1,1,21,18,0.077000," ","int(1/(cos(z)+sin(z)+2^(1/2)),z)","-\frac{2}{\left(\sqrt{2}-1\right) \left(\tan \left(\frac{z}{2}\right)+\sqrt{2}+1\right)}"," ",0,"-2/(2^(1/2)-1)/(tan(1/2*z)+2^(1/2)+1)","A"
2,1,50,24,0.014000," ","int(1/((1-x)^(1/2)+(x+1)^(1/2))^2,x)","-\frac{1}{2 x}-\frac{\left(-x \arcsin \left(x \right)-\sqrt{-x^{2}+1}\right) \sqrt{-x +1}\, \sqrt{x +1}}{2 \sqrt{-x^{2}+1}\, x}"," ",0,"-1/2/x-1/2*(-arcsin(x)*x-(-x^2+1)^(1/2))*(1-x)^(1/2)*(x+1)^(1/2)/x/(-x^2+1)^(1/2)","B"
3,1,16,21,0.019000," ","int(1/(1+cos(x))^2,x)","\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{6}+\frac{\tan \left(\frac{x}{2}\right)}{2}"," ",0,"1/6*tan(1/2*x)^3+1/2*tan(1/2*x)","A"
4,1,42,46,0.021000," ","int(sin(x)/(x+1)^(1/2),x)","\sqrt{2}\, \sqrt{\pi}\, \left(-\sin \left(1\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{x +1}}{\sqrt{\pi}}\right)+\cos \left(1\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{x +1}}{\sqrt{\pi}}\right)\right)"," ",0,"2^(1/2)*Pi^(1/2)*(cos(1)*FresnelS(2^(1/2)/Pi^(1/2)*(x+1)^(1/2))-sin(1)*FresnelC(2^(1/2)/Pi^(1/2)*(x+1)^(1/2)))","A"
5,1,42,44,0.130000," ","int(1/(cos(x)+sin(x))^6,x)","\frac{2}{\left(\tan \left(x \right)+1\right)^{4}}-\frac{4}{5 \left(\tan \left(x \right)+1\right)^{5}}-\frac{8}{3 \left(\tan \left(x \right)+1\right)^{3}}+\frac{2}{\left(\tan \left(x \right)+1\right)^{2}}-\frac{1}{\tan \left(x \right)+1}"," ",0,"2/(tan(x)+1)^4-4/5/(tan(x)+1)^5-8/3/(tan(x)+1)^3+2/(tan(x)+1)^2-1/(tan(x)+1)","A"
6,1,36,246,0.033000," ","int(ln(1/x^4+x^4),x)","x \ln \left(\frac{x^{8}+1}{x^{4}}\right)-4 x +\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{8}+1\right)+x \right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}}"," ",0,"x*ln((x^8+1)/x^4)-4*x+sum(1/_R^7*ln(x-_R),_R=RootOf(_Z^8+1))","C"
7,1,171,224,0.170000," ","int(ln(x+1)/x/(1+(x+1)^(1/2))^(1/2),x)","-8 \arctanh \left(\sqrt{1+\sqrt{x +1}}\right)+4 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2}-2\right)}{\sum}\frac{\left(-2 \ln \left(\frac{1+\sqrt{1+\sqrt{x +1}}}{\underline{\hspace{1.25 ex}}\alpha  +1}\right) \ln \left(-\underline{\hspace{1.25 ex}}\alpha  +\sqrt{1+\sqrt{x +1}}\right)-2 \ln \left(\frac{\sqrt{1+\sqrt{x +1}}-1}{\underline{\hspace{1.25 ex}}\alpha  -1}\right) \ln \left(-\underline{\hspace{1.25 ex}}\alpha  +\sqrt{1+\sqrt{x +1}}\right)+\ln \left(x +1\right) \ln \left(-\underline{\hspace{1.25 ex}}\alpha  +\sqrt{1+\sqrt{x +1}}\right)-2 \dilog \left(\frac{1+\sqrt{1+\sqrt{x +1}}}{\underline{\hspace{1.25 ex}}\alpha  +1}\right)-2 \dilog \left(\frac{\sqrt{1+\sqrt{x +1}}-1}{\underline{\hspace{1.25 ex}}\alpha  -1}\right)\right) \underline{\hspace{1.25 ex}}\alpha }{8}\right)-\frac{2 \ln \left(x +1\right)}{\sqrt{1+\sqrt{x +1}}}"," ",0,"-2*ln(x+1)/(1+(x+1)^(1/2))^(1/2)-8*arctanh((1+(x+1)^(1/2))^(1/2))+4*Sum(1/8*(ln((1+(x+1)^(1/2))^(1/2)-_alpha)*ln(x+1)-2*dilog((1+(1+(x+1)^(1/2))^(1/2))/(1+_alpha))-2*ln((1+(x+1)^(1/2))^(1/2)-_alpha)*ln((1+(1+(x+1)^(1/2))^(1/2))/(1+_alpha))-2*dilog(((1+(x+1)^(1/2))^(1/2)-1)/(-1+_alpha))-2*ln((1+(x+1)^(1/2))^(1/2)-_alpha)*ln(((1+(x+1)^(1/2))^(1/2)-1)/(-1+_alpha)))*_alpha,_alpha=RootOf(_Z^2-2))","C"
8,1,198,237,0.016000," ","int(ln(x+1)*(1+(x+1)^(1/2))^(1/2)/x,x)","4 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2}-2\right)}{\sum}\frac{\left(-2 \ln \left(\frac{1+\sqrt{1+\sqrt{x +1}}}{\underline{\hspace{1.25 ex}}\alpha  +1}\right) \ln \left(-\underline{\hspace{1.25 ex}}\alpha  +\sqrt{1+\sqrt{x +1}}\right)-2 \ln \left(\frac{\sqrt{1+\sqrt{x +1}}-1}{\underline{\hspace{1.25 ex}}\alpha  -1}\right) \ln \left(-\underline{\hspace{1.25 ex}}\alpha  +\sqrt{1+\sqrt{x +1}}\right)+\ln \left(x +1\right) \ln \left(-\underline{\hspace{1.25 ex}}\alpha  +\sqrt{1+\sqrt{x +1}}\right)-2 \dilog \left(\frac{1+\sqrt{1+\sqrt{x +1}}}{\underline{\hspace{1.25 ex}}\alpha  +1}\right)-2 \dilog \left(\frac{\sqrt{1+\sqrt{x +1}}-1}{\underline{\hspace{1.25 ex}}\alpha  -1}\right)\right) \underline{\hspace{1.25 ex}}\alpha }{4}\right)+4 \sqrt{1+\sqrt{x +1}}\, \ln \left(x +1\right)+8 \ln \left(1+\sqrt{1+\sqrt{x +1}}\right)-8 \ln \left(\sqrt{1+\sqrt{x +1}}-1\right)-16 \sqrt{1+\sqrt{x +1}}"," ",0,"4*ln(x+1)*(1+(x+1)^(1/2))^(1/2)-16*(1+(x+1)^(1/2))^(1/2)-8*ln((1+(x+1)^(1/2))^(1/2)-1)+8*ln(1+(1+(x+1)^(1/2))^(1/2))+4*Sum(1/4*(ln(x+1)*ln(-_alpha+(1+(x+1)^(1/2))^(1/2))-2*dilog((1+(1+(x+1)^(1/2))^(1/2))/(_alpha+1))-2*ln((1+(1+(x+1)^(1/2))^(1/2))/(_alpha+1))*ln(-_alpha+(1+(x+1)^(1/2))^(1/2))-2*dilog(((1+(x+1)^(1/2))^(1/2)-1)/(_alpha-1))-2*ln(((1+(x+1)^(1/2))^(1/2)-1)/(_alpha-1))*ln(-_alpha+(1+(x+1)^(1/2))^(1/2)))*_alpha,_alpha=RootOf(_Z^2-2))","C"
9,0,0,64,0.041000," ","int(1/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","\int \frac{1}{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx"," ",0,"int(1/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
10,1,34,32,0.005000," ","int((x+1)^(1/2)/(x+(1+(x+1)^(1/2))^(1/2)),x)","\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(1+2 \sqrt{1+\sqrt{x +1}}\right) \sqrt{5}}{5}\right)}{5}+2 \sqrt{x +1}+2"," ",0,"2*(x+1)^(1/2)+2+8/5*arctanh(1/5*(1+2*(1+(x+1)^(1/2))^(1/2))*5^(1/2))*5^(1/2)","A"
11,1,175,53,0.174000," ","int(1/(x-(1+(x+1)^(1/2))^(1/2)),x)","\frac{2 \sqrt{5}\, \arctanh \left(\frac{\left(1+2 \sqrt{1+\sqrt{x +1}}\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x -1\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{x +1}-1\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{x +1}+1\right) \sqrt{5}}{5}\right)}{5}+\frac{2 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{x +1}}-1\right) \sqrt{5}}{5}\right)}{5}+\frac{\ln \left(x -\sqrt{x +1}\right)}{2}-\frac{\ln \left(x +\sqrt{x +1}\right)}{2}+\ln \left(\sqrt{x +1}-\sqrt{1+\sqrt{x +1}}\right)-\ln \left(\sqrt{x +1}+\sqrt{1+\sqrt{x +1}}\right)+\frac{\ln \left(x^{2}-x -1\right)}{2}"," ",0,"1/2*ln(x^2-x-1)+1/5*5^(1/2)*arctanh(1/5*(2*x-1)*5^(1/2))+1/5*5^(1/2)*arctanh(1/5*(2*(x+1)^(1/2)+1)*5^(1/2))+2/5*arctanh(1/5*(1+2*(1+(x+1)^(1/2))^(1/2))*5^(1/2))*5^(1/2)+1/2*ln(x-(x+1)^(1/2))-ln((x+1)^(1/2)+(1+(x+1)^(1/2))^(1/2))+ln((x+1)^(1/2)-(1+(x+1)^(1/2))^(1/2))-1/2*ln(x+(x+1)^(1/2))+1/5*5^(1/2)*arctanh(1/5*(2*(x+1)^(1/2)-1)*5^(1/2))+2/5*5^(1/2)*arctanh(1/5*(2*(1+(x+1)^(1/2))^(1/2)-1)*5^(1/2))","B"
12,1,60,58,0.009000," ","int(x/(x+(1-(x+1)^(1/2))^(1/2)),x)","\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(1+2 \sqrt{1-\sqrt{x +1}}\right) \sqrt{5}}{5}\right)}{5}+\left(1-\sqrt{x +1}\right)^{2}-2+2 \sqrt{x +1}-4 \sqrt{1-\sqrt{x +1}}"," ",0,"(1-(x+1)^(1/2))^2-2+2*(x+1)^(1/2)-4*(1-(x+1)^(1/2))^(1/2)+8/5*arctanh(1/5*(1+2*(1-(x+1)^(1/2))^(1/2))*5^(1/2))*5^(1/2)","A"
13,1,109,265,0.045000," ","int((x+(x+1)^(1/2))^(1/2)/(x^2+1)/(x+1)^(1/2),x)","-\frac{\left(2 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{5}-5 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{4}+5 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}-1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+\sqrt{x +\sqrt{x +1}}-\sqrt{x +1}\right)}{2 \left(\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{7}-3 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{5}+5 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{4}+10 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{3}-18 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}+10 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-1\right)}"," ",0,"-1/2*sum((2*_R^5-5*_R^4+5*_R^2-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(x+1)^(1/2))^(1/2)-(x+1)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","C"
14,1,105,237,0.020000," ","int((x+(x+1)^(1/2))^(1/2)/(x^2+1),x)","\frac{\left(\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{6}-2 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{5}+2 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+\sqrt{x +\sqrt{x +1}}-\sqrt{x +1}\right)}{2 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{7}-6 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{5}+10 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{4}+20 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{3}-36 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}+20 \RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-2}"," ",0,"1/2*sum((_R^6-2*_R^5+2*_R+1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln(-_R+(x+(x+1)^(1/2))^(1/2)-(x+1)^(1/2)),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","C"
15,0,0,55,0.087000," ","int((1+x^(1/2)+(1+2*x+2*x^(1/2))^(1/2))^(1/2),x)","\int \sqrt{\sqrt{x}+1+\sqrt{2 x +2 \sqrt{x}+1}}\, dx"," ",0,"int((1+x^(1/2)+(1+2*x+2*x^(1/2))^(1/2))^(1/2),x)","F"
16,0,0,78,0.221000," ","int((2^(1/2)+x^(1/2)+(2+2*x+2*2^(1/2)*x^(1/2))^(1/2))^(1/2),x)","\int \sqrt{\sqrt{x}+\sqrt{2}+\sqrt{2 x +2 \sqrt{2}\, \sqrt{x}+2}}\, dx"," ",0,"int((2^(1/2)+x^(1/2)+(2+2*x+2*2^(1/2)*x^(1/2))^(1/2))^(1/2),x)","F"
17,1,298,59,0.015000," ","int((x+(x+1)^(1/2))^(1/2)/x^2,x)","-\frac{3 \arctanh \left(\frac{-1+3 \sqrt{x +1}}{2 \sqrt{\left(-1+\sqrt{x +1}\right)^{2}+3 \sqrt{x +1}-2}}\right)}{4}+\frac{\arctan \left(\frac{-3-\sqrt{x +1}}{2 \sqrt{\left(1+\sqrt{x +1}\right)^{2}-\sqrt{x +1}-2}}\right)}{4}+\frac{\ln \left(\frac{1}{2}+\sqrt{x +1}+\sqrt{\left(-1+\sqrt{x +1}\right)^{2}+3 \sqrt{x +1}-2}\right)}{2}-\frac{\ln \left(\sqrt{x +1}+\frac{1}{2}+\sqrt{\left(1+\sqrt{x +1}\right)^{2}-\sqrt{x +1}-2}\right)}{2}-\frac{\left(\left(-1+\sqrt{x +1}\right)^{2}+3 \sqrt{x +1}-2\right)^{\frac{3}{2}}}{2 \left(-1+\sqrt{x +1}\right)}+\frac{3 \sqrt{\left(-1+\sqrt{x +1}\right)^{2}+3 \sqrt{x +1}-2}}{4}+\frac{\left(2 \sqrt{x +1}+1\right) \sqrt{\left(-1+\sqrt{x +1}\right)^{2}+3 \sqrt{x +1}-2}}{4}-\frac{\left(\left(1+\sqrt{x +1}\right)^{2}-\sqrt{x +1}-2\right)^{\frac{3}{2}}}{2 \left(1+\sqrt{x +1}\right)}-\frac{\sqrt{\left(1+\sqrt{x +1}\right)^{2}-\sqrt{x +1}-2}}{4}+\frac{\left(2 \sqrt{x +1}+1\right) \sqrt{\left(1+\sqrt{x +1}\right)^{2}-\sqrt{x +1}-2}}{4}"," ",0,"-1/2/(-1+(x+1)^(1/2))*((-1+(x+1)^(1/2))^2+3*(x+1)^(1/2)-2)^(3/2)+3/4*((-1+(x+1)^(1/2))^2+3*(x+1)^(1/2)-2)^(1/2)+1/2*ln(1/2+(x+1)^(1/2)+((-1+(x+1)^(1/2))^2+3*(x+1)^(1/2)-2)^(1/2))-3/4*arctanh(1/2*(-1+3*(x+1)^(1/2))/((-1+(x+1)^(1/2))^2+3*(x+1)^(1/2)-2)^(1/2))+1/4*(2*(x+1)^(1/2)+1)*((-1+(x+1)^(1/2))^2+3*(x+1)^(1/2)-2)^(1/2)-1/2/(1+(x+1)^(1/2))*((1+(x+1)^(1/2))^2-(x+1)^(1/2)-2)^(3/2)-1/4*((1+(x+1)^(1/2))^2-(x+1)^(1/2)-2)^(1/2)-1/2*ln((x+1)^(1/2)+1/2+((1+(x+1)^(1/2))^2-(x+1)^(1/2)-2)^(1/2))+1/4*arctan(1/2*(-3-(x+1)^(1/2))/((1+(x+1)^(1/2))^2-(x+1)^(1/2)-2)^(1/2))+1/4*(2*(x+1)^(1/2)+1)*((1+(x+1)^(1/2))^2-(x+1)^(1/2)-2)^(1/2)","B"
18,0,0,72,0.057000," ","int((1/x+(1+1/x)^(1/2))^(1/2),x)","\int \sqrt{\frac{1}{x}+\sqrt{\frac{1}{x}+1}}\, dx"," ",0,"int((1/x+(1+1/x)^(1/2))^(1/2),x)","F"
19,1,49,19,0.031000," ","int((1+exp(-x))^(1/2)/(-exp(-x)+exp(x)),x)","-\frac{\sqrt{\left({\mathrm e}^{x}+1\right) {\mathrm e}^{-x}}\, \sqrt{2}\, \arctanh \left(\frac{\left(3 \,{\mathrm e}^{x}+1\right) \sqrt{2}}{4 \sqrt{{\mathrm e}^{x}+{\mathrm e}^{2 x}}}\right) {\mathrm e}^{x}}{2 \sqrt{\left({\mathrm e}^{x}+1\right) {\mathrm e}^{x}}}"," ",0,"-1/2*((exp(x)+1)/exp(x))^(1/2)*exp(x)/((exp(x)+1)*exp(x))^(1/2)*2^(1/2)*arctanh(1/4*(1+3*exp(x))*2^(1/2)/(exp(x)^2+exp(x))^(1/2))","B"
20,1,33,19,0.120000," ","int((1+exp(-x))^(1/2)/sinh(x),x)","-2 \sqrt{2}\, \sqrt{\frac{1}{\tanh \left(\frac{x}{2}\right)+1}}\, \sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \arctanh \left(\sqrt{\tanh \left(\frac{x}{2}\right)+1}\right)"," ",0,"-2*2^(1/2)*(1/(tanh(1/2*x)+1))^(1/2)*(tanh(1/2*x)+1)^(1/2)*arctanh((tanh(1/2*x)+1)^(1/2))","A"
21,1,95,88,0.141000," ","int(1/(cos(x)+cos(3*x))^5,x)","\frac{1483 \sqrt{2}\, \arctanh \left(\sqrt{2}\, \sin \left(x \right)\right)}{1024}+\frac{523 \ln \left(\sin \left(x \right)-1\right)}{512}-\frac{523 \ln \left(\sin \left(x \right)+1\right)}{512}+\frac{1}{512 \left(\sin \left(x \right)+1\right)^{2}}+\frac{43}{512 \left(\sin \left(x \right)+1\right)}-\frac{4 \left(-\frac{437 \left(\sin^{7}\left(x \right)\right)}{256}+\frac{3527 \left(\sin^{5}\left(x \right)\right)}{1536}-\frac{3257 \left(\sin^{3}\left(x \right)\right)}{3072}+\frac{331 \sin \left(x \right)}{2048}\right)}{\left(2 \left(\sin^{2}\left(x \right)\right)-1\right)^{4}}-\frac{1}{512 \left(\sin \left(x \right)-1\right)^{2}}+\frac{43}{512 \left(\sin \left(x \right)-1\right)}"," ",0,"1/512/(sin(x)+1)^2+43/512/(sin(x)+1)-523/512*ln(sin(x)+1)-4*(-437/256*sin(x)^7+3527/1536*sin(x)^5-3257/3072*sin(x)^3+331/2048*sin(x))/(2*sin(x)^2-1)^4+1483/1024*arctanh(sin(x)*2^(1/2))*2^(1/2)-1/512/(sin(x)-1)^2+43/512/(sin(x)-1)+523/512*ln(sin(x)-1)","A"
22,1,27,26,0.084000," ","int(1/(1+cos(x)+sin(x))^2,x)","-\ln \left(\tan \left(\frac{x}{2}\right)+1\right)+\frac{\tan \left(\frac{x}{2}\right)}{2}-\frac{1}{\tan \left(\frac{x}{2}\right)+1}"," ",0,"1/2*tan(1/2*x)-ln(tan(1/2*x)+1)-1/(tan(1/2*x)+1)","A"
23,1,20,19,0.052000," ","int((1+tanh(4*x))^(1/2),x)","\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{\tanh \left(4 x \right)+1}\, \sqrt{2}}{2}\right)}{4}"," ",0,"1/4*arctanh(1/2*(1+tanh(4*x))^(1/2)*2^(1/2))*2^(1/2)","A"
24,1,366,81,0.180000," ","int(tanh(x)/(exp(x)+exp(2*x))^(1/2),x)","-\frac{\sqrt{2}\, \left(4 \sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \arctan \left(\frac{2 \sqrt{\tanh \left(\frac{x}{2}\right)+1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)+4 \sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \arctan \left(\frac{2 \sqrt{\tanh \left(\frac{x}{2}\right)+1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)+\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \sqrt{2+2 \sqrt{2}}\, \ln \left(\tanh \left(\frac{x}{2}\right)+1-\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{2+2 \sqrt{2}}+\sqrt{2}\right)-\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{-2+2 \sqrt{2}}\, \sqrt{2+2 \sqrt{2}}\, \ln \left(\tanh \left(\frac{x}{2}\right)+1-\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{2+2 \sqrt{2}}+\sqrt{2}\right)-\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \sqrt{2+2 \sqrt{2}}\, \ln \left(\tanh \left(\frac{x}{2}\right)+1+\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{2+2 \sqrt{2}}+\sqrt{2}\right)+\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{-2+2 \sqrt{2}}\, \sqrt{2+2 \sqrt{2}}\, \ln \left(\tanh \left(\frac{x}{2}\right)+1+\sqrt{\tanh \left(\frac{x}{2}\right)+1}\, \sqrt{2+2 \sqrt{2}}+\sqrt{2}\right)+8 \sqrt{-2+2 \sqrt{2}}\right)}{4 \sqrt{-2+2 \sqrt{2}}\, \left(\tanh \left(\frac{x}{2}\right)-1\right) \sqrt{\frac{\tanh \left(\frac{x}{2}\right)+1}{\left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}}}"," ",0,"-1/4*2^(1/2)*((tanh(1/2*x)+1)^(1/2)*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tanh(1/2*x)+1-(tanh(1/2*x)+1)^(1/2)*(2+2*2^(1/2))^(1/2)+2^(1/2))*(2+2*2^(1/2))^(1/2)-(tanh(1/2*x)+1)^(1/2)*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tanh(1/2*x)+1+(tanh(1/2*x)+1)^(1/2)*(2+2*2^(1/2))^(1/2)+2^(1/2))*(2+2*2^(1/2))^(1/2)+4*(tanh(1/2*x)+1)^(1/2)*arctan((2*(tanh(1/2*x)+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+4*(tanh(1/2*x)+1)^(1/2)*arctan((2*(tanh(1/2*x)+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-(tanh(1/2*x)+1)^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tanh(1/2*x)+1-(tanh(1/2*x)+1)^(1/2)*(2+2*2^(1/2))^(1/2)+2^(1/2))*(2+2*2^(1/2))^(1/2)+(tanh(1/2*x)+1)^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tanh(1/2*x)+1+(tanh(1/2*x)+1)^(1/2)*(2+2*2^(1/2))^(1/2)+2^(1/2))*(2+2*2^(1/2))^(1/2)+8*(-2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2)/(tanh(1/2*x)-1)/((tanh(1/2*x)+1)/(tanh(1/2*x)-1)^2)^(1/2)","B"
25,1,75,54,0.161000," ","int((sinh(2*x)/cosh(x))^(1/2),x)","\frac{2 \sqrt{-i \left(\sinh \left(x \right)+i\right)}\, \sqrt{-i \left(-\sinh \left(x \right)+i\right)}\, \sqrt{i \sinh \left(x \right)}\, \left(2 \EllipticE \left(\sqrt{-i \sinh \left(x \right)+1}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{-i \sinh \left(x \right)+1}, \frac{\sqrt{2}}{2}\right)\right)}{\cosh \left(x \right) \sqrt{\sinh \left(x \right)}}"," ",0,"2*(-I*(sinh(x)+I))^(1/2)*(-I*(-sinh(x)+I))^(1/2)*(I*sinh(x))^(1/2)*(2*EllipticE((1-I*sinh(x))^(1/2),1/2*2^(1/2))-EllipticF((1-I*sinh(x))^(1/2),1/2*2^(1/2)))/cosh(x)/sinh(x)^(1/2)","A"
26,1,392,138,0.211000," ","int(ln(x^2+(-x^2+1)^(1/2)),x)","x \ln \left(x^{2}+\sqrt{-x^{2}+1}\right)-2 x +\frac{3 \arctanh \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{-2+\sqrt{5}}\, x}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{-2+\sqrt{5}}\, x}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{2+\sqrt{5}}\, x}\right)}{2 \sqrt{2+\sqrt{5}}}-\frac{\arctanh \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{2+\sqrt{5}}\, x}\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}}}-\arcsin \left(x \right)-\frac{\sqrt{5}\, \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{-2+\sqrt{5}}\, x}\right)}{2 \sqrt{-2+\sqrt{5}}}+\frac{\arctan \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{-2+\sqrt{5}}\, x}\right)}{2 \sqrt{-2+\sqrt{5}}}-\frac{3 \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{2+\sqrt{5}}\, x}\right)}{2 \sqrt{2+\sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{2+\sqrt{5}}\, x}\right)}{2 \sqrt{2+\sqrt{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(x^2+(-x^2+1)^(1/2))+1/(2+2*5^(1/2))^(1/2)*arctan(2*x/(2+2*5^(1/2))^(1/2))+5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2*x/(2+2*5^(1/2))^(1/2))-1/(-2+2*5^(1/2))^(1/2)*arctanh(2*x/(-2+2*5^(1/2))^(1/2))+5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2*x/(-2+2*5^(1/2))^(1/2))-2*x-3/2/(2+5^(1/2))^(1/2)*arctan(((-x^2+1)^(1/2)-1)/x/(2+5^(1/2))^(1/2))-1/2*5^(1/2)/(2+5^(1/2))^(1/2)*arctan(((-x^2+1)^(1/2)-1)/x/(2+5^(1/2))^(1/2))+3/2/(-2+5^(1/2))^(1/2)*arctanh(((-x^2+1)^(1/2)-1)/x/(-2+5^(1/2))^(1/2))-1/2*5^(1/2)/(-2+5^(1/2))^(1/2)*arctanh(((-x^2+1)^(1/2)-1)/x/(-2+5^(1/2))^(1/2))-1/2*5^(1/2)/(2+5^(1/2))^(1/2)*arctanh(((-x^2+1)^(1/2)-1)/x/(2+5^(1/2))^(1/2))-1/2/(2+5^(1/2))^(1/2)*arctanh(((-x^2+1)^(1/2)-1)/x/(2+5^(1/2))^(1/2))-1/2*5^(1/2)/(-2+5^(1/2))^(1/2)*arctan(((-x^2+1)^(1/2)-1)/x/(-2+5^(1/2))^(1/2))+1/2/(-2+5^(1/2))^(1/2)*arctan(((-x^2+1)^(1/2)-1)/x/(-2+5^(1/2))^(1/2))-arcsin(x)","B"
27,1,83,69,0.065000," ","int(ln(exp(x)+1)/(exp(2*x)+1),x)","-\frac{\ln \left({\mathrm e}^{x}+1\right) \ln \left(-\frac{{\mathrm e}^{x}}{2}+\frac{1}{2}-\frac{i \left({\mathrm e}^{x}+1\right)}{2}\right)}{2}-\frac{\ln \left({\mathrm e}^{x}+1\right) \ln \left(-\frac{{\mathrm e}^{x}}{2}+\frac{1}{2}+\frac{i \left({\mathrm e}^{x}+1\right)}{2}\right)}{2}-\dilog \left({\mathrm e}^{x}+1\right)-\frac{\dilog \left(-\frac{{\mathrm e}^{x}}{2}+\frac{1}{2}-\frac{i \left({\mathrm e}^{x}+1\right)}{2}\right)}{2}-\frac{\dilog \left(-\frac{{\mathrm e}^{x}}{2}+\frac{1}{2}+\frac{i \left({\mathrm e}^{x}+1\right)}{2}\right)}{2}"," ",0,"-dilog(exp(x)+1)-1/2*ln(exp(x)+1)*ln(1/2-1/2*exp(x)+1/2*I*(exp(x)+1))-1/2*ln(exp(x)+1)*ln(1/2-1/2*exp(x)-1/2*I*(exp(x)+1))-1/2*dilog(1/2-1/2*exp(x)+1/2*I*(exp(x)+1))-1/2*dilog(1/2-1/2*exp(x)-1/2*I*(exp(x)+1))","A"
28,0,0,133,4.107000," ","int(cosh(x)*ln(1+cosh(x)^2)^2,x)","\int \cosh \left(x \right) \ln \left(\cosh^{2}\left(x \right)+1\right)^{2}\, dx"," ",0,"int(cosh(x)*ln(1+cosh(x)^2)^2,x)","F"
29,0,0,312,6.564000," ","int(cosh(x)*ln(cosh(x)^2+sinh(x))^2,x)","\int \cosh \left(x \right) \ln \left(\cosh^{2}\left(x \right)+\sinh \left(x \right)\right)^{2}\, dx"," ",0,"int(cosh(x)*ln(cosh(x)^2+sinh(x))^2,x)","F"
30,1,730,737,0.094000," ","int(ln(x+(x+1)^(1/2))/(x^2+1),x)","-\frac{i \ln \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1-i}-\sqrt{5}}\right) \ln \left(\sqrt{1-i}+\sqrt{x +1}\right)}{2}-\frac{i \ln \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1-i}-\sqrt{5}}\right) \ln \left(\sqrt{x +1}-\sqrt{1-i}\right)}{2}+\frac{i \ln \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1+i}-\sqrt{5}}\right) \ln \left(\sqrt{1+i}+\sqrt{x +1}\right)}{2}+\frac{i \ln \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1+i}-\sqrt{5}}\right) \ln \left(\sqrt{x +1}-\sqrt{1+i}\right)}{2}-\frac{i \ln \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1-i}+\sqrt{5}}\right) \ln \left(\sqrt{1-i}+\sqrt{x +1}\right)}{2}-\frac{i \ln \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1-i}+\sqrt{5}}\right) \ln \left(\sqrt{x +1}-\sqrt{1-i}\right)}{2}+\frac{i \ln \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1+i}+\sqrt{5}}\right) \ln \left(\sqrt{1+i}+\sqrt{x +1}\right)}{2}+\frac{i \ln \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1+i}+\sqrt{5}}\right) \ln \left(\sqrt{x +1}-\sqrt{1+i}\right)}{2}+\frac{i \ln \left(x +\sqrt{x +1}\right) \ln \left(\sqrt{1-i}+\sqrt{x +1}\right)}{2}-\frac{i \ln \left(x +\sqrt{x +1}\right) \ln \left(\sqrt{1+i}+\sqrt{x +1}\right)}{2}+\frac{i \ln \left(x +\sqrt{x +1}\right) \ln \left(\sqrt{x +1}-\sqrt{1-i}\right)}{2}-\frac{i \ln \left(x +\sqrt{x +1}\right) \ln \left(\sqrt{x +1}-\sqrt{1+i}\right)}{2}-\frac{i \dilog \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1-i}-\sqrt{5}}\right)}{2}-\frac{i \dilog \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1-i}-\sqrt{5}}\right)}{2}+\frac{i \dilog \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1+i}-\sqrt{5}}\right)}{2}+\frac{i \dilog \left(\frac{1-\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1+i}-\sqrt{5}}\right)}{2}-\frac{i \dilog \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1-i}+\sqrt{5}}\right)}{2}-\frac{i \dilog \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1-i}+\sqrt{5}}\right)}{2}+\frac{i \dilog \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1-2 \sqrt{1+i}+\sqrt{5}}\right)}{2}+\frac{i \dilog \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{1+2 \sqrt{1+i}+\sqrt{5}}\right)}{2}"," ",0,"1/2*I*dilog((1+5^(1/2)+2*(x+1)^(1/2))/(1+2*(1+I)^(1/2)+5^(1/2)))+1/2*I*ln((x+1)^(1/2)-(1+I)^(1/2))*ln((1-5^(1/2)+2*(x+1)^(1/2))/(1+2*(1+I)^(1/2)-5^(1/2)))-1/2*I*ln((x+1)^(1/2)-(1-I)^(1/2))*ln((1+5^(1/2)+2*(x+1)^(1/2))/(1+2*(1-I)^(1/2)+5^(1/2)))-1/2*I*dilog((1+5^(1/2)+2*(x+1)^(1/2))/(1-2*(1-I)^(1/2)+5^(1/2)))+1/2*I*ln((1+I)^(1/2)+(x+1)^(1/2))*ln((1-5^(1/2)+2*(x+1)^(1/2))/(1-2*(1+I)^(1/2)-5^(1/2)))+1/2*I*ln((x+1)^(1/2)-(1+I)^(1/2))*ln((1+5^(1/2)+2*(x+1)^(1/2))/(1+2*(1+I)^(1/2)+5^(1/2)))+1/2*I*dilog((1+5^(1/2)+2*(x+1)^(1/2))/(1-2*(1+I)^(1/2)+5^(1/2)))-1/2*I*dilog((1+5^(1/2)+2*(x+1)^(1/2))/(1+2*(1-I)^(1/2)+5^(1/2)))-1/2*I*ln(x+(x+1)^(1/2))*ln((x+1)^(1/2)-(1+I)^(1/2))-1/2*I*ln(x+(x+1)^(1/2))*ln((1+I)^(1/2)+(x+1)^(1/2))+1/2*I*ln(x+(x+1)^(1/2))*ln((1-I)^(1/2)+(x+1)^(1/2))-1/2*I*dilog((1-5^(1/2)+2*(x+1)^(1/2))/(1-2*(1-I)^(1/2)-5^(1/2)))-1/2*I*dilog((1-5^(1/2)+2*(x+1)^(1/2))/(1+2*(1-I)^(1/2)-5^(1/2)))-1/2*I*ln((1-I)^(1/2)+(x+1)^(1/2))*ln((1+5^(1/2)+2*(x+1)^(1/2))/(1-2*(1-I)^(1/2)+5^(1/2)))+1/2*I*ln(x+(x+1)^(1/2))*ln((x+1)^(1/2)-(1-I)^(1/2))-1/2*I*ln((x+1)^(1/2)-(1-I)^(1/2))*ln((1-5^(1/2)+2*(x+1)^(1/2))/(1+2*(1-I)^(1/2)-5^(1/2)))-1/2*I*ln((1-I)^(1/2)+(x+1)^(1/2))*ln((1-5^(1/2)+2*(x+1)^(1/2))/(1-2*(1-I)^(1/2)-5^(1/2)))+1/2*I*ln((1+I)^(1/2)+(x+1)^(1/2))*ln((1+5^(1/2)+2*(x+1)^(1/2))/(1-2*(1+I)^(1/2)+5^(1/2)))+1/2*I*dilog((1-5^(1/2)+2*(x+1)^(1/2))/(1-2*(1+I)^(1/2)-5^(1/2)))+1/2*I*dilog((1-5^(1/2)+2*(x+1)^(1/2))/(1+2*(1+I)^(1/2)-5^(1/2)))","A"
31,0,0,423,0.113000," ","int(ln(x+(x+1)^(1/2))^2/(x+1)^2,x)","\int \frac{\ln \left(x +\sqrt{x +1}\right)^{2}}{\left(x +1\right)^{2}}\, dx"," ",0,"int(ln(x+(x+1)^(1/2))^2/(x+1)^2,x)","F"
32,1,252,255,0.025000," ","int(ln(x+(x+1)^(1/2))/x,x)","-\ln \left(\frac{-1+\sqrt{5}-2 \sqrt{x +1}}{\sqrt{5}-3}\right) \ln \left(-1+\sqrt{x +1}\right)-\ln \left(\frac{-1+\sqrt{5}-2 \sqrt{x +1}}{\sqrt{5}+1}\right) \ln \left(1+\sqrt{x +1}\right)-\ln \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{3+\sqrt{5}}\right) \ln \left(-1+\sqrt{x +1}\right)-\ln \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{\sqrt{5}-1}\right) \ln \left(1+\sqrt{x +1}\right)+\ln \left(-1+\sqrt{x +1}\right) \ln \left(x +\sqrt{x +1}\right)+\ln \left(1+\sqrt{x +1}\right) \ln \left(x +\sqrt{x +1}\right)-\dilog \left(\frac{-1+\sqrt{5}-2 \sqrt{x +1}}{\sqrt{5}-3}\right)-\dilog \left(\frac{-1+\sqrt{5}-2 \sqrt{x +1}}{\sqrt{5}+1}\right)-\dilog \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{3+\sqrt{5}}\right)-\dilog \left(\frac{1+\sqrt{5}+2 \sqrt{x +1}}{\sqrt{5}-1}\right)"," ",0,"ln(1+(x+1)^(1/2))*ln(x+(x+1)^(1/2))-ln(1+(x+1)^(1/2))*ln((-1+5^(1/2)-2*(x+1)^(1/2))/(5^(1/2)+1))-ln(1+(x+1)^(1/2))*ln((1+5^(1/2)+2*(x+1)^(1/2))/(5^(1/2)-1))-dilog((-1+5^(1/2)-2*(x+1)^(1/2))/(5^(1/2)+1))-dilog((1+5^(1/2)+2*(x+1)^(1/2))/(5^(1/2)-1))+ln(-1+(x+1)^(1/2))*ln(x+(x+1)^(1/2))-ln(-1+(x+1)^(1/2))*ln((-1+5^(1/2)-2*(x+1)^(1/2))/(5^(1/2)-3))-ln(-1+(x+1)^(1/2))*ln((1+5^(1/2)+2*(x+1)^(1/2))/(3+5^(1/2)))-dilog((-1+5^(1/2)-2*(x+1)^(1/2))/(5^(1/2)-3))-dilog((1+5^(1/2)+2*(x+1)^(1/2))/(3+5^(1/2)))","A"
33,1,113,58,0.172000," ","int(arctan(2*tan(x)),x)","\arctan \left(2 \tan \left(x \right)\right) \arctan \left(\tan \left(x \right)\right)+\frac{i \arctan \left(\tan \left(x \right)\right) \ln \left(1-\frac{3 \left(i \tan \left(x \right)+1\right)^{2}}{\tan^{2}\left(x \right)+1}\right)}{2}-\frac{i \arctan \left(\tan \left(x \right)\right) \ln \left(1-\frac{\left(i \tan \left(x \right)+1\right)^{2}}{3 \left(\tan^{2}\left(x \right)+1\right)}\right)}{2}+\frac{\polylog \left(2, \frac{3 \left(i \tan \left(x \right)+1\right)^{2}}{\tan^{2}\left(x \right)+1}\right)}{4}-\frac{\polylog \left(2, \frac{\left(i \tan \left(x \right)+1\right)^{2}}{3 \left(\tan^{2}\left(x \right)\right)+3}\right)}{4}"," ",0,"arctan(2*tan(x))*arctan(tan(x))+1/2*I*arctan(tan(x))*ln(1-3*(1+I*tan(x))^2/(tan(x)^2+1))+1/4*polylog(2,3*(1+I*tan(x))^2/(tan(x)^2+1))-1/2*I*arctan(tan(x))*ln(1-1/3*(1+I*tan(x))^2/(tan(x)^2+1))-1/4*polylog(2,1/3*(1+I*tan(x))^2/(tan(x)^2+1))","A"
34,0,0,41,0.592000," ","int(arctan(x)*ln(x)/x,x)","\int \frac{\arctan \left(x \right) \ln \left(x \right)}{x}\, dx"," ",0,"int(arctan(x)*ln(x)/x,x)","F"
35,1,171,134,0.382000," ","int(arctan(x)^2*(x^2+1)^(1/2),x)","\frac{\arctan \left(x \right)^{2} \ln \left(1-\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)}{2}-\frac{\arctan \left(x \right)^{2} \ln \left(1+\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)}{2}+i \polylog \left(2, -\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right) \arctan \left(x \right)-i \polylog \left(2, \frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right) \arctan \left(x \right)-\polylog \left(3, -\frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)+\polylog \left(3, \frac{i \left(i x +1\right)}{\sqrt{x^{2}+1}}\right)+\frac{\sqrt{x^{2}+1}\, \left(x \arctan \left(x \right)-2\right) \arctan \left(x \right)}{2}-2 i \arctan \left(\frac{i x +1}{\sqrt{x^{2}+1}}\right)"," ",0,"1/2*(x^2+1)^(1/2)*arctan(x)*(x*arctan(x)-2)-1/2*arctan(x)^2*ln(1+I*(1+I*x)/(x^2+1)^(1/2))+1/2*arctan(x)^2*ln(1-I*(1+I*x)/(x^2+1)^(1/2))+I*arctan(x)*polylog(2,-I*(1+I*x)/(x^2+1)^(1/2))-I*arctan(x)*polylog(2,I*(1+I*x)/(x^2+1)^(1/2))-polylog(3,-I*(1+I*x)/(x^2+1)^(1/2))+polylog(3,I*(1+I*x)/(x^2+1)^(1/2))-2*I*arctan((1+I*x)/(x^2+1)^(1/2))","A"