1,1,93,45,0.062000," ","int(arcsin(x)*ln(x),x)","-\ln \left(\tan^{2}\left(\frac{\arcsin \left(x \right)}{2}\right)+1\right)+\frac{2 \arcsin \left(x \right) \ln \left(\frac{2 \tan \left(\frac{\arcsin \left(x \right)}{2}\right)}{\tan^{2}\left(\frac{\arcsin \left(x \right)}{2}\right)+1}\right) \tan \left(\frac{\arcsin \left(x \right)}{2}\right)-2 \ln \left(\frac{2 \tan \left(\frac{\arcsin \left(x \right)}{2}\right)}{\tan^{2}\left(\frac{\arcsin \left(x \right)}{2}\right)+1}\right) \left(\tan^{2}\left(\frac{\arcsin \left(x \right)}{2}\right)\right)-2 \arcsin \left(x \right) \tan \left(\frac{\arcsin \left(x \right)}{2}\right)-4}{\tan^{2}\left(\frac{\arcsin \left(x \right)}{2}\right)+1}"," ",0,"2*(arcsin(x)*tan(1/2*arcsin(x))*ln(2*tan(1/2*arcsin(x))/(tan(1/2*arcsin(x))^2+1))-tan(1/2*arcsin(x))^2*ln(2*tan(1/2*arcsin(x))/(tan(1/2*arcsin(x))^2+1))-arcsin(x)*tan(1/2*arcsin(x))-2)/(tan(1/2*arcsin(x))^2+1)-ln(tan(1/2*arcsin(x))^2+1)","B"
2,1,16,15,0.077000," ","int(x*arcsin(x)/(-x^2+1)^(1/2),x)","x -\sqrt{-x^{2}+1}\, \arcsin \left(x \right)"," ",0,"x-(-x^2+1)^(1/2)*arcsin(x)","A"
3,1,251,49,0.967000," ","int(-arcsin(x^(1/2)-(x+1)^(1/2)),x)","-\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right) \left(\tan^{8}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)+2 \arcsin \left(\sqrt{x}-\sqrt{x +1}\right) \left(\tan^{6}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)-2 \left(\tan^{7}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)+18 \arcsin \left(\sqrt{x}-\sqrt{x +1}\right) \left(\tan^{4}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)-6 \left(\tan^{5}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)+2 \arcsin \left(\sqrt{x}-\sqrt{x +1}\right) \left(\tan^{2}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)+6 \left(\tan^{3}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)\right)+\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)+2 \tan \left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)}{16 \left(\tan^{2}\left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)+1\right)^{2} \tan \left(\frac{\arcsin \left(\sqrt{x}-\sqrt{x +1}\right)}{2}\right)^{2}}"," ",0,"-1/16*(arcsin(x^(1/2)-(x+1)^(1/2))*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^8+2*arcsin(x^(1/2)-(x+1)^(1/2))*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^6-2*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^7+18*arcsin(x^(1/2)-(x+1)^(1/2))*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^4-6*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^5+2*arcsin(x^(1/2)-(x+1)^(1/2))*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^2+6*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^3+arcsin(x^(1/2)-(x+1)^(1/2))+2*tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2))))/(tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^2+1)^2/tan(1/2*arcsin(x^(1/2)-(x+1)^(1/2)))^2","B"
4,1,426,75,0.142000," ","int(ln(1+x*(x^2+1)^(1/2)),x)","x \ln \left(\sqrt{x^{2}+1}\, x +1\right)-2 x +\frac{\arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{3 \sqrt{5}\, \arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{10 \sqrt{-2+\sqrt{5}}}-\frac{2 \sqrt{-2+\sqrt{5}}\, \sqrt{5}\, \arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{5}-\frac{\arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}-\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{3 \sqrt{5}\, \arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{10 \sqrt{2+\sqrt{5}}}-\frac{\arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}+\frac{2 \sqrt{5}\, \sqrt{2+\sqrt{5}}\, \arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{5}+\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}"," ",0,"x*ln(1+x*(x^2+1)^(1/2))+1/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)+5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)-1/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)-2*x-3/10*5^(1/2)/(2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))-1/2/(2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))+1/2/(-2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))-3/10*5^(1/2)/(-2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))-1/2/(2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))-1/2*5^(1/2)/(2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))+1/2/(-2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))-1/2*5^(1/2)/(-2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))+2/5*5^(1/2)*(2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))-2/5*(-2+5^(1/2))^(1/2)*5^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))","B"
5,1,312,39,0.604000," ","int(cos(x)^2/(1+cos(x)^2+cos(x)^4)^(1/2),x)","-\frac{2 \sqrt{\left(\cos^{2}\left(2 x \right)+4 \cos \left(2 x \right)+7\right) \left(\sin^{2}\left(2 x \right)\right)}\, \left(i \sqrt{3}-3\right) \sqrt{\frac{\left(-1+i \sqrt{3}\right) \left(\cos \left(2 x \right)-1\right)}{\left(i \sqrt{3}-3\right) \left(\cos \left(2 x \right)+1\right)}}\, \left(\cos \left(2 x \right)+1\right)^{2} \sqrt{\frac{\cos \left(2 x \right)+2+i \sqrt{3}}{\left(i \sqrt{3}+3\right) \left(\cos \left(2 x \right)+1\right)}}\, \sqrt{\frac{-\cos \left(2 x \right)+i \sqrt{3}-2}{\left(i \sqrt{3}-3\right) \left(\cos \left(2 x \right)+1\right)}}\, \EllipticPi \left(\sqrt{\frac{\left(-1+i \sqrt{3}\right) \left(\cos \left(2 x \right)-1\right)}{\left(i \sqrt{3}-3\right) \left(\cos \left(2 x \right)+1\right)}}, \frac{i \sqrt{3}-3}{-1+i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(i \sqrt{3}-3\right)}{\left(i \sqrt{3}+3\right) \left(-1+i \sqrt{3}\right)}}\right)}{\left(-1+i \sqrt{3}\right) \sqrt{\left(\cos \left(2 x \right)-1\right) \left(\cos \left(2 x \right)+1\right) \left(\cos \left(2 x \right)+2+i \sqrt{3}\right) \left(-\cos \left(2 x \right)+i \sqrt{3}-2\right)}\, \sqrt{\cos^{2}\left(2 x \right)+4 \cos \left(2 x \right)+7}\, \sin \left(2 x \right)}"," ",0,"-2*((cos(2*x)^2+4*cos(2*x)+7)*sin(2*x)^2)^(1/2)*(I*3^(1/2)-3)*((-1+I*3^(1/2))*(cos(2*x)-1)/(I*3^(1/2)-3)/(cos(2*x)+1))^(1/2)*(cos(2*x)+1)^2*((cos(2*x)+2+I*3^(1/2))/(I*3^(1/2)+3)/(cos(2*x)+1))^(1/2)*((I*3^(1/2)-cos(2*x)-2)/(I*3^(1/2)-3)/(cos(2*x)+1))^(1/2)*EllipticPi(((-1+I*3^(1/2))*(cos(2*x)-1)/(I*3^(1/2)-3)/(cos(2*x)+1))^(1/2),(I*3^(1/2)-3)/(-1+I*3^(1/2)),((1+I*3^(1/2))*(I*3^(1/2)-3)/(I*3^(1/2)+3)/(-1+I*3^(1/2)))^(1/2))/(-1+I*3^(1/2))/((cos(2*x)-1)*(cos(2*x)+1)*(cos(2*x)+2+I*3^(1/2))*(I*3^(1/2)-cos(2*x)-2))^(1/2)/sin(2*x)/(cos(2*x)^2+4*cos(2*x)+7)^(1/2)","C"
6,1,64,45,0.079000," ","int((1+tan(x)^4)^(1/2)*tan(x),x)","-\frac{\arcsinh \left(\tan^{2}\left(x \right)\right)}{2}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-2 \left(\tan^{2}\left(x \right)\right)+2\right) \sqrt{2}}{4 \sqrt{-2 \left(\tan^{2}\left(x \right)\right)+\left(\tan^{2}\left(x \right)+1\right)^{2}}}\right)}{2}+\frac{\sqrt{-2 \left(\tan^{2}\left(x \right)\right)+\left(\tan^{2}\left(x \right)+1\right)^{2}}}{2}"," ",0,"1/2*((tan(x)^2+1)^2-2*tan(x)^2)^(1/2)-1/2*arcsinh(tan(x)^2)-1/2*2^(1/2)*arctanh(1/4*(-2*tan(x)^2+2)*2^(1/2)/((tan(x)^2+1)^2-2*tan(x)^2)^(1/2))","A"
7,1,12,11,0.079000," ","int(tan(x)/(1+sec(x)^3)^(1/2),x)","-\frac{2 \arctanh \left(\sqrt{\sec^{3}\left(x \right)+1}\right)}{3}"," ",0,"-2/3*arctanh((1+sec(x)^3)^(1/2))","A"
8,1,1605,105,0.234000," ","int((2+2*tan(x)+tan(x)^2)^(1/2),x)","\text{Expression too large to display}"," ",0,"arcsinh(tan(x)+1)+1/10*(10*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+10+2*5^(1/2))^(1/2)*5^(1/2)*(-5*arctan(1/80*(-22+10*5^(1/2))^(1/2)*((5-5^(1/2))*(2*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+5^(1/2)+3))^(1/2)*(11*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+25*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+4*5^(1/2)+10)*(-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))*(5^(1/2)-5)/((-1/2*5^(1/2)+1/2+tan(x))^4/(-1/2*5^(1/2)-1/2-tan(x))^4+3*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+1))*(-10+10*5^(1/2))^(1/2)*(-22+10*5^(1/2))^(1/2)-3*arctan(1/80*(-22+10*5^(1/2))^(1/2)*((5-5^(1/2))*(2*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+5^(1/2)+3))^(1/2)*(11*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+25*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+4*5^(1/2)+10)*(-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))*(5^(1/2)-5)/((-1/2*5^(1/2)+1/2+tan(x))^4/(-1/2*5^(1/2)-1/2-tan(x))^4+3*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+1))*5^(1/2)*(-10+10*5^(1/2))^(1/2)*(-22+10*5^(1/2))^(1/2)+20*arctanh((10*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+10+2*5^(1/2))^(1/2)/(-10+10*5^(1/2))^(1/2))*5^(1/2)-60*arctanh((10*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+10+2*5^(1/2))^(1/2)/(-10+10*5^(1/2))^(1/2)))/(-2*(5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-5*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-5^(1/2)-5)/((-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))+1)^2)^(1/2)/((-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))+1)/(5^(1/2)-5)/(-10+10*5^(1/2))^(1/2)+1/5*(10*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+10+2*5^(1/2))^(1/2)*5^(1/2)*(-arctan(1/80*(-22+10*5^(1/2))^(1/2)*((5-5^(1/2))*(2*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+5^(1/2)+3))^(1/2)*(11*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+25*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+4*5^(1/2)+10)*(-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))*(5^(1/2)-5)/((-1/2*5^(1/2)+1/2+tan(x))^4/(-1/2*5^(1/2)-1/2-tan(x))^4+3*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+1))*5^(1/2)*(-10+10*5^(1/2))^(1/2)*(-22+10*5^(1/2))^(1/2)-5*arctan(1/80*(-22+10*5^(1/2))^(1/2)*((5-5^(1/2))*(2*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+5^(1/2)+3))^(1/2)*(11*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+25*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+4*5^(1/2)+10)*(-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))*(5^(1/2)-5)/((-1/2*5^(1/2)+1/2+tan(x))^4/(-1/2*5^(1/2)-1/2-tan(x))^4+3*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+1))*(-10+10*5^(1/2))^(1/2)*(-22+10*5^(1/2))^(1/2)+20*arctanh((10*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+10+2*5^(1/2))^(1/2)/(-10+10*5^(1/2))^(1/2))*5^(1/2)-20*arctanh((10*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2+10+2*5^(1/2))^(1/2)/(-10+10*5^(1/2))^(1/2)))/(-2*(5^(1/2)*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-5*(-1/2*5^(1/2)+1/2+tan(x))^2/(-1/2*5^(1/2)-1/2-tan(x))^2-5^(1/2)-5)/((-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))+1)^2)^(1/2)/((-1/2*5^(1/2)+1/2+tan(x))/(-1/2*5^(1/2)-1/2-tan(x))+1)/(5^(1/2)-5)/(-10+10*5^(1/2))^(1/2)","B"
9,1,42,31,0.070000," ","int(arctan((-1+sec(x))^(1/2))*sin(x),x)","\frac{\arctan \left(\sqrt{\sec \left(x \right)-1}\right)}{2}-\frac{\arctan \left(\sqrt{-\left(\frac{1}{\sec \left(x \right)}-1\right) \sec \left(x \right)}\right)}{\sec \left(x \right)}+\frac{\sqrt{\sec \left(x \right)-1}}{2 \sec \left(x \right)}"," ",0,"-1/sec(x)*arctan((-(1/sec(x)-1)*sec(x))^(1/2))+1/2*(-1+sec(x))^(1/2)/sec(x)+1/2*arctan((-1+sec(x))^(1/2))","A"
10,0,0,37,0.100000," ","int(exp(arcsin(x))*x^3/(-x^2+1)^(1/2),x)","\int \frac{x^{3} {\mathrm e}^{\arcsin \left(x \right)}}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int(exp(arcsin(x))*x^3/(-x^2+1)^(1/2),x)","F"
11,0,0,60,0.092000," ","int(x*ln(x^2+1)*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x)","\int \frac{x \ln \left(x +\sqrt{x^{2}+1}\right) \ln \left(x^{2}+1\right)}{\sqrt{x^{2}+1}}\, dx"," ",0,"int(x*ln(x^2+1)*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x)","F"
12,1,439,110,0.096000," ","int(arctan(x+(-x^2+1)^(1/2)),x)","x \arctan \left(x +\sqrt{-x^{2}+1}\right)+\arctan \left(\frac{\sqrt{-x^{2}+1}-1}{x}\right)-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{4}+\frac{i \sqrt{3}\, \ln \left(\frac{\left(-1-i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}+\frac{\ln \left(\frac{\left(-1-i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}+\frac{\ln \left(\frac{\left(-1+i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}-\frac{i \sqrt{3}\, \ln \left(\frac{\left(-1+i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}+\frac{i \sqrt{3}\, \ln \left(\frac{\left(1-i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}-\frac{\ln \left(\frac{\left(1-i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}-\frac{i \sqrt{3}\, \ln \left(\frac{\left(1+i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}-\frac{\ln \left(\frac{\left(1+i \sqrt{3}\right) \left(\sqrt{-x^{2}+1}-1\right)}{x}+\frac{\left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-1\right)}{8}-\frac{\ln \left(x^{4}-x^{2}+1\right)}{8}"," ",0,"x*arctan(x+(-x^2+1)^(1/2))-1/8*ln(x^4-x^2+1)-1/4*arctan(1/3*(2*x^2-1)*3^(1/2))*3^(1/2)+1/8*I*3^(1/2)*ln(((-x^2+1)^(1/2)-1)^2/x^2+(-1-I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)+1/8*ln(((-x^2+1)^(1/2)-1)^2/x^2+(-1-I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)-1/8*I*3^(1/2)*ln(((-x^2+1)^(1/2)-1)^2/x^2+(1+I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)+1/8*ln(((-x^2+1)^(1/2)-1)^2/x^2+(-1+I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)-1/8*I*3^(1/2)*ln(((-x^2+1)^(1/2)-1)^2/x^2+(-1+I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)-1/8*ln(((-x^2+1)^(1/2)-1)^2/x^2+(1+I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)+1/8*I*3^(1/2)*ln(((-x^2+1)^(1/2)-1)^2/x^2+(1-I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)-1/8*ln(((-x^2+1)^(1/2)-1)^2/x^2+(1-I*3^(1/2))*((-x^2+1)^(1/2)-1)/x-1)+arctan(((-x^2+1)^(1/2)-1)/x)","C"
13,0,0,119,0.103000," ","int(x*arctan(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","\int \frac{x \arctan \left(x +\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int(x*arctan(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","F"
14,-2,0,39,180.000000," ","int(arcsin(x)/(1+(-x^2+1)^(1/2)),x)","\int \frac{\arcsin \left(x \right)}{1+\sqrt{-x^{2}+1}}\, dx"," ",0,"int(arcsin(x)/(1+(-x^2+1)^(1/2)),x)","F"
15,0,0,28,0.101000," ","int(ln(x+(x^2+1)^(1/2))/(-x^2+1)^(3/2),x)","\int \frac{\ln \left(x +\sqrt{x^{2}+1}\right)}{\left(-x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(ln(x+(x^2+1)^(1/2))/(-x^2+1)^(3/2),x)","F"
16,0,0,18,0.191000," ","int(arcsin(x)/(x^2+1)^(3/2),x)","\int \frac{\arcsin \left(x \right)}{\left(x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsin(x)/(x^2+1)^(3/2),x)","F"
17,0,0,26,0.096000," ","int(ln(x+(x^2-1)^(1/2))/(x^2+1)^(3/2),x)","\int \frac{\ln \left(x +\sqrt{x^{2}-1}\right)}{\left(x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(ln(x+(x^2-1)^(1/2))/(x^2+1)^(3/2),x)","F"
18,1,89,37,0.138000," ","int(ln(x)/x^2/(x^2-1)^(1/2),x)","-\frac{\sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \arcsin \left(x \right)}{\sqrt{\mathrm{signum}\left(x^{2}-1\right)}}+\frac{-\frac{\sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \sqrt{-x^{2}+1}\, \ln \left(x \right)}{\sqrt{\mathrm{signum}\left(x^{2}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \sqrt{-x^{2}+1}}{\sqrt{\mathrm{signum}\left(x^{2}-1\right)}}}{x}"," ",0,"-1/signum(x^2-1)^(1/2)*(-signum(x^2-1))^(1/2)*arcsin(x)+(-1/signum(x^2-1)^(1/2)*(-signum(x^2-1))^(1/2)*(-x^2+1)^(1/2)-1/signum(x^2-1)^(1/2)*(-signum(x^2-1))^(1/2)*ln(x)*(-x^2+1)^(1/2))/x","C"
19,1,21,20,0.024000," ","int((x^3+1)^(1/2)/x,x)","-\frac{2 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}+\frac{2 \sqrt{x^{3}+1}}{3}"," ",0,"-2/3*arctanh((x^3+1)^(1/2))+2/3*(x^3+1)^(1/2)","A"
20,0,0,22,0.115000," ","int(x*ln(x+(x^2-1)^(1/2))/(x^2-1)^(1/2),x)","\int \frac{x \ln \left(x +\sqrt{x^{2}-1}\right)}{\sqrt{x^{2}-1}}\, dx"," ",0,"int(x*ln(x+(x^2-1)^(1/2))/(x^2-1)^(1/2),x)","F"
21,0,0,28,0.409000," ","int(x^3*arcsin(x)/(-x^4+1)^(1/2),x)","\int \frac{x^{3} \arcsin \left(x \right)}{\sqrt{-x^{4}+1}}\, dx"," ",0,"int(x^3*arcsin(x)/(-x^4+1)^(1/2),x)","F"
22,0,0,54,0.740000," ","int(x^3*arcsec(x)/(x^4-1)^(1/2),x)","\int \frac{x^{3} \mathrm{arcsec}\left(x \right)}{\sqrt{x^{4}-1}}\, dx"," ",0,"int(x^3*arcsec(x)/(x^4-1)^(1/2),x)","F"
23,0,0,48,0.170000," ","int(x*arctan(x)*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x)","\int \frac{x \arctan \left(x \right) \ln \left(x +\sqrt{x^{2}+1}\right)}{\sqrt{x^{2}+1}}\, dx"," ",0,"int(x*arctan(x)*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x)","F"
24,1,37,47,0.006000," ","int(x*ln(1+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","-\left(1+\sqrt{-x^{2}+1}\right) \ln \left(1+\sqrt{-x^{2}+1}\right)+1+\sqrt{-x^{2}+1}"," ",0,"-ln(1+(-x^2+1)^(1/2))*(1+(-x^2+1)^(1/2))+1+(-x^2+1)^(1/2)","A"
25,0,0,22,0.084000," ","int(x*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x)","\int \frac{x \ln \left(x +\sqrt{x^{2}+1}\right)}{\sqrt{x^{2}+1}}\, dx"," ",0,"int(x*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x)","F"
26,0,0,63,0.096000," ","int(x*ln(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","\int \frac{x \ln \left(x +\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int(x*ln(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","F"
27,1,35,35,0.109000," ","int(ln(x)/x^2/(-x^2+1)^(1/2),x)","-\arcsin \left(x \right)+\frac{-\sqrt{-x^{2}+1}\, \ln \left(x \right)-\sqrt{-x^{2}+1}}{x}"," ",0,"-arcsin(x)+(-ln(x)*(-x^2+1)^(1/2)-(-x^2+1)^(1/2))/x","A"
28,1,54,15,0.172000," ","int(x*arctan(x)/(x^2+1)^(1/2),x)","\sqrt{\left(x -i\right) \left(x +i\right)}\, \arctan \left(x \right)+\ln \left(\frac{i x +1}{\sqrt{x^{2}+1}}-i\right)-\ln \left(\frac{i x +1}{\sqrt{x^{2}+1}}+i\right)"," ",0,"((x-I)*(x+I))^(1/2)*arctan(x)+ln((I*x+1)/(x^2+1)^(1/2)-I)-ln((I*x+1)/(x^2+1)^(1/2)+I)","C"
29,0,0,48,0.335000," ","int(arctan(x)/x^2/(-x^2+1)^(1/2),x)","\int \frac{\arctan \left(x \right)}{\sqrt{-x^{2}+1}\, x^{2}}\, dx"," ",0,"int(arctan(x)/x^2/(-x^2+1)^(1/2),x)","F"
30,0,0,37,0.227000," ","int(x*arctan(x)/(-x^2+1)^(1/2),x)","\int \frac{x \arctan \left(x \right)}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int(x*arctan(x)/(-x^2+1)^(1/2),x)","F"
31,1,56,25,0.173000," ","int(arctan(x)/x^2/(x^2+1)^(1/2),x)","-\ln \left(1+\frac{i x +1}{\sqrt{x^{2}+1}}\right)+\ln \left(\frac{i x +1}{\sqrt{x^{2}+1}}-1\right)-\frac{\sqrt{\left(x -i\right) \left(x +i\right)}\, \arctan \left(x \right)}{x}"," ",0,"-((x-I)*(x+I))^(1/2)*arctan(x)/x-ln(1+(I*x+1)/(x^2+1)^(1/2))+ln((I*x+1)/(x^2+1)^(1/2)-1)","C"
32,1,20,19,0.074000," ","int(arcsin(x)/x^2/(-x^2+1)^(1/2),x)","\ln \left(x \right)-\frac{\sqrt{-x^{2}+1}\, \arcsin \left(x \right)}{x}"," ",0,"ln(x)-arcsin(x)*(-x^2+1)^(1/2)/x","A"
33,1,119,28,0.138000," ","int(x*ln(x)/(x^2-1)^(1/2),x)","\frac{\sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \left(2-2 \sqrt{-x^{2}+1}\right) \ln \left(x \right)}{2 \sqrt{\mathrm{signum}\left(x^{2}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \left(2-2 \sqrt{-x^{2}+1}\right)}{4 \sqrt{\mathrm{signum}\left(x^{2}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \left(-32 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{2}+1}}{2}\right)-16+16 \sqrt{-x^{2}+1}\right)}{32 \sqrt{\mathrm{signum}\left(x^{2}-1\right)}}"," ",0,"-1/4/signum(x^2-1)^(1/2)*(-signum(x^2-1))^(1/2)*(2-2*(-x^2+1)^(1/2))+1/2/signum(x^2-1)^(1/2)*(-signum(x^2-1))^(1/2)*ln(x)*(2-2*(-x^2+1)^(1/2))+1/32/signum(x^2-1)^(1/2)*(-signum(x^2-1))^(1/2)*(-16+16*(-x^2+1)^(1/2)-32*ln(1/2+1/2*(-x^2+1)^(1/2)))","C"
34,1,29,29,0.101000," ","int(ln(x)/x^2/(x^2+1)^(1/2),x)","\arcsinh \left(x \right)+\frac{-\sqrt{x^{2}+1}\, \ln \left(x \right)-\sqrt{x^{2}+1}}{x}"," ",0,"arcsinh(x)+(-ln(x)*(x^2+1)^(1/2)-(x^2+1)^(1/2))/x","A"
35,1,97,21,0.512000," ","int(x*arcsec(x)/(x^2-1)^(1/2),x)","-\frac{2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \,\mathrm{arcsec}\left(x \right)}{\sqrt{x^{2}-1}}+\frac{\sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\left(\frac{1}{x}+i \sqrt{-\frac{1}{x^{2}}+1}\right)^{2}+1\right)}{\sqrt{x^{2}-1}}+\frac{\left(x^{2}+i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -1\right) \mathrm{arcsec}\left(x \right)}{\sqrt{x^{2}-1}}"," ",0,"-2*I/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*arcsec(x)+1/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*arcsec(x)+1/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln((1/x+I*(-1/x^2+1)^(1/2))^2+1)","C"
36,1,39,28,0.101000," ","int(x*ln(x)/(x^2+1)^(1/2),x)","\frac{\left(-2+2 \sqrt{x^{2}+1}\right) \ln \left(x \right)}{2}+\ln \left(\frac{1}{2}+\frac{\sqrt{x^{2}+1}}{2}\right)+1-\sqrt{x^{2}+1}"," ",0,"1-(x^2+1)^(1/2)+1/2*ln(x)*(-2+2*(x^2+1)^(1/2))+ln(1/2+1/2*(x^2+1)^(1/2))","A"
37,1,14,13,0.028000," ","int(sin(x)/(1+sin(x)^2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \cos \left(x \right)}{2}\right)}{2}"," ",0,"-1/2*arctanh(1/2*cos(x)*2^(1/2))*2^(1/2)","A"
38,1,112,18,0.086000," ","int((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x)","-\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) x , i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}"," ",0,"-1/(1/2*2^(1/2)+1/2*I*2^(1/2))*(1-I*x^2)^(1/2)*(1+I*x^2)^(1/2)/(x^4+1)^(1/2)*EllipticF(x*(1/2*2^(1/2)+1/2*I*2^(1/2)),I)-2*(-1)^(3/4)*(1-I*x^2)^(1/2)*(1+I*x^2)^(1/2)/(x^4+1)^(1/2)*EllipticPi((-1)^(1/4)*x,-I,(-I)^(1/2)/(-1)^(1/4))","C"
39,1,112,18,0.025000," ","int((-x^2+1)/(x^2+1)/(x^4+1)^(1/2),x)","-\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) x , i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}"," ",0,"-1/(1/2*2^(1/2)+1/2*I*2^(1/2))*(-I*x^2+1)^(1/2)*(I*x^2+1)^(1/2)/(x^4+1)^(1/2)*EllipticF((1/2*2^(1/2)+1/2*I*2^(1/2))*x,I)-2*(-1)^(3/4)*(-I*x^2+1)^(1/2)*(I*x^2+1)^(1/2)/(x^4+1)^(1/2)*EllipticPi((-1)^(1/4)*x,I,(-I)^(1/2)/(-1)^(1/4))","C"
40,1,54,22,0.168000," ","int(ln(sin(x))/(sin(x)+1),x)","\ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)+\frac{-x \tan \left(\frac{x}{2}\right)+2 \ln \left(\frac{2 \tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)+1}\right) \tan \left(\frac{x}{2}\right)-x}{\tan \left(\frac{x}{2}\right)+1}"," ",0,"(-x-x*tan(1/2*x)+2*tan(1/2*x)*ln(2*tan(1/2*x)/(tan(1/2*x)^2+1)))/(tan(1/2*x)+1)+ln(tan(1/2*x)^2+1)","B"
41,0,0,36,0.207000," ","int(ln(sin(x))*(sin(x)+1)^(1/2),x)","\int \sqrt{\sin \left(x \right)+1}\, \ln \left(\sin \left(x \right)\right)\, dx"," ",0,"int(ln(sin(x))*(sin(x)+1)^(1/2),x)","F"
42,1,91,23,0.250000," ","int(sec(x)/(-1+sec(x)^4)^(1/2),x)","\frac{\sqrt{8}\, \sqrt{2}\, \left(-\arcsinh \left(\frac{\cos \left(x \right)-1}{\cos \left(x \right)+1}\right)+\arctanh \left(\frac{\sqrt{2}\, \sqrt{4}}{4 \sqrt{\frac{\cos^{2}\left(x \right)+1}{\left(\cos \left(x \right)+1\right)^{2}}}}\right)\right) \sqrt{\frac{\cos^{2}\left(x \right)+1}{\left(\cos \left(x \right)+1\right)^{2}}}\, \left(\sin^{3}\left(x \right)\right)}{8 \left(\cos \left(x \right)-1\right) \sqrt{-\frac{2 \left(\cos^{4}\left(x \right)-1\right)}{\cos \left(x \right)^{4}}}\, \cos \left(x \right)^{2}}"," ",0,"1/8*8^(1/2)*2^(1/2)*(arctanh(1/4*2^(1/2)*4^(1/2)/((1+cos(x)^2)/(1+cos(x))^2)^(1/2))-arcsinh((cos(x)-1)/(1+cos(x))))*sin(x)^3*((1+cos(x)^2)/(1+cos(x))^2)^(1/2)/(cos(x)-1)/cos(x)^2/(-2*(cos(x)^4-1)/cos(x)^4)^(1/2)","B"
43,1,37,27,0.060000," ","int(tan(x)/(1+tan(x)^4)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-2 \left(\tan^{2}\left(x \right)\right)+2\right) \sqrt{2}}{4 \sqrt{-2 \left(\tan^{2}\left(x \right)\right)+\left(\tan^{2}\left(x \right)+1\right)^{2}}}\right)}{4}"," ",0,"-1/4*2^(1/2)*arctanh(1/4*(-2*tan(x)^2+2)*2^(1/2)/(-2*tan(x)^2+(tan(x)^2+1)^2)^(1/2))","A"
44,1,67,29,0.409000," ","int(sin(x)/(1-sin(x)^6)^(1/2),x)","-\frac{\sqrt{\cos^{4}\left(x \right)-3 \left(\cos^{2}\left(x \right)\right)+3}\, \sqrt{3}\, \arctanh \left(\frac{\left(\cos^{2}\left(x \right)-2\right) \sqrt{3}}{2 \sqrt{\cos^{4}\left(x \right)-3 \left(\cos^{2}\left(x \right)\right)+3}}\right) \cos \left(x \right)}{6 \sqrt{\cos^{6}\left(x \right)-3 \left(\cos^{4}\left(x \right)\right)+3 \left(\cos^{2}\left(x \right)\right)}}"," ",0,"-1/6/(3*cos(x)^2-3*cos(x)^4+cos(x)^6)^(1/2)*cos(x)*(3-3*cos(x)^2+cos(x)^4)^(1/2)*3^(1/2)*arctanh(1/2*(cos(x)^2-2)*3^(1/2)/(3-3*cos(x)^2+cos(x)^4)^(1/2))","B"
45,0,0,247,0.261000," ","int((-(sec(x)-1)^(1/2)+(1+sec(x))^(1/2))^(1/2),x)","\int \sqrt{-\sqrt{\sec \left(x \right)-1}+\sqrt{\sec \left(x \right)+1}}\, dx"," ",0,"int((-(sec(x)-1)^(1/2)+(1+sec(x))^(1/2))^(1/2),x)","F"
46,1,3134,67,1.159000," ","int(x*arctan(x)^2*ln(x^2+1),x)","\text{output too large to display}"," ",0,"-1/2*x^2*arctan(x)^2+3*x*arctan(x)-1/2*arctan(x)^2-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I*(I*x+1)^2/(x^2+1))*x^2+1/2*I*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I*(I*x+1)^2/(x^2+1))*x-arctan(x)^2*ln((I*x+1)^2/(x^2+1)+1)*x^2+1/2*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^3+I*Pi*ln((I*x+1)^2/(x^2+1)+1)*csgn(I*((I*x+1)^2/(x^2+1)+1))*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^2+1/2*I*arctan(x)^2*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))*csgn(I*(I*x+1)^2/(x^2+1))^2+1/4*I*arctan(x)^2*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^3*x^2-1/2*I*arctan(x)*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^3*x-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))^2*csgn(I*(I*x+1)^2/(x^2+1))+1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)+1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I*(I*x+1)^2/(x^2+1))+1/4*I*arctan(x)^2*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))^2*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^3*x^2-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1))^3*x^2+3*ln((I*x+1)^2/(x^2+1)+1)-1/2*I*Pi*ln((I*x+1)^2/(x^2+1)+1)*csgn(I*((I*x+1)^2/(x^2+1)+1))^2*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)-1/2*I*Pi*ln((I*x+1)^2/(x^2+1)+1)*csgn(I*(I*x+1)^2/(x^2+1))*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2-1/2*I*Pi*ln((I*x+1)^2/(x^2+1)+1)*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2+1/2*I*Pi*ln((I*x+1)^2/(x^2+1)+1)*csgn(I*(I*x+1)/(x^2+1)^(1/2))^2*csgn(I*(I*x+1)^2/(x^2+1))-1/2*I*arctan(x)^2*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^2+1/2*I*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^3*x+1/2*I*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1))^3*x-I*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))*csgn(I*(I*x+1)^2/(x^2+1))^2*ln((I*x+1)^2/(x^2+1)+1)+1/2*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I*(I*x+1)^2/(x^2+1))+ln((I*x+1)^2/(x^2+1)+1)^2-3*I*arctan(x)+arctan(x)^2*ln(2)-arctan(x)^2*ln((I*x+1)^2/(x^2+1)+1)+(x^2*arctan(x)^2+2*I*arctan(x)+arctan(x)^2-2*x*arctan(x)-2*ln((I*x+1)^2/(x^2+1)+1))*ln((I*x+1)/(x^2+1)^(1/2))-1/2*arctan(x)*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^3-2*arctan(x)*ln(2)*x+2*arctan(x)*ln((I*x+1)^2/(x^2+1)+1)*x+arctan(x)^2*ln(2)*x^2+2*I*arctan(x)*ln(2)-2*ln(2)*ln((I*x+1)^2/(x^2+1)+1)+1/2*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1))^3-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1))^3+1/2*I*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^3*ln((I*x+1)^2/(x^2+1)+1)*Pi+1/2*I*csgn(I*(I*x+1)^2/(x^2+1))^3*ln((I*x+1)^2/(x^2+1)+1)*Pi-1/2*I*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^3*ln((I*x+1)^2/(x^2+1)+1)*Pi-1/2*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)-1/2*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I*(I*x+1)^2/(x^2+1))-1/2*arctan(x)*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))^2*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)+arctan(x)*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^2+1/2*arctan(x)*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))^2*csgn(I*(I*x+1)^2/(x^2+1))-arctan(x)*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))*csgn(I*(I*x+1)^2/(x^2+1))^2+1/4*I*arctan(x)^2*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^3-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^3+1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*x^2-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I*(I*x+1)^2/(x^2+1))+1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I*(I*x+1)^2/(x^2+1))*x^2+1/4*I*arctan(x)^2*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))^2*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)*x^2-1/2*I*arctan(x)^2*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^2*x^2-1/2*I*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*x-1/2*I*arctan(x)*Pi*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)^2*csgn(I*(I*x+1)^2/(x^2+1))*x-1/2*I*arctan(x)*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))^2*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)*x-I*arctan(x)*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))*csgn(I*(I*x+1)^2/(x^2+1))^2*x-1/4*I*arctan(x)^2*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))^2*csgn(I*(I*x+1)^2/(x^2+1))*x^2+1/2*I*arctan(x)^2*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))*csgn(I*(I*x+1)^2/(x^2+1))^2*x^2+1/2*I*arctan(x)*Pi*csgn(I*(I*x+1)/(x^2+1)^(1/2))^2*csgn(I*(I*x+1)^2/(x^2+1))*x+1/2*I*Pi*ln((I*x+1)^2/(x^2+1)+1)*csgn(I/((I*x+1)^2/(x^2+1)+1)^2)*csgn(I*(I*x+1)^2/(x^2+1))*csgn(I*(I*x+1)^2/(x^2+1)/((I*x+1)^2/(x^2+1)+1)^2)+I*arctan(x)*Pi*csgn(I*((I*x+1)^2/(x^2+1)+1))*csgn(I*((I*x+1)^2/(x^2+1)+1)^2)^2*x","C"
47,1,508,92,0.053000," ","int(arctan((x^2+1)^(1/2)*x),x)","x \arctan \left(\sqrt{x^{2}+1}\, x \right)+\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \sqrt{3}}{2}\right)}{3 \sqrt{\frac{\frac{\left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+1}{\left(\frac{x -1}{-x -1}+1\right)^{2}}}\, \left(\frac{x -1}{-x -1}+1\right)}+\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \sqrt{3}}{2}\right)}{3 \sqrt{\frac{\frac{\left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+1}{\left(\frac{x +1}{-x +1}+1\right)^{2}}}\, \left(\frac{x +1}{-x +1}+1\right)}-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \left(\sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \sqrt{3}}{2}\right)-3 \arctan \left(\frac{\sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \left(x -1\right)}{\left(\frac{\left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+1\right) \left(-x -1\right)}\right)\right)}{12 \sqrt{\frac{\frac{\left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+1}{\left(\frac{x -1}{-x -1}+1\right)^{2}}}\, \left(\frac{x -1}{-x -1}+1\right)}-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \left(\sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \sqrt{3}}{2}\right)-3 \arctan \left(\frac{\sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \left(x +1\right)}{\left(\frac{\left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+1\right) \left(-x +1\right)}\right)\right)}{12 \sqrt{\frac{\frac{\left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+1}{\left(\frac{x +1}{-x +1}+1\right)^{2}}}\, \left(\frac{x +1}{-x +1}+1\right)}"," ",0,"x*arctan((x^2+1)^(1/2)*x)+1/3*2^(1/2)/(((x-1)^2/(-1-x)^2+1)/((x-1)/(-1-x)+1)^2)^(1/2)/((x-1)/(-1-x)+1)*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*3^(1/2)*arctanh(1/2*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*3^(1/2))+1/3*2^(1/2)/(((x+1)^2/(-x+1)^2+1)/((x+1)/(-x+1)+1)^2)^(1/2)/((x+1)/(-x+1)+1)*(2*(x+1)^2/(-x+1)^2+2)^(1/2)*3^(1/2)*arctanh(1/2*(2*(x+1)^2/(-x+1)^2+2)^(1/2)*3^(1/2))-1/12*2^(1/2)*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*(3^(1/2)*arctanh(1/2*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*3^(1/2))-3*arctan(1/((x-1)^2/(-1-x)^2+1)*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*(x-1)/(-1-x)))/(((x-1)^2/(-1-x)^2+1)/((x-1)/(-1-x)+1)^2)^(1/2)/((x-1)/(-1-x)+1)-1/12*2^(1/2)*(2*(x+1)^2/(-x+1)^2+2)^(1/2)*(3^(1/2)*arctanh(1/2*(2*(x+1)^2/(-x+1)^2+2)^(1/2)*3^(1/2))-3*arctan(1/((x+1)^2/(-x+1)^2+1)*(2*(x+1)^2/(-x+1)^2+2)^(1/2)*(x+1)/(-x+1)))/(((x+1)^2/(-x+1)^2+1)/((x+1)/(-x+1)+1)^2)^(1/2)/((x+1)/(-x+1)+1)","B"
48,1,28,23,0.020000," ","int(-arctan(x^(1/2)-(x+1)^(1/2)),x)","-x \arctan \left(\sqrt{x}-\sqrt{x +1}\right)-\frac{\arctan \left(\sqrt{x}\right)}{2}+\frac{\sqrt{x}}{2}"," ",0,"-x*arctan(x^(1/2)-(x+1)^(1/2))+1/2*x^(1/2)-1/2*arctan(x^(1/2))","A"
49,1,138,25,0.124000," ","int(arcsin(x/(-x^2+1)^(1/2)),x)","x \arcsin \left(\frac{x}{\sqrt{-x^{2}+1}}\right)+\frac{\sqrt{\frac{2 x^{2}-1}{x^{2}-1}}\, \sqrt{-x^{2}+1}\, \left(-\arctan \left(\frac{2 x +1}{\sqrt{-2 x^{2}+1}}\right)+\arctan \left(\frac{2 x -1}{\sqrt{-2 x^{2}+1}}\right)+\sqrt{-2 x^{2}+1}\right)}{\sqrt{-2 x^{2}+1}\, \left(2+\sqrt{2}\right) \left(-2+\sqrt{2}\right)}+\frac{\sqrt{\frac{2 x^{2}-1}{x^{2}-1}}\, \sqrt{-x^{2}+1}}{2}"," ",0,"x*arcsin(x/(-x^2+1)^(1/2))+((2*x^2-1)/(x^2-1))^(1/2)*(-x^2+1)^(1/2)*((-2*x^2+1)^(1/2)-arctan((2*x+1)/(-2*x^2+1)^(1/2))+arctan((2*x-1)/(-2*x^2+1)^(1/2)))/(-2*x^2+1)^(1/2)/(2+2^(1/2))/(-2+2^(1/2))+1/2*((2*x^2-1)/(x^2-1))^(1/2)*(-x^2+1)^(1/2)","B"
50,1,198,79,0.088000," ","int(arctan((-x^2+1)^(1/2)*x),x)","x \arctan \left(\sqrt{-x^{2}+1}\, x \right)+\frac{\sqrt{5}\, \arctanh \left(\frac{\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}+4+2 \sqrt{5}}{4 \sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}+\frac{\arctanh \left(\frac{\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}+4+2 \sqrt{5}}{4 \sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-2 \sqrt{5}+4}{4 \sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{\arctan \left(\frac{\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2}}{x^{2}}-2 \sqrt{5}+4}{4 \sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}"," ",0,"x*arctan((-x^2+1)^(1/2)*x)+1/2*5^(1/2)/(2+5^(1/2))^(1/2)*arctanh(1/4*(2*((-x^2+1)^(1/2)-1)^2/x^2+4+2*5^(1/2))/(2+5^(1/2))^(1/2))+1/2*5^(1/2)/(-2+5^(1/2))^(1/2)*arctan(1/4*(2*((-x^2+1)^(1/2)-1)^2/x^2-2*5^(1/2)+4)/(-2+5^(1/2))^(1/2))+1/2/(2+5^(1/2))^(1/2)*arctanh(1/4*(2*((-x^2+1)^(1/2)-1)^2/x^2+4+2*5^(1/2))/(2+5^(1/2))^(1/2))-1/2/(-2+5^(1/2))^(1/2)*arctan(1/4*(2*((-x^2+1)^(1/2)-1)^2/x^2-2*5^(1/2)+4)/(-2+5^(1/2))^(1/2))","B"