(x^2 - 1))^2 + 1) + 1/2*log((x - sqrt(x^2 - 1))^2) - log(abs(x))","A",0
19,1,35,0,1.010727," ","integrate((x^3+1)^(1/2)/x,x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{x^{3} + 1} - \frac{1}{3} \, \log\left(\sqrt{x^{3} + 1} + 1\right) + \frac{1}{3} \, \log\left({\left| \sqrt{x^{3} + 1} - 1 \right|}\right)"," ",0,"2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(abs(sqrt(x^3 + 1) - 1))","A",0
20,1,22,0,1.095675," ","integrate(x*log(x+(x^2-1)^(1/2))/(x^2-1)^(1/2),x, algorithm=""giac"")","\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
21,1,38,0,1.101473," ","integrate(x^3*arcsin(x)/(-x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{2} + 1} x - \frac{1}{2} \, \sqrt{-x^{4} + 1} \arcsin\left(x\right) - \frac{1}{4} \, \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"1/4*sqrt(x^2 + 1)*x - 1/2*sqrt(-x^4 + 1)*arcsin(x) - 1/4*log(-x + sqrt(x^2 + 1))","A",0
22,1,52,0,1.216875," ","integrate(x^3*arcsec(x)/(x^4-1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} - 1} \arccos\left(\frac{1}{x}\right) - \frac{2 \, \sqrt{x^{2} + 1} - \log\left(\sqrt{x^{2} + 1} + 1\right) + \log\left(\sqrt{x^{2} + 1} - 1\right)}{4 \, \mathrm{sgn}\left(x\right)}"," ",0,"1/2*sqrt(x^4 - 1)*arccos(1/x) - 1/4*(2*sqrt(x^2 + 1) - log(sqrt(x^2 + 1) + 1) + log(sqrt(x^2 + 1) - 1))/sgn(x)","A",0
23,0,0,0,0.000000," ","integrate(x*arctan(x)*log(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x \arctan\left(x\right) \log\left(x + \sqrt{x^{2} + 1}\right)}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(x*arctan(x)*log(x + sqrt(x^2 + 1))/sqrt(x^2 + 1), x)","F",0
24,1,36,0,1.031786," ","integrate(x*log(1+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""giac"")","-{\left(\sqrt{-x^{2} + 1} + 1\right)} \log\left(\sqrt{-x^{2} + 1} + 1\right) + \sqrt{-x^{2} + 1} + 1"," ",0,"-(sqrt(-x^2 + 1) + 1)*log(sqrt(-x^2 + 1) + 1) + sqrt(-x^2 + 1) + 1","A",0
25,1,22,0,1.000594," ","integrate(x*log(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""giac"")","\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
26,1,122,0,1.303438," ","integrate(x*log(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 1} \log\left(x + \sqrt{-x^{2} + 1}\right) - \frac{1}{4} \, \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}{4} \, \sqrt{2} \log\left({\left| x + \frac{1}{2} \, \sqrt{2} \right|}\right) - \frac{1}{4} \, \sqrt{2} \log\left({\left| x - \frac{1}{2} \, \sqrt{2} \right|}\right) + \sqrt{-x^{2} + 1}"," ",0,"-sqrt(-x^2 + 1)*log(x + sqrt(-x^2 + 1)) - 1/4*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)) + 1/4*sqrt(2)*log(abs(x + 1/2*sqrt(2))) - 1/4*sqrt(2)*log(abs(x - 1/2*sqrt(2))) + sqrt(-x^2 + 1)","A",0
27,1,73,0,1.082012," ","integrate(log(x)/x^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)} \log\left(x\right) + \frac{x}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}} - \frac{\sqrt{-x^{2} + 1} - 1}{2 \, x} - \arcsin\left(x\right)"," ",0,"1/2*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)*log(x) + 1/2*x/(sqrt(-x^2 + 1) - 1) - 1/2*(sqrt(-x^2 + 1) - 1)/x - arcsin(x)","B",0
28,1,23,0,0.927119," ","integrate(x*arctan(x)/(x^2+1)^(1/2),x, algorithm=""giac"")","\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
29,1,104,0,1.094437," ","integrate(arctan(x)/x^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)} \arctan\left(x\right) - \frac{1}{2} \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{-x^{2} + 1}}{\sqrt{2} + \sqrt{-x^{2} + 1}}\right) - \frac{1}{2} \, \log\left(\sqrt{-x^{2} + 1} + 1\right) + \frac{1}{2} \, \log\left(-\sqrt{-x^{2} + 1} + 1\right)"," ",0,"1/2*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)*arctan(x) - 1/2*sqrt(2)*log((sqrt(2) - sqrt(-x^2 + 1))/(sqrt(2) + sqrt(-x^2 + 1))) - 1/2*log(sqrt(-x^2 + 1) + 1) + 1/2*log(-sqrt(-x^2 + 1) + 1)","B",0
30,1,108,0,1.021326," ","integrate(x*arctan(x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \pi \mathrm{sgn}\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{2} x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{4 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} - \sqrt{-x^{2} + 1} \arctan\left(x\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) + 1/2*sqrt(2)*(pi*sgn(x) + 2*arctan(-1/4*sqrt(2)*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))) - sqrt(-x^2 + 1)*arctan(x) - arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))","B",0
31,1,54,0,1.103970," ","integrate(arctan(x)/x^2/(x^2+1)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(x\right)}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 1} + \arctan\left(x\right) - \log\left({\left| -x + \sqrt{x^{2} + 1} + 1 \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + 1} - 1 \right|}\right)"," ",0,"2*arctan(x)/((x - sqrt(x^2 + 1))^2 - 1) + arctan(x) - log(abs(-x + sqrt(x^2 + 1) + 1)) + log(abs(-x + sqrt(x^2 + 1) - 1))","B",0
32,1,40,0,1.034664," ","integrate(arcsin(x)/x^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)} \arcsin\left(x\right) + \log\left({\left| x \right|}\right)"," ",0,"1/2*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)*arcsin(x) + log(abs(x))","B",0
33,1,28,0,1.011483," ","integrate(x*log(x)/(x^2-1)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} - 1} \log\left(x\right) - \sqrt{x^{2} - 1} + \arctan\left(\sqrt{x^{2} - 1}\right)"," ",0,"sqrt(x^2 - 1)*log(x) - sqrt(x^2 - 1) + arctan(sqrt(x^2 - 1))","A",0
34,1,58,0,0.974516," ","integrate(log(x)/x^2/(x^2+1)^(1/2),x, algorithm=""giac"")","\frac{2 \, \log\left(x\right)}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 1} + \frac{2}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 1} - \log\left(-x + \sqrt{x^{2} + 1}\right) + \log\left({\left| x \right|}\right)"," ",0,"2*log(x)/((x - sqrt(x^2 + 1))^2 - 1) + 2/((x - sqrt(x^2 + 1))^2 - 1) - log(-x + sqrt(x^2 + 1)) + log(abs(x))","A",0
35,1,22,0,1.094200," ","integrate(x*arcsec(x)/(x^2-1)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} - 1} \arccos\left(\frac{1}{x}\right) - \frac{\log\left({\left| x \right|}\right)}{\mathrm{sgn}\left(x\right)}"," ",0,"sqrt(x^2 - 1)*arccos(1/x) - log(abs(x))/sgn(x)","A",0
36,1,44,0,1.115281," ","integrate(x*log(x)/(x^2+1)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} + 1} \log\left(x\right) - \sqrt{x^{2} + 1} + \frac{1}{2} \, \log\left(\sqrt{x^{2} + 1} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{x^{2} + 1} - 1\right)"," ",0,"sqrt(x^2 + 1)*log(x) - sqrt(x^2 + 1) + 1/2*log(sqrt(x^2 + 1) + 1) - 1/2*log(sqrt(x^2 + 1) - 1)","A",0
37,1,27,0,1.001861," ","integrate(sin(x)/(1+sin(x)^2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \log\left(\sqrt{2} + \cos\left(x\right)\right) + \frac{1}{4} \, \sqrt{2} \log\left(\sqrt{2} - \cos\left(x\right)\right)"," ",0,"-1/4*sqrt(2)*log(sqrt(2) + cos(x)) + 1/4*sqrt(2)*log(sqrt(2) - cos(x))","B",0
38,0,0,0,0.000000," ","integrate((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 1}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 1)/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
39,0,0,0,0.000000," ","integrate((-x^2+1)/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} - 1}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 1)/(sqrt(x^4 + 1)*(x^2 + 1)), x)","F",0
40,1,36,0,1.130807," ","integrate(log(sin(x))/(1+sin(x)),x, algorithm=""giac"")","-x - \frac{2 \, \log\left(\sin\left(x\right)\right)}{\tan\left(\frac{1}{2} \, x\right) + 1} - 2 \, \log\left(\tan\left(\frac{1}{4} \, x\right)^{2} + 1\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{4} \, x\right) \right|}\right)"," ",0,"-x - 2*log(sin(x))/(tan(1/2*x) + 1) - 2*log(tan(1/4*x)^2 + 1) + 2*log(abs(tan(1/4*x)))","A",0
41,1,94,0,1.369776," ","integrate(log(sin(x))*(1+sin(x))^(1/2),x, algorithm=""giac"")","\sqrt{2} {\left(2 \, \log\left(\sin\left(x\right)\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, x\right) + {\left(\sqrt{2} \log\left({\left| \tan\left(\frac{1}{4} \, x\right) + 1 \right|}\right) - \sqrt{2} \log\left({\left| \tan\left(\frac{1}{4} \, x\right) - 1 \right|}\right) + \sqrt{2} \log\left({\left| \tan\left(\frac{1}{4} \, x\right) \right|}\right) - \frac{4 \, \sqrt{2} {\left(\tan\left(\frac{1}{4} \, x\right) - 1\right)}}{\tan\left(\frac{1}{4} \, x\right)^{2} + 1}\right)} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)\right)\right)}"," ",0,"sqrt(2)*(2*log(sin(x))*sgn(cos(-1/4*pi + 1/2*x))*sin(-1/4*pi + 1/2*x) + (sqrt(2)*log(abs(tan(1/4*x) + 1)) - sqrt(2)*log(abs(tan(1/4*x) - 1)) + sqrt(2)*log(abs(tan(1/4*x))) - 4*sqrt(2)*(tan(1/4*x) - 1)/(tan(1/4*x)^2 + 1))*sgn(cos(-1/4*pi + 1/2*x)))","B",0
42,1,92,0,2.217921," ","integrate(sec(x)/(-1+sec(x)^4)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\log\left(\tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 1} + 1\right) - \log\left(-\tan\left(\frac{1}{2} \, x\right)^{2} + \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 1} + 1\right) + \log\left(-\tan\left(\frac{1}{2} \, x\right)^{2} + \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 1}\right)\right)}}{4 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right)}"," ",0,"1/4*sqrt(2)*(log(tan(1/2*x)^2 - sqrt(tan(1/2*x)^4 + 1) + 1) - log(-tan(1/2*x)^2 + sqrt(tan(1/2*x)^4 + 1) + 1) + log(-tan(1/2*x)^2 + sqrt(tan(1/2*x)^4 + 1)))/sgn(tan(1/2*x)^5 - 2*tan(1/2*x)^3 + tan(1/2*x))","B",0
43,1,50,0,1.064663," ","integrate(tan(x)/(1+tan(x)^4)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{\tan\left(x\right)^{2} + \sqrt{2} - \sqrt{\tan\left(x\right)^{4} + 1} + 1}{\tan\left(x\right)^{2} - \sqrt{2} - \sqrt{\tan\left(x\right)^{4} + 1} + 1}\right)"," ",0,"1/4*sqrt(2)*log(-(tan(x)^2 + sqrt(2) - sqrt(tan(x)^4 + 1) + 1)/(tan(x)^2 - sqrt(2) - sqrt(tan(x)^4 + 1) + 1))","A",0
44,1,67,0,2.346525," ","integrate(sin(x)/(1-sin(x)^6)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{3} \log\left(\cos\left(x\right)^{2} + \sqrt{3} - \sqrt{\cos\left(x\right)^{4} - 3 \, \cos\left(x\right)^{2} + 3}\right) - \sqrt{3} \log\left(-\cos\left(x\right)^{2} + \sqrt{3} + \sqrt{\cos\left(x\right)^{4} - 3 \, \cos\left(x\right)^{2} + 3}\right)}{6 \, \mathrm{sgn}\left(\cos\left(x\right)\right)}"," ",0,"-1/6*(sqrt(3)*log(cos(x)^2 + sqrt(3) - sqrt(cos(x)^4 - 3*cos(x)^2 + 3)) - sqrt(3)*log(-cos(x)^2 + sqrt(3) + sqrt(cos(x)^4 - 3*cos(x)^2 + 3)))/sgn(cos(x))","B",0
45,0,0,0,0.000000," ","integrate((-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{\sec\left(x\right) + 1} - \sqrt{\sec\left(x\right) - 1}}\,{d x}"," ",0,"integrate(sqrt(sqrt(sec(x) + 1) - sqrt(sec(x) - 1)), x)","F",0
46,0,0,0,0.000000," ","integrate(x*arctan(x)^2*log(x^2+1),x, algorithm=""giac"")","\int x \arctan\left(x\right)^{2} \log\left(x^{2} + 1\right)\,{d x}"," ",0,"integrate(x*arctan(x)^2*log(x^2 + 1), x)","F",0
47,1,92,0,1.151138," ","integrate(arctan(x*(x^2+1)^(1/2)),x, algorithm=""giac"")","x \arctan\left(\sqrt{x^{2} + 1} x\right) + \frac{1}{4} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} \sqrt{x^{2} + 1} + 2\right) - \frac{1}{4} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} \sqrt{x^{2} + 1} + 2\right) - \frac{1}{2} \, \arctan\left(\sqrt{3} + 2 \, \sqrt{x^{2} + 1}\right) - \frac{1}{2} \, \arctan\left(-\sqrt{3} + 2 \, \sqrt{x^{2} + 1}\right)"," ",0,"x*arctan(sqrt(x^2 + 1)*x) + 1/4*sqrt(3)*log(x^2 + sqrt(3)*sqrt(x^2 + 1) + 2) - 1/4*sqrt(3)*log(x^2 - sqrt(3)*sqrt(x^2 + 1) + 2) - 1/2*arctan(sqrt(3) + 2*sqrt(x^2 + 1)) - 1/2*arctan(-sqrt(3) + 2*sqrt(x^2 + 1))","A",0
48,1,27,0,1.061551," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""giac"")","-x \arctan\left(-\sqrt{x + 1} + \sqrt{x}\right) + \frac{1}{2} \, \sqrt{x} - \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"-x*arctan(-sqrt(x + 1) + sqrt(x)) + 1/2*sqrt(x) - 1/2*arctan(sqrt(x))","A",0
49,1,34,0,1.331864," ","integrate(arcsin(x/(-x^2+1)^(1/2)),x, algorithm=""giac"")","x \arcsin\left(\frac{x}{\sqrt{-x^{2} + 1}}\right) + \frac{\arctan\left(\sqrt{-2 \, x^{2} + 1}\right)}{\mathrm{sgn}\left(x^{2} - 1\right)}"," ",0,"x*arcsin(x/sqrt(-x^2 + 1)) + arctan(sqrt(-2*x^2 + 1))/sgn(x^2 - 1)","A",0
50,1,111,0,1.458137," ","integrate(arctan(x*(-x^2+1)^(1/2)),x, algorithm=""giac"")","x \arctan\left(\sqrt{-x^{2} + 1} x\right) - \frac{1}{2} \, \sqrt{2 \, \sqrt{5} + 2} \arctan\left(\frac{\sqrt{-x^{2} + 1}}{\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{1}{2}}}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left(\sqrt{-x^{2} + 1} + \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| \sqrt{-x^{2} + 1} - \sqrt{\frac{1}{2} \, \sqrt{5} + \frac{1}{2}} \right|}\right)"," ",0,"x*arctan(sqrt(-x^2 + 1)*x) - 1/2*sqrt(2*sqrt(5) + 2)*arctan(sqrt(-x^2 + 1)/sqrt(1/2*sqrt(5) - 1/2)) + 1/4*sqrt(2*sqrt(5) - 2)*log(sqrt(-x^2 + 1) + sqrt(1/2*sqrt(5) + 1/2)) - 1/4*sqrt(2*sqrt(5) - 2)*log(abs(sqrt(-x^2 + 1) - sqrt(1/2*sqrt(5) + 1/2)))","A",0
