1,1,31,0,0.420442," ","integrate(1/(-b^2*x^2+a^2),x, algorithm=""maxima"")","\frac{\log\left(b x + a\right)}{2 \, a b} - \frac{\log\left(b x - a\right)}{2 \, a b}"," ",0,"1/2*log(b*x + a)/(a*b) - 1/2*log(b*x - a)/(a*b)","B",0
2,1,14,0,0.948377," ","integrate(1/(b^2*x^2+a^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b x}{a}\right)}{a b}"," ",0,"arctan(b*x/a)/(a*b)","A",0
3,1,17,0,0.425906," ","integrate(sec(2*a*x),x, algorithm=""maxima"")","\frac{\log\left(\sec\left(2 \, a x\right) + \tan\left(2 \, a x\right)\right)}{2 \, a}"," ",0,"1/2*log(sec(2*a*x) + tan(2*a*x))/a","A",0
4,1,19,0,0.428198," ","integrate(1/4/sin(1/3*x),x, algorithm=""maxima"")","-\frac{3}{8} \, \log\left(\cos\left(\frac{1}{3} \, x\right) + 1\right) + \frac{3}{8} \, \log\left(\cos\left(\frac{1}{3} \, x\right) - 1\right)"," ",0,"-3/8*log(cos(1/3*x) + 1) + 3/8*log(cos(1/3*x) - 1)","B",0
5,1,27,0,0.434273," ","integrate(-1/cos(1/4*pi+2*x),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(\sin\left(\frac{1}{4} \, \pi + 2 \, x\right) + 1\right) + \frac{1}{4} \, \log\left(\sin\left(\frac{1}{4} \, \pi + 2 \, x\right) - 1\right)"," ",0,"-1/4*log(sin(1/4*pi + 2*x) + 1) + 1/4*log(sin(1/4*pi + 2*x) - 1)","B",0
6,1,4,0,0.421118," ","integrate(sec(x)*tan(x),x, algorithm=""maxima"")","\frac{1}{\cos\left(x\right)}"," ",0,"1/cos(x)","A",0
7,1,6,0,0.443400," ","integrate(cot(x)*csc(x),x, algorithm=""maxima"")","-\frac{1}{\sin\left(x\right)}"," ",0,"-1/sin(x)","A",0
8,1,27,0,0.425684," ","integrate(tan(x)/sin(2*x),x, algorithm=""maxima"")","\frac{\sin\left(2 \, x\right)}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}"," ",0,"sin(2*x)/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
9,1,9,0,0.437052," ","integrate(1/(1+cos(x)),x, algorithm=""maxima"")","\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}"," ",0,"sin(x)/(cos(x) + 1)","A",0
10,1,10,0,0.418498," ","integrate(1/(1-cos(x)),x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{\sin\left(x\right)}"," ",0,"-(cos(x) + 1)/sin(x)","A",0
11,1,13,0,0.436356," ","integrate(sin(x)/(a-b*cos(x)),x, algorithm=""maxima"")","\frac{\log\left(b \cos\left(x\right) - a\right)}{b}"," ",0,"log(b*cos(x) - a)/b","A",0
12,1,15,0,0.986656," ","integrate(cos(x)/(a^2+b^2*sin(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b \sin\left(x\right)}{a}\right)}{a b}"," ",0,"arctan(b*sin(x)/a)/(a*b)","A",0
13,1,33,0,0.433872," ","integrate(cos(x)/(a^2-b^2*sin(x)^2),x, algorithm=""maxima"")","\frac{\log\left(b \sin\left(x\right) + a\right)}{2 \, a b} - \frac{\log\left(b \sin\left(x\right) - a\right)}{2 \, a b}"," ",0,"1/2*log(b*sin(x) + a)/(a*b) - 1/2*log(b*sin(x) - a)/(a*b)","B",0
14,1,17,0,0.438303," ","integrate(sin(2*x)/(a^2+b^2*sin(x)^2),x, algorithm=""maxima"")","\frac{\log\left(b^{2} \sin\left(x\right)^{2} + a^{2}\right)}{b^{2}}"," ",0,"log(b^2*sin(x)^2 + a^2)/b^2","A",0
15,1,20,0,0.432360," ","integrate(sin(2*x)/(a^2-b^2*sin(x)^2),x, algorithm=""maxima"")","-\frac{\log\left(b^{2} \sin\left(x\right)^{2} - a^{2}\right)}{b^{2}}"," ",0,"-log(b^2*sin(x)^2 - a^2)/b^2","A",0
16,1,18,0,0.422122," ","integrate(sin(2*x)/(a^2+b^2*cos(x)^2),x, algorithm=""maxima"")","-\frac{\log\left(b^{2} \cos\left(x\right)^{2} + a^{2}\right)}{b^{2}}"," ",0,"-log(b^2*cos(x)^2 + a^2)/b^2","A",0
17,1,19,0,0.445693," ","integrate(sin(2*x)/(a^2-b^2*cos(x)^2),x, algorithm=""maxima"")","\frac{\log\left(b^{2} \cos\left(x\right)^{2} - a^{2}\right)}{b^{2}}"," ",0,"log(b^2*cos(x)^2 - a^2)/b^2","A",0
18,1,13,0,0.946887," ","integrate(1/(4-cos(x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} \tan\left(x\right)\right)"," ",0,"1/6*sqrt(3)*arctan(2/3*sqrt(3)*tan(x))","A",0
19,1,15,0,0.428531," ","integrate(exp(x)/(-1+exp(2*x)),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(e^{x} + 1\right) + \frac{1}{2} \, \log\left(e^{x} - 1\right)"," ",0,"-1/2*log(e^x + 1) + 1/2*log(e^x - 1)","B",0
20,1,3,0,0.420367," ","integrate(1/x/log(x),x, algorithm=""maxima"")","\log\left(\log\left(x\right)\right)"," ",0,"log(log(x))","A",0
21,1,3,0,0.958152," ","integrate(1/x/(1+log(x)^2),x, algorithm=""maxima"")","\arctan\left(\log\left(x\right)\right)"," ",0,"arctan(log(x))","A",0
22,1,7,0,0.435357," ","integrate(1/x/(1-log(x)),x, algorithm=""maxima"")","-\log\left(\log\left(x\right) - 1\right)"," ",0,"-log(log(x) - 1)","A",0
23,1,9,0,0.419446," ","integrate(1/x/(1+log(x/a)),x, algorithm=""maxima"")","\log\left(\log\left(\frac{x}{a}\right) + 1\right)"," ",0,"log(log(x/a) + 1)","A",0
24,1,22,0,0.433136," ","integrate((1+x-x^(1/2))^2/x^2,x, algorithm=""maxima"")","x - 4 \, \sqrt{x} + \frac{4 \, \sqrt{x} - 1}{x} + 3 \, \log\left(x\right)"," ",0,"x - 4*sqrt(x) + (4*sqrt(x) - 1)/x + 3*log(x)","A",0
25,1,20,0,0.426804," ","integrate((2-x^(2/3))*(x+x^(1/2))/x^(3/2),x, algorithm=""maxima"")","-\frac{6}{7} \, x^{\frac{7}{6}} - \frac{3}{2} \, x^{\frac{2}{3}} + 4 \, \sqrt{x} + 2 \, \log\left(x\right)"," ",0,"-6/7*x^(7/6) - 3/2*x^(2/3) + 4*sqrt(x) + 2*log(x)","A",0
26,1,10,0,0.423325," ","integrate((-1+2*x)/(3+2*x),x, algorithm=""maxima"")","x - 2 \, \log\left(2 \, x + 3\right)"," ",0,"x - 2*log(2*x + 3)","A",0
27,1,36,0,0.970514," ","integrate((-5+2*x)/(3*x^2-2),x, algorithm=""maxima"")","-\frac{5}{12} \, \sqrt{6} \log\left(\frac{3 \, x - \sqrt{6}}{3 \, x + \sqrt{6}}\right) + \frac{1}{3} \, \log\left(3 \, x^{2} - 2\right)"," ",0,"-5/12*sqrt(6)*log((3*x - sqrt(6))/(3*x + sqrt(6))) + 1/3*log(3*x^2 - 2)","A",0
28,1,23,0,0.972037," ","integrate((-5+2*x)/(3*x^2+2),x, algorithm=""maxima"")","-\frac{5}{6} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{1}{3} \, \log\left(3 \, x^{2} + 2\right)"," ",0,"-5/6*sqrt(6)*arctan(1/2*sqrt(6)*x) + 1/3*log(3*x^2 + 2)","A",0
29,1,13,0,0.424107," ","integrate(sin(1/4*x)*sin(x),x, algorithm=""maxima"")","-\frac{2}{5} \, \sin\left(\frac{5}{4} \, x\right) + \frac{2}{3} \, \sin\left(\frac{3}{4} \, x\right)"," ",0,"-2/5*sin(5/4*x) + 2/3*sin(3/4*x)","A",0
30,1,11,0,0.431906," ","integrate(cos(3*x)*cos(4*x),x, algorithm=""maxima"")","\frac{1}{14} \, \sin\left(7 \, x\right) + \frac{1}{2} \, \sin\left(x\right)"," ",0,"1/14*sin(7*x) + 1/2*sin(x)","A",0
31,1,186,0,1.028613," ","integrate(-tan(x)*tan(a-x),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2} - 2 \, \cos\left(2 \, a\right) + 1\right)} x + {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2} - 1\right)} \arctan\left(\sin\left(2 \, a\right) + \sin\left(2 \, x\right), \cos\left(2 \, a\right) + \cos\left(2 \, x\right)\right) - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2} - 1\right)} \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) - \log\left(\cos\left(2 \, a\right)^{2} + 2 \, \cos\left(2 \, a\right) \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \sin\left(2 \, a\right)^{2} + 2 \, \sin\left(2 \, a\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2}\right) \sin\left(2 \, a\right) + \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) \sin\left(2 \, a\right)}{\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2} - 2 \, \cos\left(2 \, a\right) + 1}"," ",0,"-((cos(2*a)^2 + sin(2*a)^2 - 2*cos(2*a) + 1)*x + (cos(2*a)^2 + sin(2*a)^2 - 1)*arctan2(sin(2*a) + sin(2*x), cos(2*a) + cos(2*x)) - (cos(2*a)^2 + sin(2*a)^2 - 1)*arctan2(sin(2*x), cos(2*x) + 1) - log(cos(2*a)^2 + 2*cos(2*a)*cos(2*x) + cos(2*x)^2 + sin(2*a)^2 + 2*sin(2*a)*sin(2*x) + sin(2*x)^2)*sin(2*a) + log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)*sin(2*a))/(cos(2*a)^2 + sin(2*a)^2 - 2*cos(2*a) + 1)","B",0
32,1,10,0,0.426704," ","integrate(sin(x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x - \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x - 1/4*sin(2*x)","A",0
33,1,10,0,0.433311," ","integrate(cos(x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x + 1/4*sin(2*x)","A",0
34,1,6,0,0.430945," ","integrate(cos(x)^3*sin(x),x, algorithm=""maxima"")","-\frac{1}{4} \, \cos\left(x\right)^{4}"," ",0,"-1/4*cos(x)^4","A",0
35,1,14,0,0.428471," ","integrate(cos(x)^3/sin(x)^4,x, algorithm=""maxima"")","\frac{3 \, \sin\left(x\right)^{2} - 1}{3 \, \sin\left(x\right)^{3}}"," ",0,"1/3*(3*sin(x)^2 - 1)/sin(x)^3","A",0
36,1,9,0,0.429744," ","integrate(1/cos(x)^2/sin(x)^2,x, algorithm=""maxima"")","-\frac{1}{\tan\left(x\right)} + \tan\left(x\right)"," ",0,"-1/tan(x) + tan(x)","A",0
37,1,12,0,0.978875," ","integrate(cot(3/4*x)^2,x, algorithm=""maxima"")","-x - \frac{4}{3 \, \tan\left(\frac{3}{4} \, x\right)}"," ",0,"-x - 4/3/tan(3/4*x)","A",0
38,1,12,0,0.964632," ","integrate((1+tan(2*x))^2,x, algorithm=""maxima"")","\log\left(\sec\left(2 \, x\right)\right) + \frac{1}{2} \, \tan\left(2 \, x\right)"," ",0,"log(sec(2*x)) + 1/2*tan(2*x)","A",0
39,1,12,0,0.953060," ","integrate((-cot(x)+tan(x))^2,x, algorithm=""maxima"")","-4 \, x - \frac{1}{\tan\left(x\right)} + \tan\left(x\right)"," ",0,"-4*x - 1/tan(x) + tan(x)","A",0
40,1,14,0,0.964776," ","integrate((-sec(x)+tan(x))^2,x, algorithm=""maxima"")","-x - \frac{2}{\cos\left(x\right)} + 2 \, \tan\left(x\right)"," ",0,"-x - 2/cos(x) + 2*tan(x)","A",0
41,1,28,0,0.961729," ","integrate(sin(x)/(1+sin(x)),x, algorithm=""maxima"")","\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2/(sin(x)/(cos(x) + 1) + 1) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
42,1,23,0,0.955861," ","integrate(cos(x)/(1-cos(x)),x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{\sin\left(x\right)} - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-(cos(x) + 1)/sin(x) - 2*arctan(sin(x)/(cos(x) + 1))","A",0
43,1,18,0,0.455551," ","integrate((-1+exp(1/2*x))^3/exp(1/2*x),x, algorithm=""maxima"")","3 \, x - 6 \, e^{\left(\frac{1}{2} \, x\right)} + 2 \, e^{\left(-\frac{1}{2} \, x\right)} + e^{x}"," ",0,"3*x - 6*e^(1/2*x) + 2*e^(-1/2*x) + e^x","A",0
44,1,13,0,0.420354," ","integrate(1/(x^2-6*x+5),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(x - 1\right) + \frac{1}{4} \, \log\left(x - 5\right)"," ",0,"-1/4*log(x - 1) + 1/4*log(x - 5)","A",0
45,1,10,0,0.956498," ","integrate(x^2/(x^6-6*x^3+13),x, algorithm=""maxima"")","\frac{1}{6} \, \arctan\left(\frac{1}{2} \, x^{3} - \frac{3}{2}\right)"," ",0,"1/6*arctan(1/2*x^3 - 3/2)","A",0
46,1,35,0,0.953078," ","integrate((2+x)/(x^2-4*x-1),x, algorithm=""maxima"")","\frac{2}{5} \, \sqrt{5} \log\left(\frac{x - \sqrt{5} - 2}{x + \sqrt{5} - 2}\right) + \frac{1}{2} \, \log\left(x^{2} - 4 \, x - 1\right)"," ",0,"2/5*sqrt(5)*log((x - sqrt(5) - 2)/(x + sqrt(5) - 2)) + 1/2*log(x^2 - 4*x - 1)","A",0
47,1,25,0,0.428134," ","integrate(1/(1+(1+x)^(1/3)),x, algorithm=""maxima"")","\frac{3}{2} \, {\left(x + 1\right)}^{\frac{2}{3}} - 3 \, {\left(x + 1\right)}^{\frac{1}{3}} + 3 \, \log\left({\left(x + 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"3/2*(x + 1)^(2/3) - 3*(x + 1)^(1/3) + 3*log((x + 1)^(1/3) + 1)","A",0
48,1,18,0,0.967264," ","integrate(1/(a*x+b)/x^(1/2),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"2*arctan(a*sqrt(x)/sqrt(a*b))/sqrt(a*b)","A",0
49,1,22,0,0.956751," ","integrate(x^3*(x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{5} \, {\left(x^{2} + 1\right)}^{\frac{3}{2}} x^{2} - \frac{2}{15} \, {\left(x^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/5*(x^2 + 1)^(3/2)*x^2 - 2/15*(x^2 + 1)^(3/2)","A",0
50,1,18,0,0.956430," ","integrate(x/(a^4-x^4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \arctan\left(\frac{\sqrt{a^{4} - x^{4}}}{x^{2}}\right)"," ",0,"-1/2*arctan(sqrt(a^4 - x^4)/x^2)","A",0
51,1,12,0,0.969186," ","integrate(1/x/(-a^2+x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(\frac{a}{{\left| x \right|}}\right)}{a}"," ",0,"-arcsin(a/abs(x))/a","A",0
52,1,34,0,0.426816," ","integrate(1/x/(a^2-x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{2 \, a^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{a^{2} - x^{2}} a}{{\left| x \right|}}\right)}{a}"," ",0,"-log(2*a^2/abs(x) + 2*sqrt(a^2 - x^2)*a/abs(x))/a","A",0
53,1,12,0,0.502808," ","integrate(1/x/(a^2+x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\operatorname{arsinh}\left(\frac{a}{{\left| x \right|}}\right)}{a}"," ",0,"-arcsinh(a/abs(x))/a","A",0
54,1,8,0,0.972436," ","integrate(1/(-x^2+x+2)^(1/2),x, algorithm=""maxima"")","-\arcsin\left(-\frac{2}{3} \, x + \frac{1}{3}\right)"," ",0,"-arcsin(-2/3*x + 1/3)","A",0
55,1,16,0,0.996992," ","integrate(1/(3*x^2-4*x+5)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \operatorname{arsinh}\left(\frac{1}{11} \, \sqrt{11} {\left(3 \, x - 2\right)}\right)"," ",0,"1/3*sqrt(3)*arcsinh(1/11*sqrt(11)*(3*x - 2))","A",0
56,1,6,0,0.970654," ","integrate(1/(-x^2+x)^(1/2),x, algorithm=""maxima"")","\arcsin\left(2 \, x - 1\right)"," ",0,"arcsin(2*x - 1)","A",0
57,1,21,0,0.969030," ","integrate((1+2*x)/(-x^2+x+2)^(1/2),x, algorithm=""maxima"")","-2 \, \sqrt{-x^{2} + x + 2} - 2 \, \arcsin\left(-\frac{2}{3} \, x + \frac{1}{3}\right)"," ",0,"-2*sqrt(-x^2 + x + 2) - 2*arcsin(-2/3*x + 1/3)","A",0
58,1,33,0,0.957689," ","integrate(1/x/(-x^2+x+2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{2 \, \sqrt{2} \sqrt{-x^{2} + x + 2}}{{\left| x \right|}} + \frac{4}{{\left| x \right|}} + 1\right)"," ",0,"-1/2*sqrt(2)*log(2*sqrt(2)*sqrt(-x^2 + x + 2)/abs(x) + 4/abs(x) + 1)","A",0
59,1,17,0,0.961089," ","integrate(1/(-2+x)/(-x^2+x+2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{-x^{2} + x + 2}}{3 \, {\left(x - 2\right)}}"," ",0,"2/3*sqrt(-x^2 + x + 2)/(x - 2)","A",0
60,1,33,0,0.446628," ","integrate((2+3*sin(x))/(1-cos(x))/sin(x),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(x\right) + 1\right)}^{2}}{2 \, \sin\left(x\right)^{2}} - \frac{3 \, {\left(\cos\left(x\right) + 1\right)}}{\sin\left(x\right)} + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/2*(cos(x) + 1)^2/sin(x)^2 - 3*(cos(x) + 1)/sin(x) + log(sin(x)/(cos(x) + 1))","A",0
61,1,13,0,0.973331," ","integrate(1/(2+3*cos(x)^2),x, algorithm=""maxima"")","\frac{1}{10} \, \sqrt{10} \arctan\left(\frac{1}{5} \, \sqrt{10} \tan\left(x\right)\right)"," ",0,"1/10*sqrt(10)*arctan(1/5*sqrt(10)*tan(x))","A",0
62,1,47,0,0.437908," ","integrate((1-tan(x))/sin(2*x),x, algorithm=""maxima"")","-\frac{\sin\left(2 \, x\right)}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1} - \frac{1}{4} \, \log\left(\cos\left(2 \, x\right) + 1\right) + \frac{1}{4} \, \log\left(\cos\left(2 \, x\right) - 1\right)"," ",0,"-sin(2*x)/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) - 1/4*log(cos(2*x) + 1) + 1/4*log(cos(2*x) - 1)","B",0
63,1,15,0,0.434783," ","integrate((1+tan(x)^2)/(1-tan(x)^2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\tan\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\tan\left(x\right) - 1\right)"," ",0,"1/2*log(tan(x) + 1) - 1/2*log(tan(x) - 1)","A",0
64,1,14,0,0.430369," ","integrate((a^2-4*cos(x)^2)^(3/4)*sin(2*x),x, algorithm=""maxima"")","\frac{1}{7} \, {\left(a^{2} - 4 \, \cos\left(x\right)^{2}\right)}^{\frac{7}{4}}"," ",0,"1/7*(a^2 - 4*cos(x)^2)^(7/4)","A",0
65,1,14,0,0.434735," ","integrate(sin(2*x)/(a^2-4*sin(x)^2)^(1/3),x, algorithm=""maxima"")","-\frac{3}{8} \, {\left(a^{2} - 4 \, \sin\left(x\right)^{2}\right)}^{\frac{2}{3}}"," ",0,"-3/8*(a^2 - 4*sin(x)^2)^(2/3)","A",0
66,1,15,0,0.975325," ","integrate(1/(-1+a^(2*x))^(1/2),x, algorithm=""maxima"")","\frac{\arctan\left(\sqrt{a^{2 \, x} - 1}\right)}{\log\left(a\right)}"," ",0,"arctan(sqrt(a^(2*x) - 1))/log(a)","A",0
67,1,18,0,0.441935," ","integrate(exp(1/2*x)/(-1+exp(x))^(1/2),x, algorithm=""maxima"")","2 \, \log\left(2 \, \sqrt{e^{x} - 1} + 2 \, e^{\left(\frac{1}{2} \, x\right)}\right)"," ",0,"2*log(2*sqrt(e^x - 1) + 2*e^(1/2*x))","A",0
68,1,12,0,0.430617," ","integrate(arctan(x)^n/(x^2+1),x, algorithm=""maxima"")","\frac{\arctan\left(x\right)^{n + 1}}{n + 1}"," ",0,"arctan(x)^(n + 1)/(n + 1)","A",0
69,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
70,1,6,0,0.991381," ","integrate(1/arccos(x)^3/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2 \, \arccos\left(x\right)^{2}}"," ",0,"1/2/arccos(x)^2","A",0
71,1,17,0,0.437065," ","integrate(x*log(x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, \log\left(x\right)^{2} - 2 \, \log\left(x\right) + 1\right)} x^{2}"," ",0,"1/4*(2*log(x)^2 - 2*log(x) + 1)*x^2","A",0
72,1,13,0,0.429442," ","integrate(log(x)/x^5,x, algorithm=""maxima"")","-\frac{\log\left(x\right)}{4 \, x^{4}} - \frac{1}{16 \, x^{4}}"," ",0,"-1/4*log(x)/x^4 - 1/16/x^4","A",0
73,1,28,0,0.445238," ","integrate(x^2*log((-1+x)/x),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left(\frac{x - 1}{x}\right) - \frac{1}{6} \, x^{2} - \frac{1}{3} \, x - \frac{1}{3} \, \log\left(x - 1\right)"," ",0,"1/3*x^3*log((x - 1)/x) - 1/6*x^2 - 1/3*x - 1/3*log(x - 1)","A",0
74,1,15,0,0.431939," ","integrate(cos(x)^5,x, algorithm=""maxima"")","\frac{1}{5} \, \sin\left(x\right)^{5} - \frac{2}{3} \, \sin\left(x\right)^{3} + \sin\left(x\right)"," ",0,"1/5*sin(x)^5 - 2/3*sin(x)^3 + sin(x)","A",0
75,1,18,0,0.433787," ","integrate(cos(x)^4*sin(x)^2,x, algorithm=""maxima"")","\frac{1}{48} \, \sin\left(2 \, x\right)^{3} + \frac{1}{16} \, x - \frac{1}{64} \, \sin\left(4 \, x\right)"," ",0,"1/48*sin(2*x)^3 + 1/16*x - 1/64*sin(4*x)","A",0
76,1,42,0,0.434201," ","integrate(1/sin(x)^5,x, algorithm=""maxima"")","\frac{3 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)}{8 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}} - \frac{3}{16} \, \log\left(\cos\left(x\right) + 1\right) + \frac{3}{16} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"1/8*(3*cos(x)^3 - 5*cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) - 3/16*log(cos(x) + 1) + 3/16*log(cos(x) - 1)","B",0
77,1,11,0,0.440250," ","integrate(sin(x)/exp(x),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\cos\left(x\right) + \sin\left(x\right)\right)} e^{\left(-x\right)}"," ",0,"-1/2*(cos(x) + sin(x))*e^(-x)","A",0
78,1,19,0,0.443636," ","integrate(exp(2*x)*sin(3*x),x, algorithm=""maxima"")","-\frac{1}{13} \, {\left(3 \, \cos\left(3 \, x\right) - 2 \, \sin\left(3 \, x\right)\right)} e^{\left(2 \, x\right)}"," ",0,"-1/13*(3*cos(3*x) - 2*sin(3*x))*e^(2*x)","A",0
79,1,24,0,0.441726," ","integrate(a^x*cos(x),x, algorithm=""maxima"")","\frac{a^{x} \cos\left(x\right) \log\left(a\right) + a^{x} \sin\left(x\right)}{\log\left(a\right)^{2} + 1}"," ",0,"(a^x*cos(x)*log(a) + a^x*sin(x))/(log(a)^2 + 1)","A",0
80,1,10,0,0.434486," ","integrate(cos(log(x)),x, algorithm=""maxima"")","\frac{1}{2} \, x {\left(\cos\left(\log\left(x\right)\right) + \sin\left(\log\left(x\right)\right)\right)}"," ",0,"1/2*x*(cos(log(x)) + sin(log(x)))","A",0
81,1,94,0,0.973672," ","integrate(log(cos(x))*sec(x)^2,x, algorithm=""maxima"")","-\frac{2 \, \log\left(-\frac{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1}{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1}\right) \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}} - \frac{2 \, \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}} - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2*log(-(sin(x)^2/(cos(x) + 1)^2 - 1)/(sin(x)^2/(cos(x) + 1)^2 + 1))*sin(x)/((sin(x)^2/(cos(x) + 1)^2 - 1)*(cos(x) + 1)) - 2*sin(x)/((sin(x)^2/(cos(x) + 1)^2 - 1)*(cos(x) + 1)) - 2*arctan(sin(x)/(cos(x) + 1))","B",0
82,1,107,0,0.991605," ","integrate(x*tan(x)^2,x, algorithm=""maxima"")","-\frac{x^{2} \cos\left(2 \, x\right)^{2} + x^{2} \sin\left(2 \, x\right)^{2} + 2 \, x^{2} \cos\left(2 \, x\right) + x^{2} - {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) - 4 \, x \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-1/2*(x^2*cos(2*x)^2 + x^2*sin(2*x)^2 + 2*x^2*cos(2*x) + x^2 - (cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) - 4*x*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
83,1,33,0,0.958599," ","integrate(arcsin(x)/x^2,x, algorithm=""maxima"")","-\frac{\arcsin\left(x\right)}{x} - \log\left(\frac{2 \, \sqrt{-x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)"," ",0,"-arcsin(x)/x - log(2*sqrt(-x^2 + 1)/abs(x) + 2/abs(x))","A",0
84,1,23,0,0.973250," ","integrate(arcsin(x)^2,x, algorithm=""maxima"")","x \arcsin\left(x\right)^{2} + 2 \, \sqrt{-x^{2} + 1} \arcsin\left(x\right) - 2 \, x"," ",0,"x*arcsin(x)^2 + 2*sqrt(-x^2 + 1)*arcsin(x) - 2*x","A",0
85,1,24,0,0.993160," ","integrate(x^2*arctan(x)/(x^2+1),x, algorithm=""maxima"")","{\left(x - \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{1}{2} \, \arctan\left(x\right)^{2} - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"(x - arctan(x))*arctan(x) + 1/2*arctan(x)^2 - 1/2*log(x^2 + 1)","A",0
86,1,78,0,0.965612," ","integrate(arccos((x/(1+x))^(1/2)),x, algorithm=""maxima"")","-\frac{\arccos\left(\sqrt{\frac{x}{x + 1}}\right)}{\frac{x}{x + 1} - 1} - \frac{\sqrt{-\frac{x}{x + 1} + 1}}{2 \, {\left(\sqrt{\frac{x}{x + 1}} + 1\right)}} - \frac{\sqrt{-\frac{x}{x + 1} + 1}}{2 \, {\left(\sqrt{\frac{x}{x + 1}} - 1\right)}}"," ",0,"-arccos(sqrt(x/(x + 1)))/(x/(x + 1) - 1) - 1/2*sqrt(-x/(x + 1) + 1)/(sqrt(x/(x + 1)) + 1) - 1/2*sqrt(-x/(x + 1) + 1)/(sqrt(x/(x + 1)) - 1)","B",0
87,1,21,0,0.441852," ","integrate((3*x^2+2*x)^3,x, algorithm=""maxima"")","\frac{27}{7} \, x^{7} + 9 \, x^{6} + \frac{36}{5} \, x^{5} + 2 \, x^{4}"," ",0,"27/7*x^7 + 9*x^6 + 36/5*x^5 + 2*x^4","A",0
88,1,29,0,0.436268," ","integrate((-1+x)*(3*x^2+2*x-1)^2,x, algorithm=""maxima"")","\frac{3}{2} \, x^{6} + \frac{3}{5} \, x^{5} - \frac{7}{2} \, x^{4} - \frac{2}{3} \, x^{3} + \frac{5}{2} \, x^{2} - x"," ",0,"3/2*x^6 + 3/5*x^5 - 7/2*x^4 - 2/3*x^3 + 5/2*x^2 - x","A",0
89,1,23,0,0.434887," ","integrate(x^(-1+k)*(a+b*x^k)^n,x, algorithm=""maxima"")","\frac{{\left(b x^{k} + a\right)}^{n + 1}}{b k {\left(n + 1\right)}}"," ",0,"(b*x^k + a)^(n + 1)/(b*k*(n + 1))","A",0
90,1,22,0,0.429195," ","integrate(x^3/(1+2*x),x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} - \frac{1}{8} \, x^{2} + \frac{1}{8} \, x - \frac{1}{16} \, \log\left(2 \, x + 1\right)"," ",0,"1/6*x^3 - 1/8*x^2 + 1/8*x - 1/16*log(2*x + 1)","A",0
91,1,26,0,0.965101," ","integrate(x^6/(3*x^2+2),x, algorithm=""maxima"")","\frac{1}{15} \, x^{5} - \frac{2}{27} \, x^{3} - \frac{4}{81} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{4}{27} \, x"," ",0,"1/15*x^5 - 2/27*x^3 - 4/81*sqrt(6)*arctan(1/2*sqrt(6)*x) + 4/27*x","A",0
92,1,15,0,0.432698," ","integrate(1/(3*x^2-7*x+2),x, algorithm=""maxima"")","-\frac{1}{5} \, \log\left(3 \, x - 1\right) + \frac{1}{5} \, \log\left(x - 2\right)"," ",0,"-1/5*log(3*x - 1) + 1/5*log(x - 2)","A",0
93,1,28,0,0.999129," ","integrate((-1+3*x)/(x^2-x+1),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{3}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 3/2*log(x^2 - x + 1)","A",0
94,1,21,0,0.968381," ","integrate(x^2/(x^2+2*x+5),x, algorithm=""maxima"")","x - \frac{3}{2} \, \arctan\left(\frac{1}{2} \, x + \frac{1}{2}\right) - \log\left(x^{2} + 2 \, x + 5\right)"," ",0,"x - 3/2*arctan(1/2*x + 1/2) - log(x^2 + 2*x + 5)","A",0
95,1,38,0,0.954279," ","integrate((6*x^4-5*x^3+4*x^2)/(2*x^2-x+1),x, algorithm=""maxima"")","x^{3} - \frac{1}{2} \, x^{2} + \frac{1}{14} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(4 \, x - 1\right)}\right) + \frac{1}{4} \, \log\left(2 \, x^{2} - x + 1\right)"," ",0,"x^3 - 1/2*x^2 + 1/14*sqrt(7)*arctan(1/7*sqrt(7)*(4*x - 1)) + 1/4*log(2*x^2 - x + 1)","A",0
96,1,17,0,0.430870," ","integrate((x^2+x-1)/(x^3+x^2-6*x),x, algorithm=""maxima"")","\frac{1}{3} \, \log\left(x + 3\right) + \frac{1}{2} \, \log\left(x - 2\right) + \frac{1}{6} \, \log\left(x\right)"," ",0,"1/3*log(x + 3) + 1/2*log(x - 2) + 1/6*log(x)","A",0
97,1,25,0,0.437759," ","integrate((11*a^2-7*a*x+5*x^2)/(-6*a^3+11*a^2*x-6*a*x^2+x^3),x, algorithm=""maxima"")","\frac{9}{2} \, \log\left(-a + x\right) - 17 \, \log\left(-2 \, a + x\right) + \frac{35}{2} \, \log\left(-3 \, a + x\right)"," ",0,"9/2*log(-a + x) - 17*log(-2*a + x) + 35/2*log(-3*a + x)","A",0
98,1,25,0,0.446471," ","integrate((x^2-x+2)/(x^4-5*x^2+4),x, algorithm=""maxima"")","-\frac{2}{3} \, \log\left(x + 2\right) + \frac{2}{3} \, \log\left(x + 1\right) - \frac{1}{3} \, \log\left(x - 1\right) + \frac{1}{3} \, \log\left(x - 2\right)"," ",0,"-2/3*log(x + 2) + 2/3*log(x + 1) - 1/3*log(x - 1) + 1/3*log(x - 2)","A",0
99,1,43,0,0.982202," ","integrate((2*x^2-5)/(x^4-5*x^2+6),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{x - \sqrt{3}}{x + \sqrt{3}}\right) + \frac{1}{4} \, \sqrt{2} \log\left(\frac{x - \sqrt{2}}{x + \sqrt{2}}\right)"," ",0,"1/6*sqrt(3)*log((x - sqrt(3))/(x + sqrt(3))) + 1/4*sqrt(2)*log((x - sqrt(2))/(x + sqrt(2)))","A",0
100,1,25,0,0.432340," ","integrate(1/(-4+x)/(-3+x)/(-2+x)/(-1+x),x, algorithm=""maxima"")","-\frac{1}{6} \, \log\left(x - 1\right) + \frac{1}{2} \, \log\left(x - 2\right) - \frac{1}{2} \, \log\left(x - 3\right) + \frac{1}{6} \, \log\left(x - 4\right)"," ",0,"-1/6*log(x - 1) + 1/2*log(x - 2) - 1/2*log(x - 3) + 1/6*log(x - 4)","A",0
101,1,22,0,0.432159," ","integrate((x^2+1)/(-1+x)^3,x, algorithm=""maxima"")","-\frac{2 \, x - 1}{x^{2} - 2 \, x + 1} + \log\left(x - 1\right)"," ",0,"-(2*x - 1)/(x^2 - 2*x + 1) + log(x - 1)","A",0
102,1,32,0,0.430548," ","integrate(x^5/(3+x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} - 2 \, x^{3} + \frac{27}{2} \, x^{2} - 108 \, x + \frac{243}{x + 3} + 405 \, \log\left(x + 3\right)"," ",0,"1/4*x^4 - 2*x^3 + 27/2*x^2 - 108*x + 243/(x + 3) + 405*log(x + 3)","A",0
103,1,30,0,0.445118," ","integrate((5*x^3-2)/(x^4-8*x^3+18*x^2-27),x, algorithm=""maxima"")","-\frac{407 \, x - 955}{16 \, {\left(x^{2} - 6 \, x + 9\right)}} + \frac{7}{64} \, \log\left(x + 1\right) + \frac{313}{64} \, \log\left(x - 3\right)"," ",0,"-1/16*(407*x - 955)/(x^2 - 6*x + 9) + 7/64*log(x + 1) + 313/64*log(x - 3)","A",0
104,1,29,0,0.428106," ","integrate((x^3-6*x^2+3*x-9)/(3+x)^2/(4+x)^2,x, algorithm=""maxima"")","\frac{280 \, x + 939}{x^{2} + 7 \, x + 12} - 263 \, \log\left(x + 4\right) + 264 \, \log\left(x + 3\right)"," ",0,"(280*x + 939)/(x^2 + 7*x + 12) - 263*log(x + 4) + 264*log(x + 3)","A",0
105,1,29,0,0.429096," ","integrate((x^3+x^2+2)/x/(x^2-1)^2,x, algorithm=""maxima"")","-\frac{x + 3}{2 \, {\left(x^{2} - 1\right)}} - \frac{5}{4} \, \log\left(x + 1\right) - \frac{3}{4} \, \log\left(x - 1\right) + 2 \, \log\left(x\right)"," ",0,"-1/2*(x + 3)/(x^2 - 1) - 5/4*log(x + 1) - 3/4*log(x - 1) + 2*log(x)","A",0
106,1,40,0,0.435760," ","integrate(1/(x^6-x^5-x^4+x^3),x, algorithm=""maxima"")","-\frac{3 \, x^{2} - x - 1}{2 \, {\left(x^{3} - x^{2}\right)}} - \frac{1}{4} \, \log\left(x + 1\right) - \frac{7}{4} \, \log\left(x - 1\right) + 2 \, \log\left(x\right)"," ",0,"-1/2*(3*x^2 - x - 1)/(x^3 - x^2) - 1/4*log(x + 1) - 7/4*log(x - 1) + 2*log(x)","A",0
107,1,23,0,0.955924," ","integrate((x^4+1)/(x^3-x^2+x-1),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} + x - \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left(x - 1\right)"," ",0,"1/2*x^2 + x - arctan(x) - 1/2*log(x^2 + 1) + log(x - 1)","A",0
108,1,21,0,0.981356," ","integrate(1/x/(1+x)/(x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, \arctan\left(x\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right) - \frac{1}{2} \, \log\left(x + 1\right) + \log\left(x\right)"," ",0,"-1/2*arctan(x) - 1/4*log(x^2 + 1) - 1/2*log(x + 1) + log(x)","A",0
109,1,25,0,0.968189," ","integrate(x^2/(x^4+x^2-2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{1}{6} \, \log\left(x + 1\right) + \frac{1}{6} \, \log\left(x - 1\right)"," ",0,"1/3*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/6*log(x + 1) + 1/6*log(x - 1)","A",0
110,1,32,0,0.985977," ","integrate((x^3+4*x^2+6*x)/(x^4+2*x^3+3*x^2+4*x+2),x, algorithm=""maxima"")","\frac{4}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{1}{x + 1} + \frac{2}{3} \, \log\left(x^{2} + 2\right) - \frac{1}{3} \, \log\left(x + 1\right)"," ",0,"4/3*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/(x + 1) + 2/3*log(x^2 + 2) - 1/3*log(x + 1)","A",0
111,1,36,0,0.977212," ","integrate(x/(1+x)/(1+2*x)^2/(x^2+1),x, algorithm=""maxima"")","\frac{2}{5 \, {\left(2 \, x + 1\right)}} + \frac{1}{50} \, \arctan\left(x\right) - \frac{7}{100} \, \log\left(x^{2} + 1\right) + \frac{16}{25} \, \log\left(2 \, x + 1\right) - \frac{1}{2} \, \log\left(x + 1\right)"," ",0,"2/5/(2*x + 1) + 1/50*arctan(x) - 7/100*log(x^2 + 1) + 16/25*log(2*x + 1) - 1/2*log(x + 1)","A",0
112,1,36,0,0.989128," ","integrate((3*x^2+x-2)/(-1+x)^3/(x^2+1),x, algorithm=""maxima"")","-\frac{5 \, x - 4}{2 \, {\left(x^{2} - 2 \, x + 1\right)}} - \arctan\left(x\right) + \frac{3}{4} \, \log\left(x^{2} + 1\right) - \frac{3}{2} \, \log\left(x - 1\right)"," ",0,"-1/2*(5*x - 4)/(x^2 - 2*x + 1) - arctan(x) + 3/4*log(x^2 + 1) - 3/2*log(x - 1)","A",0
113,1,53,0,0.986197," ","integrate(1/(x^4+x^2+1),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \, \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*log(x^2 + x + 1) - 1/4*log(x^2 - x + 1)","A",0
114,1,54,0,0.977389," ","integrate((2*x^3+3)/(x^5-9*x),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + \frac{1}{6} \, \sqrt{3} \log\left(\frac{x - \sqrt{3}}{x + \sqrt{3}}\right) + \frac{1}{12} \, \log\left(x^{2} + 3\right) + \frac{1}{12} \, \log\left(x^{2} - 3\right) - \frac{1}{3} \, \log\left(x\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*x) + 1/6*sqrt(3)*log((x - sqrt(3))/(x + sqrt(3))) + 1/12*log(x^2 + 3) + 1/12*log(x^2 - 3) - 1/3*log(x)","A",0
115,1,43,0,0.978677," ","integrate((5*x^3+8*x-20)/(-4+x)^3/(x^2-4*x+8),x, algorithm=""maxima"")","-\frac{41 \, x - 81}{4 \, {\left(x^{2} - 8 \, x + 16\right)}} + \frac{3}{16} \, \arctan\left(\frac{1}{2} \, x - 1\right) + \frac{45}{32} \, \log\left(x^{2} - 4 \, x + 8\right) - \frac{45}{16} \, \log\left(x - 4\right)"," ",0,"-1/4*(41*x - 81)/(x^2 - 8*x + 16) + 3/16*arctan(1/2*x - 1) + 45/32*log(x^2 - 4*x + 8) - 45/16*log(x - 4)","A",0
116,1,35,0,0.994695," ","integrate(1/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{1}{12} \, \arctan\left(\frac{1}{2} \, x\right) + \frac{1}{6} \, \arctan\left(x\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*x) - 1/4*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/12*arctan(1/2*x) + 1/6*arctan(x)","A",0
117,1,33,0,0.425976," ","integrate(x/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x, algorithm=""maxima"")","-\frac{1}{12} \, \log\left(x^{2} + 4\right) + \frac{1}{4} \, \log\left(x^{2} + 3\right) - \frac{1}{4} \, \log\left(x^{2} + 2\right) + \frac{1}{12} \, \log\left(x^{2} + 1\right)"," ",0,"-1/12*log(x^2 + 4) + 1/4*log(x^2 + 3) - 1/4*log(x^2 + 2) + 1/12*log(x^2 + 1)","A",0
118,1,49,0,0.984807," ","integrate(1/(a^3+x^3),x, algorithm=""maxima"")","\frac{\sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right)}{3 \, a^{2}} - \frac{\log\left(a^{2} - a x + x^{2}\right)}{6 \, a^{2}} + \frac{\log\left(a + x\right)}{3 \, a^{2}}"," ",0,"1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a)/a^2 - 1/6*log(a^2 - a*x + x^2)/a^2 + 1/3*log(a + x)/a^2","A",0
119,1,49,0,0.960306," ","integrate(x/(a^3+x^3),x, algorithm=""maxima"")","\frac{\sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right)}{3 \, a} + \frac{\log\left(a^{2} - a x + x^{2}\right)}{6 \, a} - \frac{\log\left(a + x\right)}{3 \, a}"," ",0,"1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a)/a + 1/6*log(a^2 - a*x + x^2)/a - 1/3*log(a + x)/a","A",0
120,1,10,0,0.426758," ","integrate(x^2/(a^3+x^3),x, algorithm=""maxima"")","\frac{1}{3} \, \log\left(a^{3} + x^{3}\right)"," ",0,"1/3*log(a^3 + x^3)","A",0
121,1,23,0,0.431774," ","integrate(1/x/(a^3+x^3),x, algorithm=""maxima"")","-\frac{\log\left(a^{3} + x^{3}\right)}{3 \, a^{3}} + \frac{\log\left(x^{3}\right)}{3 \, a^{3}}"," ",0,"-1/3*log(a^3 + x^3)/a^3 + 1/3*log(x^3)/a^3","A",0
122,1,57,0,0.960876," ","integrate(1/x^2/(a^3+x^3),x, algorithm=""maxima"")","-\frac{\sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right)}{3 \, a^{4}} - \frac{\log\left(a^{2} - a x + x^{2}\right)}{6 \, a^{4}} + \frac{\log\left(a + x\right)}{3 \, a^{4}} - \frac{1}{a^{3} x}"," ",0,"-1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a)/a^4 - 1/6*log(a^2 - a*x + x^2)/a^4 + 1/3*log(a + x)/a^4 - 1/(a^3*x)","A",0
123,1,57,0,0.956877," ","integrate(1/x^3/(a^3+x^3),x, algorithm=""maxima"")","-\frac{\sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right)}{3 \, a^{5}} + \frac{\log\left(a^{2} - a x + x^{2}\right)}{6 \, a^{5}} - \frac{\log\left(a + x\right)}{3 \, a^{5}} - \frac{1}{2 \, a^{3} x^{2}}"," ",0,"-1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a)/a^5 + 1/6*log(a^2 - a*x + x^2)/a^5 - 1/3*log(a + x)/a^5 - 1/2/(a^3*x^2)","A",0
124,1,31,0,0.426192," ","integrate(1/x^4/(a^3+x^3),x, algorithm=""maxima"")","\frac{\log\left(a^{3} + x^{3}\right)}{3 \, a^{6}} - \frac{\log\left(x^{3}\right)}{3 \, a^{6}} - \frac{1}{3 \, a^{3} x^{3}}"," ",0,"1/3*log(a^3 + x^3)/a^6 - 1/3*log(x^3)/a^6 - 1/3/(a^3*x^3)","A",0
125,1,66,0,0.957167," ","integrate(1/x^5/(a^3+x^3),x, algorithm=""maxima"")","\frac{\sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(a - 2 \, x\right)}}{3 \, a}\right)}{3 \, a^{7}} + \frac{\log\left(a^{2} - a x + x^{2}\right)}{6 \, a^{7}} - \frac{\log\left(a + x\right)}{3 \, a^{7}} - \frac{a^{3} - 4 \, x^{3}}{4 \, a^{6} x^{4}}"," ",0,"1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(a - 2*x)/a)/a^7 + 1/6*log(a^2 - a*x + x^2)/a^7 - 1/3*log(a + x)/a^7 - 1/4*(a^3 - 4*x^3)/(a^6*x^4)","A",0
126,0,0,0,0.000000," ","integrate(1/(x^m)/(a^3+x^3),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{3} + x^{3}\right)} x^{m}}\,{d x}"," ",0,"integrate(1/((a^3 + x^3)*x^m), x)","F",0
127,1,32,0,0.974116," ","integrate(1/(a^4-x^4),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{x}{a}\right)}{2 \, a^{3}} + \frac{\log\left(a + x\right)}{4 \, a^{3}} - \frac{\log\left(-a + x\right)}{4 \, a^{3}}"," ",0,"1/2*arctan(x/a)/a^3 + 1/4*log(a + x)/a^3 - 1/4*log(-a + x)/a^3","A",0
128,1,29,0,0.421628," ","integrate(x/(a^4-x^4),x, algorithm=""maxima"")","\frac{\log\left(a^{2} + x^{2}\right)}{4 \, a^{2}} - \frac{\log\left(-a^{2} + x^{2}\right)}{4 \, a^{2}}"," ",0,"1/4*log(a^2 + x^2)/a^2 - 1/4*log(-a^2 + x^2)/a^2","B",0
129,1,25,0,0.419510," ","integrate(1/x/(a^4-x^4),x, algorithm=""maxima"")","-\frac{\log\left(-a^{4} + x^{4}\right)}{4 \, a^{4}} + \frac{\log\left(x^{4}\right)}{4 \, a^{4}}"," ",0,"-1/4*log(-a^4 + x^4)/a^4 + 1/4*log(x^4)/a^4","A",0
130,1,40,0,0.970942," ","integrate(1/x^2/(a^4-x^4),x, algorithm=""maxima"")","-\frac{\arctan\left(\frac{x}{a}\right)}{2 \, a^{5}} + \frac{\log\left(a + x\right)}{4 \, a^{5}} - \frac{\log\left(-a + x\right)}{4 \, a^{5}} - \frac{1}{a^{4} x}"," ",0,"-1/2*arctan(x/a)/a^5 + 1/4*log(a + x)/a^5 - 1/4*log(-a + x)/a^5 - 1/(a^4*x)","A",0
131,1,37,0,0.426065," ","integrate(1/x^3/(a^4-x^4),x, algorithm=""maxima"")","\frac{\log\left(a^{2} + x^{2}\right)}{4 \, a^{6}} - \frac{\log\left(-a^{2} + x^{2}\right)}{4 \, a^{6}} - \frac{1}{2 \, a^{4} x^{2}}"," ",0,"1/4*log(a^2 + x^2)/a^6 - 1/4*log(-a^2 + x^2)/a^6 - 1/2/(a^4*x^2)","A",0
132,1,40,0,0.961310," ","integrate(1/x^4/(a^4-x^4),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{x}{a}\right)}{2 \, a^{7}} + \frac{\log\left(a + x\right)}{4 \, a^{7}} - \frac{\log\left(-a + x\right)}{4 \, a^{7}} - \frac{1}{3 \, a^{4} x^{3}}"," ",0,"1/2*arctan(x/a)/a^7 + 1/4*log(a + x)/a^7 - 1/4*log(-a + x)/a^7 - 1/3/(a^4*x^3)","A",0
133,0,0,0,0.000000," ","integrate(1/(x^m)/(a^4-x^4),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{4} - x^{4}\right)} x^{m}}\,{d x}"," ",0,"integrate(1/((a^4 - x^4)*x^m), x)","F",0
134,1,13,0,0.965494," ","integrate(x/(a^4+x^4),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{x^{2}}{a^{2}}\right)}{2 \, a^{2}}"," ",0,"1/2*arctan(x^2/a^2)/a^2","A",0
135,1,98,0,0.965875," ","integrate(x^2/(a^4+x^4),x, algorithm=""maxima"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a + 2 \, x\right)}}{2 \, a}\right)}{4 \, a} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a - 2 \, x\right)}}{2 \, a}\right)}{4 \, a} - \frac{\sqrt{2} \log\left(\sqrt{2} a x + a^{2} + x^{2}\right)}{8 \, a} + \frac{\sqrt{2} \log\left(-\sqrt{2} a x + a^{2} + x^{2}\right)}{8 \, a}"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a + 2*x)/a)/a + 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a - 2*x)/a)/a - 1/8*sqrt(2)*log(sqrt(2)*a*x + a^2 + x^2)/a + 1/8*sqrt(2)*log(-sqrt(2)*a*x + a^2 + x^2)/a","A",0
136,1,180,0,0.967520," ","integrate(1/(a^5+x^5),x, algorithm=""maxima"")","\frac{\sqrt{5} {\left(\sqrt{5} + 1\right)} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{5 \, a^{4} \sqrt{2 \, \sqrt{5} + 10}} + \frac{\sqrt{5} {\left(\sqrt{5} - 1\right)} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{5 \, a^{4} \sqrt{-2 \, \sqrt{5} + 10}} - \frac{{\left(\sqrt{5} + 3\right)} \log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{10 \, a^{4} {\left(\sqrt{5} + 1\right)}} - \frac{{\left(\sqrt{5} - 3\right)} \log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{10 \, a^{4} {\left(\sqrt{5} - 1\right)}} + \frac{\log\left(a + x\right)}{5 \, a^{4}}"," ",0,"1/5*sqrt(5)*(sqrt(5) + 1)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a^4*sqrt(2*sqrt(5) + 10)) + 1/5*sqrt(5)*(sqrt(5) - 1)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a^4*sqrt(-2*sqrt(5) + 10)) - 1/10*(sqrt(5) + 3)*log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a^4*(sqrt(5) + 1)) - 1/10*(sqrt(5) - 3)*log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a^4*(sqrt(5) - 1)) + 1/5*log(a + x)/a^4","A",0
137,1,160,0,0.976345," ","integrate(x/(a^5+x^5),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{5} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{5 \, a^{3} \sqrt{2 \, \sqrt{5} + 10}} + \frac{2 \, \sqrt{5} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{5 \, a^{3} \sqrt{-2 \, \sqrt{5} + 10}} - \frac{\log\left(a + x\right)}{5 \, a^{3}} - \frac{\log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{5 \, a^{3} {\left(\sqrt{5} + 1\right)}} + \frac{\log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{5 \, a^{3} {\left(\sqrt{5} - 1\right)}}"," ",0,"-2/5*sqrt(5)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a^3*sqrt(2*sqrt(5) + 10)) + 2/5*sqrt(5)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a^3*sqrt(-2*sqrt(5) + 10)) - 1/5*log(a + x)/a^3 - 1/5*log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a^3*(sqrt(5) + 1)) + 1/5*log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a^3*(sqrt(5) - 1))","A",0
138,1,160,0,0.975637," ","integrate(x^2/(a^5+x^5),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{5} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{5 \, a^{2} \sqrt{2 \, \sqrt{5} + 10}} + \frac{2 \, \sqrt{5} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{5 \, a^{2} \sqrt{-2 \, \sqrt{5} + 10}} + \frac{\log\left(a + x\right)}{5 \, a^{2}} + \frac{\log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{5 \, a^{2} {\left(\sqrt{5} + 1\right)}} - \frac{\log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{5 \, a^{2} {\left(\sqrt{5} - 1\right)}}"," ",0,"-2/5*sqrt(5)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a^2*sqrt(2*sqrt(5) + 10)) + 2/5*sqrt(5)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a^2*sqrt(-2*sqrt(5) + 10)) + 1/5*log(a + x)/a^2 + 1/5*log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a^2*(sqrt(5) + 1)) - 1/5*log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a^2*(sqrt(5) - 1))","A",0
139,1,180,0,0.975942," ","integrate(x^3/(a^5+x^5),x, algorithm=""maxima"")","\frac{\sqrt{5} {\left(\sqrt{5} + 1\right)} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{5 \, a \sqrt{2 \, \sqrt{5} + 10}} + \frac{\sqrt{5} {\left(\sqrt{5} - 1\right)} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{5 \, a \sqrt{-2 \, \sqrt{5} + 10}} + \frac{{\left(\sqrt{5} + 3\right)} \log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{10 \, a {\left(\sqrt{5} + 1\right)}} + \frac{{\left(\sqrt{5} - 3\right)} \log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{10 \, a {\left(\sqrt{5} - 1\right)}} - \frac{\log\left(a + x\right)}{5 \, a}"," ",0,"1/5*sqrt(5)*(sqrt(5) + 1)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a*sqrt(2*sqrt(5) + 10)) + 1/5*sqrt(5)*(sqrt(5) - 1)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a*sqrt(-2*sqrt(5) + 10)) + 1/10*(sqrt(5) + 3)*log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a*(sqrt(5) + 1)) + 1/10*(sqrt(5) - 3)*log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a*(sqrt(5) - 1)) - 1/5*log(a + x)/a","A",0
140,1,10,0,0.427080," ","integrate(x^4/(a^5+x^5),x, algorithm=""maxima"")","\frac{1}{5} \, \log\left(a^{5} + x^{5}\right)"," ",0,"1/5*log(a^5 + x^5)","A",0
141,1,23,0,0.426565," ","integrate(1/x/(a^5+x^5),x, algorithm=""maxima"")","-\frac{\log\left(a^{5} + x^{5}\right)}{5 \, a^{5}} + \frac{\log\left(x^{5}\right)}{5 \, a^{5}}"," ",0,"-1/5*log(a^5 + x^5)/a^5 + 1/5*log(x^5)/a^5","A",0
142,1,192,0,0.965965," ","integrate(1/x^2/(a^5+x^5),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{5} {\left(\sqrt{5} + 1\right)} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{a \sqrt{2 \, \sqrt{5} + 10}} + \frac{2 \, \sqrt{5} {\left(\sqrt{5} - 1\right)} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{a \sqrt{-2 \, \sqrt{5} + 10}} + \frac{{\left(\sqrt{5} + 3\right)} \log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{a {\left(\sqrt{5} + 1\right)}} + \frac{{\left(\sqrt{5} - 3\right)} \log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{a {\left(\sqrt{5} - 1\right)}} - \frac{2 \, \log\left(a + x\right)}{a}}{10 \, a^{5}} - \frac{1}{a^{5} x}"," ",0,"-1/10*(2*sqrt(5)*(sqrt(5) + 1)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a*sqrt(2*sqrt(5) + 10)) + 2*sqrt(5)*(sqrt(5) - 1)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a*sqrt(-2*sqrt(5) + 10)) + (sqrt(5) + 3)*log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a*(sqrt(5) + 1)) + (sqrt(5) - 3)*log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a*(sqrt(5) - 1)) - 2*log(a + x)/a)/a^5 - 1/(a^5*x)","A",0
143,1,173,0,0.982937," ","integrate(1/x^3/(a^5+x^5),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{5} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{a^{2} \sqrt{2 \, \sqrt{5} + 10}} - \frac{2 \, \sqrt{5} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{a^{2} \sqrt{-2 \, \sqrt{5} + 10}} - \frac{\log\left(a + x\right)}{a^{2}} - \frac{\log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{a^{2} {\left(\sqrt{5} + 1\right)}} + \frac{\log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{a^{2} {\left(\sqrt{5} - 1\right)}}}{5 \, a^{5}} - \frac{1}{2 \, a^{5} x^{2}}"," ",0,"1/5*(2*sqrt(5)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a^2*sqrt(2*sqrt(5) + 10)) - 2*sqrt(5)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a^2*sqrt(-2*sqrt(5) + 10)) - log(a + x)/a^2 - log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a^2*(sqrt(5) + 1)) + log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a^2*(sqrt(5) - 1)))/a^5 - 1/2/(a^5*x^2)","A",0
144,1,172,0,0.965688," ","integrate(1/x^4/(a^5+x^5),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{5} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{a^{3} \sqrt{2 \, \sqrt{5} + 10}} - \frac{2 \, \sqrt{5} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{a^{3} \sqrt{-2 \, \sqrt{5} + 10}} + \frac{\log\left(a + x\right)}{a^{3}} + \frac{\log\left(-a x {\left(\sqrt{5} + 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{a^{3} {\left(\sqrt{5} + 1\right)}} - \frac{\log\left(a x {\left(\sqrt{5} - 1\right)} + 2 \, a^{2} + 2 \, x^{2}\right)}{a^{3} {\left(\sqrt{5} - 1\right)}}}{5 \, a^{5}} - \frac{1}{3 \, a^{5} x^{3}}"," ",0,"1/5*(2*sqrt(5)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/(a^3*sqrt(2*sqrt(5) + 10)) - 2*sqrt(5)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/(a^3*sqrt(-2*sqrt(5) + 10)) + log(a + x)/a^3 + log(-a*x*(sqrt(5) + 1) + 2*a^2 + 2*x^2)/(a^3*(sqrt(5) + 1)) - log(a*x*(sqrt(5) - 1) + 2*a^2 + 2*x^2)/(a^3*(sqrt(5) - 1)))/a^5 - 1/3/(a^5*x^3)","A",0
145,0,0,0,0.000000," ","integrate(1/(x^m)/(a^5+x^5),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{5} + x^{5}\right)} x^{m}}\,{d x}"," ",0,"integrate(1/((a^5 + x^5)*x^m), x)","F",0
146,1,27,0,0.983768," ","integrate((x^4+1)/(x^6+1),x, algorithm=""maxima"")","\frac{1}{3} \, \arctan\left(2 \, x + \sqrt{3}\right) + \frac{1}{3} \, \arctan\left(2 \, x - \sqrt{3}\right) + \frac{2}{3} \, \arctan\left(x\right)"," ",0,"1/3*arctan(2*x + sqrt(3)) + 1/3*arctan(2*x - sqrt(3)) + 2/3*arctan(x)","A",0
147,1,54,0,0.962204," ","integrate(1/(x^2+3*x+5)^3,x, algorithm=""maxima"")","\frac{12}{1331} \, \sqrt{11} \arctan\left(\frac{1}{11} \, \sqrt{11} {\left(2 \, x + 3\right)}\right) + \frac{12 \, x^{3} + 54 \, x^{2} + 136 \, x + 123}{242 \, {\left(x^{4} + 6 \, x^{3} + 19 \, x^{2} + 30 \, x + 25\right)}}"," ",0,"12/1331*sqrt(11)*arctan(1/11*sqrt(11)*(2*x + 3)) + 1/242*(12*x^3 + 54*x^2 + 136*x + 123)/(x^4 + 6*x^3 + 19*x^2 + 30*x + 25)","A",0
148,1,38,0,0.966349," ","integrate((x^4+x^2+1)/(x^2+1)^4,x, algorithm=""maxima"")","\frac{21 \, x^{5} + 40 \, x^{3} + 27 \, x}{48 \, {\left(x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1\right)}} + \frac{7}{16} \, \arctan\left(x\right)"," ",0,"1/48*(21*x^5 + 40*x^3 + 27*x)/(x^6 + 3*x^4 + 3*x^2 + 1) + 7/16*arctan(x)","A",0
149,-2,0,0,0.000000," ","integrate((A*x+B)/(a*x^2+2*b*x+c)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a*c>0)', see `assume?` for more details)Is 4*b^2-4*a*c positive or negative?","F(-2)",0
150,1,33,0,0.976732," ","integrate((5*x^3-27*x^2+55*x-41)/(x^2-4*x+5)^2,x, algorithm=""maxima"")","-\frac{x - 1}{x^{2} - 4 \, x + 5} + 2 \, \arctan\left(x - 2\right) + \frac{5}{2} \, \log\left(x^{2} - 4 \, x + 5\right)"," ",0,"-(x - 1)/(x^2 - 4*x + 5) + 2*arctan(x - 2) + 5/2*log(x^2 - 4*x + 5)","A",0
151,1,42,0,0.970981," ","integrate(1/(x^3-1)^2,x, algorithm=""maxima"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{x}{3 \, {\left(x^{3} - 1\right)}} + \frac{1}{9} \, \log\left(x^{2} + x + 1\right) - \frac{2}{9} \, \log\left(x - 1\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/3*x/(x^3 - 1) + 1/9*log(x^2 + x + 1) - 2/9*log(x - 1)","A",0
152,1,31,0,0.974042," ","integrate((3*x^4+4)/x^2/(x^2+1)^3,x, algorithm=""maxima"")","-\frac{57 \, x^{4} + 103 \, x^{2} + 32}{8 \, {\left(x^{5} + 2 \, x^{3} + x\right)}} - \frac{57}{8} \, \arctan\left(x\right)"," ",0,"-1/8*(57*x^4 + 103*x^2 + 32)/(x^5 + 2*x^3 + x) - 57/8*arctan(x)","A",0
153,1,40,0,0.957899," ","integrate(x/(x^6+1),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{12} \, \log\left(x^{4} - x^{2} + 1\right) + \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/12*log(x^4 - x^2 + 1) + 1/6*log(x^2 + 1)","A",0
154,1,14,0,0.450405," ","integrate((-1+x^(-1+n))/(-n*x+x^n),x, algorithm=""maxima"")","\frac{\log\left(n x - x^{n}\right)}{n}"," ",0,"log(n*x - x^n)/n","A",0
155,1,34,0,0.974579," ","integrate(x^3/(3*x^4-2*x^2+1),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}\right) + \frac{1}{12} \, \log\left(3 \, x^{4} - 2 \, x^{2} + 1\right)"," ",0,"1/12*sqrt(2)*arctan(1/2*sqrt(2)*(3*x^2 - 1)) + 1/12*log(3*x^4 - 2*x^2 + 1)","A",0
156,1,24,0,0.423475," ","integrate(x^5/(3*x^4+x^2-4),x, algorithm=""maxima"")","\frac{1}{6} \, x^{2} - \frac{8}{63} \, \log\left(3 \, x^{2} + 4\right) + \frac{1}{14} \, \log\left(x^{2} - 1\right)"," ",0,"1/6*x^2 - 8/63*log(3*x^2 + 4) + 1/14*log(x^2 - 1)","A",0
157,1,17,0,0.424546," ","integrate(x^2/(x^6-10*x^3+9),x, algorithm=""maxima"")","-\frac{1}{24} \, \log\left(x^{3} - 1\right) + \frac{1}{24} \, \log\left(x^{3} - 9\right)"," ",0,"-1/24*log(x^3 - 1) + 1/24*log(x^3 - 9)","A",0
158,1,32,0,0.443929," ","integrate((x^3-4*x^2+1)/(-2+x)^4,x, algorithm=""maxima"")","-\frac{6 \, x^{2} - 30 \, x + 29}{3 \, {\left(x^{3} - 6 \, x^{2} + 12 \, x - 8\right)}} + \log\left(x - 2\right)"," ",0,"-1/3*(6*x^2 - 30*x + 29)/(x^3 - 6*x^2 + 12*x - 8) + log(x - 2)","A",0
159,1,72,0,0.439617," ","integrate(x^3/(-1+x)^12,x, algorithm=""maxima"")","-\frac{165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1}{1320 \, {\left(x^{11} - 11 \, x^{10} + 55 \, x^{9} - 165 \, x^{8} + 330 \, x^{7} - 462 \, x^{6} + 462 \, x^{5} - 330 \, x^{4} + 165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1\right)}}"," ",0,"-1/1320*(165*x^3 - 55*x^2 + 11*x - 1)/(x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1)","B",0
160,1,48,0,0.459120," ","integrate((x^4-3*x)/(1+2*x)^5,x, algorithm=""maxima"")","\frac{384 \, x^{3} + 432 \, x^{2} + 368 \, x + 49}{384 \, {\left(16 \, x^{4} + 32 \, x^{3} + 24 \, x^{2} + 8 \, x + 1\right)}} + \frac{1}{32} \, \log\left(2 \, x + 1\right)"," ",0,"1/384*(384*x^3 + 432*x^2 + 368*x + 49)/(16*x^4 + 32*x^3 + 24*x^2 + 8*x + 1) + 1/32*log(2*x + 1)","A",0
161,1,38,0,0.447179," ","integrate(1/(-1+x)^2/(1+x)^3,x, algorithm=""maxima"")","-\frac{3 \, x^{2} + 3 \, x - 2}{8 \, {\left(x^{3} + x^{2} - x - 1\right)}} + \frac{3}{16} \, \log\left(x + 1\right) - \frac{3}{16} \, \log\left(x - 1\right)"," ",0,"-1/8*(3*x^2 + 3*x - 2)/(x^3 + x^2 - x - 1) + 3/16*log(x + 1) - 3/16*log(x - 1)","A",0
162,1,31,0,0.427445," ","integrate(1/(5-6*x)^2/x^2,x, algorithm=""maxima"")","-\frac{12 \, x - 5}{25 \, {\left(6 \, x^{2} - 5 \, x\right)}} - \frac{12}{125} \, \log\left(6 \, x - 5\right) + \frac{12}{125} \, \log\left(x\right)"," ",0,"-1/25*(12*x - 5)/(6*x^2 - 5*x) - 12/125*log(6*x - 5) + 12/125*log(x)","A",0
163,1,50,0,0.427137," ","integrate(1/(x^2-2*x-3)^3,x, algorithm=""maxima"")","\frac{3 \, x^{3} - 9 \, x^{2} - 11 \, x + 17}{128 \, {\left(x^{4} - 4 \, x^{3} - 2 \, x^{2} + 12 \, x + 9\right)}} - \frac{3}{512} \, \log\left(x + 1\right) + \frac{3}{512} \, \log\left(x - 3\right)"," ",0,"1/128*(3*x^3 - 9*x^2 - 11*x + 17)/(x^4 - 4*x^3 - 2*x^2 + 12*x + 9) - 3/512*log(x + 1) + 3/512*log(x - 3)","A",0
164,1,44,0,0.955181," ","integrate(1/(x^2-4*x+13)^3,x, algorithm=""maxima"")","\frac{x^{3} - 6 \, x^{2} + 27 \, x - 38}{216 \, {\left(x^{4} - 8 \, x^{3} + 42 \, x^{2} - 104 \, x + 169\right)}} + \frac{1}{648} \, \arctan\left(\frac{1}{3} \, x - \frac{2}{3}\right)"," ",0,"1/216*(x^3 - 6*x^2 + 27*x - 38)/(x^4 - 8*x^3 + 42*x^2 - 104*x + 169) + 1/648*arctan(1/3*x - 2/3)","A",0
165,1,60,0,0.425678," ","integrate(1/(2+x)^3/(3+x)^4,x, algorithm=""maxima"")","\frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} + 4175 \, x + 2627}{6 \, {\left(x^{5} + 13 \, x^{4} + 67 \, x^{3} + 171 \, x^{2} + 216 \, x + 108\right)}} - 10 \, \log\left(x + 3\right) + 10 \, \log\left(x + 2\right)"," ",0,"1/6*(60*x^4 + 630*x^3 + 2450*x^2 + 4175*x + 2627)/(x^5 + 13*x^4 + 67*x^3 + 171*x^2 + 216*x + 108) - 10*log(x + 3) + 10*log(x + 2)","A",0
166,1,40,0,0.970934," ","integrate(x^6/(x^2-2)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} + \frac{5}{2} \, \sqrt{2} \log\left(\frac{x - \sqrt{2}}{x + \sqrt{2}}\right) + 4 \, x - \frac{2 \, x}{x^{2} - 2}"," ",0,"1/3*x^3 + 5/2*sqrt(2)*log((x - sqrt(2))/(x + sqrt(2))) + 4*x - 2*x/(x^2 - 2)","A",0
167,1,41,0,0.957308," ","integrate(x^8/(x^2+4)^4,x, algorithm=""maxima"")","x + \frac{87 \, x^{5} + 544 \, x^{3} + 912 \, x}{12 \, {\left(x^{6} + 12 \, x^{4} + 48 \, x^{2} + 64\right)}} - \frac{35}{8} \, \arctan\left(\frac{1}{2} \, x\right)"," ",0,"x + 1/12*(87*x^5 + 544*x^3 + 912*x)/(x^6 + 12*x^4 + 48*x^2 + 64) - 35/8*arctan(1/2*x)","A",0
168,1,36,0,0.968547," ","integrate((-4+7*x)/(3*x^2+2*x+5)^2,x, algorithm=""maxima"")","-\frac{19}{392} \, \sqrt{14} \arctan\left(\frac{1}{14} \, \sqrt{14} {\left(3 \, x + 1\right)}\right) - \frac{19 \, x + 39}{28 \, {\left(3 \, x^{2} + 2 \, x + 5\right)}}"," ",0,"-19/392*sqrt(14)*arctan(1/14*sqrt(14)*(3*x + 1)) - 1/28*(19*x + 39)/(3*x^2 + 2*x + 5)","A",0
169,1,47,0,0.946424," ","integrate((5-4*x)/(3*x^2-4*x-2)^2,x, algorithm=""maxima"")","-\frac{7}{400} \, \sqrt{10} \log\left(\frac{3 \, x - \sqrt{10} - 2}{3 \, x + \sqrt{10} - 2}\right) - \frac{7 \, x - 18}{20 \, {\left(3 \, x^{2} - 4 \, x - 2\right)}}"," ",0,"-7/400*sqrt(10)*log((3*x - sqrt(10) - 2)/(3*x + sqrt(10) - 2)) - 1/20*(7*x - 18)/(3*x^2 - 4*x - 2)","A",0
170,1,30,0,0.954773," ","integrate(x^5/(x^4+1)^3,x, algorithm=""maxima"")","\frac{x^{6} - x^{2}}{16 \, {\left(x^{8} + 2 \, x^{4} + 1\right)}} + \frac{1}{16} \, \arctan\left(x^{2}\right)"," ",0,"1/16*(x^6 - x^2)/(x^8 + 2*x^4 + 1) + 1/16*arctan(x^2)","A",0
171,1,28,0,0.537818," ","integrate(x*(x^2+1)^3/(x^4+2*x^2+2)^2,x, algorithm=""maxima"")","\frac{1}{4 \, {\left(x^{4} + 2 \, x^{2} + 2\right)}} + \frac{1}{4} \, \log\left(x^{4} + 2 \, x^{2} + 2\right)"," ",0,"1/4/(x^4 + 2*x^2 + 2) + 1/4*log(x^4 + 2*x^2 + 2)","A",0
172,1,11,0,0.498175," ","integrate(x^3/(a^4+x^4)^3,x, algorithm=""maxima"")","-\frac{1}{8 \, {\left(a^{4} + x^{4}\right)}^{2}}"," ",0,"-1/8/(a^4 + x^4)^2","A",0
173,1,57,0,0.447205," ","integrate(1/x/(a^4+x^4)^3,x, algorithm=""maxima"")","\frac{3 \, a^{4} + 2 \, x^{4}}{8 \, {\left(a^{16} + 2 \, a^{12} x^{4} + a^{8} x^{8}\right)}} - \frac{\log\left(a^{4} + x^{4}\right)}{4 \, a^{12}} + \frac{\log\left(x^{4}\right)}{4 \, a^{12}}"," ",0,"1/8*(3*a^4 + 2*x^4)/(a^16 + 2*a^12*x^4 + a^8*x^8) - 1/4*log(a^4 + x^4)/a^12 + 1/4*log(x^4)/a^12","A",0
174,1,147,0,1.297402," ","integrate(1/x^2/(a^4+x^4)^3,x, algorithm=""maxima"")","-\frac{32 \, a^{8} + 81 \, a^{4} x^{4} + 45 \, x^{8}}{32 \, {\left(a^{20} x + 2 \, a^{16} x^{5} + a^{12} x^{9}\right)}} - \frac{45 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a + 2 \, x\right)}}{2 \, a}\right)}{a} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a - 2 \, x\right)}}{2 \, a}\right)}{a} - \frac{\sqrt{2} \log\left(\sqrt{2} a x + a^{2} + x^{2}\right)}{a} + \frac{\sqrt{2} \log\left(-\sqrt{2} a x + a^{2} + x^{2}\right)}{a}\right)}}{256 \, a^{12}}"," ",0,"-1/32*(32*a^8 + 81*a^4*x^4 + 45*x^8)/(a^20*x + 2*a^16*x^5 + a^12*x^9) - 45/256*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a + 2*x)/a)/a + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a - 2*x)/a)/a - sqrt(2)*log(sqrt(2)*a*x + a^2 + x^2)/a + sqrt(2)*log(-sqrt(2)*a*x + a^2 + x^2)/a)/a^12","A",0
175,1,60,0,1.342752," ","integrate(1/x^3/(a^4+x^4)^3,x, algorithm=""maxima"")","-\frac{8 \, a^{8} + 25 \, a^{4} x^{4} + 15 \, x^{8}}{16 \, {\left(a^{20} x^{2} + 2 \, a^{16} x^{6} + a^{12} x^{10}\right)}} - \frac{15 \, \arctan\left(\frac{x^{2}}{a^{2}}\right)}{16 \, a^{14}}"," ",0,"-1/16*(8*a^8 + 25*a^4*x^4 + 15*x^8)/(a^20*x^2 + 2*a^16*x^6 + a^12*x^10) - 15/16*arctan(x^2/a^2)/a^14","A",0
176,1,34,0,0.603195," ","integrate(x^14/(2*x^5+3)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(8 \, x^{5} + 9\right)}}{80 \, {\left(4 \, x^{10} + 12 \, x^{5} + 9\right)}} + \frac{1}{40} \, \log\left(2 \, x^{5} + 3\right)"," ",0,"3/80*(8*x^5 + 9)/(4*x^10 + 12*x^5 + 9) + 1/40*log(2*x^5 + 3)","A",0
177,1,335,0,1.208248," ","integrate(x^6/(2*x^5+3)^3,x, algorithm=""maxima"")","\frac{3^{\frac{4}{5}} 2^{\frac{4}{5}} {\left(\sqrt{5} - 5\right)} \arctan\left(\frac{3^{\frac{4}{5}} 2^{\frac{4}{5}} {\left(4 \cdot 2^{\frac{2}{5}} x + \sqrt{5} 3^{\frac{1}{5}} 2^{\frac{1}{5}} - 3^{\frac{1}{5}} 2^{\frac{1}{5}}\right)}}{6 \, \sqrt{2 \, \sqrt{5} + 10}}\right)}{750 \, {\left(\sqrt{5} 3^{\frac{2}{5}} 2^{\frac{1}{5}} - 3^{\frac{2}{5}} 2^{\frac{1}{5}}\right)} \sqrt{2 \, \sqrt{5} + 10}} + \frac{3^{\frac{4}{5}} 2^{\frac{4}{5}} {\left(\sqrt{5} + 5\right)} \arctan\left(\frac{3^{\frac{4}{5}} 2^{\frac{4}{5}} {\left(4 \cdot 2^{\frac{2}{5}} x - \sqrt{5} 3^{\frac{1}{5}} 2^{\frac{1}{5}} - 3^{\frac{1}{5}} 2^{\frac{1}{5}}\right)}}{6 \, \sqrt{-2 \, \sqrt{5} + 10}}\right)}{750 \, {\left(\sqrt{5} 3^{\frac{2}{5}} 2^{\frac{1}{5}} + 3^{\frac{2}{5}} 2^{\frac{1}{5}}\right)} \sqrt{-2 \, \sqrt{5} + 10}} - \frac{1}{1500} \cdot 3^{\frac{2}{5}} 2^{\frac{3}{5}} \log\left(2^{\frac{1}{5}} x + 3^{\frac{1}{5}}\right) + \frac{4 \, x^{7} - 9 \, x^{2}}{300 \, {\left(4 \, x^{10} + 12 \, x^{5} + 9\right)}} - \frac{\log\left(2 \cdot 2^{\frac{2}{5}} x^{2} - x {\left(\sqrt{5} 3^{\frac{1}{5}} 2^{\frac{1}{5}} + 3^{\frac{1}{5}} 2^{\frac{1}{5}}\right)} + 2 \cdot 3^{\frac{2}{5}}\right)}{250 \, {\left(\sqrt{5} 3^{\frac{3}{5}} 2^{\frac{2}{5}} + 3^{\frac{3}{5}} 2^{\frac{2}{5}}\right)}} + \frac{\log\left(2 \cdot 2^{\frac{2}{5}} x^{2} + x {\left(\sqrt{5} 3^{\frac{1}{5}} 2^{\frac{1}{5}} - 3^{\frac{1}{5}} 2^{\frac{1}{5}}\right)} + 2 \cdot 3^{\frac{2}{5}}\right)}{250 \, {\left(\sqrt{5} 3^{\frac{3}{5}} 2^{\frac{2}{5}} - 3^{\frac{3}{5}} 2^{\frac{2}{5}}\right)}}"," ",0,"1/750*3^(4/5)*2^(4/5)*(sqrt(5) - 5)*arctan(1/6*3^(4/5)*2^(4/5)*(4*2^(2/5)*x + sqrt(5)*3^(1/5)*2^(1/5) - 3^(1/5)*2^(1/5))/sqrt(2*sqrt(5) + 10))/((sqrt(5)*3^(2/5)*2^(1/5) - 3^(2/5)*2^(1/5))*sqrt(2*sqrt(5) + 10)) + 1/750*3^(4/5)*2^(4/5)*(sqrt(5) + 5)*arctan(1/6*3^(4/5)*2^(4/5)*(4*2^(2/5)*x - sqrt(5)*3^(1/5)*2^(1/5) - 3^(1/5)*2^(1/5))/sqrt(-2*sqrt(5) + 10))/((sqrt(5)*3^(2/5)*2^(1/5) + 3^(2/5)*2^(1/5))*sqrt(-2*sqrt(5) + 10)) - 1/1500*3^(2/5)*2^(3/5)*log(2^(1/5)*x + 3^(1/5)) + 1/300*(4*x^7 - 9*x^2)/(4*x^10 + 12*x^5 + 9) - 1/250*log(2*2^(2/5)*x^2 - x*(sqrt(5)*3^(1/5)*2^(1/5) + 3^(1/5)*2^(1/5)) + 2*3^(2/5))/(sqrt(5)*3^(3/5)*2^(2/5) + 3^(3/5)*2^(2/5)) + 1/250*log(2*2^(2/5)*x^2 + x*(sqrt(5)*3^(1/5)*2^(1/5) - 3^(1/5)*2^(1/5)) + 2*3^(2/5))/(sqrt(5)*3^(3/5)*2^(2/5) - 3^(3/5)*2^(2/5))","A",0
178,1,56,0,1.145505," ","integrate(9/5/x^2/(-2*x^2+3)^3,x, algorithm=""maxima"")","-\frac{1}{48} \, \sqrt{6} \log\left(\frac{2 \, x - \sqrt{6}}{2 \, x + \sqrt{6}}\right) - \frac{10 \, x^{4} - 25 \, x^{2} + 12}{20 \, {\left(4 \, x^{5} - 12 \, x^{3} + 9 \, x\right)}}"," ",0,"-1/48*sqrt(6)*log((2*x - sqrt(6))/(2*x + sqrt(6))) - 1/20*(10*x^4 - 25*x^2 + 12)/(4*x^5 - 12*x^3 + 9*x)","A",0
179,1,31,0,1.417348," ","integrate((3*x^4+4)/x^2/(x^2+1)^3,x, algorithm=""maxima"")","-\frac{57 \, x^{4} + 103 \, x^{2} + 32}{8 \, {\left(x^{5} + 2 \, x^{3} + x\right)}} - \frac{57}{8} \, \arctan\left(x\right)"," ",0,"-1/8*(57*x^4 + 103*x^2 + 32)/(x^5 + 2*x^3 + x) - 57/8*arctan(x)","A",0
180,1,38,0,0.636826," ","integrate((-x^4+5*x^3+6*x^2-3*x+5)/(x^5-x^4-2*x^3+2*x^2+x-1),x, algorithm=""maxima"")","-\frac{2 \, x^{2} + 7 \, x - 3}{2 \, {\left(x^{3} - x^{2} - x + 1\right)}} - 2 \, \log\left(x + 1\right) + \log\left(x - 1\right)"," ",0,"-1/2*(2*x^2 + 7*x - 3)/(x^3 - x^2 - x + 1) - 2*log(x + 1) + log(x - 1)","A",0
181,1,50,0,1.366477," ","integrate((x^2+1)/x/(x^3+1)^2,x, algorithm=""maxima"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{x^{2} + 1}{3 \, {\left(x^{3} + 1\right)}} - \frac{5}{18} \, \log\left(x^{2} - x + 1\right) - \frac{4}{9} \, \log\left(x + 1\right) + \log\left(x\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/3*(x^2 + 1)/(x^3 + 1) - 5/18*log(x^2 - x + 1) - 4/9*log(x + 1) + log(x)","A",0
182,1,59,0,1.425282," ","integrate((x^2-3*x-2)/(1+x)^2/(x^2+x+1)^2,x, algorithm=""maxima"")","-\frac{25}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{11 \, x^{2} + 18 \, x + 13}{3 \, {\left(x^{3} + 2 \, x^{2} + 2 \, x + 1\right)}} + \frac{1}{2} \, \log\left(x^{2} + x + 1\right) - \log\left(x + 1\right)"," ",0,"-25/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/3*(11*x^2 + 18*x + 13)/(x^3 + 2*x^2 + 2*x + 1) + 1/2*log(x^2 + x + 1) - log(x + 1)","A",0
183,1,36,0,0.479202," ","integrate(1/(1-4*x)^3/(2-3*x),x, algorithm=""maxima"")","\frac{24 \, x - 1}{50 \, {\left(16 \, x^{2} - 8 \, x + 1\right)}} - \frac{9}{125} \, \log\left(4 \, x - 1\right) + \frac{9}{125} \, \log\left(3 \, x - 2\right)"," ",0,"1/50*(24*x - 1)/(16*x^2 - 8*x + 1) - 9/125*log(4*x - 1) + 9/125*log(3*x - 2)","A",0
184,1,43,0,0.644604," ","integrate(x^3/(-5*x^2+2)^7,x, algorithm=""maxima"")","\frac{15 \, x^{2} - 1}{750 \, {\left(15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right)}}"," ",0,"1/750*(15*x^2 - 1)/(15625*x^12 - 37500*x^10 + 37500*x^8 - 20000*x^6 + 6000*x^4 - 960*x^2 + 64)","A",0
185,1,39,0,0.534834," ","integrate(x^7/(-5*x^2+2)^3,x, algorithm=""maxima"")","-\frac{1}{250} \, x^{2} + \frac{2 \, {\left(3 \, x^{2} - 1\right)}}{125 \, {\left(25 \, x^{4} - 20 \, x^{2} + 4\right)}} - \frac{3}{625} \, \log\left(5 \, x^{2} - 2\right)"," ",0,"-1/250*x^2 + 2/125*(3*x^2 - 1)/(25*x^4 - 20*x^2 + 4) - 3/625*log(5*x^2 - 2)","A",0
186,1,37,0,0.464154," ","integrate(1/(-2+x)^3/(1+x)^2,x, algorithm=""maxima"")","\frac{2 \, x^{2} - 5 \, x - 1}{18 \, {\left(x^{3} - 3 \, x^{2} + 4\right)}} - \frac{1}{27} \, \log\left(x + 1\right) + \frac{1}{27} \, \log\left(x - 2\right)"," ",0,"1/18*(2*x^2 - 5*x - 1)/(x^3 - 3*x^2 + 4) - 1/27*log(x + 1) + 1/27*log(x - 2)","A",0
187,1,60,0,0.511476," ","integrate(1/(2+x)^3/(3+x)^4,x, algorithm=""maxima"")","\frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} + 4175 \, x + 2627}{6 \, {\left(x^{5} + 13 \, x^{4} + 67 \, x^{3} + 171 \, x^{2} + 216 \, x + 108\right)}} - 10 \, \log\left(x + 3\right) + 10 \, \log\left(x + 2\right)"," ",0,"1/6*(60*x^4 + 630*x^3 + 2450*x^2 + 4175*x + 2627)/(x^5 + 13*x^4 + 67*x^3 + 171*x^2 + 216*x + 108) - 10*log(x + 3) + 10*log(x + 2)","A",0
188,1,32,0,0.510757," ","integrate(x^5/(3+x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} - 2 \, x^{3} + \frac{27}{2} \, x^{2} - 108 \, x + \frac{243}{x + 3} + 405 \, \log\left(x + 3\right)"," ",0,"1/4*x^4 - 2*x^3 + 27/2*x^2 - 108*x + 243/(x + 3) + 405*log(x + 3)","A",0
189,1,38,0,0.593664," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, c c_{1} x^{4} + \frac{1}{3} \, {\left(b_{1} c + 2 \, b c_{1}\right)} x^{3} + a b_{1} x + \frac{1}{2} \, {\left(2 \, b b_{1} + a c_{1}\right)} x^{2}"," ",0,"1/4*c*c1*x^4 + 1/3*(b1*c + 2*b*c1)*x^3 + a*b1*x + 1/2*(2*b*b1 + a*c1)*x^2","A",0
190,1,91,0,0.547348," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{6} \, c^{2} c_{1} x^{6} + \frac{1}{5} \, {\left(b_{1} c^{2} + 4 \, b c c_{1}\right)} x^{5} + \frac{1}{2} \, {\left(2 \, b b_{1} c + {\left(2 \, b^{2} + a c\right)} c_{1}\right)} x^{4} + a^{2} b_{1} x + \frac{2}{3} \, {\left(2 \, b^{2} b_{1} + a b_{1} c + 2 \, a b c_{1}\right)} x^{3} + \frac{1}{2} \, {\left(4 \, a b b_{1} + a^{2} c_{1}\right)} x^{2}"," ",0,"1/6*c^2*c1*x^6 + 1/5*(b1*c^2 + 4*b*c*c1)*x^5 + 1/2*(2*b*b1*c + (2*b^2 + a*c)*c1)*x^4 + a^2*b1*x + 2/3*(2*b^2*b1 + a*b1*c + 2*a*b*c1)*x^3 + 1/2*(4*a*b*b1 + a^2*c1)*x^2","A",0
191,1,171,0,0.634167," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{8} \, c^{3} c_{1} x^{8} + \frac{1}{7} \, {\left(b_{1} c^{3} + 6 \, b c^{2} c_{1}\right)} x^{7} + \frac{1}{2} \, {\left(2 \, b b_{1} c^{2} + {\left(4 \, b^{2} c + a c^{2}\right)} c_{1}\right)} x^{6} + \frac{1}{5} \, {\left(12 \, b^{2} b_{1} c + 3 \, a b_{1} c^{2} + 4 \, {\left(2 \, b^{3} + 3 \, a b c\right)} c_{1}\right)} x^{5} + a^{3} b_{1} x + \frac{1}{4} \, {\left(8 \, b^{3} b_{1} + 12 \, a b b_{1} c + 3 \, {\left(4 \, a b^{2} + a^{2} c\right)} c_{1}\right)} x^{4} + {\left(4 \, a b^{2} b_{1} + a^{2} b_{1} c + 2 \, a^{2} b c_{1}\right)} x^{3} + \frac{1}{2} \, {\left(6 \, a^{2} b b_{1} + a^{3} c_{1}\right)} x^{2}"," ",0,"1/8*c^3*c1*x^8 + 1/7*(b1*c^3 + 6*b*c^2*c1)*x^7 + 1/2*(2*b*b1*c^2 + (4*b^2*c + a*c^2)*c1)*x^6 + 1/5*(12*b^2*b1*c + 3*a*b1*c^2 + 4*(2*b^3 + 3*a*b*c)*c1)*x^5 + a^3*b1*x + 1/4*(8*b^3*b1 + 12*a*b*b1*c + 3*(4*a*b^2 + a^2*c)*c1)*x^4 + (4*a*b^2*b1 + a^2*b1*c + 2*a^2*b*c1)*x^3 + 1/2*(6*a^2*b*b1 + a^3*c1)*x^2","A",0
192,1,273,0,0.552576," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^4,x, algorithm=""maxima"")","\frac{1}{10} \, c^{4} c_{1} x^{10} + \frac{1}{9} \, {\left(b_{1} c^{4} + 8 \, b c^{3} c_{1}\right)} x^{9} + \frac{1}{2} \, {\left(2 \, b b_{1} c^{3} + {\left(6 \, b^{2} c^{2} + a c^{3}\right)} c_{1}\right)} x^{8} + \frac{4}{7} \, {\left(6 \, b^{2} b_{1} c^{2} + a b_{1} c^{3} + 2 \, {\left(4 \, b^{3} c + 3 \, a b c^{2}\right)} c_{1}\right)} x^{7} + \frac{1}{3} \, {\left(16 \, b^{3} b_{1} c + 12 \, a b b_{1} c^{2} + {\left(8 \, b^{4} + 24 \, a b^{2} c + 3 \, a^{2} c^{2}\right)} c_{1}\right)} x^{6} + a^{4} b_{1} x + \frac{2}{5} \, {\left(8 \, b^{4} b_{1} + 24 \, a b^{2} b_{1} c + 3 \, a^{2} b_{1} c^{2} + 4 \, {\left(4 \, a b^{3} + 3 \, a^{2} b c\right)} c_{1}\right)} x^{5} + {\left(8 \, a b^{3} b_{1} + 6 \, a^{2} b b_{1} c + {\left(6 \, a^{2} b^{2} + a^{3} c\right)} c_{1}\right)} x^{4} + \frac{4}{3} \, {\left(6 \, a^{2} b^{2} b_{1} + a^{3} b_{1} c + 2 \, a^{3} b c_{1}\right)} x^{3} + \frac{1}{2} \, {\left(8 \, a^{3} b b_{1} + a^{4} c_{1}\right)} x^{2}"," ",0,"1/10*c^4*c1*x^10 + 1/9*(b1*c^4 + 8*b*c^3*c1)*x^9 + 1/2*(2*b*b1*c^3 + (6*b^2*c^2 + a*c^3)*c1)*x^8 + 4/7*(6*b^2*b1*c^2 + a*b1*c^3 + 2*(4*b^3*c + 3*a*b*c^2)*c1)*x^7 + 1/3*(16*b^3*b1*c + 12*a*b*b1*c^2 + (8*b^4 + 24*a*b^2*c + 3*a^2*c^2)*c1)*x^6 + a^4*b1*x + 2/5*(8*b^4*b1 + 24*a*b^2*b1*c + 3*a^2*b1*c^2 + 4*(4*a*b^3 + 3*a^2*b*c)*c1)*x^5 + (8*a*b^3*b1 + 6*a^2*b*b1*c + (6*a^2*b^2 + a^3*c)*c1)*x^4 + 4/3*(6*a^2*b^2*b1 + a^3*b1*c + 2*a^3*b*c1)*x^3 + 1/2*(8*a^3*b*b1 + a^4*c1)*x^2","A",0
193,0,0,0,0.000000," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^n,x, algorithm=""maxima"")","\int {\left(c_{1} x + b_{1}\right)} {\left(c x^{2} + 2 \, b x + a\right)}^{n}\,{d x}"," ",0,"integrate((c1*x + b1)*(c*x^2 + 2*b*x + a)^n, x)","F",0
194,-2,0,0,0.000000," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a*c>0)', see `assume?` for more details)Is 4*b^2-4*a*c positive or negative?","F(-2)",0
195,-2,0,0,0.000000," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a*c>0)', see `assume?` for more details)Is 4*b^2-4*a*c positive or negative?","F(-2)",0
196,-2,0,0,0.000000," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a*c>0)', see `assume?` for more details)Is 4*b^2-4*a*c positive or negative?","F(-2)",0
197,-2,0,0,0.000000," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a)^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a*c>0)', see `assume?` for more details)Is 4*b^2-4*a*c positive or negative?","F(-2)",0
198,0,0,0,0.000000," ","integrate((c1*x+b1)/((c*x^2+2*b*x+a)^n),x, algorithm=""maxima"")","\int \frac{c_{1} x + b_{1}}{{\left(c x^{2} + 2 \, b x + a\right)}^{n}}\,{d x}"," ",0,"integrate((c1*x + b1)/(c*x^2 + 2*b*x + a)^n, x)","F",0
199,1,41,0,1.381429," ","integrate(x/(2*x^2+6*x+3),x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{3} \log\left(\frac{2 \, x - \sqrt{3} + 3}{2 \, x + \sqrt{3} + 3}\right) + \frac{1}{4} \, \log\left(2 \, x^{2} + 6 \, x + 3\right)"," ",0,"-1/4*sqrt(3)*log((2*x - sqrt(3) + 3)/(2*x + sqrt(3) + 3)) + 1/4*log(2*x^2 + 6*x + 3)","A",0
200,1,67,0,1.255504," ","integrate((-3+2*x)/(2*x^2+6*x+3)^3,x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{3} \log\left(\frac{2 \, x - \sqrt{3} + 3}{2 \, x + \sqrt{3} + 3}\right) - \frac{8 \, x^{3} + 36 \, x^{2} + 44 \, x + 13}{4 \, {\left(4 \, x^{4} + 24 \, x^{3} + 48 \, x^{2} + 36 \, x + 9\right)}}"," ",0,"-1/6*sqrt(3)*log((2*x - sqrt(3) + 3)/(2*x + sqrt(3) + 3)) - 1/4*(8*x^3 + 36*x^2 + 44*x + 13)/(4*x^4 + 24*x^3 + 48*x^2 + 36*x + 9)","A",0
201,1,30,0,0.645824," ","integrate((-1+x)/(x^2+5*x+4)^2,x, algorithm=""maxima"")","\frac{7 \, x + 13}{9 \, {\left(x^{2} + 5 \, x + 4\right)}} - \frac{7}{27} \, \log\left(x + 4\right) + \frac{7}{27} \, \log\left(x + 1\right)"," ",0,"1/9*(7*x + 13)/(x^2 + 5*x + 4) - 7/27*log(x + 4) + 7/27*log(x + 1)","A",0
202,1,90,0,0.558989," ","integrate(1/(x^2+3*x+2)^5,x, algorithm=""maxima"")","\frac{840 \, x^{7} + 8820 \, x^{6} + 38920 \, x^{5} + 93450 \, x^{4} + 131768 \, x^{3} + 109116 \, x^{2} + 49176 \, x + 9315}{12 \, {\left(x^{8} + 12 \, x^{7} + 62 \, x^{6} + 180 \, x^{5} + 321 \, x^{4} + 360 \, x^{3} + 248 \, x^{2} + 96 \, x + 16\right)}} - 70 \, \log\left(x + 2\right) + 70 \, \log\left(x + 1\right)"," ",0,"1/12*(840*x^7 + 8820*x^6 + 38920*x^5 + 93450*x^4 + 131768*x^3 + 109116*x^2 + 49176*x + 9315)/(x^8 + 12*x^7 + 62*x^6 + 180*x^5 + 321*x^4 + 360*x^3 + 248*x^2 + 96*x + 16) - 70*log(x + 2) + 70*log(x + 1)","A",0
203,1,69,0,1.313818," ","integrate(1/x^3/(2*x^2-6*x+7)^2,x, algorithm=""maxima"")","\frac{234}{60025} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} {\left(2 \, x - 3\right)}\right) - \frac{276 \, x^{3} - 814 \, x^{2} + 630 \, x + 245}{3430 \, {\left(2 \, x^{4} - 6 \, x^{3} + 7 \, x^{2}\right)}} - \frac{40}{2401} \, \log\left(2 \, x^{2} - 6 \, x + 7\right) + \frac{80}{2401} \, \log\left(x\right)"," ",0,"234/60025*sqrt(5)*arctan(1/5*sqrt(5)*(2*x - 3)) - 1/3430*(276*x^3 - 814*x^2 + 630*x + 245)/(2*x^4 - 6*x^3 + 7*x^2) - 40/2401*log(2*x^2 - 6*x + 7) + 80/2401*log(x)","A",0
204,1,90,0,0.554429," ","integrate(x^9/(x^2+3*x+2)^5,x, algorithm=""maxima"")","-\frac{17496 \, x^{7} + 184200 \, x^{6} + 813888 \, x^{5} + 1955853 \, x^{4} + 2759400 \, x^{3} + 2286008 \, x^{2} + 1030560 \, x + 195280}{12 \, {\left(x^{8} + 12 \, x^{7} + 62 \, x^{6} + 180 \, x^{5} + 321 \, x^{4} + 360 \, x^{3} + 248 \, x^{2} + 96 \, x + 16\right)}} + 1472 \, \log\left(x + 2\right) - 1471 \, \log\left(x + 1\right)"," ",0,"-1/12*(17496*x^7 + 184200*x^6 + 813888*x^5 + 1955853*x^4 + 2759400*x^3 + 2286008*x^2 + 1030560*x + 195280)/(x^8 + 12*x^7 + 62*x^6 + 180*x^5 + 321*x^4 + 360*x^3 + 248*x^2 + 96*x + 16) + 1472*log(x + 2) - 1471*log(x + 1)","A",0
205,1,94,0,0.617937," ","integrate((1+2*x)^2/(2*x^2+5*x+3)^5,x, algorithm=""maxima"")","\frac{238080 \, x^{7} + 2083200 \, x^{6} + 7757440 \, x^{5} + 15934000 \, x^{4} + 19495776 \, x^{3} + 14209160 \, x^{2} + 5712464 \, x + 977397}{12 \, {\left(16 \, x^{8} + 160 \, x^{7} + 696 \, x^{6} + 1720 \, x^{5} + 2641 \, x^{4} + 2580 \, x^{3} + 1566 \, x^{2} + 540 \, x + 81\right)}} - 2480 \, \log\left(2 \, x + 3\right) + 2480 \, \log\left(x + 1\right)"," ",0,"1/12*(238080*x^7 + 2083200*x^6 + 7757440*x^5 + 15934000*x^4 + 19495776*x^3 + 14209160*x^2 + 5712464*x + 977397)/(16*x^8 + 160*x^7 + 696*x^6 + 1720*x^5 + 2641*x^4 + 2580*x^3 + 1566*x^2 + 540*x + 81) - 2480*log(2*x + 3) + 2480*log(x + 1)","A",0
206,1,39,0,0.510732," ","integrate((-b*x^2+a)^3/x^7,x, algorithm=""maxima"")","-\frac{1}{2} \, b^{3} \log\left(x^{2}\right) - \frac{18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}}"," ",0,"-1/2*b^3*log(x^2) - 1/12*(18*a*b^2*x^4 - 9*a^2*b*x^2 + 2*a^3)/x^6","A",0
207,1,83,0,1.112629," ","integrate(x^13/(a^4+x^4)^5,x, algorithm=""maxima"")","-\frac{15 \, a^{12} x^{2} + 55 \, a^{8} x^{6} + 73 \, a^{4} x^{10} - 15 \, x^{14}}{768 \, {\left(a^{20} + 4 \, a^{16} x^{4} + 6 \, a^{12} x^{8} + 4 \, a^{8} x^{12} + a^{4} x^{16}\right)}} + \frac{5 \, \arctan\left(\frac{x^{2}}{a^{2}}\right)}{256 \, a^{6}}"," ",0,"-1/768*(15*a^12*x^2 + 55*a^8*x^6 + 73*a^4*x^10 - 15*x^14)/(a^20 + 4*a^16*x^4 + 6*a^12*x^8 + 4*a^8*x^12 + a^4*x^16) + 5/256*arctan(x^2/a^2)/a^6","A",0
208,1,31,0,0.533433," ","integrate(x^(3/2)*(x^2+1)*(-x+2*x^(1/2))^2,x, algorithm=""maxima"")","\frac{2}{13} \, x^{\frac{13}{2}} - \frac{2}{3} \, x^{6} + \frac{8}{11} \, x^{\frac{11}{2}} + \frac{2}{9} \, x^{\frac{9}{2}} - x^{4} + \frac{8}{7} \, x^{\frac{7}{2}}"," ",0,"2/13*x^(13/2) - 2/3*x^6 + 8/11*x^(11/2) + 2/9*x^(9/2) - x^4 + 8/7*x^(7/2)","A",0
209,1,31,0,0.499477," ","integrate((-3*x^(3/5)+x^(3/2))^2*(-1/3*x^(2/3)+4*x^(3/2)),x, algorithm=""maxima"")","\frac{8}{11} \, x^{\frac{11}{2}} - \frac{1}{14} \, x^{\frac{14}{3}} - \frac{120}{23} \, x^{\frac{23}{5}} + \frac{60}{113} \, x^{\frac{113}{30}} + \frac{360}{37} \, x^{\frac{37}{10}} - \frac{45}{43} \, x^{\frac{43}{15}}"," ",0,"8/11*x^(11/2) - 1/14*x^(14/3) - 120/23*x^(23/5) + 60/113*x^(113/30) + 360/37*x^(37/10) - 45/43*x^(43/15)","A",0
210,1,18,0,0.717666," ","integrate(1/(1+(1+x)^(1/2)),x, algorithm=""maxima"")","2 \, \sqrt{x + 1} - 2 \, \log\left(\sqrt{x + 1} + 1\right)"," ",0,"2*sqrt(x + 1) - 2*log(sqrt(x + 1) + 1)","A",0
211,1,12,0,0.522343," ","integrate(x/(1+(1+x)^(1/2)),x, algorithm=""maxima"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - x - 1"," ",0,"2/3*(x + 1)^(3/2) - x - 1","A",0
212,1,20,0,0.478388," ","integrate((1+(1+x)^(1/2))/(-1+(1+x)^(1/2)),x, algorithm=""maxima"")","x + 4 \, \sqrt{x + 1} + 4 \, \log\left(\sqrt{x + 1} - 1\right) + 1"," ",0,"x + 4*sqrt(x + 1) + 4*log(sqrt(x + 1) - 1) + 1","A",0
213,1,25,0,0.518345," ","integrate(1/((1+x)^(2/3)-(1+x)^(1/2)),x, algorithm=""maxima"")","3 \, {\left(x + 1\right)}^{\frac{1}{3}} + 6 \, {\left(x + 1\right)}^{\frac{1}{6}} + 6 \, \log\left({\left(x + 1\right)}^{\frac{1}{6}} - 1\right)"," ",0,"3*(x + 1)^(1/3) + 6*(x + 1)^(1/6) + 6*log((x + 1)^(1/6) - 1)","A",0
214,1,19,0,0.494361," ","integrate((1+x^(1/4))^(1/3)/x^(1/2),x, algorithm=""maxima"")","\frac{12}{7} \, {\left(x^{\frac{1}{4}} + 1\right)}^{\frac{7}{3}} - 3 \, {\left(x^{\frac{1}{4}} + 1\right)}^{\frac{4}{3}}"," ",0,"12/7*(x^(1/4) + 1)^(7/3) - 3*(x^(1/4) + 1)^(4/3)","A",0
215,1,55,0,0.679553," ","integrate(1/x^3/(1+x)^(3/2),x, algorithm=""maxima"")","\frac{15 \, {\left(x + 1\right)}^{2} - 25 \, x - 17}{4 \, {\left({\left(x + 1\right)}^{\frac{5}{2}} - 2 \, {\left(x + 1\right)}^{\frac{3}{2}} + \sqrt{x + 1}\right)}} - \frac{15}{8} \, \log\left(\sqrt{x + 1} + 1\right) + \frac{15}{8} \, \log\left(\sqrt{x + 1} - 1\right)"," ",0,"1/4*(15*(x + 1)^2 - 25*x - 17)/((x + 1)^(5/2) - 2*(x + 1)^(3/2) + sqrt(x + 1)) - 15/8*log(sqrt(x + 1) + 1) + 15/8*log(sqrt(x + 1) - 1)","A",0
216,1,111,0,0.522761," ","integrate(1/(1-x)^(7/2)/x^5,x, algorithm=""maxima"")","\frac{45045 \, {\left(x - 1\right)}^{6} + 165165 \, {\left(x - 1\right)}^{5} + 219219 \, {\left(x - 1\right)}^{4} + 119691 \, {\left(x - 1\right)}^{3} + 18304 \, {\left(x - 1\right)}^{2} - 1664 \, x + 2048}{960 \, {\left({\left(-x + 1\right)}^{\frac{13}{2}} - 4 \, {\left(-x + 1\right)}^{\frac{11}{2}} + 6 \, {\left(-x + 1\right)}^{\frac{9}{2}} - 4 \, {\left(-x + 1\right)}^{\frac{7}{2}} + {\left(-x + 1\right)}^{\frac{5}{2}}\right)}} - \frac{3003}{128} \, \log\left(\sqrt{-x + 1} + 1\right) + \frac{3003}{128} \, \log\left(\sqrt{-x + 1} - 1\right)"," ",0,"1/960*(45045*(x - 1)^6 + 165165*(x - 1)^5 + 219219*(x - 1)^4 + 119691*(x - 1)^3 + 18304*(x - 1)^2 - 1664*x + 2048)/((-x + 1)^(13/2) - 4*(-x + 1)^(11/2) + 6*(-x + 1)^(9/2) - 4*(-x + 1)^(7/2) + (-x + 1)^(5/2)) - 3003/128*log(sqrt(-x + 1) + 1) + 3003/128*log(sqrt(-x + 1) - 1)","A",0
217,1,105,0,1.393446," ","integrate(1/(-1+x)^(2/3)/x^5,x, algorithm=""maxima"")","\frac{110}{243} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{220 \, {\left(x - 1\right)}^{\frac{10}{3}} + 792 \, {\left(x - 1\right)}^{\frac{7}{3}} + 1023 \, {\left(x - 1\right)}^{\frac{4}{3}} + 532 \, {\left(x - 1\right)}^{\frac{1}{3}}}{324 \, {\left({\left(x - 1\right)}^{4} + 4 \, {\left(x - 1\right)}^{3} + 6 \, {\left(x - 1\right)}^{2} + 4 \, x - 3\right)}} - \frac{55}{243} \, \log\left({\left(x - 1\right)}^{\frac{2}{3}} - {\left(x - 1\right)}^{\frac{1}{3}} + 1\right) + \frac{110}{243} \, \log\left({\left(x - 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"110/243*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x - 1)^(1/3) - 1)) + 1/324*(220*(x - 1)^(10/3) + 792*(x - 1)^(7/3) + 1023*(x - 1)^(4/3) + 532*(x - 1)^(1/3))/((x - 1)^4 + 4*(x - 1)^3 + 6*(x - 1)^2 + 4*x - 3) - 55/243*log((x - 1)^(2/3) - (x - 1)^(1/3) + 1) + 110/243*log((x - 1)^(1/3) + 1)","A",0
218,1,43,0,1.380855," ","integrate(((1-x)/(1+x))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-\frac{x - 1}{x + 1}}}{\frac{x - 1}{x + 1} - 1} - 2 \, \arctan\left(\sqrt{-\frac{x - 1}{x + 1}}\right)"," ",0,"-2*sqrt(-(x - 1)/(x + 1))/((x - 1)/(x + 1) - 1) - 2*arctan(sqrt(-(x - 1)/(x + 1)))","A",0
219,1,130,0,1.448721," ","integrate(x*((-a+x)/(b-x))^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \arctan\left(\sqrt{-\frac{a - x}{b - x}}\right) - \frac{{\left(a^{2} - 6 \, a b + 5 \, b^{2}\right)} \left(-\frac{a - x}{b - x}\right)^{\frac{3}{2}} - {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sqrt{-\frac{a - x}{b - x}}}{4 \, {\left(\frac{{\left(a - x\right)}^{2}}{{\left(b - x\right)}^{2}} - \frac{2 \, {\left(a - x\right)}}{b - x} + 1\right)}}"," ",0,"-1/4*(a^2 + 2*a*b - 3*b^2)*arctan(sqrt(-(a - x)/(b - x))) - 1/4*((a^2 - 6*a*b + 5*b^2)*(-(a - x)/(b - x))^(3/2) - (a^2 + 2*a*b - 3*b^2)*sqrt(-(a - x)/(b - x)))/((a - x)^2/(b - x)^2 - 2*(a - x)/(b - x) + 1)","A",0
220,0,0,0,0.000000," ","integrate((-5+x)^(1/2)*(3+x)^(1/2)/(-1+x)/(x^2-25),x, algorithm=""maxima"")","\int \frac{\sqrt{x + 3} \sqrt{x - 5}}{{\left(x^{2} - 25\right)} {\left(x - 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x + 3)*sqrt(x - 5)/((x^2 - 25)*(x - 1)), x)","F",0
221,0,0,0,0.000000," ","integrate(x^2*(-x^2+1)^(1/4)*(1+x)^(1/2)/(1-x)^(1/2)/((1-x)^(1/2)-(1+x)^(1/2)),x, algorithm=""maxima"")","-\int \frac{{\left(-x^{2} + 1\right)}^{\frac{1}{4}} \sqrt{x + 1} x^{2}}{\sqrt{-x + 1} {\left(\sqrt{x + 1} - \sqrt{-x + 1}\right)}}\,{d x}"," ",0,"-integrate((-x^2 + 1)^(1/4)*sqrt(x + 1)*x^2/(sqrt(-x + 1)*(sqrt(x + 1) - sqrt(-x + 1))), x)","F",0
222,0,0,0,0.000000," ","integrate(x*(1+x)^(2/3)*(1-x)^(1/2)/(-(1-x)^(5/6)*(1+x)^(1/3)+(1-x)^(2/3)*(1+x)^(1/2)),x, algorithm=""maxima"")","\int \frac{{\left(x + 1\right)}^{\frac{2}{3}} x \sqrt{-x + 1}}{\sqrt{x + 1} {\left(-x + 1\right)}^{\frac{2}{3}} - {\left(x + 1\right)}^{\frac{1}{3}} {\left(-x + 1\right)}^{\frac{5}{6}}}\,{d x}"," ",0,"integrate((x + 1)^(2/3)*x*sqrt(-x + 1)/(sqrt(x + 1)*(-x + 1)^(2/3) - (x + 1)^(1/3)*(-x + 1)^(5/6)), x)","F",0
223,0,0,0,0.000000," ","integrate(1/((-1+x)^4*(1+x)^2)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left({\left(x + 1\right)}^{2} {\left(x - 1\right)}^{4}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((x + 1)^2*(x - 1)^4)^(-1/3), x)","F",0
224,0,0,0,0.000000," ","integrate(1/((-1+x)^3*(2+x)^5)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{\left({\left(x + 2\right)}^{5} {\left(x - 1\right)}^{3}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(((x + 2)^5*(x - 1)^3)^(-1/4), x)","F",0
225,0,0,0,0.000000," ","integrate(1/((-1+x)^7*(1+x)^2)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left({\left(x + 1\right)}^{2} {\left(x - 1\right)}^{7}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((x + 1)^2*(x - 1)^7)^(-1/3), x)","F",0
226,0,0,0,0.000000," ","integrate(1/((-1+x)^2*(1+x))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left({\left(x + 1\right)} {\left(x - 1\right)}^{2}\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(((x + 1)*(x - 1)^2)^(-1/3), x)","F",0
227,0,0,0,0.000000," ","integrate((1/x+x)/((-2+x)*(1+x)^3)^(1/2),x, algorithm=""maxima"")","\int \frac{x + \frac{1}{x}}{\sqrt{{\left(x + 1\right)}^{3} {\left(x - 2\right)}}}\,{d x}"," ",0,"integrate((x + 1/x)/sqrt((x + 1)^3*(x - 2)), x)","F",0
228,0,0,0,0.000000," ","integrate(((-1+x)^2*(1+x))^(1/3)/x^2,x, algorithm=""maxima"")","\int \frac{\left({\left(x + 1\right)} {\left(x - 1\right)}^{2}\right)^{\frac{1}{3}}}{x^{2}}\,{d x}"," ",0,"integrate(((x + 1)*(x - 1)^2)^(1/3)/x^2, x)","F",0
229,1,51,0,0.530561," ","integrate(1/(x^2-2*x-3)^(5/2),x, algorithm=""maxima"")","\frac{x}{24 \, \sqrt{x^{2} - 2 \, x - 3}} - \frac{1}{24 \, \sqrt{x^{2} - 2 \, x - 3}} - \frac{x}{12 \, {\left(x^{2} - 2 \, x - 3\right)}^{\frac{3}{2}}} + \frac{1}{12 \, {\left(x^{2} - 2 \, x - 3\right)}^{\frac{3}{2}}}"," ",0,"1/24*x/sqrt(x^2 - 2*x - 3) - 1/24/sqrt(x^2 - 2*x - 3) - 1/12*x/(x^2 - 2*x - 3)^(3/2) + 1/12/(x^2 - 2*x - 3)^(3/2)","A",0
230,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{x^{3} - 5 \, x^{2} + 3 \, x + 9}}\,{d x}"," ",0,"integrate(1/sqrt(x^3 - 5*x^2 + 3*x + 9), x)","F",0
231,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} - 5 \, x^{2} + 3 \, x + 9\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((x^3 - 5*x^2 + 3*x + 9)^(-3/2), x)","F",0
232,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} - 5 \, x^{2} + 3 \, x + 9\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 - 5*x^2 + 3*x + 9)^(-1/3), x)","F",0
233,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(2/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} - 5 \, x^{2} + 3 \, x + 9\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((x^3 - 5*x^2 + 3*x + 9)^(-2/3), x)","F",0
234,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(4/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} - 5 \, x^{2} + 3 \, x + 9\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((x^3 - 5*x^2 + 3*x + 9)^(-4/3), x)","F",0
235,1,16,0,1.296942," ","integrate(1/(-2*x^2+3*x+4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \arcsin\left(-\frac{1}{41} \, \sqrt{41} {\left(4 \, x - 3\right)}\right)"," ",0,"-1/2*sqrt(2)*arcsin(-1/41*sqrt(41)*(4*x - 3))","A",0
236,1,8,0,1.167627," ","integrate(1/(-x^2+4*x-3)^(1/2),x, algorithm=""maxima"")","-\arcsin\left(-x + 2\right)"," ",0,"-arcsin(-x + 2)","A",0
237,1,11,0,1.097169," ","integrate(1/(-3*x^2-5*x-2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \arcsin\left(6 \, x + 5\right)"," ",0,"1/3*sqrt(3)*arcsin(6*x + 5)","A",0
238,0,0,0,0.000000," ","integrate(1/(x^2+4)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 4\right)} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/((x^2 + 4)*sqrt(-x^2 + 1)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(x^2+4)/(4*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{4 \, x^{2} + 1} {\left(x^{2} + 4\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(4*x^2 + 1)*(x^2 + 4)), x)","F",0
240,1,112,0,1.375309," ","integrate(x/(-x^2+3)/(-x^2+5)^(1/2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{3} {\left(\sqrt{3} \sqrt{2} \log\left(\sqrt{3} + \frac{2 \, \sqrt{2} \sqrt{-x^{2} + 5}}{{\left| 2 \, x + 2 \, \sqrt{3} \right|}} + \frac{4}{{\left| 2 \, x + 2 \, \sqrt{3} \right|}}\right) + \sqrt{3} \sqrt{2} \log\left(-\sqrt{3} + \frac{2 \, \sqrt{2} \sqrt{-x^{2} + 5}}{{\left| 2 \, x - 2 \, \sqrt{3} \right|}} + \frac{4}{{\left| 2 \, x - 2 \, \sqrt{3} \right|}}\right)\right)}"," ",0,"1/12*sqrt(3)*(sqrt(3)*sqrt(2)*log(sqrt(3) + 2*sqrt(2)*sqrt(-x^2 + 5)/abs(2*x + 2*sqrt(3)) + 4/abs(2*x + 2*sqrt(3))) + sqrt(3)*sqrt(2)*log(-sqrt(3) + 2*sqrt(2)*sqrt(-x^2 + 5)/abs(2*x - 2*sqrt(3)) + 4/abs(2*x - 2*sqrt(3))))","B",0
241,1,101,0,1.371840," ","integrate(x/(-x^2+5)/(-x^2+3)^(1/2),x, algorithm=""maxima"")","-\frac{1}{20} \, \sqrt{5} {\left(\sqrt{5} \sqrt{2} \arcsin\left(\frac{2 \, \sqrt{5} \sqrt{3} x}{3 \, {\left| 2 \, x + 2 \, \sqrt{5} \right|}} + \frac{2 \, \sqrt{3}}{{\left| 2 \, x + 2 \, \sqrt{5} \right|}}\right) - \sqrt{5} \sqrt{2} \arcsin\left(\frac{2 \, \sqrt{5} \sqrt{3} x}{3 \, {\left| 2 \, x - 2 \, \sqrt{5} \right|}} - \frac{2 \, \sqrt{3}}{{\left| 2 \, x - 2 \, \sqrt{5} \right|}}\right)\right)}"," ",0,"-1/20*sqrt(5)*(sqrt(5)*sqrt(2)*arcsin(2/3*sqrt(5)*sqrt(3)*x/abs(2*x + 2*sqrt(5)) + 2*sqrt(3)/abs(2*x + 2*sqrt(5))) - sqrt(5)*sqrt(2)*arcsin(2/3*sqrt(5)*sqrt(3)*x/abs(2*x - 2*sqrt(5)) - 2*sqrt(3)/abs(2*x - 2*sqrt(5))))","B",0
242,0,0,0,0.000000," ","integrate(1/(x^4-1)/(x^2+2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{4} - 1\right)} \sqrt{x^{2} + 2}}\,{d x}"," ",0,"integrate(1/((x^4 - 1)*sqrt(x^2 + 2)), x)","F",0
243,1,54,0,1.295337," ","integrate(x/(x^2-1)/(x^2+2*x+4)^(1/2),x, algorithm=""maxima"")","-\frac{1}{14} \, \sqrt{7} \operatorname{arsinh}\left(\frac{4 \, \sqrt{3} x}{3 \, {\left| 2 \, x - 2 \right|}} + \frac{10 \, \sqrt{3}}{3 \, {\left| 2 \, x - 2 \right|}}\right) - \frac{1}{6} \, \sqrt{3} \operatorname{arsinh}\left(\frac{2 \, \sqrt{3}}{{\left| 2 \, x + 2 \right|}}\right)"," ",0,"-1/14*sqrt(7)*arcsinh(4/3*sqrt(3)*x/abs(2*x - 2) + 10/3*sqrt(3)/abs(2*x - 2)) - 1/6*sqrt(3)*arcsinh(2*sqrt(3)/abs(2*x + 2))","A",0
244,0,0,0,0.000000," ","integrate(1/(x^3-8)/(x^2+2*x+5)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} - 8\right)} \sqrt{x^{2} + 2 \, x + 5}}\,{d x}"," ",0,"integrate(1/((x^3 - 8)*sqrt(x^2 + 2*x + 5)), x)","F",0
245,0,0,0,0.000000," ","integrate(x/(x^2+x+4)/(4*x^2+4*x+5)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{4 \, x^{2} + 4 \, x + 5} {\left(x^{2} + x + 4\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(4*x^2 + 4*x + 5)*(x^2 + x + 4)), x)","F",0
246,0,0,0,0.000000," ","integrate((3+x)/(x^2+1)/(x^2+x+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x + 3}{\sqrt{x^{2} + x + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate((x + 3)/(sqrt(x^2 + x + 1)*(x^2 + 1)), x)","F",0
247,0,0,0,0.000000," ","integrate((1+2*x)/(3*x^2+4*x+4)/(x^2+6*x-1)^(1/2),x, algorithm=""maxima"")","\int \frac{2 \, x + 1}{{\left(3 \, x^{2} + 4 \, x + 4\right)} \sqrt{x^{2} + 6 \, x - 1}}\,{d x}"," ",0,"integrate((2*x + 1)/((3*x^2 + 4*x + 4)*sqrt(x^2 + 6*x - 1)), x)","F",0
248,0,0,0,0.000000," ","integrate((A*x+B)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x, algorithm=""maxima"")","\int \frac{A x + B}{\sqrt{10 \, x^{2} - 22 \, x + 13} {\left(5 \, x^{2} - 18 \, x + 17\right)}}\,{d x}"," ",0,"integrate((A*x + B)/(sqrt(10*x^2 - 22*x + 13)*(5*x^2 - 18*x + 17)), x)","F",0
249,0,0,0,0.000000," ","integrate((-2+x)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x, algorithm=""maxima"")","\int \frac{x - 2}{\sqrt{10 \, x^{2} - 22 \, x + 13} {\left(5 \, x^{2} - 18 \, x + 17\right)}}\,{d x}"," ",0,"integrate((x - 2)/(sqrt(10*x^2 - 22*x + 13)*(5*x^2 - 18*x + 17)), x)","F",0
250,1,48,0,1.223967," ","integrate(x^4*(-x^2+5)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(-x^{2} + 5\right)}^{\frac{3}{2}} x^{3} - \frac{5}{8} \, {\left(-x^{2} + 5\right)}^{\frac{3}{2}} x + \frac{25}{16} \, \sqrt{-x^{2} + 5} x + \frac{125}{16} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} x\right)"," ",0,"-1/6*(-x^2 + 5)^(3/2)*x^3 - 5/8*(-x^2 + 5)^(3/2)*x + 25/16*sqrt(-x^2 + 5)*x + 125/16*arcsin(1/5*sqrt(5)*x)","A",0
251,1,37,0,1.092232," ","integrate(1/x^6/(x^2+2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{x^{2} + 2}}{15 \, x} + \frac{\sqrt{x^{2} + 2}}{15 \, x^{3}} - \frac{\sqrt{x^{2} + 2}}{10 \, x^{5}}"," ",0,"-1/15*sqrt(x^2 + 2)/x + 1/15*sqrt(x^2 + 2)/x^3 - 1/10*sqrt(x^2 + 2)/x^5","A",0
252,1,37,0,0.541757," ","integrate(1/(2*x^2+3)^(7/2),x, algorithm=""maxima"")","\frac{8 \, x}{405 \, \sqrt{2 \, x^{2} + 3}} + \frac{4 \, x}{135 \, {\left(2 \, x^{2} + 3\right)}^{\frac{3}{2}}} + \frac{x}{15 \, {\left(2 \, x^{2} + 3\right)}^{\frac{5}{2}}}"," ",0,"8/405*x/sqrt(2*x^2 + 3) + 4/135*x/(2*x^2 + 3)^(3/2) + 1/15*x/(2*x^2 + 3)^(5/2)","A",0
253,1,10,0,0.457638," ","integrate(x/(1+x^2+a*(x^2+1)^(1/2)),x, algorithm=""maxima"")","\log\left(a + \sqrt{x^{2} + 1}\right)"," ",0,"log(a + sqrt(x^2 + 1))","A",0
254,1,10,0,1.425130," ","integrate((x^2-x+1)/(x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{1}{\sqrt{x^{2} + 1}} + \operatorname{arsinh}\left(x\right)"," ",0,"1/sqrt(x^2 + 1) + arcsinh(x)","A",0
255,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(x^2+2),x, algorithm=""maxima"")","\frac{\sqrt{x^{2} + 1} x}{x^{2} + 2} + \int \frac{\sqrt{x^{2} + 1} x^{4}}{x^{6} + 5 \, x^{4} + 8 \, x^{2} + 4}\,{d x}"," ",0,"sqrt(x^2 + 1)*x/(x^2 + 2) + integrate(sqrt(x^2 + 1)*x^4/(x^6 + 5*x^4 + 8*x^2 + 4), x)","F",0
256,0,0,0,0.000000," ","integrate(1/(x^2+2)^2/(x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 2\right)}^{2} \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(1/((x^2 + 2)^2*sqrt(x^2 + 1)), x)","F",0
257,1,107,0,1.463747," ","integrate(x^2/(x^2-6)/(x^2-2)^(1/2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{6} {\left(2 \, \sqrt{6} \log\left(x + \sqrt{x^{2} - 2}\right) - 3 \, \log\left(\sqrt{6} + \frac{4 \, \sqrt{x^{2} - 2}}{{\left| 2 \, x - 2 \, \sqrt{6} \right|}} + \frac{8}{{\left| 2 \, x - 2 \, \sqrt{6} \right|}}\right) + 3 \, \log\left(-\sqrt{6} + \frac{4 \, \sqrt{x^{2} - 2}}{{\left| 2 \, x + 2 \, \sqrt{6} \right|}} + \frac{8}{{\left| 2 \, x + 2 \, \sqrt{6} \right|}}\right)\right)}"," ",0,"1/12*sqrt(6)*(2*sqrt(6)*log(x + sqrt(x^2 - 2)) - 3*log(sqrt(6) + 4*sqrt(x^2 - 2)/abs(2*x - 2*sqrt(6)) + 8/abs(2*x - 2*sqrt(6))) + 3*log(-sqrt(6) + 4*sqrt(x^2 - 2)/abs(2*x + 2*sqrt(6)) + 8/abs(2*x + 2*sqrt(6))))","B",0
258,0,0,0,0.000000," ","integrate((x^2+5)/(x^2+1)^2/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} + 5}{{\left(x^{2} + 1\right)}^{2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate((x^2 + 5)/((x^2 + 1)^2*sqrt(-x^2 + 1)), x)","F",0
259,0,0,0,0.000000," ","integrate((4*x-(-x^2+1)^(1/2))/(5+(-x^2+1)^(1/2)),x, algorithm=""maxima"")","-x - 4 \, \sqrt{-x^{2} + 1} + 5 \, \int \frac{1}{\sqrt{x + 1} \sqrt{-x + 1} + 5}\,{d x} + 20 \, \log\left(\sqrt{-x^{2} + 1} + 5\right)"," ",0,"-x - 4*sqrt(-x^2 + 1) + 5*integrate(1/(sqrt(x + 1)*sqrt(-x + 1) + 5), x) + 20*log(sqrt(-x^2 + 1) + 5)","F",0
260,0,0,0,0.000000," ","integrate(x^2*(2-(x^2+1)^(1/2))/(1-x^3+(x^2+1)^(3/2))/(x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{2} \, \arctan\left(x\right) + \int -\frac{3 \, x^{10} - 4 \, x^{9} + 5 \, x^{8} - 2 \, x^{7} + 15 \, x^{6} + 6 \, x^{5} + 9 \, x^{4}}{2 \, {\left(2 \, x^{13} + 7 \, x^{11} - 4 \, x^{10} + 11 \, x^{9} - 11 \, x^{8} + 13 \, x^{7} - 13 \, x^{6} + 11 \, x^{5} - 11 \, x^{4} + 4 \, x^{3} - 7 \, x^{2} - 2 \, {\left(x^{12} + 3 \, x^{10} - 2 \, x^{9} + 3 \, x^{8} - 6 \, x^{7} + 2 \, x^{6} - 6 \, x^{5} + 3 \, x^{4} - 2 \, x^{3} + 3 \, x^{2} + 1\right)} \sqrt{x^{2} + 1} - 2\right)}}\,{d x} + \frac{1}{6} \, \log\left(x^{2} + x + 1\right) + \frac{1}{6} \, \log\left(x - 1\right)"," ",0,"-1/2*x/(x^2 + 1) + 1/2*arctan(x) + integrate(-1/2*(3*x^10 - 4*x^9 + 5*x^8 - 2*x^7 + 15*x^6 + 6*x^5 + 9*x^4)/(2*x^13 + 7*x^11 - 4*x^10 + 11*x^9 - 11*x^8 + 13*x^7 - 13*x^6 + 11*x^5 - 11*x^4 + 4*x^3 - 7*x^2 - 2*(x^12 + 3*x^10 - 2*x^9 + 3*x^8 - 6*x^7 + 2*x^6 - 6*x^5 + 3*x^4 - 2*x^3 + 3*x^2 + 1)*sqrt(x^2 + 1) - 2), x) + 1/6*log(x^2 + x + 1) + 1/6*log(x - 1)","F",0
261,1,63,0,1.174681," ","integrate(x*(2*r*x-x^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, r^{3} \arcsin\left(\frac{r - x}{r}\right) - \frac{1}{2} \, \sqrt{2 \, r x - x^{2}} r^{2} + \frac{1}{2} \, \sqrt{2 \, r x - x^{2}} r x - \frac{1}{3} \, {\left(2 \, r x - x^{2}\right)}^{\frac{3}{2}}"," ",0,"-1/2*r^3*arcsin((r - x)/r) - 1/2*sqrt(2*r*x - x^2)*r^2 + 1/2*sqrt(2*r*x - x^2)*r*x - 1/3*(2*r*x - x^2)^(3/2)","A",0
262,1,81,0,1.184289," ","integrate(x^2*(2*r*x-x^2)^(1/2),x, algorithm=""maxima"")","-\frac{5}{8} \, r^{4} \arcsin\left(\frac{r - x}{r}\right) - \frac{5}{8} \, \sqrt{2 \, r x - x^{2}} r^{3} + \frac{5}{8} \, \sqrt{2 \, r x - x^{2}} r^{2} x - \frac{5}{12} \, {\left(2 \, r x - x^{2}\right)}^{\frac{3}{2}} r - \frac{1}{4} \, {\left(2 \, r x - x^{2}\right)}^{\frac{3}{2}} x"," ",0,"-5/8*r^4*arcsin((r - x)/r) - 5/8*sqrt(2*r*x - x^2)*r^3 + 5/8*sqrt(2*r*x - x^2)*r^2*x - 5/12*(2*r*x - x^2)^(3/2)*r - 1/4*(2*r*x - x^2)^(3/2)*x","A",0
263,1,101,0,1.100107," ","integrate(x^3*(2*r*x-x^2)^(1/2),x, algorithm=""maxima"")","-\frac{7}{8} \, r^{5} \arcsin\left(\frac{r - x}{r}\right) - \frac{7}{8} \, \sqrt{2 \, r x - x^{2}} r^{4} + \frac{7}{8} \, \sqrt{2 \, r x - x^{2}} r^{3} x - \frac{7}{12} \, {\left(2 \, r x - x^{2}\right)}^{\frac{3}{2}} r^{2} - \frac{7}{20} \, {\left(2 \, r x - x^{2}\right)}^{\frac{3}{2}} r x - \frac{1}{5} \, {\left(2 \, r x - x^{2}\right)}^{\frac{3}{2}} x^{2}"," ",0,"-7/8*r^5*arcsin((r - x)/r) - 7/8*sqrt(2*r*x - x^2)*r^4 + 7/8*sqrt(2*r*x - x^2)*r^3*x - 7/12*(2*r*x - x^2)^(3/2)*r^2 - 7/20*(2*r*x - x^2)^(3/2)*r*x - 1/5*(2*r*x - x^2)^(3/2)*x^2","A",0
264,1,54,0,1.331509," ","integrate(1/(x^2-1)/(x^2+2*x)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{3} \log\left(\frac{2 \, \sqrt{3} \sqrt{x^{2} + 2 \, x}}{{\left| 2 \, x - 2 \right|}} + \frac{6}{{\left| 2 \, x - 2 \right|}} + 2\right) + \frac{1}{2} \, \arcsin\left(\frac{2}{{\left| 2 \, x + 2 \right|}}\right)"," ",0,"-1/6*sqrt(3)*log(2*sqrt(3)*sqrt(x^2 + 2*x)/abs(2*x - 2) + 6/abs(2*x - 2) + 2) + 1/2*arcsin(2/abs(2*x + 2))","A",0
265,1,66,0,1.329980," ","integrate((-2+3*x)/(1+x)^3/(-x^2+2*x)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{3} \arcsin\left(\frac{2 \, x}{{\left| x + 1 \right|}} - \frac{1}{{\left| x + 1 \right|}}\right) - \frac{5 \, \sqrt{-x^{2} + 2 \, x}}{6 \, {\left(x^{2} + 2 \, x + 1\right)}} - \frac{2 \, \sqrt{-x^{2} + 2 \, x}}{3 \, {\left(x + 1\right)}}"," ",0,"-1/6*sqrt(3)*arcsin(2*x/abs(x + 1) - 1/abs(x + 1)) - 5/6*sqrt(-x^2 + 2*x)/(x^2 + 2*x + 1) - 2/3*sqrt(-x^2 + 2*x)/(x + 1)","A",0
266,1,11,0,1.404201," ","integrate(1/(x^2+x+1)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"arcsinh(1/3*sqrt(3)*(2*x + 1))","A",0
267,1,48,0,1.264100," ","integrate(x^3/(x^2+x+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{x^{2} + x + 1} x^{2} - \frac{5}{12} \, \sqrt{x^{2} + x + 1} x - \frac{1}{24} \, \sqrt{x^{2} + x + 1} + \frac{7}{16} \, \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"1/3*sqrt(x^2 + x + 1)*x^2 - 5/12*sqrt(x^2 + x + 1)*x - 1/24*sqrt(x^2 + x + 1) + 7/16*arcsinh(1/3*sqrt(3)*(2*x + 1))","A",0
268,1,22,0,0.593494," ","integrate(1/(x^2+x+1)^(3/2),x, algorithm=""maxima"")","\frac{4 \, x}{3 \, \sqrt{x^{2} + x + 1}} + \frac{2}{3 \, \sqrt{x^{2} + x + 1}}"," ",0,"4/3*x/sqrt(x^2 + x + 1) + 2/3/sqrt(x^2 + x + 1)","A",0
269,1,22,0,0.430836," ","integrate(x/(x^2+x+1)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, x}{3 \, \sqrt{x^{2} + x + 1}} - \frac{4}{3 \, \sqrt{x^{2} + x + 1}}"," ",0,"-2/3*x/sqrt(x^2 + x + 1) - 4/3/sqrt(x^2 + x + 1)","A",0
270,1,47,0,1.105330," ","integrate(x^3/(x^2+x+1)^(3/2),x, algorithm=""maxima"")","\frac{x^{2}}{\sqrt{x^{2} + x + 1}} + \frac{7 \, x}{3 \, \sqrt{x^{2} + x + 1}} + \frac{5}{3 \, \sqrt{x^{2} + x + 1}} - \frac{3}{2} \, \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"x^2/sqrt(x^2 + x + 1) + 7/3*x/sqrt(x^2 + x + 1) + 5/3/sqrt(x^2 + x + 1) - 3/2*arcsinh(1/3*sqrt(3)*(2*x + 1))","A",0
271,1,56,0,1.161860," ","integrate(x^2*(x^2+x+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(x^{2} + x + 1\right)}^{\frac{3}{2}} x - \frac{5}{24} \, {\left(x^{2} + x + 1\right)}^{\frac{3}{2}} + \frac{1}{32} \, \sqrt{x^{2} + x + 1} x + \frac{1}{64} \, \sqrt{x^{2} + x + 1} + \frac{3}{128} \, \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"1/4*(x^2 + x + 1)^(3/2)*x - 5/24*(x^2 + x + 1)^(3/2) + 1/32*sqrt(x^2 + x + 1)*x + 1/64*sqrt(x^2 + x + 1) + 3/128*arcsinh(1/3*sqrt(3)*(2*x + 1))","A",0
272,1,56,0,1.285259," ","integrate((x^2+x+1)^(3/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(x^{2} + x + 1\right)}^{\frac{3}{2}} x + \frac{1}{8} \, {\left(x^{2} + x + 1\right)}^{\frac{3}{2}} + \frac{9}{32} \, \sqrt{x^{2} + x + 1} x + \frac{9}{64} \, \sqrt{x^{2} + x + 1} + \frac{27}{128} \, \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"1/4*(x^2 + x + 1)^(3/2)*x + 1/8*(x^2 + x + 1)^(3/2) + 9/32*sqrt(x^2 + x + 1)*x + 9/64*sqrt(x^2 + x + 1) + 27/128*arcsinh(1/3*sqrt(3)*(2*x + 1))","A",0
273,1,77,0,1.430264," ","integrate((x^2+x+1)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(x^{2} + x + 1\right)}^{\frac{5}{2}} x + \frac{1}{12} \, {\left(x^{2} + x + 1\right)}^{\frac{5}{2}} + \frac{5}{32} \, {\left(x^{2} + x + 1\right)}^{\frac{3}{2}} x + \frac{5}{64} \, {\left(x^{2} + x + 1\right)}^{\frac{3}{2}} + \frac{45}{256} \, \sqrt{x^{2} + x + 1} x + \frac{45}{512} \, \sqrt{x^{2} + x + 1} + \frac{135}{1024} \, \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right)"," ",0,"1/6*(x^2 + x + 1)^(5/2)*x + 1/12*(x^2 + x + 1)^(5/2) + 5/32*(x^2 + x + 1)^(3/2)*x + 5/64*(x^2 + x + 1)^(3/2) + 45/256*sqrt(x^2 + x + 1)*x + 45/512*sqrt(x^2 + x + 1) + 135/1024*arcsinh(1/3*sqrt(3)*(2*x + 1))","A",0
274,1,37,0,1.033412," ","integrate(1/x^2/(x^2+x+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{x^{2} + x + 1}}{x} + \frac{1}{2} \, \operatorname{arsinh}\left(\frac{\sqrt{3} x}{3 \, {\left| x \right|}} + \frac{2 \, \sqrt{3}}{3 \, {\left| x \right|}}\right)"," ",0,"-sqrt(x^2 + x + 1)/x + 1/2*arcsinh(1/3*sqrt(3)*x/abs(x) + 2/3*sqrt(3)/abs(x))","A",0
275,1,50,0,1.235027," ","integrate(1/x^3/(x^2+x+1)^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{x^{2} + x + 1}}{4 \, x} - \frac{\sqrt{x^{2} + x + 1}}{2 \, x^{2}} + \frac{1}{8} \, \operatorname{arsinh}\left(\frac{\sqrt{3} x}{3 \, {\left| x \right|}} + \frac{2 \, \sqrt{3}}{3 \, {\left| x \right|}}\right)"," ",0,"3/4*sqrt(x^2 + x + 1)/x - 1/2*sqrt(x^2 + x + 1)/x^2 + 1/8*arcsinh(1/3*sqrt(3)*x/abs(x) + 2/3*sqrt(3)/abs(x))","A",0
276,1,58,0,1.421486," ","integrate(1/x^2/(x^2+x+1)^(3/2),x, algorithm=""maxima"")","-\frac{5 \, x}{3 \, \sqrt{x^{2} + x + 1}} - \frac{7}{3 \, \sqrt{x^{2} + x + 1}} - \frac{1}{\sqrt{x^{2} + x + 1} x} + \frac{3}{2} \, \operatorname{arsinh}\left(\frac{\sqrt{3} x}{3 \, {\left| x \right|}} + \frac{2 \, \sqrt{3}}{3 \, {\left| x \right|}}\right)"," ",0,"-5/3*x/sqrt(x^2 + x + 1) - 7/3/sqrt(x^2 + x + 1) - 1/(sqrt(x^2 + x + 1)*x) + 3/2*arcsinh(1/3*sqrt(3)*x/abs(x) + 2/3*sqrt(3)/abs(x))","A",0
277,1,71,0,1.086868," ","integrate(1/x^3/(x^2+x+1)^(3/2),x, algorithm=""maxima"")","\frac{37 \, x}{12 \, \sqrt{x^{2} + x + 1}} + \frac{23}{12 \, \sqrt{x^{2} + x + 1}} + \frac{5}{4 \, \sqrt{x^{2} + x + 1} x} - \frac{1}{2 \, \sqrt{x^{2} + x + 1} x^{2}} - \frac{3}{8} \, \operatorname{arsinh}\left(\frac{\sqrt{3} x}{3 \, {\left| x \right|}} + \frac{2 \, \sqrt{3}}{3 \, {\left| x \right|}}\right)"," ",0,"37/12*x/sqrt(x^2 + x + 1) + 23/12/sqrt(x^2 + x + 1) + 5/4/(sqrt(x^2 + x + 1)*x) - 1/2/(sqrt(x^2 + x + 1)*x^2) - 3/8*arcsinh(1/3*sqrt(3)*x/abs(x) + 2/3*sqrt(3)/abs(x))","A",0
278,1,25,0,1.238242," ","integrate(1/(1+x)/(x^2+x+1)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\frac{\sqrt{3} x}{3 \, {\left| x + 1 \right|}} - \frac{\sqrt{3}}{3 \, {\left| x + 1 \right|}}\right)"," ",0,"arcsinh(1/3*sqrt(3)*x/abs(x + 1) - 1/3*sqrt(3)/abs(x + 1))","A",0
279,0,0,0,0.000000," ","integrate(1/(x^3-x)/(x^2+2*x+4)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} - x\right)} \sqrt{x^{2} + 2 \, x + 4}}\,{d x}"," ",0,"integrate(1/((x^3 - x)*sqrt(x^2 + 2*x + 4)), x)","F",0
280,1,61,0,1.300302," ","integrate((x^2+2*x+4)^(1/2)/(-1+x)^2,x, algorithm=""maxima"")","-\frac{2}{7} \, \sqrt{7} \operatorname{arsinh}\left(\frac{2 \, \sqrt{3} x}{3 \, {\left| x - 1 \right|}} + \frac{5 \, \sqrt{3}}{3 \, {\left| x - 1 \right|}}\right) - \frac{\sqrt{x^{2} + 2 \, x + 4}}{x - 1} + \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} x + \frac{1}{3} \, \sqrt{3}\right)"," ",0,"-2/7*sqrt(7)*arcsinh(2/3*sqrt(3)*x/abs(x - 1) + 5/3*sqrt(3)/abs(x - 1)) - sqrt(x^2 + 2*x + 4)/(x - 1) + arcsinh(1/3*sqrt(3)*x + 1/3*sqrt(3))","A",0
281,0,0,0,0.000000," ","integrate((3+2*x)/(x^2+2*x+3)^2/(x^2+2*x+4)^(1/2),x, algorithm=""maxima"")","\int \frac{2 \, x + 3}{\sqrt{x^{2} + 2 \, x + 4} {\left(x^{2} + 2 \, x + 3\right)}^{2}}\,{d x}"," ",0,"integrate((2*x + 3)/(sqrt(x^2 + 2*x + 4)*(x^2 + 2*x + 3)^2), x)","F",0
282,1,28,0,1.416588," ","integrate((2*x^3+3*x^2)/(2*x^2+x-3)/(x^2+2*x-3)^(1/2),x, algorithm=""maxima"")","\sqrt{x^{2} + 2 \, x - 3} - \frac{\sqrt{x^{2} + 2 \, x - 3}}{2 \, {\left(x - 1\right)}}"," ",0,"sqrt(x^2 + 2*x - 3) - 1/2*sqrt(x^2 + 2*x - 3)/(x - 1)","A",0
283,0,0,0,0.000000," ","integrate((x^4+1)/(x^2+x+1)/(x^2+x+2)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{\sqrt{x^{2} + x + 2} {\left(x^{2} + x + 1\right)}}\,{d x}"," ",0,"integrate((x^4 + 1)/(sqrt(x^2 + x + 2)*(x^2 + x + 1)), x)","F",0
284,1,76,0,0.631801," ","integrate(1/(x^2+2*x+4)^(7/2),x, algorithm=""maxima"")","\frac{8 \, x}{405 \, \sqrt{x^{2} + 2 \, x + 4}} + \frac{8}{405 \, \sqrt{x^{2} + 2 \, x + 4}} + \frac{4 \, x}{135 \, {\left(x^{2} + 2 \, x + 4\right)}^{\frac{3}{2}}} + \frac{4}{135 \, {\left(x^{2} + 2 \, x + 4\right)}^{\frac{3}{2}}} + \frac{x}{15 \, {\left(x^{2} + 2 \, x + 4\right)}^{\frac{5}{2}}} + \frac{1}{15 \, {\left(x^{2} + 2 \, x + 4\right)}^{\frac{5}{2}}}"," ",0,"8/405*x/sqrt(x^2 + 2*x + 4) + 8/405/sqrt(x^2 + 2*x + 4) + 4/135*x/(x^2 + 2*x + 4)^(3/2) + 4/135/(x^2 + 2*x + 4)^(3/2) + 1/15*x/(x^2 + 2*x + 4)^(5/2) + 1/15/(x^2 + 2*x + 4)^(5/2)","A",0
285,1,59,0,0.437476," ","integrate(1/(3*x^2+8*x+1)^(5/2),x, algorithm=""maxima"")","\frac{6 \, x}{169 \, \sqrt{3 \, x^{2} + 8 \, x + 1}} + \frac{8}{169 \, \sqrt{3 \, x^{2} + 8 \, x + 1}} - \frac{x}{13 \, {\left(3 \, x^{2} + 8 \, x + 1\right)}^{\frac{3}{2}}} - \frac{4}{39 \, {\left(3 \, x^{2} + 8 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"6/169*x/sqrt(3*x^2 + 8*x + 1) + 8/169/sqrt(3*x^2 + 8*x + 1) - 1/13*x/(3*x^2 + 8*x + 1)^(3/2) - 4/39/(3*x^2 + 8*x + 1)^(3/2)","A",0
286,1,59,0,0.681048," ","integrate(1/(-3*x^2+4*x+5)^(5/2),x, algorithm=""maxima"")","\frac{6 \, x}{361 \, \sqrt{-3 \, x^{2} + 4 \, x + 5}} - \frac{4}{361 \, \sqrt{-3 \, x^{2} + 4 \, x + 5}} + \frac{x}{19 \, {\left(-3 \, x^{2} + 4 \, x + 5\right)}^{\frac{3}{2}}} - \frac{2}{57 \, {\left(-3 \, x^{2} + 4 \, x + 5\right)}^{\frac{3}{2}}}"," ",0,"6/361*x/sqrt(-3*x^2 + 4*x + 5) - 4/361/sqrt(-3*x^2 + 4*x + 5) + 1/19*x/(-3*x^2 + 4*x + 5)^(3/2) - 2/57/(-3*x^2 + 4*x + 5)^(3/2)","A",0
287,0,0,0,0.000000," ","integrate(1/(1+(x^2+2*x+2)^(1/2)),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{x^{2} + 2 \, x + 2} + 1}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 2*x + 2) + 1), x)","F",0
288,0,0,0,0.000000," ","integrate(1/(x+(x^2+x+1)^(1/2)),x, algorithm=""maxima"")","\int \frac{1}{x + \sqrt{x^{2} + x + 1}}\,{d x}"," ",0,"integrate(1/(x + sqrt(x^2 + x + 1)), x)","F",0
289,0,0,0,0.000000," ","integrate(x^2/(1+2*x+2*(x^2+x+1)^(1/2)),x, algorithm=""maxima"")","\int \frac{x^{2}}{2 \, x + 2 \, \sqrt{x^{2} + x + 1} + 1}\,{d x}"," ",0,"integrate(x^2/(2*x + 2*sqrt(x^2 + x + 1) + 1), x)","F",0
290,0,0,0,0.000000," ","integrate((-3*x+(x^2+x+1)^(1/2))/(-1+(x^2+x+1)^(1/2)),x, algorithm=""maxima"")","\frac{3}{4} \, x^{2} + \frac{1}{2} \, x + \int -\frac{3 \, x^{3} + 2 \, x^{2} - x}{2 \, {\left(x^{2} + x - 2 \, \sqrt{x^{2} + x + 1} + 2\right)}}\,{d x}"," ",0,"3/4*x^2 + 1/2*x + integrate(-1/2*(3*x^3 + 2*x^2 - x)/(x^2 + x - 2*sqrt(x^2 + x + 1) + 2), x)","F",0
291,0,0,0,0.000000," ","integrate((1+x)/(-(x^2+x+1)^(1/2)+(x^2+2*x+4)^(1/2)),x, algorithm=""maxima"")","\int \frac{x + 1}{\sqrt{x^{2} + 2 \, x + 4} - \sqrt{x^{2} + x + 1}}\,{d x}"," ",0,"integrate((x + 1)/(sqrt(x^2 + 2*x + 4) - sqrt(x^2 + x + 1)), x)","F",0
292,1,38,0,1.366043," ","integrate(1/x^3/(-1+x)^(1/2),x, algorithm=""maxima"")","\frac{3 \, {\left(x - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{x - 1}}{4 \, {\left({\left(x - 1\right)}^{2} + 2 \, x - 1\right)}} + \frac{3}{4} \, \arctan\left(\sqrt{x - 1}\right)"," ",0,"1/4*(3*(x - 1)^(3/2) + 5*sqrt(x - 1))/((x - 1)^2 + 2*x - 1) + 3/4*arctan(sqrt(x - 1))","A",0
293,1,11,0,0.521087," ","integrate(1/(1-3/x)^(4/3)/x^2,x, algorithm=""maxima"")","-\frac{1}{{\left(-\frac{3}{x} + 1\right)}^{\frac{1}{3}}}"," ",0,"-1/(-3/x + 1)^(1/3)","A",0
294,1,76,0,1.088032," ","integrate((-1+3*x)^(4/3)/x^2,x, algorithm=""maxima"")","-4 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(3 \, x - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + 9 \, {\left(3 \, x - 1\right)}^{\frac{1}{3}} + \frac{{\left(3 \, x - 1\right)}^{\frac{1}{3}}}{x} + 2 \, \log\left({\left(3 \, x - 1\right)}^{\frac{2}{3}} - {\left(3 \, x - 1\right)}^{\frac{1}{3}} + 1\right) - 4 \, \log\left({\left(3 \, x - 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"-4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(3*x - 1)^(1/3) - 1)) + 9*(3*x - 1)^(1/3) + (3*x - 1)^(1/3)/x + 2*log((3*x - 1)^(2/3) - (3*x - 1)^(1/3) + 1) - 4*log((3*x - 1)^(1/3) + 1)","A",0
295,1,28,0,0.612221," ","integrate((4-3*x)^(4/3)*x^2,x, algorithm=""maxima"")","-\frac{1}{117} \, {\left(-3 \, x + 4\right)}^{\frac{13}{3}} + \frac{4}{45} \, {\left(-3 \, x + 4\right)}^{\frac{10}{3}} - \frac{16}{63} \, {\left(-3 \, x + 4\right)}^{\frac{7}{3}}"," ",0,"-1/117*(-3*x + 4)^(13/3) + 4/45*(-3*x + 4)^(10/3) - 16/63*(-3*x + 4)^(7/3)","A",0
296,1,52,0,1.067854," ","integrate((1-2*x^(1/3))^(3/4)/x,x, algorithm=""maxima"")","4 \, {\left(-2 \, x^{\frac{1}{3}} + 1\right)}^{\frac{3}{4}} + 6 \, \arctan\left({\left(-2 \, x^{\frac{1}{3}} + 1\right)}^{\frac{1}{4}}\right) - 3 \, \log\left({\left(-2 \, x^{\frac{1}{3}} + 1\right)}^{\frac{1}{4}} + 1\right) + 3 \, \log\left({\left(-2 \, x^{\frac{1}{3}} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"4*(-2*x^(1/3) + 1)^(3/4) + 6*arctan((-2*x^(1/3) + 1)^(1/4)) - 3*log((-2*x^(1/3) + 1)^(1/4) + 1) + 3*log((-2*x^(1/3) + 1)^(1/4) - 1)","A",0
297,1,45,0,0.466576," ","integrate(x/(3-2*x^(1/2))^(3/4),x, algorithm=""maxima"")","\frac{1}{26} \, {\left(-2 \, \sqrt{x} + 3\right)}^{\frac{13}{4}} - \frac{1}{2} \, {\left(-2 \, \sqrt{x} + 3\right)}^{\frac{9}{4}} + \frac{27}{10} \, {\left(-2 \, \sqrt{x} + 3\right)}^{\frac{5}{4}} - \frac{27}{2} \, {\left(-2 \, \sqrt{x} + 3\right)}^{\frac{1}{4}}"," ",0,"1/26*(-2*sqrt(x) + 3)^(13/4) - 1/2*(-2*sqrt(x) + 3)^(9/4) + 27/10*(-2*sqrt(x) + 3)^(5/4) - 27/2*(-2*sqrt(x) + 3)^(1/4)","A",0
298,1,157,0,1.202087," ","integrate((-1+2*x^(1/2))^(5/4)/x^2,x, algorithm=""maxima"")","\frac{5}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(2 \, \sqrt{x} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{5}{4} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(2 \, \sqrt{x} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{5}{8} \, \sqrt{2} \log\left(\sqrt{2} {\left(2 \, \sqrt{x} - 1\right)}^{\frac{1}{4}} + \sqrt{2 \, \sqrt{x} - 1} + 1\right) - \frac{5}{8} \, \sqrt{2} \log\left(-\sqrt{2} {\left(2 \, \sqrt{x} - 1\right)}^{\frac{1}{4}} + \sqrt{2 \, \sqrt{x} - 1} + 1\right) - \frac{9 \, {\left(2 \, \sqrt{x} - 1\right)}^{\frac{5}{4}} + 5 \, {\left(2 \, \sqrt{x} - 1\right)}^{\frac{1}{4}}}{{\left(2 \, \sqrt{x} - 1\right)}^{2} + 4 \, \sqrt{x} - 1}"," ",0,"5/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(2*sqrt(x) - 1)^(1/4))) + 5/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(2*sqrt(x) - 1)^(1/4))) + 5/8*sqrt(2)*log(sqrt(2)*(2*sqrt(x) - 1)^(1/4) + sqrt(2*sqrt(x) - 1) + 1) - 5/8*sqrt(2)*log(-sqrt(2)*(2*sqrt(x) - 1)^(1/4) + sqrt(2*sqrt(x) - 1) + 1) - (9*(2*sqrt(x) - 1)^(5/4) + 5*(2*sqrt(x) - 1)^(1/4))/((2*sqrt(x) - 1)^2 + 4*sqrt(x) - 1)","A",0
299,1,9,0,0.481635," ","integrate(x^6*(x^7+1)^(1/3),x, algorithm=""maxima"")","\frac{3}{28} \, {\left(x^{7} + 1\right)}^{\frac{4}{3}}"," ",0,"3/28*(x^7 + 1)^(4/3)","A",0
300,1,9,0,0.601510," ","integrate(x^6/(x^7+1)^(5/3),x, algorithm=""maxima"")","-\frac{3}{14 \, {\left(x^{7} + 1\right)}^{\frac{2}{3}}}"," ",0,"-3/14/(x^7 + 1)^(2/3)","A",0
301,1,64,0,1.299101," ","integrate(1/x/(2*x^7-27)^(2/3),x, algorithm=""maxima"")","\frac{1}{63} \, \sqrt{3} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(2 \, {\left(2 \, x^{7} - 27\right)}^{\frac{1}{3}} - 3\right)}\right) - \frac{1}{126} \, \log\left({\left(2 \, x^{7} - 27\right)}^{\frac{2}{3}} - 3 \, {\left(2 \, x^{7} - 27\right)}^{\frac{1}{3}} + 9\right) + \frac{1}{63} \, \log\left({\left(2 \, x^{7} - 27\right)}^{\frac{1}{3}} + 3\right)"," ",0,"1/63*sqrt(3)*arctan(1/9*sqrt(3)*(2*(2*x^7 - 27)^(1/3) - 3)) - 1/126*log((2*x^7 - 27)^(2/3) - 3*(2*x^7 - 27)^(1/3) + 9) + 1/63*log((2*x^7 - 27)^(1/3) + 3)","A",0
302,1,66,0,1.349802," ","integrate((x^7+1)^(2/3)/x^8,x, algorithm=""maxima"")","\frac{2}{21} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(x^{7} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) - \frac{{\left(x^{7} + 1\right)}^{\frac{2}{3}}}{7 \, x^{7}} - \frac{1}{21} \, \log\left({\left(x^{7} + 1\right)}^{\frac{2}{3}} + {\left(x^{7} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{2}{21} \, \log\left({\left(x^{7} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"2/21*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^7 + 1)^(1/3) + 1)) - 1/7*(x^7 + 1)^(2/3)/x^7 - 1/21*log((x^7 + 1)^(2/3) + (x^7 + 1)^(1/3) + 1) + 2/21*log((x^7 + 1)^(1/3) - 1)","A",0
303,1,83,0,1.401597," ","integrate((4*x^4+3)^(1/4)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{2 \, x}\right) - \frac{1}{4} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}}{\sqrt{2} + \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}}\right) - \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(4*x^4 + 3)^(1/4)/x) - 1/4*sqrt(2)*log(-(sqrt(2) - (4*x^4 + 3)^(1/4)/x)/(sqrt(2) + (4*x^4 + 3)^(1/4)/x)) - (4*x^4 + 3)^(1/4)/x","A",0
304,1,130,0,1.241432," ","integrate(x^2*(4*x^4+3)^(5/4),x, algorithm=""maxima"")","\frac{45}{256} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{2 \, x}\right) - \frac{45}{512} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}}{\sqrt{2} + \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}}\right) + \frac{9 \, {\left(\frac{20 \, {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x} - \frac{9 \, {\left(4 \, x^{4} + 3\right)}^{\frac{5}{4}}}{x^{5}}\right)}}{32 \, {\left(\frac{8 \, {\left(4 \, x^{4} + 3\right)}}{x^{4}} - \frac{{\left(4 \, x^{4} + 3\right)}^{2}}{x^{8}} - 16\right)}}"," ",0,"45/256*sqrt(2)*arctan(1/2*sqrt(2)*(4*x^4 + 3)^(1/4)/x) - 45/512*sqrt(2)*log(-(sqrt(2) - (4*x^4 + 3)^(1/4)/x)/(sqrt(2) + (4*x^4 + 3)^(1/4)/x)) + 9/32*(20*(4*x^4 + 3)^(1/4)/x - 9*(4*x^4 + 3)^(5/4)/x^5)/(8*(4*x^4 + 3)/x^4 - (4*x^4 + 3)^2/x^8 - 16)","A",0
305,1,129,0,1.200724," ","integrate(x^6*(4*x^4+3)^(1/4),x, algorithm=""maxima"")","-\frac{27}{1024} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{2 \, x}\right) + \frac{27}{2048} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}}{\sqrt{2} + \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}}\right) - \frac{9 \, {\left(\frac{12 \, {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x} + \frac{{\left(4 \, x^{4} + 3\right)}^{\frac{5}{4}}}{x^{5}}\right)}}{128 \, {\left(\frac{8 \, {\left(4 \, x^{4} + 3\right)}}{x^{4}} - \frac{{\left(4 \, x^{4} + 3\right)}^{2}}{x^{8}} - 16\right)}}"," ",0,"-27/1024*sqrt(2)*arctan(1/2*sqrt(2)*(4*x^4 + 3)^(1/4)/x) + 27/2048*sqrt(2)*log(-(sqrt(2) - (4*x^4 + 3)^(1/4)/x)/(sqrt(2) + (4*x^4 + 3)^(1/4)/x)) - 9/128*(12*(4*x^4 + 3)^(1/4)/x + (4*x^4 + 3)^(5/4)/x^5)/(8*(4*x^4 + 3)/x^4 - (4*x^4 + 3)^2/x^8 - 16)","A",0
306,0,0,0,0.000000," ","integrate((x*(-x^2+1))^(1/3),x, algorithm=""maxima"")","\int \left(-{\left(x^{2} - 1\right)} x\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((-(x^2 - 1)*x)^(1/3), x)","F",0
307,0,0,0,0.000000," ","integrate(((1+x^(1/3))*x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{x {\left(x^{\frac{1}{3}} + 1\right)}}\,{d x}"," ",0,"integrate(sqrt(x*(x^(1/3) + 1)), x)","F",0
308,0,0,0,0.000000," ","integrate(x^3/(x^4-1)/(2*x^8+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{2 \, x^{8} + 1} {\left(x^{4} - 1\right)}}\,{d x}"," ",0,"integrate(x^3/(sqrt(2*x^8 + 1)*(x^4 - 1)), x)","F",0
309,0,0,0,0.000000," ","integrate(x^9*(x^10+x^5+1)^(1/2),x, algorithm=""maxima"")","\int \sqrt{x^{10} + x^{5} + 1} x^{9}\,{d x}"," ",0,"integrate(sqrt(x^10 + x^5 + 1)*x^9, x)","F",0
310,1,52,0,1.206698," ","integrate(1/x^5/(x^4+2*x^2+4)^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{x^{4} + 2 \, x^{2} + 4}}{64 \, x^{2}} - \frac{\sqrt{x^{4} + 2 \, x^{2} + 4}}{16 \, x^{4}} + \frac{1}{128} \, \operatorname{arsinh}\left(\frac{1}{3} \, \sqrt{3} + \frac{4 \, \sqrt{3}}{3 \, x^{2}}\right)"," ",0,"3/64*sqrt(x^4 + 2*x^2 + 4)/x^2 - 1/16*sqrt(x^4 + 2*x^2 + 4)/x^4 + 1/128*arcsinh(1/3*sqrt(3) + 4/3*sqrt(3)/x^2)","A",0
311,1,52,0,0.482434," ","integrate((x^2-1)/x/(x^4+3*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(2 \, x^{2} + 2 \, \sqrt{x^{4} + 3 \, x^{2} + 1} + 3\right) + \frac{1}{2} \, \log\left(\frac{2 \, \sqrt{x^{4} + 3 \, x^{2} + 1}}{x^{2}} + \frac{2}{x^{2}} + 3\right)"," ",0,"1/2*log(2*x^2 + 2*sqrt(x^4 + 3*x^2 + 1) + 3) + 1/2*log(2*sqrt(x^4 + 3*x^2 + 1)/x^2 + 2/x^2 + 3)","B",0
312,1,13,0,0.598534," ","integrate((2*x^3-3*x)*(x^4-3*x^2)^(3/5),x, algorithm=""maxima"")","\frac{5}{16} \, {\left(x^{4} - 3 \, x^{2}\right)}^{\frac{8}{5}}"," ",0,"5/16*(x^4 - 3*x^2)^(8/5)","A",0
313,1,34,0,0.566611," ","integrate((-2*x^5+3*x^8-x^2*(3*x^3-1)^(2/3))/(3*x^3-1)^(3/4),x, algorithm=""maxima"")","\frac{4}{243} \, {\left(3 \, x^{3} - 1\right)}^{\frac{9}{4}} - \frac{4}{33} \, {\left(3 \, x^{3} - 1\right)}^{\frac{11}{12}} - \frac{4}{27} \, {\left(3 \, x^{3} - 1\right)}^{\frac{1}{4}}"," ",0,"4/243*(3*x^3 - 1)^(9/4) - 4/33*(3*x^3 - 1)^(11/12) - 4/27*(3*x^3 - 1)^(1/4)","A",0
314,0,0,0,0.000000," ","integrate(1/(x^3-1)/(x^3+2)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} + 2\right)}^{\frac{1}{3}} {\left(x^{3} - 1\right)}}\,{d x}"," ",0,"integrate(1/((x^3 + 2)^(1/3)*(x^3 - 1)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(x^4+1)/(x^4+2)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{4} + 2\right)}^{\frac{1}{4}} {\left(x^{4} + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^4 + 2)^(1/4)*(x^4 + 1)), x)","F",0
316,1,94,0,1.209724," ","integrate((x^3-1)/(x^3+2)^(1/3),x, algorithm=""maxima"")","\frac{5}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(\frac{2 \, {\left(x^{3} + 2\right)}^{\frac{1}{3}}}{x} + 1\right)}\right) + \frac{2 \, {\left(x^{3} + 2\right)}^{\frac{2}{3}}}{3 \, x^{2} {\left(\frac{x^{3} + 2}{x^{3}} - 1\right)}} - \frac{5}{18} \, \log\left(\frac{{\left(x^{3} + 2\right)}^{\frac{1}{3}}}{x} + \frac{{\left(x^{3} + 2\right)}^{\frac{2}{3}}}{x^{2}} + 1\right) + \frac{5}{9} \, \log\left(\frac{{\left(x^{3} + 2\right)}^{\frac{1}{3}}}{x} - 1\right)"," ",0,"5/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(x^3 + 2)^(1/3)/x + 1)) + 2/3*(x^3 + 2)^(2/3)/(x^2*((x^3 + 2)/x^3 - 1)) - 5/18*log((x^3 + 2)^(1/3)/x + (x^3 + 2)^(2/3)/x^2 + 1) + 5/9*log((x^3 + 2)^(1/3)/x - 1)","A",0
317,0,0,0,0.000000," ","integrate((x^4+1)^(3/4)/(x^4+2)^2,x, algorithm=""maxima"")","\int \frac{{\left(x^{4} + 1\right)}^{\frac{3}{4}}}{{\left(x^{4} + 2\right)}^{2}}\,{d x}"," ",0,"integrate((x^4 + 1)^(3/4)/(x^4 + 2)^2, x)","F",0
318,1,73,0,0.566896," ","integrate((x^5-2)^2/(x^5+3)^(16/5),x, algorithm=""maxima"")","-\frac{4 \, x^{11} {\left(\frac{11 \, {\left(x^{5} + 3\right)}}{x^{5}} - \frac{33 \, {\left(x^{5} + 3\right)}^{2}}{x^{10}} - 3\right)}}{891 \, {\left(x^{5} + 3\right)}^{\frac{11}{5}}} - \frac{2 \, x^{11} {\left(\frac{11 \, {\left(x^{5} + 3\right)}}{x^{5}} - 6\right)}}{297 \, {\left(x^{5} + 3\right)}^{\frac{11}{5}}} + \frac{x^{11}}{33 \, {\left(x^{5} + 3\right)}^{\frac{11}{5}}}"," ",0,"-4/891*x^11*(11*(x^5 + 3)/x^5 - 33*(x^5 + 3)^2/x^10 - 3)/(x^5 + 3)^(11/5) - 2/297*x^11*(11*(x^5 + 3)/x^5 - 6)/(x^5 + 3)^(11/5) + 1/33*x^11/(x^5 + 3)^(11/5)","B",0
319,0,0,0,0.000000," ","integrate(1/(x^3+3*x^2+3*x)/(x^3+3*x^2+3*x+3)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{3} + 3 \, x^{2} + 3 \, x + 3\right)}^{\frac{1}{3}} {\left(x^{3} + 3 \, x^{2} + 3 \, x\right)}}\,{d x}"," ",0,"integrate(1/((x^3 + 3*x^2 + 3*x + 3)^(1/3)*(x^3 + 3*x^2 + 3*x)), x)","F",0
320,0,0,0,0.000000," ","integrate((-x^2+1)/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""maxima"")","-\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
321,0,0,0,0.000000," ","integrate((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""maxima"")","-\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
322,1,57,0,1.173007," ","integrate((x^2+1)/x/(x^4+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} - 1\right) + \frac{1}{4} \, \log\left(\frac{\sqrt{x^{4} + 1}}{x^{2}} + 1\right) - \frac{1}{4} \, \log\left(\frac{\sqrt{x^{4} + 1}}{x^{2}} - 1\right)"," ",0,"-1/4*log(sqrt(x^4 + 1) + 1) + 1/4*log(sqrt(x^4 + 1) - 1) + 1/4*log(sqrt(x^4 + 1)/x^2 + 1) - 1/4*log(sqrt(x^4 + 1)/x^2 - 1)","B",0
323,1,57,0,1.276765," ","integrate((x^2-1)/x/(x^4+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} + 1\right) - \frac{1}{4} \, \log\left(\sqrt{x^{4} + 1} - 1\right) + \frac{1}{4} \, \log\left(\frac{\sqrt{x^{4} + 1}}{x^{2}} + 1\right) - \frac{1}{4} \, \log\left(\frac{\sqrt{x^{4} + 1}}{x^{2}} - 1\right)"," ",0,"1/4*log(sqrt(x^4 + 1) + 1) - 1/4*log(sqrt(x^4 + 1) - 1) + 1/4*log(sqrt(x^4 + 1)/x^2 + 1) - 1/4*log(sqrt(x^4 + 1)/x^2 - 1)","B",0
324,0,0,0,0.000000," ","integrate((x^2+1)/(-x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""maxima"")","-\int \frac{x^{2} + 1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"-integrate((x^2 + 1)/(sqrt(x^4 + x^2 + 1)*(x^2 - 1)), x)","F",0
325,0,0,0,0.000000," ","integrate((-x^2+1)/(x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""maxima"")","-\int \frac{x^{2} - 1}{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"-integrate((x^2 - 1)/(sqrt(x^4 + x^2 + 1)*(x^2 + 1)), x)","F",0
326,1,22,0,0.874253," ","integrate((x^4-1)/x^2/(x^4+x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{x^{2} + x + 1} \sqrt{x^{2} - x + 1}}{x}"," ",0,"sqrt(x^2 + x + 1)*sqrt(x^2 - x + 1)/x","A",0
327,0,0,0,0.000000," ","integrate((-x^2+1)/(2*a*x+x^2+1)/(2*a*x^3+x^4+2*b*x^2+2*a*x+1)^(1/2),x, algorithm=""maxima"")","-\int \frac{x^{2} - 1}{\sqrt{2 \, a x^{3} + x^{4} + 2 \, b x^{2} + 2 \, a x + 1} {\left(2 \, a x + x^{2} + 1\right)}}\,{d x}"," ",0,"-integrate((x^2 - 1)/(sqrt(2*a*x^3 + x^4 + 2*b*x^2 + 2*a*x + 1)*(2*a*x + x^2 + 1)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{4} + 1\right)} \sqrt{-x^{2} + \sqrt{x^{4} + 1}}}\,{d x}"," ",0,"integrate(1/((x^4 + 1)*sqrt(-x^2 + sqrt(x^4 + 1))), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(1+x^(2*n))/(-x^2+(1+x^(2*n))^(1/n))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-x^{2} + {\left(x^{2 \, n} + 1\right)}^{\left(\frac{1}{n}\right)}} {\left(x^{2 \, n} + 1\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + (x^(2*n) + 1)^(1/n))*(x^(2*n) + 1)), x)","F",0
330,1,10,0,0.573833," ","integrate(cos(x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x + 1/4*sin(2*x)","A",0
331,1,9,0,0.497016," ","integrate(cos(x)^3,x, algorithm=""maxima"")","-\frac{1}{3} \, \sin\left(x\right)^{3} + \sin\left(x\right)"," ",0,"-1/3*sin(x)^3 + sin(x)","A",0
332,1,16,0,0.498654," ","integrate(sin(x)^4,x, algorithm=""maxima"")","\frac{3}{8} \, x + \frac{1}{32} \, \sin\left(4 \, x\right) - \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"3/8*x + 1/32*sin(4*x) - 1/4*sin(2*x)","A",0
333,1,24,0,0.439817," ","integrate(cos(x)^6,x, algorithm=""maxima"")","-\frac{1}{48} \, \sin\left(2 \, x\right)^{3} + \frac{5}{16} \, x + \frac{3}{64} \, \sin\left(4 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-1/48*sin(2*x)^3 + 5/16*x + 3/64*sin(4*x) + 1/4*sin(2*x)","A",0
334,1,30,0,0.582678," ","integrate(sin(x)^8,x, algorithm=""maxima"")","\frac{1}{24} \, \sin\left(2 \, x\right)^{3} + \frac{35}{128} \, x + \frac{1}{1024} \, \sin\left(8 \, x\right) + \frac{7}{128} \, \sin\left(4 \, x\right) - \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/24*sin(2*x)^3 + 35/128*x + 1/1024*sin(8*x) + 7/128*sin(4*x) - 1/4*sin(2*x)","A",0
335,1,23,0,0.488024," ","integrate(cos(1/4*pi+1/2*x)^4,x, algorithm=""maxima"")","\frac{3}{16} \, \pi + \frac{3}{8} \, x + \frac{1}{16} \, \sin\left(\pi + 2 \, x\right) + \frac{1}{2} \, \sin\left(\frac{1}{2} \, \pi + x\right)"," ",0,"3/16*pi + 3/8*x + 1/16*sin(pi + 2*x) + 1/2*sin(1/2*pi + x)","A",0
336,1,23,0,0.572028," ","integrate(-cos(5/12*pi+3*x)^3,x, algorithm=""maxima"")","\frac{1}{9} \, \sin\left(\frac{5}{12} \, \pi + 3 \, x\right)^{3} - \frac{1}{3} \, \sin\left(\frac{5}{12} \, \pi + 3 \, x\right)"," ",0,"1/9*sin(5/12*pi + 3*x)^3 - 1/3*sin(5/12*pi + 3*x)","A",0
337,1,20,0,0.505145," ","integrate(1/sin(x)^6,x, algorithm=""maxima"")","-\frac{15 \, \tan\left(x\right)^{4} + 10 \, \tan\left(x\right)^{2} + 3}{15 \, \tan\left(x\right)^{5}}"," ",0,"-1/15*(15*tan(x)^4 + 10*tan(x)^2 + 3)/tan(x)^5","A",0
338,1,54,0,0.514511," ","integrate(csc(x)^7,x, algorithm=""maxima"")","\frac{15 \, \cos\left(x\right)^{5} - 40 \, \cos\left(x\right)^{3} + 33 \, \cos\left(x\right)}{48 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)}} - \frac{5}{32} \, \log\left(\cos\left(x\right) + 1\right) + \frac{5}{32} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"1/48*(15*cos(x)^5 - 40*cos(x)^3 + 33*cos(x))/(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1) - 5/32*log(cos(x) + 1) + 5/32*log(cos(x) - 1)","A",0
339,1,33,0,0.487779," ","integrate(1/cos(x)^12,x, algorithm=""maxima"")","\frac{1}{11} \, \tan\left(x\right)^{11} + \frac{5}{9} \, \tan\left(x\right)^{9} + \frac{10}{7} \, \tan\left(x\right)^{7} + 2 \, \tan\left(x\right)^{5} + \frac{5}{3} \, \tan\left(x\right)^{3} + \tan\left(x\right)"," ",0,"1/11*tan(x)^11 + 5/9*tan(x)^9 + 10/7*tan(x)^7 + 2*tan(x)^5 + 5/3*tan(x)^3 + tan(x)","A",0
340,1,51,0,0.506539," ","integrate(1/cos(1/4*pi+3*x)^3,x, algorithm=""maxima"")","-\frac{\sin\left(\frac{1}{4} \, \pi + 3 \, x\right)}{6 \, {\left(\sin\left(\frac{1}{4} \, \pi + 3 \, x\right)^{2} - 1\right)}} + \frac{1}{12} \, \log\left(\sin\left(\frac{1}{4} \, \pi + 3 \, x\right) + 1\right) - \frac{1}{12} \, \log\left(\sin\left(\frac{1}{4} \, \pi + 3 \, x\right) - 1\right)"," ",0,"-1/6*sin(1/4*pi + 3*x)/(sin(1/4*pi + 3*x)^2 - 1) + 1/12*log(sin(1/4*pi + 3*x) + 1) - 1/12*log(sin(1/4*pi + 3*x) - 1)","A",0
341,1,18,0,1.339899," ","integrate(tan(x)^6,x, algorithm=""maxima"")","\frac{1}{5} \, \tan\left(x\right)^{5} - \frac{1}{3} \, \tan\left(x\right)^{3} - x + \tan\left(x\right)"," ",0,"1/5*tan(x)^5 - 1/3*tan(x)^3 - x + tan(x)","A",0
342,1,22,0,0.614286," ","integrate(1/tan(x)^5,x, algorithm=""maxima"")","\frac{4 \, \sin\left(x\right)^{2} - 1}{4 \, \sin\left(x\right)^{4}} + \frac{1}{2} \, \log\left(\sin\left(x\right)^{2}\right)"," ",0,"1/4*(4*sin(x)^2 - 1)/sin(x)^4 + 1/2*log(sin(x)^2)","A",0
343,1,30,0,1.323496," ","integrate(cot(1/4*pi+1/3*x)^4,x, algorithm=""maxima"")","\frac{3}{4} \, \pi + x + \frac{3 \, \tan\left(\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)^{2} - 1}{\tan\left(\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)^{3}}"," ",0,"3/4*pi + x + (3*tan(1/4*pi + 1/3*x)^2 - 1)/tan(1/4*pi + 1/3*x)^3","A",0
344,1,24,0,0.570304," ","integrate(cos(x)^6*sin(x)^4,x, algorithm=""maxima"")","\frac{1}{320} \, \sin\left(2 \, x\right)^{5} + \frac{3}{256} \, x + \frac{1}{2048} \, \sin\left(8 \, x\right) - \frac{1}{256} \, \sin\left(4 \, x\right)"," ",0,"1/320*sin(2*x)^5 + 3/256*x + 1/2048*sin(8*x) - 1/256*sin(4*x)","A",0
345,1,25,0,0.549044," ","integrate(cos(x)^6*sin(x)^7,x, algorithm=""maxima"")","\frac{1}{13} \, \cos\left(x\right)^{13} - \frac{3}{11} \, \cos\left(x\right)^{11} + \frac{1}{3} \, \cos\left(x\right)^{9} - \frac{1}{7} \, \cos\left(x\right)^{7}"," ",0,"1/13*cos(x)^13 - 3/11*cos(x)^11 + 1/3*cos(x)^9 - 1/7*cos(x)^7","A",0
346,1,40,0,0.529848," ","integrate(sin(x)^11/cos(x),x, algorithm=""maxima"")","-\frac{1}{10} \, \sin\left(x\right)^{10} - \frac{1}{8} \, \sin\left(x\right)^{8} - \frac{1}{6} \, \sin\left(x\right)^{6} - \frac{1}{4} \, \sin\left(x\right)^{4} - \frac{1}{2} \, \sin\left(x\right)^{2} - \frac{1}{2} \, \log\left(\sin\left(x\right)^{2} - 1\right)"," ",0,"-1/10*sin(x)^10 - 1/8*sin(x)^8 - 1/6*sin(x)^6 - 1/4*sin(x)^4 - 1/2*sin(x)^2 - 1/2*log(sin(x)^2 - 1)","A",0
347,1,37,0,0.486711," ","integrate(1/cos(x)^6/sin(x)^6,x, algorithm=""maxima"")","\frac{1}{5} \, \tan\left(x\right)^{5} + \frac{5}{3} \, \tan\left(x\right)^{3} - \frac{150 \, \tan\left(x\right)^{4} + 25 \, \tan\left(x\right)^{2} + 3}{15 \, \tan\left(x\right)^{5}} + 10 \, \tan\left(x\right)"," ",0,"1/5*tan(x)^5 + 5/3*tan(x)^3 - 1/15*(150*tan(x)^4 + 25*tan(x)^2 + 3)/tan(x)^5 + 10*tan(x)","A",0
348,1,10,0,0.571769," ","integrate(cos(x)^2*sin(x)^2,x, algorithm=""maxima"")","\frac{1}{8} \, x - \frac{1}{32} \, \sin\left(4 \, x\right)"," ",0,"1/8*x - 1/32*sin(4*x)","A",0
349,1,16,0,0.488554," ","integrate(cos(x)^4*sin(x)^4,x, algorithm=""maxima"")","\frac{3}{128} \, x + \frac{1}{1024} \, \sin\left(8 \, x\right) - \frac{1}{128} \, \sin\left(4 \, x\right)"," ",0,"3/128*x + 1/1024*sin(8*x) - 1/128*sin(4*x)","A",0
350,1,24,0,0.471342," ","integrate(cos(x)^6*sin(x)^6,x, algorithm=""maxima"")","\frac{1}{6144} \, \sin\left(4 \, x\right)^{3} + \frac{5}{1024} \, x + \frac{3}{8192} \, \sin\left(8 \, x\right) - \frac{1}{512} \, \sin\left(4 \, x\right)"," ",0,"1/6144*sin(4*x)^3 + 5/1024*x + 3/8192*sin(8*x) - 1/512*sin(4*x)","A",0
351,1,30,0,0.649403," ","integrate(cos(x)^8*sin(x)^8,x, algorithm=""maxima"")","\frac{1}{12288} \, \sin\left(4 \, x\right)^{3} + \frac{35}{32768} \, x + \frac{1}{524288} \, \sin\left(16 \, x\right) + \frac{7}{65536} \, \sin\left(8 \, x\right) - \frac{1}{2048} \, \sin\left(4 \, x\right)"," ",0,"1/12288*sin(4*x)^3 + 35/32768*x + 1/524288*sin(16*x) + 7/65536*sin(8*x) - 1/2048*sin(4*x)","A",0
352,0,0,0,0.000000," ","integrate(cos(x)^(2*m)*sin(x)^(2*m),x, algorithm=""maxima"")","\int \cos\left(x\right)^{2 \, m} \sin\left(x\right)^{2 \, m}\,{d x}"," ",0,"integrate(cos(x)^(2*m)*sin(x)^(2*m), x)","F",0
353,1,41,0,0.473966," ","integrate(1/cos(1/4*pi+2*x)/sin(1/4*pi+2*x)^3,x, algorithm=""maxima"")","-\frac{1}{4 \, \sin\left(\frac{1}{4} \, \pi + 2 \, x\right)^{2}} - \frac{1}{4} \, \log\left(\sin\left(\frac{1}{4} \, \pi + 2 \, x\right)^{2} - 1\right) + \frac{1}{4} \, \log\left(\sin\left(\frac{1}{4} \, \pi + 2 \, x\right)^{2}\right)"," ",0,"-1/4/sin(1/4*pi + 2*x)^2 - 1/4*log(sin(1/4*pi + 2*x)^2 - 1) + 1/4*log(sin(1/4*pi + 2*x)^2)","A",0
354,1,6,0,0.490973," ","integrate(sec(x)^2*tan(x)^2,x, algorithm=""maxima"")","\frac{1}{3} \, \tan\left(x\right)^{3}"," ",0,"1/3*tan(x)^3","A",0
355,1,14,0,0.555088," ","integrate(cot(x)^3*csc(x),x, algorithm=""maxima"")","\frac{3 \, \sin\left(x\right)^{2} - 1}{3 \, \sin\left(x\right)^{3}}"," ",0,"1/3*(3*sin(x)^2 - 1)/sin(x)^3","A",0
356,1,6,0,0.474557," ","integrate(sec(x)^3*tan(x),x, algorithm=""maxima"")","\frac{1}{3 \, \cos\left(x\right)^{3}}"," ",0,"1/3/cos(x)^3","A",0
357,1,38,0,0.532267," ","integrate(cot(x)^2*csc(x)^3,x, algorithm=""maxima"")","-\frac{\cos\left(x\right)^{3} + \cos\left(x\right)}{8 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}} + \frac{1}{16} \, \log\left(\cos\left(x\right) + 1\right) - \frac{1}{16} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"-1/8*(cos(x)^3 + cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) + 1/16*log(cos(x) + 1) - 1/16*log(cos(x) - 1)","A",0
358,1,14,0,0.503234," ","integrate(cos(x)^3/sin(x)^7,x, algorithm=""maxima"")","\frac{3 \, \sin\left(x\right)^{2} - 2}{12 \, \sin\left(x\right)^{6}}"," ",0,"1/12*(3*sin(x)^2 - 2)/sin(x)^6","A",0
359,1,19,0,0.540885," ","integrate(sec(x)^(3/2)*tan(x)^5,x, algorithm=""maxima"")","\frac{2}{3 \, \cos\left(x\right)^{\frac{3}{2}}} - \frac{4}{7 \, \cos\left(x\right)^{\frac{7}{2}}} + \frac{2}{11 \, \cos\left(x\right)^{\frac{11}{2}}}"," ",0,"2/3/cos(x)^(3/2) - 4/7/cos(x)^(7/2) + 2/11/cos(x)^(11/2)","A",0
360,1,13,0,0.599524," ","integrate(sec(x)^4*tan(x)^(3/2),x, algorithm=""maxima"")","\frac{2}{9} \, \tan\left(x\right)^{\frac{9}{2}} + \frac{2}{5} \, \tan\left(x\right)^{\frac{5}{2}}"," ",0,"2/9*tan(x)^(9/2) + 2/5*tan(x)^(5/2)","A",0
361,1,54,0,0.437633," ","integrate(cot(x)^4*csc(x)^3,x, algorithm=""maxima"")","\frac{3 \, \cos\left(x\right)^{5} + 8 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)}{48 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)}} - \frac{1}{32} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{32} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"1/48*(3*cos(x)^5 + 8*cos(x)^3 - 3*cos(x))/(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1) - 1/32*log(cos(x) + 1) + 1/32*log(cos(x) - 1)","A",0
362,1,74,0,0.666243," ","integrate(sec(1/4*pi+1/2*x)^3*tan(1/4*pi+1/2*x)^2,x, algorithm=""maxima"")","\frac{\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)^{3} + \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)}{4 \, {\left(\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)^{4} - 2 \, \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)^{2} + 1\right)}} - \frac{1}{8} \, \log\left(\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right) + 1\right) + \frac{1}{8} \, \log\left(\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right) - 1\right)"," ",0,"1/4*(sin(1/4*pi + 1/2*x)^3 + sin(1/4*pi + 1/2*x))/(sin(1/4*pi + 1/2*x)^4 - 2*sin(1/4*pi + 1/2*x)^2 + 1) - 1/8*log(sin(1/4*pi + 1/2*x) + 1) + 1/8*log(sin(1/4*pi + 1/2*x) - 1)","A",0
363,1,115,0,1.353297," ","integrate((1+cot(x)^3)*(a*sec(x)^2-sin(2*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\tan\left(x\right)^{3} + 3 \, \tan\left(x\right)\right)} a^{2} - \frac{1}{2} \, a^{2} {\left(\frac{1}{\sin\left(x\right)^{2}} + \log\left(\sin\left(x\right)^{2} - 1\right) - \log\left(\sin\left(x\right)^{2}\right)\right)} + 4 \, a {\left(x + \frac{1}{\tan\left(x\right)}\right)} + 2 \, a \log\left(-\sin\left(x\right)^{2} + 1\right) + \frac{1}{2} \, x + \frac{1}{8} \, \cos\left(4 \, x\right) + \frac{3}{2} \, \cos\left(2 \, x\right) + 2 \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + 2 \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - \frac{1}{8} \, \sin\left(4 \, x\right)"," ",0,"1/3*(tan(x)^3 + 3*tan(x))*a^2 - 1/2*a^2*(1/sin(x)^2 + log(sin(x)^2 - 1) - log(sin(x)^2)) + 4*a*(x + 1/tan(x)) + 2*a*log(-sin(x)^2 + 1) + 1/2*x + 1/8*cos(4*x) + 3/2*cos(2*x) + 2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 1/8*sin(4*x)","A",0
364,1,54,0,0.453423," ","integrate((4-3*cos(x))*(1-1/2*sin(x))^4,x, algorithm=""maxima"")","-\frac{3}{80} \, \sin\left(x\right)^{5} + \frac{3}{8} \, \sin\left(x\right)^{4} - \frac{2}{3} \, \cos\left(x\right)^{3} - \frac{3}{2} \, \sin\left(x\right)^{3} - 3 \, \cos\left(x\right)^{2} + \frac{227}{32} \, x + 10 \, \cos\left(x\right) + \frac{1}{128} \, \sin\left(4 \, x\right) - \frac{25}{16} \, \sin\left(2 \, x\right) - 3 \, \sin\left(x\right)"," ",0,"-3/80*sin(x)^5 + 3/8*sin(x)^4 - 2/3*cos(x)^3 - 3/2*sin(x)^3 - 3*cos(x)^2 + 227/32*x + 10*cos(x) + 1/128*sin(4*x) - 25/16*sin(2*x) - 3*sin(x)","A",0
365,1,36,0,1.271030," ","integrate((1/2-3*cot(x))*(3-2*cot(x))^3,x, algorithm=""maxima"")","-\frac{285}{2} \, x - \frac{4 \, {\left(39 \, \tan\left(x\right)^{2} - 14 \, \tan\left(x\right) + 2\right)}}{\tan\left(x\right)^{3}} - 2 \, \log\left(\tan\left(x\right)^{2} + 1\right) + 4 \, \log\left(\tan\left(x\right)\right)"," ",0,"-285/2*x - 4*(39*tan(x)^2 - 14*tan(x) + 2)/tan(x)^3 - 2*log(tan(x)^2 + 1) + 4*log(tan(x))","A",0
366,1,14,0,1.281482," ","integrate(cos(5*x)/cos(x)^5,x, algorithm=""maxima"")","\frac{5}{3} \, \tan\left(x\right)^{3} + 16 \, x - 15 \, \tan\left(x\right)"," ",0,"5/3*tan(x)^3 + 16*x - 15*tan(x)","A",0
367,1,21,0,0.445135," ","integrate(cos(4*x)/cos(x),x, algorithm=""maxima"")","-\frac{8}{3} \, \sin\left(x\right)^{3} + \frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\sin\left(x\right) - 1\right)"," ",0,"-8/3*sin(x)^3 + 1/2*log(sin(x) + 1) - 1/2*log(sin(x) - 1)","B",0
368,1,13,0,0.422088," ","integrate(cos(x)*cos(4*x),x, algorithm=""maxima"")","\frac{1}{10} \, \sin\left(5 \, x\right) + \frac{1}{6} \, \sin\left(3 \, x\right)"," ",0,"1/10*sin(5*x) + 1/6*sin(3*x)","A",0
369,1,54,0,0.448130," ","integrate(cos(4*x)/cos(x)^5,x, algorithm=""maxima"")","\frac{5 \, \sin\left(x\right)^{3} - 3 \, \sin\left(x\right)}{8 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} + \frac{3 \, \sin\left(x\right)}{\sin\left(x\right)^{2} - 1} + \frac{35}{16} \, \log\left(\sin\left(x\right) + 1\right) - \frac{35}{16} \, \log\left(\sin\left(x\right) - 1\right)"," ",0,"1/8*(5*sin(x)^3 - 3*sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) + 3*sin(x)/(sin(x)^2 - 1) + 35/16*log(sin(x) + 1) - 35/16*log(sin(x) - 1)","B",0
370,1,30,0,0.456425," ","integrate(cos(x)^4*cos(4*x),x, algorithm=""maxima"")","-\frac{1}{6} \, \sin\left(2 \, x\right)^{3} + \frac{1}{16} \, x + \frac{1}{128} \, \sin\left(8 \, x\right) + \frac{3}{32} \, \sin\left(4 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-1/6*sin(2*x)^3 + 1/16*x + 1/128*sin(8*x) + 3/32*sin(4*x) + 1/4*sin(2*x)","A",0
371,1,33,0,0.432678," ","integrate(cos(5*x)/sin(x)^5,x, algorithm=""maxima"")","\frac{5}{\sin\left(x\right)^{2}} + \frac{4 \, \sin\left(x\right)^{2} - 1}{4 \, \sin\left(x\right)^{4}} + \frac{11}{2} \, \log\left(\sin\left(x\right)^{2}\right) + 5 \, \log\left(\sin\left(x\right)\right)"," ",0,"5/sin(x)^2 + 1/4*(4*sin(x)^2 - 1)/sin(x)^4 + 11/2*log(sin(x)^2) + 5*log(sin(x))","A",0
372,1,19,0,0.426892," ","integrate(sin(4*x)/sin(x)^4,x, algorithm=""maxima"")","-\frac{2}{\sin\left(x\right)^{2}} - 2 \, \log\left(\sin\left(x\right)^{2}\right) - 4 \, \log\left(\sin\left(x\right)\right)"," ",0,"-2/sin(x)^2 - 2*log(sin(x)^2) - 4*log(sin(x))","A",0
373,1,208,0,1.070668," ","integrate(cos(x)/sin(x)/(2+sin(2*x)),x, algorithm=""maxima"")","-\frac{1}{24} \, \sqrt{3} {\left(\sqrt{3} \log\left(-2 \, {\left(4 \, \sin\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \sin\left(2 \, x\right) + 1\right) - 2 \, \sqrt{3} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - 2 \, \sqrt{3} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 2 \, \arctan\left(\frac{2 \, \sqrt{3} \cos\left(2 \, x\right)}{\cos\left(2 \, x\right)^{2} - 2 \, {\left(\sqrt{3} - 2\right)} \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 4 \, \sqrt{3} + 7}, \frac{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) + 1}{\cos\left(2 \, x\right)^{2} - 2 \, {\left(\sqrt{3} - 2\right)} \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 4 \, \sqrt{3} + 7}\right)\right)}"," ",0,"-1/24*sqrt(3)*(sqrt(3)*log(-2*(4*sin(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 16*cos(2*x)^2 + 8*cos(2*x)*sin(4*x) + sin(4*x)^2 + 16*sin(2*x)^2 + 8*sin(2*x) + 1) - 2*sqrt(3)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - 2*sqrt(3)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 2*arctan2(2*sqrt(3)*cos(2*x)/(cos(2*x)^2 - 2*(sqrt(3) - 2)*sin(2*x) + sin(2*x)^2 - 4*sqrt(3) + 7), (cos(2*x)^2 + sin(2*x)^2 + 4*sin(2*x) + 1)/(cos(2*x)^2 - 2*(sqrt(3) - 2)*sin(2*x) + sin(2*x)^2 - 4*sqrt(3) + 7)))","B",0
374,1,92,0,0.453877," ","integrate(cos(x)^2/cos(3*x)/sin(x),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(-2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/4*log(-2*(cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 + sin(4*x)^2 - 2*sin(4*x)*sin(2*x) + sin(2*x)^2 - 2*cos(2*x) + 1) + 1/2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
375,1,9,0,0.959510," ","integrate(sin(2*x)/(cos(x)^4+sin(x)^4),x, algorithm=""maxima"")","\arctan\left(2 \, \sin\left(x\right)^{2} - 1\right)"," ",0,"arctan(2*sin(x)^2 - 1)","A",0
376,1,27,0,0.960307," ","integrate(1/(4+sin(x)+cos(x)*3^(1/2)),x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{6} \, \sqrt{3} {\left(\frac{{\left(\sqrt{3} - 4\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/6*sqrt(3)*((sqrt(3) - 4)*sin(x)/(cos(x) + 1) - 1))","A",0
377,1,39,0,0.973079," ","integrate(1/(3+4*cos(x)+4*sin(x)),x, algorithm=""maxima"")","-\frac{1}{23} \, \sqrt{23} \log\left(-\frac{\sqrt{23} - \frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 4}{\sqrt{23} + \frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 4}\right)"," ",0,"-1/23*sqrt(23)*log(-(sqrt(23) - sin(x)/(cos(x) + 1) + 4)/(sqrt(23) + sin(x)/(cos(x) + 1) - 4))","A",0
378,1,7,0,0.955086," ","integrate(1/(4-3*cos(x)^2+5*sin(x)^2),x, algorithm=""maxima"")","\frac{1}{3} \, \arctan\left(3 \, \tan\left(x\right)\right)"," ",0,"1/3*arctan(3*tan(x))","A",0
379,1,28,0,0.955774," ","integrate(1/(4+4*cot(x)+tan(x)),x, algorithm=""maxima"")","\frac{4}{25} \, x + \frac{2}{5 \, {\left(\tan\left(x\right) + 2\right)}} + \frac{3}{50} \, \log\left(\tan\left(x\right)^{2} + 1\right) - \frac{3}{25} \, \log\left(\tan\left(x\right) + 2\right)"," ",0,"4/25*x + 2/5/(tan(x) + 2) + 3/50*log(tan(x)^2 + 1) - 3/25*log(tan(x) + 2)","A",0
380,1,38,0,0.964480," ","integrate(1/(2*sec(x)+sin(x))^2,x, algorithm=""maxima"")","\frac{8}{225} \, \sqrt{15} \arctan\left(\frac{1}{15} \, \sqrt{15} {\left(4 \, \tan\left(x\right) + 1\right)}\right) + \frac{4 \, \tan\left(x\right) + 1}{15 \, {\left(2 \, \tan\left(x\right)^{2} + \tan\left(x\right) + 2\right)}}"," ",0,"8/225*sqrt(15)*arctan(1/15*sqrt(15)*(4*tan(x) + 1)) + 1/15*(4*tan(x) + 1)/(2*tan(x)^2 + tan(x) + 2)","A",0
381,1,28,0,0.970506," ","integrate(1/(cos(x)+2*sec(x))^2,x, algorithm=""maxima"")","\frac{1}{36} \, \sqrt{6} \arctan\left(\frac{1}{3} \, \sqrt{6} \tan\left(x\right)\right) + \frac{\tan\left(x\right)}{6 \, {\left(2 \, \tan\left(x\right)^{2} + 3\right)}}"," ",0,"1/36*sqrt(6)*arctan(1/3*sqrt(6)*tan(x)) + 1/6*tan(x)/(2*tan(x)^2 + 3)","A",0
382,1,44,0,1.003625," ","integrate((5-tan(x)-6*tan(x)^2)/(1+3*tan(x))^3,x, algorithm=""maxima"")","-\frac{67}{250} \, x - \frac{87 \, \tan\left(x\right) + 64}{50 \, {\left(9 \, \tan\left(x\right)^{2} + 6 \, \tan\left(x\right) + 1\right)}} + \frac{14}{125} \, \log\left(\tan\left(x\right)^{2} + 1\right) - \frac{28}{125} \, \log\left(3 \, \tan\left(x\right) + 1\right)"," ",0,"-67/250*x - 1/50*(87*tan(x) + 64)/(9*tan(x)^2 + 6*tan(x) + 1) + 14/125*log(tan(x)^2 + 1) - 28/125*log(3*tan(x) + 1)","A",0
383,0,0,0,0.000000," ","integrate(cos(x)^2/cos(3*x),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right)^{2}}{\cos\left(3 \, x\right)}\,{d x}"," ",0,"integrate(cos(x)^2/cos(3*x), x)","F",0
384,1,129,0,0.982853," ","integrate(sin(x)/cos(2*x),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right)"," ",0,"1/8*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) - 1/8*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1)","B",0
385,1,128,0,1.018176," ","integrate(sin(x)^2/cos(2*x),x, algorithm=""maxima"")","-\frac{1}{2} \, x - \frac{1}{8} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{8} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{8} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right)"," ",0,"-1/2*x - 1/8*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) + 1/8*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/8*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/8*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2)","B",0
386,1,81,0,0.976302," ","integrate(sin(x)^3/cos(3*x),x, algorithm=""maxima"")","-\frac{1}{48} \, \log\left(-2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)"," ",0,"-1/48*log(-2*(cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 + sin(4*x)^2 - 2*sin(4*x)*sin(2*x) + sin(2*x)^2 - 2*cos(2*x) + 1) + 1/6*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
387,1,129,0,0.999865," ","integrate(cos(x)/sin(3*x),x, algorithm=""maxima"")","-\frac{1}{12} \, \log\left(2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/12*log(2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1) - 1/12*log(-2*(cos(x) - 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 - 2*sin(2*x)*sin(x) + sin(x)^2 - 2*cos(x) + 1) + 1/6*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/6*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
388,1,171,0,1.035852," ","integrate(sin(x)/sin(4*x),x, algorithm=""maxima"")","\frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/8*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/8*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","B",0
389,1,171,0,1.039253," ","integrate(sin(x)^3/sin(4*x),x, algorithm=""maxima"")","\frac{1}{32} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{32} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{32} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{32} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"1/32*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/32*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/32*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/32*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/8*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/8*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","B",0
390,0,0,0,0.000000," ","integrate((1+sin(2*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sin\left(2 \, x\right) + 1}\,{d x}"," ",0,"integrate(sqrt(sin(2*x) + 1), x)","F",0
391,0,0,0,0.000000," ","integrate((1-sin(2*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-\sin\left(2 \, x\right) + 1}\,{d x}"," ",0,"integrate(sqrt(-sin(2*x) + 1), x)","F",0
392,1,41,0,1.142127," ","integrate(1/(1+cos(2*x))^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \frac{1}{4} \, \sqrt{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"1/4*sqrt(2)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 1/4*sqrt(2)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","A",0
393,1,101,0,1.166617," ","integrate(1/(1-cos(2*x))^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + 1\right) + \frac{1}{4} \, \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} - 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + 1\right)"," ",0,"-1/4*sqrt(2)*log(cos(1/2*arctan2(sin(2*x), cos(2*x)))^2 + sin(1/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*cos(1/2*arctan2(sin(2*x), cos(2*x))) + 1) + 1/4*sqrt(2)*log(cos(1/2*arctan2(sin(2*x), cos(2*x)))^2 + sin(1/2*arctan2(sin(2*x), cos(2*x)))^2 - 2*cos(1/2*arctan2(sin(2*x), cos(2*x))) + 1)","B",0
394,1,433,0,1.219702," ","integrate(1/(1-cos(3*x))^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\sin\left(6 \, x\right) - 2 \, \sin\left(3 \, x\right)\right)} \cos\left(\frac{3}{2} \, \pi + \frac{3}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - 4 \, {\left(\sin\left(6 \, x\right) - 2 \, \sin\left(3 \, x\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + {\left(2 \, {\left(2 \, \cos\left(3 \, x\right) - 1\right)} \cos\left(6 \, x\right) - \cos\left(6 \, x\right)^{2} - 4 \, \cos\left(3 \, x\right)^{2} - \sin\left(6 \, x\right)^{2} + 4 \, \sin\left(6 \, x\right) \sin\left(3 \, x\right) - 4 \, \sin\left(3 \, x\right)^{2} + 4 \, \cos\left(3 \, x\right) - 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(3 \, x\right) - 1\right)} \cos\left(6 \, x\right) - \cos\left(6 \, x\right)^{2} - 4 \, \cos\left(3 \, x\right)^{2} - \sin\left(6 \, x\right)^{2} + 4 \, \sin\left(6 \, x\right) \sin\left(3 \, x\right) - 4 \, \sin\left(3 \, x\right)^{2} + 4 \, \cos\left(3 \, x\right) - 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(6 \, x\right) - 2 \, \cos\left(3 \, x\right) + 1\right)} \sin\left(\frac{3}{2} \, \pi + \frac{3}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 4 \, {\left(\cos\left(6 \, x\right) - 2 \, \cos\left(3 \, x\right) + 1\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)}{12 \, {\left(\sqrt{2} \cos\left(6 \, x\right)^{2} + 4 \, \sqrt{2} \cos\left(3 \, x\right)^{2} + \sqrt{2} \sin\left(6 \, x\right)^{2} - 4 \, \sqrt{2} \sin\left(6 \, x\right) \sin\left(3 \, x\right) + 4 \, \sqrt{2} \sin\left(3 \, x\right)^{2} - 2 \, {\left(2 \, \sqrt{2} \cos\left(3 \, x\right) - \sqrt{2}\right)} \cos\left(6 \, x\right) - 4 \, \sqrt{2} \cos\left(3 \, x\right) + \sqrt{2}\right)}}"," ",0,"1/12*(4*(sin(6*x) - 2*sin(3*x))*cos(3/2*pi + 3/2*arctan2(sin(3*x), cos(3*x))) - 4*(sin(6*x) - 2*sin(3*x))*cos(1/2*pi + 1/2*arctan2(sin(3*x), cos(3*x))) + (2*(2*cos(3*x) - 1)*cos(6*x) - cos(6*x)^2 - 4*cos(3*x)^2 - sin(6*x)^2 + 4*sin(6*x)*sin(3*x) - 4*sin(3*x)^2 + 4*cos(3*x) - 1)*log(cos(1/2*arctan2(sin(3*x), cos(3*x)))^2 + sin(1/2*arctan2(sin(3*x), cos(3*x)))^2 + 2*cos(1/2*arctan2(sin(3*x), cos(3*x))) + 1) - (2*(2*cos(3*x) - 1)*cos(6*x) - cos(6*x)^2 - 4*cos(3*x)^2 - sin(6*x)^2 + 4*sin(6*x)*sin(3*x) - 4*sin(3*x)^2 + 4*cos(3*x) - 1)*log(cos(1/2*arctan2(sin(3*x), cos(3*x)))^2 + sin(1/2*arctan2(sin(3*x), cos(3*x)))^2 - 2*cos(1/2*arctan2(sin(3*x), cos(3*x))) + 1) - 4*(cos(6*x) - 2*cos(3*x) + 1)*sin(3/2*pi + 3/2*arctan2(sin(3*x), cos(3*x))) + 4*(cos(6*x) - 2*cos(3*x) + 1)*sin(1/2*pi + 1/2*arctan2(sin(3*x), cos(3*x))))/(sqrt(2)*cos(6*x)^2 + 4*sqrt(2)*cos(3*x)^2 + sqrt(2)*sin(6*x)^2 - 4*sqrt(2)*sin(6*x)*sin(3*x) + 4*sqrt(2)*sin(3*x)^2 - 2*(2*sqrt(2)*cos(3*x) - sqrt(2))*cos(6*x) - 4*sqrt(2)*cos(3*x) + sqrt(2))","B",0
395,0,0,0,0.000000," ","integrate((1-sin(2/3*x))^(5/2),x, algorithm=""maxima"")","\int {\left(-\sin\left(\frac{2}{3} \, x\right) + 1\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((-sin(2/3*x) + 1)^(5/2), x)","F",0
396,1,43,0,0.429389," ","integrate(cos(x)*(-cos(x)^2+2*(1+2*sin(x))^(1/4))/(1+2*sin(x))^(3/2),x, algorithm=""maxima"")","\frac{1}{12} \, {\left(2 \, \sin\left(x\right) + 1\right)}^{\frac{3}{2}} - \frac{16 \, {\left(2 \, \sin\left(x\right) + 1\right)}^{\frac{1}{4}} - 3}{4 \, \sqrt{2 \, \sin\left(x\right) + 1}} - \frac{1}{2} \, \sqrt{2 \, \sin\left(x\right) + 1}"," ",0,"1/12*(2*sin(x) + 1)^(3/2) - 1/4*(16*(2*sin(x) + 1)^(1/4) - 3)/sqrt(2*sin(x) + 1) - 1/2*sqrt(2*sin(x) + 1)","A",0
397,1,80,0,0.964016," ","integrate(tan(x)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(x\right)}\right)}\right) - \frac{1}{4} \, \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) + \frac{1}{4} \, \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(x)))) - 1/4*sqrt(2)*log(sqrt(2)*sqrt(tan(x)) + tan(x) + 1) + 1/4*sqrt(2)*log(-sqrt(2)*sqrt(tan(x)) + tan(x) + 1)","A",0
398,1,52,0,0.948455," ","integrate(1/tan(5*x)^(1/3),x, algorithm=""maxima"")","\frac{1}{10} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(5 \, x\right)^{\frac{2}{3}} - 1\right)}\right) - \frac{1}{20} \, \log\left(\tan\left(5 \, x\right)^{\frac{4}{3}} - \tan\left(5 \, x\right)^{\frac{2}{3}} + 1\right) + \frac{1}{10} \, \log\left(\tan\left(5 \, x\right)^{\frac{2}{3}} + 1\right)"," ",0,"1/10*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(5*x)^(2/3) - 1)) - 1/20*log(tan(5*x)^(4/3) - tan(5*x)^(2/3) + 1) + 1/10*log(tan(5*x)^(2/3) + 1)","A",0
399,1,3213,0,2.139865," ","integrate(1/(4+3*tan(2*x))^(3/2),x, algorithm=""maxima"")","-\frac{2000 \, {\left(3 \, \cos\left(4 \, x\right) + \sin\left(4 \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{3} + 2000 \, {\left(3 \, \cos\left(4 \, x\right) + \sin\left(4 \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} - 2000 \, {\left(\cos\left(4 \, x\right) - 3 \, \sin\left(4 \, x\right) - 3\right)} \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{3} - 80 \, {\left(48 \, \cos\left(4 \, x\right) + 25 \, \sin\left(4 \, x\right) - 27\right)} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right) - 80 \, {\left(25 \, {\left(\cos\left(4 \, x\right) - 3 \, \sin\left(4 \, x\right) - 3\right)} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} - 25 \, \cos\left(4 \, x\right) + 48 \, \sin\left(4 \, x\right) + 75\right)} \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right) + 9 \, {\left(18 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2}\right)} \arctan\left(\frac{1}{3} \cdot 25^{\frac{1}{4}} {\left(25 \, \cos\left(4 \, x\right)^{4} + 25 \, \sin\left(4 \, x\right)^{4} + 64 \, \cos\left(4 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(4 \, x\right)^{2} + 32 \, \cos\left(4 \, x\right) + 25\right)} \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right)^{3} + 78 \, \cos\left(4 \, x\right)^{2} + 48 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 64 \, \cos\left(4 \, x\right) + 25\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{8}{3} \, \cos\left(4 \, x\right)^{2} + \frac{2}{9} \, {\left(7 \, \cos\left(4 \, x\right) + 16\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right)^{2} - \frac{8}{3} \, \cos\left(4 \, x\right), \frac{7}{9} \, \cos\left(4 \, x\right)^{2} + \frac{8}{3} \, {\left(2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) - \frac{7}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{25}{9}\right)\right) + \cos\left(4 \, x\right) - \frac{4}{3} \, \sin\left(4 \, x\right), \frac{1}{3} \cdot 25^{\frac{1}{4}} {\left(25 \, \cos\left(4 \, x\right)^{4} + 25 \, \sin\left(4 \, x\right)^{4} + 64 \, \cos\left(4 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(4 \, x\right)^{2} + 32 \, \cos\left(4 \, x\right) + 25\right)} \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right)^{3} + 78 \, \cos\left(4 \, x\right)^{2} + 48 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 64 \, \cos\left(4 \, x\right) + 25\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{8}{3} \, \cos\left(4 \, x\right)^{2} + \frac{2}{9} \, {\left(7 \, \cos\left(4 \, x\right) + 16\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right)^{2} - \frac{8}{3} \, \cos\left(4 \, x\right), \frac{7}{9} \, \cos\left(4 \, x\right)^{2} + \frac{8}{3} \, {\left(2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) - \frac{7}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{25}{9}\right)\right) - \frac{4}{3} \, \cos\left(4 \, x\right) - \sin\left(4 \, x\right) - \frac{4}{3}\right) + 18 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2}\right)} \arctan\left(\frac{2}{3} \cdot 4^{\frac{1}{4}} {\left(4 \, \cos\left(4 \, x\right)^{4} + 4 \, \sin\left(4 \, x\right)^{4} + 16 \, \cos\left(4 \, x\right)^{3} + {\left(8 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(4 \, x\right) + 17\right)} \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right)^{3} + 33 \, \cos\left(4 \, x\right)^{2} + 12 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 34 \, \cos\left(4 \, x\right) + 13\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\frac{32}{9} \, {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \cos\left(4 \, x\right) + \frac{8}{3}, \frac{16}{9} \, \cos\left(4 \, x\right)^{2} - \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) - \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right)\right) + \frac{4}{3} \, \sin\left(4 \, x\right) + 1, \frac{2}{3} \cdot 4^{\frac{1}{4}} {\left(4 \, \cos\left(4 \, x\right)^{4} + 4 \, \sin\left(4 \, x\right)^{4} + 16 \, \cos\left(4 \, x\right)^{3} + {\left(8 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(4 \, x\right) + 17\right)} \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right)^{3} + 33 \, \cos\left(4 \, x\right)^{2} + 12 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 34 \, \cos\left(4 \, x\right) + 13\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\frac{32}{9} \, {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \cos\left(4 \, x\right) + \frac{8}{3}, \frac{16}{9} \, \cos\left(4 \, x\right)^{2} - \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) - \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right)\right) + \frac{4}{3} \, \cos\left(4 \, x\right) + \frac{4}{3}\right) + 13 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2}\right)} \log\left(-\frac{2}{9} \cdot 25^{\frac{1}{4}} {\left(25 \, \cos\left(4 \, x\right)^{4} + 25 \, \sin\left(4 \, x\right)^{4} + 64 \, \cos\left(4 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(4 \, x\right)^{2} + 32 \, \cos\left(4 \, x\right) + 25\right)} \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right)^{3} + 78 \, \cos\left(4 \, x\right)^{2} + 48 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 64 \, \cos\left(4 \, x\right) + 25\right)}^{\frac{1}{4}} {\left(4 \, \cos\left(4 \, x\right) + 3 \, \sin\left(4 \, x\right) + 4\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{8}{3} \, \cos\left(4 \, x\right)^{2} + \frac{2}{9} \, {\left(7 \, \cos\left(4 \, x\right) + 16\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right)^{2} - \frac{8}{3} \, \cos\left(4 \, x\right), \frac{7}{9} \, \cos\left(4 \, x\right)^{2} + \frac{8}{3} \, {\left(2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) - \frac{7}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{25}{9}\right)\right) + \frac{5}{9} \, \sqrt{25 \, \cos\left(4 \, x\right)^{4} + 25 \, \sin\left(4 \, x\right)^{4} + 64 \, \cos\left(4 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(4 \, x\right)^{2} + 32 \, \cos\left(4 \, x\right) + 25\right)} \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right)^{3} + 78 \, \cos\left(4 \, x\right)^{2} + 48 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 64 \, \cos\left(4 \, x\right) + 25} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{8}{3} \, \cos\left(4 \, x\right)^{2} + \frac{2}{9} \, {\left(7 \, \cos\left(4 \, x\right) + 16\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right)^{2} - \frac{8}{3} \, \cos\left(4 \, x\right), \frac{7}{9} \, \cos\left(4 \, x\right)^{2} + \frac{8}{3} \, {\left(2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) - \frac{7}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{25}{9}\right)\right)^{2} + \frac{2}{9} \cdot 25^{\frac{1}{4}} {\left(25 \, \cos\left(4 \, x\right)^{4} + 25 \, \sin\left(4 \, x\right)^{4} + 64 \, \cos\left(4 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(4 \, x\right)^{2} + 32 \, \cos\left(4 \, x\right) + 25\right)} \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right)^{3} + 78 \, \cos\left(4 \, x\right)^{2} + 48 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 64 \, \cos\left(4 \, x\right) + 25\right)}^{\frac{1}{4}} {\left(3 \, \cos\left(4 \, x\right) - 4 \, \sin\left(4 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{8}{3} \, \cos\left(4 \, x\right)^{2} + \frac{2}{9} \, {\left(7 \, \cos\left(4 \, x\right) + 16\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right)^{2} - \frac{8}{3} \, \cos\left(4 \, x\right), \frac{7}{9} \, \cos\left(4 \, x\right)^{2} + \frac{8}{3} \, {\left(2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) - \frac{7}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{25}{9}\right)\right) + \frac{5}{9} \, \sqrt{25 \, \cos\left(4 \, x\right)^{4} + 25 \, \sin\left(4 \, x\right)^{4} + 64 \, \cos\left(4 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(4 \, x\right)^{2} + 32 \, \cos\left(4 \, x\right) + 25\right)} \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right)^{3} + 78 \, \cos\left(4 \, x\right)^{2} + 48 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 64 \, \cos\left(4 \, x\right) + 25} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{8}{3} \, \cos\left(4 \, x\right)^{2} + \frac{2}{9} \, {\left(7 \, \cos\left(4 \, x\right) + 16\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right)^{2} - \frac{8}{3} \, \cos\left(4 \, x\right), \frac{7}{9} \, \cos\left(4 \, x\right)^{2} + \frac{8}{3} \, {\left(2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) - \frac{7}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{25}{9}\right)\right)^{2} + \frac{25}{9} \, \cos\left(4 \, x\right)^{2} + \frac{25}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right) - 13 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2}\right)} \log\left(\frac{16}{9} \cdot 4^{\frac{1}{4}} {\left(4 \, \cos\left(4 \, x\right)^{4} + 4 \, \sin\left(4 \, x\right)^{4} + 16 \, \cos\left(4 \, x\right)^{3} + {\left(8 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(4 \, x\right) + 17\right)} \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right)^{3} + 33 \, \cos\left(4 \, x\right)^{2} + 12 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 34 \, \cos\left(4 \, x\right) + 13\right)}^{\frac{1}{4}} {\left(\cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\frac{32}{9} \, {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \cos\left(4 \, x\right) + \frac{8}{3}, \frac{16}{9} \, \cos\left(4 \, x\right)^{2} - \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) - \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right)\right) + \frac{8}{9} \, \sqrt{4 \, \cos\left(4 \, x\right)^{4} + 4 \, \sin\left(4 \, x\right)^{4} + 16 \, \cos\left(4 \, x\right)^{3} + {\left(8 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(4 \, x\right) + 17\right)} \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right)^{3} + 33 \, \cos\left(4 \, x\right)^{2} + 12 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 34 \, \cos\left(4 \, x\right) + 13} \cos\left(\frac{1}{2} \, \arctan\left(\frac{32}{9} \, {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \cos\left(4 \, x\right) + \frac{8}{3}, \frac{16}{9} \, \cos\left(4 \, x\right)^{2} - \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) - \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right)\right)^{2} + \frac{4}{9} \cdot 4^{\frac{1}{4}} {\left(4 \, \cos\left(4 \, x\right)^{4} + 4 \, \sin\left(4 \, x\right)^{4} + 16 \, \cos\left(4 \, x\right)^{3} + {\left(8 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(4 \, x\right) + 17\right)} \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right)^{3} + 33 \, \cos\left(4 \, x\right)^{2} + 12 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 34 \, \cos\left(4 \, x\right) + 13\right)}^{\frac{1}{4}} {\left(4 \, \sin\left(4 \, x\right) + 3\right)} \sin\left(\frac{1}{2} \, \arctan\left(\frac{32}{9} \, {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \cos\left(4 \, x\right) + \frac{8}{3}, \frac{16}{9} \, \cos\left(4 \, x\right)^{2} - \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) - \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right)\right) + \frac{8}{9} \, \sqrt{4 \, \cos\left(4 \, x\right)^{4} + 4 \, \sin\left(4 \, x\right)^{4} + 16 \, \cos\left(4 \, x\right)^{3} + {\left(8 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(4 \, x\right) + 17\right)} \sin\left(4 \, x\right)^{2} + 12 \, \sin\left(4 \, x\right)^{3} + 33 \, \cos\left(4 \, x\right)^{2} + 12 \, {\left(\cos\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 34 \, \cos\left(4 \, x\right) + 13} \sin\left(\frac{1}{2} \, \arctan\left(\frac{32}{9} \, {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(4 \, x\right) + \frac{8}{3} \, \cos\left(4 \, x\right) + \frac{8}{3}, \frac{16}{9} \, \cos\left(4 \, x\right)^{2} - \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) - \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{16}{9}\right)\right)^{2} + \frac{16}{9} \, \cos\left(4 \, x\right)^{2} + \frac{16}{9} \, \sin\left(4 \, x\right)^{2} + \frac{32}{9} \, \cos\left(4 \, x\right) + \frac{8}{3} \, \sin\left(4 \, x\right) + \frac{25}{9}\right)\right)} {\left(2 \, {\left(32 \, \cos\left(4 \, x\right) - 24 \, \sin\left(4 \, x\right) + 7\right)} \cos\left(8 \, x\right) + 25 \, \cos\left(8 \, x\right)^{2} + 64 \, \cos\left(4 \, x\right)^{2} + 16 \, {\left(3 \, \cos\left(4 \, x\right) + 4 \, \sin\left(4 \, x\right) + 3\right)} \sin\left(8 \, x\right) + 25 \, \sin\left(8 \, x\right)^{2} + 64 \, \sin\left(4 \, x\right)^{2} + 64 \, \cos\left(4 \, x\right) + 48 \, \sin\left(4 \, x\right) + 25\right)}^{\frac{1}{4}}}{18000 \, {\left(2 \, {\left(32 \, \cos\left(4 \, x\right) - 24 \, \sin\left(4 \, x\right) + 7\right)} \cos\left(8 \, x\right) + 25 \, \cos\left(8 \, x\right)^{2} + 64 \, \cos\left(4 \, x\right)^{2} + 16 \, {\left(3 \, \cos\left(4 \, x\right) + 4 \, \sin\left(4 \, x\right) + 3\right)} \sin\left(8 \, x\right) + 25 \, \sin\left(8 \, x\right)^{2} + 64 \, \sin\left(4 \, x\right)^{2} + 64 \, \cos\left(4 \, x\right) + 48 \, \sin\left(4 \, x\right) + 25\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(-3 \, \cos\left(8 \, x\right) + 4 \, \sin\left(8 \, x\right) + 8 \, \sin\left(4 \, x\right) + 3, 4 \, \cos\left(8 \, x\right) + 8 \, \cos\left(4 \, x\right) + 3 \, \sin\left(8 \, x\right) + 4\right)\right)^{2}\right)}}"," ",0,"-1/18000*(2000*(3*cos(4*x) + sin(4*x))*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^3 + 2000*(3*cos(4*x) + sin(4*x))*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 - 2000*(cos(4*x) - 3*sin(4*x) - 3)*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^3 - 80*(48*cos(4*x) + 25*sin(4*x) - 27)*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4)) - 80*(25*(cos(4*x) - 3*sin(4*x) - 3)*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 - 25*cos(4*x) + 48*sin(4*x) + 75)*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4)) + 9*(18*(sqrt(2)*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 + sqrt(2)*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2)*arctan2(1/3*25^(1/4)*(25*cos(4*x)^4 + 25*sin(4*x)^4 + 64*cos(4*x)^3 + 2*(25*cos(4*x)^2 + 32*cos(4*x) + 25)*sin(4*x)^2 + 48*sin(4*x)^3 + 78*cos(4*x)^2 + 48*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 64*cos(4*x) + 25)^(1/4)*sin(1/2*arctan2(-8/3*cos(4*x)^2 + 2/9*(7*cos(4*x) + 16)*sin(4*x) + 8/3*sin(4*x)^2 - 8/3*cos(4*x), 7/9*cos(4*x)^2 + 8/3*(2*cos(4*x) + 1)*sin(4*x) - 7/9*sin(4*x)^2 + 32/9*cos(4*x) + 25/9)) + cos(4*x) - 4/3*sin(4*x), 1/3*25^(1/4)*(25*cos(4*x)^4 + 25*sin(4*x)^4 + 64*cos(4*x)^3 + 2*(25*cos(4*x)^2 + 32*cos(4*x) + 25)*sin(4*x)^2 + 48*sin(4*x)^3 + 78*cos(4*x)^2 + 48*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 64*cos(4*x) + 25)^(1/4)*cos(1/2*arctan2(-8/3*cos(4*x)^2 + 2/9*(7*cos(4*x) + 16)*sin(4*x) + 8/3*sin(4*x)^2 - 8/3*cos(4*x), 7/9*cos(4*x)^2 + 8/3*(2*cos(4*x) + 1)*sin(4*x) - 7/9*sin(4*x)^2 + 32/9*cos(4*x) + 25/9)) - 4/3*cos(4*x) - sin(4*x) - 4/3) + 18*(sqrt(2)*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 + sqrt(2)*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2)*arctan2(2/3*4^(1/4)*(4*cos(4*x)^4 + 4*sin(4*x)^4 + 16*cos(4*x)^3 + (8*cos(4*x)^2 + 16*cos(4*x) + 17)*sin(4*x)^2 + 12*sin(4*x)^3 + 33*cos(4*x)^2 + 12*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 34*cos(4*x) + 13)^(1/4)*sin(1/2*arctan2(32/9*(cos(4*x) + 1)*sin(4*x) + 8/3*cos(4*x) + 8/3, 16/9*cos(4*x)^2 - 16/9*sin(4*x)^2 + 32/9*cos(4*x) - 8/3*sin(4*x) + 16/9)) + 4/3*sin(4*x) + 1, 2/3*4^(1/4)*(4*cos(4*x)^4 + 4*sin(4*x)^4 + 16*cos(4*x)^3 + (8*cos(4*x)^2 + 16*cos(4*x) + 17)*sin(4*x)^2 + 12*sin(4*x)^3 + 33*cos(4*x)^2 + 12*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 34*cos(4*x) + 13)^(1/4)*cos(1/2*arctan2(32/9*(cos(4*x) + 1)*sin(4*x) + 8/3*cos(4*x) + 8/3, 16/9*cos(4*x)^2 - 16/9*sin(4*x)^2 + 32/9*cos(4*x) - 8/3*sin(4*x) + 16/9)) + 4/3*cos(4*x) + 4/3) + 13*(sqrt(2)*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 + sqrt(2)*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2)*log(-2/9*25^(1/4)*(25*cos(4*x)^4 + 25*sin(4*x)^4 + 64*cos(4*x)^3 + 2*(25*cos(4*x)^2 + 32*cos(4*x) + 25)*sin(4*x)^2 + 48*sin(4*x)^3 + 78*cos(4*x)^2 + 48*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 64*cos(4*x) + 25)^(1/4)*(4*cos(4*x) + 3*sin(4*x) + 4)*cos(1/2*arctan2(-8/3*cos(4*x)^2 + 2/9*(7*cos(4*x) + 16)*sin(4*x) + 8/3*sin(4*x)^2 - 8/3*cos(4*x), 7/9*cos(4*x)^2 + 8/3*(2*cos(4*x) + 1)*sin(4*x) - 7/9*sin(4*x)^2 + 32/9*cos(4*x) + 25/9)) + 5/9*sqrt(25*cos(4*x)^4 + 25*sin(4*x)^4 + 64*cos(4*x)^3 + 2*(25*cos(4*x)^2 + 32*cos(4*x) + 25)*sin(4*x)^2 + 48*sin(4*x)^3 + 78*cos(4*x)^2 + 48*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 64*cos(4*x) + 25)*cos(1/2*arctan2(-8/3*cos(4*x)^2 + 2/9*(7*cos(4*x) + 16)*sin(4*x) + 8/3*sin(4*x)^2 - 8/3*cos(4*x), 7/9*cos(4*x)^2 + 8/3*(2*cos(4*x) + 1)*sin(4*x) - 7/9*sin(4*x)^2 + 32/9*cos(4*x) + 25/9))^2 + 2/9*25^(1/4)*(25*cos(4*x)^4 + 25*sin(4*x)^4 + 64*cos(4*x)^3 + 2*(25*cos(4*x)^2 + 32*cos(4*x) + 25)*sin(4*x)^2 + 48*sin(4*x)^3 + 78*cos(4*x)^2 + 48*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 64*cos(4*x) + 25)^(1/4)*(3*cos(4*x) - 4*sin(4*x))*sin(1/2*arctan2(-8/3*cos(4*x)^2 + 2/9*(7*cos(4*x) + 16)*sin(4*x) + 8/3*sin(4*x)^2 - 8/3*cos(4*x), 7/9*cos(4*x)^2 + 8/3*(2*cos(4*x) + 1)*sin(4*x) - 7/9*sin(4*x)^2 + 32/9*cos(4*x) + 25/9)) + 5/9*sqrt(25*cos(4*x)^4 + 25*sin(4*x)^4 + 64*cos(4*x)^3 + 2*(25*cos(4*x)^2 + 32*cos(4*x) + 25)*sin(4*x)^2 + 48*sin(4*x)^3 + 78*cos(4*x)^2 + 48*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 64*cos(4*x) + 25)*sin(1/2*arctan2(-8/3*cos(4*x)^2 + 2/9*(7*cos(4*x) + 16)*sin(4*x) + 8/3*sin(4*x)^2 - 8/3*cos(4*x), 7/9*cos(4*x)^2 + 8/3*(2*cos(4*x) + 1)*sin(4*x) - 7/9*sin(4*x)^2 + 32/9*cos(4*x) + 25/9))^2 + 25/9*cos(4*x)^2 + 25/9*sin(4*x)^2 + 32/9*cos(4*x) + 8/3*sin(4*x) + 16/9) - 13*(sqrt(2)*cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 + sqrt(2)*sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2)*log(16/9*4^(1/4)*(4*cos(4*x)^4 + 4*sin(4*x)^4 + 16*cos(4*x)^3 + (8*cos(4*x)^2 + 16*cos(4*x) + 17)*sin(4*x)^2 + 12*sin(4*x)^3 + 33*cos(4*x)^2 + 12*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 34*cos(4*x) + 13)^(1/4)*(cos(4*x) + 1)*cos(1/2*arctan2(32/9*(cos(4*x) + 1)*sin(4*x) + 8/3*cos(4*x) + 8/3, 16/9*cos(4*x)^2 - 16/9*sin(4*x)^2 + 32/9*cos(4*x) - 8/3*sin(4*x) + 16/9)) + 8/9*sqrt(4*cos(4*x)^4 + 4*sin(4*x)^4 + 16*cos(4*x)^3 + (8*cos(4*x)^2 + 16*cos(4*x) + 17)*sin(4*x)^2 + 12*sin(4*x)^3 + 33*cos(4*x)^2 + 12*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 34*cos(4*x) + 13)*cos(1/2*arctan2(32/9*(cos(4*x) + 1)*sin(4*x) + 8/3*cos(4*x) + 8/3, 16/9*cos(4*x)^2 - 16/9*sin(4*x)^2 + 32/9*cos(4*x) - 8/3*sin(4*x) + 16/9))^2 + 4/9*4^(1/4)*(4*cos(4*x)^4 + 4*sin(4*x)^4 + 16*cos(4*x)^3 + (8*cos(4*x)^2 + 16*cos(4*x) + 17)*sin(4*x)^2 + 12*sin(4*x)^3 + 33*cos(4*x)^2 + 12*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 34*cos(4*x) + 13)^(1/4)*(4*sin(4*x) + 3)*sin(1/2*arctan2(32/9*(cos(4*x) + 1)*sin(4*x) + 8/3*cos(4*x) + 8/3, 16/9*cos(4*x)^2 - 16/9*sin(4*x)^2 + 32/9*cos(4*x) - 8/3*sin(4*x) + 16/9)) + 8/9*sqrt(4*cos(4*x)^4 + 4*sin(4*x)^4 + 16*cos(4*x)^3 + (8*cos(4*x)^2 + 16*cos(4*x) + 17)*sin(4*x)^2 + 12*sin(4*x)^3 + 33*cos(4*x)^2 + 12*(cos(4*x)^2 + 2*cos(4*x) + 1)*sin(4*x) + 34*cos(4*x) + 13)*sin(1/2*arctan2(32/9*(cos(4*x) + 1)*sin(4*x) + 8/3*cos(4*x) + 8/3, 16/9*cos(4*x)^2 - 16/9*sin(4*x)^2 + 32/9*cos(4*x) - 8/3*sin(4*x) + 16/9))^2 + 16/9*cos(4*x)^2 + 16/9*sin(4*x)^2 + 32/9*cos(4*x) + 8/3*sin(4*x) + 25/9))*(2*(32*cos(4*x) - 24*sin(4*x) + 7)*cos(8*x) + 25*cos(8*x)^2 + 64*cos(4*x)^2 + 16*(3*cos(4*x) + 4*sin(4*x) + 3)*sin(8*x) + 25*sin(8*x)^2 + 64*sin(4*x)^2 + 64*cos(4*x) + 48*sin(4*x) + 25)^(1/4))/((2*(32*cos(4*x) - 24*sin(4*x) + 7)*cos(8*x) + 25*cos(8*x)^2 + 64*cos(4*x)^2 + 16*(3*cos(4*x) + 4*sin(4*x) + 3)*sin(8*x) + 25*sin(8*x)^2 + 64*sin(4*x)^2 + 64*cos(4*x) + 48*sin(4*x) + 25)^(1/4)*(cos(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2 + sin(1/2*arctan2(-3*cos(8*x) + 4*sin(8*x) + 8*sin(4*x) + 3, 4*cos(8*x) + 8*cos(4*x) + 3*sin(8*x) + 4))^2))","B",0
400,1,30,0,0.430499," ","integrate((-(4-3*tan(x))^(1/2)+3*tan(x))/cos(x)^2/(4-3*tan(x))^(3/2),x, algorithm=""maxima"")","\frac{2}{3} \, \sqrt{-3 \, \tan\left(x\right) + 4} + \frac{8}{3 \, \sqrt{-3 \, \tan\left(x\right) + 4}} + \frac{1}{3} \, \log\left(-3 \, \tan\left(x\right) + 4\right)"," ",0,"2/3*sqrt(-3*tan(x) + 4) + 8/3/sqrt(-3*tan(x) + 4) + 1/3*log(-3*tan(x) + 4)","A",0
401,1,117,0,0.970435," ","integrate(tan(x)/(-1+tan(x)^(1/2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} {\left(\sqrt{2} - 2\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) - \frac{1}{4} \, \sqrt{2} {\left(\sqrt{2} + 2\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(x\right)}\right)}\right) - \frac{1}{8} \, \sqrt{2} {\left(\sqrt{2} - 2\right)} \log\left(\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) - \frac{1}{8} \, \sqrt{2} {\left(\sqrt{2} + 2\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) - \frac{1}{\sqrt{\tan\left(x\right)} - 1} + \log\left(\sqrt{\tan\left(x\right)} - 1\right)"," ",0,"1/4*sqrt(2)*(sqrt(2) - 2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) - 1/4*sqrt(2)*(sqrt(2) + 2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(x)))) - 1/8*sqrt(2)*(sqrt(2) - 2)*log(sqrt(2)*sqrt(tan(x)) + tan(x) + 1) - 1/8*sqrt(2)*(sqrt(2) + 2)*log(-sqrt(2)*sqrt(tan(x)) + tan(x) + 1) - 1/(sqrt(tan(x)) - 1) + log(sqrt(tan(x)) - 1)","A",0
402,0,0,0,0.000000," ","integrate(sin(x)/sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(x\right)}{\sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(sin(x)/sqrt(sin(2*x)), x)","F",0
403,0,0,0,0.000000," ","integrate(cos(x)/sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right)}{\sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(cos(x)/sqrt(sin(2*x)), x)","F",0
404,0,0,0,0.000000," ","integrate(sin(x)*sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sin\left(2 \, x\right)} \sin\left(x\right)\,{d x}"," ",0,"integrate(sqrt(sin(2*x))*sin(x), x)","F",0
405,0,0,0,0.000000," ","integrate((cos(x)-sin(x))*sin(2*x)^(1/2),x, algorithm=""maxima"")","\int {\left(\cos\left(x\right) - \sin\left(x\right)\right)} \sqrt{\sin\left(2 \, x\right)}\,{d x}"," ",0,"integrate((cos(x) - sin(x))*sqrt(sin(2*x)), x)","F",0
406,0,0,0,0.000000," ","integrate(sin(x)^7/sin(2*x)^(7/2),x, algorithm=""maxima"")","\int \frac{\sin\left(x\right)^{7}}{\sin\left(2 \, x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sin(x)^7/sin(2*x)^(7/2), x)","F",0
407,0,0,0,0.000000," ","integrate(cos(x)^7/sin(2*x)^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right)^{7}}{\sin\left(2 \, x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(x)^7/sin(2*x)^(7/2), x)","F",0
408,0,0,0,0.000000," ","integrate(sin(2*x)^(3/2)/sin(x)^5,x, algorithm=""maxima"")","\int \frac{\sin\left(2 \, x\right)^{\frac{3}{2}}}{\sin\left(x\right)^{5}}\,{d x}"," ",0,"integrate(sin(2*x)^(3/2)/sin(x)^5, x)","F",0
409,0,0,0,0.000000," ","integrate(1/cos(x)^3/sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(x\right)^{3} \sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(1/(cos(x)^3*sqrt(sin(2*x))), x)","F",0
410,0,0,0,0.000000," ","integrate(1/sin(x)/sin(2*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sin\left(2 \, x\right)^{\frac{3}{2}} \sin\left(x\right)}\,{d x}"," ",0,"integrate(1/(sin(2*x)^(3/2)*sin(x)), x)","F",0
411,-1,0,0,0.000000," ","integrate(cos(x)^3*(cos(2*x)-3*tan(x))/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,1,6,0,1.051797," ","integrate((sin(x)/cos(x)^5)^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, \tan\left(x\right)^{\frac{3}{2}}"," ",0,"2/3*tan(x)^(3/2)","A",0
413,0,0,0,0.000000," ","integrate((sin(x)^5/cos(x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\frac{\sin\left(x\right)^{5}}{\cos\left(x\right)}}\,{d x}"," ",0,"integrate(sqrt(sin(x)^5/cos(x)), x)","F",0
414,1,13,0,0.998781," ","integrate((sin(x)^2/cos(x)^14)^(1/3),x, algorithm=""maxima"")","\frac{3}{11} \, \tan\left(x\right)^{\frac{11}{3}} + \frac{3}{5} \, \tan\left(x\right)^{\frac{5}{3}}"," ",0,"3/11*tan(x)^(11/3) + 3/5*tan(x)^(5/3)","A",0
415,1,77,0,1.010421," ","integrate(1/(cos(x)^11*sin(x)^13)^(1/4),x, algorithm=""maxima"")","\frac{4}{23} \, \tan\left(x\right)^{\frac{23}{4}} + \frac{8}{15} \, \tan\left(x\right)^{\frac{15}{4}} + \frac{4}{7} \, \tan\left(x\right)^{\frac{7}{4}} - \frac{4 \, {\left(35 \, \tan\left(x\right)^{7} + 161 \, \tan\left(x\right)^{5} + 345 \, \tan\left(x\right)^{3} - 805 \, \tan\left(x\right)\right)}}{805 \, \tan\left(x\right)^{\frac{5}{4}}} + \frac{4 \, {\left(21 \, \tan\left(x\right)^{7} + 135 \, \tan\left(x\right)^{5} - 945 \, \tan\left(x\right)^{3} - 35 \, \tan\left(x\right)\right)}}{315 \, \tan\left(x\right)^{\frac{13}{4}}}"," ",0,"4/23*tan(x)^(23/4) + 8/15*tan(x)^(15/4) + 4/7*tan(x)^(7/4) - 4/805*(35*tan(x)^7 + 161*tan(x)^5 + 345*tan(x)^3 - 805*tan(x))/tan(x)^(5/4) + 4/315*(21*tan(x)^7 + 135*tan(x)^5 - 945*tan(x)^3 - 35*tan(x))/tan(x)^(13/4)","A",0
416,0,0,0,0.000000," ","integrate((cos(2*x)-sin(2*x)^(1/2))/(cos(x)^3*sin(x))^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{2} \int \frac{2 \, {\left({\left({\left({\left(\cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - \sin\left(4 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) \sin\left(4 \, x\right) + {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right) + {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) \sin\left(4 \, x\right) + {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left(\cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - \sin\left(4 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right)\right)}}{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}\,{d x} - \frac{1}{2} \, \sqrt{2} \int -\frac{2 \, {\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) \sin\left(4 \, x\right) + {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left(\cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - \sin\left(4 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right) - {\left({\left({\left(\cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - \sin\left(4 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) \sin\left(4 \, x\right) + {\left(\cos\left(4 \, x\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right)\right)}}{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}\,{d x} - \frac{1}{2} \, \sqrt{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{2} \, \sqrt{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"1/2*sqrt(2)*integrate(2*((((cos(4*x) + 1)*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - sin(4*x)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) + (cos(1/2*arctan2(sin(x), -cos(x) + 1))*sin(4*x) + (cos(4*x) + 1)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*cos(3/2*arctan2(sin(2*x), cos(2*x) + 1)) + ((cos(1/2*arctan2(sin(x), -cos(x) + 1))*sin(4*x) + (cos(4*x) + 1)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) - ((cos(4*x) + 1)*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - sin(4*x)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*sin(3/2*arctan2(sin(2*x), cos(2*x) + 1)))/((cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^(3/4)*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)), x) - 1/2*sqrt(2)*integrate(-2*(((cos(1/2*arctan2(sin(x), -cos(x) + 1))*sin(4*x) + (cos(4*x) + 1)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) - ((cos(4*x) + 1)*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - sin(4*x)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*cos(3/2*arctan2(sin(2*x), cos(2*x) + 1)) - (((cos(4*x) + 1)*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - sin(4*x)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) + (cos(1/2*arctan2(sin(x), -cos(x) + 1))*sin(4*x) + (cos(4*x) + 1)*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*sin(3/2*arctan2(sin(2*x), cos(2*x) + 1)))/((cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^(3/4)*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)), x) - 1/2*sqrt(2)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/2*sqrt(2)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","F",0
417,0,0,0,0.000000," ","integrate((-2*sin(2*x)+(cos(x)*sin(x)^3)^(1/2))/(-(cos(x)^3*sin(x))^(1/2)+tan(x)^(1/2)),x, algorithm=""maxima"")","-2 \, \int -\frac{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - {\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) + {\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right) - {\left({\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) + {\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - {\left({\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right)\right)}}{4 \, {\left({\left({\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)^{2} + {\left({\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}\,{d x} + 2 \, \int \frac{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - {\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) + {\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right) - {\left({\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) + {\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right) - {\left({\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) - \sqrt{2} \sin\left(3 \, x\right) + 2 \, \sqrt{2} \sin\left(2 \, x\right) - \sqrt{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sqrt{2} \cos\left(3 \, x\right) - 2 \, \sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sqrt{2} \cos\left(3 \, x\right) + 2 \, \sqrt{2} \cos\left(2 \, x\right) - \sqrt{2} \cos\left(x\right) + \sqrt{2} \sin\left(3 \, x\right) - 2 \, \sqrt{2} \sin\left(2 \, x\right) + \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)\right)\right)}}{4 \, {\left({\left({\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - \cos\left(x\right)\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) - \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - \cos\left(x\right)\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) - \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)^{2} + {\left({\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - \cos\left(x\right)\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) - \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - \cos\left(x\right)\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \cos\left(x\right) - \cos\left(x\right)^{2} + 2 \, {\left(2 \, \sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}\,{d x} + \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-2*integrate(-1/4*(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^(1/4)*(((((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - ((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) + (((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) + ((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*cos(1/2*arctan2(sin(2*x), cos(2*x) + 1)) - ((((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) + ((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) - (((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - ((sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*sin(1/2*arctan2(sin(2*x), cos(2*x) + 1)))/((((2*(2*cos(2*x) + cos(x))*cos(3*x) + cos(3*x)^2 + 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) + cos(x)^2 + 2*(2*sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) + sin(x)^2)*cos(1/2*arctan2(sin(x), -cos(x) + 1))^2 + (2*(2*cos(2*x) + cos(x))*cos(3*x) + cos(3*x)^2 + 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) + cos(x)^2 + 2*(2*sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) + sin(x)^2)*sin(1/2*arctan2(sin(x), -cos(x) + 1))^2)*cos(1/2*arctan2(sin(x), cos(x) + 1))^2 + ((2*(2*cos(2*x) + cos(x))*cos(3*x) + cos(3*x)^2 + 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) + cos(x)^2 + 2*(2*sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) + sin(x)^2)*cos(1/2*arctan2(sin(x), -cos(x) + 1))^2 + (2*(2*cos(2*x) + cos(x))*cos(3*x) + cos(3*x)^2 + 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) + cos(x)^2 + 2*(2*sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) + sin(x)^2)*sin(1/2*arctan2(sin(x), -cos(x) + 1))^2)*sin(1/2*arctan2(sin(x), cos(x) + 1))^2)*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)), x) + 2*integrate(1/4*(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^(1/4)*(((((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - ((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) + (((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) + ((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*cos(1/2*arctan2(sin(2*x), cos(2*x) + 1)) - ((((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) + ((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) - (((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*cos(4*x) - (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(1/2*arctan2(sin(x), -cos(x) + 1)) - ((sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) - sqrt(2)*sin(3*x) + 2*sqrt(2)*sin(2*x) - sqrt(2)*sin(x))*cos(4*x) + (sqrt(2)*cos(3*x) - 2*sqrt(2)*cos(2*x) + sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(4*x) - sqrt(2)*cos(3*x) + 2*sqrt(2)*cos(2*x) - sqrt(2)*cos(x) + sqrt(2)*sin(3*x) - 2*sqrt(2)*sin(2*x) + sqrt(2)*sin(x))*sin(1/2*arctan2(sin(x), -cos(x) + 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))*sin(1/2*arctan2(sin(2*x), cos(2*x) + 1)))/((((2*(2*cos(2*x) - cos(x))*cos(3*x) - cos(3*x)^2 - 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) - cos(x)^2 + 2*(2*sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) - sin(x)^2)*cos(1/2*arctan2(sin(x), -cos(x) + 1))^2 + (2*(2*cos(2*x) - cos(x))*cos(3*x) - cos(3*x)^2 - 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) - cos(x)^2 + 2*(2*sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) - sin(x)^2)*sin(1/2*arctan2(sin(x), -cos(x) + 1))^2)*cos(1/2*arctan2(sin(x), cos(x) + 1))^2 + ((2*(2*cos(2*x) - cos(x))*cos(3*x) - cos(3*x)^2 - 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) - cos(x)^2 + 2*(2*sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) - sin(x)^2)*cos(1/2*arctan2(sin(x), -cos(x) + 1))^2 + (2*(2*cos(2*x) - cos(x))*cos(3*x) - cos(3*x)^2 - 4*cos(2*x)^2 + 4*cos(2*x)*cos(x) - cos(x)^2 + 2*(2*sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - 4*sin(2*x)^2 + 4*sin(2*x)*sin(x) - sin(x)^2)*sin(1/2*arctan2(sin(x), -cos(x) + 1))^2)*sin(1/2*arctan2(sin(x), cos(x) + 1))^2)*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)), x) + 1/2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
418,1,60,0,1.174536," ","integrate(((sin(x)/cos(x)^7)^(1/3)-3*tan(x))/(cos(x)^5*sin(x))^(2/3),x, algorithm=""maxima"")","-\frac{3}{20} \, \tan\left(x\right)^{\frac{20}{3}} - \frac{3}{7} \, \tan\left(x\right)^{\frac{14}{3}} - \frac{9}{10} \, \tan\left(x\right)^{\frac{10}{3}} - \frac{3}{8} \, \tan\left(x\right)^{\frac{8}{3}} - \frac{9}{4} \, \tan\left(x\right)^{\frac{4}{3}} + \frac{3 \, {\left(14 \, \tan\left(x\right)^{7} + 60 \, \tan\left(x\right)^{5} + 105 \, \tan\left(x\right)^{3} + 140 \, \tan\left(x\right)\right)}}{280 \, \tan\left(x\right)^{\frac{1}{3}}}"," ",0,"-3/20*tan(x)^(20/3) - 3/7*tan(x)^(14/3) - 9/10*tan(x)^(10/3) - 3/8*tan(x)^(8/3) - 9/4*tan(x)^(4/3) + 3/280*(14*tan(x)^7 + 60*tan(x)^5 + 105*tan(x)^3 + 140*tan(x))/tan(x)^(1/3)","A",0
419,1,55,0,0.956644," ","integrate((1+2*cos(x)^2)^(5/2)*sin(x),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(2 \, \cos\left(x\right)^{2} + 1\right)}^{\frac{5}{2}} \cos\left(x\right) - \frac{5}{24} \, {\left(2 \, \cos\left(x\right)^{2} + 1\right)}^{\frac{3}{2}} \cos\left(x\right) - \frac{5}{32} \, \sqrt{2} \operatorname{arsinh}\left(\sqrt{2} \cos\left(x\right)\right) - \frac{5}{16} \, \sqrt{2 \, \cos\left(x\right)^{2} + 1} \cos\left(x\right)"," ",0,"-1/6*(2*cos(x)^2 + 1)^(5/2)*cos(x) - 5/24*(2*cos(x)^2 + 1)^(3/2)*cos(x) - 5/32*sqrt(2)*arcsinh(sqrt(2)*cos(x)) - 5/16*sqrt(2*cos(x)^2 + 1)*cos(x)","A",0
420,1,53,0,0.975789," ","integrate(cos(x)*(5*cos(x)^2+sin(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(-4 \, \sin\left(x\right)^{2} + 5\right)}^{\frac{5}{2}} \sin\left(x\right) + \frac{25}{24} \, {\left(-4 \, \sin\left(x\right)^{2} + 5\right)}^{\frac{3}{2}} \sin\left(x\right) + \frac{125}{16} \, \sqrt{-4 \, \sin\left(x\right)^{2} + 5} \sin\left(x\right) + \frac{625}{32} \, \arcsin\left(\frac{2}{5} \, \sqrt{5} \sin\left(x\right)\right)"," ",0,"1/6*(-4*sin(x)^2 + 5)^(5/2)*sin(x) + 25/24*(-4*sin(x)^2 + 5)^(3/2)*sin(x) + 125/16*sqrt(-4*sin(x)^2 + 5)*sin(x) + 625/32*arcsin(2/5*sqrt(5)*sin(x))","A",0
421,1,36,0,1.212589," ","integrate(cos(x)*(-cos(x)^2-5*sin(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(-4 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{3}{2}} \sin\left(x\right) - \frac{3}{8} \, \sqrt{-4 \, \sin\left(x\right)^{2} - 1} \sin\left(x\right) - \frac{3}{16} i \, \operatorname{arsinh}\left(2 \, \sin\left(x\right)\right)"," ",0,"1/4*(-4*sin(x)^2 - 1)^(3/2)*sin(x) - 3/8*sqrt(-4*sin(x)^2 - 1)*sin(x) - 3/16*I*arcsinh(2*sin(x))","C",0
422,1,43,0,0.423273," ","integrate(sin(x)/(5*cos(x)^2-2*sin(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{\cos\left(x\right)}{15 \, \sqrt{7 \, \cos\left(x\right)^{2} - 2}} - \frac{\cos\left(x\right)}{15 \, {\left(7 \, \cos\left(x\right)^{2} - 2\right)}^{\frac{3}{2}}} + \frac{\cos\left(x\right)}{10 \, {\left(7 \, \cos\left(x\right)^{2} - 2\right)}^{\frac{5}{2}}}"," ",0,"1/15*cos(x)/sqrt(7*cos(x)^2 - 2) - 1/15*cos(x)/(7*cos(x)^2 - 2)^(3/2) + 1/10*cos(x)/(7*cos(x)^2 - 2)^(5/2)","A",0
423,1,716,0,1.317462," ","integrate(cos(x)*cos(2*x)/(2-5*sin(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{5 \, \cos\left(\frac{1}{2} \, \arctan\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right), 5 \, \cos\left(4 \, x\right) - 2 \, \cos\left(2 \, x\right) + 5\right)\right) \sin\left(2 \, x\right) - 5 \, {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right), 5 \, \cos\left(4 \, x\right) - 2 \, \cos\left(2 \, x\right) + 5\right)\right) + 2 \, {\left(-10 \, {\left(2 \, \cos\left(2 \, x\right) - 5\right)} \cos\left(4 \, x\right) + 25 \, \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 25 \, \sin\left(4 \, x\right)^{2} - 20 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} - 20 \, \cos\left(2 \, x\right) + 25\right)}^{\frac{1}{4}} {\left(\sqrt{5} \arctan\left(\frac{1}{12} \, \sqrt{6} {\left(\sqrt{6} \left(\frac{25}{36}\right)^{\frac{1}{4}} {\left(25 \, \cos\left(2 \, x\right)^{4} + 25 \, \sin\left(2 \, x\right)^{4} - 20 \, \cos\left(2 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(2 \, x\right)^{2} - 10 \, \cos\left(2 \, x\right) - 23\right)} \sin\left(2 \, x\right)^{2} + 54 \, \cos\left(2 \, x\right)^{2} - 20 \, \cos\left(2 \, x\right) + 25\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\frac{5}{12} \, {\left(5 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right), \frac{25}{24} \, \cos\left(2 \, x\right)^{2} - \frac{25}{24} \, \sin\left(2 \, x\right)^{2} - \frac{5}{12} \, \cos\left(2 \, x\right) + \frac{25}{24}\right)\right) + 5 \, \sin\left(2 \, x\right)\right)}, \frac{5}{12} \, \sqrt{6} \cos\left(2 \, x\right) + \frac{1}{2} \, \left(\frac{25}{36}\right)^{\frac{1}{4}} {\left(25 \, \cos\left(2 \, x\right)^{4} + 25 \, \sin\left(2 \, x\right)^{4} - 20 \, \cos\left(2 \, x\right)^{3} + 2 \, {\left(25 \, \cos\left(2 \, x\right)^{2} - 10 \, \cos\left(2 \, x\right) - 23\right)} \sin\left(2 \, x\right)^{2} + 54 \, \cos\left(2 \, x\right)^{2} - 20 \, \cos\left(2 \, x\right) + 25\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\frac{5}{12} \, {\left(5 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right), \frac{25}{24} \, \cos\left(2 \, x\right)^{2} - \frac{25}{24} \, \sin\left(2 \, x\right)^{2} - \frac{5}{12} \, \cos\left(2 \, x\right) + \frac{25}{24}\right)\right) - \frac{1}{12} \, \sqrt{6}\right) + \sqrt{5} \arctan\left(\frac{1}{12} \, \sqrt{6} {\left(\sqrt{6} \left(\frac{1}{36}\right)^{\frac{1}{4}} {\left(\cos\left(2 \, x\right)^{4} + \sin\left(2 \, x\right)^{4} - 20 \, \cos\left(2 \, x\right)^{3} + 2 \, {\left(\cos\left(2 \, x\right)^{2} - 10 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(2 \, x\right)^{2} + 198 \, \cos\left(2 \, x\right)^{2} - 980 \, \cos\left(2 \, x\right) + 2401\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\frac{1}{12} \, {\left(\cos\left(2 \, x\right) - 5\right)} \sin\left(2 \, x\right), \frac{1}{24} \, \cos\left(2 \, x\right)^{2} - \frac{1}{24} \, \sin\left(2 \, x\right)^{2} - \frac{5}{12} \, \cos\left(2 \, x\right) + \frac{49}{24}\right)\right) + \sin\left(2 \, x\right)\right)}, \frac{1}{12} \, \sqrt{6} \cos\left(2 \, x\right) + \frac{1}{2} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} {\left(\cos\left(2 \, x\right)^{4} + \sin\left(2 \, x\right)^{4} - 20 \, \cos\left(2 \, x\right)^{3} + 2 \, {\left(\cos\left(2 \, x\right)^{2} - 10 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(2 \, x\right)^{2} + 198 \, \cos\left(2 \, x\right)^{2} - 980 \, \cos\left(2 \, x\right) + 2401\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\frac{1}{12} \, {\left(\cos\left(2 \, x\right) - 5\right)} \sin\left(2 \, x\right), \frac{1}{24} \, \cos\left(2 \, x\right)^{2} - \frac{1}{24} \, \sin\left(2 \, x\right)^{2} - \frac{5}{12} \, \cos\left(2 \, x\right) + \frac{49}{24}\right)\right) - \frac{5}{12} \, \sqrt{6}\right)\right)}}{50 \, {\left(-10 \, {\left(2 \, \cos\left(2 \, x\right) - 5\right)} \cos\left(4 \, x\right) + 25 \, \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 25 \, \sin\left(4 \, x\right)^{2} - 20 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} - 20 \, \cos\left(2 \, x\right) + 25\right)}^{\frac{1}{4}}}"," ",0,"1/50*(5*cos(1/2*arctan2(5*sin(4*x) - 2*sin(2*x), 5*cos(4*x) - 2*cos(2*x) + 5))*sin(2*x) - 5*(cos(2*x) - 1)*sin(1/2*arctan2(5*sin(4*x) - 2*sin(2*x), 5*cos(4*x) - 2*cos(2*x) + 5)) + 2*(-10*(2*cos(2*x) - 5)*cos(4*x) + 25*cos(4*x)^2 + 4*cos(2*x)^2 + 25*sin(4*x)^2 - 20*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 - 20*cos(2*x) + 25)^(1/4)*(sqrt(5)*arctan2(1/12*sqrt(6)*(sqrt(6)*(25/36)^(1/4)*(25*cos(2*x)^4 + 25*sin(2*x)^4 - 20*cos(2*x)^3 + 2*(25*cos(2*x)^2 - 10*cos(2*x) - 23)*sin(2*x)^2 + 54*cos(2*x)^2 - 20*cos(2*x) + 25)^(1/4)*sin(1/2*arctan2(5/12*(5*cos(2*x) - 1)*sin(2*x), 25/24*cos(2*x)^2 - 25/24*sin(2*x)^2 - 5/12*cos(2*x) + 25/24)) + 5*sin(2*x)), 5/12*sqrt(6)*cos(2*x) + 1/2*(25/36)^(1/4)*(25*cos(2*x)^4 + 25*sin(2*x)^4 - 20*cos(2*x)^3 + 2*(25*cos(2*x)^2 - 10*cos(2*x) - 23)*sin(2*x)^2 + 54*cos(2*x)^2 - 20*cos(2*x) + 25)^(1/4)*cos(1/2*arctan2(5/12*(5*cos(2*x) - 1)*sin(2*x), 25/24*cos(2*x)^2 - 25/24*sin(2*x)^2 - 5/12*cos(2*x) + 25/24)) - 1/12*sqrt(6)) + sqrt(5)*arctan2(1/12*sqrt(6)*(sqrt(6)*(1/36)^(1/4)*(cos(2*x)^4 + sin(2*x)^4 - 20*cos(2*x)^3 + 2*(cos(2*x)^2 - 10*cos(2*x) + 1)*sin(2*x)^2 + 198*cos(2*x)^2 - 980*cos(2*x) + 2401)^(1/4)*sin(1/2*arctan2(1/12*(cos(2*x) - 5)*sin(2*x), 1/24*cos(2*x)^2 - 1/24*sin(2*x)^2 - 5/12*cos(2*x) + 49/24)) + sin(2*x)), 1/12*sqrt(6)*cos(2*x) + 1/2*(1/36)^(1/4)*(cos(2*x)^4 + sin(2*x)^4 - 20*cos(2*x)^3 + 2*(cos(2*x)^2 - 10*cos(2*x) + 1)*sin(2*x)^2 + 198*cos(2*x)^2 - 980*cos(2*x) + 2401)^(1/4)*cos(1/2*arctan2(1/12*(cos(2*x) - 5)*sin(2*x), 1/24*cos(2*x)^2 - 1/24*sin(2*x)^2 - 5/12*cos(2*x) + 49/24)) - 5/12*sqrt(6))))/(-10*(2*cos(2*x) - 5)*cos(4*x) + 25*cos(4*x)^2 + 4*cos(2*x)^2 + 25*sin(4*x)^2 - 20*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 - 20*cos(2*x) + 25)^(1/4)","B",0
424,1,69,0,0.996439," ","integrate(sin(5*x)/(5*cos(x)^2+9*sin(x)^2)^(5/2),x, algorithm=""maxima"")","-2 \, {\left(\frac{2 \, \cos\left(x\right)^{2}}{{\left(-4 \, \cos\left(x\right)^{2} + 9\right)}^{\frac{3}{2}}} - \frac{3}{{\left(-4 \, \cos\left(x\right)^{2} + 9\right)}^{\frac{3}{2}}}\right)} \cos\left(x\right) + \frac{52 \, \cos\left(x\right)}{243 \, \sqrt{-4 \, \cos\left(x\right)^{2} + 9}} + \frac{26 \, \cos\left(x\right)}{27 \, {\left(-4 \, \cos\left(x\right)^{2} + 9\right)}^{\frac{3}{2}}} - \frac{1}{2} \, \arcsin\left(\frac{2}{3} \, \cos\left(x\right)\right)"," ",0,"-2*(2*cos(x)^2/(-4*cos(x)^2 + 9)^(3/2) - 3/(-4*cos(x)^2 + 9)^(3/2))*cos(x) + 52/243*cos(x)/sqrt(-4*cos(x)^2 + 9) + 26/27*cos(x)/(-4*cos(x)^2 + 9)^(3/2) - 1/2*arcsin(2/3*cos(x))","A",0
425,1,192,0,0.525920," ","integrate(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(11 \, x\right) + 14 \, \cos\left(9 \, x\right) + 58 \, \cos\left(7 \, x\right) + 94 \, \cos\left(5 \, x\right) + 58 \, \cos\left(3 \, x\right) + 15 \, \cos\left(x\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right) + 3 \, \sin\left(2 \, x\right), -\cos\left(4 \, x\right) - 3 \, \cos\left(2 \, x\right) - 1\right)\right) - {\left(\sin\left(11 \, x\right) + 14 \, \sin\left(9 \, x\right) + 58 \, \sin\left(7 \, x\right) + 94 \, \sin\left(5 \, x\right) + 58 \, \sin\left(3 \, x\right) + 13 \, \sin\left(x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right) + 3 \, \sin\left(2 \, x\right), -\cos\left(4 \, x\right) - 3 \, \cos\left(2 \, x\right) - 1\right)\right)}{8 \, {\left(2 \, {\left(3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 9 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 6 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 9 \, \sin\left(2 \, x\right)^{2} + 6 \, \cos\left(2 \, x\right) + 1\right)}^{\frac{5}{4}}}"," ",0,"-1/8*((cos(11*x) + 14*cos(9*x) + 58*cos(7*x) + 94*cos(5*x) + 58*cos(3*x) + 15*cos(x))*cos(5/2*arctan2(sin(4*x) + 3*sin(2*x), -cos(4*x) - 3*cos(2*x) - 1)) - (sin(11*x) + 14*sin(9*x) + 58*sin(7*x) + 94*sin(5*x) + 58*sin(3*x) + 13*sin(x))*sin(5/2*arctan2(sin(4*x) + 3*sin(2*x), -cos(4*x) - 3*cos(2*x) - 1)))/(2*(3*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 9*cos(2*x)^2 + sin(4*x)^2 + 6*sin(4*x)*sin(2*x) + 9*sin(2*x)^2 + 6*cos(2*x) + 1)^(5/4)","B",0
426,1,115,0,1.023359," ","integrate((-2*cos(x)^3*(-1+sin(x))+cos(2*x)*sin(x))/sin(x)^2/(-5+sin(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{2}{5} \, \sqrt{5} \arcsin\left(\frac{\sqrt{5}}{{\left| \sin\left(x\right) \right|}}\right) - \frac{1}{10} i \, \sqrt{5} \operatorname{arsinh}\left(\frac{\cos\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{2}{\cos\left(x\right) + 1}\right) - \frac{1}{10} i \, \sqrt{5} \operatorname{arsinh}\left(-\frac{\cos\left(x\right)}{2 \, {\left(\cos\left(x\right) - 1\right)}} - \frac{2}{\cos\left(x\right) - 1}\right) + 2 \, \sqrt{\sin\left(x\right)^{2} - 5} + \frac{2 \, \sqrt{\sin\left(x\right)^{2} - 5}}{5 \, \sin\left(x\right)} - 2 i \, \operatorname{arsinh}\left(\frac{1}{2} \, \cos\left(x\right)\right) - 2 \, \log\left(2 \, \sqrt{\sin\left(x\right)^{2} - 5} + 2 \, \sin\left(x\right)\right)"," ",0,"2/5*sqrt(5)*arcsin(sqrt(5)/abs(sin(x))) - 1/10*I*sqrt(5)*arcsinh(1/2*cos(x)/(cos(x) + 1) - 2/(cos(x) + 1)) - 1/10*I*sqrt(5)*arcsinh(-1/2*cos(x)/(cos(x) - 1) - 2/(cos(x) - 1)) + 2*sqrt(sin(x)^2 - 5) + 2/5*sqrt(sin(x)^2 - 5)/sin(x) - 2*I*arcsinh(1/2*cos(x)) - 2*log(2*sqrt(sin(x)^2 - 5) + 2*sin(x))","C",0
427,-1,0,0,0.000000," ","integrate(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,1,25,0,0.443353," ","integrate((2-3*sin(x)^2)^(3/5)*sin(4*x),x, algorithm=""maxima"")","-\frac{20}{117} \, {\left(-3 \, \sin\left(x\right)^{2} + 2\right)}^{\frac{13}{5}} + \frac{5}{36} \, {\left(-3 \, \sin\left(x\right)^{2} + 2\right)}^{\frac{8}{5}}"," ",0,"-20/117*(-3*sin(x)^2 + 2)^(13/5) + 5/36*(-3*sin(x)^2 + 2)^(8/5)","A",0
429,1,488,0,1.150326," ","integrate(cos(x)*cos(2*x)^(1/2),x, algorithm=""maxima"")","\frac{1}{16} \, \sqrt{2} {\left(2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(2 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)} + \arctan\left(-{\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(2 \, x\right) - \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)}, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(2 \, x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + \sin\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(2 \, x\right) - \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)}, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(2 \, x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + \sin\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right), {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right), {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) - 1\right)\right)}"," ",0,"1/16*sqrt(2)*(2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(2*x) - (cos(2*x) - 1)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))) + arctan2(-(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(2*x) - cos(2*x)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))), (cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(2*x)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + sin(2*x)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))) + 1) - arctan2(-(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(2*x) - cos(2*x)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))), (cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(2*x)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + sin(2*x)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))) - 1) - arctan2((cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1)), (cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + 1) + arctan2((cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1)), (cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) - 1))","B",0
430,1,790,0,1.203940," ","integrate(cos(2*x)^(3/2)*sin(x),x, algorithm=""maxima"")","-\frac{1}{128} \, \sqrt{2} {\left(4 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(\cos\left(4 \, x\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(4 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \cos\left(4 \, x\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) - {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) \sin\left(4 \, x\right) - {\left(\cos\left(4 \, x\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) - \sin\left(4 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)} + 3 \, \log\left(\sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 1\right) - 3 \, \log\left(\sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 1\right) + 3 \, \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} + 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)\right)} + 1\right) - 3 \, \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} - 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)\right)} + 1\right)\right)}"," ",0,"-1/128*sqrt(2)*(4*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(((cos(4*x) - 2)*cos(1/2*arctan2(sin(4*x), cos(4*x))) + sin(4*x)*sin(1/2*arctan2(sin(4*x), cos(4*x))) + cos(4*x) - 2)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) - (cos(1/2*arctan2(sin(4*x), cos(4*x)))*sin(4*x) - (cos(4*x) - 2)*sin(1/2*arctan2(sin(4*x), cos(4*x))) - sin(4*x))*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))) + 3*log(sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + 1) - 3*log(sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 - 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + 1) + 3*log(((cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + (cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2)*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1) + 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*cos(1/2*arctan2(sin(4*x), cos(4*x))) + sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(1/2*arctan2(sin(4*x), cos(4*x)))) + 1) - 3*log(((cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + (cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2)*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1) - 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*cos(1/2*arctan2(sin(4*x), cos(4*x))) + sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(1/2*arctan2(sin(4*x), cos(4*x)))) + 1))","B",0
431,1,90,0,1.019500," ","integrate(sin(x)/cos(2*x)^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)}{3 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{3}{4}}}"," ",0,"-1/3*(sqrt(2)*sin(3/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(3/2*arctan2(sin(4*x), cos(4*x))) + (sqrt(2)*cos(3/2*arctan2(sin(4*x), cos(4*x))) + sqrt(2))*cos(3/2*arctan2(sin(4*x), cos(4*x) + 1)))/(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(3/4)","B",0
432,0,0,0,0.000000," ","integrate(cos(2*x)^(3/2)/cos(x)^3,x, algorithm=""maxima"")","\int \frac{\cos\left(2 \, x\right)^{\frac{3}{2}}}{\cos\left(x\right)^{3}}\,{d x}"," ",0,"integrate(cos(2*x)^(3/2)/cos(x)^3, x)","F",0
433,1,1359,0,1.614168," ","integrate((3*sin(x)^3-cos(x)*sin(4*x))/cos(2*x)^(7/2)/csc(x)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(4 \, \sqrt{2} \sin\left(4 \, x\right) \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + 4 \, {\left(\sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + 3 \, \sqrt{2} \cos\left(8 \, x\right) + 7 \, \sqrt{2} \cos\left(4 \, x\right) + 4 \, \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 12 \, \sqrt{2} \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) - 12 \, {\left(\sqrt{2} \cos\left(4 \, x\right)^{2} + \sqrt{2} \sin\left(4 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) - 4 \, {\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) \sin\left(4 \, x\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) - 3 \, \sqrt{2} \sin\left(8 \, x\right) - 7 \, \sqrt{2} \sin\left(4 \, x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) - 3 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sqrt{2} \cos\left(4 \, x\right)^{2} + \sqrt{2} \sin\left(4 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \log\left(\sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 1\right) - {\left(\sqrt{2} \cos\left(4 \, x\right)^{2} + \sqrt{2} \sin\left(4 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \log\left(\sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 1\right) + {\left(\sqrt{2} \cos\left(4 \, x\right)^{2} + \sqrt{2} \sin\left(4 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} + 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)\right)} + 1\right) - {\left(\sqrt{2} \cos\left(4 \, x\right)^{2} + \sqrt{2} \sin\left(4 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} - 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)\right)} + 1\right)\right)}}{48 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{5}{4}}} + \frac{{\left({\left(15 \, \cos\left(8 \, x\right) + 70 \, \cos\left(4 \, x\right) + 43\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + 5 \, {\left(3 \, \sin\left(8 \, x\right) + 14 \, \sin\left(4 \, x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) - 12\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 15 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) - {\left(5 \, {\left(3 \, \sin\left(8 \, x\right) + 14 \, \sin\left(4 \, x\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) - {\left(15 \, \cos\left(8 \, x\right) + 70 \, \cos\left(4 \, x\right) + 43\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 40 \, \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)}{20 \, {\left(\sqrt{2} \cos\left(4 \, x\right)^{2} + \sqrt{2} \sin\left(4 \, x\right)^{2} + 2 \, \sqrt{2} \cos\left(4 \, x\right) + \sqrt{2}\right)} {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}}}"," ",0,"1/48*(4*(4*sqrt(2)*sin(4*x)*sin(5/2*arctan2(sin(4*x), cos(4*x))) + 4*(sqrt(2)*cos(4*x) + sqrt(2))*cos(5/2*arctan2(sin(4*x), cos(4*x))) + 3*sqrt(2)*cos(8*x) + 7*sqrt(2)*cos(4*x) + 4*sqrt(2))*cos(5/2*arctan2(sin(4*x), cos(4*x) + 1)) + 12*sqrt(2)*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(3/2*arctan2(sin(4*x), cos(4*x) + 1)) - 12*(sqrt(2)*cos(4*x)^2 + sqrt(2)*sin(4*x)^2 + 2*sqrt(2)*cos(4*x) + sqrt(2))*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) - 4*(4*sqrt(2)*cos(5/2*arctan2(sin(4*x), cos(4*x)))*sin(4*x) - 4*(sqrt(2)*cos(4*x) + sqrt(2))*sin(5/2*arctan2(sin(4*x), cos(4*x))) - 3*sqrt(2)*sin(8*x) - 7*sqrt(2)*sin(4*x))*sin(5/2*arctan2(sin(4*x), cos(4*x) + 1)) - 3*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*((sqrt(2)*cos(4*x)^2 + sqrt(2)*sin(4*x)^2 + 2*sqrt(2)*cos(4*x) + sqrt(2))*log(sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + 1) - (sqrt(2)*cos(4*x)^2 + sqrt(2)*sin(4*x)^2 + 2*sqrt(2)*cos(4*x) + sqrt(2))*log(sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 - 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + 1) + (sqrt(2)*cos(4*x)^2 + sqrt(2)*sin(4*x)^2 + 2*sqrt(2)*cos(4*x) + sqrt(2))*log(((cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + (cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2)*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1) + 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*cos(1/2*arctan2(sin(4*x), cos(4*x))) + sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(1/2*arctan2(sin(4*x), cos(4*x)))) + 1) - (sqrt(2)*cos(4*x)^2 + sqrt(2)*sin(4*x)^2 + 2*sqrt(2)*cos(4*x) + sqrt(2))*log(((cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + (cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2)*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1) - 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))*cos(1/2*arctan2(sin(4*x), cos(4*x))) + sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))*sin(1/2*arctan2(sin(4*x), cos(4*x)))) + 1)))/(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(5/4) + 1/20*(((15*cos(8*x) + 70*cos(4*x) + 43)*cos(5/2*arctan2(sin(4*x), cos(4*x))) + 5*(3*sin(8*x) + 14*sin(4*x))*sin(5/2*arctan2(sin(4*x), cos(4*x))) - 12)*cos(5/2*arctan2(sin(4*x), cos(4*x) + 1)) + 15*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) - (5*(3*sin(8*x) + 14*sin(4*x))*cos(5/2*arctan2(sin(4*x), cos(4*x))) - (15*cos(8*x) + 70*cos(4*x) + 43)*sin(5/2*arctan2(sin(4*x), cos(4*x))))*sin(5/2*arctan2(sin(4*x), cos(4*x) + 1)) + 40*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(3/2*arctan2(sin(4*x), cos(4*x) + 1)))/((sqrt(2)*cos(4*x)^2 + sqrt(2)*sin(4*x)^2 + 2*sqrt(2)*cos(4*x) + sqrt(2))*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4))","B",0
434,0,0,0,0.000000," ","integrate((4-5*sec(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(-5 \, \sec\left(x\right)^{2} + 4\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-5*sec(x)^2 + 4)^(3/2), x)","F",0
435,0,0,0,0.000000," ","integrate(1/(4-5*sec(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-5 \, \sec\left(x\right)^{2} + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-5*sec(x)^2 + 4)^(-3/2), x)","F",0
436,-1,0,0,0.000000," ","integrate((-2*cot(x)^2+sin(x))/(1+5*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,1,63,0,0.483637," ","integrate((-3+cos(2*x))/cos(x)^4/(4-cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{48} \, {\left(-\frac{1}{\tan\left(x\right)^{2}} + 4\right)}^{\frac{3}{2}} \tan\left(x\right)^{3} + \frac{3}{16} \, \sqrt{-\frac{1}{\tan\left(x\right)^{2}} + 4} \tan\left(x\right) - \frac{8 \, \tan\left(x\right)^{4} + 26 \, \tan\left(x\right)^{2} - 7}{8 \, \sqrt{2 \, \tan\left(x\right) + 1} \sqrt{2 \, \tan\left(x\right) - 1}}"," ",0,"-1/48*(-1/tan(x)^2 + 4)^(3/2)*tan(x)^3 + 3/16*sqrt(-1/tan(x)^2 + 4)*tan(x) - 1/8*(8*tan(x)^4 + 26*tan(x)^2 - 7)/(sqrt(2*tan(x) + 1)*sqrt(2*tan(x) - 1))","B",0
438,0,0,0,0.000000," ","integrate((3+sin(x)^2)*tan(x)^3/(-2+cos(x)^2)/(5-4*sec(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(\sin\left(x\right)^{2} + 3\right)} \tan\left(x\right)^{3}}{{\left(\cos\left(x\right)^{2} - 2\right)} {\left(-4 \, \sec\left(x\right)^{2} + 5\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((sin(x)^2 + 3)*tan(x)^3/((cos(x)^2 - 2)*(-4*sec(x)^2 + 5)^(3/2)), x)","F",0
439,1,47,0,0.976424," ","integrate((sec(x)^2-3*(4*sec(x)^2+5*tan(x)^2)^(1/2)*tan(x))/sin(x)^2/(4*sec(x)^2+5*tan(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{7 \, \tan\left(x\right)}{8 \, \sqrt{9 \, \tan\left(x\right)^{2} + 4}} - \frac{1}{4 \, \sqrt{9 \, \tan\left(x\right)^{2} + 4} \tan\left(x\right)} + \frac{3}{8} \, \log\left(9 \, \tan\left(x\right)^{2} + 4\right) - \frac{3}{4} \, \log\left(\tan\left(x\right)\right)"," ",0,"-7/8*tan(x)/sqrt(9*tan(x)^2 + 4) - 1/4/(sqrt(9*tan(x)^2 + 4)*tan(x)) + 3/8*log(9*tan(x)^2 + 4) - 3/4*log(tan(x))","A",0
440,0,0,0,0.000000," ","integrate(tan(x)*(1+5*tan(x)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(5 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{5}{2}} \tan\left(x\right)\,{d x}"," ",0,"integrate((5*tan(x)^2 + 1)^(5/2)*tan(x), x)","F",0
441,0,0,0,0.000000," ","integrate(tan(x)/(1+5*tan(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(5 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(x)/(5*tan(x)^2 + 1)^(5/2), x)","F",0
442,0,0,0,0.000000," ","integrate(tan(x)/(a^3+b^3*tan(x)^2)^(1/3),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(b^{3} \tan\left(x\right)^{2} + a^{3}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(x)/(b^3*tan(x)^2 + a^3)^(1/3), x)","F",0
443,0,0,0,0.000000," ","integrate(tan(x)*(1-7*tan(x)^2)^(2/3),x, algorithm=""maxima"")","\int {\left(-7 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{2}{3}} \tan\left(x\right)\,{d x}"," ",0,"integrate((-7*tan(x)^2 + 1)^(2/3)*tan(x), x)","F",0
444,1,71,0,0.980589," ","integrate(cot(x)/(a^4+b^4*csc(x)^2)^(1/4),x, algorithm=""maxima"")","-\frac{\arctan\left(\frac{{\left(a^{4} + \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}}}{a}\right)}{a} + \frac{\log\left(a + {\left(a^{4} + \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}}\right)}{2 \, a} - \frac{\log\left(-a + {\left(a^{4} + \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}}\right)}{2 \, a}"," ",0,"-arctan((a^4 + b^4/sin(x)^2)^(1/4)/a)/a + 1/2*log(a + (a^4 + b^4/sin(x)^2)^(1/4))/a - 1/2*log(-a + (a^4 + b^4/sin(x)^2)^(1/4))/a","A",0
445,1,74,0,0.967384," ","integrate(cot(x)/(a^4-b^4*csc(x)^2)^(1/4),x, algorithm=""maxima"")","-\frac{\arctan\left(\frac{{\left(a^{4} - \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}}}{a}\right)}{a} + \frac{\log\left(a + {\left(a^{4} - \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}}\right)}{2 \, a} - \frac{\log\left(-a + {\left(a^{4} - \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}}\right)}{2 \, a}"," ",0,"-arctan((a^4 - b^4/sin(x)^2)^(1/4)/a)/a + 1/2*log(a + (a^4 - b^4/sin(x)^2)^(1/4))/a - 1/2*log(-a + (a^4 - b^4/sin(x)^2)^(1/4))/a","A",0
446,-1,0,0,0.000000," ","integrate(tan(x)*((1-3*sec(x)^2)^(1/3)*sin(x)^2+3*tan(x)^2)/cos(x)^2/(1-3*sec(x)^2)^(5/6)/(1-(1-3*sec(x)^2)^(1/2)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,0,0,0,0.000000," ","integrate((-cos(2*x)+2*tan(x)^2)/cos(x)^2/(tan(x)*tan(2*x))^(3/2),x, algorithm=""maxima"")","\int \frac{2 \, \tan\left(x\right)^{2} - \cos\left(2 \, x\right)}{\left(\tan\left(2 \, x\right) \tan\left(x\right)\right)^{\frac{3}{2}} \cos\left(x\right)^{2}}\,{d x}"," ",0,"integrate((2*tan(x)^2 - cos(2*x))/((tan(2*x)*tan(x))^(3/2)*cos(x)^2), x)","F",0
448,1,136,0,0.983409," ","integrate(tan(x)/(a^3-b^3*cos(x)^n)^(4/3),x, algorithm=""maxima"")","-\frac{\sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(a + 2 \, {\left(-b^{3} \cos\left(x\right)^{n} + a^{3}\right)}^{\frac{1}{3}}\right)}}{3 \, a}\right)}{a^{4} n} + \frac{\log\left(a^{2} + {\left(-b^{3} \cos\left(x\right)^{n} + a^{3}\right)}^{\frac{1}{3}} a + {\left(-b^{3} \cos\left(x\right)^{n} + a^{3}\right)}^{\frac{2}{3}}\right)}{2 \, a^{4} n} - \frac{\log\left(-a + {\left(-b^{3} \cos\left(x\right)^{n} + a^{3}\right)}^{\frac{1}{3}}\right)}{a^{4} n} - \frac{3}{{\left(-b^{3} \cos\left(x\right)^{n} + a^{3}\right)}^{\frac{1}{3}} a^{3} n}"," ",0,"-sqrt(3)*arctan(1/3*sqrt(3)*(a + 2*(-b^3*cos(x)^n + a^3)^(1/3))/a)/(a^4*n) + 1/2*log(a^2 + (-b^3*cos(x)^n + a^3)^(1/3)*a + (-b^3*cos(x)^n + a^3)^(2/3))/(a^4*n) - log(-a + (-b^3*cos(x)^n + a^3)^(1/3))/(a^4*n) - 3/((-b^3*cos(x)^n + a^3)^(1/3)*a^3*n)","A",0
449,1,145,0,0.967351," ","integrate((1+2*cos(x)^9)^(5/6)*tan(x),x, algorithm=""maxima"")","-\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} + 1\right)}\right) - \frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} - 1\right)}\right) - \frac{2}{15} \, {\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{5}{6}} + \frac{1}{18} \, \log\left({\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{3}} + {\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} + 1\right) - \frac{1}{18} \, \log\left({\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{3}} - {\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} + 1\right) + \frac{1}{9} \, \log\left({\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} + 1\right) - \frac{1}{9} \, \log\left({\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} - 1\right)"," ",0,"-1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(2*cos(x)^9 + 1)^(1/6) + 1)) - 1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(2*cos(x)^9 + 1)^(1/6) - 1)) - 2/15*(2*cos(x)^9 + 1)^(5/6) + 1/18*log((2*cos(x)^9 + 1)^(1/3) + (2*cos(x)^9 + 1)^(1/6) + 1) - 1/18*log((2*cos(x)^9 + 1)^(1/3) - (2*cos(x)^9 + 1)^(1/6) + 1) + 1/9*log((2*cos(x)^9 + 1)^(1/6) + 1) - 1/9*log((2*cos(x)^9 + 1)^(1/6) - 1)","B",0
450,1,37,0,0.432559," ","integrate(cot(x)*sin(x)^9/(2-5*sin(x)^3)^(4/3),x, algorithm=""maxima"")","-\frac{1}{625} \, {\left(-5 \, \sin\left(x\right)^{3} + 2\right)}^{\frac{5}{3}} + \frac{2}{125} \, {\left(-5 \, \sin\left(x\right)^{3} + 2\right)}^{\frac{2}{3}} + \frac{4}{125 \, {\left(-5 \, \sin\left(x\right)^{3} + 2\right)}^{\frac{1}{3}}}"," ",0,"-1/625*(-5*sin(x)^3 + 2)^(5/3) + 2/125*(-5*sin(x)^3 + 2)^(2/3) + 4/125/(-5*sin(x)^3 + 2)^(1/3)","A",0
451,1,86,0,0.690373," ","integrate(tan(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x, algorithm=""maxima"")","-\frac{3 \, {\left(\frac{{\left(9 \, \sin\left(x\right)^{2} - 1\right)} {\left(3 \, \sin\left(x\right) - 1\right)}^{\frac{1}{3}} {\left(\sin\left(x\right) + 1\right)}^{\frac{1}{3}} {\left(\sin\left(x\right) - 1\right)}^{\frac{1}{3}}}{{\left(3 \, \sin\left(x\right) + 1\right)}^{\frac{1}{3}}} + \frac{2 \, {\left(9 \, \sin\left(x\right)^{2} - 1\right)} {\left(\sin\left(x\right) + 1\right)}^{\frac{2}{3}} {\left(\sin\left(x\right) - 1\right)}^{\frac{2}{3}}}{{\left(3 \, \sin\left(x\right) + 1\right)}^{\frac{2}{3}}}\right)}}{32 \, {\left(\sin\left(x\right)^{2} - 1\right)} {\left(3 \, \sin\left(x\right) - 1\right)}^{\frac{2}{3}}}"," ",0,"-3/32*((9*sin(x)^2 - 1)*(3*sin(x) - 1)^(1/3)*(sin(x) + 1)^(1/3)*(sin(x) - 1)^(1/3)/(3*sin(x) + 1)^(1/3) + 2*(9*sin(x)^2 - 1)*(sin(x) + 1)^(2/3)*(sin(x) - 1)^(2/3)/(3*sin(x) + 1)^(2/3))/((sin(x)^2 - 1)*(3*sin(x) - 1)^(2/3))","B",0
452,0,0,0,0.000000," ","integrate(cot(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x, algorithm=""maxima"")","\int \frac{{\left({\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}} + 1\right)} \cot\left(x\right)}{{\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{2}{3}} \cos\left(x\right)^{2}}\,{d x}"," ",0,"integrate(((-8*tan(x)^2 + 1)^(1/3) + 1)*cot(x)/((-8*tan(x)^2 + 1)^(2/3)*cos(x)^2), x)","F",0
453,1,100,0,0.993440," ","integrate((5*cos(x)^2-(-1+5*sin(x)^2)^(1/2))*tan(x)/(-1+5*sin(x)^2)^(1/4)/(2+(-1+5*sin(x)^2)^(1/2)),x, algorithm=""maxima"")","-\frac{3}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(5 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - {\left(5 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{1}{4}}}{\sqrt{2} + {\left(5 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{1}{4}}}\right) + 2 \, {\left(5 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{1}{4}} - \frac{{\left(5 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{1}{4}}}{2 \, {\left(\sqrt{5 \, \sin\left(x\right)^{2} - 1} + 2\right)}}"," ",0,"-3/2*sqrt(2)*arctan(1/2*sqrt(2)*(5*sin(x)^2 - 1)^(1/4)) + 1/8*sqrt(2)*log(-(sqrt(2) - (5*sin(x)^2 - 1)^(1/4))/(sqrt(2) + (5*sin(x)^2 - 1)^(1/4))) + 2*(5*sin(x)^2 - 1)^(1/4) - 1/2*(5*sin(x)^2 - 1)^(1/4)/(sqrt(5*sin(x)^2 - 1) + 2)","A",0
454,0,0,0,0.000000," ","integrate(cos(x)^4*cos(2*x)^(2/3)*tan(x),x, algorithm=""maxima"")","\int \cos\left(2 \, x\right)^{\frac{2}{3}} \cos\left(x\right)^{4} \tan\left(x\right)\,{d x}"," ",0,"integrate(cos(2*x)^(2/3)*cos(x)^4*tan(x), x)","F",0
455,0,0,0,0.000000," ","integrate(sin(x)^6*tan(x)/cos(2*x)^(3/4),x, algorithm=""maxima"")","\int \frac{\sin\left(x\right)^{6} \tan\left(x\right)}{\cos\left(2 \, x\right)^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(sin(x)^6*tan(x)/cos(2*x)^(3/4), x)","F",0
456,1,259,0,1.062499," ","integrate((tan(x)*tan(2*x))^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \log\left(4 \, \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + 4 \, \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + 4\right) - \frac{1}{4} \, \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2}\right)} + 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(2 \, x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + \sin\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)}\right)"," ",0,"1/4*log(4*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + 4*sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + 8*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + 4) - 1/4*log(cos(2*x)^2 + sin(2*x)^2 + sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2) + 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(2*x)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + sin(2*x)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))))","B",0
457,-2,0,0,0.000000," ","integrate((cot(2*x)/cot(x))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
458,1,27,0,0.414912," ","integrate(1/x^5/(x^2+5),x, algorithm=""maxima"")","\frac{2 \, x^{2} - 5}{100 \, x^{4}} - \frac{1}{250} \, \log\left(x^{2} + 5\right) + \frac{1}{250} \, \log\left(x^{2}\right)"," ",0,"1/100*(2*x^2 - 5)/x^4 - 1/250*log(x^2 + 5) + 1/250*log(x^2)","A",0
459,1,30,0,0.948280," ","integrate(1/x^6/(x^2+5),x, algorithm=""maxima"")","-\frac{1}{625} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right) - \frac{3 \, x^{4} - 5 \, x^{2} + 15}{375 \, x^{5}}"," ",0,"-1/625*sqrt(5)*arctan(1/5*sqrt(5)*x) - 1/375*(3*x^4 - 5*x^2 + 15)/x^5","A",0
460,1,46,0,0.423161," ","integrate(1/x/(x^2-4)^4,x, algorithm=""maxima"")","-\frac{3 \, x^{4} - 30 \, x^{2} + 88}{384 \, {\left(x^{6} - 12 \, x^{4} + 48 \, x^{2} - 64\right)}} - \frac{1}{512} \, \log\left(x^{2} - 4\right) + \frac{1}{512} \, \log\left(x^{2}\right)"," ",0,"-1/384*(3*x^4 - 30*x^2 + 88)/(x^6 - 12*x^4 + 48*x^2 - 64) - 1/512*log(x^2 - 4) + 1/512*log(x^2)","A",0
461,1,33,0,0.960018," ","integrate(1/x/(x^2-2)^(5/2),x, algorithm=""maxima"")","-\frac{1}{8} \, \sqrt{2} \arcsin\left(\frac{\sqrt{2}}{{\left| x \right|}}\right) + \frac{1}{4 \, \sqrt{x^{2} - 2}} - \frac{1}{6 \, {\left(x^{2} - 2\right)}^{\frac{3}{2}}}"," ",0,"-1/8*sqrt(2)*arcsin(sqrt(2)/abs(x)) + 1/4/sqrt(x^2 - 2) - 1/6/(x^2 - 2)^(3/2)","A",0
462,1,42,0,0.948058," ","integrate((x^2-10)^(5/2)/x,x, algorithm=""maxima"")","\frac{1}{5} \, {\left(x^{2} - 10\right)}^{\frac{5}{2}} - \frac{10}{3} \, {\left(x^{2} - 10\right)}^{\frac{3}{2}} + 100 \, \sqrt{10} \arcsin\left(\frac{\sqrt{10}}{{\left| x \right|}}\right) + 100 \, \sqrt{x^{2} - 10}"," ",0,"1/5*(x^2 - 10)^(5/2) - 10/3*(x^2 - 10)^(3/2) + 100*sqrt(10)*arcsin(sqrt(10)/abs(x)) + 100*sqrt(x^2 - 10)","A",0
463,1,14,0,0.422091," ","integrate(x^(1+2*n),x, algorithm=""maxima"")","\frac{x^{2 \, n + 2}}{2 \, {\left(n + 1\right)}}"," ",0,"1/2*x^(2*n + 2)/(n + 1)","A",0
464,1,35,0,0.466977," ","integrate(x^7/(x^2-5)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} - \frac{25 \, {\left(6 \, x^{2} - 25\right)}}{4 \, {\left(x^{4} - 10 \, x^{2} + 25\right)}} + \frac{15}{2} \, \log\left(x^{2} - 5\right)"," ",0,"1/2*x^2 - 25/4*(6*x^2 - 25)/(x^4 - 10*x^2 + 25) + 15/2*log(x^2 - 5)","A",0
465,1,36,0,0.426083," ","integrate((3*x^5-4*x^3)/(x^2-1)^5,x, algorithm=""maxima"")","-\frac{18 \, x^{4} - 28 \, x^{2} + 7}{24 \, {\left(x^{8} - 4 \, x^{6} + 6 \, x^{4} - 4 \, x^{2} + 1\right)}}"," ",0,"-1/24*(18*x^4 - 28*x^2 + 7)/(x^8 - 4*x^6 + 6*x^4 - 4*x^2 + 1)","A",0
466,1,19,0,0.422759," ","integrate(x^3*(x^2+1)^(9/14),x, algorithm=""maxima"")","\frac{7}{37} \, {\left(x^{2} + 1\right)}^{\frac{37}{14}} - \frac{7}{23} \, {\left(x^{2} + 1\right)}^{\frac{23}{14}}"," ",0,"7/37*(x^2 + 1)^(37/14) - 7/23*(x^2 + 1)^(23/14)","A",0
467,1,28,0,0.421487," ","integrate(x^5/(x^2-4)^(13/6),x, algorithm=""maxima"")","\frac{3}{5} \, {\left(x^{2} - 4\right)}^{\frac{5}{6}} - \frac{24}{{\left(x^{2} - 4\right)}^{\frac{1}{6}}} - \frac{48}{7 \, {\left(x^{2} - 4\right)}^{\frac{7}{6}}}"," ",0,"3/5*(x^2 - 4)^(5/6) - 24/(x^2 - 4)^(1/6) - 48/7/(x^2 - 4)^(7/6)","A",0
468,1,25,0,0.426638," ","integrate(1/(2*x^2+1)^(5/2),x, algorithm=""maxima"")","\frac{2 \, x}{3 \, \sqrt{2 \, x^{2} + 1}} + \frac{x}{3 \, {\left(2 \, x^{2} + 1\right)}^{\frac{3}{2}}}"," ",0,"2/3*x/sqrt(2*x^2 + 1) + 1/3*x/(2*x^2 + 1)^(3/2)","A",0
469,1,51,0,0.422481," ","integrate(1/(x^2-2*x-1)^(5/2),x, algorithm=""maxima"")","\frac{x}{6 \, \sqrt{x^{2} - 2 \, x - 1}} - \frac{1}{6 \, \sqrt{x^{2} - 2 \, x - 1}} - \frac{x}{6 \, {\left(x^{2} - 2 \, x - 1\right)}^{\frac{3}{2}}} + \frac{1}{6 \, {\left(x^{2} - 2 \, x - 1\right)}^{\frac{3}{2}}}"," ",0,"1/6*x/sqrt(x^2 - 2*x - 1) - 1/6/sqrt(x^2 - 2*x - 1) - 1/6*x/(x^2 - 2*x - 1)^(3/2) + 1/6/(x^2 - 2*x - 1)^(3/2)","A",0
470,1,35,0,1.001456," ","integrate(1/x^4/(x^2-8)^(3/2),x, algorithm=""maxima"")","-\frac{x}{192 \, \sqrt{x^{2} - 8}} + \frac{1}{48 \, \sqrt{x^{2} - 8} x} + \frac{1}{24 \, \sqrt{x^{2} - 8} x^{3}}"," ",0,"-1/192*x/sqrt(x^2 - 8) + 1/48/(sqrt(x^2 - 8)*x) + 1/24/(sqrt(x^2 - 8)*x^3)","A",0
471,1,16,0,0.435925," ","integrate((x^2+5)^2/x^(13/3),x, algorithm=""maxima"")","\frac{3}{2} \, x^{\frac{2}{3}} - \frac{15 \, {\left(x^{2} + 1\right)}}{2 \, x^{\frac{10}{3}}}"," ",0,"3/2*x^(2/3) - 15/2*(x^2 + 1)/x^(10/3)","A",0
472,1,53,0,0.450073," ","integrate(1/x^7/(x^2+1)^3,x, algorithm=""maxima"")","-\frac{60 \, x^{8} + 90 \, x^{6} + 20 \, x^{4} - 5 \, x^{2} + 2}{12 \, {\left(x^{10} + 2 \, x^{8} + x^{6}\right)}} + 5 \, \log\left(x^{2} + 1\right) - 5 \, \log\left(x^{2}\right)"," ",0,"-1/12*(60*x^8 + 90*x^6 + 20*x^4 - 5*x^2 + 2)/(x^10 + 2*x^8 + x^6) + 5*log(x^2 + 1) - 5*log(x^2)","A",0
473,0,0,0,0.000000," ","integrate(((x^2+2)/x^2)^(7/9)/(x^2+2)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(\frac{x^{2} + 2}{x^{2}}\right)^{\frac{7}{9}}}{{\left(x^{2} + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(((x^2 + 2)/x^2)^(7/9)/(x^2 + 2)^(3/2), x)","F",0
474,1,79,0,0.976811," ","integrate(x^4/(-x^2+10^(1/2))^(9/2),x, algorithm=""maxima"")","\frac{x}{175 \, \sqrt{-x^{2} + \sqrt{10}}} + \frac{\sqrt{10} x}{350 \, {\left(-x^{2} + \sqrt{10}\right)}^{\frac{3}{2}}} + \frac{x^{3}}{4 \, {\left(-x^{2} + \sqrt{10}\right)}^{\frac{7}{2}}} + \frac{3 \, x}{140 \, {\left(-x^{2} + \sqrt{10}\right)}^{\frac{5}{2}}} - \frac{3 \, \sqrt{10} x}{28 \, {\left(-x^{2} + \sqrt{10}\right)}^{\frac{7}{2}}}"," ",0,"1/175*x/sqrt(-x^2 + sqrt(10)) + 1/350*sqrt(10)*x/(-x^2 + sqrt(10))^(3/2) + 1/4*x^3/(-x^2 + sqrt(10))^(7/2) + 3/140*x/(-x^2 + sqrt(10))^(5/2) - 3/28*sqrt(10)*x/(-x^2 + sqrt(10))^(7/2)","B",0
475,1,21,0,0.958791," ","integrate(x^2/(-x^2+3)^(3/2),x, algorithm=""maxima"")","\frac{x}{\sqrt{-x^{2} + 3}} - \arcsin\left(\frac{1}{3} \, \sqrt{3} x\right)"," ",0,"x/sqrt(-x^2 + 3) - arcsin(1/3*sqrt(3)*x)","A",0
476,1,45,0,0.965538," ","integrate((-x^2+25)^(3/2)/x^4,x, algorithm=""maxima"")","\frac{1}{25} \, \sqrt{-x^{2} + 25} x + \frac{2 \, {\left(-x^{2} + 25\right)}^{\frac{3}{2}}}{75 \, x} - \frac{{\left(-x^{2} + 25\right)}^{\frac{5}{2}}}{75 \, x^{3}} + \arcsin\left(\frac{1}{5} \, x\right)"," ",0,"1/25*sqrt(-x^2 + 25)*x + 2/75*(-x^2 + 25)^(3/2)/x - 1/75*(-x^2 + 25)^(5/2)/x^3 + arcsin(1/5*x)","A",0
477,1,37,0,0.421748," ","integrate(1/(-2*x^2+1)^(7/2),x, algorithm=""maxima"")","\frac{8 \, x}{15 \, \sqrt{-2 \, x^{2} + 1}} + \frac{4 \, x}{15 \, {\left(-2 \, x^{2} + 1\right)}^{\frac{3}{2}}} + \frac{x}{5 \, {\left(-2 \, x^{2} + 1\right)}^{\frac{5}{2}}}"," ",0,"8/15*x/sqrt(-2*x^2 + 1) + 4/15*x/(-2*x^2 + 1)^(3/2) + 1/5*x/(-2*x^2 + 1)^(5/2)","A",0
478,1,59,0,0.457649," ","integrate(1/(-x^2+6*x-7)^(5/2),x, algorithm=""maxima"")","\frac{x}{6 \, \sqrt{-x^{2} + 6 \, x - 7}} - \frac{1}{2 \, \sqrt{-x^{2} + 6 \, x - 7}} + \frac{x}{6 \, {\left(-x^{2} + 6 \, x - 7\right)}^{\frac{3}{2}}} - \frac{1}{2 \, {\left(-x^{2} + 6 \, x - 7\right)}^{\frac{3}{2}}}"," ",0,"1/6*x/sqrt(-x^2 + 6*x - 7) - 1/2/sqrt(-x^2 + 6*x - 7) + 1/6*x/(-x^2 + 6*x - 7)^(3/2) - 1/2/(-x^2 + 6*x - 7)^(3/2)","A",0
479,1,32,0,0.431543," ","integrate((-2*x^2-2*x+1)^3,x, algorithm=""maxima"")","-\frac{8}{7} \, x^{7} - 4 \, x^{6} - \frac{12}{5} \, x^{5} + 4 \, x^{4} + 2 \, x^{3} - 3 \, x^{2} + x"," ",0,"-8/7*x^7 - 4*x^6 - 12/5*x^5 + 4*x^4 + 2*x^3 - 3*x^2 + x","A",0
480,1,29,0,0.455307," ","integrate((-1+5*x)*(x^2-x-1)^2,x, algorithm=""maxima"")","\frac{5}{6} \, x^{6} - \frac{11}{5} \, x^{5} - \frac{3}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{3}{2} \, x^{2} - x"," ",0,"5/6*x^6 - 11/5*x^5 - 3/4*x^4 + 11/3*x^3 + 3/2*x^2 - x","A",0
481,1,59,0,0.468229," ","integrate((1+3*x)/(2*x^2-8*x+1)^(5/2),x, algorithm=""maxima"")","\frac{2 \, x}{21 \, \sqrt{2 \, x^{2} - 8 \, x + 1}} - \frac{4}{21 \, \sqrt{2 \, x^{2} - 8 \, x + 1}} - \frac{x}{3 \, {\left(2 \, x^{2} - 8 \, x + 1\right)}^{\frac{3}{2}}} + \frac{1}{6 \, {\left(2 \, x^{2} - 8 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"2/21*x/sqrt(2*x^2 - 8*x + 1) - 4/21/sqrt(2*x^2 - 8*x + 1) - 1/3*x/(2*x^2 - 8*x + 1)^(3/2) + 1/6/(2*x^2 - 8*x + 1)^(3/2)","A",0
482,1,76,0,0.555443," ","integrate((8*x^3-8*x-1)/(-4*x^2+2*x+1)^(5/2),x, algorithm=""maxima"")","-\frac{122 \, x}{75 \, \sqrt{-4 \, x^{2} + 2 \, x + 1}} + \frac{2 \, x^{2}}{{\left(-4 \, x^{2} + 2 \, x + 1\right)}^{\frac{3}{2}}} + \frac{61}{150 \, \sqrt{-4 \, x^{2} + 2 \, x + 1}} - \frac{19 \, x}{15 \, {\left(-4 \, x^{2} + 2 \, x + 1\right)}^{\frac{3}{2}}} - \frac{23}{30 \, {\left(-4 \, x^{2} + 2 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"-122/75*x/sqrt(-4*x^2 + 2*x + 1) + 2*x^2/(-4*x^2 + 2*x + 1)^(3/2) + 61/150/sqrt(-4*x^2 + 2*x + 1) - 19/15*x/(-4*x^2 + 2*x + 1)^(3/2) - 23/30/(-4*x^2 + 2*x + 1)^(3/2)","B",0
483,1,55,0,0.512892," ","integrate(x^2*cos(x)^5,x, algorithm=""maxima"")","\frac{1}{200} \, x \cos\left(5 \, x\right) + \frac{5}{72} \, x \cos\left(3 \, x\right) + \frac{5}{4} \, x \cos\left(x\right) + \frac{1}{2000} \, {\left(25 \, x^{2} - 2\right)} \sin\left(5 \, x\right) + \frac{5}{432} \, {\left(9 \, x^{2} - 2\right)} \sin\left(3 \, x\right) + \frac{5}{8} \, {\left(x^{2} - 2\right)} \sin\left(x\right)"," ",0,"1/200*x*cos(5*x) + 5/72*x*cos(3*x) + 5/4*x*cos(x) + 1/2000*(25*x^2 - 2)*sin(5*x) + 5/432*(9*x^2 - 2)*sin(3*x) + 5/8*(x^2 - 2)*sin(x)","A",0
484,1,49,0,0.455439," ","integrate(x^3*sin(x)^3,x, algorithm=""maxima"")","\frac{1}{36} \, {\left(3 \, x^{3} - 2 \, x\right)} \cos\left(3 \, x\right) - \frac{3}{4} \, {\left(x^{3} - 6 \, x\right)} \cos\left(x\right) - \frac{1}{108} \, {\left(9 \, x^{2} - 2\right)} \sin\left(3 \, x\right) + \frac{9}{4} \, {\left(x^{2} - 2\right)} \sin\left(x\right)"," ",0,"1/36*(3*x^3 - 2*x)*cos(3*x) - 3/4*(x^3 - 6*x)*cos(x) - 1/108*(9*x^2 - 2)*sin(3*x) + 9/4*(x^2 - 2)*sin(x)","A",0
485,1,66,0,0.564298," ","integrate(x^2*sin(x)^6,x, algorithm=""maxima"")","\frac{5}{48} \, x^{3} - \frac{1}{576} \, x \cos\left(6 \, x\right) + \frac{3}{128} \, x \cos\left(4 \, x\right) - \frac{15}{64} \, x \cos\left(2 \, x\right) - \frac{1}{3456} \, {\left(18 \, x^{2} - 1\right)} \sin\left(6 \, x\right) + \frac{3}{512} \, {\left(8 \, x^{2} - 1\right)} \sin\left(4 \, x\right) - \frac{15}{128} \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)"," ",0,"5/48*x^3 - 1/576*x*cos(6*x) + 3/128*x*cos(4*x) - 15/64*x*cos(2*x) - 1/3456*(18*x^2 - 1)*sin(6*x) + 3/512*(8*x^2 - 1)*sin(4*x) - 15/128*(2*x^2 - 1)*sin(2*x)","A",0
486,1,35,0,0.608708," ","integrate(x^2*cos(x)*sin(x)^2,x, algorithm=""maxima"")","-\frac{1}{18} \, x \cos\left(3 \, x\right) + \frac{1}{2} \, x \cos\left(x\right) - \frac{1}{108} \, {\left(9 \, x^{2} - 2\right)} \sin\left(3 \, x\right) + \frac{1}{4} \, {\left(x^{2} - 2\right)} \sin\left(x\right)"," ",0,"-1/18*x*cos(3*x) + 1/2*x*cos(x) - 1/108*(9*x^2 - 2)*sin(3*x) + 1/4*(x^2 - 2)*sin(x)","A",0
487,-2,0,0,0.000000," ","integrate(x*cos(x)^4/sin(x)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
488,1,619,0,1.470900," ","integrate(x*sin(x)^3/cos(x)^4,x, algorithm=""maxima"")","-\frac{48 \, x \sin\left(3 \, x\right) \sin\left(2 \, x\right) + 4 \, {\left(6 \, x \cos\left(5 \, x\right) + 4 \, x \cos\left(3 \, x\right) + 6 \, x \cos\left(x\right) + \sin\left(5 \, x\right) - \sin\left(x\right)\right)} \cos\left(6 \, x\right) + 12 \, {\left(6 \, x \cos\left(4 \, x\right) + 6 \, x \cos\left(2 \, x\right) + 2 \, x - \sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) + 12 \, {\left(4 \, x \cos\left(3 \, x\right) + 6 \, x \cos\left(x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 16 \, {\left(3 \, x \cos\left(2 \, x\right) + x\right)} \cos\left(3 \, x\right) + 12 \, {\left(6 \, x \cos\left(x\right) - \sin\left(x\right)\right)} \cos\left(2 \, x\right) + 24 \, x \cos\left(x\right) - 5 \, {\left(2 \, {\left(3 \, \cos\left(4 \, x\right) + 3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + \cos\left(6 \, x\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 9 \, \cos\left(4 \, x\right)^{2} + 9 \, \cos\left(2 \, x\right)^{2} + 6 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + \sin\left(6 \, x\right)^{2} + 9 \, \sin\left(4 \, x\right)^{2} + 18 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 9 \, \sin\left(2 \, x\right)^{2} + 6 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + 5 \, {\left(2 \, {\left(3 \, \cos\left(4 \, x\right) + 3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + \cos\left(6 \, x\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 9 \, \cos\left(4 \, x\right)^{2} + 9 \, \cos\left(2 \, x\right)^{2} + 6 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + \sin\left(6 \, x\right)^{2} + 9 \, \sin\left(4 \, x\right)^{2} + 18 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 9 \, \sin\left(2 \, x\right)^{2} + 6 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, {\left(6 \, x \sin\left(5 \, x\right) + 4 \, x \sin\left(3 \, x\right) + 6 \, x \sin\left(x\right) - \cos\left(5 \, x\right) + \cos\left(x\right)\right)} \sin\left(6 \, x\right) + 4 \, {\left(18 \, x \sin\left(4 \, x\right) + 18 \, x \sin\left(2 \, x\right) + 3 \, \cos\left(4 \, x\right) + 3 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(5 \, x\right) + 12 \, {\left(4 \, x \sin\left(3 \, x\right) + 6 \, x \sin\left(x\right) + \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 12 \, {\left(6 \, x \sin\left(x\right) + \cos\left(x\right)\right)} \sin\left(2 \, x\right) - 4 \, \sin\left(x\right)}{12 \, {\left(2 \, {\left(3 \, \cos\left(4 \, x\right) + 3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + \cos\left(6 \, x\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 9 \, \cos\left(4 \, x\right)^{2} + 9 \, \cos\left(2 \, x\right)^{2} + 6 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + \sin\left(6 \, x\right)^{2} + 9 \, \sin\left(4 \, x\right)^{2} + 18 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 9 \, \sin\left(2 \, x\right)^{2} + 6 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-1/12*(48*x*sin(3*x)*sin(2*x) + 4*(6*x*cos(5*x) + 4*x*cos(3*x) + 6*x*cos(x) + sin(5*x) - sin(x))*cos(6*x) + 12*(6*x*cos(4*x) + 6*x*cos(2*x) + 2*x - sin(4*x) - sin(2*x))*cos(5*x) + 12*(4*x*cos(3*x) + 6*x*cos(x) - sin(x))*cos(4*x) + 16*(3*x*cos(2*x) + x)*cos(3*x) + 12*(6*x*cos(x) - sin(x))*cos(2*x) + 24*x*cos(x) - 5*(2*(3*cos(4*x) + 3*cos(2*x) + 1)*cos(6*x) + cos(6*x)^2 + 6*(3*cos(2*x) + 1)*cos(4*x) + 9*cos(4*x)^2 + 9*cos(2*x)^2 + 6*(sin(4*x) + sin(2*x))*sin(6*x) + sin(6*x)^2 + 9*sin(4*x)^2 + 18*sin(4*x)*sin(2*x) + 9*sin(2*x)^2 + 6*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 5*(2*(3*cos(4*x) + 3*cos(2*x) + 1)*cos(6*x) + cos(6*x)^2 + 6*(3*cos(2*x) + 1)*cos(4*x) + 9*cos(4*x)^2 + 9*cos(2*x)^2 + 6*(sin(4*x) + sin(2*x))*sin(6*x) + sin(6*x)^2 + 9*sin(4*x)^2 + 18*sin(4*x)*sin(2*x) + 9*sin(2*x)^2 + 6*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*(6*x*sin(5*x) + 4*x*sin(3*x) + 6*x*sin(x) - cos(5*x) + cos(x))*sin(6*x) + 4*(18*x*sin(4*x) + 18*x*sin(2*x) + 3*cos(4*x) + 3*cos(2*x) + 1)*sin(5*x) + 12*(4*x*sin(3*x) + 6*x*sin(x) + cos(x))*sin(4*x) + 12*(6*x*sin(x) + cos(x))*sin(2*x) - 4*sin(x))/(2*(3*cos(4*x) + 3*cos(2*x) + 1)*cos(6*x) + cos(6*x)^2 + 6*(3*cos(2*x) + 1)*cos(4*x) + 9*cos(4*x)^2 + 9*cos(2*x)^2 + 6*(sin(4*x) + sin(2*x))*sin(6*x) + sin(6*x)^2 + 9*sin(4*x)^2 + 18*sin(4*x)*sin(2*x) + 9*sin(2*x)^2 + 6*cos(2*x) + 1)","B",0
489,1,132,0,0.603327," ","integrate(x*sin(x)/cos(x)^3,x, algorithm=""maxima"")","\frac{4 \, x \cos\left(2 \, x\right)^{2} + 4 \, x \sin\left(2 \, x\right)^{2} + {\left(2 \, x \cos\left(2 \, x\right) + \sin\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 2 \, x \cos\left(2 \, x\right) + {\left(2 \, x \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 1\right)} \sin\left(4 \, x\right) - \sin\left(2 \, x\right)}{2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1}"," ",0,"(4*x*cos(2*x)^2 + 4*x*sin(2*x)^2 + (2*x*cos(2*x) + sin(2*x))*cos(4*x) + 2*x*cos(2*x) + (2*x*sin(2*x) - cos(2*x) - 1)*sin(4*x) - sin(2*x))/(2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)","B",0
490,1,66,0,1.466861," ","integrate(x*sin(x)^3/cos(x),x, algorithm=""maxima"")","\frac{1}{2} i \, x^{2} - i \, x \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) + \frac{1}{4} \, x \cos\left(2 \, x\right) - \frac{1}{2} \, x \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) + \frac{1}{2} i \, {\rm Li}_2\left(-e^{\left(2 i \, x\right)}\right) - \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/2*I*x^2 - I*x*arctan2(sin(2*x), cos(2*x) + 1) + 1/4*x*cos(2*x) - 1/2*x*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) + 1/2*I*dilog(-e^(2*I*x)) - 1/8*sin(2*x)","A",0
491,1,213,0,1.296937," ","integrate(x*sin(x)^3/cos(x)^3,x, algorithm=""maxima"")","-\frac{x^{2} \cos\left(4 \, x\right) + i \, x^{2} \sin\left(4 \, x\right) + x^{2} - {\left(2 \, x \cos\left(4 \, x\right) + 4 \, x \cos\left(2 \, x\right) + 2 i \, x \sin\left(4 \, x\right) + 4 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) + 2 \, {\left(x^{2} + 2 i \, x + 1\right)} \cos\left(2 \, x\right) + {\left(\cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + i \, \sin\left(4 \, x\right) + 2 i \, \sin\left(2 \, x\right) + 1\right)} {\rm Li}_2\left(-e^{\left(2 i \, x\right)}\right) - {\left(-i \, x \cos\left(4 \, x\right) - 2 i \, x \cos\left(2 \, x\right) + x \sin\left(4 \, x\right) + 2 \, x \sin\left(2 \, x\right) - i \, x\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) - {\left(-2 i \, x^{2} + 4 \, x - 2 i\right)} \sin\left(2 \, x\right) + 2}{-2 i \, \cos\left(4 \, x\right) - 4 i \, \cos\left(2 \, x\right) + 2 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right) - 2 i}"," ",0,"-(x^2*cos(4*x) + I*x^2*sin(4*x) + x^2 - (2*x*cos(4*x) + 4*x*cos(2*x) + 2*I*x*sin(4*x) + 4*I*x*sin(2*x) + 2*x)*arctan2(sin(2*x), cos(2*x) + 1) + 2*(x^2 + 2*I*x + 1)*cos(2*x) + (cos(4*x) + 2*cos(2*x) + I*sin(4*x) + 2*I*sin(2*x) + 1)*dilog(-e^(2*I*x)) - (-I*x*cos(4*x) - 2*I*x*cos(2*x) + x*sin(4*x) + 2*x*sin(2*x) - I*x)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) - (-2*I*x^2 + 4*x - 2*I)*sin(2*x) + 2)/(-2*I*cos(4*x) - 4*I*cos(2*x) + 2*sin(4*x) + 4*sin(2*x) - 2*I)","B",0
492,1,78,0,1.175401," ","integrate((2*x+sin(2*x))/(cos(x)+x*sin(x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(2 \, x\right)^{2} + 2 \, x \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}{{\left(x^{2} + 1\right)} \cos\left(2 \, x\right)^{2} + {\left(x^{2} + 1\right)} \sin\left(2 \, x\right)^{2} + x^{2} - 2 \, {\left(x^{2} - 1\right)} \cos\left(2 \, x\right) + 4 \, x \sin\left(2 \, x\right) + 1}"," ",0,"-2*(cos(2*x)^2 + 2*x*sin(2*x) + sin(2*x)^2 + 2*cos(2*x) + 1)/((x^2 + 1)*cos(2*x)^2 + (x^2 + 1)*sin(2*x)^2 + x^2 - 2*(x^2 - 1)*cos(2*x) + 4*x*sin(2*x) + 1)","B",0
493,1,69,0,0.703520," ","integrate(x^2/(x*cos(x)-sin(x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, x \cos\left(2 \, x\right) + {\left(x^{2} - 1\right)} \sin\left(2 \, x\right)\right)}}{{\left(x^{2} + 1\right)} \cos\left(2 \, x\right)^{2} + {\left(x^{2} + 1\right)} \sin\left(2 \, x\right)^{2} + x^{2} + 2 \, {\left(x^{2} - 1\right)} \cos\left(2 \, x\right) - 4 \, x \sin\left(2 \, x\right) + 1}"," ",0,"2*(2*x*cos(2*x) + (x^2 - 1)*sin(2*x))/((x^2 + 1)*cos(2*x)^2 + (x^2 + 1)*sin(2*x)^2 + x^2 + 2*(x^2 - 1)*cos(2*x) - 4*x*sin(2*x) + 1)","B",0
494,-2,0,0,0.000000," ","integrate(a^(m*x)*b^(n*x),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((log(b)*n)/(log(a)*m)>0)', see `assume?` for more details)Is (log(b)*n)/(log(a)*m) equal to -1?","F(-2)",0
495,-2,0,0,0.000000," ","integrate((a^x-b^x)^2/(a^x)/(b^x),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(-log(b)/log(a)>0)', see `assume?` for more details)Is -log(b)/log(a) equal to -1?","F(-2)",0
496,1,7,0,0.553952," ","integrate(-1/exp(x)+exp(x),x, algorithm=""maxima"")","e^{\left(-x\right)} + e^{x}"," ",0,"e^(-x) + e^x","A",0
497,1,16,0,0.523893," ","integrate((-1/exp(x)+exp(x))^2,x, algorithm=""maxima"")","-2 \, x + \frac{1}{2} \, e^{\left(2 \, x\right)} - \frac{1}{2} \, e^{\left(-2 \, x\right)}"," ",0,"-2*x + 1/2*e^(2*x) - 1/2*e^(-2*x)","A",0
498,1,23,0,0.542118," ","integrate((-1/exp(x)+exp(x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, e^{\left(3 \, x\right)} - 3 \, e^{\left(-x\right)} + \frac{1}{3} \, e^{\left(-3 \, x\right)} - 3 \, e^{x}"," ",0,"1/3*e^(3*x) - 3*e^(-x) + 1/3*e^(-3*x) - 3*e^x","A",0
499,1,28,0,0.498565," ","integrate((-1/exp(x)+exp(x))^4,x, algorithm=""maxima"")","6 \, x + \frac{1}{4} \, e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 2 \, e^{\left(-2 \, x\right)} - \frac{1}{4} \, e^{\left(-4 \, x\right)}"," ",0,"6*x + 1/4*e^(4*x) - 2*e^(2*x) + 2*e^(-2*x) - 1/4*e^(-4*x)","A",0
500,0,0,0,0.000000," ","integrate((-1/exp(x)+exp(x))^n,x, algorithm=""maxima"")","\int {\left(-e^{\left(-x\right)} + e^{x}\right)}^{n}\,{d x}"," ",0,"integrate((-e^(-x) + e^x)^n, x)","F",0
501,1,41,0,0.558459," ","integrate((1/(a^(4*x))-a^(2*x))^3,x, algorithm=""maxima"")","3 \, x - \frac{a^{6 \, x}}{6 \, \log\left(a\right)} - \frac{1}{12 \, a^{12 \, x} \log\left(a\right)} + \frac{1}{2 \, a^{6 \, x} \log\left(a\right)}"," ",0,"3*x - 1/6*a^(6*x)/log(a) - 1/12/(a^(12*x)*log(a)) + 1/2/(a^(6*x)*log(a))","A",0
502,1,27,0,0.628232," ","integrate(a^(k*x)+a^(l*x),x, algorithm=""maxima"")","\frac{a^{k x}}{k \log\left(a\right)} + \frac{a^{l x}}{l \log\left(a\right)}"," ",0,"a^(k*x)/(k*log(a)) + a^(l*x)/(l*log(a))","A",0
503,1,51,0,0.447962," ","integrate((a^(k*x)+a^(l*x))^2,x, algorithm=""maxima"")","\frac{2 \, a^{k x + l x}}{{\left(k + l\right)} \log\left(a\right)} + \frac{a^{2 \, k x}}{2 \, k \log\left(a\right)} + \frac{a^{2 \, l x}}{2 \, l \log\left(a\right)}"," ",0,"2*a^(k*x + l*x)/((k + l)*log(a)) + 1/2*a^(2*k*x)/(k*log(a)) + 1/2*a^(2*l*x)/(l*log(a))","A",0
504,1,77,0,0.554178," ","integrate((a^(k*x)+a^(l*x))^3,x, algorithm=""maxima"")","\frac{3 \, a^{2 \, k x + l x}}{{\left(2 \, k + l\right)} \log\left(a\right)} + \frac{3 \, a^{k x + 2 \, l x}}{{\left(k + 2 \, l\right)} \log\left(a\right)} + \frac{a^{3 \, k x}}{3 \, k \log\left(a\right)} + \frac{a^{3 \, l x}}{3 \, l \log\left(a\right)}"," ",0,"3*a^(2*k*x + l*x)/((2*k + l)*log(a)) + 3*a^(k*x + 2*l*x)/((k + 2*l)*log(a)) + 1/3*a^(3*k*x)/(k*log(a)) + 1/3*a^(3*l*x)/(l*log(a))","A",0
505,1,99,0,0.552205," ","integrate((a^(k*x)+a^(l*x))^4,x, algorithm=""maxima"")","\frac{4 \, a^{3 \, k x + l x}}{{\left(3 \, k + l\right)} \log\left(a\right)} + \frac{4 \, a^{k x + 3 \, l x}}{{\left(k + 3 \, l\right)} \log\left(a\right)} + \frac{3 \, a^{2 \, k x + 2 \, l x}}{{\left(k + l\right)} \log\left(a\right)} + \frac{a^{4 \, k x}}{4 \, k \log\left(a\right)} + \frac{a^{4 \, l x}}{4 \, l \log\left(a\right)}"," ",0,"4*a^(3*k*x + l*x)/((3*k + l)*log(a)) + 4*a^(k*x + 3*l*x)/((k + 3*l)*log(a)) + 3*a^(2*k*x + 2*l*x)/((k + l)*log(a)) + 1/4*a^(4*k*x)/(k*log(a)) + 1/4*a^(4*l*x)/(l*log(a))","A",0
506,0,0,0,0.000000," ","integrate((a^(k*x)+a^(l*x))^n,x, algorithm=""maxima"")","\int {\left(a^{k x} + a^{l x}\right)}^{n}\,{d x}"," ",0,"integrate((a^(k*x) + a^(l*x))^n, x)","F",0
507,1,28,0,0.453677," ","integrate(a^(k*x)-a^(l*x),x, algorithm=""maxima"")","\frac{a^{k x}}{k \log\left(a\right)} - \frac{a^{l x}}{l \log\left(a\right)}"," ",0,"a^(k*x)/(k*log(a)) - a^(l*x)/(l*log(a))","A",0
508,1,51,0,0.551913," ","integrate((a^(k*x)-a^(l*x))^2,x, algorithm=""maxima"")","-\frac{2 \, a^{k x + l x}}{{\left(k + l\right)} \log\left(a\right)} + \frac{a^{2 \, k x}}{2 \, k \log\left(a\right)} + \frac{a^{2 \, l x}}{2 \, l \log\left(a\right)}"," ",0,"-2*a^(k*x + l*x)/((k + l)*log(a)) + 1/2*a^(2*k*x)/(k*log(a)) + 1/2*a^(2*l*x)/(l*log(a))","A",0
509,1,77,0,0.527032," ","integrate((a^(k*x)-a^(l*x))^3,x, algorithm=""maxima"")","-\frac{3 \, a^{2 \, k x + l x}}{{\left(2 \, k + l\right)} \log\left(a\right)} + \frac{3 \, a^{k x + 2 \, l x}}{{\left(k + 2 \, l\right)} \log\left(a\right)} + \frac{a^{3 \, k x}}{3 \, k \log\left(a\right)} - \frac{a^{3 \, l x}}{3 \, l \log\left(a\right)}"," ",0,"-3*a^(2*k*x + l*x)/((2*k + l)*log(a)) + 3*a^(k*x + 2*l*x)/((k + 2*l)*log(a)) + 1/3*a^(3*k*x)/(k*log(a)) - 1/3*a^(3*l*x)/(l*log(a))","A",0
510,1,99,0,0.489649," ","integrate((a^(k*x)-a^(l*x))^4,x, algorithm=""maxima"")","-\frac{4 \, a^{3 \, k x + l x}}{{\left(3 \, k + l\right)} \log\left(a\right)} - \frac{4 \, a^{k x + 3 \, l x}}{{\left(k + 3 \, l\right)} \log\left(a\right)} + \frac{3 \, a^{2 \, k x + 2 \, l x}}{{\left(k + l\right)} \log\left(a\right)} + \frac{a^{4 \, k x}}{4 \, k \log\left(a\right)} + \frac{a^{4 \, l x}}{4 \, l \log\left(a\right)}"," ",0,"-4*a^(3*k*x + l*x)/((3*k + l)*log(a)) - 4*a^(k*x + 3*l*x)/((k + 3*l)*log(a)) + 3*a^(2*k*x + 2*l*x)/((k + l)*log(a)) + 1/4*a^(4*k*x)/(k*log(a)) + 1/4*a^(4*l*x)/(l*log(a))","A",0
511,0,0,0,0.000000," ","integrate((a^(k*x)-a^(l*x))^n,x, algorithm=""maxima"")","\int {\left(a^{k x} - a^{l x}\right)}^{n}\,{d x}"," ",0,"integrate((a^(k*x) - a^(l*x))^n, x)","F",0
512,1,15,0,0.569538," ","integrate(1+a^(m*x),x, algorithm=""maxima"")","x + \frac{a^{m x}}{m \log\left(a\right)}"," ",0,"x + a^(m*x)/(m*log(a))","A",0
513,1,31,0,0.528820," ","integrate((1+a^(m*x))^2,x, algorithm=""maxima"")","x + \frac{a^{2 \, m x}}{2 \, m \log\left(a\right)} + \frac{2 \, a^{m x}}{m \log\left(a\right)}"," ",0,"x + 1/2*a^(2*m*x)/(m*log(a)) + 2*a^(m*x)/(m*log(a))","A",0
514,1,46,0,0.571660," ","integrate((1+a^(m*x))^3,x, algorithm=""maxima"")","x + \frac{a^{3 \, m x}}{3 \, m \log\left(a\right)} + \frac{3 \, a^{2 \, m x}}{2 \, m \log\left(a\right)} + \frac{3 \, a^{m x}}{m \log\left(a\right)}"," ",0,"x + 1/3*a^(3*m*x)/(m*log(a)) + 3/2*a^(2*m*x)/(m*log(a)) + 3*a^(m*x)/(m*log(a))","A",0
515,1,61,0,0.510018," ","integrate((1+a^(m*x))^4,x, algorithm=""maxima"")","x + \frac{a^{4 \, m x}}{4 \, m \log\left(a\right)} + \frac{4 \, a^{3 \, m x}}{3 \, m \log\left(a\right)} + \frac{3 \, a^{2 \, m x}}{m \log\left(a\right)} + \frac{4 \, a^{m x}}{m \log\left(a\right)}"," ",0,"x + 1/4*a^(4*m*x)/(m*log(a)) + 4/3*a^(3*m*x)/(m*log(a)) + 3*a^(2*m*x)/(m*log(a)) + 4*a^(m*x)/(m*log(a))","A",0
516,0,0,0,0.000000," ","integrate((1+a^(m*x))^n,x, algorithm=""maxima"")","\int {\left(a^{m x} + 1\right)}^{n}\,{d x}"," ",0,"integrate((a^(m*x) + 1)^n, x)","F",0
517,1,16,0,0.676877," ","integrate(1-a^(m*x),x, algorithm=""maxima"")","x - \frac{a^{m x}}{m \log\left(a\right)}"," ",0,"x - a^(m*x)/(m*log(a))","A",0
518,1,31,0,0.537477," ","integrate((1-a^(m*x))^2,x, algorithm=""maxima"")","x + \frac{a^{2 \, m x}}{2 \, m \log\left(a\right)} - \frac{2 \, a^{m x}}{m \log\left(a\right)}"," ",0,"x + 1/2*a^(2*m*x)/(m*log(a)) - 2*a^(m*x)/(m*log(a))","A",0
519,1,46,0,0.495708," ","integrate((1-a^(m*x))^3,x, algorithm=""maxima"")","x - \frac{a^{3 \, m x}}{3 \, m \log\left(a\right)} + \frac{3 \, a^{2 \, m x}}{2 \, m \log\left(a\right)} - \frac{3 \, a^{m x}}{m \log\left(a\right)}"," ",0,"x - 1/3*a^(3*m*x)/(m*log(a)) + 3/2*a^(2*m*x)/(m*log(a)) - 3*a^(m*x)/(m*log(a))","A",0
520,1,61,0,0.506281," ","integrate((1-a^(m*x))^4,x, algorithm=""maxima"")","x + \frac{a^{4 \, m x}}{4 \, m \log\left(a\right)} - \frac{4 \, a^{3 \, m x}}{3 \, m \log\left(a\right)} + \frac{3 \, a^{2 \, m x}}{m \log\left(a\right)} - \frac{4 \, a^{m x}}{m \log\left(a\right)}"," ",0,"x + 1/4*a^(4*m*x)/(m*log(a)) - 4/3*a^(3*m*x)/(m*log(a)) + 3*a^(2*m*x)/(m*log(a)) - 4*a^(m*x)/(m*log(a))","A",0
521,0,0,0,0.000000," ","integrate((1-a^(m*x))^n,x, algorithm=""maxima"")","\int {\left(-a^{m x} + 1\right)}^{n}\,{d x}"," ",0,"integrate((-a^(m*x) + 1)^n, x)","F",0
522,1,23,0,0.445525," ","integrate(1/(b+a*exp(n*x)),x, algorithm=""maxima"")","\frac{x}{b} - \frac{\log\left(a e^{\left(n x\right)} + b\right)}{b n}"," ",0,"x/b - log(a*e^(n*x) + b)/(b*n)","A",0
523,1,100,0,1.365943," ","integrate(exp(x)/(b+a*exp(3*x)),x, algorithm=""maxima"")","\frac{\sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} - 2 \, e^{x}\right)}}{3 \, \left(\frac{b}{a}\right)^{\frac{1}{3}}}\right)}{3 \, a \left(\frac{b}{a}\right)^{\frac{2}{3}}} - \frac{\log\left(-\left(\frac{b}{a}\right)^{\frac{1}{3}} e^{x} + \left(\frac{b}{a}\right)^{\frac{2}{3}} + e^{\left(2 \, x\right)}\right)}{6 \, a \left(\frac{b}{a}\right)^{\frac{2}{3}}} + \frac{\log\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} + e^{x}\right)}{3 \, a \left(\frac{b}{a}\right)^{\frac{2}{3}}}"," ",0,"1/3*sqrt(3)*arctan(-1/3*sqrt(3)*((b/a)^(1/3) - 2*e^x)/(b/a)^(1/3))/(a*(b/a)^(2/3)) - 1/6*log(-(b/a)^(1/3)*e^x + (b/a)^(2/3) + e^(2*x))/(a*(b/a)^(2/3)) + 1/3*log((b/a)^(1/3) + e^x)/(a*(b/a)^(2/3))","A",0
524,1,11,0,0.483748," ","integrate((-1+exp(x))/(1+exp(x)),x, algorithm=""maxima"")","-x + 2 \, \log\left(e^{x} + 1\right)"," ",0,"-x + 2*log(e^x + 1)","A",0
525,1,37,0,1.336140," ","integrate(exp(4*x)/(1-2*exp(2*x)+3*exp(4*x)),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(3 \, e^{\left(2 \, x\right)} - 1\right)}\right) + \frac{1}{12} \, \log\left(3 \, e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 1\right)"," ",0,"1/12*sqrt(2)*arctan(1/2*sqrt(2)*(3*e^(2*x) - 1)) + 1/12*log(3*e^(4*x) - 2*e^(2*x) + 1)","A",0
526,1,28,0,1.155237," ","integrate((exp(x)+exp(5*x))/(-1+exp(x)-exp(2*x)+exp(3*x)),x, algorithm=""maxima"")","-\arctan\left(e^{x}\right) + \frac{1}{2} \, e^{\left(2 \, x\right)} + e^{x} - \frac{1}{2} \, \log\left(e^{\left(2 \, x\right)} + 1\right) + \log\left(e^{x} - 1\right)"," ",0,"-arctan(e^x) + 1/2*e^(2*x) + e^x - 1/2*log(e^(2*x) + 1) + log(e^x - 1)","A",0
527,1,32,0,0.585339," ","integrate(exp(n*x)*(a+b*exp(n*x))^(r/s),x, algorithm=""maxima"")","\frac{{\left(b e^{\left(n x\right)} + a\right)}^{\frac{r}{s} + 1}}{b n {\left(\frac{r}{s} + 1\right)}}"," ",0,"(b*e^(n*x) + a)^(r/s + 1)/(b*n*(r/s + 1))","A",0
528,1,56,0,1.310130," ","integrate((1-2*exp(1/3*x))^(1/4),x, algorithm=""maxima"")","12 \, {\left(-2 \, e^{\left(\frac{1}{3} \, x\right)} + 1\right)}^{\frac{1}{4}} - 6 \, \arctan\left({\left(-2 \, e^{\left(\frac{1}{3} \, x\right)} + 1\right)}^{\frac{1}{4}}\right) - 3 \, \log\left({\left(-2 \, e^{\left(\frac{1}{3} \, x\right)} + 1\right)}^{\frac{1}{4}} + 1\right) + 3 \, \log\left({\left(-2 \, e^{\left(\frac{1}{3} \, x\right)} + 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"12*(-2*e^(1/3*x) + 1)^(1/4) - 6*arctan((-2*e^(1/3*x) + 1)^(1/4)) - 3*log((-2*e^(1/3*x) + 1)^(1/4) + 1) + 3*log((-2*e^(1/3*x) + 1)^(1/4) - 1)","A",0
529,0,0,0,0.000000," ","integrate((a+b*exp(n*x))^(r/s),x, algorithm=""maxima"")","\int {\left(b e^{\left(n x\right)} + a\right)}^{\frac{r}{s}}\,{d x}"," ",0,"integrate((b*e^(n*x) + a)^(r/s), x)","F",0
530,1,7,0,0.545742," ","integrate(exp(x)/(a^2+exp(2*x))^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\frac{e^{x}}{a}\right)"," ",0,"arcsinh(e^x/a)","A",0
531,1,20,0,0.613944," ","integrate(exp(x)/(-a^2+exp(2*x))^(1/2),x, algorithm=""maxima"")","\log\left(2 \, \sqrt{-a^{2} + e^{\left(2 \, x\right)}} + 2 \, e^{x}\right)"," ",0,"log(2*sqrt(-a^2 + e^(2*x)) + 2*e^x)","A",0
532,1,39,0,1.300386," ","integrate(exp(3/4*x)/(-2+exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))^(1/2),x, algorithm=""maxima"")","-\frac{2}{3} \, \log\left(\frac{4 \, \sqrt{e^{\left(\frac{3}{2} \, x\right)} + e^{\left(\frac{3}{4} \, x\right)} - 2}}{{\left| e^{\left(\frac{3}{4} \, x\right)} - 2 \right|}} + \frac{8}{{\left| e^{\left(\frac{3}{4} \, x\right)} - 2 \right|}} + 5\right)"," ",0,"-2/3*log(4*sqrt(e^(3/2*x) + e^(3/4*x) - 2)/abs(e^(3/4*x) - 2) + 8/abs(e^(3/4*x) - 2) + 5)","A",0
533,0,0,0,0.000000," ","integrate((-3+exp(7*x))^(2/3)/exp(2*x),x, algorithm=""maxima"")","\int {\left(e^{\left(7 \, x\right)} - 3\right)}^{\frac{2}{3}} e^{\left(-2 \, x\right)}\,{d x}"," ",0,"integrate((e^(7*x) - 3)^(2/3)*e^(-2*x), x)","F",0
534,1,49,0,0.565488," ","integrate(exp(2*x)/(3-exp(1/2*x))^(3/4),x, algorithm=""maxima"")","\frac{8}{13} \, {\left(-e^{\left(\frac{1}{2} \, x\right)} + 3\right)}^{\frac{13}{4}} - 8 \, {\left(-e^{\left(\frac{1}{2} \, x\right)} + 3\right)}^{\frac{9}{4}} + \frac{216}{5} \, {\left(-e^{\left(\frac{1}{2} \, x\right)} + 3\right)}^{\frac{5}{4}} - 216 \, {\left(-e^{\left(\frac{1}{2} \, x\right)} + 3\right)}^{\frac{1}{4}}"," ",0,"8/13*(-e^(1/2*x) + 3)^(13/4) - 8*(-e^(1/2*x) + 3)^(9/4) + 216/5*(-e^(1/2*x) + 3)^(5/4) - 216*(-e^(1/2*x) + 3)^(1/4)","A",0
535,1,19,0,0.505110," ","integrate(x^3/exp(1/2*x),x, algorithm=""maxima"")","-2 \, {\left(x^{3} + 6 \, x^{2} + 24 \, x + 48\right)} e^{\left(-\frac{1}{2} \, x\right)}"," ",0,"-2*(x^3 + 6*x^2 + 24*x + 48)*e^(-1/2*x)","A",0
536,1,7,0,0.580657," ","integrate(1/exp(1/2*x)/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, \Gamma\left(-2, \frac{1}{2} \, x\right)"," ",0,"-1/4*gamma(-2, 1/2*x)","A",0
537,1,27,0,0.458262," ","integrate(a^(3*x)*x^2,x, algorithm=""maxima"")","\frac{{\left(9 \, x^{2} \log\left(a\right)^{2} - 6 \, x \log\left(a\right) + 2\right)} a^{3 \, x}}{27 \, \log\left(a\right)^{3}}"," ",0,"1/27*(9*x^2*log(a)^2 - 6*x*log(a) + 2)*a^(3*x)/log(a)^3","A",0
538,1,18,0,0.556408," ","integrate(exp(x^2)*x*(x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(x^{2} - 1\right)} e^{\left(x^{2}\right)} + \frac{1}{2} \, e^{\left(x^{2}\right)}"," ",0,"1/2*(x^2 - 1)*e^(x^2) + 1/2*e^(x^2)","A",0
539,1,25,0,1.164690," ","integrate(x/(exp(-x)+exp(x))^2,x, algorithm=""maxima"")","\frac{x e^{\left(2 \, x\right)}}{2 \, {\left(e^{\left(2 \, x\right)} + 1\right)}} - \frac{1}{4} \, \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"1/2*x*e^(2*x)/(e^(2*x) + 1) - 1/4*log(e^(2*x) + 1)","A",0
540,1,21,0,0.646598," ","integrate(exp(x)*(-x^2-x+1)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(x^{2} - 1\right)} e^{x}}{\sqrt{x + 1} \sqrt{-x + 1}}"," ",0,"-(x^2 - 1)*e^x/(sqrt(x + 1)*sqrt(-x + 1))","A",0
541,1,19,0,0.547469," ","integrate(cos(2*x)/exp(3*x),x, algorithm=""maxima"")","-\frac{1}{13} \, {\left(3 \, \cos\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} e^{\left(-3 \, x\right)}"," ",0,"-1/13*(3*cos(2*x) - 2*sin(2*x))*e^(-3*x)","A",0
542,1,39,0,0.661230," ","integrate((cos(1/2*x)+sin(1/2*x))/exp(x)^(1/3),x, algorithm=""maxima"")","-\frac{6}{13} \, {\left(3 \, \cos\left(\frac{1}{2} \, x\right) + 2 \, \sin\left(\frac{1}{2} \, x\right)\right)} e^{\left(-\frac{1}{3} \, x\right)} - \frac{6}{13} \, {\left(2 \, \cos\left(\frac{1}{2} \, x\right) - 3 \, \sin\left(\frac{1}{2} \, x\right)\right)} e^{\left(-\frac{1}{3} \, x\right)}"," ",0,"-6/13*(3*cos(1/2*x) + 2*sin(1/2*x))*e^(-1/3*x) - 6/13*(2*cos(1/2*x) - 3*sin(1/2*x))*e^(-1/3*x)","A",0
543,1,31,0,1.348782," ","integrate(cos(3/2*x)/(3^(3*x))^(1/4),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(\frac{3}{2} \, x\right) \log\left(3\right) - 2 \, \sin\left(\frac{3}{2} \, x\right)\right)}}{3 \, {\left(\log\left(3\right)^{2} + 4\right)} 3^{\frac{3}{4} \, x}}"," ",0,"-4/3*(cos(3/2*x)*log(3) - 2*sin(3/2*x))/((log(3)^2 + 4)*3^(3/4*x))","A",0
544,1,45,0,0.620364," ","integrate(exp(m*x)*cos(x)^2,x, algorithm=""maxima"")","\frac{m^{2} \cos\left(2 \, x\right) e^{\left(m x\right)} + 2 \, m e^{\left(m x\right)} \sin\left(2 \, x\right) + {\left(m^{2} + 4\right)} e^{\left(m x\right)}}{2 \, {\left(m^{3} + 4 \, m\right)}}"," ",0,"1/2*(m^2*cos(2*x)*e^(m*x) + 2*m*e^(m*x)*sin(2*x) + (m^2 + 4)*e^(m*x))/(m^3 + 4*m)","A",0
545,1,73,0,0.553402," ","integrate(exp(m*x)*sin(x)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(m^{2} + 1\right)} \cos\left(3 \, x\right) e^{\left(m x\right)} - 3 \, {\left(m^{2} + 9\right)} \cos\left(x\right) e^{\left(m x\right)} - {\left(m^{3} + m\right)} e^{\left(m x\right)} \sin\left(3 \, x\right) + 3 \, {\left(m^{3} + 9 \, m\right)} e^{\left(m x\right)} \sin\left(x\right)}{4 \, {\left(m^{4} + 10 \, m^{2} + 9\right)}}"," ",0,"1/4*(3*(m^2 + 1)*cos(3*x)*e^(m*x) - 3*(m^2 + 9)*cos(x)*e^(m*x) - (m^3 + m)*e^(m*x)*sin(3*x) + 3*(m^3 + 9*m)*e^(m*x)*sin(x))/(m^4 + 10*m^2 + 9)","A",0
546,1,27,0,0.629735," ","integrate(cos(1/3*x)^3/exp(x)^(1/2),x, algorithm=""maxima"")","-\frac{1}{130} \, {\left(135 \, \cos\left(\frac{1}{3} \, x\right) + 13 \, \cos\left(x\right) - 90 \, \sin\left(\frac{1}{3} \, x\right) - 26 \, \sin\left(x\right)\right)} e^{\left(-\frac{1}{2} \, x\right)}"," ",0,"-1/130*(135*cos(1/3*x) + 13*cos(x) - 90*sin(1/3*x) - 26*sin(x))*e^(-1/2*x)","A",0
547,1,27,0,0.531996," ","integrate(exp(2*x)*cos(x)^2*sin(x)^2,x, algorithm=""maxima"")","-\frac{1}{80} \, \cos\left(4 \, x\right) e^{\left(2 \, x\right)} - \frac{1}{40} \, e^{\left(2 \, x\right)} \sin\left(4 \, x\right) + \frac{1}{16} \, e^{\left(2 \, x\right)}"," ",0,"-1/80*cos(4*x)*e^(2*x) - 1/40*e^(2*x)*sin(4*x) + 1/16*e^(2*x)","A",0
548,1,27,0,0.524221," ","integrate(exp(3*x)*cos(3/2*x)^2*sin(3/2*x)^2,x, algorithm=""maxima"")","-\frac{1}{120} \, \cos\left(6 \, x\right) e^{\left(3 \, x\right)} - \frac{1}{60} \, e^{\left(3 \, x\right)} \sin\left(6 \, x\right) + \frac{1}{24} \, e^{\left(3 \, x\right)}"," ",0,"-1/120*cos(6*x)*e^(3*x) - 1/60*e^(3*x)*sin(6*x) + 1/24*e^(3*x)","A",0
549,-1,0,0,0.000000," ","integrate(exp(m*x)*tan(x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(exp(m*x)/sin(x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(exp(m*x)/cos(x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,0,0,0,0.000000," ","integrate(exp(x)/(1+cos(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)} \int \frac{e^{x} \sin\left(x\right)}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\,{d x} - e^{x} \sin\left(x\right)\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}"," ",0,"-2*((cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)*integrate(e^x*sin(x)/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1), x) - e^x*sin(x))/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)","F",0
553,0,0,0,0.000000," ","integrate(exp(x)/(1-cos(x)),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)} \int \frac{e^{x} \sin\left(x\right)}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}\,{d x} - e^{x} \sin\left(x\right)\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}"," ",0,"2*((cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)*integrate(e^x*sin(x)/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1), x) - e^x*sin(x))/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
554,0,0,0,0.000000," ","integrate(exp(x)/(1+sin(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(x\right) e^{x} - {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right)} \int \frac{\cos\left(x\right) e^{x}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1}\,{d x}\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1}"," ",0,"-2*(cos(x)*e^x - (cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)*integrate(cos(x)*e^x/(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1), x))/(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)","F",0
555,0,0,0,0.000000," ","integrate(exp(x)/(1-sin(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(x\right) e^{x} - {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)} \int \frac{\cos\left(x\right) e^{x}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1}\,{d x}\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1}"," ",0,"2*(cos(x)*e^x - (cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)*integrate(cos(x)*e^x/(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1), x))/(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","F",0
556,1,22,0,0.715959," ","integrate(exp(x)*(1-sin(x))/(1-cos(x)),x, algorithm=""maxima"")","-\frac{2 \, e^{x} \sin\left(x\right)}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}"," ",0,"-2*e^x*sin(x)/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","A",0
557,0,0,0,0.000000," ","integrate(exp(x)*(1+sin(x))/(1-cos(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)} \int \frac{e^{x} \sin\left(x\right)}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}\,{d x} - e^{x} \sin\left(x\right)\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}"," ",0,"2*(2*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)*integrate(e^x*sin(x)/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1), x) - e^x*sin(x))/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
558,1,22,0,0.722409," ","integrate(exp(x)*(1+sin(x))/(1+cos(x)),x, algorithm=""maxima"")","\frac{2 \, e^{x} \sin\left(x\right)}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}"," ",0,"2*e^x*sin(x)/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)","A",0
559,0,0,0,0.000000," ","integrate(exp(x)*(1-sin(x))/(1+cos(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)} \int \frac{e^{x} \sin\left(x\right)}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\,{d x} - e^{x} \sin\left(x\right)\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}"," ",0,"-2*(2*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)*integrate(e^x*sin(x)/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1), x) - e^x*sin(x))/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)","F",0
560,0,0,0,0.000000," ","integrate(exp(x)*(1-cos(x))/(1-sin(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(x\right) e^{x} - 2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)} \int \frac{\cos\left(x\right) e^{x}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1}\,{d x}\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1}"," ",0,"2*(cos(x)*e^x - 2*(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)*integrate(cos(x)*e^x/(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1), x))/(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","F",0
561,1,22,0,0.737797," ","integrate(exp(x)*(1+cos(x))/(1-sin(x)),x, algorithm=""maxima"")","\frac{2 \, \cos\left(x\right) e^{x}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1}"," ",0,"2*cos(x)*e^x/(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","A",0
562,0,0,0,0.000000," ","integrate(exp(x)*(1+cos(x))/(1+sin(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(x\right) e^{x} - 2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right)} \int \frac{\cos\left(x\right) e^{x}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1}\,{d x}\right)}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1}"," ",0,"-2*(cos(x)*e^x - 2*(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)*integrate(cos(x)*e^x/(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1), x))/(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)","F",0
563,1,22,0,0.716923," ","integrate(exp(x)*(1-cos(x))/(1+sin(x)),x, algorithm=""maxima"")","-\frac{2 \, \cos\left(x\right) e^{x}}{\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1}"," ",0,"-2*cos(x)*e^x/(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1)","A",0
564,1,17,0,0.439234," ","integrate(exp(x)*x*cos(x),x, algorithm=""maxima"")","\frac{1}{2} \, x \cos\left(x\right) e^{x} + \frac{1}{2} \, {\left(x - 1\right)} e^{x} \sin\left(x\right)"," ",0,"1/2*x*cos(x)*e^x + 1/2*(x - 1)*e^x*sin(x)","A",0
565,1,26,0,0.461857," ","integrate(exp(x)*x^2*sin(x),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(x^{2} - 2 \, x + 1\right)} \cos\left(x\right) e^{x} + \frac{1}{2} \, {\left(x^{2} - 1\right)} e^{x} \sin\left(x\right)"," ",0,"-1/2*(x^2 - 2*x + 1)*cos(x)*e^x + 1/2*(x^2 - 1)*e^x*sin(x)","A",0
566,1,33,0,0.459798," ","integrate(x^2*sin(x)/exp(3*x),x, algorithm=""maxima"")","-\frac{1}{250} \, {\left({\left(25 \, x^{2} + 30 \, x + 13\right)} \cos\left(x\right) + {\left(75 \, x^{2} + 40 \, x + 9\right)} \sin\left(x\right)\right)} e^{\left(-3 \, x\right)}"," ",0,"-1/250*((25*x^2 + 30*x + 13)*cos(x) + (75*x^2 + 40*x + 9)*sin(x))*e^(-3*x)","A",0
567,1,77,0,0.476600," ","integrate(exp(1/2*x)*x^2*cos(x)^3,x, algorithm=""maxima"")","\frac{1}{101306} \, {\left(1369 \, x^{2} + 5180 \, x - 856\right)} \cos\left(3 \, x\right) e^{\left(\frac{1}{2} \, x\right)} + \frac{3}{250} \, {\left(25 \, x^{2} + 60 \, x - 88\right)} \cos\left(x\right) e^{\left(\frac{1}{2} \, x\right)} + \frac{3}{50653} \, {\left(1369 \, x^{2} - 296 \, x - 264\right)} e^{\left(\frac{1}{2} \, x\right)} \sin\left(3 \, x\right) + \frac{3}{125} \, {\left(25 \, x^{2} - 40 \, x - 8\right)} e^{\left(\frac{1}{2} \, x\right)} \sin\left(x\right)"," ",0,"1/101306*(1369*x^2 + 5180*x - 856)*cos(3*x)*e^(1/2*x) + 3/250*(25*x^2 + 60*x - 88)*cos(x)*e^(1/2*x) + 3/50653*(1369*x^2 - 296*x - 264)*e^(1/2*x)*sin(3*x) + 3/125*(25*x^2 - 40*x - 8)*e^(1/2*x)*sin(x)","A",0
568,1,41,0,0.445509," ","integrate(exp(2*x)*x^2*sin(4*x),x, algorithm=""maxima"")","-\frac{1}{250} \, {\left(50 \, x^{2} - 20 \, x - 1\right)} \cos\left(4 \, x\right) e^{\left(2 \, x\right)} + \frac{1}{500} \, {\left(50 \, x^{2} + 30 \, x - 11\right)} e^{\left(2 \, x\right)} \sin\left(4 \, x\right)"," ",0,"-1/250*(50*x^2 - 20*x - 1)*cos(4*x)*e^(2*x) + 1/500*(50*x^2 + 30*x - 11)*e^(2*x)*sin(4*x)","A",0
569,1,77,0,0.489624," ","integrate(exp(1/2*x)*x^2*cos(x)*sin(x)^2,x, algorithm=""maxima"")","-\frac{1}{101306} \, {\left(1369 \, x^{2} + 5180 \, x - 856\right)} \cos\left(3 \, x\right) e^{\left(\frac{1}{2} \, x\right)} + \frac{1}{250} \, {\left(25 \, x^{2} + 60 \, x - 88\right)} \cos\left(x\right) e^{\left(\frac{1}{2} \, x\right)} - \frac{3}{50653} \, {\left(1369 \, x^{2} - 296 \, x - 264\right)} e^{\left(\frac{1}{2} \, x\right)} \sin\left(3 \, x\right) + \frac{1}{125} \, {\left(25 \, x^{2} - 40 \, x - 8\right)} e^{\left(\frac{1}{2} \, x\right)} \sin\left(x\right)"," ",0,"-1/101306*(1369*x^2 + 5180*x - 856)*cos(3*x)*e^(1/2*x) + 1/250*(25*x^2 + 60*x - 88)*cos(x)*e^(1/2*x) - 3/50653*(1369*x^2 - 296*x - 264)*e^(1/2*x)*sin(3*x) + 1/125*(25*x^2 - 40*x - 8)*e^(1/2*x)*sin(x)","A",0
570,1,2,0,0.423194," ","integrate(cosh(x),x, algorithm=""maxima"")","\sinh\left(x\right)"," ",0,"sinh(x)","A",0
571,1,2,0,0.424125," ","integrate(sinh(x),x, algorithm=""maxima"")","\cosh\left(x\right)"," ",0,"cosh(x)","A",0
572,1,3,0,0.420667," ","integrate(tanh(x),x, algorithm=""maxima"")","\log\left(\cosh\left(x\right)\right)"," ",0,"log(cosh(x))","A",0
573,1,3,0,0.420890," ","integrate(coth(x),x, algorithm=""maxima"")","\log\left(\sinh\left(x\right)\right)"," ",0,"log(sinh(x))","A",0
574,1,3,0,0.426743," ","integrate(sech(x),x, algorithm=""maxima"")","\arctan\left(\sinh\left(x\right)\right)"," ",0,"arctan(sinh(x))","A",0
575,1,5,0,0.430879," ","integrate(csch(x),x, algorithm=""maxima"")","\log\left(\tanh\left(\frac{1}{2} \, x\right)\right)"," ",0,"log(tanh(1/2*x))","A",0
576,1,16,0,0.429607," ","integrate(cosh(x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x + \frac{1}{8} \, e^{\left(2 \, x\right)} - \frac{1}{8} \, e^{\left(-2 \, x\right)}"," ",0,"1/2*x + 1/8*e^(2*x) - 1/8*e^(-2*x)","A",0
577,1,35,0,0.428809," ","integrate(sinh(x)^5,x, algorithm=""maxima"")","\frac{1}{160} \, e^{\left(5 \, x\right)} - \frac{5}{96} \, e^{\left(3 \, x\right)} + \frac{5}{16} \, e^{\left(-x\right)} - \frac{5}{96} \, e^{\left(-3 \, x\right)} + \frac{1}{160} \, e^{\left(-5 \, x\right)} + \frac{5}{16} \, e^{x}"," ",0,"1/160*e^(5*x) - 5/96*e^(3*x) + 5/16*e^(-x) - 5/96*e^(-3*x) + 1/160*e^(-5*x) + 5/16*e^x","B",0
578,1,38,0,0.434045," ","integrate(tanh(x)^4,x, algorithm=""maxima"")","x - \frac{4 \, {\left(3 \, e^{\left(-2 \, x\right)} + 3 \, e^{\left(-4 \, x\right)} + 2\right)}}{3 \, {\left(3 \, e^{\left(-2 \, x\right)} + 3 \, e^{\left(-4 \, x\right)} + e^{\left(-6 \, x\right)} + 1\right)}}"," ",0,"x - 4/3*(3*e^(-2*x) + 3*e^(-4*x) + 2)/(3*e^(-2*x) + 3*e^(-4*x) + e^(-6*x) + 1)","B",0
579,1,45,0,0.429334," ","integrate(csch(x)^3,x, algorithm=""maxima"")","\frac{e^{\left(-x\right)} + e^{\left(-3 \, x\right)}}{2 \, e^{\left(-2 \, x\right)} - e^{\left(-4 \, x\right)} - 1} + \frac{1}{2} \, \log\left(e^{\left(-x\right)} + 1\right) - \frac{1}{2} \, \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"(e^(-x) + e^(-3*x))/(2*e^(-2*x) - e^(-4*x) - 1) + 1/2*log(e^(-x) + 1) - 1/2*log(e^(-x) - 1)","B",0
580,1,61,0,1.013813," ","integrate(1/cosh(x)^5,x, algorithm=""maxima"")","\frac{3 \, e^{\left(-x\right)} + 11 \, e^{\left(-3 \, x\right)} - 11 \, e^{\left(-5 \, x\right)} - 3 \, e^{\left(-7 \, x\right)}}{4 \, {\left(4 \, e^{\left(-2 \, x\right)} + 6 \, e^{\left(-4 \, x\right)} + 4 \, e^{\left(-6 \, x\right)} + e^{\left(-8 \, x\right)} + 1\right)}} - \frac{3}{4} \, \arctan\left(e^{\left(-x\right)}\right)"," ",0,"1/4*(3*e^(-x) + 11*e^(-3*x) - 11*e^(-5*x) - 3*e^(-7*x))/(4*e^(-2*x) + 6*e^(-4*x) + 4*e^(-6*x) + e^(-8*x) + 1) - 3/4*arctan(e^(-x))","B",0
581,1,35,0,0.955275," ","integrate(tanh(x)^5/sech(x)^4,x, algorithm=""maxima"")","-\frac{1}{64} \, {\left(12 \, e^{\left(-2 \, x\right)} - 1\right)} e^{\left(4 \, x\right)} + x - \frac{3}{16} \, e^{\left(-2 \, x\right)} + \frac{1}{64} \, e^{\left(-4 \, x\right)} + \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-1/64*(12*e^(-2*x) - 1)*e^(4*x) + x - 3/16*e^(-2*x) + 1/64*e^(-4*x) + log(e^(-2*x) + 1)","B",0
582,0,0,0,0.000000," ","integrate(sech(x)^(3/4)*tanh(x)^5,x, algorithm=""maxima"")","\int \operatorname{sech}\left(x\right)^{\frac{3}{4}} \tanh\left(x\right)^{5}\,{d x}"," ",0,"integrate(sech(x)^(3/4)*tanh(x)^5, x)","F",0
583,-2,0,0,0.000000," ","integrate(1/(a+b*cosh(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
584,1,49,0,0.431723," ","integrate(1/(1+cosh(x))^2,x, algorithm=""maxima"")","\frac{2 \, e^{\left(-x\right)}}{3 \, e^{\left(-x\right)} + 3 \, e^{\left(-2 \, x\right)} + e^{\left(-3 \, x\right)} + 1} + \frac{2}{3 \, {\left(3 \, e^{\left(-x\right)} + 3 \, e^{\left(-2 \, x\right)} + e^{\left(-3 \, x\right)} + 1\right)}}"," ",0,"2*e^(-x)/(3*e^(-x) + 3*e^(-2*x) + e^(-3*x) + 1) + 2/3/(3*e^(-x) + 3*e^(-2*x) + e^(-3*x) + 1)","B",0
585,1,41,0,0.435595," ","integrate(1/(a+b*tanh(x)),x, algorithm=""maxima"")","-\frac{b \log\left(-{\left(a - b\right)} e^{\left(-2 \, x\right)} - a - b\right)}{a^{2} - b^{2}} + \frac{x}{a + b}"," ",0,"-b*log(-(a - b)*e^(-2*x) - a - b)/(a^2 - b^2) + x/(a + b)","A",0
586,1,76,0,0.980812," ","integrate(1/(a^2+b^2*cosh(x)^2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{b^{2} e^{\left(-2 \, x\right)} + 2 \, a^{2} + b^{2} - 2 \, \sqrt{a^{2} + b^{2}} a}{b^{2} e^{\left(-2 \, x\right)} + 2 \, a^{2} + b^{2} + 2 \, \sqrt{a^{2} + b^{2}} a}\right)}{2 \, \sqrt{a^{2} + b^{2}} a}"," ",0,"-1/2*log((b^2*e^(-2*x) + 2*a^2 + b^2 - 2*sqrt(a^2 + b^2)*a)/(b^2*e^(-2*x) + 2*a^2 + b^2 + 2*sqrt(a^2 + b^2)*a))/(sqrt(a^2 + b^2)*a)","B",0
587,-2,0,0,0.000000," ","integrate(1/(a^2-b^2*cosh(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
588,1,69,0,0.964185," ","integrate(1/(1-sinh(x)^4),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - e^{\left(-x\right)} + 1}{\sqrt{2} + e^{\left(-x\right)} - 1}\right) - \frac{1}{8} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - e^{\left(-x\right)} - 1}{\sqrt{2} + e^{\left(-x\right)} + 1}\right) + \frac{1}{e^{\left(-2 \, x\right)} + 1}"," ",0,"1/8*sqrt(2)*log(-(sqrt(2) - e^(-x) + 1)/(sqrt(2) + e^(-x) - 1)) - 1/8*sqrt(2)*log(-(sqrt(2) - e^(-x) - 1)/(sqrt(2) + e^(-x) + 1)) + 1/(e^(-2*x) + 1)","B",0
589,1,70,0,1.032656," ","integrate((cosh(x)^3-sinh(x)^3)/(cosh(x)^3+sinh(x)^3),x, algorithm=""maxima"")","\frac{4}{9} \, \sqrt{3} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, \sqrt{3} e^{\left(-x\right)} + 3^{\frac{1}{4}} \sqrt{2}\right)}\right) - \frac{4}{9} \, \sqrt{3} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, \sqrt{3} e^{\left(-x\right)} - 3^{\frac{1}{4}} \sqrt{2}\right)}\right) - \frac{1}{6} \, e^{\left(-2 \, x\right)}"," ",0,"4/9*sqrt(3)*arctan(1/6*3^(3/4)*sqrt(2)*(2*sqrt(3)*e^(-x) + 3^(1/4)*sqrt(2))) - 4/9*sqrt(3)*arctan(1/6*3^(3/4)*sqrt(2)*(2*sqrt(3)*e^(-x) - 3^(1/4)*sqrt(2))) - 1/6*e^(-2*x)","B",0
590,1,42,0,0.436574," ","integrate(cosh(x)*cosh(2*x)*cosh(3*x),x, algorithm=""maxima"")","\frac{1}{96} \, {\left(3 \, e^{\left(-2 \, x\right)} + 6 \, e^{\left(-4 \, x\right)} + 2\right)} e^{\left(6 \, x\right)} + \frac{1}{4} \, x - \frac{1}{16} \, e^{\left(-2 \, x\right)} - \frac{1}{32} \, e^{\left(-4 \, x\right)} - \frac{1}{48} \, e^{\left(-6 \, x\right)}"," ",0,"1/96*(3*e^(-2*x) + 6*e^(-4*x) + 2)*e^(6*x) + 1/4*x - 1/16*e^(-2*x) - 1/32*e^(-4*x) - 1/48*e^(-6*x)","A",0
591,1,42,0,0.446304," ","integrate(cosh(3/2*x)*sinh(x)*sinh(5/2*x),x, algorithm=""maxima"")","-\frac{1}{240} \, {\left(10 \, e^{\left(-2 \, x\right)} - 15 \, e^{\left(-3 \, x\right)} - 6\right)} e^{\left(5 \, x\right)} - \frac{1}{4} \, x - \frac{1}{16} \, e^{\left(-2 \, x\right)} + \frac{1}{24} \, e^{\left(-3 \, x\right)} - \frac{1}{40} \, e^{\left(-5 \, x\right)}"," ",0,"-1/240*(10*e^(-2*x) - 15*e^(-3*x) - 6)*e^(5*x) - 1/4*x - 1/16*e^(-2*x) + 1/24*e^(-3*x) - 1/40*e^(-5*x)","A",0
592,0,0,0,0.000000," ","integrate(cosh(x)*(-cosh(2*x)+tanh(x))/(sinh(x)^2+sinh(2*x))/sinh(2*x)^(1/2),x, algorithm=""maxima"")","-\int \frac{{\left(\cosh\left(2 \, x\right) - \tanh\left(x\right)\right)} \cosh\left(x\right)}{{\left(\sinh\left(x\right)^{2} + \sinh\left(2 \, x\right)\right)} \sqrt{\sinh\left(2 \, x\right)}}\,{d x}"," ",0,"-integrate((cosh(2*x) - tanh(x))*cosh(x)/((sinh(x)^2 + sinh(2*x))*sqrt(sinh(2*x))), x)","F",0
593,1,125,0,0.581778," ","integrate(sinh(x)/(-9+4*cosh(x)^2)^(5/2),x, algorithm=""maxima"")","-\frac{1855 \, e^{\left(-2 \, x\right)} - 8485 \, e^{\left(-4 \, x\right)} + 5285 \, e^{\left(-6 \, x\right)} - 980 \, e^{\left(-8 \, x\right)} + 56 \, e^{\left(-10 \, x\right)} - 106}{12150 \, {\left(3 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} + 1\right)}^{\frac{5}{2}} {\left(-3 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} + 1\right)}^{\frac{5}{2}}} + \frac{980 \, e^{\left(-2 \, x\right)} - 5285 \, e^{\left(-4 \, x\right)} + 8485 \, e^{\left(-6 \, x\right)} - 1855 \, e^{\left(-8 \, x\right)} + 106 \, e^{\left(-10 \, x\right)} - 56}{12150 \, {\left(3 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} + 1\right)}^{\frac{5}{2}} {\left(-3 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} + 1\right)}^{\frac{5}{2}}}"," ",0,"-1/12150*(1855*e^(-2*x) - 8485*e^(-4*x) + 5285*e^(-6*x) - 980*e^(-8*x) + 56*e^(-10*x) - 106)/((3*e^(-x) + e^(-2*x) + 1)^(5/2)*(-3*e^(-x) + e^(-2*x) + 1)^(5/2)) + 1/12150*(980*e^(-2*x) - 5285*e^(-4*x) + 8485*e^(-6*x) - 1855*e^(-8*x) + 106*e^(-10*x) - 56)/((3*e^(-x) + e^(-2*x) + 1)^(5/2)*(-3*e^(-x) + e^(-2*x) + 1)^(5/2))","B",0
594,1,177,0,1.212557," ","integrate(sinh(x)^2*sinh(2*x)/(1-sinh(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{16 \, e^{\left(-x\right)}}{{\left(2 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} - 1\right)}^{\frac{3}{2}} {\left(2 \, e^{\left(-x\right)} - e^{\left(-2 \, x\right)} + 1\right)}^{\frac{3}{2}}} + \frac{62 \, e^{\left(-3 \, x\right)}}{{\left(2 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} - 1\right)}^{\frac{3}{2}} {\left(2 \, e^{\left(-x\right)} - e^{\left(-2 \, x\right)} + 1\right)}^{\frac{3}{2}}} - \frac{16 \, e^{\left(-5 \, x\right)}}{{\left(2 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} - 1\right)}^{\frac{3}{2}} {\left(2 \, e^{\left(-x\right)} - e^{\left(-2 \, x\right)} + 1\right)}^{\frac{3}{2}}} + \frac{e^{\left(-7 \, x\right)}}{{\left(2 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} - 1\right)}^{\frac{3}{2}} {\left(2 \, e^{\left(-x\right)} - e^{\left(-2 \, x\right)} + 1\right)}^{\frac{3}{2}}} + \frac{e^{x}}{{\left(2 \, e^{\left(-x\right)} + e^{\left(-2 \, x\right)} - 1\right)}^{\frac{3}{2}} {\left(2 \, e^{\left(-x\right)} - e^{\left(-2 \, x\right)} + 1\right)}^{\frac{3}{2}}}"," ",0,"-16*e^(-x)/((2*e^(-x) + e^(-2*x) - 1)^(3/2)*(2*e^(-x) - e^(-2*x) + 1)^(3/2)) + 62*e^(-3*x)/((2*e^(-x) + e^(-2*x) - 1)^(3/2)*(2*e^(-x) - e^(-2*x) + 1)^(3/2)) - 16*e^(-5*x)/((2*e^(-x) + e^(-2*x) - 1)^(3/2)*(2*e^(-x) - e^(-2*x) + 1)^(3/2)) + e^(-7*x)/((2*e^(-x) + e^(-2*x) - 1)^(3/2)*(2*e^(-x) - e^(-2*x) + 1)^(3/2)) + e^x/((2*e^(-x) + e^(-2*x) - 1)^(3/2)*(2*e^(-x) - e^(-2*x) + 1)^(3/2))","B",0
595,0,0,0,0.000000," ","integrate(cosh(x)/cosh(2*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\cosh\left(x\right)}{\sqrt{\cosh\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(cosh(x)/sqrt(cosh(2*x)), x)","F",0
596,1,49,0,1.120673," ","integrate(x*tanh(x)^2,x, algorithm=""maxima"")","-\frac{x e^{\left(2 \, x\right)}}{e^{\left(2 \, x\right)} + 1} + \frac{x^{2} + {\left(x^{2} - 2 \, x\right)} e^{\left(2 \, x\right)}}{2 \, {\left(e^{\left(2 \, x\right)} + 1\right)}} + \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"-x*e^(2*x)/(e^(2*x) + 1) + 1/2*(x^2 + (x^2 - 2*x)*e^(2*x))/(e^(2*x) + 1) + log(e^(2*x) + 1)","B",0
597,1,53,0,0.643121," ","integrate(x*coth(x)^2,x, algorithm=""maxima"")","-\frac{x e^{\left(2 \, x\right)}}{e^{\left(2 \, x\right)} - 1} - \frac{x^{2} - {\left(x^{2} - 2 \, x\right)} e^{\left(2 \, x\right)}}{2 \, {\left(e^{\left(2 \, x\right)} - 1\right)}} + \log\left(e^{x} + 1\right) + \log\left(e^{x} - 1\right)"," ",0,"-x*e^(2*x)/(e^(2*x) - 1) - 1/2*(x^2 - (x^2 - 2*x)*e^(2*x))/(e^(2*x) - 1) + log(e^x + 1) + log(e^x - 1)","B",0
598,1,13,0,0.494192," ","integrate((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x, algorithm=""maxima"")","{\left(x - 1\right)} e^{x} + \frac{1}{2} \, e^{\left(2 \, x\right)}"," ",0,"(x - 1)*e^x + 1/2*e^(2*x)","A",0
599,1,35,0,0.448962," ","integrate((x+cosh(x)+sinh(x))/(1+cosh(x)),x, algorithm=""maxima"")","x + \frac{2 \, x e^{x}}{e^{x} + 1} - \frac{2}{e^{\left(-x\right)} + 1} + \log\left(\cosh\left(x\right) + 1\right) - 2 \, \log\left(e^{x} + 1\right)"," ",0,"x + 2*x*e^x/(e^x + 1) - 2/(e^(-x) + 1) + log(cosh(x) + 1) - 2*log(e^x + 1)","B",0
600,1,22,0,0.434138," ","integrate(exp(2*x)/sinh(x)^4,x, algorithm=""maxima"")","\frac{8}{3 \, {\left(3 \, e^{\left(-2 \, x\right)} - 3 \, e^{\left(-4 \, x\right)} + e^{\left(-6 \, x\right)} - 1\right)}}"," ",0,"8/3/(3*e^(-2*x) - 3*e^(-4*x) + e^(-6*x) - 1)","A",0
601,1,75,0,0.456589," ","integrate(1/exp(2*x)/cosh(x)^4,x, algorithm=""maxima"")","\frac{8 \, e^{\left(-2 \, x\right)}}{3 \, e^{\left(-2 \, x\right)} + 3 \, e^{\left(-4 \, x\right)} + e^{\left(-6 \, x\right)} + 1} + \frac{8 \, e^{\left(-4 \, x\right)}}{3 \, e^{\left(-2 \, x\right)} + 3 \, e^{\left(-4 \, x\right)} + e^{\left(-6 \, x\right)} + 1} + \frac{8}{3 \, {\left(3 \, e^{\left(-2 \, x\right)} + 3 \, e^{\left(-4 \, x\right)} + e^{\left(-6 \, x\right)} + 1\right)}}"," ",0,"8*e^(-2*x)/(3*e^(-2*x) + 3*e^(-4*x) + e^(-6*x) + 1) + 8*e^(-4*x)/(3*e^(-2*x) + 3*e^(-4*x) + e^(-6*x) + 1) + 8/3/(3*e^(-2*x) + 3*e^(-4*x) + e^(-6*x) + 1)","B",0
602,1,6,0,0.435099," ","integrate(exp(x)/(cosh(x)-sinh(x)),x, algorithm=""maxima"")","\frac{1}{2} \, e^{\left(2 \, x\right)}"," ",0,"1/2*e^(2*x)","A",0
603,-2,0,0,0.000000," ","integrate(exp(m*x)/(cosh(x)+sinh(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(-m>0)', see `assume?` for more details)Is -m equal to -1?","F(-2)",0
604,1,1,0,0.429834," ","integrate(exp(x)/(cosh(x)+sinh(x)),x, algorithm=""maxima"")","x"," ",0,"x","A",0
605,1,16,0,0.462287," ","integrate(exp(x)/(1-cosh(x)),x, algorithm=""maxima"")","\frac{2}{e^{x} - 1} - 2 \, \log\left(e^{x} - 1\right)"," ",0,"2/(e^x - 1) - 2*log(e^x - 1)","A",0
606,1,11,0,0.443663," ","integrate(exp(x)*(1+sinh(x))/(1+cosh(x)),x, algorithm=""maxima"")","\frac{2}{e^{x} + 1} + e^{x}"," ",0,"2/(e^x + 1) + e^x","A",0
607,1,11,0,0.442141," ","integrate(exp(x)*(1-sinh(x))/(1-cosh(x)),x, algorithm=""maxima"")","\frac{2}{e^{x} - 1} + e^{x}"," ",0,"2/(e^x - 1) + e^x","A",0
608,1,26,0,0.417178," ","integrate(x^m*log(x),x, algorithm=""maxima"")","\frac{x^{m + 1} \log\left(x\right)}{m + 1} - \frac{x^{m + 1}}{{\left(m + 1\right)}^{2}}"," ",0,"x^(m + 1)*log(x)/(m + 1) - x^(m + 1)/(m + 1)^2","A",0
609,1,42,0,0.421622," ","integrate(x^m*log(x)^2,x, algorithm=""maxima"")","\frac{x^{m + 1} \log\left(x\right)^{2}}{m + 1} - \frac{2 \, x^{m + 1} \log\left(x\right)}{{\left(m + 1\right)}^{2}} + \frac{2 \, x^{m + 1}}{{\left(m + 1\right)}^{3}}"," ",0,"x^(m + 1)*log(x)^2/(m + 1) - 2*x^(m + 1)*log(x)/(m + 1)^2 + 2*x^(m + 1)/(m + 1)^3","A",0
610,1,22,0,0.423825," ","integrate(log(x)^2/x^(5/2),x, algorithm=""maxima"")","-\frac{2 \, \log\left(x\right)^{2}}{3 \, x^{\frac{3}{2}}} - \frac{8 \, \log\left(x\right)}{9 \, x^{\frac{3}{2}}} - \frac{16}{27 \, x^{\frac{3}{2}}}"," ",0,"-2/3*log(x)^2/x^(3/2) - 8/9*log(x)/x^(3/2) - 16/27/x^(3/2)","A",0
611,1,25,0,0.420810," ","integrate((b*x+a)*log(x),x, algorithm=""maxima"")","-\frac{1}{4} \, b x^{2} - a x + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} \log\left(x\right)"," ",0,"-1/4*b*x^2 - a*x + 1/2*(b*x^2 + 2*a*x)*log(x)","A",0
612,1,69,0,0.432413," ","integrate((b*x+a)^3*log(x),x, algorithm=""maxima"")","-\frac{1}{16} \, b^{3} x^{4} - \frac{1}{3} \, a b^{2} x^{3} - \frac{3}{4} \, a^{2} b x^{2} - a^{3} x + \frac{1}{4} \, {\left(b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2} + 4 \, a^{3} x\right)} \log\left(x\right)"," ",0,"-1/16*b^3*x^4 - 1/3*a*b^2*x^3 - 3/4*a^2*b*x^2 - a^3*x + 1/4*(b^3*x^4 + 4*a*b^2*x^3 + 6*a^2*b*x^2 + 4*a^3*x)*log(x)","A",0
613,1,36,0,0.468308," ","integrate(-1-8*log(x)^2+3*log(x)^3,x, algorithm=""maxima"")","3 \, {\left(\log\left(x\right)^{3} - 3 \, \log\left(x\right)^{2} + 6 \, \log\left(x\right) - 6\right)} x - 8 \, {\left(\log\left(x\right)^{2} - 2 \, \log\left(x\right) + 2\right)} x - x"," ",0,"3*(log(x)^3 - 3*log(x)^2 + 6*log(x) - 6)*x - 8*(log(x)^2 - 2*log(x) + 2)*x - x","A",0
614,1,66,0,0.441546," ","integrate((x^4+1)*(1-2*log(x)+log(x)^3),x, algorithm=""maxima"")","\frac{1}{625} \, {\left(125 \, \log\left(x\right)^{3} - 75 \, \log\left(x\right)^{2} + 30 \, \log\left(x\right) - 6\right)} x^{5} - \frac{2}{25} \, x^{5} {\left(5 \, \log\left(x\right) - 1\right)} + \frac{1}{5} \, x^{5} + {\left(\log\left(x\right)^{3} - 3 \, \log\left(x\right)^{2} + 6 \, \log\left(x\right) - 6\right)} x - 2 \, x {\left(\log\left(x\right) - 1\right)} + x"," ",0,"1/625*(125*log(x)^3 - 75*log(x)^2 + 30*log(x) - 6)*x^5 - 2/25*x^5*(5*log(x) - 1) + 1/5*x^5 + (log(x)^3 - 3*log(x)^2 + 6*log(x) - 6)*x - 2*x*(log(x) - 1) + x","A",0
615,1,8,0,0.536592," ","integrate(1/x^3/log(x)^4,x, algorithm=""maxima"")","-8 \, \Gamma\left(-3, 2 \, \log\left(x\right)\right)"," ",0,"-8*gamma(-3, 2*log(x))","A",0
616,1,25,0,0.432519," ","integrate(log(x)/(b*x+a),x, algorithm=""maxima"")","\frac{\log\left(\frac{b x}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a}\right)}{b}"," ",0,"(log(b*x/a + 1)*log(x) + dilog(-b*x/a))/b","A",0
617,1,38,0,0.425534," ","integrate(log(x)/(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\frac{\log\left(b x + a\right)}{a} - \frac{\log\left(x\right)}{a}}{b} - \frac{\log\left(x\right)}{{\left(b x + a\right)} b}"," ",0,"-(log(b*x + a)/a - log(x)/a)/b - log(x)/((b*x + a)*b)","A",0
618,1,12,0,0.416946," ","integrate(log(x)^n/x,x, algorithm=""maxima"")","\frac{\log\left(x\right)^{n + 1}}{n + 1}"," ",0,"log(x)^(n + 1)/(n + 1)","A",0
619,1,19,0,0.425853," ","integrate((a+b*log(x))^n/x,x, algorithm=""maxima"")","\frac{{\left(b \log\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"(b*log(x) + a)^(n + 1)/(b*(n + 1))","A",0
620,1,11,0,0.417808," ","integrate(1/x/(a+b*log(x)),x, algorithm=""maxima"")","\frac{\log\left(b \log\left(x\right) + a\right)}{b}"," ",0,"log(b*log(x) + a)/b","A",0
621,-2,0,0,0.000000," ","integrate(1/x/((a+b*log(x))^n),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(-n>0)', see `assume?` for more details)Is -n equal to -1?","F(-2)",0
622,1,7,0,0.418942," ","integrate(1/x/(a^2+log(x)^2)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\frac{\log\left(x\right)}{a}\right)"," ",0,"arcsinh(log(x)/a)","A",0
623,1,20,0,0.431765," ","integrate(1/x/(-a^2+log(x)^2)^(1/2),x, algorithm=""maxima"")","\log\left(2 \, \sqrt{-a^{2} + \log\left(x\right)^{2}} + 2 \, \log\left(x\right)\right)"," ",0,"log(2*sqrt(-a^2 + log(x)^2) + 2*log(x))","A",0
624,1,7,0,0.996651," ","integrate(1/x/(a^2-log(x)^2)^(1/2),x, algorithm=""maxima"")","\arcsin\left(\frac{\log\left(x\right)}{a}\right)"," ",0,"arcsin(log(x)/a)","A",0
625,1,13,0,0.421173," ","integrate(1/x/log(x)/(a^2+log(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\operatorname{arsinh}\left(\frac{a}{{\left| \log\left(x\right) \right|}}\right)}{a}"," ",0,"-arcsinh(a/abs(log(x)))/a","A",0
626,1,37,0,0.428287," ","integrate(1/x/log(x)/(a^2-log(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{2 \, a^{2}}{{\left| \log\left(x\right) \right|}} + \frac{2 \, \sqrt{a^{2} - \log\left(x\right)^{2}} a}{{\left| \log\left(x\right) \right|}}\right)}{a}"," ",0,"-log(2*a^2/abs(log(x)) + 2*sqrt(a^2 - log(x)^2)*a/abs(log(x)))/a","A",0
627,1,13,0,0.953526," ","integrate(1/x/log(x)/(-a^2+log(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\arcsin\left(\frac{a}{{\left| \log\left(x\right) \right|}}\right)}{a}"," ",0,"-arcsin(a/abs(log(x)))/a","A",0
628,1,11,0,0.417811," ","integrate(log(log(x))/x,x, algorithm=""maxima"")","\log\left(x\right) \log\left(\log\left(x\right)\right) - \log\left(x\right)"," ",0,"log(x)*log(log(x)) - log(x)","A",0
629,1,15,0,0.420929," ","integrate(log(log(x))^2/x,x, algorithm=""maxima"")","{\left(\log\left(\log\left(x\right)\right)^{2} - 2 \, \log\left(\log\left(x\right)\right) + 2\right)} \log\left(x\right)"," ",0,"(log(log(x))^2 - 2*log(log(x)) + 2)*log(x)","A",0
630,1,22,0,0.420276," ","integrate(log(log(x))^3/x,x, algorithm=""maxima"")","{\left(\log\left(\log\left(x\right)\right)^{3} - 3 \, \log\left(\log\left(x\right)\right)^{2} + 6 \, \log\left(\log\left(x\right)\right) - 6\right)} \log\left(x\right)"," ",0,"(log(log(x))^3 - 3*log(log(x))^2 + 6*log(log(x)) - 6)*log(x)","A",0
631,1,29,0,0.424335," ","integrate(log(log(x))^4/x,x, algorithm=""maxima"")","{\left(\log\left(\log\left(x\right)\right)^{4} - 4 \, \log\left(\log\left(x\right)\right)^{3} + 12 \, \log\left(\log\left(x\right)\right)^{2} - 24 \, \log\left(\log\left(x\right)\right) + 24\right)} \log\left(x\right)"," ",0,"(log(log(x))^4 - 4*log(log(x))^3 + 12*log(log(x))^2 - 24*log(log(x)) + 24)*log(x)","A",0
632,1,29,0,0.554814," ","integrate(log(log(x))^n/x,x, algorithm=""maxima"")","-\left(-\log\left(\log\left(x\right)\right)\right)^{-n - 1} \log\left(\log\left(x\right)\right)^{n + 1} \Gamma\left(n + 1, -\log\left(\log\left(x\right)\right)\right)"," ",0,"-(-log(log(x)))^(-n - 1)*log(log(x))^(n + 1)*gamma(n + 1, -log(log(x)))","A",0
633,1,4,0,0.423378," ","integrate(cot(x)/log(sin(x)),x, algorithm=""maxima"")","\log\left(\log\left(\sin\left(x\right)\right)\right)"," ",0,"log(log(sin(x)))","A",0
634,1,9,0,0.430393," ","integrate((1/cos(x)+cos(x))*tan(x),x, algorithm=""maxima"")","\frac{1}{\cos\left(x\right)} - \cos\left(x\right)"," ",0,"1/cos(x) - cos(x)","A",0
635,1,11,0,0.433439," ","integrate(log(cosh(x))*sinh(x),x, algorithm=""maxima"")","\cosh\left(x\right) \log\left(\cosh\left(x\right)\right) - \cosh\left(x\right)"," ",0,"cosh(x)*log(cosh(x)) - cosh(x)","A",0
636,1,7,0,0.425351," ","integrate(log(cosh(x))*tanh(x),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\cosh\left(x\right)\right)^{2}"," ",0,"1/2*log(cosh(x))^2","A",0
637,0,0,0,0.000000," ","integrate(log(x-(x^2+1)^(1/2)),x, algorithm=""maxima"")","x \log\left(x - \sqrt{x^{2} + 1}\right) - x + \arctan\left(x\right) + \int -\frac{x}{x^{3} - {\left(x^{2} + 1\right)}^{\frac{3}{2}} + x}\,{d x}"," ",0,"x*log(x - sqrt(x^2 + 1)) - x + arctan(x) + integrate(-x/(x^3 - (x^2 + 1)^(3/2) + x), x)","F",0
638,1,25,0,0.430409," ","integrate(log(-1+x)/x^3,x, algorithm=""maxima"")","\frac{1}{2 \, x} - \frac{\log\left(x - 1\right)}{2 \, x^{2}} + \frac{1}{2} \, \log\left(x - 1\right) - \frac{1}{2} \, \log\left(x\right)"," ",0,"1/2/x - 1/2*log(x - 1)/x^2 + 1/2*log(x - 1) - 1/2*log(x)","A",0
639,1,20,0,0.439521," ","integrate((-1/exp(x)+exp(x))*log(1+exp(2*x)),x, algorithm=""maxima"")","{\left(e^{\left(-x\right)} + e^{x}\right)} \log\left(e^{\left(2 \, x\right)} + 1\right) - 2 \, e^{x}"," ",0,"(e^(-x) + e^x)*log(e^(2*x) + 1) - 2*e^x","A",0
640,1,42,0,0.448499," ","integrate(exp(3/2*x)*log(-1+exp(x)),x, algorithm=""maxima"")","\frac{2}{3} \, e^{\left(\frac{3}{2} \, x\right)} \log\left(e^{x} - 1\right) - \frac{4}{9} \, e^{\left(\frac{3}{2} \, x\right)} - \frac{4}{3} \, e^{\left(\frac{1}{2} \, x\right)} + \frac{2}{3} \, \log\left(e^{\left(\frac{1}{2} \, x\right)} + 1\right) - \frac{2}{3} \, \log\left(e^{\left(\frac{1}{2} \, x\right)} - 1\right)"," ",0,"2/3*e^(3/2*x)*log(e^x - 1) - 4/9*e^(3/2*x) - 4/3*e^(1/2*x) + 2/3*log(e^(1/2*x) + 1) - 2/3*log(e^(1/2*x) - 1)","A",0
641,1,25,0,0.422171," ","integrate(cos(x)^3*log(sin(x)),x, algorithm=""maxima"")","\frac{1}{9} \, \sin\left(x\right)^{3} - \frac{1}{3} \, {\left(\sin\left(x\right)^{3} - 3 \, \sin\left(x\right)\right)} \log\left(\sin\left(x\right)\right) - \sin\left(x\right)"," ",0,"1/9*sin(x)^3 - 1/3*(sin(x)^3 - 3*sin(x))*log(sin(x)) - sin(x)","A",0
642,1,25,0,0.432397," ","integrate(log(tan(x))/cos(x)^4,x, algorithm=""maxima"")","-\frac{1}{9} \, \tan\left(x\right)^{3} + \frac{1}{3} \, {\left(\tan\left(x\right)^{3} + 3 \, \tan\left(x\right)\right)} \log\left(\tan\left(x\right)\right) - \tan\left(x\right)"," ",0,"-1/9*tan(x)^3 + 1/3*(tan(x)^3 + 3*tan(x))*log(tan(x)) - tan(x)","A",0
643,1,56,0,0.440092," ","integrate(log(cos(1/2*x))/(1+cos(x)),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{x \cos\left(x\right)^{2} + x \sin\left(x\right)^{2} + 2 \, x \cos\left(x\right) + x - 4 \, \sin\left(x\right)}{2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}}"," ",0,"log(cos(1/2*x))*sin(x)/(cos(x) + 1) - 1/2*(x*cos(x)^2 + x*sin(x)^2 + 2*x*cos(x) + x - 4*sin(x))/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)","B",0
644,1,86,0,0.961903," ","integrate(cos(x)*log(sin(x))/(1+cos(x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)} \log\left(\frac{2 \, \sin\left(x\right)}{{\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}}\right) + \frac{5 \, \sin\left(x\right)}{6 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{\sin\left(x\right)^{3}}{18 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{4}{3} \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"1/6*(3*sin(x)/(cos(x) + 1) - sin(x)^3/(cos(x) + 1)^3)*log(2*sin(x)/((sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1))) + 5/6*sin(x)/(cos(x) + 1) - 1/18*sin(x)^3/(cos(x) + 1)^3 - 4/3*arctan(sin(x)/(cos(x) + 1))","A",0
645,1,51,0,0.956715," ","integrate(arccos(x)^2/x^5,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{2 \, \sqrt{-x^{2} + 1}}{x} + \frac{\sqrt{-x^{2} + 1}}{x^{3}}\right)} \arccos\left(x\right) - \frac{1}{12 \, x^{2}} - \frac{\arccos\left(x\right)^{2}}{4 \, x^{4}} + \frac{1}{3} \, \log\left(x\right)"," ",0,"1/6*(2*sqrt(-x^2 + 1)/x + sqrt(-x^2 + 1)/x^3)*arccos(x) - 1/12/x^2 - 1/4*arccos(x)^2/x^4 + 1/3*log(x)","A",0
646,1,47,0,0.973868," ","integrate(x^2*arcsin(x)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arcsin\left(x\right)^{2} - \frac{2}{27} \, x^{3} + \frac{2}{9} \, {\left(\sqrt{-x^{2} + 1} x^{2} + 2 \, \sqrt{-x^{2} + 1}\right)} \arcsin\left(x\right) - \frac{4}{9} \, x"," ",0,"1/3*x^3*arcsin(x)^2 - 2/27*x^3 + 2/9*(sqrt(-x^2 + 1)*x^2 + 2*sqrt(-x^2 + 1))*arcsin(x) - 4/9*x","A",0
647,1,44,0,0.997694," ","integrate(x^3*arctan(x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arctan\left(x\right)^{2} + \frac{1}{12} \, x^{2} - \frac{1}{6} \, {\left(x^{3} - 3 \, x + 3 \, \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{1}{4} \, \arctan\left(x\right)^{2} - \frac{1}{3} \, \log\left(x^{2} + 1\right)"," ",0,"1/4*x^4*arctan(x)^2 + 1/12*x^2 - 1/6*(x^3 - 3*x + 3*arctan(x))*arctan(x) + 1/4*arctan(x)^2 - 1/3*log(x^2 + 1)","A",0
648,1,64,0,0.976457," ","integrate(arctan(x)^2/x^5,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, x^{2} - 1}{x^{3}} + 3 \, \arctan\left(x\right)\right)} \arctan\left(x\right) - \frac{3 \, x^{2} \arctan\left(x\right)^{2} - 4 \, x^{2} \log\left(x^{2} + 1\right) + 8 \, x^{2} \log\left(x\right) + 1}{12 \, x^{2}} - \frac{\arctan\left(x\right)^{2}}{4 \, x^{4}}"," ",0,"1/6*((3*x^2 - 1)/x^3 + 3*arctan(x))*arctan(x) - 1/12*(3*x^2*arctan(x)^2 - 4*x^2*log(x^2 + 1) + 8*x^2*log(x) + 1)/x^2 - 1/4*arctan(x)^2/x^4","A",0
649,1,95,0,1.227400," ","integrate(x^3*arccsc(x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arccsc}\left(x\right)^{2} + \frac{2 \, x^{4} \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) + 2 \, x^{2} \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) + {\left(x^{2} + 2 \, \log\left(x^{2}\right)\right)} \sqrt{x + 1} \sqrt{x - 1} - 4 \, \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right)}{12 \, \sqrt{x + 1} \sqrt{x - 1}}"," ",0,"1/4*x^4*arccsc(x)^2 + 1/12*(2*x^4*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) + 2*x^2*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) + (x^2 + 2*log(x^2))*sqrt(x + 1)*sqrt(x - 1) - 4*arctan2(1, sqrt(x + 1)*sqrt(x - 1)))/(sqrt(x + 1)*sqrt(x - 1))","A",0
650,0,0,0,0.000000," ","integrate(arcsec(x)^4/x^5,x, algorithm=""maxima"")","\frac{8 \, x^{4} \int \frac{12 \, {\left(x^{2} - 1\right)} \log\left(x^{2}\right)^{2} \log\left(x\right)^{2} - 16 \, {\left(x^{2} - 1\right)} \log\left(x^{2}\right) \log\left(x\right)^{3} + 8 \, {\left(x^{2} - 1\right)} \log\left(x\right)^{4} + {\left(x^{2} - 4 \, {\left(x^{2} - 1\right)} \log\left(x\right) - 1\right)} \log\left(x^{2}\right)^{3} - 12 \, {\left(4 \, {\left(x^{2} - 1\right)} \log\left(x\right)^{2} + {\left(x^{2} - 4 \, {\left(x^{2} - 1\right)} \log\left(x\right) - 1\right)} \log\left(x^{2}\right)\right)} \arctan\left(\sqrt{x + 1} \sqrt{x - 1}\right)^{2} + 2 \, {\left(4 \, \arctan\left(\sqrt{x + 1} \sqrt{x - 1}\right)^{3} - 3 \, \arctan\left(\sqrt{x + 1} \sqrt{x - 1}\right) \log\left(x^{2}\right)^{2}\right)} \sqrt{x + 1} \sqrt{x - 1}}{x^{7} - x^{5}}\,{d x} - 16 \, \arctan\left(\sqrt{x + 1} \sqrt{x - 1}\right)^{4} + 24 \, \arctan\left(\sqrt{x + 1} \sqrt{x - 1}\right)^{2} \log\left(x^{2}\right)^{2} - \log\left(x^{2}\right)^{4}}{64 \, x^{4}}"," ",0,"1/64*(64*x^4*integrate(1/8*(12*(x^2 - 1)*log(x^2)^2*log(x)^2 - 16*(x^2 - 1)*log(x^2)*log(x)^3 + 8*(x^2 - 1)*log(x)^4 + (x^2 - 4*(x^2 - 1)*log(x) - 1)*log(x^2)^3 - 12*(4*(x^2 - 1)*log(x)^2 + (x^2 - 4*(x^2 - 1)*log(x) - 1)*log(x^2))*arctan(sqrt(x + 1)*sqrt(x - 1))^2 + 2*(4*arctan(sqrt(x + 1)*sqrt(x - 1))^3 - 3*arctan(sqrt(x + 1)*sqrt(x - 1))*log(x^2)^2)*sqrt(x + 1)*sqrt(x - 1))/(x^7 - x^5), x) - 16*arctan(sqrt(x + 1)*sqrt(x - 1))^4 + 24*arctan(sqrt(x + 1)*sqrt(x - 1))^2*log(x^2)^2 - log(x^2)^4)/x^4","F",0
651,1,30,0,0.972047," ","integrate(arcsin(x)*(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{2} + \frac{1}{2} \, {\left(\sqrt{-x^{2} + 1} x + \arcsin\left(x\right)\right)} \arcsin\left(x\right) - \frac{1}{4} \, \arcsin\left(x\right)^{2}"," ",0,"-1/4*x^2 + 1/2*(sqrt(-x^2 + 1)*x + arcsin(x))*arcsin(x) - 1/4*arcsin(x)^2","A",0
652,1,30,0,0.968149," ","integrate(arccos(x)*(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} + \frac{1}{2} \, {\left(\sqrt{-x^{2} + 1} x + \arcsin\left(x\right)\right)} \arccos\left(x\right) + \frac{1}{4} \, \arcsin\left(x\right)^{2}"," ",0,"1/4*x^2 + 1/2*(sqrt(-x^2 + 1)*x + arcsin(x))*arccos(x) + 1/4*arcsin(x)^2","A",0
653,1,22,0,0.956173," ","integrate(x*arccos(x)*(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{9} \, x^{3} - \frac{1}{3} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} \arccos\left(x\right) - \frac{1}{3} \, x"," ",0,"1/9*x^3 - 1/3*(-x^2 + 1)^(3/2)*arccos(x) - 1/3*x","A",0
654,1,50,0,1.020765," ","integrate((-x^2+1)^(3/2)*arcsin(x),x, algorithm=""maxima"")","\frac{1}{16} \, x^{4} - \frac{5}{16} \, x^{2} + \frac{1}{8} \, {\left(2 \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-x^{2} + 1} x + 3 \, \arcsin\left(x\right)\right)} \arcsin\left(x\right) - \frac{3}{16} \, \arcsin\left(x\right)^{2}"," ",0,"1/16*x^4 - 5/16*x^2 + 1/8*(2*(-x^2 + 1)^(3/2)*x + 3*sqrt(-x^2 + 1)*x + 3*arcsin(x))*arcsin(x) - 3/16*arcsin(x)^2","A",0
655,1,27,0,0.982046," ","integrate(x*(-x^2+1)^(3/2)*arcsin(x),x, algorithm=""maxima"")","\frac{1}{25} \, x^{5} - \frac{1}{5} \, {\left(-x^{2} + 1\right)}^{\frac{5}{2}} \arcsin\left(x\right) - \frac{2}{15} \, x^{3} + \frac{1}{5} \, x"," ",0,"1/25*x^5 - 1/5*(-x^2 + 1)^(5/2)*arcsin(x) - 2/15*x^3 + 1/5*x","A",0
656,1,49,0,0.959944," ","integrate(x^3*(-x^2+1)^(3/2)*arccos(x),x, algorithm=""maxima"")","-\frac{1}{49} \, x^{7} + \frac{8}{175} \, x^{5} - \frac{1}{105} \, x^{3} - \frac{1}{35} \, {\left(5 \, {\left(-x^{2} + 1\right)}^{\frac{5}{2}} x^{2} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{5}{2}}\right)} \arccos\left(x\right) - \frac{2}{35} \, x"," ",0,"-1/49*x^7 + 8/175*x^5 - 1/105*x^3 - 1/35*(5*(-x^2 + 1)^(5/2)*x^2 + 2*(-x^2 + 1)^(5/2))*arccos(x) - 2/35*x","A",0
657,0,0,0,0.000000," ","integrate((-x^2+1)^(3/2)*arccos(x)/x,x, algorithm=""maxima"")","\int \frac{{\left(-x^{2} + 1\right)}^{\frac{3}{2}} \arccos\left(x\right)}{x}\,{d x}"," ",0,"integrate((-x^2 + 1)^(3/2)*arccos(x)/x, x)","F",0
658,1,35,0,0.973729," ","integrate((-x^2+1)^(3/2)*arcsin(x)/x^6,x, algorithm=""maxima"")","-\frac{{\left(-x^{2} + 1\right)}^{\frac{5}{2}} \arcsin\left(x\right)}{5 \, x^{5}} + \frac{4 \, x^{2} - 1}{20 \, x^{4}} + \frac{1}{10} \, \log\left(x^{2}\right)"," ",0,"-1/5*(-x^2 + 1)^(5/2)*arcsin(x)/x^5 + 1/20*(4*x^2 - 1)/x^4 + 1/10*log(x^2)","A",0
659,1,32,0,0.972393," ","integrate(x^2*arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} - \frac{1}{2} \, {\left(\sqrt{-x^{2} + 1} x - \arcsin\left(x\right)\right)} \arcsin\left(x\right) - \frac{1}{4} \, \arcsin\left(x\right)^{2}"," ",0,"1/4*x^2 - 1/2*(sqrt(-x^2 + 1)*x - arcsin(x))*arcsin(x) - 1/4*arcsin(x)^2","A",0
660,1,52,0,0.973505," ","integrate(x^4*arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{16} \, x^{4} + \frac{3}{16} \, x^{2} - \frac{1}{8} \, {\left(2 \, \sqrt{-x^{2} + 1} x^{3} + 3 \, \sqrt{-x^{2} + 1} x - 3 \, \arcsin\left(x\right)\right)} \arcsin\left(x\right) - \frac{3}{16} \, \arcsin\left(x\right)^{2}"," ",0,"1/16*x^4 + 3/16*x^2 - 1/8*(2*sqrt(-x^2 + 1)*x^3 + 3*sqrt(-x^2 + 1)*x - 3*arcsin(x))*arcsin(x) - 3/16*arcsin(x)^2","A",0
661,1,25,0,0.958040," ","integrate(x*arcsin(x)/(-x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{\arcsin\left(x\right)}{\sqrt{-x^{2} + 1}} - \frac{1}{2} \, \log\left(x + 1\right) + \frac{1}{2} \, \log\left(x - 1\right)"," ",0,"arcsin(x)/sqrt(-x^2 + 1) - 1/2*log(x + 1) + 1/2*log(x - 1)","A",0
662,1,25,0,0.989860," ","integrate(x*arccos(x)/(-x^2+1)^(3/2),x, algorithm=""maxima"")","\frac{\arccos\left(x\right)}{\sqrt{-x^{2} + 1}} + \frac{1}{2} \, \log\left(x + 1\right) - \frac{1}{2} \, \log\left(x - 1\right)"," ",0,"arccos(x)/sqrt(-x^2 + 1) + 1/2*log(x + 1) - 1/2*log(x - 1)","A",0
663,1,48,0,0.961351," ","integrate(arcsin(x)/(-x^2+1)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-x^{2} + 1}} + \frac{x}{{\left(-x^{2} + 1\right)}^{\frac{3}{2}}}\right)} \arcsin\left(x\right) + \frac{1}{6 \, {\left(x^{2} - 1\right)}} + \frac{1}{3} \, \log\left(-3 \, x^{2} + 3\right)"," ",0,"1/3*(2*x/sqrt(-x^2 + 1) + x/(-x^2 + 1)^(3/2))*arcsin(x) + 1/6/(x^2 - 1) + 1/3*log(-3*x^2 + 3)","A",0
664,1,45,0,0.969077," ","integrate(x^3*arcsin(x)/(-x^2+1)^(3/2),x, algorithm=""maxima"")","-{\left(\frac{x^{2}}{\sqrt{-x^{2} + 1}} - \frac{2}{\sqrt{-x^{2} + 1}}\right)} \arcsin\left(x\right) - x - \frac{1}{2} \, \log\left(x + 1\right) + \frac{1}{2} \, \log\left(x - 1\right)"," ",0,"-(x^2/sqrt(-x^2 + 1) - 2/sqrt(-x^2 + 1))*arcsin(x) - x - 1/2*log(x + 1) + 1/2*log(x - 1)","A",0
665,0,0,0,0.000000," ","integrate(arcsin(x)/x/(-x^2+1)^(3/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(x\right)}{{\left(-x^{2} + 1\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arcsin(x)/((-x^2 + 1)^(3/2)*x), x)","F",0
666,1,42,0,0.954332," ","integrate(arccos(x)/x^4/(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{2 \, \sqrt{-x^{2} + 1}}{x} + \frac{\sqrt{-x^{2} + 1}}{x^{3}}\right)} \arccos\left(x\right) + \frac{1}{6 \, x^{2}} - \frac{2}{3} \, \log\left(x\right)"," ",0,"-1/3*(2*sqrt(-x^2 + 1)/x + sqrt(-x^2 + 1)/x^3)*arccos(x) + 1/6/x^2 - 2/3*log(x)","A",0
667,1,52,0,0.962856," ","integrate(x*arccos(x)^2*(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} \arccos\left(x\right)^{2} - \frac{2}{27} \, \sqrt{-x^{2} + 1} x^{2} + \frac{2}{9} \, {\left(x^{3} - 3 \, x\right)} \arccos\left(x\right) + \frac{14}{27} \, \sqrt{-x^{2} + 1}"," ",0,"-1/3*(-x^2 + 1)^(3/2)*arccos(x)^2 - 2/27*sqrt(-x^2 + 1)*x^2 + 2/9*(x^3 - 3*x)*arccos(x) + 14/27*sqrt(-x^2 + 1)","A",0
668,0,0,0,0.000000," ","integrate(x^2*arcsin(x)^3/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arcsin\left(x\right)^{3}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arcsin(x)^3/sqrt(-x^2 + 1), x)","F",0
669,1,26,0,0.956820," ","integrate(x*arctan(x)/(x^2+1)^2,x, algorithm=""maxima"")","\frac{x}{4 \, {\left(x^{2} + 1\right)}} - \frac{\arctan\left(x\right)}{2 \, {\left(x^{2} + 1\right)}} + \frac{1}{4} \, \arctan\left(x\right)"," ",0,"1/4*x/(x^2 + 1) - 1/2*arctan(x)/(x^2 + 1) + 1/4*arctan(x)","A",0
670,1,39,0,0.956522," ","integrate(x*arctan(x)/(x^2+1)^3,x, algorithm=""maxima"")","\frac{3 \, x^{3} + 5 \, x}{32 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}} - \frac{\arctan\left(x\right)}{4 \, {\left(x^{2} + 1\right)}^{2}} + \frac{3}{32} \, \arctan\left(x\right)"," ",0,"1/32*(3*x^3 + 5*x)/(x^4 + 2*x^2 + 1) - 1/4*arctan(x)/(x^2 + 1)^2 + 3/32*arctan(x)","A",0
671,1,24,0,0.999232," ","integrate(x^2*arctan(x)/(x^2+1),x, algorithm=""maxima"")","{\left(x - \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{1}{2} \, \arctan\left(x\right)^{2} - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"(x - arctan(x))*arctan(x) + 1/2*arctan(x)^2 - 1/2*log(x^2 + 1)","A",0
672,0,0,0,0.000000," ","integrate(x^3*arctan(x)/(x^2+1),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x^3*arctan(x)/(x^2 + 1), x)","F",0
673,1,40,0,0.976468," ","integrate(x^2*arctan(x)/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{x}{x^{2} + 1} - \arctan\left(x\right)\right)} \arctan\left(x\right) - \frac{{\left(x^{2} + 1\right)} \arctan\left(x\right)^{2} + 1}{4 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/2*(x/(x^2 + 1) - arctan(x))*arctan(x) - 1/4*((x^2 + 1)*arctan(x)^2 + 1)/(x^2 + 1)","A",0
674,0,0,0,0.000000," ","integrate(x^3*arctan(x)/(x^2+1)^2,x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(x\right)}{{\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctan(x)/(x^2 + 1)^2, x)","F",0
675,0,0,0,0.000000," ","integrate(x^5*arctan(x)/(x^2+1)^2,x, algorithm=""maxima"")","\int \frac{x^{5} \arctan\left(x\right)}{{\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^5*arctan(x)/(x^2 + 1)^2, x)","F",0
676,1,21,0,0.949230," ","integrate((x^2+1)*arctan(x)/x^2,x, algorithm=""maxima"")","{\left(x - \frac{1}{x}\right)} \arctan\left(x\right) - \log\left(x^{2} + 1\right) + \log\left(x\right)"," ",0,"(x - 1/x)*arctan(x) - log(x^2 + 1) + log(x)","A",0
677,1,31,0,0.947253," ","integrate((x^2+1)*arctan(x)/x^5,x, algorithm=""maxima"")","-\frac{3 \, x^{2} + 1}{12 \, x^{3}} - \frac{{\left(2 \, x^{2} + 1\right)} \arctan\left(x\right)}{4 \, x^{4}} - \frac{1}{4} \, \arctan\left(x\right)"," ",0,"-1/12*(3*x^2 + 1)/x^3 - 1/4*(2*x^2 + 1)*arctan(x)/x^4 - 1/4*arctan(x)","A",0
678,1,71,0,1.116006," ","integrate((x^2+1)^2*arctan(x)/x^5,x, algorithm=""maxima"")","-\frac{3 \, \pi x^{4} \log\left(x^{2} + 1\right) - 12 \, x^{4} \arctan\left(x\right) \log\left(x\right) + 6 i \, x^{4} {\rm Li}_2\left(i \, x + 1\right) - 6 i \, x^{4} {\rm Li}_2\left(-i \, x + 1\right) + 9 \, x^{3} + 3 \, {\left(3 \, x^{4} + 4 \, x^{2} + 1\right)} \arctan\left(x\right) + x}{12 \, x^{4}}"," ",0,"-1/12*(3*pi*x^4*log(x^2 + 1) - 12*x^4*arctan(x)*log(x) + 6*I*x^4*dilog(I*x + 1) - 6*I*x^4*dilog(-I*x + 1) + 9*x^3 + 3*(3*x^4 + 4*x^2 + 1)*arctan(x) + x)/x^4","A",0
679,1,27,0,0.991833," ","integrate(arctan(x)/x^2/(x^2+1),x, algorithm=""maxima"")","-{\left(\frac{1}{x} + \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{1}{2} \, \arctan\left(x\right)^{2} - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left(x\right)"," ",0,"-(1/x + arctan(x))*arctan(x) + 1/2*arctan(x)^2 - 1/2*log(x^2 + 1) + log(x)","A",0
680,1,36,0,0.963490," ","integrate(arctan(x)^2/x^3,x, algorithm=""maxima"")","-{\left(\frac{1}{x} + \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{1}{2} \, \arctan\left(x\right)^{2} - \frac{\arctan\left(x\right)^{2}}{2 \, x^{2}} - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left(x\right)"," ",0,"-(1/x + arctan(x))*arctan(x) + 1/2*arctan(x)^2 - 1/2*arctan(x)^2/x^2 - 1/2*log(x^2 + 1) + log(x)","A",0
681,1,71,0,0.971552," ","integrate((x^2+1)*arctan(x)^2/x^5,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{3 \, x^{2} + 1}{x^{3}} + 3 \, \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{3 \, x^{2} \arctan\left(x\right)^{2} - 2 \, x^{2} \log\left(x^{2} + 1\right) + 4 \, x^{2} \log\left(x\right) - 1}{12 \, x^{2}} - \frac{{\left(2 \, x^{2} + 1\right)} \arctan\left(x\right)^{2}}{4 \, x^{4}}"," ",0,"-1/6*((3*x^2 + 1)/x^3 + 3*arctan(x))*arctan(x) + 1/12*(3*x^2*arctan(x)^2 - 2*x^2*log(x^2 + 1) + 4*x^2*log(x) - 1)/x^2 - 1/4*(2*x^2 + 1)*arctan(x)^2/x^4","A",0
682,1,94,0,1.037254," ","integrate(x^3*arctan(x)^2/(x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{5 \, x^{3} + 3 \, x}{x^{4} + 2 \, x^{2} + 1} + 5 \, \arctan\left(x\right)\right)} \arctan\left(x\right) - \frac{{\left(2 \, x^{2} + 1\right)} \arctan\left(x\right)^{2}}{4 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}} - \frac{5 \, {\left(x^{4} + 2 \, x^{2} + 1\right)} \arctan\left(x\right)^{2} - 5 \, x^{2} - 4}{32 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/16*((5*x^3 + 3*x)/(x^4 + 2*x^2 + 1) + 5*arctan(x))*arctan(x) - 1/4*(2*x^2 + 1)*arctan(x)^2/(x^4 + 2*x^2 + 1) - 1/32*(5*(x^4 + 2*x^2 + 1)*arctan(x)^2 - 5*x^2 - 4)/(x^4 + 2*x^2 + 1)","A",0
683,0,0,0,0.000000," ","integrate(arcsec(x)*(x^2-1)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{x^{2} - 1} \operatorname{arcsec}\left(x\right)}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^2 - 1)*arcsec(x)/x^2, x)","F",0
684,0,0,0,0.000000," ","integrate((x^2-1)^(5/2)*arccsc(x)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(x^{2} - 1\right)}^{\frac{5}{2}} \operatorname{arccsc}\left(x\right)}{x^{3}}\,{d x}"," ",0,"integrate((x^2 - 1)^(5/2)*arccsc(x)/x^3, x)","F",0
685,1,27,0,0.991634," ","integrate(arcsec(x)*(x^2-1)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{{\left(x^{2} - 1\right)}^{\frac{3}{2}} \operatorname{arcsec}\left(x\right)}{3 \, x^{3}} + \frac{3 \, x^{2} - 1}{9 \, x^{3}}"," ",0,"1/3*(x^2 - 1)^(3/2)*arcsec(x)/x^3 + 1/9*(3*x^2 - 1)/x^3","A",0
686,1,48,0,0.643338," ","integrate(arcsec(x)/(x^2-1)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{x^{2} - 1}} - \frac{x}{{\left(x^{2} - 1\right)}^{\frac{3}{2}}}\right)} \operatorname{arcsec}\left(x\right) - \frac{x}{6 \, {\left(x^{2} - 1\right)}} + \frac{5}{12} \, \log\left(x + 1\right) - \frac{5}{12} \, \log\left(x - 1\right)"," ",0,"1/3*(2*x/sqrt(x^2 - 1) - x/(x^2 - 1)^(3/2))*arcsec(x) - 1/6*x/(x^2 - 1) + 5/12*log(x + 1) - 5/12*log(x - 1)","A",0
687,1,46,0,0.644670," ","integrate(x^2*arcsec(x)/(x^2-1)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{x}{\sqrt{x^{2} - 1}} + \frac{x}{{\left(x^{2} - 1\right)}^{\frac{3}{2}}}\right)} \operatorname{arcsec}\left(x\right) - \frac{x}{6 \, {\left(x^{2} - 1\right)}} - \frac{1}{12} \, \log\left(x + 1\right) + \frac{1}{12} \, \log\left(x - 1\right)"," ",0,"-1/3*(x/sqrt(x^2 - 1) + x/(x^2 - 1)^(3/2))*arcsec(x) - 1/6*x/(x^2 - 1) - 1/12*log(x + 1) + 1/12*log(x - 1)","A",0
688,0,0,0,0.000000," ","integrate(x^3*arcsec(x)/(x^2-1)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{arcsec}\left(x\right)}{{\left(x^{2} - 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3*arcsec(x)/(x^2 - 1)^(5/2), x)","F",0
689,0,0,0,0.000000," ","integrate(x^6*arcsec(x)/(x^2-1)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{6} \operatorname{arcsec}\left(x\right)}{{\left(x^{2} - 1\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^6*arcsec(x)/(x^2 - 1)^(5/2), x)","F",0
690,1,17,0,1.027274," ","integrate(arcsec(x)/x^2/(x^2-1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{x^{2} - 1} \operatorname{arcsec}\left(x\right)}{x} + \frac{1}{x}"," ",0,"sqrt(x^2 - 1)*arcsec(x)/x + 1/x","A",0
691,1,123,0,2.207092," ","integrate(arccsc(x)/x^2/(x^2-1)^(5/2),x, algorithm=""maxima"")","\frac{32 \, x^{4} \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) - {\left(x^{3} - x\right)} \sqrt{x + 1} \sqrt{x - 1} {\left(\frac{2 \, {\left(5 \, x^{2} - 6\right)}}{x^{3} - x} + 11 \, \log\left(x + 1\right) - 11 \, \log\left(x - 1\right)\right)} - 48 \, x^{2} \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) + 12 \, \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right)}{12 \, {\left(x^{3} - x\right)} \sqrt{x + 1} \sqrt{x - 1}}"," ",0,"1/12*(32*x^4*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) - (x^3 - x)*sqrt(x + 1)*sqrt(x - 1)*(2*(5*x^2 - 6)/(x^3 - x) + 11*log(x + 1) - 11*log(x - 1)) - 48*x^2*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) + 12*arctan2(1, sqrt(x + 1)*sqrt(x - 1)))/((x^3 - x)*sqrt(x + 1)*sqrt(x - 1))","B",0
692,1,58,0,1.030194," ","integrate(arccsc(x)^4/x^2/(x^2-1)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{x^{2} - 1} \operatorname{arccsc}\left(x\right)^{4}}{x} - 12 \, \sqrt{-\frac{1}{x^{2}} + 1} \operatorname{arccsc}\left(x\right)^{2} - \frac{4 \, \operatorname{arccsc}\left(x\right)^{3}}{x} + 24 \, \sqrt{-\frac{1}{x^{2}} + 1} + \frac{24 \, \operatorname{arccsc}\left(x\right)}{x}"," ",0,"sqrt(x^2 - 1)*arccsc(x)^4/x - 12*sqrt(-1/x^2 + 1)*arccsc(x)^2 - 4*arccsc(x)^3/x + 24*sqrt(-1/x^2 + 1) + 24*arccsc(x)/x","A",0
693,0,0,0,0.000000," ","integrate((x^2-1)^(3/2)*arcsec(x)^2/x^5,x, algorithm=""maxima"")","\int \frac{{\left(x^{2} - 1\right)}^{\frac{3}{2}} \operatorname{arcsec}\left(x\right)^{2}}{x^{5}}\,{d x}"," ",0,"integrate((x^2 - 1)^(3/2)*arcsec(x)^2/x^5, x)","F",0
694,1,93,0,2.185108," ","integrate(arcsec(x)^3*(x^2-1)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{{\left(x^{2} - 1\right)}^{\frac{3}{2}} \operatorname{arcsec}\left(x\right)^{3}}{3 \, x^{3}} + \frac{{\left(3 \, x^{2} - 1\right)} \operatorname{arcsec}\left(x\right)^{2}}{3 \, x^{3}} - \frac{2 \, {\left({\left(21 \, x^{2} - 1\right)} \sqrt{x + 1} \sqrt{x - 1} + 3 \, {\left(7 \, x^{4} - 8 \, x^{2} + 1\right)} \arctan\left(\sqrt{x + 1} \sqrt{x - 1}\right)\right)}}{27 \, \sqrt{x + 1} \sqrt{x - 1} x^{3}}"," ",0,"1/3*(x^2 - 1)^(3/2)*arcsec(x)^3/x^3 + 1/3*(3*x^2 - 1)*arcsec(x)^2/x^3 - 2/27*((21*x^2 - 1)*sqrt(x + 1)*sqrt(x - 1) + 3*(7*x^4 - 8*x^2 + 1)*arctan(sqrt(x + 1)*sqrt(x - 1)))/(sqrt(x + 1)*sqrt(x - 1)*x^3)","A",0
695,1,103,0,1.008393," ","integrate(arcsin(((-a+x)/(a+x))^(1/2)),x, algorithm=""maxima"")","a {\left(\frac{2 \, \arcsin\left(\sqrt{-\frac{a - x}{a + x}}\right)}{\frac{a - x}{a + x} + 1} + \frac{\sqrt{\frac{a - x}{a + x} + 1}}{\sqrt{-\frac{a - x}{a + x}} + 1} + \frac{\sqrt{\frac{a - x}{a + x} + 1}}{\sqrt{-\frac{a - x}{a + x}} - 1}\right)}"," ",0,"a*(2*arcsin(sqrt(-(a - x)/(a + x)))/((a - x)/(a + x) + 1) + sqrt((a - x)/(a + x) + 1)/(sqrt(-(a - x)/(a + x)) + 1) + sqrt((a - x)/(a + x) + 1)/(sqrt(-(a - x)/(a + x)) - 1))","B",0
696,1,89,0,0.981933," ","integrate(arctan(((-a+x)/(a+x))^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{4 \, \arctan\left(\sqrt{-\frac{a - x}{a + x}}\right)}{\frac{a - x}{a + x} + 1} - 2 \, \arctan\left(\sqrt{-\frac{a - x}{a + x}}\right) - \log\left(\sqrt{-\frac{a - x}{a + x}} + 1\right) + \log\left(\sqrt{-\frac{a - x}{a + x}} - 1\right)\right)}"," ",0,"1/2*a*(4*arctan(sqrt(-(a - x)/(a + x)))/((a - x)/(a + x) + 1) - 2*arctan(sqrt(-(a - x)/(a + x))) - log(sqrt(-(a - x)/(a + x)) + 1) + log(sqrt(-(a - x)/(a + x)) - 1))","B",0
697,1,31,0,0.957954," ","integrate(arctan(x)/(1+x)^3,x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(x + 1\right)}} - \frac{\arctan\left(x\right)}{2 \, {\left(x + 1\right)}^{2}} - \frac{1}{8} \, \log\left(x^{2} + 1\right) + \frac{1}{4} \, \log\left(x + 1\right)"," ",0,"-1/4/(x + 1) - 1/2*arctan(x)/(x + 1)^2 - 1/8*log(x^2 + 1) + 1/4*log(x + 1)","A",0
698,1,118,0,1.199800," ","integrate(-arctan(a-x)/(a+x),x, algorithm=""maxima"")","-\frac{1}{2} \, \arctan\left(\frac{a + x}{4 \, a^{2} + 1}, \frac{2 \, {\left(a^{2} + a x\right)}}{4 \, a^{2} + 1}\right) \log\left(a^{2} - 2 \, a x + x^{2} + 1\right) + \frac{1}{2} \, \arctan\left(-a + x\right) \log\left(\frac{a^{2} + 2 \, a x + x^{2}}{4 \, a^{2} + 1}\right) - \frac{1}{2} i \, {\rm Li}_2\left(-\frac{-i \, a + i \, x + 1}{2 i \, a - 1}\right) + \frac{1}{2} i \, {\rm Li}_2\left(-\frac{-i \, a + i \, x - 1}{2 i \, a + 1}\right)"," ",0,"-1/2*arctan2((a + x)/(4*a^2 + 1), 2*(a^2 + a*x)/(4*a^2 + 1))*log(a^2 - 2*a*x + x^2 + 1) + 1/2*arctan(-a + x)*log((a^2 + 2*a*x + x^2)/(4*a^2 + 1)) - 1/2*I*dilog(-(-I*a + I*x + 1)/(2*I*a - 1)) + 1/2*I*dilog(-(-I*a + I*x - 1)/(2*I*a + 1))","A",0
699,0,0,0,0.000000," ","integrate(arcsin((-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(\sqrt{-x^{2} + 1}\right)}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(arcsin(sqrt(-x^2 + 1))/sqrt(-x^2 + 1), x)","F",0
700,1,25,0,0.473093," ","integrate(x*arctan((x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""maxima"")","\sqrt{x^{2} + 1} \arctan\left(\sqrt{x^{2} + 1}\right) - \frac{1}{2} \, \log\left(x^{2} + 2\right)"," ",0,"sqrt(x^2 + 1)*arctan(sqrt(x^2 + 1)) - 1/2*log(x^2 + 2)","A",0
701,0,0,0,0.000000," ","integrate(arcsin(x)/(1-x)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{1}{8} \, {\left(7 \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{x + 1}}{\sqrt{2} + \sqrt{x + 1}}\right) + 16 \, \sqrt{x + 1} - \frac{4 \, \sqrt{x + 1}}{x - 1}\right)} {\left(x - 1\right)} \sqrt{-x + 1} + \arctan\left(x, \sqrt{x + 1} \sqrt{-x + 1}\right)\right)}}{3 \, {\left(x - 1\right)} \sqrt{-x + 1}}"," ",0,"-2/3*(3*(x - 1)*sqrt(-x + 1)*integrate(1/3*sqrt(x + 1)*x^2/(x^5 - x^4 - x^3 + x^2 + (x^3 - x^2 - x + 1)*e^(log(x + 1) + log(-x + 1))), x) + arctan2(x, sqrt(x + 1)*sqrt(-x + 1)))/((x - 1)*sqrt(-x + 1))","F",0
702,1,116,0,3.438693," ","integrate((-1+x)^(5/2)*arccsc(x),x, algorithm=""maxima"")","\frac{4}{35} \, {\left(x + 1\right)}^{\frac{5}{2}} - \frac{20}{21} \, {\left(x + 1\right)}^{\frac{3}{2}} + \frac{2}{7} \, {\left(x^{3} \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) - 3 \, x^{2} \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) + 3 \, x \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right) - \arctan\left(1, \sqrt{x + 1} \sqrt{x - 1}\right)\right)} \sqrt{x - 1} + 4 \, \sqrt{x + 1} + \frac{2}{7} \, \log\left(\sqrt{x + 1} + 1\right) - \frac{2}{7} \, \log\left(\sqrt{x + 1} - 1\right)"," ",0,"4/35*(x + 1)^(5/2) - 20/21*(x + 1)^(3/2) + 2/7*(x^3*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) - 3*x^2*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) + 3*x*arctan2(1, sqrt(x + 1)*sqrt(x - 1)) - arctan2(1, sqrt(x + 1)*sqrt(x - 1)))*sqrt(x - 1) + 4*sqrt(x + 1) + 2/7*log(sqrt(x + 1) + 1) - 2/7*log(sqrt(x + 1) - 1)","A",0
703,0,0,0,0.000000," ","integrate(arcsin(sinh(x))*sech(x)^4,x, algorithm=""maxima"")","-\frac{4 \, {\left(3 \, e^{\left(2 \, x\right)} + 1\right)} \arctan\left(e^{\left(2 \, x\right)} - 1, \sqrt{e^{\left(2 \, x\right)} + 2 \, e^{x} - 1} \sqrt{-e^{\left(2 \, x\right)} + 2 \, e^{x} + 1}\right) + 16 \, {\left(e^{\left(6 \, x\right)} + 3 \, e^{\left(4 \, x\right)} + 3 \, e^{\left(2 \, x\right)} + 1\right)} \int -\frac{{\left(3 \, e^{\left(4 \, x\right)} + e^{\left(2 \, x\right)}\right)} e^{\left(\frac{1}{2} \, \log\left(e^{\left(2 \, x\right)} + 2 \, e^{x} - 1\right) + \frac{1}{2} \, \log\left(-e^{\left(2 \, x\right)} + 2 \, e^{x} + 1\right)\right)}}{{\left(e^{\left(8 \, x\right)} - 4 \, e^{\left(6 \, x\right)} - 10 \, e^{\left(4 \, x\right)} - 4 \, e^{\left(2 \, x\right)} + 1\right)} {\left(e^{\left(2 \, x\right)} + 2 \, e^{x} - 1\right)} {\left(e^{\left(2 \, x\right)} - 2 \, e^{x} - 1\right)} - e^{\left(12 \, x\right)} + 6 \, e^{\left(10 \, x\right)} + e^{\left(8 \, x\right)} - 12 \, e^{\left(6 \, x\right)} + e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} - 1}\,{d x}}{3 \, {\left(e^{\left(6 \, x\right)} + 3 \, e^{\left(4 \, x\right)} + 3 \, e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"-1/3*(4*(3*e^(2*x) + 1)*arctan2(e^(2*x) - 1, sqrt(e^(2*x) + 2*e^x - 1)*sqrt(-e^(2*x) + 2*e^x + 1)) + 3*(e^(6*x) + 3*e^(4*x) + 3*e^(2*x) + 1)*integrate(16/3*(3*e^(4*x) + e^(2*x))*e^(1/2*log(e^(2*x) + 2*e^x - 1) + 1/2*log(-e^(2*x) + 2*e^x + 1))/((e^(8*x) - 4*e^(6*x) - 10*e^(4*x) - 4*e^(2*x) + 1)*e^(log(e^(2*x) + 2*e^x - 1) + log(-e^(2*x) + 2*e^x + 1)) + e^(12*x) - 6*e^(10*x) - e^(8*x) + 12*e^(6*x) - e^(4*x) - 6*e^(2*x) + 1), x))/(e^(6*x) + 3*e^(4*x) + 3*e^(2*x) + 1)","F",0
704,1,54,0,1.010061," ","integrate(arccot(cosh(x))*cosh(x)/sinh(x)^4,x, algorithm=""maxima"")","-\frac{1}{24} \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(-2 \, x\right)} - 3}{2 \, \sqrt{2} + e^{\left(-2 \, x\right)} + 3}\right) - \frac{1}{3 \, {\left(e^{\left(-2 \, x\right)} - 1\right)}} - \frac{\operatorname{arccot}\left(\cosh\left(x\right)\right)}{3 \, \sinh\left(x\right)^{3}}"," ",0,"-1/24*sqrt(2)*log(-(2*sqrt(2) - e^(-2*x) - 3)/(2*sqrt(2) + e^(-2*x) + 3)) - 1/3/(e^(-2*x) - 1) - 1/3*arccot(cosh(x))/sinh(x)^3","A",0
705,1,16,0,1.000711," ","integrate(exp(x)*arcsin(tanh(x)),x, algorithm=""maxima"")","\arcsin\left(\tanh\left(x\right)\right) e^{x} - \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"arcsin(tanh(x))*e^x - log(e^(2*x) + 1)","A",0
