1,1,18,0,0.175653," ","integrate(1/(cos(z)+sin(z)+2^(1/2)),z, algorithm=""giac"")","-\frac{2 \, {\left(\sqrt{2} + 1\right)}}{\sqrt{2} + \tan\left(\frac{1}{2} \, z\right) + 1}"," ",0,"-2*(sqrt(2) + 1)/(sqrt(2) + tan(1/2*z) + 1)","A",0
2,1,147,0,0.243093," ","integrate(1/((1-x)^(1/2)+(1+x)^(1/2))^2,x, algorithm=""giac"")","\frac{1}{2} \, \pi + \frac{2 \, {\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{x + 1}} - \frac{\sqrt{x + 1}}{\sqrt{2} - \sqrt{-x + 1}}\right)}}{{\left(\frac{\sqrt{2} - \sqrt{-x + 1}}{\sqrt{x + 1}} - \frac{\sqrt{x + 1}}{\sqrt{2} - \sqrt{-x + 1}}\right)}^{2} - 4} - \frac{1}{2 \, x} + \arctan\left(\frac{\sqrt{x + 1} {\left(\frac{{\left(\sqrt{2} - \sqrt{-x + 1}\right)}^{2}}{x + 1} - 1\right)}}{2 \, {\left(\sqrt{2} - \sqrt{-x + 1}\right)}}\right)"," ",0,"1/2*pi + 2*((sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) - sqrt(x + 1)/(sqrt(2) - sqrt(-x + 1)))/(((sqrt(2) - sqrt(-x + 1))/sqrt(x + 1) - sqrt(x + 1)/(sqrt(2) - sqrt(-x + 1)))^2 - 4) - 1/2/x + arctan(1/2*sqrt(x + 1)*((sqrt(2) - sqrt(-x + 1))^2/(x + 1) - 1)/(sqrt(2) - sqrt(-x + 1)))","B",0
3,1,15,0,0.169732," ","integrate(1/(1+cos(x))^2,x, algorithm=""giac"")","\frac{1}{6} \, \tan\left(\frac{1}{2} \, x\right)^{3} + \frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"1/6*tan(1/2*x)^3 + 1/2*tan(1/2*x)","A",0
4,1,43,0,0.175411," ","integrate(sin(x)/(1+x)^(1/2),x, algorithm=""giac"")","-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{i} + \left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x + 1}\right) e^{\left(-i\right)}"," ",0,"-(1/4*I + 1/4)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x + 1))*e^I + (1/4*I - 1/4)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x + 1))*e^(-I)","C",0
5,1,32,0,0.167786," ","integrate(1/(cos(x)+sin(x))^6,x, algorithm=""giac"")","-\frac{15 \, \tan\left(x\right)^{4} + 30 \, \tan\left(x\right)^{3} + 40 \, \tan\left(x\right)^{2} + 20 \, \tan\left(x\right) + 7}{15 \, {\left(\tan\left(x\right) + 1\right)}^{5}}"," ",0,"-1/15*(15*tan(x)^4 + 30*tan(x)^3 + 40*tan(x)^2 + 20*tan(x) + 7)/(tan(x) + 1)^5","A",0
6,1,248,0,0.196863," ","integrate(log(1/x^4+x^4),x, algorithm=""giac"")","x \log\left(x^{4} + \frac{1}{x^{4}}\right) + \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{2} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{2} \, \sqrt{\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{2} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{2} \, \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right) - 4 \, x"," ",0,"x*log(x^4 + 1/x^4) + sqrt(sqrt(2) + 2)*arctan((2*x + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + sqrt(sqrt(2) + 2)*arctan((2*x - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + sqrt(-sqrt(2) + 2)*arctan((2*x + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + sqrt(-sqrt(2) + 2)*arctan((2*x - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/2*sqrt(sqrt(2) + 2)*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/2*sqrt(sqrt(2) + 2)*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/2*sqrt(-sqrt(2) + 2)*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/2*sqrt(-sqrt(2) + 2)*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - 4*x","A",0
7,0,0,0,0.000000," ","integrate(log(1+x)/x/(1+(1+x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \frac{\log\left(x + 1\right)}{x \sqrt{\sqrt{x + 1} + 1}}\,{d x}"," ",0,"integrate(log(x + 1)/(x*sqrt(sqrt(x + 1) + 1)), x)","F",0
8,0,0,0,0.000000," ","integrate(log(1+x)*(1+(1+x)^(1/2))^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{\sqrt{x + 1} + 1} \log\left(x + 1\right)}{x}\,{d x}"," ",0,"integrate(sqrt(sqrt(x + 1) + 1)*log(x + 1)/x, x)","F",0
9,0,0,0,0.000000," ","integrate(1/(1+(x+(x^2+1)^(1/2))^(1/2)),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x + \sqrt{x^{2} + 1}} + 1}\,{d x}"," ",0,"integrate(1/(sqrt(x + sqrt(x^2 + 1)) + 1), x)","F",0
10,1,51,0,0.186299," ","integrate((1+x)^(1/2)/(x+(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","-\frac{4}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - 2 \, \sqrt{\sqrt{x + 1} + 1} - 1}{\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} + 1}\right) + 2 \, \sqrt{x + 1} + 2"," ",0,"-4/5*sqrt(5)*log(-(sqrt(5) - 2*sqrt(sqrt(x + 1) + 1) - 1)/(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) + 1)) + 2*sqrt(x + 1) + 2","A",0
11,1,67,0,0.811054," ","integrate(1/(x-(1+(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","-\frac{2}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} - 1 \right|}}{{\left| \sqrt{5} + 2 \, \sqrt{\sqrt{x + 1} + 1} - 1 \right|}}\right) + 2 \, \log\left({\left| \sqrt{x + 1} - \sqrt{\sqrt{x + 1} + 1} \right|}\right)"," ",0,"-2/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) - 1)/abs(sqrt(5) + 2*sqrt(sqrt(x + 1) + 1) - 1)) + 2*log(abs(sqrt(x + 1) - sqrt(sqrt(x + 1) + 1)))","A",0
12,1,79,0,0.714654," ","integrate(x/(x+(1-(1+x)^(1/2))^(1/2)),x, algorithm=""giac"")","{\left(\sqrt{x + 1} - 1\right)}^{2} - \frac{4}{5} \, \sqrt{5} \log\left(\frac{{\left| -\sqrt{5} + 2 \, \sqrt{-\sqrt{x + 1} + 1} + 1 \right|}}{\sqrt{5} + 2 \, \sqrt{-\sqrt{x + 1} + 1} + 1}\right) + 2 \, \sqrt{x + 1} - 4 \, \sqrt{-\sqrt{x + 1} + 1} - 2"," ",0,"(sqrt(x + 1) - 1)^2 - 4/5*sqrt(5)*log(abs(-sqrt(5) + 2*sqrt(-sqrt(x + 1) + 1) + 1)/(sqrt(5) + 2*sqrt(-sqrt(x + 1) + 1) + 1)) + 2*sqrt(x + 1) - 4*sqrt(-sqrt(x + 1) + 1) - 2","A",0
13,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(x^2+1)/(1+x)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
14,0,0,0,0.000000," ","integrate((x+(1+x)^(1/2))^(1/2)/(x^2+1),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
15,0,0,0,0.000000," ","integrate((1+x^(1/2)+(1+2*x+2*x^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{2 \, x + 2 \, \sqrt{x} + 1} + \sqrt{x} + 1}\,{d x}"," ",0,"integrate(sqrt(sqrt(2*x + 2*sqrt(x) + 1) + sqrt(x) + 1), x)","F",0
16,-2,0,0,0.000000," ","integrate((2^(1/2)+x^(1/2)+(2+2*x+2*2^(1/2)*x^(1/2))^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [x]=[-28]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [x]=[79]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.47"Done"","F(-2)",0
17,1,188,0,0.679267," ","integrate((x+(1+x)^(1/2))^(1/2)/x^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{3} - 3 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{2} - \sqrt{x + \sqrt{x + 1}} + \sqrt{x + 1} + 1}{{\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{4} - 2 \, {\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1}\right)}^{2} + 4 \, \sqrt{x + \sqrt{x + 1}} - 4 \, \sqrt{x + 1}} + \frac{1}{2} \, \arctan\left(\sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} - 1\right) - \frac{3}{4} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} + 2 \right|}\right) + \frac{3}{4} \, \log\left({\left| \sqrt{x + \sqrt{x + 1}} - \sqrt{x + 1} \right|}\right)"," ",0,"-(2*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^3 - 3*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^2 - sqrt(x + sqrt(x + 1)) + sqrt(x + 1) + 1)/((sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^4 - 2*(sqrt(x + sqrt(x + 1)) - sqrt(x + 1))^2 + 4*sqrt(x + sqrt(x + 1)) - 4*sqrt(x + 1)) + 1/2*arctan(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) - 1) - 3/4*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1) + 2)) + 3/4*log(abs(sqrt(x + sqrt(x + 1)) - sqrt(x + 1)))","B",0
18,0,0,0,0.000000," ","integrate((1/x+(1+1/x)^(1/2))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sqrt{\frac{1}{x} + 1} + \frac{1}{x}}\,{d x}"," ",0,"integrate(sqrt(sqrt(1/x + 1) + 1/x), x)","F",0
19,1,75,0,0.249463," ","integrate((1+exp(-x))^(1/2)/(-exp(-x)+exp(x)),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{\sqrt{2} - 1}{\sqrt{2} + 1}\right) + \frac{1}{2} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} - 2 \, e^{x} + 2 \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} - 2 \, e^{x} + 2 \right|}}\right)"," ",0,"-1/2*sqrt(2)*log((sqrt(2) - 1)/(sqrt(2) + 1)) + 1/2*sqrt(2)*log(abs(-2*sqrt(2) + 2*sqrt(e^(2*x) + e^x) - 2*e^x + 2)/abs(2*sqrt(2) + 2*sqrt(e^(2*x) + e^x) - 2*e^x + 2))","B",0
20,1,74,0,0.245685," ","integrate((1+exp(-x))^(1/2)/sinh(x),x, algorithm=""giac"")","-\sqrt{2} \log\left(\frac{\sqrt{2} - 1}{\sqrt{2} + 1}\right) + \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} - 2 \, e^{x} + 2 \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} - 2 \, e^{x} + 2 \right|}}\right)"," ",0,"-sqrt(2)*log((sqrt(2) - 1)/(sqrt(2) + 1)) + sqrt(2)*log(abs(-2*sqrt(2) + 2*sqrt(e^(2*x) + e^x) - 2*e^x + 2)/abs(2*sqrt(2) + 2*sqrt(e^(2*x) + e^x) - 2*e^x + 2))","B",0
21,1,104,0,0.204140," ","integrate(1/(cos(x)+cos(3*x))^5,x, algorithm=""giac"")","-\frac{1483}{2048} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}\right) + \frac{43 \, \sin\left(x\right)^{3} - 45 \, \sin\left(x\right)}{256 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2}} + \frac{10488 \, \sin\left(x\right)^{7} - 14108 \, \sin\left(x\right)^{5} + 6514 \, \sin\left(x\right)^{3} - 993 \, \sin\left(x\right)}{1536 \, {\left(2 \, \sin\left(x\right)^{2} - 1\right)}^{4}} - \frac{523}{512} \, \log\left(\sin\left(x\right) + 1\right) + \frac{523}{512} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-1483/2048*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(x))/abs(2*sqrt(2) + 4*sin(x))) + 1/256*(43*sin(x)^3 - 45*sin(x))/(sin(x)^2 - 1)^2 + 1/1536*(10488*sin(x)^7 - 14108*sin(x)^5 + 6514*sin(x)^3 - 993*sin(x))/(2*sin(x)^2 - 1)^4 - 523/512*log(sin(x) + 1) + 523/512*log(-sin(x) + 1)","A",0
22,1,30,0,0.179379," ","integrate(1/(1+cos(x)+sin(x))^2,x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right) + 1} - \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) + \frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"tan(1/2*x)/(tan(1/2*x) + 1) - log(abs(tan(1/2*x) + 1)) + 1/2*tan(1/2*x)","A",0
23,1,21,0,0.216503," ","integrate((1+tanh(4*x))^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \log\left(\sqrt{e^{\left(8 \, x\right)} + 1} - e^{\left(4 \, x\right)}\right)"," ",0,"-1/4*sqrt(2)*log(sqrt(e^(8*x) + 1) - e^(4*x))","A",0
24,1,377,0,0.591222," ","integrate(tanh(x)/(exp(x)+exp(2*x))^(1/2),x, algorithm=""giac"")","-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2 \, \sqrt{2} - 2} {\left(\frac{i}{\sqrt{2} - 1} + 1\right)} \log\left(\sqrt{2} {\left(\left(20 i + 40\right) \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} - \left(20 i + 40\right) \, e^{x}\right)} + 10 \, \sqrt{2} \sqrt{10 \, \sqrt{2} - 14} + \left(40 i - 20\right) \, \sqrt{2} - \left(2 i + 14\right) \, \sqrt{10 \, \sqrt{2} - 14} - \left(28 i + 56\right) \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} + \left(28 i + 56\right) \, e^{x} - 56 i + 28\right) + \left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2 \, \sqrt{2} - 2} {\left(\frac{i}{\sqrt{2} - 1} + 1\right)} \log\left(\sqrt{2} {\left(\left(20 i + 40\right) \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} - \left(20 i + 40\right) \, e^{x}\right)} - 10 \, \sqrt{2} \sqrt{10 \, \sqrt{2} - 14} + \left(40 i - 20\right) \, \sqrt{2} + \left(2 i + 14\right) \, \sqrt{10 \, \sqrt{2} - 14} - \left(28 i + 56\right) \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} + \left(28 i + 56\right) \, e^{x} - 56 i + 28\right) - \left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2 \, \sqrt{2} + 2} {\left(\frac{i}{\sqrt{2} + 1} + 1\right)} \log\left(4 \, \sqrt{2} {\left(\sqrt{e^{\left(2 \, x\right)} + e^{x}} - e^{x}\right)} + 2 \, \sqrt{2} \sqrt{2 \, \sqrt{2} - 2} - 4 i \, \sqrt{2} - \left(2 i + 2\right) \, \sqrt{2 \, \sqrt{2} - 2} - 4 \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} + 4 \, e^{x} + 4 i\right) + \left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2 \, \sqrt{2} + 2} {\left(\frac{i}{\sqrt{2} + 1} + 1\right)} \log\left(4 \, \sqrt{2} {\left(\sqrt{e^{\left(2 \, x\right)} + e^{x}} - e^{x}\right)} - 2 \, \sqrt{2} \sqrt{2 \, \sqrt{2} - 2} - 4 i \, \sqrt{2} + \left(2 i + 2\right) \, \sqrt{2 \, \sqrt{2} - 2} - 4 \, \sqrt{e^{\left(2 \, x\right)} + e^{x}} + 4 \, e^{x} + 4 i\right) + \frac{2}{\sqrt{e^{\left(2 \, x\right)} + e^{x}} - e^{x}}"," ",0,"-(1/4*I + 1/4)*sqrt(2*sqrt(2) - 2)*(I/(sqrt(2) - 1) + 1)*log(sqrt(2)*((20*I + 40)*sqrt(e^(2*x) + e^x) - (20*I + 40)*e^x) + 10*sqrt(2)*sqrt(10*sqrt(2) - 14) + (40*I - 20)*sqrt(2) - (2*I + 14)*sqrt(10*sqrt(2) - 14) - (28*I + 56)*sqrt(e^(2*x) + e^x) + (28*I + 56)*e^x - 56*I + 28) + (1/4*I + 1/4)*sqrt(2*sqrt(2) - 2)*(I/(sqrt(2) - 1) + 1)*log(sqrt(2)*((20*I + 40)*sqrt(e^(2*x) + e^x) - (20*I + 40)*e^x) - 10*sqrt(2)*sqrt(10*sqrt(2) - 14) + (40*I - 20)*sqrt(2) + (2*I + 14)*sqrt(10*sqrt(2) - 14) - (28*I + 56)*sqrt(e^(2*x) + e^x) + (28*I + 56)*e^x - 56*I + 28) - (1/4*I + 1/4)*sqrt(2*sqrt(2) + 2)*(I/(sqrt(2) + 1) + 1)*log(4*sqrt(2)*(sqrt(e^(2*x) + e^x) - e^x) + 2*sqrt(2)*sqrt(2*sqrt(2) - 2) - 4*I*sqrt(2) - (2*I + 2)*sqrt(2*sqrt(2) - 2) - 4*sqrt(e^(2*x) + e^x) + 4*e^x + 4*I) + (1/4*I + 1/4)*sqrt(2*sqrt(2) + 2)*(I/(sqrt(2) + 1) + 1)*log(4*sqrt(2)*(sqrt(e^(2*x) + e^x) - e^x) - 2*sqrt(2)*sqrt(2*sqrt(2) - 2) - 4*I*sqrt(2) + (2*I + 2)*sqrt(2*sqrt(2) - 2) - 4*sqrt(e^(2*x) + e^x) + 4*e^x + 4*I) + 2/(sqrt(e^(2*x) + e^x) - e^x)","B",0
25,0,0,0,0.000000," ","integrate((sinh(2*x)/cosh(x))^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{\sinh\left(2 \, x\right)}{\cosh\left(x\right)}}\,{d x}"," ",0,"integrate(sqrt(sinh(2*x)/cosh(x)), x)","F",0
26,1,301,0,0.385546," ","integrate(log(x^2+(-x^2+1)^(1/2)),x, algorithm=""giac"")","x \log\left(x^{2} + \sqrt{-x^{2} + 1}\right) - \frac{1}{2} \, \pi \mathrm{sgn}\left(x\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}{2} \, \sqrt{2 \, \sqrt{5} + 2} \arctan\left(-\frac{\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}}{\sqrt{2 \, \sqrt{5} + 2}}\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| \sqrt{2 \, \sqrt{5} - 2} - \frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} \right|}\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 2} \log\left({\left| -\sqrt{2 \, \sqrt{5} - 2} - \frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} \right|}\right) - 2 \, x - \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,"x*log(x^2 + sqrt(-x^2 + 1)) - 1/2*pi*sgn(x) + 1/2*sqrt(2*sqrt(5) + 2)*arctan(x/sqrt(1/2*sqrt(5) + 1/2)) - 1/2*sqrt(2*sqrt(5) + 2)*arctan(-(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt(2*sqrt(5) + 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(1/2*sqrt(5) - 1/2))) - 1/4*sqrt(2*sqrt(5) - 2)*log(abs(sqrt(2*sqrt(5) - 2) - x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x)) + 1/4*sqrt(2*sqrt(5) - 2)*log(abs(-sqrt(2*sqrt(5) - 2) - x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x)) - 2*x - arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))","B",0
27,0,0,0,0.000000," ","integrate(log(1+exp(x))/(1+exp(2*x)),x, algorithm=""giac"")","\int \frac{\log\left(e^{x} + 1\right)}{e^{\left(2 \, x\right)} + 1}\,{d x}"," ",0,"integrate(log(e^x + 1)/(e^(2*x) + 1), x)","F",0
28,0,0,0,0.000000," ","integrate(cosh(x)*log(1+cosh(x)^2)^2,x, algorithm=""giac"")","\int \cosh\left(x\right) \log\left(\cosh\left(x\right)^{2} + 1\right)^{2}\,{d x}"," ",0,"integrate(cosh(x)*log(cosh(x)^2 + 1)^2, x)","F",0
29,0,0,0,0.000000," ","integrate(cosh(x)*log(cosh(x)^2+sinh(x))^2,x, algorithm=""giac"")","\int \cosh\left(x\right) \log\left(\cosh\left(x\right)^{2} + \sinh\left(x\right)\right)^{2}\,{d x}"," ",0,"integrate(cosh(x)*log(cosh(x)^2 + sinh(x))^2, x)","F",0
30,0,0,0,0.000000," ","integrate(log(x+(1+x)^(1/2))/(x^2+1),x, algorithm=""giac"")","\int \frac{\log\left(x + \sqrt{x + 1}\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(log(x + sqrt(x + 1))/(x^2 + 1), x)","F",0
31,0,0,0,0.000000," ","integrate(log(x+(1+x)^(1/2))^2/(1+x)^2,x, algorithm=""giac"")","\int \frac{\log\left(x + \sqrt{x + 1}\right)^{2}}{{\left(x + 1\right)}^{2}}\,{d x}"," ",0,"integrate(log(x + sqrt(x + 1))^2/(x + 1)^2, x)","F",0
32,0,0,0,0.000000," ","integrate(log(x+(1+x)^(1/2))/x,x, algorithm=""giac"")","\int \frac{\log\left(x + \sqrt{x + 1}\right)}{x}\,{d x}"," ",0,"integrate(log(x + sqrt(x + 1))/x, x)","F",0
33,0,0,0,0.000000," ","integrate(arctan(2*tan(x)),x, algorithm=""giac"")","\int \arctan\left(2 \, \tan\left(x\right)\right)\,{d x}"," ",0,"integrate(arctan(2*tan(x)), x)","F",0
34,0,0,0,0.000000," ","integrate(arctan(x)*log(x)/x,x, algorithm=""giac"")","\int \frac{\arctan\left(x\right) \log\left(x\right)}{x}\,{d x}"," ",0,"integrate(arctan(x)*log(x)/x, x)","F",0
35,0,0,0,0.000000," ","integrate(arctan(x)^2*(x^2+1)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{2} + 1} \arctan\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)*arctan(x)^2, x)","F",0
