1,1,33,0,1.012415," ","integrate(1/(-b^2*x^2+a^2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right)}{2 \, a b} - \frac{\log\left({\left| b x - a \right|}\right)}{2 \, a b}"," ",0,"1/2*log(abs(b*x + a))/(a*b) - 1/2*log(abs(b*x - a))/(a*b)","B",0
2,1,14,0,0.922087," ","integrate(1/(b^2*x^2+a^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b x}{a}\right)}{a b}"," ",0,"arctan(b*x/a)/(a*b)","A",0
3,-2,0,0,0.000000," ","integrate(sec(2*a*x),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)2/a*1/2*(-1/8*ln(abs(sin(2*a*x)+1/sin(2*a*x)-2))+1/8*ln(abs(sin(2*a*x)+1/sin(2*a*x)+2)))","F(-2)",0
4,1,23,0,0.845204," ","integrate(1/4/sin(1/3*x),x, algorithm=""giac"")","-\frac{3}{8} \, \log\left(3 \, \cos\left(\frac{1}{3} \, x\right) + 3\right) + \frac{3}{8} \, \log\left(-3 \, \cos\left(\frac{1}{3} \, x\right) + 3\right)"," ",0,"-3/8*log(3*cos(1/3*x) + 3) + 3/8*log(-3*cos(1/3*x) + 3)","B",0
5,1,29,0,0.995229," ","integrate(-1/cos(1/4*pi+2*x),x, algorithm=""giac"")","-\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
6,1,4,0,0.925057," ","integrate(sec(x)*tan(x),x, algorithm=""giac"")","\frac{1}{\cos\left(x\right)}"," ",0,"1/cos(x)","A",0
7,1,6,0,0.994944," ","integrate(cot(x)*csc(x),x, algorithm=""giac"")","-\frac{1}{\sin\left(x\right)}"," ",0,"-1/sin(x)","A",0
8,1,4,0,1.009179," ","integrate(tan(x)/sin(2*x),x, algorithm=""giac"")","\frac{1}{2} \, \tan\left(x\right)"," ",0,"1/2*tan(x)","A",0
9,1,30,0,0.852717," ","integrate(1/(1+cos(x)),x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(x^{2} + 1\right)} {\left(\frac{x^{2} - 1}{x^{2} + 1} - 1\right)}}"," ",0,"-2*tan(1/2*x)/((x^2 + 1)*((x^2 - 1)/(x^2 + 1) - 1))","B",0
10,1,8,0,1.075063," ","integrate(1/(1-cos(x)),x, algorithm=""giac"")","-\frac{1}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-1/tan(1/2*x)","A",0
11,1,14,0,1.083863," ","integrate(sin(x)/(a-b*cos(x)),x, algorithm=""giac"")","\frac{\log\left({\left| b \cos\left(x\right) - a \right|}\right)}{b}"," ",0,"log(abs(b*cos(x) - a))/b","A",0
12,1,15,0,0.884979," ","integrate(cos(x)/(a^2+b^2*sin(x)^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{b \sin\left(x\right)}{a}\right)}{a b}"," ",0,"arctan(b*sin(x)/a)/(a*b)","A",0
13,1,35,0,1.093210," ","integrate(cos(x)/(a^2-b^2*sin(x)^2),x, algorithm=""giac"")","\frac{\log\left({\left| b \sin\left(x\right) + a \right|}\right)}{2 \, a b} - \frac{\log\left({\left| b \sin\left(x\right) - a \right|}\right)}{2 \, a b}"," ",0,"1/2*log(abs(b*sin(x) + a))/(a*b) - 1/2*log(abs(b*sin(x) - a))/(a*b)","B",0
14,1,17,0,1.039873," ","integrate(sin(2*x)/(a^2+b^2*sin(x)^2),x, algorithm=""giac"")","\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
15,1,21,0,0.934000," ","integrate(sin(2*x)/(a^2-b^2*sin(x)^2),x, algorithm=""giac"")","-\frac{\log\left({\left| b^{2} \sin\left(x\right)^{2} - a^{2} \right|}\right)}{b^{2}}"," ",0,"-log(abs(b^2*sin(x)^2 - a^2))/b^2","A",0
16,1,18,0,0.919067," ","integrate(sin(2*x)/(a^2+b^2*cos(x)^2),x, algorithm=""giac"")","-\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
17,1,20,0,0.958964," ","integrate(sin(2*x)/(a^2-b^2*cos(x)^2),x, algorithm=""giac"")","\frac{\log\left({\left| b^{2} \cos\left(x\right)^{2} - a^{2} \right|}\right)}{b^{2}}"," ",0,"log(abs(b^2*cos(x)^2 - a^2))/b^2","A",0
18,1,46,0,0.833227," ","integrate(1/(4-cos(x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} {\left(x + \arctan\left(-\frac{\sqrt{3} \sin\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right)}{\sqrt{3} \cos\left(2 \, x\right) + \sqrt{3} - 2 \, \cos\left(2 \, x\right) + 2}\right)\right)}"," ",0,"1/6*sqrt(3)*(x + arctan(-(sqrt(3)*sin(2*x) - 2*sin(2*x))/(sqrt(3)*cos(2*x) + sqrt(3) - 2*cos(2*x) + 2)))","A",0
19,1,16,0,0.794036," ","integrate(exp(x)/(-1+exp(2*x)),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(e^{x} + 1\right) + \frac{1}{2} \, \log\left({\left| e^{x} - 1 \right|}\right)"," ",0,"-1/2*log(e^x + 1) + 1/2*log(abs(e^x - 1))","B",0
20,1,4,0,0.850241," ","integrate(1/x/log(x),x, algorithm=""giac"")","\log\left({\left| \log\left(x\right) \right|}\right)"," ",0,"log(abs(log(x)))","A",0
21,1,3,0,0.933552," ","integrate(1/x/(1+log(x)^2),x, algorithm=""giac"")","\arctan\left(\log\left(x\right)\right)"," ",0,"arctan(log(x))","A",0
22,1,22,0,0.999284," ","integrate(1/x/(1-log(x)),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\frac{1}{4} \, \pi^{2} {\left(\mathrm{sgn}\left(x\right) - 1\right)}^{2} + {\left(\log\left({\left| x \right|}\right) - 1\right)}^{2}\right)"," ",0,"-1/2*log(1/4*pi^2*(sgn(x) - 1)^2 + (log(abs(x)) - 1)^2)","B",0
23,1,9,0,0.877929," ","integrate(1/x/(1+log(x/a)),x, algorithm=""giac"")","\log\left(\log\left(\frac{x}{a}\right) + 1\right)"," ",0,"log(log(x/a) + 1)","A",0
24,1,23,0,1.001950," ","integrate((1+x-x^(1/2))^2/x^2,x, algorithm=""giac"")","x - 4 \, \sqrt{x} + \frac{4 \, \sqrt{x} - 1}{x} + 3 \, \log\left({\left| x \right|}\right)"," ",0,"x - 4*sqrt(x) + (4*sqrt(x) - 1)/x + 3*log(abs(x))","A",0
25,1,21,0,0.972585," ","integrate((2-x^(2/3))*(x+x^(1/2))/x^(3/2),x, algorithm=""giac"")","-\frac{6}{7} \, x^{\frac{7}{6}} - \frac{3}{2} \, x^{\frac{2}{3}} + 4 \, \sqrt{x} + 2 \, \log\left({\left| x \right|}\right)"," ",0,"-6/7*x^(7/6) - 3/2*x^(2/3) + 4*sqrt(x) + 2*log(abs(x))","A",0
26,1,11,0,0.888568," ","integrate((-1+2*x)/(3+2*x),x, algorithm=""giac"")","x - 2 \, \log\left({\left| 2 \, x + 3 \right|}\right)"," ",0,"x - 2*log(abs(2*x + 3))","A",0
27,1,37,0,0.961451," ","integrate((-5+2*x)/(3*x^2-2),x, algorithm=""giac"")","\frac{1}{12} \, {\left(5 \, \sqrt{6} + 4\right)} \log\left({\left| x + \frac{1}{3} \, \sqrt{6} \right|}\right) - \frac{1}{12} \, {\left(5 \, \sqrt{6} - 4\right)} \log\left({\left| x - \frac{1}{3} \, \sqrt{6} \right|}\right)"," ",0,"1/12*(5*sqrt(6) + 4)*log(abs(x + 1/3*sqrt(6))) - 1/12*(5*sqrt(6) - 4)*log(abs(x - 1/3*sqrt(6)))","A",0
28,1,21,0,0.850661," ","integrate((-5+2*x)/(3*x^2+2),x, algorithm=""giac"")","-\frac{5}{6} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x\right) + \frac{1}{3} \, \log\left(x^{2} + \frac{2}{3}\right)"," ",0,"-5/6*sqrt(6)*arctan(1/2*sqrt(6)*x) + 1/3*log(x^2 + 2/3)","A",0
29,1,13,0,1.235028," ","integrate(sin(1/4*x)*sin(x),x, algorithm=""giac"")","-\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
30,1,11,0,0.853805," ","integrate(cos(3*x)*cos(4*x),x, algorithm=""giac"")","\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
31,1,18,0,0.952453," ","integrate(-tan(x)*tan(a-x),x, algorithm=""giac"")","-x + \frac{\log\left({\left| \tan\left(a\right) \tan\left(x\right) + 1 \right|}\right)}{\tan\left(a\right)}"," ",0,"-x + log(abs(tan(a)*tan(x) + 1))/tan(a)","A",0
32,1,10,0,0.942741," ","integrate(sin(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, x - \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x - 1/4*sin(2*x)","A",0
33,1,10,0,0.826326," ","integrate(cos(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x + 1/4*sin(2*x)","A",0
34,1,6,0,0.944761," ","integrate(cos(x)^3*sin(x),x, algorithm=""giac"")","-\frac{1}{4} \, \cos\left(x\right)^{4}"," ",0,"-1/4*cos(x)^4","A",0
35,1,14,0,1.109402," ","integrate(cos(x)^3/sin(x)^4,x, algorithm=""giac"")","\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
36,1,9,0,1.018054," ","integrate(1/cos(x)^2/sin(x)^2,x, algorithm=""giac"")","-\frac{1}{\tan\left(x\right)} + \tan\left(x\right)"," ",0,"-1/tan(x) + tan(x)","A",0
37,1,18,0,1.188414," ","integrate(cot(3/4*x)^2,x, algorithm=""giac"")","-x - \frac{2}{3 \, \tan\left(\frac{3}{8} \, x\right)} + \frac{2}{3} \, \tan\left(\frac{3}{8} \, x\right)"," ",0,"-x - 2/3/tan(3/8*x) + 2/3*tan(3/8*x)","A",0
38,1,22,0,1.028268," ","integrate((1+tan(2*x))^2,x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\frac{4}{\tan\left(2 \, x\right)^{2} + 1}\right) + \frac{1}{2} \, \tan\left(2 \, x\right)"," ",0,"-1/2*log(4/(tan(2*x)^2 + 1)) + 1/2*tan(2*x)","A",0
39,1,12,0,0.833865," ","integrate((-cot(x)+tan(x))^2,x, algorithm=""giac"")","-4 \, x - \frac{1}{\tan\left(x\right)} + \tan\left(x\right)"," ",0,"-4*x - 1/tan(x) + tan(x)","A",0
40,1,14,0,0.785094," ","integrate((-sec(x)+tan(x))^2,x, algorithm=""giac"")","-x - \frac{4}{\tan\left(\frac{1}{2} \, x\right) + 1}"," ",0,"-x - 4/(tan(1/2*x) + 1)","A",0
41,1,12,0,1.082602," ","integrate(sin(x)/(1+sin(x)),x, algorithm=""giac"")","x + \frac{2}{\tan\left(\frac{1}{2} \, x\right) + 1}"," ",0,"x + 2/(tan(1/2*x) + 1)","A",0
42,1,12,0,1.012535," ","integrate(cos(x)/(1-cos(x)),x, algorithm=""giac"")","-x - \frac{1}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-x - 1/tan(1/2*x)","A",0
43,1,18,0,0.917751," ","integrate((-1+exp(1/2*x))^3/exp(1/2*x),x, algorithm=""giac"")","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
44,1,15,0,0.845681," ","integrate(1/(x^2-6*x+5),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left({\left| x - 1 \right|}\right) + \frac{1}{4} \, \log\left({\left| x - 5 \right|}\right)"," ",0,"-1/4*log(abs(x - 1)) + 1/4*log(abs(x - 5))","A",0
45,1,10,0,0.990615," ","integrate(x^2/(x^6-6*x^3+13),x, algorithm=""giac"")","\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
46,1,44,0,0.940259," ","integrate((2+x)/(x^2-4*x-1),x, algorithm=""giac"")","\frac{2}{5} \, \sqrt{5} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{5} - 4 \right|}}{{\left| 2 \, x + 2 \, \sqrt{5} - 4 \right|}}\right) + \frac{1}{2} \, \log\left({\left| x^{2} - 4 \, x - 1 \right|}\right)"," ",0,"2/5*sqrt(5)*log(abs(2*x - 2*sqrt(5) - 4)/abs(2*x + 2*sqrt(5) - 4)) + 1/2*log(abs(x^2 - 4*x - 1))","A",0
47,1,25,0,1.048837," ","integrate(1/(1+(1+x)^(1/3)),x, algorithm=""giac"")","\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
48,1,18,0,0.959251," ","integrate(1/(a*x+b)/x^(1/2),x, algorithm=""giac"")","\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
49,1,19,0,1.027658," ","integrate(x^3*(x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{2} + 1\right)}^{\frac{5}{2}} - \frac{1}{3} \, {\left(x^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/5*(x^2 + 1)^(5/2) - 1/3*(x^2 + 1)^(3/2)","A",0
50,1,10,0,1.058230," ","integrate(x/(a^4-x^4)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \arcsin\left(\frac{x^{2}}{a^{2}}\right)"," ",0,"1/2*arcsin(x^2/a^2)","A",0
51,1,20,0,0.826059," ","integrate(1/x/(-a^2+x^2)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{-a^{2} + x^{2}}}{a}\right)}{a}"," ",0,"arctan(sqrt(-a^2 + x^2)/a)/a","A",0
52,1,43,0,0.853325," ","integrate(1/x/(a^2-x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| a + \sqrt{a^{2} - x^{2}} \right|}\right)}{2 \, a} + \frac{\log\left({\left| -a + \sqrt{a^{2} - x^{2}} \right|}\right)}{2 \, a}"," ",0,"-1/2*log(abs(a + sqrt(a^2 - x^2)))/a + 1/2*log(abs(-a + sqrt(a^2 - x^2)))/a","B",0
53,1,37,0,1.073776," ","integrate(1/x/(a^2+x^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left(a + \sqrt{a^{2} + x^{2}}\right)}{2 \, a} + \frac{\log\left(-a + \sqrt{a^{2} + x^{2}}\right)}{2 \, a}"," ",0,"-1/2*log(a + sqrt(a^2 + x^2))/a + 1/2*log(-a + sqrt(a^2 + x^2))/a","A",0
54,1,6,0,1.076674," ","integrate(1/(-x^2+x+2)^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{2}{3} \, x - \frac{1}{3}\right)"," ",0,"arcsin(2/3*x - 1/3)","A",0
55,1,33,0,1.080837," ","integrate(1/(3*x^2-4*x+5)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \log\left(-\sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} - 4 \, x + 5}\right)} + 2\right)"," ",0,"-1/3*sqrt(3)*log(-sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 - 4*x + 5)) + 2)","B",0
56,1,6,0,0.863254," ","integrate(1/(-x^2+x)^(1/2),x, algorithm=""giac"")","\arcsin\left(2 \, x - 1\right)"," ",0,"arcsin(2*x - 1)","A",0
57,1,21,0,0.929995," ","integrate((1+2*x)/(-x^2+x+2)^(1/2),x, algorithm=""giac"")","-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
58,1,71,0,1.193008," ","integrate(1/x/(-x^2+x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} + \frac{2 \, {\left(2 \, \sqrt{-x^{2} + x + 2} - 3\right)}}{2 \, x - 1} - 6 \right|}}{{\left| 4 \, \sqrt{2} + \frac{2 \, {\left(2 \, \sqrt{-x^{2} + x + 2} - 3\right)}}{2 \, x - 1} - 6 \right|}}\right)"," ",0,"-1/2*sqrt(2)*log(abs(-4*sqrt(2) + 2*(2*sqrt(-x^2 + x + 2) - 3)/(2*x - 1) - 6)/abs(4*sqrt(2) + 2*(2*sqrt(-x^2 + x + 2) - 3)/(2*x - 1) - 6))","B",0
59,1,28,0,0.780399," ","integrate(1/(-2+x)/(-x^2+x+2)^(1/2),x, algorithm=""giac"")","-\frac{4}{3 \, {\left(\frac{2 \, \sqrt{-x^{2} + x + 2} - 3}{2 \, x - 1} + 1\right)}}"," ",0,"-4/3/((2*sqrt(-x^2 + x + 2) - 3)/(2*x - 1) + 1)","A",0
60,1,31,0,1.064931," ","integrate((2+3*sin(x))/(1-cos(x))/sin(x),x, algorithm=""giac"")","-\frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, x\right) + 1}{2 \, \tan\left(\frac{1}{2} \, x\right)^{2}} + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"-1/2*(3*tan(1/2*x)^2 + 6*tan(1/2*x) + 1)/tan(1/2*x)^2 + log(abs(tan(1/2*x)))","A",0
61,1,46,0,0.820780," ","integrate(1/(2+3*cos(x)^2),x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{10} {\left(x + \arctan\left(-\frac{\sqrt{10} \sin\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right)}{\sqrt{10} \cos\left(2 \, x\right) + \sqrt{10} - 2 \, \cos\left(2 \, x\right) + 2}\right)\right)}"," ",0,"1/10*sqrt(10)*(x + arctan(-(sqrt(10)*sin(2*x) - 2*sin(2*x))/(sqrt(10)*cos(2*x) + sqrt(10) - 2*cos(2*x) + 2)))","A",0
62,1,11,0,0.959464," ","integrate((1-tan(x))/sin(2*x),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| \tan\left(x\right) \right|}\right) - \frac{1}{2} \, \tan\left(x\right)"," ",0,"1/2*log(abs(tan(x))) - 1/2*tan(x)","A",0
63,1,17,0,1.098360," ","integrate((1+tan(x)^2)/(1-tan(x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| \tan\left(x\right) + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| \tan\left(x\right) - 1 \right|}\right)"," ",0,"1/2*log(abs(tan(x) + 1)) - 1/2*log(abs(tan(x) - 1))","A",0
64,1,14,0,0.999235," ","integrate((a^2-4*cos(x)^2)^(3/4)*sin(2*x),x, algorithm=""giac"")","\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
65,1,14,0,0.924582," ","integrate(sin(2*x)/(a^2-4*sin(x)^2)^(1/3),x, algorithm=""giac"")","-\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
66,1,15,0,0.837515," ","integrate(1/(-1+a^(2*x))^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\sqrt{a^{2 \, x} - 1}\right)}{\log\left(a\right)}"," ",0,"arctan(sqrt(a^(2*x) - 1))/log(a)","A",0
67,1,16,0,0.932913," ","integrate(exp(1/2*x)/(-1+exp(x))^(1/2),x, algorithm=""giac"")","-2 \, \log\left(-\sqrt{e^{x} - 1} + e^{\left(\frac{1}{2} \, x\right)}\right)"," ",0,"-2*log(-sqrt(e^x - 1) + e^(1/2*x))","A",0
68,1,12,0,0.951230," ","integrate(arctan(x)^n/(x^2+1),x, algorithm=""giac"")","\frac{\arctan\left(x\right)^{n + 1}}{n + 1}"," ",0,"arctan(x)^(n + 1)/(n + 1)","A",0
69,1,15,0,1.078904," ","integrate(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left| a \right|} \arcsin\left(\frac{x}{a}\right)^{\frac{5}{2}}}{5 \, a}"," ",0,"2/5*abs(a)*arcsin(x/a)^(5/2)/a","A",0
70,1,6,0,0.926705," ","integrate(1/arccos(x)^3/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2 \, \arccos\left(x\right)^{2}}"," ",0,"1/2/arccos(x)^2","A",0
71,1,22,0,0.876230," ","integrate(x*log(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} \log\left(x\right)^{2} - \frac{1}{2} \, x^{2} \log\left(x\right) + \frac{1}{4} \, x^{2}"," ",0,"1/2*x^2*log(x)^2 - 1/2*x^2*log(x) + 1/4*x^2","A",0
72,1,13,0,0.794630," ","integrate(log(x)/x^5,x, algorithm=""giac"")","-\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
73,1,70,0,1.047630," ","integrate(x^2*log((-1+x)/x),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(x - 1\right)}}{x} - 3}{6 \, {\left(\frac{x - 1}{x} - 1\right)}^{2}} - \frac{\log\left(\frac{x - 1}{x}\right)}{3 \, {\left(\frac{x - 1}{x} - 1\right)}^{3}} - \frac{1}{3} \, \log\left(\frac{{\left| x - 1 \right|}}{{\left| x \right|}}\right) + \frac{1}{3} \, \log\left({\left| \frac{x - 1}{x} - 1 \right|}\right)"," ",0,"1/6*(2*(x - 1)/x - 3)/((x - 1)/x - 1)^2 - 1/3*log((x - 1)/x)/((x - 1)/x - 1)^3 - 1/3*log(abs(x - 1)/abs(x)) + 1/3*log(abs((x - 1)/x - 1))","B",0
74,1,15,0,0.939079," ","integrate(cos(x)^5,x, algorithm=""giac"")","\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
75,1,22,0,0.869046," ","integrate(cos(x)^4*sin(x)^2,x, algorithm=""giac"")","\frac{1}{16} \, x - \frac{1}{192} \, \sin\left(6 \, x\right) - \frac{1}{64} \, \sin\left(4 \, x\right) + \frac{1}{64} \, \sin\left(2 \, x\right)"," ",0,"1/16*x - 1/192*sin(6*x) - 1/64*sin(4*x) + 1/64*sin(2*x)","A",0
76,1,38,0,0.991108," ","integrate(1/sin(x)^5,x, algorithm=""giac"")","\frac{3 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)}{8 \, {\left(\cos\left(x\right)^{2} - 1\right)}^{2}} - \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)^2 - 1)^2 - 3/16*log(cos(x) + 1) + 3/16*log(-cos(x) + 1)","A",0
77,1,11,0,0.935155," ","integrate(sin(x)/exp(x),x, algorithm=""giac"")","-\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
78,1,19,0,0.883211," ","integrate(exp(2*x)*sin(3*x),x, algorithm=""giac"")","-\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
79,1,329,0,1.141636," ","integrate(a^x*cos(x),x, algorithm=""giac"")","{\left| a \right|}^{x} {\left(\frac{2 \, \cos\left(\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi x + x\right) \log\left({\left| a \right|}\right)}{{\left(\pi - \pi \mathrm{sgn}\left(a\right) - 2\right)}^{2} + 4 \, \log\left({\left| a \right|}\right)^{2}} - \frac{{\left(\pi - \pi \mathrm{sgn}\left(a\right) - 2\right)} \sin\left(\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi x + x\right)}{{\left(\pi - \pi \mathrm{sgn}\left(a\right) - 2\right)}^{2} + 4 \, \log\left({\left| a \right|}\right)^{2}}\right)} + {\left| a \right|}^{x} {\left(\frac{2 \, \cos\left(\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi x - x\right) \log\left({\left| a \right|}\right)}{{\left(\pi - \pi \mathrm{sgn}\left(a\right) + 2\right)}^{2} + 4 \, \log\left({\left| a \right|}\right)^{2}} - \frac{{\left(\pi - \pi \mathrm{sgn}\left(a\right) + 2\right)} \sin\left(\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi x - x\right)}{{\left(\pi - \pi \mathrm{sgn}\left(a\right) + 2\right)}^{2} + 4 \, \log\left({\left| a \right|}\right)^{2}}\right)} - \frac{1}{2} i \, {\left| a \right|}^{x} {\left(-\frac{2 i \, e^{\left(\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi x + i \, x\right)}}{-2 i \, \pi + 2 i \, \pi \mathrm{sgn}\left(a\right) + 4 \, \log\left({\left| a \right|}\right) + 4 i} + \frac{2 i \, e^{\left(-\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi x - i \, x\right)}}{2 i \, \pi - 2 i \, \pi \mathrm{sgn}\left(a\right) + 4 \, \log\left({\left| a \right|}\right) - 4 i}\right)} - \frac{1}{2} i \, {\left| a \right|}^{x} {\left(-\frac{2 i \, e^{\left(\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi x - i \, x\right)}}{-2 i \, \pi + 2 i \, \pi \mathrm{sgn}\left(a\right) + 4 \, \log\left({\left| a \right|}\right) - 4 i} + \frac{2 i \, e^{\left(-\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi x + i \, x\right)}}{2 i \, \pi - 2 i \, \pi \mathrm{sgn}\left(a\right) + 4 \, \log\left({\left| a \right|}\right) + 4 i}\right)}"," ",0,"abs(a)^x*(2*cos(1/2*pi*x*sgn(a) - 1/2*pi*x + x)*log(abs(a))/((pi - pi*sgn(a) - 2)^2 + 4*log(abs(a))^2) - (pi - pi*sgn(a) - 2)*sin(1/2*pi*x*sgn(a) - 1/2*pi*x + x)/((pi - pi*sgn(a) - 2)^2 + 4*log(abs(a))^2)) + abs(a)^x*(2*cos(1/2*pi*x*sgn(a) - 1/2*pi*x - x)*log(abs(a))/((pi - pi*sgn(a) + 2)^2 + 4*log(abs(a))^2) - (pi - pi*sgn(a) + 2)*sin(1/2*pi*x*sgn(a) - 1/2*pi*x - x)/((pi - pi*sgn(a) + 2)^2 + 4*log(abs(a))^2)) - 1/2*I*abs(a)^x*(-2*I*e^(1/2*I*pi*x*sgn(a) - 1/2*I*pi*x + I*x)/(-2*I*pi + 2*I*pi*sgn(a) + 4*log(abs(a)) + 4*I) + 2*I*e^(-1/2*I*pi*x*sgn(a) + 1/2*I*pi*x - I*x)/(2*I*pi - 2*I*pi*sgn(a) + 4*log(abs(a)) - 4*I)) - 1/2*I*abs(a)^x*(-2*I*e^(1/2*I*pi*x*sgn(a) - 1/2*I*pi*x - I*x)/(-2*I*pi + 2*I*pi*sgn(a) + 4*log(abs(a)) - 4*I) + 2*I*e^(-1/2*I*pi*x*sgn(a) + 1/2*I*pi*x + I*x)/(2*I*pi - 2*I*pi*sgn(a) + 4*log(abs(a)) + 4*I))","C",0
80,1,13,0,0.909026," ","integrate(cos(log(x)),x, algorithm=""giac"")","\frac{1}{2} \, x \cos\left(\log\left(x\right)\right) + \frac{1}{2} \, x \sin\left(\log\left(x\right)\right)"," ",0,"1/2*x*cos(log(x)) + 1/2*x*sin(log(x))","A",0
81,1,12,0,0.988938," ","integrate(log(cos(x))*sec(x)^2,x, algorithm=""giac"")","\log\left(\cos\left(x\right)\right) \tan\left(x\right) - x + \tan\left(x\right)"," ",0,"log(cos(x))*tan(x) - x + tan(x)","A",0
82,1,23,0,1.000011," ","integrate(x*tan(x)^2,x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} + x \tan\left(x\right) + \frac{1}{2} \, \log\left(\frac{4}{\tan\left(x\right)^{2} + 1}\right)"," ",0,"-1/2*x^2 + x*tan(x) + 1/2*log(4/(tan(x)^2 + 1))","A",0
83,1,38,0,0.952740," ","integrate(arcsin(x)/x^2,x, algorithm=""giac"")","-\frac{\arcsin\left(x\right)}{x} - \frac{1}{2} \, \log\left(\sqrt{-x^{2} + 1} + 1\right) + \frac{1}{2} \, \log\left(-\sqrt{-x^{2} + 1} + 1\right)"," ",0,"-arcsin(x)/x - 1/2*log(sqrt(-x^2 + 1) + 1) + 1/2*log(-sqrt(-x^2 + 1) + 1)","A",0
84,1,23,0,0.960725," ","integrate(arcsin(x)^2,x, algorithm=""giac"")","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
85,1,19,0,0.985709," ","integrate(x^2*arctan(x)/(x^2+1),x, algorithm=""giac"")","x \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) - 1/2*arctan(x)^2 - 1/2*log(x^2 + 1)","A",0
86,-2,0,0,0.000000," ","integrate(arccos((x/(1+x))^(1/2)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x+1)]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, choosing root of [1,0,%%%{2,[2,2]%%%}+%%%{2,[2,1]%%%}+%%%{-4,[0,2]%%%}+%%%{-6,[0,1]%%%}+%%%{-2,[0,0]%%%},0,%%%{1,[4,4]%%%}+%%%{2,[4,3]%%%}+%%%{1,[4,2]%%%}+%%%{-2,[2,3]%%%}+%%%{-4,[2,2]%%%}+%%%{-2,[2,1]%%%}+%%%{1,[0,2]%%%}+%%%{2,[0,1]%%%}+%%%{1,[0,0]%%%}] at parameters values [86,-97]Warning, choosing root of [1,0,%%%{2,[2,2]%%%}+%%%{-2,[2,1]%%%}+%%%{-4,[0,2]%%%}+%%%{6,[0,1]%%%}+%%%{-2,[0,0]%%%},0,%%%{1,[4,4]%%%}+%%%{-2,[4,3]%%%}+%%%{1,[4,2]%%%}+%%%{2,[2,3]%%%}+%%%{-4,[2,2]%%%}+%%%{2,[2,1]%%%}+%%%{1,[0,2]%%%}+%%%{-2,[0,1]%%%}+%%%{1,[0,0]%%%}] at parameters values [-82,7]Undef/Unsigned Inf encountered in limit"Limit: Max order reached or unable to make series expansion Error: Bad Argument Value"","F(-2)",0
87,1,21,0,0.943591," ","integrate((3*x^2+2*x)^3,x, algorithm=""giac"")","\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
88,1,29,0,0.890845," ","integrate((-1+x)*(3*x^2+2*x-1)^2,x, algorithm=""giac"")","\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
89,1,23,0,0.976705," ","integrate(x^(-1+k)*(a+b*x^k)^n,x, algorithm=""giac"")","\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
90,1,23,0,0.985833," ","integrate(x^3/(1+2*x),x, algorithm=""giac"")","\frac{1}{6} \, x^{3} - \frac{1}{8} \, x^{2} + \frac{1}{8} \, x - \frac{1}{16} \, \log\left({\left| 2 \, x + 1 \right|}\right)"," ",0,"1/6*x^3 - 1/8*x^2 + 1/8*x - 1/16*log(abs(2*x + 1))","A",0
91,1,26,0,0.848875," ","integrate(x^6/(3*x^2+2),x, algorithm=""giac"")","\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
92,1,17,0,0.815787," ","integrate(1/(3*x^2-7*x+2),x, algorithm=""giac"")","-\frac{1}{5} \, \log\left({\left| 3 \, x - 1 \right|}\right) + \frac{1}{5} \, \log\left({\left| x - 2 \right|}\right)"," ",0,"-1/5*log(abs(3*x - 1)) + 1/5*log(abs(x - 2))","A",0
93,1,28,0,0.862567," ","integrate((-1+3*x)/(x^2-x+1),x, algorithm=""giac"")","\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
94,1,21,0,0.904045," ","integrate(x^2/(x^2+2*x+5),x, algorithm=""giac"")","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
95,1,38,0,0.928718," ","integrate((6*x^4-5*x^3+4*x^2)/(2*x^2-x+1),x, algorithm=""giac"")","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
96,1,20,0,0.882916," ","integrate((x^2+x-1)/(x^3+x^2-6*x),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| x + 3 \right|}\right) + \frac{1}{2} \, \log\left({\left| x - 2 \right|}\right) + \frac{1}{6} \, \log\left({\left| x \right|}\right)"," ",0,"1/3*log(abs(x + 3)) + 1/2*log(abs(x - 2)) + 1/6*log(abs(x))","A",0
97,1,28,0,0.969465," ","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=""giac"")","\frac{9}{2} \, \log\left({\left| -a + x \right|}\right) - 17 \, \log\left({\left| -2 \, a + x \right|}\right) + \frac{35}{2} \, \log\left({\left| -3 \, a + x \right|}\right)"," ",0,"9/2*log(abs(-a + x)) - 17*log(abs(-2*a + x)) + 35/2*log(abs(-3*a + x))","A",0
98,1,29,0,0.994036," ","integrate((x^2-x+2)/(x^4-5*x^2+4),x, algorithm=""giac"")","-\frac{2}{3} \, \log\left({\left| x + 2 \right|}\right) + \frac{2}{3} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right) + \frac{1}{3} \, \log\left({\left| x - 2 \right|}\right)"," ",0,"-2/3*log(abs(x + 2)) + 2/3*log(abs(x + 1)) - 1/3*log(abs(x - 1)) + 1/3*log(abs(x - 2))","A",0
99,1,59,0,0.989403," ","integrate((2*x^2-5)/(x^4-5*x^2+6),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{3} \right|}}{{\left| 2 \, x + 2 \, \sqrt{3} \right|}}\right) + \frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} \right|}}\right)"," ",0,"1/6*sqrt(3)*log(abs(2*x - 2*sqrt(3))/abs(2*x + 2*sqrt(3))) + 1/4*sqrt(2)*log(abs(2*x - 2*sqrt(2))/abs(2*x + 2*sqrt(2)))","B",0
100,1,29,0,0.886379," ","integrate(1/(-4+x)/(-3+x)/(-2+x)/(-1+x),x, algorithm=""giac"")","-\frac{1}{6} \, \log\left({\left| x - 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| x - 2 \right|}\right) - \frac{1}{2} \, \log\left({\left| x - 3 \right|}\right) + \frac{1}{6} \, \log\left({\left| x - 4 \right|}\right)"," ",0,"-1/6*log(abs(x - 1)) + 1/2*log(abs(x - 2)) - 1/2*log(abs(x - 3)) + 1/6*log(abs(x - 4))","A",0
101,1,18,0,0.994025," ","integrate((x^2+1)/(-1+x)^3,x, algorithm=""giac"")","-\frac{2 \, x - 1}{{\left(x - 1\right)}^{2}} + \log\left({\left| x - 1 \right|}\right)"," ",0,"-(2*x - 1)/(x - 1)^2 + log(abs(x - 1))","A",0
102,1,45,0,1.036665," ","integrate(x^5/(3+x)^2,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(x + 3\right)}^{4} {\left(\frac{20}{x + 3} - \frac{180}{{\left(x + 3\right)}^{2}} + \frac{1080}{{\left(x + 3\right)}^{3}} - 1\right)} + \frac{243}{x + 3} + 405 \, \log\left({\left| x + 3 \right|}\right)"," ",0,"-1/4*(x + 3)^4*(20/(x + 3) - 180/(x + 3)^2 + 1080/(x + 3)^3 - 1) + 243/(x + 3) + 405*log(abs(x + 3))","A",0
103,1,27,0,0.881302," ","integrate((5*x^3-2)/(x^4-8*x^3+18*x^2-27),x, algorithm=""giac"")","-\frac{407 \, x - 955}{16 \, {\left(x - 3\right)}^{2}} + \frac{7}{64} \, \log\left({\left| x + 1 \right|}\right) + \frac{313}{64} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"-1/16*(407*x - 955)/(x - 3)^2 + 7/64*log(abs(x + 1)) + 313/64*log(abs(x - 3))","A",0
104,1,37,0,0.856015," ","integrate((x^3-6*x^2+3*x-9)/(3+x)^2/(4+x)^2,x, algorithm=""giac"")","\frac{181}{x + 4} - \frac{99}{\frac{1}{x + 4} - 1} + \log\left({\left| x + 4 \right|}\right) + 264 \, \log\left({\left| -\frac{1}{x + 4} + 1 \right|}\right)"," ",0,"181/(x + 4) - 99/(1/(x + 4) - 1) + log(abs(x + 4)) + 264*log(abs(-1/(x + 4) + 1))","A",0
105,1,35,0,1.105878," ","integrate((x^3+x^2+2)/x/(x^2-1)^2,x, algorithm=""giac"")","-\frac{x + 3}{2 \, {\left(x + 1\right)} {\left(x - 1\right)}} - \frac{5}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{3}{4} \, \log\left({\left| x - 1 \right|}\right) + 2 \, \log\left({\left| x \right|}\right)"," ",0,"-1/2*(x + 3)/((x + 1)*(x - 1)) - 5/4*log(abs(x + 1)) - 3/4*log(abs(x - 1)) + 2*log(abs(x))","A",0
106,1,40,0,1.025505," ","integrate(1/(x^6-x^5-x^4+x^3),x, algorithm=""giac"")","-\frac{3 \, x^{2} - x - 1}{2 \, {\left(x - 1\right)} x^{2}} - \frac{1}{4} \, \log\left({\left| x + 1 \right|}\right) - \frac{7}{4} \, \log\left({\left| x - 1 \right|}\right) + 2 \, \log\left({\left| x \right|}\right)"," ",0,"-1/2*(3*x^2 - x - 1)/((x - 1)*x^2) - 1/4*log(abs(x + 1)) - 7/4*log(abs(x - 1)) + 2*log(abs(x))","A",0
107,1,24,0,1.057115," ","integrate((x^4+1)/(x^3-x^2+x-1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + x - \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right) + \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*x^2 + x - arctan(x) - 1/2*log(x^2 + 1) + log(abs(x - 1))","A",0
108,1,23,0,0.778609," ","integrate(1/x/(1+x)/(x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \arctan\left(x\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right) - \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/2*arctan(x) - 1/4*log(x^2 + 1) - 1/2*log(abs(x + 1)) + log(abs(x))","A",0
109,1,27,0,0.958988," ","integrate(x^2/(x^4+x^2-2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{1}{6} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{6} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/3*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/6*log(abs(x + 1)) + 1/6*log(abs(x - 1))","A",0
110,1,33,0,0.980882," ","integrate((x^3+4*x^2+6*x)/(x^4+2*x^3+3*x^2+4*x+2),x, algorithm=""giac"")","\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({\left| x + 1 \right|}\right)"," ",0,"4/3*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/(x + 1) + 2/3*log(x^2 + 2) - 1/3*log(abs(x + 1))","A",0
111,1,62,0,1.039291," ","integrate(x/(1+x)/(1+2*x)^2/(x^2+1),x, algorithm=""giac"")","\frac{2}{5 \, {\left(2 \, x + 1\right)}} + \frac{1}{50} \, \arctan\left(-\frac{5}{2 \, {\left(2 \, x + 1\right)}} + \frac{1}{2}\right) - \frac{7}{100} \, \log\left(-\frac{2}{2 \, x + 1} + \frac{5}{{\left(2 \, x + 1\right)}^{2}} + 1\right) - \frac{1}{2} \, \log\left({\left| -\frac{1}{2 \, x + 1} - 1 \right|}\right)"," ",0,"2/5/(2*x + 1) + 1/50*arctan(-5/2/(2*x + 1) + 1/2) - 7/100*log(-2/(2*x + 1) + 5/(2*x + 1)^2 + 1) - 1/2*log(abs(-1/(2*x + 1) - 1))","A",0
112,1,32,0,0.907619," ","integrate((3*x^2+x-2)/(-1+x)^3/(x^2+1),x, algorithm=""giac"")","-\frac{5 \, x - 4}{2 \, {\left(x - 1\right)}^{2}} - \arctan\left(x\right) + \frac{3}{4} \, \log\left(x^{2} + 1\right) - \frac{3}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*(5*x - 4)/(x - 1)^2 - arctan(x) + 3/4*log(x^2 + 1) - 3/2*log(abs(x - 1))","A",0
113,1,53,0,0.993008," ","integrate(1/(x^4+x^2+1),x, algorithm=""giac"")","\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
114,1,64,0,1.115777," ","integrate((2*x^3+3)/(x^5-9*x),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + \frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{3} \right|}}{{\left| 2 \, x + 2 \, \sqrt{3} \right|}}\right) + \frac{1}{12} \, \log\left(x^{2} + 3\right) + \frac{1}{12} \, \log\left({\left| x^{2} - 3 \right|}\right) - \frac{1}{3} \, \log\left({\left| x \right|}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*x) + 1/6*sqrt(3)*log(abs(2*x - 2*sqrt(3))/abs(2*x + 2*sqrt(3))) + 1/12*log(x^2 + 3) + 1/12*log(abs(x^2 - 3)) - 1/3*log(abs(x))","A",0
115,1,39,0,0.962515," ","integrate((5*x^3+8*x-20)/(-4+x)^3/(x^2-4*x+8),x, algorithm=""giac"")","-\frac{41 \, x - 81}{4 \, {\left(x - 4\right)}^{2}} + \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({\left| x - 4 \right|}\right)"," ",0,"-1/4*(41*x - 81)/(x - 4)^2 + 3/16*arctan(1/2*x - 1) + 45/32*log(x^2 - 4*x + 8) - 45/16*log(abs(x - 4))","A",0
116,1,35,0,0.859307," ","integrate(1/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x, algorithm=""giac"")","\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
117,1,33,0,0.971412," ","integrate(x/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x, algorithm=""giac"")","-\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
118,1,50,0,0.878088," ","integrate(1/(a^3+x^3),x, algorithm=""giac"")","\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({\left| a + x \right|}\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(abs(a + x))/a^2","A",0
119,1,50,0,1.109904," ","integrate(x/(a^3+x^3),x, algorithm=""giac"")","\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({\left| a + x \right|}\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(abs(a + x))/a","A",0
120,1,11,0,0.932789," ","integrate(x^2/(a^3+x^3),x, algorithm=""giac"")","\frac{1}{3} \, \log\left({\left| a^{3} + x^{3} \right|}\right)"," ",0,"1/3*log(abs(a^3 + x^3))","A",0
121,1,22,0,0.867906," ","integrate(1/x/(a^3+x^3),x, algorithm=""giac"")","-\frac{\log\left({\left| a^{3} + x^{3} \right|}\right)}{3 \, a^{3}} + \frac{\log\left({\left| x \right|}\right)}{a^{3}}"," ",0,"-1/3*log(abs(a^3 + x^3))/a^3 + log(abs(x))/a^3","A",0
122,1,58,0,0.928321," ","integrate(1/x^2/(a^3+x^3),x, algorithm=""giac"")","-\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({\left| a + x \right|}\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(abs(a + x))/a^4 - 1/(a^3*x)","A",0
123,1,58,0,0.989270," ","integrate(1/x^3/(a^3+x^3),x, algorithm=""giac"")","-\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({\left| a + x \right|}\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(abs(a + x))/a^5 - 1/2/(a^3*x^2)","A",0
124,1,40,0,0.903858," ","integrate(1/x^4/(a^3+x^3),x, algorithm=""giac"")","\frac{\log\left({\left| a^{3} + x^{3} \right|}\right)}{3 \, a^{6}} - \frac{\log\left({\left| x \right|}\right)}{a^{6}} - \frac{a^{3} - x^{3}}{3 \, a^{6} x^{3}}"," ",0,"1/3*log(abs(a^3 + x^3))/a^6 - log(abs(x))/a^6 - 1/3*(a^3 - x^3)/(a^6*x^3)","A",0
125,1,67,0,0.919315," ","integrate(1/x^5/(a^3+x^3),x, algorithm=""giac"")","\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({\left| a + x \right|}\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(abs(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=""giac"")","\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
127,1,34,0,0.859954," ","integrate(1/(a^4-x^4),x, algorithm=""giac"")","\frac{\arctan\left(\frac{x}{a}\right)}{2 \, a^{3}} + \frac{\log\left({\left| a + x \right|}\right)}{4 \, a^{3}} - \frac{\log\left({\left| -a + x \right|}\right)}{4 \, a^{3}}"," ",0,"1/2*arctan(x/a)/a^3 + 1/4*log(abs(a + x))/a^3 - 1/4*log(abs(-a + x))/a^3","A",0
128,1,30,0,0.814643," ","integrate(x/(a^4-x^4),x, algorithm=""giac"")","\frac{\log\left(a^{2} + x^{2}\right)}{4 \, a^{2}} - \frac{\log\left({\left| -a^{2} + x^{2} \right|}\right)}{4 \, a^{2}}"," ",0,"1/4*log(a^2 + x^2)/a^2 - 1/4*log(abs(-a^2 + x^2))/a^2","B",0
129,1,26,0,0.948179," ","integrate(1/x/(a^4-x^4),x, algorithm=""giac"")","\frac{\log\left(x^{4}\right)}{4 \, a^{4}} - \frac{\log\left({\left| -a^{4} + x^{4} \right|}\right)}{4 \, a^{4}}"," ",0,"1/4*log(x^4)/a^4 - 1/4*log(abs(-a^4 + x^4))/a^4","A",0
130,1,42,0,0.932478," ","integrate(1/x^2/(a^4-x^4),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{x}{a}\right)}{2 \, a^{5}} + \frac{\log\left({\left| a + x \right|}\right)}{4 \, a^{5}} - \frac{\log\left({\left| -a + x \right|}\right)}{4 \, a^{5}} - \frac{1}{a^{4} x}"," ",0,"-1/2*arctan(x/a)/a^5 + 1/4*log(abs(a + x))/a^5 - 1/4*log(abs(-a + x))/a^5 - 1/(a^4*x)","A",0
131,1,38,0,0.967349," ","integrate(1/x^3/(a^4-x^4),x, algorithm=""giac"")","\frac{\log\left(a^{2} + x^{2}\right)}{4 \, a^{6}} - \frac{\log\left({\left| -a^{2} + x^{2} \right|}\right)}{4 \, a^{6}} - \frac{1}{2 \, a^{4} x^{2}}"," ",0,"1/4*log(a^2 + x^2)/a^6 - 1/4*log(abs(-a^2 + x^2))/a^6 - 1/2/(a^4*x^2)","A",0
132,1,42,0,1.049928," ","integrate(1/x^4/(a^4-x^4),x, algorithm=""giac"")","\frac{\arctan\left(\frac{x}{a}\right)}{2 \, a^{7}} + \frac{\log\left({\left| a + x \right|}\right)}{4 \, a^{7}} - \frac{\log\left({\left| -a + x \right|}\right)}{4 \, a^{7}} - \frac{1}{3 \, a^{4} x^{3}}"," ",0,"1/2*arctan(x/a)/a^7 + 1/4*log(abs(a + x))/a^7 - 1/4*log(abs(-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=""giac"")","\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
134,1,13,0,0.968500," ","integrate(x/(a^4+x^4),x, algorithm=""giac"")","\frac{\arctan\left(\frac{x^{2}}{a^{2}}\right)}{2 \, a^{2}}"," ",0,"1/2*arctan(x^2/a^2)/a^2","A",0
135,1,114,0,0.967668," ","integrate(x^2/(a^4+x^4),x, algorithm=""giac"")","\frac{\sqrt{2} {\left| a \right|} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left| a \right|} + 2 \, x\right)}}{2 \, {\left| a \right|}}\right)}{4 \, a^{2}} + \frac{\sqrt{2} {\left| a \right|} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left| a \right|} - 2 \, x\right)}}{2 \, {\left| a \right|}}\right)}{4 \, a^{2}} - \frac{\sqrt{2} {\left| a \right|} \log\left(\sqrt{2} x {\left| a \right|} + x^{2} + {\left| a \right|}^{2}\right)}{8 \, a^{2}} + \frac{\sqrt{2} {\left| a \right|} \log\left(-\sqrt{2} x {\left| a \right|} + x^{2} + {\left| a \right|}^{2}\right)}{8 \, a^{2}}"," ",0,"1/4*sqrt(2)*abs(a)*arctan(1/2*sqrt(2)*(sqrt(2)*abs(a) + 2*x)/abs(a))/a^2 + 1/4*sqrt(2)*abs(a)*arctan(-1/2*sqrt(2)*(sqrt(2)*abs(a) - 2*x)/abs(a))/a^2 - 1/8*sqrt(2)*abs(a)*log(sqrt(2)*x*abs(a) + x^2 + abs(a)^2)/a^2 + 1/8*sqrt(2)*abs(a)*log(-sqrt(2)*x*abs(a) + x^2 + abs(a)^2)/a^2","A",0
136,1,177,0,1.013462," ","integrate(1/(a^5+x^5),x, algorithm=""giac"")","\frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a^{4}} + \frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a^{4}} - \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a^{4}} + \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a^{4}} - \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a^{4}} + \frac{\log\left({\left| a + x \right|}\right)}{5 \, a^{4}}"," ",0,"1/10*sqrt(2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a^4 + 1/10*sqrt(-2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a^4 - 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a^4 + 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a^4 - 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a^4 + 1/5*log(abs(a + x))/a^4","A",0
137,1,177,0,0.887551," ","integrate(x/(a^5+x^5),x, algorithm=""giac"")","-\frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a^{3}} + \frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a^{3}} - \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a^{3}} + \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a^{3}} + \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a^{3}} - \frac{\log\left({\left| a + x \right|}\right)}{5 \, a^{3}}"," ",0,"-1/10*sqrt(-2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a^3 + 1/10*sqrt(2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a^3 - 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a^3 + 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a^3 + 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a^3 - 1/5*log(abs(a + x))/a^3","A",0
138,1,177,0,0.993001," ","integrate(x^2/(a^5+x^5),x, algorithm=""giac"")","-\frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a^{2}} + \frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a^{2}} + \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a^{2}} - \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a^{2}} - \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a^{2}} + \frac{\log\left({\left| a + x \right|}\right)}{5 \, a^{2}}"," ",0,"-1/10*sqrt(-2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a^2 + 1/10*sqrt(2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a^2 + 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a^2 - 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a^2 - 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a^2 + 1/5*log(abs(a + x))/a^2","A",0
139,1,177,0,0.929356," ","integrate(x^3/(a^5+x^5),x, algorithm=""giac"")","\frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a} + \frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a} + \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a} - \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a} + \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a} - \frac{\log\left({\left| a + x \right|}\right)}{5 \, a}"," ",0,"1/10*sqrt(2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a + 1/10*sqrt(-2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a + 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a - 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a + 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a - 1/5*log(abs(a + x))/a","A",0
140,1,11,0,0.952138," ","integrate(x^4/(a^5+x^5),x, algorithm=""giac"")","\frac{1}{5} \, \log\left({\left| a^{5} + x^{5} \right|}\right)"," ",0,"1/5*log(abs(a^5 + x^5))","A",0
141,1,22,0,0.900691," ","integrate(1/x/(a^5+x^5),x, algorithm=""giac"")","-\frac{\log\left({\left| a^{5} + x^{5} \right|}\right)}{5 \, a^{5}} + \frac{\log\left({\left| x \right|}\right)}{a^{5}}"," ",0,"-1/5*log(abs(a^5 + x^5))/a^5 + log(abs(x))/a^5","A",0
142,1,185,0,1.099168," ","integrate(1/x^2/(a^5+x^5),x, algorithm=""giac"")","-\frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a^{6}} - \frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a^{6}} - \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a^{6}} + \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a^{6}} - \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a^{6}} + \frac{\log\left({\left| a + x \right|}\right)}{5 \, a^{6}} - \frac{1}{a^{5} x}"," ",0,"-1/10*sqrt(2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a^6 - 1/10*sqrt(-2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a^6 - 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a^6 + 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a^6 - 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a^6 + 1/5*log(abs(a + x))/a^6 - 1/(a^5*x)","A",0
143,1,185,0,0.987550," ","integrate(1/x^3/(a^5+x^5),x, algorithm=""giac"")","\frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a^{7}} - \frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a^{7}} - \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a^{7}} + \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a^{7}} + \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a^{7}} - \frac{\log\left({\left| a + x \right|}\right)}{5 \, a^{7}} - \frac{1}{2 \, a^{5} x^{2}}"," ",0,"1/10*sqrt(-2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a^7 - 1/10*sqrt(2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a^7 - 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a^7 + 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a^7 + 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a^7 - 1/5*log(abs(a + x))/a^7 - 1/2/(a^5*x^2)","A",0
144,1,185,0,1.049540," ","integrate(1/x^4/(a^5+x^5),x, algorithm=""giac"")","\frac{\sqrt{-2 \, \sqrt{5} + 10} \arctan\left(\frac{a {\left(\sqrt{5} - 1\right)} + 4 \, x}{a \sqrt{2 \, \sqrt{5} + 10}}\right)}{10 \, a^{8}} - \frac{\sqrt{2 \, \sqrt{5} + 10} \arctan\left(-\frac{a {\left(\sqrt{5} + 1\right)} - 4 \, x}{a \sqrt{-2 \, \sqrt{5} + 10}}\right)}{10 \, a^{8}} + \frac{\sqrt{5} \log\left(a^{2} - \frac{1}{2} \, {\left(\sqrt{5} a + a\right)} x + x^{2}\right)}{20 \, a^{8}} - \frac{\sqrt{5} \log\left(a^{2} + \frac{1}{2} \, {\left(\sqrt{5} a - a\right)} x + x^{2}\right)}{20 \, a^{8}} - \frac{\log\left({\left| a^{4} - a^{3} x + a^{2} x^{2} - a x^{3} + x^{4} \right|}\right)}{20 \, a^{8}} + \frac{\log\left({\left| a + x \right|}\right)}{5 \, a^{8}} - \frac{1}{3 \, a^{5} x^{3}}"," ",0,"1/10*sqrt(-2*sqrt(5) + 10)*arctan((a*(sqrt(5) - 1) + 4*x)/(a*sqrt(2*sqrt(5) + 10)))/a^8 - 1/10*sqrt(2*sqrt(5) + 10)*arctan(-(a*(sqrt(5) + 1) - 4*x)/(a*sqrt(-2*sqrt(5) + 10)))/a^8 + 1/20*sqrt(5)*log(a^2 - 1/2*(sqrt(5)*a + a)*x + x^2)/a^8 - 1/20*sqrt(5)*log(a^2 + 1/2*(sqrt(5)*a - a)*x + x^2)/a^8 - 1/20*log(abs(a^4 - a^3*x + a^2*x^2 - a*x^3 + x^4))/a^8 + 1/5*log(abs(a + x))/a^8 - 1/3/(a^5*x^3)","A",0
145,0,0,0,0.000000," ","integrate(1/(x^m)/(a^5+x^5),x, algorithm=""giac"")","\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
146,1,27,0,0.882972," ","integrate((x^4+1)/(x^6+1),x, algorithm=""giac"")","\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
147,1,44,0,1.051766," ","integrate(1/(x^2+3*x+5)^3,x, algorithm=""giac"")","\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^{2} + 3 \, x + 5\right)}^{2}}"," ",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^2 + 3*x + 5)^2","A",0
148,1,28,0,0.914811," ","integrate((x^4+x^2+1)/(x^2+1)^4,x, algorithm=""giac"")","\frac{21 \, x^{5} + 40 \, x^{3} + 27 \, x}{48 \, {\left(x^{2} + 1\right)}^{3}} + \frac{7}{16} \, \arctan\left(x\right)"," ",0,"1/48*(21*x^5 + 40*x^3 + 27*x)/(x^2 + 1)^3 + 7/16*arctan(x)","A",0
149,1,92,0,0.992258," ","integrate((A*x+B)/(a*x^2+2*b*x+c)^2,x, algorithm=""giac"")","-\frac{{\left(B a - A b\right)} \arctan\left(\frac{a x + b}{\sqrt{-b^{2} + a c}}\right)}{2 \, {\left(b^{2} - a c\right)} \sqrt{-b^{2} + a c}} - \frac{B a x - A b x + B b - A c}{2 \, {\left(a x^{2} + 2 \, b x + c\right)} {\left(b^{2} - a c\right)}}"," ",0,"-1/2*(B*a - A*b)*arctan((a*x + b)/sqrt(-b^2 + a*c))/((b^2 - a*c)*sqrt(-b^2 + a*c)) - 1/2*(B*a*x - A*b*x + B*b - A*c)/((a*x^2 + 2*b*x + c)*(b^2 - a*c))","A",0
150,1,33,0,0.918058," ","integrate((5*x^3-27*x^2+55*x-41)/(x^2-4*x+5)^2,x, algorithm=""giac"")","-\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
151,1,43,0,0.950015," ","integrate(1/(x^3-1)^2,x, algorithm=""giac"")","\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({\left| x - 1 \right|}\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(abs(x - 1))","A",0
152,1,28,0,1.058825," ","integrate((3*x^4+4)/x^2/(x^2+1)^3,x, algorithm=""giac"")","-\frac{25 \, x^{3} + 39 \, x}{8 \, {\left(x^{2} + 1\right)}^{2}} - \frac{4}{x} - \frac{57}{8} \, \arctan\left(x\right)"," ",0,"-1/8*(25*x^3 + 39*x)/(x^2 + 1)^2 - 4/x - 57/8*arctan(x)","A",0
153,1,40,0,0.934225," ","integrate(x/(x^6+1),x, algorithm=""giac"")","\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
154,0,0,0,0.000000," ","integrate((-1+x^(-1+n))/(-n*x+x^n),x, algorithm=""giac"")","\int -\frac{x^{n - 1} - 1}{n x - x^{n}}\,{d x}"," ",0,"integrate(-(x^(n - 1) - 1)/(n*x - x^n), x)","F",0
155,1,34,0,1.514461," ","integrate(x^3/(3*x^4-2*x^2+1),x, algorithm=""giac"")","\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
156,1,25,0,0.908325," ","integrate(x^5/(3*x^4+x^2-4),x, algorithm=""giac"")","\frac{1}{6} \, x^{2} - \frac{8}{63} \, \log\left(3 \, x^{2} + 4\right) + \frac{1}{14} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"1/6*x^2 - 8/63*log(3*x^2 + 4) + 1/14*log(abs(x^2 - 1))","A",0
157,1,19,0,0.909938," ","integrate(x^2/(x^6-10*x^3+9),x, algorithm=""giac"")","-\frac{1}{24} \, \log\left({\left| x^{3} - 1 \right|}\right) + \frac{1}{24} \, \log\left({\left| x^{3} - 9 \right|}\right)"," ",0,"-1/24*log(abs(x^3 - 1)) + 1/24*log(abs(x^3 - 9))","A",0
158,1,23,0,0.846981," ","integrate((x^3-4*x^2+1)/(-2+x)^4,x, algorithm=""giac"")","-\frac{6 \, x^{2} - 30 \, x + 29}{3 \, {\left(x - 2\right)}^{3}} + \log\left({\left| x - 2 \right|}\right)"," ",0,"-1/3*(6*x^2 - 30*x + 29)/(x - 2)^3 + log(abs(x - 2))","A",0
159,1,22,0,0.995060," ","integrate(x^3/(-1+x)^12,x, algorithm=""giac"")","-\frac{165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1}{1320 \, {\left(x - 1\right)}^{11}}"," ",0,"-1/1320*(165*x^3 - 55*x^2 + 11*x - 1)/(x - 1)^11","A",0
160,1,55,0,0.886873," ","integrate((x^4-3*x)/(1+2*x)^5,x, algorithm=""giac"")","\frac{1}{8 \, {\left(2 \, x + 1\right)}} - \frac{3}{32 \, {\left(2 \, x + 1\right)}^{2}} + \frac{7}{24 \, {\left(2 \, x + 1\right)}^{3}} - \frac{25}{128 \, {\left(2 \, x + 1\right)}^{4}} - \frac{1}{32} \, \log\left(\frac{{\left| 2 \, x + 1 \right|}}{2 \, {\left(2 \, x + 1\right)}^{2}}\right)"," ",0,"1/8/(2*x + 1) - 3/32/(2*x + 1)^2 + 7/24/(2*x + 1)^3 - 25/128/(2*x + 1)^4 - 1/32*log(1/2*abs(2*x + 1)/(2*x + 1)^2)","A",0
161,1,43,0,1.063279," ","integrate(1/(-1+x)^2/(1+x)^3,x, algorithm=""giac"")","-\frac{1}{8 \, {\left(x - 1\right)}} + \frac{\frac{12}{x - 1} + 5}{32 \, {\left(\frac{2}{x - 1} + 1\right)}^{2}} + \frac{3}{16} \, \log\left({\left| -\frac{2}{x - 1} - 1 \right|}\right)"," ",0,"-1/8/(x - 1) + 1/32*(12/(x - 1) + 5)/(2/(x - 1) + 1)^2 + 3/16*log(abs(-2/(x - 1) - 1))","A",0
162,1,40,0,0.982248," ","integrate(1/(5-6*x)^2/x^2,x, algorithm=""giac"")","-\frac{6}{25 \, {\left(6 \, x - 5\right)}} + \frac{6}{125 \, {\left(\frac{5}{6 \, x - 5} + 1\right)}} + \frac{12}{125} \, \log\left({\left| -\frac{5}{6 \, x - 5} - 1 \right|}\right)"," ",0,"-6/25/(6*x - 5) + 6/125/(5/(6*x - 5) + 1) + 12/125*log(abs(-5/(6*x - 5) - 1))","A",0
163,1,42,0,0.946884," ","integrate(1/(x^2-2*x-3)^3,x, algorithm=""giac"")","\frac{3 \, x^{3} - 9 \, x^{2} - 11 \, x + 17}{128 \, {\left(x^{2} - 2 \, x - 3\right)}^{2}} - \frac{3}{512} \, \log\left({\left| x + 1 \right|}\right) + \frac{3}{512} \, \log\left({\left| x - 3 \right|}\right)"," ",0,"1/128*(3*x^3 - 9*x^2 - 11*x + 17)/(x^2 - 2*x - 3)^2 - 3/512*log(abs(x + 1)) + 3/512*log(abs(x - 3))","A",0
164,1,34,0,0.850590," ","integrate(1/(x^2-4*x+13)^3,x, algorithm=""giac"")","\frac{x^{3} - 6 \, x^{2} + 27 \, x - 38}{216 \, {\left(x^{2} - 4 \, x + 13\right)}^{2}} + \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^2 - 4*x + 13)^2 + 1/648*arctan(1/3*x - 2/3)","A",0
165,1,47,0,0.908174," ","integrate(1/(2+x)^3/(3+x)^4,x, algorithm=""giac"")","\frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} + 4175 \, x + 2627}{6 \, {\left(x + 3\right)}^{3} {\left(x + 2\right)}^{2}} - 10 \, \log\left({\left| x + 3 \right|}\right) + 10 \, \log\left({\left| x + 2 \right|}\right)"," ",0,"1/6*(60*x^4 + 630*x^3 + 2450*x^2 + 4175*x + 2627)/((x + 3)^3*(x + 2)^2) - 10*log(abs(x + 3)) + 10*log(abs(x + 2))","A",0
166,1,48,0,1.080586," ","integrate(x^6/(x^2-2)^2,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + \frac{5}{2} \, \sqrt{2} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{2} \right|}}{{\left| 2 \, x + 2 \, \sqrt{2} \right|}}\right) + 4 \, x - \frac{2 \, x}{x^{2} - 2}"," ",0,"1/3*x^3 + 5/2*sqrt(2)*log(abs(2*x - 2*sqrt(2))/abs(2*x + 2*sqrt(2))) + 4*x - 2*x/(x^2 - 2)","A",0
167,1,31,0,0.940725," ","integrate(x^8/(x^2+4)^4,x, algorithm=""giac"")","x + \frac{87 \, x^{5} + 544 \, x^{3} + 912 \, x}{12 \, {\left(x^{2} + 4\right)}^{3}} - \frac{35}{8} \, \arctan\left(\frac{1}{2} \, x\right)"," ",0,"x + 1/12*(87*x^5 + 544*x^3 + 912*x)/(x^2 + 4)^3 - 35/8*arctan(1/2*x)","A",0
168,1,36,0,0.850743," ","integrate((-4+7*x)/(3*x^2+2*x+5)^2,x, algorithm=""giac"")","-\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
169,1,51,0,0.945236," ","integrate((5-4*x)/(3*x^2-4*x-2)^2,x, algorithm=""giac"")","-\frac{7}{400} \, \sqrt{10} \log\left(\frac{{\left| 6 \, x - 2 \, \sqrt{10} - 4 \right|}}{{\left| 6 \, x + 2 \, \sqrt{10} - 4 \right|}}\right) - \frac{7 \, x - 18}{20 \, {\left(3 \, x^{2} - 4 \, x - 2\right)}}"," ",0,"-7/400*sqrt(10)*log(abs(6*x - 2*sqrt(10) - 4)/abs(6*x + 2*sqrt(10) - 4)) - 1/20*(7*x - 18)/(3*x^2 - 4*x - 2)","A",0
170,1,40,0,1.011568," ","integrate(x^5/(x^4+1)^3,x, algorithm=""giac"")","\frac{x^{2} - \frac{1}{x^{2}}}{16 \, {\left({\left(x^{2} - \frac{1}{x^{2}}\right)}^{2} + 4\right)}} + \frac{1}{32} \, \arctan\left(\frac{x^{4} - 1}{2 \, x^{2}}\right)"," ",0,"1/16*(x^2 - 1/x^2)/((x^2 - 1/x^2)^2 + 4) + 1/32*arctan(1/2*(x^4 - 1)/x^2)","A",0
171,1,32,0,1.605115," ","integrate(x*(x^2+1)^3/(x^4+2*x^2+2)^2,x, algorithm=""giac"")","\frac{1}{4 \, {\left(x^{4} + 2 \, x^{2} + 2\right)}} - \frac{1}{4} \, \log\left(\frac{1}{2 \, {\left(x^{4} + 2 \, x^{2} + 2\right)}}\right)"," ",0,"1/4/(x^4 + 2*x^2 + 2) - 1/4*log(1/2/(x^4 + 2*x^2 + 2))","A",0
172,1,11,0,0.926333," ","integrate(x^3/(a^4+x^4)^3,x, algorithm=""giac"")","-\frac{1}{8 \, {\left(a^{4} + x^{4}\right)}^{2}}"," ",0,"-1/8/(a^4 + x^4)^2","A",0
173,1,56,0,0.942949," ","integrate(1/x/(a^4+x^4)^3,x, algorithm=""giac"")","-\frac{\log\left(a^{4} + x^{4}\right)}{4 \, a^{12}} + \frac{\log\left(x^{4}\right)}{4 \, a^{12}} + \frac{6 \, a^{8} + 8 \, a^{4} x^{4} + 3 \, x^{8}}{8 \, {\left(a^{4} + x^{4}\right)}^{2} a^{12}}"," ",0,"-1/4*log(a^4 + x^4)/a^12 + 1/4*log(x^4)/a^12 + 1/8*(6*a^8 + 8*a^4*x^4 + 3*x^8)/((a^4 + x^4)^2*a^12)","A",0
174,1,150,0,0.927304," ","integrate(1/x^2/(a^4+x^4)^3,x, algorithm=""giac"")","-\frac{45 \, \sqrt{2} {\left| a \right|} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left| a \right|} + 2 \, x\right)}}{2 \, {\left| a \right|}}\right)}{128 \, a^{14}} - \frac{45 \, \sqrt{2} {\left| a \right|} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left| a \right|} - 2 \, x\right)}}{2 \, {\left| a \right|}}\right)}{128 \, a^{14}} + \frac{45 \, \sqrt{2} {\left| a \right|} \log\left(\sqrt{2} x {\left| a \right|} + x^{2} + {\left| a \right|}^{2}\right)}{256 \, a^{14}} - \frac{45 \, \sqrt{2} {\left| a \right|} \log\left(-\sqrt{2} x {\left| a \right|} + x^{2} + {\left| a \right|}^{2}\right)}{256 \, a^{14}} - \frac{17 \, a^{4} x^{3} + 13 \, x^{7}}{32 \, {\left(a^{4} + x^{4}\right)}^{2} a^{12}} - \frac{1}{a^{12} x}"," ",0,"-45/128*sqrt(2)*abs(a)*arctan(1/2*sqrt(2)*(sqrt(2)*abs(a) + 2*x)/abs(a))/a^14 - 45/128*sqrt(2)*abs(a)*arctan(-1/2*sqrt(2)*(sqrt(2)*abs(a) - 2*x)/abs(a))/a^14 + 45/256*sqrt(2)*abs(a)*log(sqrt(2)*x*abs(a) + x^2 + abs(a)^2)/a^14 - 45/256*sqrt(2)*abs(a)*log(-sqrt(2)*x*abs(a) + x^2 + abs(a)^2)/a^14 - 1/32*(17*a^4*x^3 + 13*x^7)/((a^4 + x^4)^2*a^12) - 1/(a^12*x)","A",0
175,1,50,0,0.881809," ","integrate(1/x^3/(a^4+x^4)^3,x, algorithm=""giac"")","-\frac{9 \, a^{4} x^{2} + 7 \, x^{6}}{16 \, {\left(a^{4} + x^{4}\right)}^{2} a^{12}} - \frac{15 \, \arctan\left(\frac{x^{2}}{a^{2}}\right)}{16 \, a^{14}} - \frac{1}{2 \, a^{12} x^{2}}"," ",0,"-1/16*(9*a^4*x^2 + 7*x^6)/((a^4 + x^4)^2*a^12) - 15/16*arctan(x^2/a^2)/a^14 - 1/2/(a^12*x^2)","A",0
176,1,30,0,0.974795," ","integrate(x^14/(2*x^5+3)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(x^{10} + x^{5}\right)}}{20 \, {\left(2 \, x^{5} + 3\right)}^{2}} + \frac{1}{40} \, \log\left({\left| 2 \, x^{5} + 3 \right|}\right)"," ",0,"-3/20*(x^10 + x^5)/(2*x^5 + 3)^2 + 1/40*log(abs(2*x^5 + 3))","A",0
177,1,250,0,1.827518," ","integrate(x^6/(2*x^5+3)^3,x, algorithm=""giac"")","-\frac{1}{3000} \, {\left(\sqrt{5} \left(\frac{3}{2}\right)^{\frac{2}{5}} \sqrt{2 \, \sqrt{5} + 10} - \left(\frac{3}{2}\right)^{\frac{2}{5}} \sqrt{2 \, \sqrt{5} + 10}\right)} \arctan\left(\frac{2 \, \left(\frac{3}{2}\right)^{\frac{4}{5}} {\left(\left(\frac{3}{2}\right)^{\frac{1}{5}} {\left(\sqrt{5} - 1\right)} + 4 \, x\right)}}{3 \, \sqrt{2 \, \sqrt{5} + 10}}\right) + \frac{1}{3000} \, {\left(\sqrt{5} \left(\frac{3}{2}\right)^{\frac{2}{5}} \sqrt{-2 \, \sqrt{5} + 10} + \left(\frac{3}{2}\right)^{\frac{2}{5}} \sqrt{-2 \, \sqrt{5} + 10}\right)} \arctan\left(-\frac{2 \, \left(\frac{3}{2}\right)^{\frac{4}{5}} {\left(\left(\frac{3}{2}\right)^{\frac{1}{5}} {\left(\sqrt{5} + 1\right)} - 4 \, x\right)}}{3 \, \sqrt{-2 \, \sqrt{5} + 10}}\right) - \frac{1}{6000} \, {\left(\left(\frac{3}{2}\right)^{\frac{2}{5}} {\left(\sqrt{5} - 5\right)} + \sqrt{5} \left(\frac{3}{2}\right)^{\frac{2}{5}} + 3 \, \left(\frac{3}{2}\right)^{\frac{2}{5}}\right)} \log\left(x^{2} - \frac{1}{2} \, x {\left(\sqrt{5} \left(\frac{3}{2}\right)^{\frac{1}{5}} + \left(\frac{3}{2}\right)^{\frac{1}{5}}\right)} + \left(\frac{3}{2}\right)^{\frac{2}{5}}\right) + \frac{1}{6000} \, {\left(\left(\frac{3}{2}\right)^{\frac{2}{5}} {\left(\sqrt{5} + 5\right)} + \sqrt{5} \left(\frac{3}{2}\right)^{\frac{2}{5}} - 3 \, \left(\frac{3}{2}\right)^{\frac{2}{5}}\right)} \log\left(x^{2} + \frac{1}{2} \, x {\left(\sqrt{5} \left(\frac{3}{2}\right)^{\frac{1}{5}} - \left(\frac{3}{2}\right)^{\frac{1}{5}}\right)} + \left(\frac{3}{2}\right)^{\frac{2}{5}}\right) - \frac{1}{750} \, \left(\frac{3}{2}\right)^{\frac{2}{5}} \log\left({\left| x + \left(\frac{3}{2}\right)^{\frac{1}{5}} \right|}\right) + \frac{4 \, x^{7} - 9 \, x^{2}}{300 \, {\left(2 \, x^{5} + 3\right)}^{2}}"," ",0,"-1/3000*(sqrt(5)*(3/2)^(2/5)*sqrt(2*sqrt(5) + 10) - (3/2)^(2/5)*sqrt(2*sqrt(5) + 10))*arctan(2/3*(3/2)^(4/5)*((3/2)^(1/5)*(sqrt(5) - 1) + 4*x)/sqrt(2*sqrt(5) + 10)) + 1/3000*(sqrt(5)*(3/2)^(2/5)*sqrt(-2*sqrt(5) + 10) + (3/2)^(2/5)*sqrt(-2*sqrt(5) + 10))*arctan(-2/3*(3/2)^(4/5)*((3/2)^(1/5)*(sqrt(5) + 1) - 4*x)/sqrt(-2*sqrt(5) + 10)) - 1/6000*((3/2)^(2/5)*(sqrt(5) - 5) + sqrt(5)*(3/2)^(2/5) + 3*(3/2)^(2/5))*log(x^2 - 1/2*x*(sqrt(5)*(3/2)^(1/5) + (3/2)^(1/5)) + (3/2)^(2/5)) + 1/6000*((3/2)^(2/5)*(sqrt(5) + 5) + sqrt(5)*(3/2)^(2/5) - 3*(3/2)^(2/5))*log(x^2 + 1/2*x*(sqrt(5)*(3/2)^(1/5) - (3/2)^(1/5)) + (3/2)^(2/5)) - 1/750*(3/2)^(2/5)*log(abs(x + (3/2)^(1/5))) + 1/300*(4*x^7 - 9*x^2)/(2*x^5 + 3)^2","A",0
178,1,55,0,1.098698," ","integrate(9/5/x^2/(-2*x^2+3)^3,x, algorithm=""giac"")","-\frac{1}{48} \, \sqrt{6} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{6} \right|}}{{\left| 4 \, x + 2 \, \sqrt{6} \right|}}\right) - \frac{14 \, x^{3} - 27 \, x}{60 \, {\left(2 \, x^{2} - 3\right)}^{2}} - \frac{1}{15 \, x}"," ",0,"-1/48*sqrt(6)*log(abs(4*x - 2*sqrt(6))/abs(4*x + 2*sqrt(6))) - 1/60*(14*x^3 - 27*x)/(2*x^2 - 3)^2 - 1/15/x","A",0
179,1,28,0,0.924378," ","integrate((3*x^4+4)/x^2/(x^2+1)^3,x, algorithm=""giac"")","-\frac{25 \, x^{3} + 39 \, x}{8 \, {\left(x^{2} + 1\right)}^{2}} - \frac{4}{x} - \frac{57}{8} \, \arctan\left(x\right)"," ",0,"-1/8*(25*x^3 + 39*x)/(x^2 + 1)^2 - 4/x - 57/8*arctan(x)","A",0
180,1,35,0,0.872143," ","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=""giac"")","-\frac{2 \, x^{2} + 7 \, x - 3}{2 \, {\left(x + 1\right)} {\left(x - 1\right)}^{2}} - 2 \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/2*(2*x^2 + 7*x - 3)/((x + 1)*(x - 1)^2) - 2*log(abs(x + 1)) + log(abs(x - 1))","A",0
181,1,60,0,0.937380," ","integrate((x^2+1)/x/(x^3+1)^2,x, algorithm=""giac"")","\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^{2} - x + 1\right)} {\left(x + 1\right)}} - \frac{5}{18} \, \log\left(x^{2} - x + 1\right) - \frac{4}{9} \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/3*(x^2 + 1)/((x^2 - x + 1)*(x + 1)) - 5/18*log(x^2 - x + 1) - 4/9*log(abs(x + 1)) + log(abs(x))","A",0
182,1,72,0,0.903072," ","integrate((x^2-3*x-2)/(1+x)^2/(x^2+x+1)^2,x, algorithm=""giac"")","-\frac{25}{9} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(\frac{2}{x + 1} - 1\right)}\right) + \frac{\frac{7}{x + 1} - 2}{3 \, {\left(\frac{1}{x + 1} - \frac{1}{{\left(x + 1\right)}^{2}} - 1\right)}} - \frac{2}{x + 1} + \frac{1}{2} \, \log\left(-\frac{1}{x + 1} + \frac{1}{{\left(x + 1\right)}^{2}} + 1\right)"," ",0,"-25/9*sqrt(3)*arctan(-1/3*sqrt(3)*(2/(x + 1) - 1)) + 1/3*(7/(x + 1) - 2)/(1/(x + 1) - 1/(x + 1)^2 - 1) - 2/(x + 1) + 1/2*log(-1/(x + 1) + 1/(x + 1)^2 + 1)","A",0
183,1,33,0,0.766833," ","integrate(1/(1-4*x)^3/(2-3*x),x, algorithm=""giac"")","\frac{24 \, x - 1}{50 \, {\left(4 \, x - 1\right)}^{2}} - \frac{9}{125} \, \log\left({\left| 4 \, x - 1 \right|}\right) + \frac{9}{125} \, \log\left({\left| 3 \, x - 2 \right|}\right)"," ",0,"1/50*(24*x - 1)/(4*x - 1)^2 - 9/125*log(abs(4*x - 1)) + 9/125*log(abs(3*x - 2))","A",0
184,1,18,0,1.104172," ","integrate(x^3/(-5*x^2+2)^7,x, algorithm=""giac"")","\frac{15 \, x^{2} - 1}{750 \, {\left(5 \, x^{2} - 2\right)}^{6}}"," ",0,"1/750*(15*x^2 - 1)/(5*x^2 - 2)^6","A",0
185,1,40,0,1.031566," ","integrate(x^7/(-5*x^2+2)^3,x, algorithm=""giac"")","-\frac{1}{250} \, x^{2} + \frac{225 \, x^{4} - 120 \, x^{2} + 16}{1250 \, {\left(5 \, x^{2} - 2\right)}^{2}} - \frac{3}{625} \, \log\left({\left| 5 \, x^{2} - 2 \right|}\right)"," ",0,"-1/250*x^2 + 1/1250*(225*x^4 - 120*x^2 + 16)/(5*x^2 - 2)^2 - 3/625*log(abs(5*x^2 - 2))","A",0
186,1,43,0,0.788706," ","integrate(1/(-2+x)^3/(1+x)^2,x, algorithm=""giac"")","\frac{1}{27 \, {\left(x + 1\right)}} - \frac{\frac{18}{x + 1} - 5}{162 \, {\left(\frac{3}{x + 1} - 1\right)}^{2}} + \frac{1}{27} \, \log\left({\left| -\frac{3}{x + 1} + 1 \right|}\right)"," ",0,"1/27/(x + 1) - 1/162*(18/(x + 1) - 5)/(3/(x + 1) - 1)^2 + 1/27*log(abs(-3/(x + 1) + 1))","A",0
187,1,47,0,0.971511," ","integrate(1/(2+x)^3/(3+x)^4,x, algorithm=""giac"")","\frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} + 4175 \, x + 2627}{6 \, {\left(x + 3\right)}^{3} {\left(x + 2\right)}^{2}} - 10 \, \log\left({\left| x + 3 \right|}\right) + 10 \, \log\left({\left| x + 2 \right|}\right)"," ",0,"1/6*(60*x^4 + 630*x^3 + 2450*x^2 + 4175*x + 2627)/((x + 3)^3*(x + 2)^2) - 10*log(abs(x + 3)) + 10*log(abs(x + 2))","A",0
188,1,45,0,0.879203," ","integrate(x^5/(3+x)^2,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(x + 3\right)}^{4} {\left(\frac{20}{x + 3} - \frac{180}{{\left(x + 3\right)}^{2}} + \frac{1080}{{\left(x + 3\right)}^{3}} - 1\right)} + \frac{243}{x + 3} + 405 \, \log\left({\left| x + 3 \right|}\right)"," ",0,"-1/4*(x + 3)^4*(20/(x + 3) - 180/(x + 3)^2 + 1080/(x + 3)^3 - 1) + 243/(x + 3) + 405*log(abs(x + 3))","A",0
189,1,39,0,0.974044," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, c c_{1} x^{4} + \frac{1}{3} \, b_{1} c x^{3} + \frac{2}{3} \, b c_{1} x^{3} + b b_{1} x^{2} + \frac{1}{2} \, a c_{1} x^{2} + a b_{1} x"," ",0,"1/4*c*c1*x^4 + 1/3*b1*c*x^3 + 2/3*b*c1*x^3 + b*b1*x^2 + 1/2*a*c1*x^2 + a*b1*x","A",0
190,1,98,0,1.106076," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} c_{1} x^{6} + \frac{1}{5} \, b_{1} c^{2} x^{5} + \frac{4}{5} \, b c c_{1} x^{5} + b b_{1} c x^{4} + b^{2} c_{1} x^{4} + \frac{1}{2} \, a c c_{1} x^{4} + \frac{4}{3} \, b^{2} b_{1} x^{3} + \frac{2}{3} \, a b_{1} c x^{3} + \frac{4}{3} \, a b c_{1} x^{3} + 2 \, a b b_{1} x^{2} + \frac{1}{2} \, a^{2} c_{1} x^{2} + a^{2} b_{1} x"," ",0,"1/6*c^2*c1*x^6 + 1/5*b1*c^2*x^5 + 4/5*b*c*c1*x^5 + b*b1*c*x^4 + b^2*c1*x^4 + 1/2*a*c*c1*x^4 + 4/3*b^2*b1*x^3 + 2/3*a*b1*c*x^3 + 4/3*a*b*c1*x^3 + 2*a*b*b1*x^2 + 1/2*a^2*c1*x^2 + a^2*b1*x","A",0
191,1,188,0,0.977758," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, c^{3} c_{1} x^{8} + \frac{1}{7} \, b_{1} c^{3} x^{7} + \frac{6}{7} \, b c^{2} c_{1} x^{7} + b b_{1} c^{2} x^{6} + 2 \, b^{2} c c_{1} x^{6} + \frac{1}{2} \, a c^{2} c_{1} x^{6} + \frac{12}{5} \, b^{2} b_{1} c x^{5} + \frac{3}{5} \, a b_{1} c^{2} x^{5} + \frac{8}{5} \, b^{3} c_{1} x^{5} + \frac{12}{5} \, a b c c_{1} x^{5} + 2 \, b^{3} b_{1} x^{4} + 3 \, a b b_{1} c x^{4} + 3 \, a b^{2} c_{1} x^{4} + \frac{3}{4} \, a^{2} c c_{1} x^{4} + 4 \, a b^{2} b_{1} x^{3} + a^{2} b_{1} c x^{3} + 2 \, a^{2} b c_{1} x^{3} + 3 \, a^{2} b b_{1} x^{2} + \frac{1}{2} \, a^{3} c_{1} x^{2} + a^{3} b_{1} x"," ",0,"1/8*c^3*c1*x^8 + 1/7*b1*c^3*x^7 + 6/7*b*c^2*c1*x^7 + b*b1*c^2*x^6 + 2*b^2*c*c1*x^6 + 1/2*a*c^2*c1*x^6 + 12/5*b^2*b1*c*x^5 + 3/5*a*b1*c^2*x^5 + 8/5*b^3*c1*x^5 + 12/5*a*b*c*c1*x^5 + 2*b^3*b1*x^4 + 3*a*b*b1*c*x^4 + 3*a*b^2*c1*x^4 + 3/4*a^2*c*c1*x^4 + 4*a*b^2*b1*x^3 + a^2*b1*c*x^3 + 2*a^2*b*c1*x^3 + 3*a^2*b*b1*x^2 + 1/2*a^3*c1*x^2 + a^3*b1*x","A",0
192,1,307,0,1.029617," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^4,x, algorithm=""giac"")","\frac{1}{10} \, c^{4} c_{1} x^{10} + \frac{1}{9} \, b_{1} c^{4} x^{9} + \frac{8}{9} \, b c^{3} c_{1} x^{9} + b b_{1} c^{3} x^{8} + 3 \, b^{2} c^{2} c_{1} x^{8} + \frac{1}{2} \, a c^{3} c_{1} x^{8} + \frac{24}{7} \, b^{2} b_{1} c^{2} x^{7} + \frac{4}{7} \, a b_{1} c^{3} x^{7} + \frac{32}{7} \, b^{3} c c_{1} x^{7} + \frac{24}{7} \, a b c^{2} c_{1} x^{7} + \frac{16}{3} \, b^{3} b_{1} c x^{6} + 4 \, a b b_{1} c^{2} x^{6} + \frac{8}{3} \, b^{4} c_{1} x^{6} + 8 \, a b^{2} c c_{1} x^{6} + a^{2} c^{2} c_{1} x^{6} + \frac{16}{5} \, b^{4} b_{1} x^{5} + \frac{48}{5} \, a b^{2} b_{1} c x^{5} + \frac{6}{5} \, a^{2} b_{1} c^{2} x^{5} + \frac{32}{5} \, a b^{3} c_{1} x^{5} + \frac{24}{5} \, a^{2} b c c_{1} x^{5} + 8 \, a b^{3} b_{1} x^{4} + 6 \, a^{2} b b_{1} c x^{4} + 6 \, a^{2} b^{2} c_{1} x^{4} + a^{3} c c_{1} x^{4} + 8 \, a^{2} b^{2} b_{1} x^{3} + \frac{4}{3} \, a^{3} b_{1} c x^{3} + \frac{8}{3} \, a^{3} b c_{1} x^{3} + 4 \, a^{3} b b_{1} x^{2} + \frac{1}{2} \, a^{4} c_{1} x^{2} + a^{4} b_{1} x"," ",0,"1/10*c^4*c1*x^10 + 1/9*b1*c^4*x^9 + 8/9*b*c^3*c1*x^9 + b*b1*c^3*x^8 + 3*b^2*c^2*c1*x^8 + 1/2*a*c^3*c1*x^8 + 24/7*b^2*b1*c^2*x^7 + 4/7*a*b1*c^3*x^7 + 32/7*b^3*c*c1*x^7 + 24/7*a*b*c^2*c1*x^7 + 16/3*b^3*b1*c*x^6 + 4*a*b*b1*c^2*x^6 + 8/3*b^4*c1*x^6 + 8*a*b^2*c*c1*x^6 + a^2*c^2*c1*x^6 + 16/5*b^4*b1*x^5 + 48/5*a*b^2*b1*c*x^5 + 6/5*a^2*b1*c^2*x^5 + 32/5*a*b^3*c1*x^5 + 24/5*a^2*b*c*c1*x^5 + 8*a*b^3*b1*x^4 + 6*a^2*b*b1*c*x^4 + 6*a^2*b^2*c1*x^4 + a^3*c*c1*x^4 + 8*a^2*b^2*b1*x^3 + 4/3*a^3*b1*c*x^3 + 8/3*a^3*b*c1*x^3 + 4*a^3*b*b1*x^2 + 1/2*a^4*c1*x^2 + a^4*b1*x","A",0
193,0,0,0,0.000000," ","integrate((c1*x+b1)*(c*x^2+2*b*x+a)^n,x, algorithm=""giac"")","\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
194,1,60,0,0.770788," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a),x, algorithm=""giac"")","\frac{c_{1} \log\left(c x^{2} + 2 \, b x + a\right)}{2 \, c} + \frac{{\left(b_{1} c - b c_{1}\right)} \arctan\left(\frac{c x + b}{\sqrt{-b^{2} + a c}}\right)}{\sqrt{-b^{2} + a c} c}"," ",0,"1/2*c1*log(c*x^2 + 2*b*x + a)/c + (b1*c - b*c1)*arctan((c*x + b)/sqrt(-b^2 + a*c))/(sqrt(-b^2 + a*c)*c)","A",0
195,1,92,0,1.135130," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(b_{1} c - b c_{1}\right)} \arctan\left(\frac{c x + b}{\sqrt{-b^{2} + a c}}\right)}{2 \, {\left(b^{2} - a c\right)} \sqrt{-b^{2} + a c}} - \frac{b_{1} c x - b c_{1} x + b b_{1} - a c_{1}}{2 \, {\left(c x^{2} + 2 \, b x + a\right)} {\left(b^{2} - a c\right)}}"," ",0,"-1/2*(b1*c - b*c1)*arctan((c*x + b)/sqrt(-b^2 + a*c))/((b^2 - a*c)*sqrt(-b^2 + a*c)) - 1/2*(b1*c*x - b*c1*x + b*b1 - a*c1)/((c*x^2 + 2*b*x + a)*(b^2 - a*c))","A",0
196,1,194,0,1.034194," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b_{1} c^{2} - b c c_{1}\right)} \arctan\left(\frac{c x + b}{\sqrt{-b^{2} + a c}}\right)}{8 \, {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} \sqrt{-b^{2} + a c}} + \frac{3 \, b_{1} c^{3} x^{3} - 3 \, b c^{2} c_{1} x^{3} + 9 \, b b_{1} c^{2} x^{2} - 9 \, b^{2} c c_{1} x^{2} + 4 \, b^{2} b_{1} c x + 5 \, a b_{1} c^{2} x - 4 \, b^{3} c_{1} x - 5 \, a b c c_{1} x - 2 \, b^{3} b_{1} + 5 \, a b b_{1} c - a b^{2} c_{1} - 2 \, a^{2} c c_{1}}{8 \, {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} {\left(c x^{2} + 2 \, b x + a\right)}^{2}}"," ",0,"3/8*(b1*c^2 - b*c*c1)*arctan((c*x + b)/sqrt(-b^2 + a*c))/((b^4 - 2*a*b^2*c + a^2*c^2)*sqrt(-b^2 + a*c)) + 1/8*(3*b1*c^3*x^3 - 3*b*c^2*c1*x^3 + 9*b*b1*c^2*x^2 - 9*b^2*c*c1*x^2 + 4*b^2*b1*c*x + 5*a*b1*c^2*x - 4*b^3*c1*x - 5*a*b*c*c1*x - 2*b^3*b1 + 5*a*b*b1*c - a*b^2*c1 - 2*a^2*c*c1)/((b^4 - 2*a*b^2*c + a^2*c^2)*(c*x^2 + 2*b*x + a)^2)","A",0
197,1,363,0,0.853541," ","integrate((c1*x+b1)/(c*x^2+2*b*x+a)^4,x, algorithm=""giac"")","-\frac{5 \, {\left(b_{1} c^{3} - b c^{2} c_{1}\right)} \arctan\left(\frac{c x + b}{\sqrt{-b^{2} + a c}}\right)}{16 \, {\left(b^{6} - 3 \, a b^{4} c + 3 \, a^{2} b^{2} c^{2} - a^{3} c^{3}\right)} \sqrt{-b^{2} + a c}} - \frac{15 \, b_{1} c^{5} x^{5} - 15 \, b c^{4} c_{1} x^{5} + 75 \, b b_{1} c^{4} x^{4} - 75 \, b^{2} c^{3} c_{1} x^{4} + 110 \, b^{2} b_{1} c^{3} x^{3} + 40 \, a b_{1} c^{4} x^{3} - 110 \, b^{3} c^{2} c_{1} x^{3} - 40 \, a b c^{3} c_{1} x^{3} + 30 \, b^{3} b_{1} c^{2} x^{2} + 120 \, a b b_{1} c^{3} x^{2} - 30 \, b^{4} c c_{1} x^{2} - 120 \, a b^{2} c^{2} c_{1} x^{2} - 12 \, b^{4} b_{1} c x + 54 \, a b^{2} b_{1} c^{2} x + 33 \, a^{2} b_{1} c^{3} x + 12 \, b^{5} c_{1} x - 54 \, a b^{3} c c_{1} x - 33 \, a^{2} b c^{2} c_{1} x + 8 \, b^{5} b_{1} - 26 \, a b^{3} b_{1} c + 33 \, a^{2} b b_{1} c^{2} + 2 \, a b^{4} c_{1} - 9 \, a^{2} b^{2} c c_{1} - 8 \, a^{3} c^{2} c_{1}}{48 \, {\left(b^{6} - 3 \, a b^{4} c + 3 \, a^{2} b^{2} c^{2} - a^{3} c^{3}\right)} {\left(c x^{2} + 2 \, b x + a\right)}^{3}}"," ",0,"-5/16*(b1*c^3 - b*c^2*c1)*arctan((c*x + b)/sqrt(-b^2 + a*c))/((b^6 - 3*a*b^4*c + 3*a^2*b^2*c^2 - a^3*c^3)*sqrt(-b^2 + a*c)) - 1/48*(15*b1*c^5*x^5 - 15*b*c^4*c1*x^5 + 75*b*b1*c^4*x^4 - 75*b^2*c^3*c1*x^4 + 110*b^2*b1*c^3*x^3 + 40*a*b1*c^4*x^3 - 110*b^3*c^2*c1*x^3 - 40*a*b*c^3*c1*x^3 + 30*b^3*b1*c^2*x^2 + 120*a*b*b1*c^3*x^2 - 30*b^4*c*c1*x^2 - 120*a*b^2*c^2*c1*x^2 - 12*b^4*b1*c*x + 54*a*b^2*b1*c^2*x + 33*a^2*b1*c^3*x + 12*b^5*c1*x - 54*a*b^3*c*c1*x - 33*a^2*b*c^2*c1*x + 8*b^5*b1 - 26*a*b^3*b1*c + 33*a^2*b*b1*c^2 + 2*a*b^4*c1 - 9*a^2*b^2*c*c1 - 8*a^3*c^2*c1)/((b^6 - 3*a*b^4*c + 3*a^2*b^2*c^2 - a^3*c^3)*(c*x^2 + 2*b*x + a)^3)","B",0
198,0,0,0,0.000000," ","integrate((c1*x+b1)/((c*x^2+2*b*x+a)^n),x, algorithm=""giac"")","\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
199,1,46,0,0.957727," ","integrate(x/(2*x^2+6*x+3),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{3} + 6 \right|}}{{\left| 4 \, x + 2 \, \sqrt{3} + 6 \right|}}\right) + \frac{1}{4} \, \log\left({\left| 2 \, x^{2} + 6 \, x + 3 \right|}\right)"," ",0,"-1/4*sqrt(3)*log(abs(4*x - 2*sqrt(3) + 6)/abs(4*x + 2*sqrt(3) + 6)) + 1/4*log(abs(2*x^2 + 6*x + 3))","A",0
200,1,61,0,1.156982," ","integrate((-3+2*x)/(2*x^2+6*x+3)^3,x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| 4 \, x - 2 \, \sqrt{3} + 6 \right|}}{{\left| 4 \, x + 2 \, \sqrt{3} + 6 \right|}}\right) - \frac{8 \, x^{3} + 36 \, x^{2} + 44 \, x + 13}{4 \, {\left(2 \, x^{2} + 6 \, x + 3\right)}^{2}}"," ",0,"-1/6*sqrt(3)*log(abs(4*x - 2*sqrt(3) + 6)/abs(4*x + 2*sqrt(3) + 6)) - 1/4*(8*x^3 + 36*x^2 + 44*x + 13)/(2*x^2 + 6*x + 3)^2","A",0
201,1,32,0,0.980663," ","integrate((-1+x)/(x^2+5*x+4)^2,x, algorithm=""giac"")","\frac{7 \, x + 13}{9 \, {\left(x^{2} + 5 \, x + 4\right)}} - \frac{7}{27} \, \log\left({\left| x + 4 \right|}\right) + \frac{7}{27} \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/9*(7*x + 13)/(x^2 + 5*x + 4) - 7/27*log(abs(x + 4)) + 7/27*log(abs(x + 1))","A",0
202,1,62,0,0.898980," ","integrate(1/(x^2+3*x+2)^5,x, algorithm=""giac"")","\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^{2} + 3 \, x + 2\right)}^{4}} - 70 \, \log\left({\left| x + 2 \right|}\right) + 70 \, \log\left({\left| x + 1 \right|}\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^2 + 3*x + 2)^4 - 70*log(abs(x + 2)) + 70*log(abs(x + 1))","A",0
203,1,67,0,1.163137," ","integrate(1/x^3/(2*x^2-6*x+7)^2,x, algorithm=""giac"")","\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^{2} - 6 \, x + 7\right)} x^{2}} - \frac{40}{2401} \, \log\left(2 \, x^{2} - 6 \, x + 7\right) + \frac{80}{2401} \, \log\left({\left| x \right|}\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^2 - 6*x + 7)*x^2) - 40/2401*log(2*x^2 - 6*x + 7) + 80/2401*log(abs(x))","A",0
204,1,62,0,0.977922," ","integrate(x^9/(x^2+3*x+2)^5,x, algorithm=""giac"")","-\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 + 2\right)}^{4} {\left(x + 1\right)}^{4}} + 1472 \, \log\left({\left| x + 2 \right|}\right) - 1471 \, \log\left({\left| x + 1 \right|}\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 + 2)^4*(x + 1)^4) + 1472*log(abs(x + 2)) - 1471*log(abs(x + 1))","A",0
205,1,66,0,1.070347," ","integrate((1+2*x)^2/(2*x^2+5*x+3)^5,x, algorithm=""giac"")","\frac{238080 \, x^{7} + 2083200 \, x^{6} + 7757440 \, x^{5} + 15934000 \, x^{4} + 19495776 \, x^{3} + 14209160 \, x^{2} + 5712464 \, x + 977397}{12 \, {\left(2 \, x^{2} + 5 \, x + 3\right)}^{4}} - 2480 \, \log\left({\left| 2 \, x + 3 \right|}\right) + 2480 \, \log\left({\left| x + 1 \right|}\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)/(2*x^2 + 5*x + 3)^4 - 2480*log(abs(2*x + 3)) + 2480*log(abs(x + 1))","A",0
206,1,47,0,0.971356," ","integrate((-b*x^2+a)^3/x^7,x, algorithm=""giac"")","-\frac{1}{2} \, b^{3} \log\left(x^{2}\right) + \frac{11 \, b^{3} x^{6} - 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*(11*b^3*x^6 - 18*a*b^2*x^4 + 9*a^2*b*x^2 - 2*a^3)/x^6","A",0
207,1,58,0,0.964911," ","integrate(x^13/(a^4+x^4)^5,x, algorithm=""giac"")","\frac{5 \, \arctan\left(\frac{x^{2}}{a^{2}}\right)}{256 \, a^{6}} - \frac{15 \, a^{12} x^{2} + 55 \, a^{8} x^{6} + 73 \, a^{4} x^{10} - 15 \, x^{14}}{768 \, {\left(a^{4} + x^{4}\right)}^{4} a^{4}}"," ",0,"5/256*arctan(x^2/a^2)/a^6 - 1/768*(15*a^12*x^2 + 55*a^8*x^6 + 73*a^4*x^10 - 15*x^14)/((a^4 + x^4)^4*a^4)","A",0
208,1,31,0,0.994153," ","integrate(x^(3/2)*(x^2+1)*(-x+2*x^(1/2))^2,x, algorithm=""giac"")","\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
209,1,31,0,1.054908," ","integrate((-3*x^(3/5)+x^(3/2))^2*(-1/3*x^(2/3)+4*x^(3/2)),x, algorithm=""giac"")","\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
210,1,18,0,0.835172," ","integrate(1/(1+(1+x)^(1/2)),x, algorithm=""giac"")","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
211,1,12,0,0.923755," ","integrate(x/(1+(1+x)^(1/2)),x, algorithm=""giac"")","\frac{2}{3} \, {\left(x + 1\right)}^{\frac{3}{2}} - x - 1"," ",0,"2/3*(x + 1)^(3/2) - x - 1","A",0
212,1,21,0,0.866928," ","integrate((1+(1+x)^(1/2))/(-1+(1+x)^(1/2)),x, algorithm=""giac"")","x + 4 \, \sqrt{x + 1} + 4 \, \log\left({\left| \sqrt{x + 1} - 1 \right|}\right) + 1"," ",0,"x + 4*sqrt(x + 1) + 4*log(abs(sqrt(x + 1) - 1)) + 1","A",0
213,1,26,0,1.178057," ","integrate(1/((1+x)^(2/3)-(1+x)^(1/2)),x, algorithm=""giac"")","3 \, {\left(x + 1\right)}^{\frac{1}{3}} + 6 \, {\left(x + 1\right)}^{\frac{1}{6}} + 6 \, \log\left({\left| {\left(x + 1\right)}^{\frac{1}{6}} - 1 \right|}\right)"," ",0,"3*(x + 1)^(1/3) + 6*(x + 1)^(1/6) + 6*log(abs((x + 1)^(1/6) - 1))","A",0
214,1,19,0,0.915471," ","integrate((1+x^(1/4))^(1/3)/x^(1/2),x, algorithm=""giac"")","\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
215,1,49,0,1.006435," ","integrate(1/x^3/(1+x)^(3/2),x, algorithm=""giac"")","\frac{2}{\sqrt{x + 1}} + \frac{7 \, {\left(x + 1\right)}^{\frac{3}{2}} - 9 \, \sqrt{x + 1}}{4 \, x^{2}} - \frac{15}{8} \, \log\left(\sqrt{x + 1} + 1\right) + \frac{15}{8} \, \log\left({\left| \sqrt{x + 1} - 1 \right|}\right)"," ",0,"2/sqrt(x + 1) + 1/4*(7*(x + 1)^(3/2) - 9*sqrt(x + 1))/x^2 - 15/8*log(sqrt(x + 1) + 1) + 15/8*log(abs(sqrt(x + 1) - 1))","A",0
216,1,104,0,0.917911," ","integrate(1/(1-x)^(7/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(225 \, {\left(x - 1\right)}^{2} - 25 \, x + 28\right)}}{15 \, {\left(x - 1\right)}^{2} \sqrt{-x + 1}} - \frac{3249 \, {\left(x - 1\right)}^{3} \sqrt{-x + 1} + 10633 \, {\left(x - 1\right)}^{2} \sqrt{-x + 1} - 11767 \, {\left(-x + 1\right)}^{\frac{3}{2}} + 4431 \, \sqrt{-x + 1}}{192 \, x^{4}} - \frac{3003}{128} \, \log\left(\sqrt{-x + 1} + 1\right) + \frac{3003}{128} \, \log\left({\left| \sqrt{-x + 1} - 1 \right|}\right)"," ",0,"2/15*(225*(x - 1)^2 - 25*x + 28)/((x - 1)^2*sqrt(-x + 1)) - 1/192*(3249*(x - 1)^3*sqrt(-x + 1) + 10633*(x - 1)^2*sqrt(-x + 1) - 11767*(-x + 1)^(3/2) + 4431*sqrt(-x + 1))/x^4 - 3003/128*log(sqrt(-x + 1) + 1) + 3003/128*log(abs(sqrt(-x + 1) - 1))","A",0
217,1,82,0,1.138310," ","integrate(1/(-1+x)^(2/3)/x^5,x, algorithm=""giac"")","\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 \, x^{4}} - \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^4 - 55/243*log((x - 1)^(2/3) - (x - 1)^(1/3) + 1) + 110/243*log((x - 1)^(1/3) + 1)","A",0
218,1,29,0,0.919838," ","integrate(((1-x)/(1+x))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \pi \mathrm{sgn}\left(x + 1\right) + \arcsin\left(x\right) \mathrm{sgn}\left(x + 1\right) + \sqrt{-x^{2} + 1} \mathrm{sgn}\left(x + 1\right)"," ",0,"1/2*pi*sgn(x + 1) + arcsin(x)*sgn(x + 1) + sqrt(-x^2 + 1)*sgn(x + 1)","A",0
219,1,103,0,1.029452," ","integrate(x*((-a+x)/(b-x))^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(a^{2} \mathrm{sgn}\left(-b + x\right) + 2 \, a b \mathrm{sgn}\left(-b + x\right) - 3 \, b^{2} \mathrm{sgn}\left(-b + x\right)\right)} \arcsin\left(\frac{a + b - 2 \, x}{a - b}\right) \mathrm{sgn}\left(-a + b\right) - \frac{1}{4} \, \sqrt{-a b + a x + b x - x^{2}} {\left(a \mathrm{sgn}\left(-b + x\right) - 3 \, b \mathrm{sgn}\left(-b + x\right) - 2 \, x \mathrm{sgn}\left(-b + x\right)\right)}"," ",0,"1/8*(a^2*sgn(-b + x) + 2*a*b*sgn(-b + x) - 3*b^2*sgn(-b + x))*arcsin((a + b - 2*x)/(a - b))*sgn(-a + b) - 1/4*sqrt(-a*b + a*x + b*x - x^2)*(a*sgn(-b + x) - 3*b*sgn(-b + x) - 2*x*sgn(-b + x))","A",0
220,1,74,0,0.957647," ","integrate((-5+x)^(1/2)*(3+x)^(1/2)/(-1+x)/(x^2-25),x, algorithm=""giac"")","-\frac{1}{30} \, \sqrt{5} \log\left(\frac{{\left(\sqrt{x + 3} - \sqrt{x - 5}\right)}^{2} - 4 \, \sqrt{5} + 12}{{\left(\sqrt{x + 3} - \sqrt{x - 5}\right)}^{2} + 4 \, \sqrt{5} + 12}\right) - \frac{1}{3} \, \arctan\left(\frac{1}{8} \, {\left(\sqrt{x + 3} - \sqrt{x - 5}\right)}^{2}\right)"," ",0,"-1/30*sqrt(5)*log(((sqrt(x + 3) - sqrt(x - 5))^2 - 4*sqrt(5) + 12)/((sqrt(x + 3) - sqrt(x - 5))^2 + 4*sqrt(5) + 12)) - 1/3*arctan(1/8*(sqrt(x + 3) - sqrt(x - 5))^2)","B",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=""giac"")","\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,-1,0,0,0.000000," ","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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,0,0,0,0.000000," ","integrate(1/((-1+x)^4*(1+x)^2)^(1/3),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
227,1,177,0,0.834866," ","integrate((1/x+x)/((-2+x)*(1+x)^3)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \arcsin\left(\frac{4}{3 \, x} + \frac{1}{3}\right)}{2 \, \mathrm{sgn}\left(\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)} + \frac{\log\left({\left| 2 \, \sqrt{2} + \frac{2 \, \sqrt{2} \sqrt{-\frac{1}{x} - \frac{2}{x^{2}} + 1} - 3}{\frac{4}{x} + 1} + 3 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)} - \frac{\log\left({\left| -2 \, \sqrt{2} + \frac{2 \, \sqrt{2} \sqrt{-\frac{1}{x} - \frac{2}{x^{2}} + 1} - 3}{\frac{4}{x} + 1} + 3 \right|}\right)}{\mathrm{sgn}\left(\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)} + \frac{8 \, \sqrt{2}}{3 \, {\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{1}{x} - \frac{2}{x^{2}} + 1} - 3}{\frac{4}{x} + 1} - 1\right)} \mathrm{sgn}\left(\frac{1}{x^{2}} + \frac{1}{x^{3}}\right)}"," ",0,"-1/2*sqrt(2)*arcsin(4/3/x + 1/3)/sgn(1/x^2 + 1/x^3) + log(abs(2*sqrt(2) + (2*sqrt(2)*sqrt(-1/x - 2/x^2 + 1) - 3)/(4/x + 1) + 3))/sgn(1/x^2 + 1/x^3) - log(abs(-2*sqrt(2) + (2*sqrt(2)*sqrt(-1/x - 2/x^2 + 1) - 3)/(4/x + 1) + 3))/sgn(1/x^2 + 1/x^3) + 8/3*sqrt(2)/(((2*sqrt(2)*sqrt(-1/x - 2/x^2 + 1) - 3)/(4/x + 1) - 1)*sgn(1/x^2 + 1/x^3))","A",0
228,0,0,0,0.000000," ","integrate(((-1+x)^2*(1+x))^(1/3)/x^2,x, algorithm=""giac"")","\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
229,1,23,0,0.663183," ","integrate(1/(x^2-2*x-3)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(x - 3\right)} x - 3\right)} x + 5}{24 \, {\left(x^{2} - 2 \, x - 3\right)}^{\frac{3}{2}}}"," ",0,"1/24*(((x - 3)*x - 3)*x + 5)/(x^2 - 2*x - 3)^(3/2)","A",0
230,1,34,0,0.648581," ","integrate(1/(x^3-5*x^2+3*x+9)^(1/2),x, algorithm=""giac"")","-\frac{\log\left(\sqrt{x + 1} + 2\right)}{2 \, \mathrm{sgn}\left(x - 3\right)} + \frac{\log\left({\left| \sqrt{x + 1} - 2 \right|}\right)}{2 \, \mathrm{sgn}\left(x - 3\right)}"," ",0,"-1/2*log(sqrt(x + 1) + 2)/sgn(x - 3) + 1/2*log(abs(sqrt(x + 1) - 2))/sgn(x - 3)","A",0
231,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
232,0,0,0,0.000000," ","integrate(1/(x^3-5*x^2+3*x+9)^(1/3),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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
235,1,16,0,0.657954," ","integrate(1/(-2*x^2+3*x+4)^(1/2),x, algorithm=""giac"")","\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
236,1,4,0,0.627290," ","integrate(1/(-x^2+4*x-3)^(1/2),x, algorithm=""giac"")","\arcsin\left(x - 2\right)"," ",0,"arcsin(x - 2)","A",0
237,1,11,0,0.633490," ","integrate(1/(-3*x^2-5*x-2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arcsin\left(6 \, x + 5\right)"," ",0,"1/3*sqrt(3)*arcsin(6*x + 5)","A",0
238,1,51,0,0.632034," ","integrate(1/(x^2+4)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{5} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{5} x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)}"," ",0,"1/20*sqrt(5)*(pi*sgn(x) + 2*arctan(-1/5*sqrt(5)*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)))","B",0
239,1,57,0,0.636735," ","integrate(1/(x^2+4)/(4*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{60} \, \sqrt{15} \log\left(\frac{{\left(2 \, x - \sqrt{4 \, x^{2} + 1}\right)}^{2} - 8 \, \sqrt{15} + 31}{{\left(2 \, x - \sqrt{4 \, x^{2} + 1}\right)}^{2} + 8 \, \sqrt{15} + 31}\right)"," ",0,"-1/60*sqrt(15)*log(((2*x - sqrt(4*x^2 + 1))^2 - 8*sqrt(15) + 31)/((2*x - sqrt(4*x^2 + 1))^2 + 8*sqrt(15) + 31))","B",0
240,1,42,0,0.618658," ","integrate(x/(-x^2+3)/(-x^2+5)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\sqrt{2} + \sqrt{-x^{2} + 5}\right) - \frac{1}{4} \, \sqrt{2} \log\left({\left| -\sqrt{2} + \sqrt{-x^{2} + 5} \right|}\right)"," ",0,"1/4*sqrt(2)*log(sqrt(2) + sqrt(-x^2 + 5)) - 1/4*sqrt(2)*log(abs(-sqrt(2) + sqrt(-x^2 + 5)))","B",0
241,1,20,0,0.589234," ","integrate(x/(-x^2+5)/(-x^2+3)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-x^{2} + 3}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-x^2 + 3))","A",0
242,1,74,0,0.650248," ","integrate(1/(x^4-1)/(x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(\frac{{\left| 2 \, {\left(x - \sqrt{x^{2} + 2}\right)}^{2} - 4 \, \sqrt{3} - 8 \right|}}{{\left| 2 \, {\left(x - \sqrt{x^{2} + 2}\right)}^{2} + 4 \, \sqrt{3} - 8 \right|}}\right) + \frac{1}{2} \, \arctan\left(\frac{1}{2} \, {\left(x - \sqrt{x^{2} + 2}\right)}^{2}\right)"," ",0,"-1/12*sqrt(3)*log(abs(2*(x - sqrt(x^2 + 2))^2 - 4*sqrt(3) - 8)/abs(2*(x - sqrt(x^2 + 2))^2 + 4*sqrt(3) - 8)) + 1/2*arctan(1/2*(x - sqrt(x^2 + 2))^2)","B",0
243,1,109,0,0.734013," ","integrate(x/(x^2-1)/(x^2+2*x+4)^(1/2),x, algorithm=""giac"")","\frac{1}{14} \, \sqrt{7} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{7} + 2 \, \sqrt{x^{2} + 2 \, x + 4} + 2 \right|}}{{\left| -2 \, x + 2 \, \sqrt{7} + 2 \, \sqrt{x^{2} + 2 \, x + 4} + 2 \right|}}\right) + \frac{1}{6} \, \sqrt{3} \log\left(-\frac{{\left| -2 \, x - 2 \, \sqrt{3} + 2 \, \sqrt{x^{2} + 2 \, x + 4} - 2 \right|}}{2 \, {\left(x - \sqrt{3} - \sqrt{x^{2} + 2 \, x + 4} + 1\right)}}\right)"," ",0,"1/14*sqrt(7)*log(abs(-2*x - 2*sqrt(7) + 2*sqrt(x^2 + 2*x + 4) + 2)/abs(-2*x + 2*sqrt(7) + 2*sqrt(x^2 + 2*x + 4) + 2)) + 1/6*sqrt(3)*log(-1/2*abs(-2*x - 2*sqrt(3) + 2*sqrt(x^2 + 2*x + 4) - 2)/(x - sqrt(3) - sqrt(x^2 + 2*x + 4) + 1))","B",0
244,1,164,0,0.715315," ","integrate(1/(x^3-8)/(x^2+2*x+5)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - \sqrt{x^{2} + 2 \, x + 5} + 2\right)}\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - \sqrt{x^{2} + 2 \, x + 5}\right)}\right) + \frac{1}{156} \, \sqrt{13} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{13} + 2 \, \sqrt{x^{2} + 2 \, x + 5} + 4 \right|}}{{\left| -2 \, x + 2 \, \sqrt{13} + 2 \, \sqrt{x^{2} + 2 \, x + 5} + 4 \right|}}\right) - \frac{1}{24} \, \log\left({\left(x - \sqrt{x^{2} + 2 \, x + 5}\right)}^{2} + 4 \, x - 4 \, \sqrt{x^{2} + 2 \, x + 5} + 7\right) + \frac{1}{24} \, \log\left({\left(x - \sqrt{x^{2} + 2 \, x + 5}\right)}^{2} + 3\right)"," ",0,"1/12*sqrt(3)*arctan(-1/3*sqrt(3)*(x - sqrt(x^2 + 2*x + 5) + 2)) - 1/12*sqrt(3)*arctan(-1/3*sqrt(3)*(x - sqrt(x^2 + 2*x + 5))) + 1/156*sqrt(13)*log(abs(-2*x - 2*sqrt(13) + 2*sqrt(x^2 + 2*x + 5) + 4)/abs(-2*x + 2*sqrt(13) + 2*sqrt(x^2 + 2*x + 5) + 4)) - 1/24*log((x - sqrt(x^2 + 2*x + 5))^2 + 4*x - 4*sqrt(x^2 + 2*x + 5) + 7) + 1/24*log((x - sqrt(x^2 + 2*x + 5))^2 + 3)","B",0
245,1,165,0,0.711681," ","integrate(x/(x^2+x+4)/(4*x^2+4*x+5)^(1/2),x, algorithm=""giac"")","\frac{1}{165} \, \sqrt{165} \sqrt{15} \arctan\left(-\frac{2 \, x - \sqrt{4 \, x^{2} + 4 \, x + 5} + 1}{\sqrt{15} + \sqrt{11}}\right) - \frac{1}{165} \, \sqrt{165} \sqrt{15} \arctan\left(-\frac{2 \, x - \sqrt{4 \, x^{2} + 4 \, x + 5} + 1}{\sqrt{15} - \sqrt{11}}\right) - \frac{1}{330} \, \sqrt{165} \log\left(90000 \, {\left(2 \, x - \sqrt{4 \, x^{2} + 4 \, x + 5} + 1\right)}^{2} + 90000 \, {\left(\sqrt{15} + \sqrt{11}\right)}^{2}\right) + \frac{1}{330} \, \sqrt{165} \log\left(90000 \, {\left(2 \, x - \sqrt{4 \, x^{2} + 4 \, x + 5} + 1\right)}^{2} + 90000 \, {\left(\sqrt{15} - \sqrt{11}\right)}^{2}\right)"," ",0,"1/165*sqrt(165)*sqrt(15)*arctan(-(2*x - sqrt(4*x^2 + 4*x + 5) + 1)/(sqrt(15) + sqrt(11))) - 1/165*sqrt(165)*sqrt(15)*arctan(-(2*x - sqrt(4*x^2 + 4*x + 5) + 1)/(sqrt(15) - sqrt(11))) - 1/330*sqrt(165)*log(90000*(2*x - sqrt(4*x^2 + 4*x + 5) + 1)^2 + 90000*(sqrt(15) + sqrt(11))^2) + 1/330*sqrt(165)*log(90000*(2*x - sqrt(4*x^2 + 4*x + 5) + 1)^2 + 90000*(sqrt(15) - sqrt(11))^2)","B",0
246,1,152,0,0.678952," ","integrate((3+x)/(x^2+1)/(x^2+x+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(\pi + 4 \, \arctan\left(-{\left(x - \sqrt{x^{2} + x + 1}\right)} {\left(\sqrt{2} + 2\right)} - \sqrt{2} - 1\right)\right)} + \frac{1}{2} \, \sqrt{2} {\left(\pi + 4 \, \arctan\left({\left(x - \sqrt{x^{2} + x + 1}\right)} {\left(\sqrt{2} - 2\right)} + \sqrt{2} - 1\right)\right)} - \frac{1}{2} \, \sqrt{2} \log\left({\left(x + \sqrt{2} - \sqrt{x^{2} + x + 1} - 1\right)}^{2} + {\left(x - \sqrt{x^{2} + x + 1} + 1\right)}^{2}\right) + \frac{1}{2} \, \sqrt{2} \log\left({\left(x - \sqrt{2} - \sqrt{x^{2} + x + 1} - 1\right)}^{2} + {\left(x - \sqrt{x^{2} + x + 1} + 1\right)}^{2}\right)"," ",0,"-1/2*sqrt(2)*(pi + 4*arctan(-(x - sqrt(x^2 + x + 1))*(sqrt(2) + 2) - sqrt(2) - 1)) + 1/2*sqrt(2)*(pi + 4*arctan((x - sqrt(x^2 + x + 1))*(sqrt(2) - 2) + sqrt(2) - 1)) - 1/2*sqrt(2)*log((x + sqrt(2) - sqrt(x^2 + x + 1) - 1)^2 + (x - sqrt(x^2 + x + 1) + 1)^2) + 1/2*sqrt(2)*log((x - sqrt(2) - sqrt(x^2 + x + 1) - 1)^2 + (x - sqrt(x^2 + x + 1) + 1)^2)","B",0
247,1,257,0,0.660598," ","integrate((1+2*x)/(3*x^2+4*x+4)/(x^2+6*x-1)^(1/2),x, algorithm=""giac"")","-\frac{5}{84} \, \sqrt{7} \sqrt{2} {\left(\arctan\left(2\right) + \arctan\left(\frac{1}{8} \, {\left(x - \sqrt{x^{2} + 6 \, x - 1}\right)} {\left(\sqrt{14} + \sqrt{2}\right)} + \frac{1}{8} \, \sqrt{14} + \frac{3}{8} \, \sqrt{2}\right)\right)} + \frac{5}{84} \, \sqrt{7} \sqrt{2} {\left(\arctan\left(\frac{1}{2}\right) + \arctan\left(-\frac{1}{8} \, {\left(x - \sqrt{x^{2} + 6 \, x - 1}\right)} {\left(\sqrt{14} - \sqrt{2}\right)} - \frac{1}{8} \, \sqrt{14} + \frac{3}{8} \, \sqrt{2}\right)\right)} + \frac{1}{42} \, \sqrt{7} \log\left(4 \, {\left(4 \, \sqrt{7} \sqrt{2} + 3 \, x + \sqrt{7} - 4 \, \sqrt{2} - 3 \, \sqrt{x^{2} + 6 \, x - 1} + 2\right)}^{2} + 16 \, {\left(\sqrt{7} \sqrt{2} - 3 \, x - \sqrt{7} - \sqrt{2} + 3 \, \sqrt{x^{2} + 6 \, x - 1} - 2\right)}^{2}\right) - \frac{1}{42} \, \sqrt{7} \log\left(4 \, {\left(4 \, \sqrt{7} \sqrt{2} + 3 \, x - \sqrt{7} + 4 \, \sqrt{2} - 3 \, \sqrt{x^{2} + 6 \, x - 1} + 2\right)}^{2} + 16 \, {\left(\sqrt{7} \sqrt{2} - 3 \, x + \sqrt{7} + \sqrt{2} + 3 \, \sqrt{x^{2} + 6 \, x - 1} - 2\right)}^{2}\right)"," ",0,"-5/84*sqrt(7)*sqrt(2)*(arctan(2) + arctan(1/8*(x - sqrt(x^2 + 6*x - 1))*(sqrt(14) + sqrt(2)) + 1/8*sqrt(14) + 3/8*sqrt(2))) + 5/84*sqrt(7)*sqrt(2)*(arctan(1/2) + arctan(-1/8*(x - sqrt(x^2 + 6*x - 1))*(sqrt(14) - sqrt(2)) - 1/8*sqrt(14) + 3/8*sqrt(2))) + 1/42*sqrt(7)*log(4*(4*sqrt(7)*sqrt(2) + 3*x + sqrt(7) - 4*sqrt(2) - 3*sqrt(x^2 + 6*x - 1) + 2)^2 + 16*(sqrt(7)*sqrt(2) - 3*x - sqrt(7) - sqrt(2) + 3*sqrt(x^2 + 6*x - 1) - 2)^2) - 1/42*sqrt(7)*log(4*(4*sqrt(7)*sqrt(2) + 3*x - sqrt(7) + 4*sqrt(2) - 3*sqrt(x^2 + 6*x - 1) + 2)^2 + 16*(sqrt(7)*sqrt(2) - 3*x + sqrt(7) + sqrt(2) + 3*sqrt(x^2 + 6*x - 1) - 2)^2)","B",0
248,1,629,0,0.992162," ","integrate((A*x+B)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{35} {\left(2 \, A^{2} + 3 \, A B + B^{2}\right)} \sqrt{A^{2} + 2 \, A B + B^{2}} {\left(\arctan\left(3\right) + \arctan\left(-\frac{5 \, {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} {\left(300 \, \sqrt{14} - 1129\right)} - 7658 \, \sqrt{35} + 14361 \, \sqrt{10}}{2329 \, \sqrt{35} - 4358 \, \sqrt{10}}\right)\right)}}{35 \, {\left(15 \, A^{2} + 14 \, A B + 3 \, B^{2} - \sqrt{289 \, A^{4} + 612 \, A^{3} B + 494 \, A^{2} B^{2} + 180 \, A B^{3} + 25 \, B^{4}}\right)}} - \frac{2 \, \sqrt{35} {\left(2 \, A^{2} + 3 \, A B + B^{2}\right)} \sqrt{A^{2} + 2 \, A B + B^{2}} {\left(\arctan\left(\frac{1}{7}\right) + \arctan\left(-\frac{5 \, {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} {\left(62556 \, \sqrt{14} + 245977\right)} - 1617962 \, \sqrt{35} - 3089577 \, \sqrt{10}}{496201 \, \sqrt{35} + 929846 \, \sqrt{10}}\right)\right)}}{35 \, {\left(15 \, A^{2} + 14 \, A B + 3 \, B^{2} - \sqrt{289 \, A^{4} + 612 \, A^{3} B + 494 \, A^{2} B^{2} + 180 \, A B^{3} + 25 \, B^{4}}\right)}} + \frac{1}{140} \, \sqrt{35} \sqrt{A^{2} + 2 \, A B + B^{2}} \log\left(25 \, {\left(546 \, \sqrt{14} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} + 2807 \, \sqrt{10} x - 234 \, \sqrt{35} \sqrt{14} - 1014 \, \sqrt{14} \sqrt{10} - 1203 \, \sqrt{35} - 5213 \, \sqrt{10} - 2807 \, \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2} + 25 \, {\left(78 \, \sqrt{14} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} + 401 \, \sqrt{10} x + 48 \, \sqrt{35} \sqrt{14} + 208 \, \sqrt{14} \sqrt{10} + 141 \, \sqrt{35} + 611 \, \sqrt{10} - 401 \, \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2}\right) - \frac{1}{140} \, \sqrt{35} \sqrt{A^{2} + 2 \, A B + B^{2}} \log\left(625 \, {\left(18 \, \sqrt{14} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} - 75 \, \sqrt{10} x + 8 \, \sqrt{35} \sqrt{14} - 24 \, \sqrt{14} \sqrt{10} - 37 \, \sqrt{35} + 111 \, \sqrt{10} + 75 \, \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2} + 625 \, {\left(6 \, \sqrt{14} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} - 25 \, \sqrt{10} x + 6 \, \sqrt{35} \sqrt{14} - 18 \, \sqrt{14} \sqrt{10} - 25 \, \sqrt{35} + 75 \, \sqrt{10} + 25 \, \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2}\right)"," ",0,"2/35*sqrt(35)*(2*A^2 + 3*A*B + B^2)*sqrt(A^2 + 2*A*B + B^2)*(arctan(3) + arctan(-(5*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13))*(300*sqrt(14) - 1129) - 7658*sqrt(35) + 14361*sqrt(10))/(2329*sqrt(35) - 4358*sqrt(10))))/(15*A^2 + 14*A*B + 3*B^2 - sqrt(289*A^4 + 612*A^3*B + 494*A^2*B^2 + 180*A*B^3 + 25*B^4)) - 2/35*sqrt(35)*(2*A^2 + 3*A*B + B^2)*sqrt(A^2 + 2*A*B + B^2)*(arctan(1/7) + arctan(-(5*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13))*(62556*sqrt(14) + 245977) - 1617962*sqrt(35) - 3089577*sqrt(10))/(496201*sqrt(35) + 929846*sqrt(10))))/(15*A^2 + 14*A*B + 3*B^2 - sqrt(289*A^4 + 612*A^3*B + 494*A^2*B^2 + 180*A*B^3 + 25*B^4)) + 1/140*sqrt(35)*sqrt(A^2 + 2*A*B + B^2)*log(25*(546*sqrt(14)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) + 2807*sqrt(10)*x - 234*sqrt(35)*sqrt(14) - 1014*sqrt(14)*sqrt(10) - 1203*sqrt(35) - 5213*sqrt(10) - 2807*sqrt(10*x^2 - 22*x + 13))^2 + 25*(78*sqrt(14)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) + 401*sqrt(10)*x + 48*sqrt(35)*sqrt(14) + 208*sqrt(14)*sqrt(10) + 141*sqrt(35) + 611*sqrt(10) - 401*sqrt(10*x^2 - 22*x + 13))^2) - 1/140*sqrt(35)*sqrt(A^2 + 2*A*B + B^2)*log(625*(18*sqrt(14)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) - 75*sqrt(10)*x + 8*sqrt(35)*sqrt(14) - 24*sqrt(14)*sqrt(10) - 37*sqrt(35) + 111*sqrt(10) + 75*sqrt(10*x^2 - 22*x + 13))^2 + 625*(6*sqrt(14)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) - 25*sqrt(10)*x + 6*sqrt(35)*sqrt(14) - 18*sqrt(14)*sqrt(10) - 25*sqrt(35) + 75*sqrt(10) + 25*sqrt(10*x^2 - 22*x + 13))^2)","B",0
249,1,231,0,1.838743," ","integrate((-2+x)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x, algorithm=""giac"")","\frac{1}{140} \, \sqrt{35} \log\left({\left| 21875000000 \, \sqrt{14} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2} + 82031250000 \, {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2} - 91875000000 \, \sqrt{35} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} - 172812500000 \, \sqrt{10} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} + 240625000000 \, \sqrt{14} + 913281250000 \right|}\right) - \frac{1}{140} \, \sqrt{35} \log\left({\left| -21875000000 \, \sqrt{14} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2} + 82031250000 \, {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)}^{2} + 91875000000 \, \sqrt{35} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} - 172812500000 \, \sqrt{10} {\left(\sqrt{10} x - \sqrt{10 \, x^{2} - 22 \, x + 13}\right)} - 240625000000 \, \sqrt{14} + 913281250000 \right|}\right)"," ",0,"1/140*sqrt(35)*log(abs(21875000000*sqrt(14)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13))^2 + 82031250000*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13))^2 - 91875000000*sqrt(35)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) - 172812500000*sqrt(10)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) + 240625000000*sqrt(14) + 913281250000)) - 1/140*sqrt(35)*log(abs(-21875000000*sqrt(14)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13))^2 + 82031250000*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13))^2 + 91875000000*sqrt(35)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) - 172812500000*sqrt(10)*(sqrt(10)*x - sqrt(10*x^2 - 22*x + 13)) - 240625000000*sqrt(14) + 913281250000))","B",0
250,1,36,0,0.595977," ","integrate(x^4*(-x^2+5)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, x^{2} - 5\right)} x^{2} - 75\right)} \sqrt{-x^{2} + 5} x + \frac{125}{16} \, \arcsin\left(\frac{1}{5} \, \sqrt{5} x\right)"," ",0,"1/48*(2*(4*x^2 - 5)*x^2 - 75)*sqrt(-x^2 + 5)*x + 125/16*arcsin(1/5*sqrt(5)*x)","A",0
251,1,51,0,0.625659," ","integrate(1/x^6/(x^2+2)^(1/2),x, algorithm=""giac"")","\frac{32 \, {\left(5 \, {\left(x - \sqrt{x^{2} + 2}\right)}^{4} - 5 \, {\left(x - \sqrt{x^{2} + 2}\right)}^{2} + 2\right)}}{15 \, {\left({\left(x - \sqrt{x^{2} + 2}\right)}^{2} - 2\right)}^{5}}"," ",0,"32/15*(5*(x - sqrt(x^2 + 2))^4 - 5*(x - sqrt(x^2 + 2))^2 + 2)/((x - sqrt(x^2 + 2))^2 - 2)^5","A",0
252,1,26,0,0.644613," ","integrate(1/(2*x^2+3)^(7/2),x, algorithm=""giac"")","\frac{{\left(8 \, {\left(4 \, x^{2} + 15\right)} x^{2} + 135\right)} x}{405 \, {\left(2 \, x^{2} + 3\right)}^{\frac{5}{2}}}"," ",0,"1/405*(8*(4*x^2 + 15)*x^2 + 135)*x/(2*x^2 + 3)^(5/2)","A",0
253,1,11,0,0.640606," ","integrate(x/(1+x^2+a*(x^2+1)^(1/2)),x, algorithm=""giac"")","\log\left({\left| a + \sqrt{x^{2} + 1} \right|}\right)"," ",0,"log(abs(a + sqrt(x^2 + 1)))","A",0
254,1,22,0,0.672385," ","integrate((x^2-x+1)/(x^2+1)^(3/2),x, algorithm=""giac"")","\frac{1}{\sqrt{x^{2} + 1}} - \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"1/sqrt(x^2 + 1) - log(-x + sqrt(x^2 + 1))","B",0
255,1,64,0,0.631798," ","integrate((x^2+1)^(1/2)/(x^2+2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 2 \, \sqrt{2} + 3}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} + 2 \, \sqrt{2} + 3}\right) - \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"1/4*sqrt(2)*log(((x - sqrt(x^2 + 1))^2 - 2*sqrt(2) + 3)/((x - sqrt(x^2 + 1))^2 + 2*sqrt(2) + 3)) - log(-x + sqrt(x^2 + 1))","B",0
256,1,101,0,0.641947," ","integrate(1/(x^2+2)^2/(x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{3}{16} \, \sqrt{2} \log\left(\frac{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 2 \, \sqrt{2} + 3}{{\left(x - \sqrt{x^{2} + 1}\right)}^{2} + 2 \, \sqrt{2} + 3}\right) - \frac{3 \, {\left(x - \sqrt{x^{2} + 1}\right)}^{2} + 1}{2 \, {\left({\left(x - \sqrt{x^{2} + 1}\right)}^{4} + 6 \, {\left(x - \sqrt{x^{2} + 1}\right)}^{2} + 1\right)}}"," ",0,"-3/16*sqrt(2)*log(((x - sqrt(x^2 + 1))^2 - 2*sqrt(2) + 3)/((x - sqrt(x^2 + 1))^2 + 2*sqrt(2) + 3)) - 1/2*(3*(x - sqrt(x^2 + 1))^2 + 1)/((x - sqrt(x^2 + 1))^4 + 6*(x - sqrt(x^2 + 1))^2 + 1)","B",0
257,1,72,0,0.657313," ","integrate(x^2/(x^2-6)/(x^2-2)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{6} \log\left(\frac{{\left| 2 \, {\left(x - \sqrt{x^{2} - 2}\right)}^{2} - 8 \, \sqrt{6} - 20 \right|}}{{\left| 2 \, {\left(x - \sqrt{x^{2} - 2}\right)}^{2} + 8 \, \sqrt{6} - 20 \right|}}\right) - \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} - 2}\right)}^{2}\right)"," ",0,"-1/4*sqrt(6)*log(abs(2*(x - sqrt(x^2 - 2))^2 - 8*sqrt(6) - 20)/abs(2*(x - sqrt(x^2 - 2))^2 + 8*sqrt(6) - 20)) - 1/2*log((x - sqrt(x^2 - 2))^2)","B",0
258,1,123,0,0.647870," ","integrate((x^2+5)/(x^2+1)^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\sqrt{2} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{2} x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{4 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} - \frac{2 \, {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{{\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}^{2} + 8}"," ",0,"sqrt(2)*(pi*sgn(x) + 2*arctan(-1/4*sqrt(2)*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))) - 2*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/((x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)^2 + 8)","B",0
259,1,135,0,0.687014," ","integrate((4*x-(-x^2+1)^(1/2))/(5+(-x^2+1)^(1/2)),x, algorithm=""giac"")","\frac{25}{12} \, \sqrt{6} \arctan\left(\frac{1}{12} \, \sqrt{6} x\right) - \frac{25}{12} \, \sqrt{6} \arctan\left(-\frac{\sqrt{6} {\left(\sqrt{-x^{2} + 1} - 1\right)}}{3 \, x}\right) - \frac{25}{12} \, \sqrt{6} \arctan\left(-\frac{\sqrt{6} {\left(\sqrt{-x^{2} + 1} - 1\right)}}{2 \, x}\right) - x - 4 \, \sqrt{-x^{2} + 1} + 5 \, \arcsin\left(x\right) + 10 \, \log\left(x^{2} + 24\right) - 10 \, \log\left(\frac{3 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 2\right) + 10 \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 3\right)"," ",0,"25/12*sqrt(6)*arctan(1/12*sqrt(6)*x) - 25/12*sqrt(6)*arctan(-1/3*sqrt(6)*(sqrt(-x^2 + 1) - 1)/x) - 25/12*sqrt(6)*arctan(-1/2*sqrt(6)*(sqrt(-x^2 + 1) - 1)/x) - x - 4*sqrt(-x^2 + 1) + 5*arcsin(x) + 10*log(x^2 + 24) - 10*log(3*(sqrt(-x^2 + 1) - 1)^2/x^2 + 2) + 10*log(2*(sqrt(-x^2 + 1) - 1)^2/x^2 + 3)","B",0
260,1,176,0,0.673309," ","integrate(x^2*(2-(x^2+1)^(1/2))/(1-x^3+(x^2+1)^(3/2))/(x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, x^{2} - \frac{1}{18} \, \sqrt{x^{2} + 1} {\left(3 \, x - 16\right)} + \frac{4}{27} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(3 \, x - 3 \, \sqrt{x^{2} + 1} - 1\right)}\right) + \frac{4}{27} \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} {\left(3 \, x + 1\right)}\right) - \frac{4}{27} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(x - \sqrt{x^{2} + 1} + 1\right)}\right) + \frac{8}{9} \, x + \frac{7}{54} \, \log\left(3 \, {\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 2 \, x + 2 \, \sqrt{x^{2} + 1} + 1\right) - \frac{7}{54} \, \log\left({\left(x - \sqrt{x^{2} + 1}\right)}^{2} + 2 \, x - 2 \, \sqrt{x^{2} + 1} + 3\right) - \frac{7}{54} \, \log\left(3 \, x^{2} + 2 \, x + 3\right) + \frac{41}{54} \, \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-1/6*x^2 - 1/18*sqrt(x^2 + 1)*(3*x - 16) + 4/27*sqrt(2)*arctan(-1/2*sqrt(2)*(3*x - 3*sqrt(x^2 + 1) - 1)) + 4/27*sqrt(2)*arctan(1/4*sqrt(2)*(3*x + 1)) - 4/27*sqrt(2)*arctan(-1/2*sqrt(2)*(x - sqrt(x^2 + 1) + 1)) + 8/9*x + 7/54*log(3*(x - sqrt(x^2 + 1))^2 - 2*x + 2*sqrt(x^2 + 1) + 1) - 7/54*log((x - sqrt(x^2 + 1))^2 + 2*x - 2*sqrt(x^2 + 1) + 3) - 7/54*log(3*x^2 + 2*x + 3) + 41/54*log(-x + sqrt(x^2 + 1))","A",0
261,1,45,0,0.645537," ","integrate(x*(2*r*x-x^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, r^{3} \arcsin\left(\frac{r - x}{r}\right) \mathrm{sgn}\left(r\right) - \frac{1}{6} \, {\left(3 \, r^{2} + {\left(r - 2 \, x\right)} x\right)} \sqrt{2 \, r x - x^{2}}"," ",0,"-1/2*r^3*arcsin((r - x)/r)*sgn(r) - 1/6*(3*r^2 + (r - 2*x)*x)*sqrt(2*r*x - x^2)","A",0
262,1,54,0,0.657644," ","integrate(x^2*(2*r*x-x^2)^(1/2),x, algorithm=""giac"")","-\frac{5}{8} \, r^{4} \arcsin\left(\frac{r - x}{r}\right) \mathrm{sgn}\left(r\right) - \frac{1}{24} \, {\left(15 \, r^{3} + {\left(5 \, r^{2} + 2 \, {\left(r - 3 \, x\right)} x\right)} x\right)} \sqrt{2 \, r x - x^{2}}"," ",0,"-5/8*r^4*arcsin((r - x)/r)*sgn(r) - 1/24*(15*r^3 + (5*r^2 + 2*(r - 3*x)*x)*x)*sqrt(2*r*x - x^2)","A",0
263,1,63,0,0.634417," ","integrate(x^3*(2*r*x-x^2)^(1/2),x, algorithm=""giac"")","-\frac{7}{8} \, r^{5} \arcsin\left(\frac{r - x}{r}\right) \mathrm{sgn}\left(r\right) - \frac{1}{120} \, {\left(105 \, r^{4} + {\left(35 \, r^{3} + 2 \, {\left(7 \, r^{2} + 3 \, {\left(r - 4 \, x\right)} x\right)} x\right)} x\right)} \sqrt{2 \, r x - x^{2}}"," ",0,"-7/8*r^5*arcsin((r - x)/r)*sgn(r) - 1/120*(105*r^4 + (35*r^3 + 2*(7*r^2 + 3*(r - 4*x)*x)*x)*x)*sqrt(2*r*x - x^2)","A",0
264,1,71,0,0.708714," ","integrate(1/(x^2-1)/(x^2+2*x)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{3} + 2 \, \sqrt{x^{2} + 2 \, x} + 2 \right|}}{{\left| -2 \, x + 2 \, \sqrt{3} + 2 \, \sqrt{x^{2} + 2 \, x} + 2 \right|}}\right) - \arctan\left(-x + \sqrt{x^{2} + 2 \, x} - 1\right)"," ",0,"1/6*sqrt(3)*log(abs(-2*x - 2*sqrt(3) + 2*sqrt(x^2 + 2*x) + 2)/abs(-2*x + 2*sqrt(3) + 2*sqrt(x^2 + 2*x) + 2)) - arctan(-x + sqrt(x^2 + 2*x) - 1)","A",0
265,1,147,0,0.665849," ","integrate((-2+3*x)/(1+x)^3/(-x^2+2*x)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{x - 1} - 1\right)}\right) + \frac{\frac{34 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{x - 1} - \frac{39 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}^{2}}{{\left(x - 1\right)}^{2}} + \frac{18 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}^{3}}{{\left(x - 1\right)}^{3}} - 26}{24 \, {\left(\frac{\sqrt{-x^{2} + 2 \, x} - 1}{x - 1} - \frac{{\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}^{2}}{{\left(x - 1\right)}^{2}} - 1\right)}^{2}}"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*(sqrt(-x^2 + 2*x) - 1)/(x - 1) - 1)) + 1/24*(34*(sqrt(-x^2 + 2*x) - 1)/(x - 1) - 39*(sqrt(-x^2 + 2*x) - 1)^2/(x - 1)^2 + 18*(sqrt(-x^2 + 2*x) - 1)^3/(x - 1)^3 - 26)/((sqrt(-x^2 + 2*x) - 1)/(x - 1) - (sqrt(-x^2 + 2*x) - 1)^2/(x - 1)^2 - 1)^2","B",0
266,1,18,0,0.650627," ","integrate(1/(x^2+x+1)^(1/2),x, algorithm=""giac"")","-\log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"-log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
267,1,39,0,0.631144," ","integrate(x^3/(x^2+x+1)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(2 \, {\left(4 \, x - 5\right)} x - 1\right)} \sqrt{x^{2} + x + 1} - \frac{7}{16} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"1/24*(2*(4*x - 5)*x - 1)*sqrt(x^2 + x + 1) - 7/16*log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
268,1,15,0,0.699475," ","integrate(1/(x^2+x+1)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, x + 1\right)}}{3 \, \sqrt{x^{2} + x + 1}}"," ",0,"2/3*(2*x + 1)/sqrt(x^2 + x + 1)","A",0
269,1,13,0,0.654413," ","integrate(x/(x^2+x+1)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(x + 2\right)}}{3 \, \sqrt{x^{2} + x + 1}}"," ",0,"-2/3*(x + 2)/sqrt(x^2 + x + 1)","A",0
270,1,38,0,0.644377," ","integrate(x^3/(x^2+x+1)^(3/2),x, algorithm=""giac"")","\frac{{\left(3 \, x + 7\right)} x + 5}{3 \, \sqrt{x^{2} + x + 1}} + \frac{3}{2} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"1/3*((3*x + 7)*x + 5)/sqrt(x^2 + x + 1) + 3/2*log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
271,1,44,0,0.646278," ","integrate(x^2*(x^2+x+1)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, {\left(2 \, {\left(4 \, {\left(6 \, x + 1\right)} x + 7\right)} x - 37\right)} \sqrt{x^{2} + x + 1} - \frac{3}{128} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"1/192*(2*(4*(6*x + 1)*x + 7)*x - 37)*sqrt(x^2 + x + 1) - 3/128*log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
272,1,44,0,0.634163," ","integrate((x^2+x+1)^(3/2),x, algorithm=""giac"")","\frac{1}{64} \, {\left(2 \, {\left(4 \, {\left(2 \, x + 3\right)} x + 21\right)} x + 17\right)} \sqrt{x^{2} + x + 1} - \frac{27}{128} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"1/64*(2*(4*(2*x + 3)*x + 21)*x + 17)*sqrt(x^2 + x + 1) - 27/128*log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
273,1,54,0,0.617047," ","integrate((x^2+x+1)^(5/2),x, algorithm=""giac"")","\frac{1}{1536} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, x + 5\right)} x + 79\right)} x + 157\right)} x + 571\right)} x + 383\right)} \sqrt{x^{2} + x + 1} - \frac{135}{1024} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"1/1536*(2*(4*(2*(8*(2*x + 5)*x + 79)*x + 157)*x + 571)*x + 383)*sqrt(x^2 + x + 1) - 135/1024*log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
274,1,67,0,0.646735," ","integrate(1/x^2/(x^2+x+1)^(1/2),x, algorithm=""giac"")","\frac{x - \sqrt{x^{2} + x + 1} + 2}{{\left(x - \sqrt{x^{2} + x + 1}\right)}^{2} - 1} + \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 1 \right|}\right)"," ",0,"(x - sqrt(x^2 + x + 1) + 2)/((x - sqrt(x^2 + x + 1))^2 - 1) + 1/2*log(abs(-x + sqrt(x^2 + x + 1) + 1)) - 1/2*log(abs(-x + sqrt(x^2 + x + 1) - 1))","B",0
275,1,84,0,0.668141," ","integrate(1/x^3/(x^2+x+1)^(1/2),x, algorithm=""giac"")","\frac{{\left(x - \sqrt{x^{2} + x + 1}\right)}^{3} + 9 \, x - 9 \, \sqrt{x^{2} + x + 1} + 8}{4 \, {\left({\left(x - \sqrt{x^{2} + x + 1}\right)}^{2} - 1\right)}^{2}} + \frac{1}{8} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 1 \right|}\right)"," ",0,"1/4*((x - sqrt(x^2 + x + 1))^3 + 9*x - 9*sqrt(x^2 + x + 1) + 8)/((x - sqrt(x^2 + x + 1))^2 - 1)^2 + 1/8*log(abs(-x + sqrt(x^2 + x + 1) + 1)) - 1/8*log(abs(-x + sqrt(x^2 + x + 1) - 1))","A",0
276,1,80,0,0.620595," ","integrate(1/x^2/(x^2+x+1)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(x + 2\right)}}{3 \, \sqrt{x^{2} + x + 1}} + \frac{x - \sqrt{x^{2} + x + 1} + 2}{{\left(x - \sqrt{x^{2} + x + 1}\right)}^{2} - 1} + \frac{3}{2} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} + 1 \right|}\right) - \frac{3}{2} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 1 \right|}\right)"," ",0,"-2/3*(x + 2)/sqrt(x^2 + x + 1) + (x - sqrt(x^2 + x + 1) + 2)/((x - sqrt(x^2 + x + 1))^2 - 1) + 3/2*log(abs(-x + sqrt(x^2 + x + 1) + 1)) - 3/2*log(abs(-x + sqrt(x^2 + x + 1) - 1))","A",0
277,1,117,0,0.625155," ","integrate(1/x^3/(x^2+x+1)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, x + 1\right)}}{3 \, \sqrt{x^{2} + x + 1}} - \frac{3 \, {\left(x - \sqrt{x^{2} + x + 1}\right)}^{3} + 8 \, {\left(x - \sqrt{x^{2} + x + 1}\right)}^{2} - 13 \, x + 13 \, \sqrt{x^{2} + x + 1} - 16}{4 \, {\left({\left(x - \sqrt{x^{2} + x + 1}\right)}^{2} - 1\right)}^{2}} - \frac{3}{8} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} + 1 \right|}\right) + \frac{3}{8} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 1 \right|}\right)"," ",0,"2/3*(2*x + 1)/sqrt(x^2 + x + 1) - 1/4*(3*(x - sqrt(x^2 + x + 1))^3 + 8*(x - sqrt(x^2 + x + 1))^2 - 13*x + 13*sqrt(x^2 + x + 1) - 16)/((x - sqrt(x^2 + x + 1))^2 - 1)^2 - 3/8*log(abs(-x + sqrt(x^2 + x + 1) + 1)) + 3/8*log(abs(-x + sqrt(x^2 + x + 1) - 1))","A",0
278,1,32,0,0.660282," ","integrate(1/(1+x)/(x^2+x+1)^(1/2),x, algorithm=""giac"")","-\log\left({\left| -x + \sqrt{x^{2} + x + 1} \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 2 \right|}\right)"," ",0,"-log(abs(-x + sqrt(x^2 + x + 1))) + log(abs(-x + sqrt(x^2 + x + 1) - 2))","A",0
279,1,147,0,0.727382," ","integrate(1/(x^3-x)/(x^2+2*x+4)^(1/2),x, algorithm=""giac"")","\frac{1}{14} \, \sqrt{7} \log\left(\frac{{\left| -2 \, x - 2 \, \sqrt{7} + 2 \, \sqrt{x^{2} + 2 \, x + 4} + 2 \right|}}{{\left| -2 \, x + 2 \, \sqrt{7} + 2 \, \sqrt{x^{2} + 2 \, x + 4} + 2 \right|}}\right) + \frac{1}{6} \, \sqrt{3} \log\left(-\frac{{\left| -2 \, x - 2 \, \sqrt{3} + 2 \, \sqrt{x^{2} + 2 \, x + 4} - 2 \right|}}{2 \, {\left(x - \sqrt{3} - \sqrt{x^{2} + 2 \, x + 4} + 1\right)}}\right) + \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} + 2 \, x + 4} + 2 \right|}\right) - \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} + 2 \, x + 4} - 2 \right|}\right)"," ",0,"1/14*sqrt(7)*log(abs(-2*x - 2*sqrt(7) + 2*sqrt(x^2 + 2*x + 4) + 2)/abs(-2*x + 2*sqrt(7) + 2*sqrt(x^2 + 2*x + 4) + 2)) + 1/6*sqrt(3)*log(-1/2*abs(-2*x - 2*sqrt(3) + 2*sqrt(x^2 + 2*x + 4) - 2)/(x - sqrt(3) - sqrt(x^2 + 2*x + 4) + 1)) + 1/2*log(abs(-x + sqrt(x^2 + 2*x + 4) + 2)) - 1/2*log(abs(-x + sqrt(x^2 + 2*x + 4) - 2))","B",0
280,1,33,0,0.658354," ","integrate((x^2+2*x+4)^(1/2)/(-1+x)^2,x, algorithm=""giac"")","-\sqrt{\frac{4}{x - 1} + \frac{7}{{\left(x - 1\right)}^{2}} + 1} \mathrm{sgn}\left(\frac{1}{x - 1}\right) + \mathrm{sgn}\left(\frac{1}{x - 1}\right)"," ",0,"-sqrt(4/(x - 1) + 7/(x - 1)^2 + 1)*sgn(1/(x - 1)) + sgn(1/(x - 1))","A",0
281,1,235,0,0.664832," ","integrate((3+2*x)/(x^2+2*x+3)^2/(x^2+2*x+4)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(x - \sqrt{x^{2} + 2 \, x + 4} + 2\right)}\right) - \frac{1}{8} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}\right) + \frac{4 \, {\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{3} + 13 \, {\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{2} + 26 \, x - 26 \, \sqrt{x^{2} + 2 \, x + 4} + 26}{2 \, {\left({\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{4} + 4 \, {\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{3} + 8 \, {\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{2} + 8 \, x - 8 \, \sqrt{x^{2} + 2 \, x + 4} + 12\right)}} - \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{2} + 4 \, x - 4 \, \sqrt{x^{2} + 2 \, x + 4} + 6\right) + \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} + 2 \, x + 4}\right)}^{2} + 2\right)"," ",0,"1/8*sqrt(2)*arctan(-1/2*sqrt(2)*(x - sqrt(x^2 + 2*x + 4) + 2)) - 1/8*sqrt(2)*arctan(-1/2*sqrt(2)*(x - sqrt(x^2 + 2*x + 4))) + 1/2*(4*(x - sqrt(x^2 + 2*x + 4))^3 + 13*(x - sqrt(x^2 + 2*x + 4))^2 + 26*x - 26*sqrt(x^2 + 2*x + 4) + 26)/((x - sqrt(x^2 + 2*x + 4))^4 + 4*(x - sqrt(x^2 + 2*x + 4))^3 + 8*(x - sqrt(x^2 + 2*x + 4))^2 + 8*x - 8*sqrt(x^2 + 2*x + 4) + 12) - 1/2*log((x - sqrt(x^2 + 2*x + 4))^2 + 4*x - 4*sqrt(x^2 + 2*x + 4) + 6) + 1/2*log((x - sqrt(x^2 + 2*x + 4))^2 + 2)","B",0
282,1,30,0,0.653532," ","integrate((2*x^3+3*x^2)/(2*x^2+x-3)/(x^2+2*x-3)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} + 2 \, x - 3} + \frac{2}{x - \sqrt{x^{2} + 2 \, x - 3} - 1}"," ",0,"sqrt(x^2 + 2*x - 3) + 2/(x - sqrt(x^2 + 2*x - 3) - 1)","A",0
283,1,148,0,0.680345," ","integrate((x^4+1)/(x^2+x+1)/(x^2+x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{2} + x + 2} {\left(2 \, x - 7\right)} - \frac{1}{3} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 2 \, \sqrt{x^{2} + x + 2} + 3\right)}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 2 \, \sqrt{x^{2} + x + 2} - 1\right)}\right) + \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} + x + 2}\right)}^{2} + 3 \, x - 3 \, \sqrt{x^{2} + x + 2} + 3\right) - \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} + x + 2}\right)}^{2} - x + \sqrt{x^{2} + x + 2} + 1\right) + \frac{1}{8} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 2} - 1\right)"," ",0,"1/4*sqrt(x^2 + x + 2)*(2*x - 7) - 1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(2*x - 2*sqrt(x^2 + x + 2) + 3)) + 1/3*sqrt(3)*arctan(-1/3*sqrt(3)*(2*x - 2*sqrt(x^2 + x + 2) - 1)) + 1/2*log((x - sqrt(x^2 + x + 2))^2 + 3*x - 3*sqrt(x^2 + x + 2) + 3) - 1/2*log((x - sqrt(x^2 + x + 2))^2 - x + sqrt(x^2 + x + 2) + 1) + 1/8*log(-2*x + 2*sqrt(x^2 + x + 2) - 1)","B",0
284,1,33,0,0.632950," ","integrate(1/(x^2+2*x+4)^(7/2),x, algorithm=""giac"")","\frac{{\left(4 \, {\left({\left(2 \, {\left(x + 5\right)} x + 35\right)} x + 65\right)} x + 355\right)} x + 203}{405 \, {\left(x^{2} + 2 \, x + 4\right)}^{\frac{5}{2}}}"," ",0,"1/405*((4*((2*(x + 5)*x + 35)*x + 65)*x + 355)*x + 203)/(x^2 + 2*x + 4)^(5/2)","A",0
285,1,27,0,0.648035," ","integrate(1/(3*x^2+8*x+1)^(5/2),x, algorithm=""giac"")","\frac{9 \, {\left(6 \, {\left(x + 4\right)} x + 19\right)} x - 28}{507 \, {\left(3 \, x^{2} + 8 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"1/507*(9*(6*(x + 4)*x + 19)*x - 28)/(3*x^2 + 8*x + 1)^(3/2)","A",0
286,1,39,0,0.711142," ","integrate(1/(-3*x^2+4*x+5)^(5/2),x, algorithm=""giac"")","-\frac{{\left(9 \, {\left(6 \, {\left(x - 2\right)} x - 11\right)} x + 98\right)} \sqrt{-3 \, x^{2} + 4 \, x + 5}}{1083 \, {\left(3 \, x^{2} - 4 \, x - 5\right)}^{2}}"," ",0,"-1/1083*(9*(6*(x - 2)*x - 11)*x + 98)*sqrt(-3*x^2 + 4*x + 5)/(3*x^2 - 4*x - 5)^2","A",0
287,1,60,0,0.657128," ","integrate(1/(1+(x^2+2*x+2)^(1/2)),x, algorithm=""giac"")","\frac{2}{{\left(x - \sqrt{x^{2} + 2 \, x + 2}\right)}^{2} + 2 \, x - 2 \, \sqrt{x^{2} + 2 \, x + 2}} + \frac{1}{x + 1} - \log\left(-x + \sqrt{x^{2} + 2 \, x + 2} - 1\right)"," ",0,"2/((x - sqrt(x^2 + 2*x + 2))^2 + 2*x - 2*sqrt(x^2 + 2*x + 2)) + 1/(x + 1) - log(-x + sqrt(x^2 + 2*x + 2) - 1)","B",0
288,1,66,0,0.651789," ","integrate(1/(x+(x^2+x+1)^(1/2)),x, algorithm=""giac"")","-x + \sqrt{x^{2} + x + 1} + \frac{1}{2} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right) + \log\left({\left| x + 1 \right|}\right) - \log\left({\left| -x + \sqrt{x^{2} + x + 1} \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 2 \right|}\right)"," ",0,"-x + sqrt(x^2 + x + 1) + 1/2*log(-2*x + 2*sqrt(x^2 + x + 1) - 1) + log(abs(x + 1)) - log(abs(-x + sqrt(x^2 + x + 1))) + log(abs(-x + sqrt(x^2 + x + 1) - 2))","A",0
289,1,54,0,0.620787," ","integrate(x^2/(1+2*x+2*(x^2+x+1)^(1/2)),x, algorithm=""giac"")","-\frac{1}{6} \, x^{4} - \frac{1}{9} \, x^{3} + \frac{1}{288} \, {\left(2 \, {\left(4 \, {\left(6 \, x + 1\right)} x + 7\right)} x - 37\right)} \sqrt{x^{2} + x + 1} - \frac{1}{64} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right)"," ",0,"-1/6*x^4 - 1/9*x^3 + 1/288*(2*(4*(6*x + 1)*x + 7)*x - 37)*sqrt(x^2 + x + 1) - 1/64*log(-2*x + 2*sqrt(x^2 + x + 1) - 1)","A",0
290,1,105,0,0.666989," ","integrate((-3*x+(x^2+x+1)^(1/2))/(-1+(x^2+x+1)^(1/2)),x, algorithm=""giac"")","x - 3 \, \sqrt{x^{2} + x + 1} - \frac{5}{2} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x + 1} - 1\right) - 4 \, \log\left({\left| x + 1 \right|}\right) + \log\left({\left| x \right|}\right) - \log\left({\left| -x + \sqrt{x^{2} + x + 1} + 1 \right|}\right) + 4 \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 1 \right|}\right) - 4 \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 2 \right|}\right)"," ",0,"x - 3*sqrt(x^2 + x + 1) - 5/2*log(-2*x + 2*sqrt(x^2 + x + 1) - 1) - 4*log(abs(x + 1)) + log(abs(x)) - log(abs(-x + sqrt(x^2 + x + 1) + 1)) + 4*log(abs(-x + sqrt(x^2 + x + 1))) + log(abs(-x + sqrt(x^2 + x + 1) - 1)) - 4*log(abs(-x + sqrt(x^2 + x + 1) - 2))","A",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=""giac"")","\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
292,1,29,0,0.614729," ","integrate(1/x^3/(-1+x)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(x - 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{x - 1}}{4 \, x^{2}} + \frac{3}{4} \, \arctan\left(\sqrt{x - 1}\right)"," ",0,"1/4*(3*(x - 1)^(3/2) + 5*sqrt(x - 1))/x^2 + 3/4*arctan(sqrt(x - 1))","A",0
293,1,11,0,0.648381," ","integrate(1/(1-3/x)^(4/3)/x^2,x, algorithm=""giac"")","-\frac{1}{\left(\frac{x - 3}{x}\right)^{\frac{1}{3}}}"," ",0,"-1/((x - 3)/x)^(1/3)","A",0
294,1,76,0,0.652267," ","integrate((-1+3*x)^(4/3)/x^2,x, algorithm=""giac"")","-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
295,1,49,0,0.631830," ","integrate((4-3*x)^(4/3)*x^2,x, algorithm=""giac"")","-\frac{1}{117} \, {\left(3 \, x - 4\right)}^{4} {\left(-3 \, x + 4\right)}^{\frac{1}{3}} - \frac{4}{45} \, {\left(3 \, x - 4\right)}^{3} {\left(-3 \, x + 4\right)}^{\frac{1}{3}} - \frac{16}{63} \, {\left(3 \, x - 4\right)}^{2} {\left(-3 \, x + 4\right)}^{\frac{1}{3}}"," ",0,"-1/117*(3*x - 4)^4*(-3*x + 4)^(1/3) - 4/45*(3*x - 4)^3*(-3*x + 4)^(1/3) - 16/63*(3*x - 4)^2*(-3*x + 4)^(1/3)","A",0
296,1,53,0,8.180231," ","integrate((1-2*x^(1/3))^(3/4)/x,x, algorithm=""giac"")","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| {\left(-2 \, x^{\frac{1}{3}} + 1\right)}^{\frac{1}{4}} - 1 \right|}\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(abs((-2*x^(1/3) + 1)^(1/4) - 1))","A",0
297,1,63,0,0.597698," ","integrate(x/(3-2*x^(1/2))^(3/4),x, algorithm=""giac"")","-\frac{1}{26} \, {\left(2 \, \sqrt{x} - 3\right)}^{3} {\left(-2 \, \sqrt{x} + 3\right)}^{\frac{1}{4}} - \frac{1}{2} \, {\left(2 \, \sqrt{x} - 3\right)}^{2} {\left(-2 \, \sqrt{x} + 3\right)}^{\frac{1}{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)^3*(-2*sqrt(x) + 3)^(1/4) - 1/2*(2*sqrt(x) - 3)^2*(-2*sqrt(x) + 3)^(1/4) + 27/10*(-2*sqrt(x) + 3)^(5/4) - 27/2*(-2*sqrt(x) + 3)^(1/4)","A",0
298,1,142,0,0.603383," ","integrate((-1+2*x^(1/2))^(5/4)/x^2,x, algorithm=""giac"")","\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}}}{4 \, x}"," ",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) - 1/4*(9*(2*sqrt(x) - 1)^(5/4) + 5*(2*sqrt(x) - 1)^(1/4))/x","A",0
299,1,9,0,0.631981," ","integrate(x^6*(x^7+1)^(1/3),x, algorithm=""giac"")","\frac{3}{28} \, {\left(x^{7} + 1\right)}^{\frac{4}{3}}"," ",0,"3/28*(x^7 + 1)^(4/3)","A",0
300,1,9,0,0.616367," ","integrate(x^6/(x^7+1)^(5/3),x, algorithm=""giac"")","-\frac{3}{14 \, {\left(x^{7} + 1\right)}^{\frac{2}{3}}}"," ",0,"-3/14/(x^7 + 1)^(2/3)","A",0
301,1,65,0,0.615299," ","integrate(1/x/(2*x^7-27)^(2/3),x, algorithm=""giac"")","\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| {\left(2 \, x^{7} - 27\right)}^{\frac{1}{3}} + 3 \right|}\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(abs((2*x^7 - 27)^(1/3) + 3))","A",0
302,1,67,0,0.636358," ","integrate((x^7+1)^(2/3)/x^8,x, algorithm=""giac"")","\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| {\left(x^{7} + 1\right)}^{\frac{1}{3}} - 1 \right|}\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(abs((x^7 + 1)^(1/3) - 1))","A",0
303,1,83,0,0.674456," ","integrate((4*x^4+3)^(1/4)/x^2,x, algorithm=""giac"")","\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
304,1,110,0,0.653210," ","integrate(x^2*(4*x^4+3)^(5/4),x, algorithm=""giac"")","\frac{1}{32} \, x^{8} {\left(\frac{9 \, {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}} {\left(\frac{3}{x^{4}} + 4\right)}}{x} - \frac{20 \, {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}\right)} + \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)"," ",0,"1/32*x^8*(9*(4*x^4 + 3)^(1/4)*(3/x^4 + 4)/x - 20*(4*x^4 + 3)^(1/4)/x) + 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))","A",0
305,1,109,0,0.670519," ","integrate(x^6*(4*x^4+3)^(1/4),x, algorithm=""giac"")","\frac{1}{128} \, x^{8} {\left(\frac{{\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}} {\left(\frac{3}{x^{4}} + 4\right)}}{x} + \frac{12 \, {\left(4 \, x^{4} + 3\right)}^{\frac{1}{4}}}{x}\right)} - \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)"," ",0,"1/128*x^8*((4*x^4 + 3)^(1/4)*(3/x^4 + 4)/x + 12*(4*x^4 + 3)^(1/4)/x) - 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))","A",0
306,1,69,0,0.675721," ","integrate((x*(-x^2+1))^(1/3),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} {\left(\frac{1}{x^{2}} - 1\right)}^{\frac{1}{3}} - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\frac{1}{x^{2}} - 1\right)}^{\frac{1}{3}} - 1\right)}\right) + \frac{1}{12} \, \log\left({\left(\frac{1}{x^{2}} - 1\right)}^{\frac{2}{3}} - {\left(\frac{1}{x^{2}} - 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{6} \, \log\left({\left| {\left(\frac{1}{x^{2}} - 1\right)}^{\frac{1}{3}} + 1 \right|}\right)"," ",0,"1/2*x^2*(1/x^2 - 1)^(1/3) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(1/x^2 - 1)^(1/3) - 1)) + 1/12*log((1/x^2 - 1)^(2/3) - (1/x^2 - 1)^(1/3) + 1) - 1/6*log(abs((1/x^2 - 1)^(1/3) + 1))","A",0
307,1,66,0,0.925027," ","integrate(((1+x^(1/3))*x)^(1/2),x, algorithm=""giac"")","\frac{1}{1280} \, {\left(2 \, {\left(2 \, {\left(4 \, {\left(6 \, x^{\frac{1}{3}} {\left(8 \, x^{\frac{1}{3}} + 1\right)} - 7\right)} x^{\frac{1}{3}} + 35\right)} x^{\frac{1}{3}} - 105\right)} \sqrt{x^{\frac{2}{3}} + x^{\frac{1}{3}}} - 105 \, \log\left({\left| 2 \, \sqrt{x^{\frac{2}{3}} + x^{\frac{1}{3}}} - 2 \, x^{\frac{1}{3}} - 1 \right|}\right)\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/1280*(2*(2*(4*(6*x^(1/3)*(8*x^(1/3) + 1) - 7)*x^(1/3) + 35)*x^(1/3) - 105)*sqrt(x^(2/3) + x^(1/3)) - 105*log(abs(2*sqrt(x^(2/3) + x^(1/3)) - 2*x^(1/3) - 1)))*sgn(x)","A",0
308,1,70,0,0.662225," ","integrate(x^3/(x^4-1)/(2*x^8+1)^(1/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(-\frac{{\left| -2 \, \sqrt{2} x^{4} - 2 \, \sqrt{3} + 2 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{8} + 1} \right|}}{2 \, {\left(\sqrt{2} x^{4} - \sqrt{3} - \sqrt{2} - \sqrt{2 \, x^{8} + 1}\right)}}\right)"," ",0,"1/12*sqrt(3)*log(-1/2*abs(-2*sqrt(2)*x^4 - 2*sqrt(3) + 2*sqrt(2) + 2*sqrt(2*x^8 + 1))/(sqrt(2)*x^4 - sqrt(3) - sqrt(2) - sqrt(2*x^8 + 1)))","B",0
309,1,49,0,0.640219," ","integrate(x^9*(x^10+x^5+1)^(1/2),x, algorithm=""giac"")","\frac{1}{120} \, \sqrt{x^{10} + x^{5} + 1} {\left(2 \, {\left(4 \, x^{5} + 1\right)} x^{5} + 5\right)} + \frac{3}{80} \, \log\left(-2 \, x^{5} + 2 \, \sqrt{x^{10} + x^{5} + 1} - 1\right)"," ",0,"1/120*sqrt(x^10 + x^5 + 1)*(2*(4*x^5 + 1)*x^5 + 5) + 3/80*log(-2*x^5 + 2*sqrt(x^10 + x^5 + 1) - 1)","A",0
310,1,112,0,0.667723," ","integrate(1/x^5/(x^4+2*x^2+4)^(1/2),x, algorithm=""giac"")","\frac{{\left(x^{2} - \sqrt{x^{4} + 2 \, x^{2} + 4}\right)}^{3} + 36 \, x^{2} - 36 \, \sqrt{x^{4} + 2 \, x^{2} + 4} + 64}{32 \, {\left({\left(x^{2} - \sqrt{x^{4} + 2 \, x^{2} + 4}\right)}^{2} - 4\right)}^{2}} - \frac{1}{128} \, \log\left(x^{2} - \sqrt{x^{4} + 2 \, x^{2} + 4} + 2\right) + \frac{1}{128} \, \log\left(-x^{2} + \sqrt{x^{4} + 2 \, x^{2} + 4} + 2\right)"," ",0,"1/32*((x^2 - sqrt(x^4 + 2*x^2 + 4))^3 + 36*x^2 - 36*sqrt(x^4 + 2*x^2 + 4) + 64)/((x^2 - sqrt(x^4 + 2*x^2 + 4))^2 - 4)^2 - 1/128*log(x^2 - sqrt(x^4 + 2*x^2 + 4) + 2) + 1/128*log(-x^2 + sqrt(x^4 + 2*x^2 + 4) + 2)","A",0
311,1,69,0,0.628204," ","integrate((x^2-1)/x/(x^4+3*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 3 \, x^{2} + 1} + 3\right) + \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 3 \, x^{2} + 1} + 1\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 3 \, x^{2} + 1} - 1\right)"," ",0,"-1/2*log(2*x^2 - 2*sqrt(x^4 + 3*x^2 + 1) + 3) + 1/2*log(-x^2 + sqrt(x^4 + 3*x^2 + 1) + 1) - 1/2*log(-x^2 + sqrt(x^4 + 3*x^2 + 1) - 1)","B",0
312,1,13,0,0.627738," ","integrate((2*x^3-3*x)*(x^4-3*x^2)^(3/5),x, algorithm=""giac"")","\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
313,1,34,0,0.624748," ","integrate((-2*x^5+3*x^8-x^2*(3*x^3-1)^(2/3))/(3*x^3-1)^(3/4),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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
316,0,0,0,0.000000," ","integrate((x^3-1)/(x^3+2)^(1/3),x, algorithm=""giac"")","\int \frac{x^{3} - 1}{{\left(x^{3} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x^3 - 1)/(x^3 + 2)^(1/3), x)","F",0
317,0,0,0,0.000000," ","integrate((x^4+1)^(3/4)/(x^4+2)^2,x, algorithm=""giac"")","\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
318,0,0,0,0.000000," ","integrate((x^5-2)^2/(x^5+3)^(16/5),x, algorithm=""giac"")","\int \frac{{\left(x^{5} - 2\right)}^{2}}{{\left(x^{5} + 3\right)}^{\frac{16}{5}}}\,{d x}"," ",0,"integrate((x^5 - 2)^2/(x^5 + 3)^(16/5), x)","F",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=""giac"")","\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=""giac"")","\int -\frac{x^{2} - 1}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 - 1)/(sqrt(x^4 + 1)*(x^2 + 1)), x)","F",0
321,0,0,0,0.000000," ","integrate((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2} + 1}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-(x^2 + 1)/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
322,1,51,0,0.642205," ","integrate((x^2+1)/x/(x^4+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} + 1} + 1\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1} + 1\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"1/2*log(x^2 - sqrt(x^4 + 1) + 1) - 1/2*log(-x^2 + sqrt(x^4 + 1) + 1) - 1/2*log(-x^2 + sqrt(x^4 + 1))","B",0
323,1,51,0,0.604270," ","integrate((x^2-1)/x/(x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{4} + 1} + 1\right) + \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1} + 1\right) - \frac{1}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 1}\right)"," ",0,"-1/2*log(x^2 - sqrt(x^4 + 1) + 1) + 1/2*log(-x^2 + sqrt(x^4 + 1) + 1) - 1/2*log(-x^2 + sqrt(x^4 + 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=""giac"")","\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=""giac"")","\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
326,0,0,0,0.000000," ","integrate((x^4-1)/x^2/(x^4+x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4} - 1}{\sqrt{x^{4} + x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((x^4 - 1)/(sqrt(x^4 + x^2 + 1)*x^2), x)","F",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=""giac"")","\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=""giac"")","\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=""giac"")","\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
330,1,10,0,0.600369," ","integrate(cos(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x + 1/4*sin(2*x)","A",0
331,1,9,0,0.605143," ","integrate(cos(x)^3,x, algorithm=""giac"")","-\frac{1}{3} \, \sin\left(x\right)^{3} + \sin\left(x\right)"," ",0,"-1/3*sin(x)^3 + sin(x)","A",0
332,1,16,0,0.592321," ","integrate(sin(x)^4,x, algorithm=""giac"")","\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
333,1,22,0,0.584983," ","integrate(cos(x)^6,x, algorithm=""giac"")","\frac{5}{16} \, x + \frac{1}{192} \, \sin\left(6 \, x\right) + \frac{3}{64} \, \sin\left(4 \, x\right) + \frac{15}{64} \, \sin\left(2 \, x\right)"," ",0,"5/16*x + 1/192*sin(6*x) + 3/64*sin(4*x) + 15/64*sin(2*x)","A",0
334,1,28,0,0.608970," ","integrate(sin(x)^8,x, algorithm=""giac"")","\frac{35}{128} \, x + \frac{1}{1024} \, \sin\left(8 \, x\right) - \frac{1}{96} \, \sin\left(6 \, x\right) + \frac{7}{128} \, \sin\left(4 \, x\right) - \frac{7}{32} \, \sin\left(2 \, x\right)"," ",0,"35/128*x + 1/1024*sin(8*x) - 1/96*sin(6*x) + 7/128*sin(4*x) - 7/32*sin(2*x)","A",0
335,1,14,0,0.591352," ","integrate(cos(1/4*pi+1/2*x)^4,x, algorithm=""giac"")","\frac{3}{8} \, x + \frac{1}{2} \, \cos\left(x\right) - \frac{1}{16} \, \sin\left(2 \, x\right)"," ",0,"3/8*x + 1/2*cos(x) - 1/16*sin(2*x)","A",0
336,1,23,0,0.744000," ","integrate(-cos(5/12*pi+3*x)^3,x, algorithm=""giac"")","\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
337,1,20,0,0.590928," ","integrate(1/sin(x)^6,x, algorithm=""giac"")","-\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
338,1,112,0,0.615704," ","integrate(csc(x)^7,x, algorithm=""giac"")","-\frac{{\left(\frac{9 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - \frac{45 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{110 \, {\left(\cos\left(x\right) - 1\right)}^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{384 \, {\left(\cos\left(x\right) - 1\right)}^{3}} - \frac{15 \, {\left(\cos\left(x\right) - 1\right)}}{128 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{3 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{128 \, {\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(\cos\left(x\right) - 1\right)}^{3}}{384 \, {\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5}{32} \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)"," ",0,"-1/384*(9*(cos(x) - 1)/(cos(x) + 1) - 45*(cos(x) - 1)^2/(cos(x) + 1)^2 + 110*(cos(x) - 1)^3/(cos(x) + 1)^3 - 1)*(cos(x) + 1)^3/(cos(x) - 1)^3 - 15/128*(cos(x) - 1)/(cos(x) + 1) + 3/128*(cos(x) - 1)^2/(cos(x) + 1)^2 - 1/384*(cos(x) - 1)^3/(cos(x) + 1)^3 + 5/32*log(-(cos(x) - 1)/(cos(x) + 1))","B",0
339,1,33,0,0.606901," ","integrate(1/cos(x)^12,x, algorithm=""giac"")","\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
340,1,53,0,0.640485," ","integrate(1/cos(1/4*pi+3*x)^3,x, algorithm=""giac"")","-\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
341,1,18,0,0.592119," ","integrate(tan(x)^6,x, algorithm=""giac"")","\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
342,1,37,0,0.827951," ","integrate(1/tan(x)^5,x, algorithm=""giac"")","-\frac{3 \, \tan\left(x\right)^{4} - 2 \, \tan\left(x\right)^{2} + 1}{4 \, \tan\left(x\right)^{4}} - \frac{1}{2} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \frac{1}{2} \, \log\left(\tan\left(x\right)^{2}\right)"," ",0,"-1/4*(3*tan(x)^4 - 2*tan(x)^2 + 1)/tan(x)^4 - 1/2*log(tan(x)^2 + 1) + 1/2*log(tan(x)^2)","B",0
343,1,53,0,1.117625," ","integrate(cot(1/4*pi+1/3*x)^4,x, algorithm=""giac"")","\frac{3}{4} \, \pi + \frac{1}{8} \, \tan\left(\frac{1}{8} \, \pi + \frac{1}{6} \, x\right)^{3} + x + \frac{15 \, \tan\left(\frac{1}{8} \, \pi + \frac{1}{6} \, x\right)^{2} - 1}{8 \, \tan\left(\frac{1}{8} \, \pi + \frac{1}{6} \, x\right)^{3}} - \frac{15}{8} \, \tan\left(\frac{1}{8} \, \pi + \frac{1}{6} \, x\right)"," ",0,"3/4*pi + 1/8*tan(1/8*pi + 1/6*x)^3 + x + 1/8*(15*tan(1/8*pi + 1/6*x)^2 - 1)/tan(1/8*pi + 1/6*x)^3 - 15/8*tan(1/8*pi + 1/6*x)","B",0
344,1,34,0,0.767994," ","integrate(cos(x)^6*sin(x)^4,x, algorithm=""giac"")","\frac{3}{256} \, x + \frac{1}{5120} \, \sin\left(10 \, x\right) + \frac{1}{2048} \, \sin\left(8 \, x\right) - \frac{1}{1024} \, \sin\left(6 \, x\right) - \frac{1}{256} \, \sin\left(4 \, x\right) + \frac{1}{512} \, \sin\left(2 \, x\right)"," ",0,"3/256*x + 1/5120*sin(10*x) + 1/2048*sin(8*x) - 1/1024*sin(6*x) - 1/256*sin(4*x) + 1/512*sin(2*x)","A",0
345,1,25,0,0.827968," ","integrate(cos(x)^6*sin(x)^7,x, algorithm=""giac"")","\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
346,1,42,0,0.819712," ","integrate(sin(x)^11/cos(x),x, algorithm=""giac"")","-\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
347,1,26,0,0.830491," ","integrate(1/cos(x)^6/sin(x)^6,x, algorithm=""giac"")","-\frac{32 \, {\left(15 \, \tan\left(2 \, x\right)^{4} + 10 \, \tan\left(2 \, x\right)^{2} + 3\right)}}{15 \, \tan\left(2 \, x\right)^{5}}"," ",0,"-32/15*(15*tan(2*x)^4 + 10*tan(2*x)^2 + 3)/tan(2*x)^5","A",0
348,1,10,0,0.999741," ","integrate(cos(x)^2*sin(x)^2,x, algorithm=""giac"")","\frac{1}{8} \, x - \frac{1}{32} \, \sin\left(4 \, x\right)"," ",0,"1/8*x - 1/32*sin(4*x)","A",0
349,1,16,0,0.976444," ","integrate(cos(x)^4*sin(x)^4,x, algorithm=""giac"")","\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
350,1,22,0,0.885380," ","integrate(cos(x)^6*sin(x)^6,x, algorithm=""giac"")","\frac{5}{1024} \, x - \frac{1}{24576} \, \sin\left(12 \, x\right) + \frac{3}{8192} \, \sin\left(8 \, x\right) - \frac{15}{8192} \, \sin\left(4 \, x\right)"," ",0,"5/1024*x - 1/24576*sin(12*x) + 3/8192*sin(8*x) - 15/8192*sin(4*x)","A",0
351,1,28,0,0.627576," ","integrate(cos(x)^8*sin(x)^8,x, algorithm=""giac"")","\frac{35}{32768} \, x + \frac{1}{524288} \, \sin\left(16 \, x\right) - \frac{1}{49152} \, \sin\left(12 \, x\right) + \frac{7}{65536} \, \sin\left(8 \, x\right) - \frac{7}{16384} \, \sin\left(4 \, x\right)"," ",0,"35/32768*x + 1/524288*sin(16*x) - 1/49152*sin(12*x) + 7/65536*sin(8*x) - 7/16384*sin(4*x)","A",0
352,0,0,0,0.000000," ","integrate(cos(x)^(2*m)*sin(x)^(2*m),x, algorithm=""giac"")","\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
353,1,132,0,0.751532," ","integrate(1/cos(1/4*pi+2*x)/sin(1/4*pi+2*x)^3,x, algorithm=""giac"")","-\frac{{\left(\frac{4 \, {\left(\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) - 1\right)}}{\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) + 1} - 1\right)} {\left(\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) + 1\right)}}{16 \, {\left(\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) - 1\right)}} + \frac{\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) - 1}{16 \, {\left(\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) + 1\right)}} + \frac{1}{4} \, \log\left(-\frac{\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) - 1}{\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) + 1}\right) - \frac{1}{2} \, \log\left({\left| -\frac{\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) - 1}{\cos\left(\frac{1}{4} \, \pi + 2 \, x\right) + 1} - 1 \right|}\right)"," ",0,"-1/16*(4*(cos(1/4*pi + 2*x) - 1)/(cos(1/4*pi + 2*x) + 1) - 1)*(cos(1/4*pi + 2*x) + 1)/(cos(1/4*pi + 2*x) - 1) + 1/16*(cos(1/4*pi + 2*x) - 1)/(cos(1/4*pi + 2*x) + 1) + 1/4*log(-(cos(1/4*pi + 2*x) - 1)/(cos(1/4*pi + 2*x) + 1)) - 1/2*log(abs(-(cos(1/4*pi + 2*x) - 1)/(cos(1/4*pi + 2*x) + 1) - 1))","B",0
354,1,6,0,0.623219," ","integrate(sec(x)^2*tan(x)^2,x, algorithm=""giac"")","\frac{1}{3} \, \tan\left(x\right)^{3}"," ",0,"1/3*tan(x)^3","A",0
355,1,14,0,0.602354," ","integrate(cot(x)^3*csc(x),x, algorithm=""giac"")","\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
356,1,6,0,0.627541," ","integrate(sec(x)^3*tan(x),x, algorithm=""giac"")","\frac{1}{3 \, \cos\left(x\right)^{3}}"," ",0,"1/3/cos(x)^3","A",0
357,1,47,0,0.615128," ","integrate(cot(x)^2*csc(x)^3,x, algorithm=""giac"")","-\frac{\frac{1}{\cos\left(x\right)} + \cos\left(x\right)}{8 \, {\left({\left(\frac{1}{\cos\left(x\right)} + \cos\left(x\right)\right)}^{2} - 4\right)}} + \frac{1}{32} \, \log\left({\left| \frac{1}{\cos\left(x\right)} + \cos\left(x\right) + 2 \right|}\right) - \frac{1}{32} \, \log\left({\left| \frac{1}{\cos\left(x\right)} + \cos\left(x\right) - 2 \right|}\right)"," ",0,"-1/8*(1/cos(x) + cos(x))/((1/cos(x) + cos(x))^2 - 4) + 1/32*log(abs(1/cos(x) + cos(x) + 2)) - 1/32*log(abs(1/cos(x) + cos(x) - 2))","B",0
358,1,14,0,0.611625," ","integrate(cos(x)^3/sin(x)^7,x, algorithm=""giac"")","\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
359,1,20,0,0.652963," ","integrate(sec(x)^(3/2)*tan(x)^5,x, algorithm=""giac"")","\frac{2 \, {\left(77 \, \cos\left(x\right)^{4} - 66 \, \cos\left(x\right)^{2} + 21\right)}}{231 \, \cos\left(x\right)^{\frac{11}{2}}}"," ",0,"2/231*(77*cos(x)^4 - 66*cos(x)^2 + 21)/cos(x)^(11/2)","A",0
360,1,13,0,0.604932," ","integrate(sec(x)^4*tan(x)^(3/2),x, algorithm=""giac"")","\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
361,1,44,0,0.614981," ","integrate(cot(x)^4*csc(x)^3,x, algorithm=""giac"")","\frac{3 \, \cos\left(x\right)^{5} + 8 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)}{48 \, {\left(\cos\left(x\right)^{2} - 1\right)}^{3}} - \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)^2 - 1)^3 - 1/32*log(cos(x) + 1) + 1/32*log(-cos(x) + 1)","A",0
362,1,95,0,0.947117," ","integrate(sec(1/4*pi+1/2*x)^3*tan(1/4*pi+1/2*x)^2,x, algorithm=""giac"")","\frac{\frac{1}{\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)} + \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)}{4 \, {\left({\left(\frac{1}{\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)} + \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)\right)}^{2} - 4\right)}} - \frac{1}{16} \, \log\left({\left| \frac{1}{\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)} + \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right) + 2 \right|}\right) + \frac{1}{16} \, \log\left({\left| \frac{1}{\sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right)} + \sin\left(\frac{1}{4} \, \pi + \frac{1}{2} \, x\right) - 2 \right|}\right)"," ",0,"1/4*(1/sin(1/4*pi + 1/2*x) + sin(1/4*pi + 1/2*x))/((1/sin(1/4*pi + 1/2*x) + sin(1/4*pi + 1/2*x))^2 - 4) - 1/16*log(abs(1/sin(1/4*pi + 1/2*x) + sin(1/4*pi + 1/2*x) + 2)) + 1/16*log(abs(1/sin(1/4*pi + 1/2*x) + sin(1/4*pi + 1/2*x) - 2))","A",0
363,1,149,0,0.635803," ","integrate((1+cot(x)^3)*(a*sec(x)^2-sin(2*x))^2,x, algorithm=""giac"")","\frac{1}{3} \, a^{2} \tan\left(x\right)^{3} + a^{2} \tan\left(x\right) + \frac{1}{2} \, {\left(8 \, a + 1\right)} x - 2 \, {\left(a + 1\right)} \log\left(\tan\left(x\right)^{2} + 1\right) + {\left(a^{2} + 4\right)} \log\left({\left| \tan\left(x\right) \right|}\right) - \frac{a^{2} \tan\left(x\right)^{6} - 4 \, a \tan\left(x\right)^{6} + 3 \, a^{2} \tan\left(x\right)^{4} - 8 \, a \tan\left(x\right)^{5} - 8 \, a \tan\left(x\right)^{4} - \tan\left(x\right)^{5} + 3 \, a^{2} \tan\left(x\right)^{2} - 16 \, a \tan\left(x\right)^{3} - 4 \, \tan\left(x\right)^{4} - 4 \, a \tan\left(x\right)^{2} + \tan\left(x\right)^{3} + a^{2} - 8 \, a \tan\left(x\right) - 6 \, \tan\left(x\right)^{2}}{2 \, {\left(\tan\left(x\right)^{3} + \tan\left(x\right)\right)}^{2}}"," ",0,"1/3*a^2*tan(x)^3 + a^2*tan(x) + 1/2*(8*a + 1)*x - 2*(a + 1)*log(tan(x)^2 + 1) + (a^2 + 4)*log(abs(tan(x))) - 1/2*(a^2*tan(x)^6 - 4*a*tan(x)^6 + 3*a^2*tan(x)^4 - 8*a*tan(x)^5 - 8*a*tan(x)^4 - tan(x)^5 + 3*a^2*tan(x)^2 - 16*a*tan(x)^3 - 4*tan(x)^4 - 4*a*tan(x)^2 + tan(x)^3 + a^2 - 8*a*tan(x) - 6*tan(x)^2)/(tan(x)^3 + tan(x))^2","A",0
364,1,54,0,0.601008," ","integrate((4-3*cos(x))*(1-1/2*sin(x))^4,x, algorithm=""giac"")","\frac{227}{32} \, x + \frac{3}{64} \, \cos\left(4 \, x\right) - \frac{1}{6} \, \cos\left(3 \, x\right) - \frac{27}{16} \, \cos\left(2 \, x\right) + \frac{19}{2} \, \cos\left(x\right) - \frac{3}{1280} \, \sin\left(5 \, x\right) + \frac{1}{128} \, \sin\left(4 \, x\right) + \frac{99}{256} \, \sin\left(3 \, x\right) - \frac{25}{16} \, \sin\left(2 \, x\right) - \frac{531}{128} \, \sin\left(x\right)"," ",0,"227/32*x + 3/64*cos(4*x) - 1/6*cos(3*x) - 27/16*cos(2*x) + 19/2*cos(x) - 3/1280*sin(5*x) + 1/128*sin(4*x) + 99/256*sin(3*x) - 25/16*sin(2*x) - 531/128*sin(x)","A",0
365,1,75,0,0.673615," ","integrate((1/2-3*cot(x))*(3-2*cot(x))^3,x, algorithm=""giac"")","\tan\left(\frac{1}{2} \, x\right)^{3} + 14 \, \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{285}{2} \, x - \frac{22 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 225 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 42 \, \tan\left(\frac{1}{2} \, x\right) + 3}{3 \, \tan\left(\frac{1}{2} \, x\right)^{3}} - 4 \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + 4 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right) + 75 \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"tan(1/2*x)^3 + 14*tan(1/2*x)^2 - 285/2*x - 1/3*(22*tan(1/2*x)^3 + 225*tan(1/2*x)^2 - 42*tan(1/2*x) + 3)/tan(1/2*x)^3 - 4*log(tan(1/2*x)^2 + 1) + 4*log(abs(tan(1/2*x))) + 75*tan(1/2*x)","B",0
366,1,14,0,0.619626," ","integrate(cos(5*x)/cos(x)^5,x, algorithm=""giac"")","\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
367,1,23,0,0.604263," ","integrate(cos(4*x)/cos(x),x, algorithm=""giac"")","-\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
368,1,13,0,0.614398," ","integrate(cos(x)*cos(4*x),x, algorithm=""giac"")","\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
369,1,38,0,0.592416," ","integrate(cos(4*x)/cos(x)^5,x, algorithm=""giac"")","\frac{29 \, \sin\left(x\right)^{3} - 27 \, \sin\left(x\right)}{8 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2}} + \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*(29*sin(x)^3 - 27*sin(x))/(sin(x)^2 - 1)^2 + 35/16*log(sin(x) + 1) - 35/16*log(-sin(x) + 1)","A",0
370,1,28,0,0.627714," ","integrate(cos(x)^4*cos(4*x),x, algorithm=""giac"")","\frac{1}{16} \, x + \frac{1}{128} \, \sin\left(8 \, x\right) + \frac{1}{24} \, \sin\left(6 \, x\right) + \frac{3}{32} \, \sin\left(4 \, x\right) + \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/16*x + 1/128*sin(8*x) + 1/24*sin(6*x) + 3/32*sin(4*x) + 1/8*sin(2*x)","A",0
371,1,21,0,0.633368," ","integrate(cos(5*x)/sin(x)^5,x, algorithm=""giac"")","\frac{24 \, \sin\left(x\right)^{2} - 1}{4 \, \sin\left(x\right)^{4}} + 16 \, \log\left({\left| \sin\left(x\right) \right|}\right)"," ",0,"1/4*(24*sin(x)^2 - 1)/sin(x)^4 + 16*log(abs(sin(x)))","A",0
372,1,13,0,0.603220," ","integrate(sin(4*x)/sin(x)^4,x, algorithm=""giac"")","-\frac{2}{\sin\left(x\right)^{2}} - 8 \, \log\left({\left| \sin\left(x\right) \right|}\right)"," ",0,"-2/sin(x)^2 - 8*log(abs(sin(x)))","A",0
373,1,75,0,0.637085," ","integrate(cos(x)/sin(x)/(2+sin(2*x)),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} {\left(x + \arctan\left(-\frac{\sqrt{3} \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right) - 1}{\sqrt{3} \cos\left(2 \, x\right) + \sqrt{3} - 2 \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right) + 2}\right)\right)} - \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + \tan\left(x\right) + 1\right) + \frac{1}{2} \, \log\left({\left| \tan\left(x\right) \right|}\right)"," ",0,"-1/6*sqrt(3)*(x + arctan(-(sqrt(3)*sin(2*x) - cos(2*x) - 2*sin(2*x) - 1)/(sqrt(3)*cos(2*x) + sqrt(3) - 2*cos(2*x) + sin(2*x) + 2))) - 1/4*log(tan(x)^2 + tan(x) + 1) + 1/2*log(abs(tan(x)))","A",0
374,1,24,0,0.635294," ","integrate(cos(x)^2/cos(3*x)/sin(x),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(-\cos\left(x\right)^{2} + 1\right) - \frac{1}{2} \, \log\left({\left| 4 \, \cos\left(x\right)^{2} - 3 \right|}\right)"," ",0,"1/2*log(-cos(x)^2 + 1) - 1/2*log(abs(4*cos(x)^2 - 3))","B",0
375,1,9,0,0.605628," ","integrate(sin(2*x)/(cos(x)^4+sin(x)^4),x, algorithm=""giac"")","\arctan\left(2 \, \sin\left(x\right)^{2} - 1\right)"," ",0,"arctan(2*sin(x)^2 - 1)","A",0
376,1,78,0,0.639087," ","integrate(1/(4+sin(x)+cos(x)*3^(1/2)),x, algorithm=""giac"")","\frac{{\left(x + 2 \, \arctan\left(\frac{\sqrt{3} \cos\left(x\right) - 8 \, \sqrt{3} \sin\left(x\right) + \sqrt{3} + 4 \, \cos\left(x\right) + 7 \, \sin\left(x\right) + 4}{8 \, \sqrt{3} \cos\left(x\right) + \sqrt{3} \sin\left(x\right) + 8 \, \sqrt{3} - 7 \, \cos\left(x\right) + 4 \, \sin\left(x\right) + 19}\right)\right)} {\left(\sqrt{3} + 4\right)}}{2 \, {\left(4 \, \sqrt{3} + 3\right)}}"," ",0,"1/2*(x + 2*arctan((sqrt(3)*cos(x) - 8*sqrt(3)*sin(x) + sqrt(3) + 4*cos(x) + 7*sin(x) + 4)/(8*sqrt(3)*cos(x) + sqrt(3)*sin(x) + 8*sqrt(3) - 7*cos(x) + 4*sin(x) + 19)))*(sqrt(3) + 4)/(4*sqrt(3) + 3)","A",0
377,1,37,0,0.677791," ","integrate(1/(3+4*cos(x)+4*sin(x)),x, algorithm=""giac"")","-\frac{1}{23} \, \sqrt{23} \log\left(\frac{{\left| -2 \, \sqrt{23} + 2 \, \tan\left(\frac{1}{2} \, x\right) - 8 \right|}}{{\left| 2 \, \sqrt{23} + 2 \, \tan\left(\frac{1}{2} \, x\right) - 8 \right|}}\right)"," ",0,"-1/23*sqrt(23)*log(abs(-2*sqrt(23) + 2*tan(1/2*x) - 8)/abs(2*sqrt(23) + 2*tan(1/2*x) - 8))","A",0
378,1,20,0,0.633229," ","integrate(1/(4-3*cos(x)^2+5*sin(x)^2),x, algorithm=""giac"")","\frac{1}{3} \, x - \frac{1}{3} \, \arctan\left(\frac{\sin\left(2 \, x\right)}{\cos\left(2 \, x\right) - 2}\right)"," ",0,"1/3*x - 1/3*arctan(sin(2*x)/(cos(2*x) - 2))","A",0
379,1,29,0,0.630510," ","integrate(1/(4+4*cot(x)+tan(x)),x, algorithm=""giac"")","\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({\left| \tan\left(x\right) + 2 \right|}\right)"," ",0,"4/25*x + 2/5/(tan(x) + 2) + 3/50*log(tan(x)^2 + 1) - 3/25*log(abs(tan(x) + 2))","A",0
380,1,78,0,0.640200," ","integrate(1/(2*sec(x)+sin(x))^2,x, algorithm=""giac"")","\frac{8}{225} \, \sqrt{15} {\left(x + \arctan\left(-\frac{\sqrt{15} \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right) - 1}{\sqrt{15} \cos\left(2 \, x\right) + \sqrt{15} - 4 \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right) + 4}\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)*(x + arctan(-(sqrt(15)*sin(2*x) - cos(2*x) - 4*sin(2*x) - 1)/(sqrt(15)*cos(2*x) + sqrt(15) - 4*cos(2*x) + sin(2*x) + 4))) + 1/15*(4*tan(x) + 1)/(2*tan(x)^2 + tan(x) + 2)","A",0
381,1,61,0,0.633025," ","integrate(1/(cos(x)+2*sec(x))^2,x, algorithm=""giac"")","\frac{1}{36} \, \sqrt{6} {\left(x + \arctan\left(-\frac{\sqrt{6} \sin\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right)}{\sqrt{6} \cos\left(2 \, x\right) + \sqrt{6} - 2 \, \cos\left(2 \, x\right) + 2}\right)\right)} + \frac{\tan\left(x\right)}{6 \, {\left(2 \, \tan\left(x\right)^{2} + 3\right)}}"," ",0,"1/36*sqrt(6)*(x + arctan(-(sqrt(6)*sin(2*x) - 2*sin(2*x))/(sqrt(6)*cos(2*x) + sqrt(6) - 2*cos(2*x) + 2))) + 1/6*tan(x)/(2*tan(x)^2 + 3)","A",0
382,1,39,0,0.636412," ","integrate((5-tan(x)-6*tan(x)^2)/(1+3*tan(x))^3,x, algorithm=""giac"")","-\frac{67}{250} \, x - \frac{87 \, \tan\left(x\right) + 64}{50 \, {\left(3 \, \tan\left(x\right) + 1\right)}^{2}} + \frac{14}{125} \, \log\left(\tan\left(x\right)^{2} + 1\right) - \frac{28}{125} \, \log\left({\left| 3 \, \tan\left(x\right) + 1 \right|}\right)"," ",0,"-67/250*x - 1/50*(87*tan(x) + 64)/(3*tan(x) + 1)^2 + 14/125*log(tan(x)^2 + 1) - 28/125*log(abs(3*tan(x) + 1))","A",0
383,1,21,0,0.645761," ","integrate(cos(x)^2/cos(3*x),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| 2 \, \sin\left(x\right) + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| 2 \, \sin\left(x\right) - 1 \right|}\right)"," ",0,"1/4*log(abs(2*sin(x) + 1)) - 1/4*log(abs(2*sin(x) - 1))","B",0
384,1,49,0,0.676877," ","integrate(sin(x)/cos(2*x),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 6 \right|}}{{\left| 4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 6 \right|}}\right)"," ",0,"1/4*sqrt(2)*log(abs(-4*sqrt(2) - 2*(cos(x) - 1)/(cos(x) + 1) - 6)/abs(4*sqrt(2) - 2*(cos(x) - 1)/(cos(x) + 1) - 6))","B",0
385,1,20,0,0.650280," ","integrate(sin(x)^2/cos(2*x),x, algorithm=""giac"")","-\frac{1}{2} \, x + \frac{1}{4} \, \log\left({\left| \tan\left(x\right) + 1 \right|}\right) - \frac{1}{4} \, \log\left({\left| \tan\left(x\right) - 1 \right|}\right)"," ",0,"-1/2*x + 1/4*log(abs(tan(x) + 1)) - 1/4*log(abs(tan(x) - 1))","A",0
386,1,24,0,0.607058," ","integrate(sin(x)^3/cos(3*x),x, algorithm=""giac"")","\frac{1}{6} \, \log\left(-\sin\left(x\right)^{2} + 1\right) - \frac{1}{24} \, \log\left({\left| 4 \, \sin\left(x\right)^{2} - 1 \right|}\right)"," ",0,"1/6*log(-sin(x)^2 + 1) - 1/24*log(abs(4*sin(x)^2 - 1))","A",0
387,1,24,0,0.606987," ","integrate(cos(x)/sin(3*x),x, algorithm=""giac"")","\frac{1}{6} \, \log\left(-\cos\left(x\right)^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| 4 \, \cos\left(x\right)^{2} - 1 \right|}\right)"," ",0,"1/6*log(-cos(x)^2 + 1) - 1/6*log(abs(4*cos(x)^2 - 1))","A",0
388,1,48,0,0.644517," ","integrate(sin(x)/sin(4*x),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}\right) - \frac{1}{8} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-1/8*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(x))/abs(2*sqrt(2) + 4*sin(x))) - 1/8*log(sin(x) + 1) + 1/8*log(-sin(x) + 1)","B",0
389,1,48,0,0.663645," ","integrate(sin(x)^3/sin(4*x),x, algorithm=""giac"")","-\frac{1}{16} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}\right) - \frac{1}{8} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-1/16*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(x))/abs(2*sqrt(2) + 4*sin(x))) - 1/8*log(sin(x) + 1) + 1/8*log(-sin(x) + 1)","B",0
390,1,17,0,0.611821," ","integrate((1+sin(2*x))^(1/2),x, algorithm=""giac"")","\sqrt{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + x\right)\right) \sin\left(-\frac{1}{4} \, \pi + x\right)"," ",0,"sqrt(2)*sgn(cos(-1/4*pi + x))*sin(-1/4*pi + x)","A",0
391,1,29,0,0.653050," ","integrate((1-sin(2*x))^(1/2),x, algorithm=""giac"")","-\sqrt{2} {\left(\cos\left(-\frac{1}{4} \, \pi + x\right) \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + x\right)\right) - \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + x\right)\right)\right)}"," ",0,"-sqrt(2)*(cos(-1/4*pi + x)*sgn(sin(-1/4*pi + x)) - sgn(sin(-1/4*pi + x)))","A",0
392,1,41,0,0.626786," ","integrate(1/(1+cos(2*x))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) + 2 \right|}\right)}{8 \, \mathrm{sgn}\left(\cos\left(x\right)\right)} - \frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) - 2 \right|}\right)}{8 \, \mathrm{sgn}\left(\cos\left(x\right)\right)}"," ",0,"1/8*sqrt(2)*log(abs(1/sin(x) + sin(x) + 2))/sgn(cos(x)) - 1/8*sqrt(2)*log(abs(1/sin(x) + sin(x) - 2))/sgn(cos(x))","A",0
393,1,16,0,0.636975," ","integrate(1/(1-cos(2*x))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"1/2*sqrt(2)*log(abs(tan(1/2*x)))/sgn(sin(x))","A",0
394,1,59,0,0.806009," ","integrate(1/(1-cos(3*x))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\frac{2 \, \sqrt{\tan\left(\frac{3}{2} \, x\right)^{2} + 1}}{\tan\left(\frac{3}{2} \, x\right)^{2}} + \log\left(\sqrt{\tan\left(\frac{3}{2} \, x\right)^{2} + 1} + 1\right) - \log\left(\sqrt{\tan\left(\frac{3}{2} \, x\right)^{2} + 1} - 1\right)\right)}}{24 \, \mathrm{sgn}\left(\tan\left(\frac{3}{2} \, x\right)\right)}"," ",0,"-1/24*sqrt(2)*(2*sqrt(tan(3/2*x)^2 + 1)/tan(3/2*x)^2 + log(sqrt(tan(3/2*x)^2 + 1) + 1) - log(sqrt(tan(3/2*x)^2 + 1) - 1))/sgn(tan(3/2*x))","A",0
395,1,110,0,0.751898," ","integrate((1-sin(2/3*x))^(5/2),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{2} {\left(5 \, \cos\left(\frac{1}{4} \, \pi + x\right) \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)\right) + 90 \, \cos\left(\frac{1}{4} \, \pi - \frac{1}{3} \, x\right) \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)\right) - 3 \, \cos\left(\frac{1}{4} \, \pi - \frac{5}{3} \, x\right) \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)\right) + 60 \, \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{1}{3} \, x\right) + 20 \, \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)\right) \sin\left(\frac{1}{4} \, \pi - x\right) - 128 \, \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{3} \, x\right)\right)\right)}"," ",0,"-1/20*sqrt(2)*(5*cos(1/4*pi + x)*sgn(sin(-1/4*pi + 1/3*x)) + 90*cos(1/4*pi - 1/3*x)*sgn(sin(-1/4*pi + 1/3*x)) - 3*cos(1/4*pi - 5/3*x)*sgn(sin(-1/4*pi + 1/3*x)) + 60*sgn(sin(-1/4*pi + 1/3*x))*sin(1/4*pi + 1/3*x) + 20*sgn(sin(-1/4*pi + 1/3*x))*sin(1/4*pi - x) - 128*sgn(sin(-1/4*pi + 1/3*x)))","B",0
396,1,43,0,0.648532," ","integrate(cos(x)*(-cos(x)^2+2*(1+2*sin(x))^(1/4))/(1+2*sin(x))^(3/2),x, algorithm=""giac"")","\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
397,1,80,0,0.595659," ","integrate(tan(x)^(1/2),x, algorithm=""giac"")","\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
398,0,0,0,0.000000," ","integrate(1/tan(5*x)^(1/3),x, algorithm=""giac"")","\int \frac{1}{\tan\left(5 \, x\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(5*x)^(-1/3), x)","F",0
399,0,0,0,0.000000," ","integrate(1/(4+3*tan(2*x))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, \tan\left(2 \, x\right) + 4\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*tan(2*x) + 4)^(-3/2), x)","F",0
400,1,31,0,0.633075," ","integrate((-(4-3*tan(x))^(1/2)+3*tan(x))/cos(x)^2/(4-3*tan(x))^(3/2),x, algorithm=""giac"")","\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({\left| -3 \, \tan\left(x\right) + 4 \right|}\right)"," ",0,"2/3*sqrt(-3*tan(x) + 4) + 8/3/sqrt(-3*tan(x) + 4) + 1/3*log(abs(-3*tan(x) + 4))","A",0
401,1,111,0,0.671513," ","integrate(tan(x)/(-1+tan(x)^(1/2))^2,x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\sqrt{2} - 1\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) - \frac{1}{2} \, {\left(\sqrt{2} + 1\right)} \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) - \frac{1}{\sqrt{\tan\left(x\right)} - 1} - \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \log\left({\left| \sqrt{\tan\left(x\right)} - 1 \right|}\right)"," ",0,"-1/2*(sqrt(2) - 1)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) - 1/2*(sqrt(2) + 1)*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) - 1/(sqrt(tan(x)) - 1) - 1/4*log(tan(x)^2 + 1) + log(abs(sqrt(tan(x)) - 1))","A",0
402,0,0,0,0.000000," ","integrate(sin(x)/sin(2*x)^(1/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
411,0,0,0,0.000000," ","integrate(cos(x)^3*(cos(2*x)-3*tan(x))/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(\cos\left(2 \, x\right) - 3 \, \tan\left(x\right)\right)} \cos\left(x\right)^{3}}{{\left(\sin\left(x\right)^{2} - \sin\left(2 \, x\right)\right)} \sin\left(2 \, x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((cos(2*x) - 3*tan(x))*cos(x)^3/((sin(x)^2 - sin(2*x))*sin(2*x)^(5/2)), x)","F",0
412,0,0,0,0.000000," ","integrate((sin(x)/cos(x)^5)^(1/2),x, algorithm=""giac"")","\int \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right)^{5}}}\,{d x}"," ",0,"integrate(sqrt(sin(x)/cos(x)^5), x)","F",0
413,0,0,0,0.000000," ","integrate((sin(x)^5/cos(x))^(1/2),x, algorithm=""giac"")","\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
414,0,0,0,0.000000," ","integrate((sin(x)^2/cos(x)^14)^(1/3),x, algorithm=""giac"")","\int \left(\frac{\sin\left(x\right)^{2}}{\cos\left(x\right)^{14}}\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((sin(x)^2/cos(x)^14)^(1/3), x)","F",0
415,0,0,0,0.000000," ","integrate(1/(cos(x)^11*sin(x)^13)^(1/4),x, algorithm=""giac"")","\int \frac{1}{\left(\cos\left(x\right)^{11} \sin\left(x\right)^{13}\right)^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((cos(x)^11*sin(x)^13)^(-1/4), x)","F",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=""giac"")","\int -\frac{\sqrt{\sin\left(2 \, x\right)} - \cos\left(2 \, x\right)}{\sqrt{\cos\left(x\right)^{3} \sin\left(x\right)}}\,{d x}"," ",0,"integrate(-(sqrt(sin(2*x)) - cos(2*x))/sqrt(cos(x)^3*sin(x)), x)","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=""giac"")","\int -\frac{\sqrt{\cos\left(x\right) \sin\left(x\right)^{3}} - 2 \, \sin\left(2 \, x\right)}{\sqrt{\cos\left(x\right)^{3} \sin\left(x\right)} - \sqrt{\tan\left(x\right)}}\,{d x}"," ",0,"integrate(-(sqrt(cos(x)*sin(x)^3) - 2*sin(2*x))/(sqrt(cos(x)^3*sin(x)) - sqrt(tan(x))), x)","F",0
418,0,0,0,0.000000," ","integrate(((sin(x)/cos(x)^7)^(1/3)-3*tan(x))/(cos(x)^5*sin(x))^(2/3),x, algorithm=""giac"")","\int \frac{\left(\frac{\sin\left(x\right)}{\cos\left(x\right)^{7}}\right)^{\frac{1}{3}} - 3 \, \tan\left(x\right)}{\left(\cos\left(x\right)^{5} \sin\left(x\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(((sin(x)/cos(x)^7)^(1/3) - 3*tan(x))/(cos(x)^5*sin(x))^(2/3), x)","F",0
419,1,55,0,0.667304," ","integrate((1+2*cos(x)^2)^(5/2)*sin(x),x, algorithm=""giac"")","-\frac{1}{48} \, {\left(4 \, {\left(8 \, \cos\left(x\right)^{2} + 13\right)} \cos\left(x\right)^{2} + 33\right)} \sqrt{2 \, \cos\left(x\right)^{2} + 1} \cos\left(x\right) + \frac{5}{32} \, \sqrt{2} \log\left(-\sqrt{2} \cos\left(x\right) + \sqrt{2 \, \cos\left(x\right)^{2} + 1}\right)"," ",0,"-1/48*(4*(8*cos(x)^2 + 13)*cos(x)^2 + 33)*sqrt(2*cos(x)^2 + 1)*cos(x) + 5/32*sqrt(2)*log(-sqrt(2)*cos(x) + sqrt(2*cos(x)^2 + 1))","A",0
420,1,41,0,0.678997," ","integrate(cos(x)*(5*cos(x)^2+sin(x)^2)^(5/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(8 \, {\left(16 \, \sin\left(x\right)^{2} - 65\right)} \sin\left(x\right)^{2} + 825\right)} \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,"1/48*(8*(16*sin(x)^2 - 65)*sin(x)^2 + 825)*sqrt(-4*sin(x)^2 + 5)*sin(x) + 625/32*arcsin(2/5*sqrt(5)*sin(x))","A",0
421,1,41,0,0.636801," ","integrate(cos(x)*(-cos(x)^2-5*sin(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{8} i \, {\left(8 \, \sin\left(x\right)^{2} + 5\right)} \sqrt{4 \, \sin\left(x\right)^{2} + 1} \sin\left(x\right) + \frac{3}{16} i \, \log\left(\sqrt{4 \, \sin\left(x\right)^{2} + 1} - 2 \, \sin\left(x\right)\right)"," ",0,"-1/8*I*(8*sin(x)^2 + 5)*sqrt(4*sin(x)^2 + 1)*sin(x) + 3/16*I*log(sqrt(4*sin(x)^2 + 1) - 2*sin(x))","C",0
422,1,30,0,0.674300," ","integrate(sin(x)/(5*cos(x)^2-2*sin(x)^2)^(7/2),x, algorithm=""giac"")","\frac{{\left(14 \, {\left(7 \, \cos\left(x\right)^{2} - 5\right)} \cos\left(x\right)^{2} + 15\right)} \cos\left(x\right)}{30 \, {\left(7 \, \cos\left(x\right)^{2} - 2\right)}^{\frac{5}{2}}}"," ",0,"1/30*(14*(7*cos(x)^2 - 5)*cos(x)^2 + 15)*cos(x)/(7*cos(x)^2 - 2)^(5/2)","A",0
423,1,38,0,0.697593," ","integrate(cos(x)*cos(2*x)/(2-5*sin(x)^2)^(3/2),x, algorithm=""giac"")","\frac{2}{25} \, \sqrt{5} \arcsin\left(\frac{1}{2} \, \sqrt{10} \sin\left(x\right)\right) - \frac{\sqrt{-5 \, \sin\left(x\right)^{2} + 2} \sin\left(x\right)}{10 \, {\left(5 \, \sin\left(x\right)^{2} - 2\right)}}"," ",0,"2/25*sqrt(5)*arcsin(1/2*sqrt(10)*sin(x)) - 1/10*sqrt(-5*sin(x)^2 + 2)*sin(x)/(5*sin(x)^2 - 2)","A",0
424,1,40,0,0.676270," ","integrate(sin(5*x)/(5*cos(x)^2+9*sin(x)^2)^(5/2),x, algorithm=""giac"")","-\frac{20 \, {\left(59 \, \cos\left(x\right)^{2} - 108\right)} \sqrt{-4 \, \cos\left(x\right)^{2} + 9} \cos\left(x\right)}{243 \, {\left(4 \, \cos\left(x\right)^{2} - 9\right)}^{2}} - \frac{1}{2} \, \arcsin\left(\frac{2}{3} \, \cos\left(x\right)\right)"," ",0,"-20/243*(59*cos(x)^2 - 108)*sqrt(-4*cos(x)^2 + 9)*cos(x)/(4*cos(x)^2 - 9)^2 - 1/2*arcsin(2/3*cos(x))","A",0
425,1,33,0,0.637500," ","integrate(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{4 \, \sin\left(x\right)^{2} - 5} - \frac{20 \, \sin\left(x\right)^{2} - 23}{8 \, {\left(4 \, \sin\left(x\right)^{2} - 5\right)}^{\frac{3}{2}}}"," ",0,"1/8*sqrt(4*sin(x)^2 - 5) - 1/8*(20*sin(x)^2 - 23)/(4*sin(x)^2 - 5)^(3/2)","A",0
426,0,0,0,0.000000," ","integrate((-2*cos(x)^3*(-1+sin(x))+cos(2*x)*sin(x))/sin(x)^2/(-5+sin(x)^2)^(1/2),x, algorithm=""giac"")","\int -\frac{2 \, {\left(\sin\left(x\right) - 1\right)} \cos\left(x\right)^{3} - \cos\left(2 \, x\right) \sin\left(x\right)}{\sqrt{\sin\left(x\right)^{2} - 5} \sin\left(x\right)^{2}}\,{d x}"," ",0,"integrate(-(2*(sin(x) - 1)*cos(x)^3 - cos(2*x)*sin(x))/(sqrt(sin(x)^2 - 5)*sin(x)^2), x)","F",0
427,0,0,0,0.000000," ","integrate(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x, algorithm=""giac"")","\int -\frac{\cos\left(3 \, x\right)}{\sqrt{8 \, \cos\left(x\right)^{2} - 1} - \sqrt{3 \, \cos\left(x\right)^{2} - \sin\left(x\right)^{2}}}\,{d x}"," ",0,"integrate(-cos(3*x)/(sqrt(8*cos(x)^2 - 1) - sqrt(3*cos(x)^2 - sin(x)^2)), x)","F",0
428,1,35,0,0.655324," ","integrate((2-3*sin(x)^2)^(3/5)*sin(4*x),x, algorithm=""giac"")","-\frac{20}{117} \, {\left(3 \, \sin\left(x\right)^{2} - 2\right)}^{2} {\left(-3 \, \sin\left(x\right)^{2} + 2\right)}^{\frac{3}{5}} + \frac{5}{36} \, {\left(-3 \, \sin\left(x\right)^{2} + 2\right)}^{\frac{8}{5}}"," ",0,"-20/117*(3*sin(x)^2 - 2)^2*(-3*sin(x)^2 + 2)^(3/5) + 5/36*(-3*sin(x)^2 + 2)^(8/5)","A",0
429,1,27,0,0.691807," ","integrate(cos(x)*cos(2*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \arcsin\left(\sqrt{2} \sin\left(x\right)\right) + \frac{1}{2} \, \sqrt{-2 \, \sin\left(x\right)^{2} + 1} \sin\left(x\right)"," ",0,"1/4*sqrt(2)*arcsin(sqrt(2)*sin(x)) + 1/2*sqrt(-2*sin(x)^2 + 1)*sin(x)","A",0
430,1,48,0,0.678472," ","integrate(cos(2*x)^(3/2)*sin(x),x, algorithm=""giac"")","-\frac{1}{8} \, {\left(4 \, \cos\left(x\right)^{2} - 5\right)} \sqrt{2 \, \cos\left(x\right)^{2} - 1} \cos\left(x\right) + \frac{3}{16} \, \sqrt{2} \log\left({\left| -\sqrt{2} \cos\left(x\right) + \sqrt{2 \, \cos\left(x\right)^{2} - 1} \right|}\right)"," ",0,"-1/8*(4*cos(x)^2 - 5)*sqrt(2*cos(x)^2 - 1)*cos(x) + 3/16*sqrt(2)*log(abs(-sqrt(2)*cos(x) + sqrt(2*cos(x)^2 - 1)))","A",0
431,1,46,0,0.966064," ","integrate(sin(x)/cos(2*x)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 15\right)} \tan\left(\frac{1}{2} \, x\right)^{2} + 15\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - 1}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{\frac{3}{2}}}"," ",0,"1/3*(((tan(1/2*x)^2 - 15)*tan(1/2*x)^2 + 15)*tan(1/2*x)^2 - 1)/(tan(1/2*x)^4 - 6*tan(1/2*x)^2 + 1)^(3/2)","B",0
432,0,0,0,0.000000," ","integrate(cos(2*x)^(3/2)/cos(x)^3,x, algorithm=""giac"")","\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
433,1,55,0,0.727232," ","integrate((3*sin(x)^3-cos(x)*sin(4*x))/cos(2*x)^(7/2)/csc(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \log\left({\left| -\sqrt{2} \cos\left(x\right) + \sqrt{2 \, \cos\left(x\right)^{2} - 1} \right|}\right) + \frac{{\left({\left(169 \, \cos\left(x\right)^{2} - 200\right)} \cos\left(x\right)^{2} + 60\right)} \cos\left(x\right)}{15 \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)}^{\frac{5}{2}}}"," ",0,"1/2*sqrt(2)*log(abs(-sqrt(2)*cos(x) + sqrt(2*cos(x)^2 - 1))) + 1/15*((169*cos(x)^2 - 200)*cos(x)^2 + 60)*cos(x)/(2*cos(x)^2 - 1)^(5/2)","A",0
434,0,0,0,0.000000," ","integrate((4-5*sec(x)^2)^(3/2),x, algorithm=""giac"")","\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=""giac"")","\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
436,0,0,0,0.000000," ","integrate((-2*cot(x)^2+sin(x))/(1+5*tan(x)^2)^(3/2),x, algorithm=""giac"")","\int -\frac{2 \, \cot\left(x\right)^{2} - \sin\left(x\right)}{{\left(5 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(2*cot(x)^2 - sin(x))/(5*tan(x)^2 + 1)^(3/2), x)","F",0
437,1,340,0,1.143520," ","integrate((-3+cos(2*x))/cos(x)^4/(4-cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15948 \, \sqrt{5} - 49185 i\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{-15296 i \, \sqrt{5} + 98560} + \frac{82 \, \sqrt{5} + \frac{939 \, \sqrt{5} {\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}^{2}}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 9\right)}^{2}} + \frac{537 \, \sqrt{5} {\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}^{4}}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 9\right)}^{4}} + \frac{975 \, {\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} - 9} + \frac{2255 \, {\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}^{3}}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 9\right)}^{3}} + \frac{255 \, {\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}^{5}}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 9\right)}^{5}}}{96 \, {\left(\frac{\sqrt{5} {\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} - 9} + \frac{{\left(4 \, \sqrt{5} - \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}\right)}^{2}}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 9\right)}^{2}} + 1\right)}^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}"," ",0,"-2*(15948*sqrt(5) - 49185*I)*sgn(tan(1/2*x))/(-15296*I*sqrt(5) + 98560) + 1/96*(82*sqrt(5) + 939*sqrt(5)*(4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))^2/(tan(1/2*x)^2 - 9)^2 + 537*sqrt(5)*(4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))^4/(tan(1/2*x)^2 - 9)^4 + 975*(4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))/(tan(1/2*x)^2 - 9) + 2255*(4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))^3/(tan(1/2*x)^2 - 9)^3 + 255*(4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))^5/(tan(1/2*x)^2 - 9)^5)/((sqrt(5)*(4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))/(tan(1/2*x)^2 - 9) + (4*sqrt(5) - sqrt(-tan(1/2*x)^4 + 18*tan(1/2*x)^2 - 1))^2/(tan(1/2*x)^2 - 9)^2 + 1)^3*sgn(tan(1/2*x)))","C",0
438,1,171,0,0.930434," ","integrate((3+sin(x)^2)*tan(x)^3/(-2+cos(x)^2)/(5-4*sec(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{1}{4500} \, \sqrt{15} \sqrt{5} {\left(6 i \, \sqrt{15} \pi + 12 \, \sqrt{15} \log\left(2\right) - 25 \, \log\left(-\frac{\sqrt{15} + 5}{\sqrt{15} - 5}\right)\right)} \mathrm{sgn}\left(\cos\left(x\right)\right) - \frac{\sqrt{15} \sqrt{5} \log\left(-\frac{2 \, {\left({\left(\sqrt{5} \cos\left(x\right) - \sqrt{5 \, \cos\left(x\right)^{2} - 4}\right)}^{2} - 4 \, \sqrt{15} - 16\right)}}{{\left| 2 \, {\left(\sqrt{5} \cos\left(x\right) - \sqrt{5 \, \cos\left(x\right)^{2} - 4}\right)}^{2} + 8 \, \sqrt{15} - 32 \right|}}\right)}{180 \, \mathrm{sgn}\left(\cos\left(x\right)\right)} + \frac{\sqrt{5} \log\left({\left(\sqrt{5} \cos\left(x\right) - \sqrt{5 \, \cos\left(x\right)^{2} - 4}\right)}^{2}\right)}{50 \, \mathrm{sgn}\left(\cos\left(x\right)\right)} - \frac{2 \, \cos\left(x\right)}{15 \, \sqrt{5 \, \cos\left(x\right)^{2} - 4} \mathrm{sgn}\left(\cos\left(x\right)\right)}"," ",0,"-1/4500*sqrt(15)*sqrt(5)*(6*I*sqrt(15)*pi + 12*sqrt(15)*log(2) - 25*log(-(sqrt(15) + 5)/(sqrt(15) - 5)))*sgn(cos(x)) - 1/180*sqrt(15)*sqrt(5)*log(-2*((sqrt(5)*cos(x) - sqrt(5*cos(x)^2 - 4))^2 - 4*sqrt(15) - 16)/abs(2*(sqrt(5)*cos(x) - sqrt(5*cos(x)^2 - 4))^2 + 8*sqrt(15) - 32))/sgn(cos(x)) + 1/50*sqrt(5)*log((sqrt(5)*cos(x) - sqrt(5*cos(x)^2 - 4))^2)/sgn(cos(x)) - 2/15*cos(x)/(sqrt(5*cos(x)^2 - 4)*sgn(cos(x)))","C",0
439,0,0,0,0.000000," ","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=""giac"")","\int \frac{\sec\left(x\right)^{2} - 3 \, \sqrt{4 \, \sec\left(x\right)^{2} + 5 \, \tan\left(x\right)^{2}} \tan\left(x\right)}{{\left(4 \, \sec\left(x\right)^{2} + 5 \, \tan\left(x\right)^{2}\right)}^{\frac{3}{2}} \sin\left(x\right)^{2}}\,{d x}"," ",0,"integrate((sec(x)^2 - 3*sqrt(4*sec(x)^2 + 5*tan(x)^2)*tan(x))/((4*sec(x)^2 + 5*tan(x)^2)^(3/2)*sin(x)^2), x)","F",0
440,1,52,0,0.619218," ","integrate(tan(x)*(1+5*tan(x)^2)^(5/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(5 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{5}{2}} - \frac{4}{3} \, {\left(5 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}} + 16 \, \sqrt{5 \, \tan\left(x\right)^{2} + 1} - 32 \, \arctan\left(\frac{1}{2} \, \sqrt{5 \, \tan\left(x\right)^{2} + 1}\right)"," ",0,"1/5*(5*tan(x)^2 + 1)^(5/2) - 4/3*(5*tan(x)^2 + 1)^(3/2) + 16*sqrt(5*tan(x)^2 + 1) - 32*arctan(1/2*sqrt(5*tan(x)^2 + 1))","A",0
441,1,36,0,0.610075," ","integrate(tan(x)/(1+5*tan(x)^2)^(5/2),x, algorithm=""giac"")","\frac{15 \, \tan\left(x\right)^{2} - 1}{48 \, {\left(5 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{1}{32} \, \arctan\left(\frac{1}{2} \, \sqrt{5 \, \tan\left(x\right)^{2} + 1}\right)"," ",0,"1/48*(15*tan(x)^2 - 1)/(5*tan(x)^2 + 1)^(3/2) + 1/32*arctan(1/2*sqrt(5*tan(x)^2 + 1))","A",0
442,1,186,0,0.761180," ","integrate(tan(x)/(a^3+b^3*tan(x)^2)^(1/3),x, algorithm=""giac"")","\frac{3 \, {\left(a^{3} - b^{3}\right)}^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(b^{3} \tan\left(x\right)^{2} + a^{3}\right)}^{\frac{1}{3}} + {\left(a^{3} - b^{3}\right)}^{\frac{1}{3}}\right)}}{3 \, {\left(a^{3} - b^{3}\right)}^{\frac{1}{3}}}\right)}{2 \, {\left(\sqrt{3} a^{3} - \sqrt{3} b^{3}\right)}} - \frac{\log\left({\left(b^{3} \tan\left(x\right)^{2} + a^{3}\right)}^{\frac{2}{3}} + {\left(b^{3} \tan\left(x\right)^{2} + a^{3}\right)}^{\frac{1}{3}} {\left(a^{3} - b^{3}\right)}^{\frac{1}{3}} + {\left(a^{3} - b^{3}\right)}^{\frac{2}{3}}\right)}{4 \, {\left(a^{3} - b^{3}\right)}^{\frac{1}{3}}} + \frac{\log\left({\left| {\left(b^{3} \tan\left(x\right)^{2} + a^{3}\right)}^{\frac{1}{3}} - {\left(a^{3} - b^{3}\right)}^{\frac{1}{3}} \right|}\right)}{2 \, {\left(a^{3} - b^{3}\right)}^{\frac{1}{3}}}"," ",0,"3/2*(a^3 - b^3)^(2/3)*arctan(1/3*sqrt(3)*(2*(b^3*tan(x)^2 + a^3)^(1/3) + (a^3 - b^3)^(1/3))/(a^3 - b^3)^(1/3))/(sqrt(3)*a^3 - sqrt(3)*b^3) - 1/4*log((b^3*tan(x)^2 + a^3)^(2/3) + (b^3*tan(x)^2 + a^3)^(1/3)*(a^3 - b^3)^(1/3) + (a^3 - b^3)^(2/3))/(a^3 - b^3)^(1/3) + 1/2*log(abs((b^3*tan(x)^2 + a^3)^(1/3) - (a^3 - b^3)^(1/3)))/(a^3 - b^3)^(1/3)","A",0
443,1,79,0,0.655018," ","integrate(tan(x)*(1-7*tan(x)^2)^(2/3),x, algorithm=""giac"")","2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left({\left(-7 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{3}{4} \, {\left(-7 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{2}{3}} - \log\left({\left(-7 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{2}{3}} + 2 \, {\left(-7 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}} + 4\right) + 2 \, \log\left({\left| {\left(-7 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}} - 2 \right|}\right)"," ",0,"2*sqrt(3)*arctan(1/3*sqrt(3)*((-7*tan(x)^2 + 1)^(1/3) + 1)) + 3/4*(-7*tan(x)^2 + 1)^(2/3) - log((-7*tan(x)^2 + 1)^(2/3) + 2*(-7*tan(x)^2 + 1)^(1/3) + 4) + 2*log(abs((-7*tan(x)^2 + 1)^(1/3) - 2))","A",0
444,1,73,0,1.347845," ","integrate(cot(x)/(a^4+b^4*csc(x)^2)^(1/4),x, algorithm=""giac"")","-\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({\left| a + {\left(a^{4} + \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}} \right|}\right)}{2 \, a} - \frac{\log\left({\left| -a + {\left(a^{4} + \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}} \right|}\right)}{2 \, a}"," ",0,"-arctan((a^4 + b^4/sin(x)^2)^(1/4)/a)/a + 1/2*log(abs(a + (a^4 + b^4/sin(x)^2)^(1/4)))/a - 1/2*log(abs(-a + (a^4 + b^4/sin(x)^2)^(1/4)))/a","A",0
445,1,76,0,1.078072," ","integrate(cot(x)/(a^4-b^4*csc(x)^2)^(1/4),x, algorithm=""giac"")","-\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({\left| a + {\left(a^{4} - \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}} \right|}\right)}{2 \, a} - \frac{\log\left({\left| -a + {\left(a^{4} - \frac{b^{4}}{\sin\left(x\right)^{2}}\right)}^{\frac{1}{4}} \right|}\right)}{2 \, a}"," ",0,"-arctan((a^4 - b^4/sin(x)^2)^(1/4)/a)/a + 1/2*log(abs(a + (a^4 - b^4/sin(x)^2)^(1/4)))/a - 1/2*log(abs(-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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,1,193,0,1.874294," ","integrate((-cos(2*x)+2*tan(x)^2)/cos(x)^2/(tan(x)*tan(2*x))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(2 \, {\left(-\tan\left(x\right)^{2} + 1\right)}^{\frac{3}{2}} + 3 \, \sqrt{-\tan\left(x\right)^{2} + 1}\right)}}{12 \, \mathrm{sgn}\left(\tan\left(x\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(x\right)\right)} + \frac{11 \, \sqrt{2} \log\left(\sqrt{-\tan\left(x\right)^{2} + 1} + 1\right)}{16 \, \mathrm{sgn}\left(\tan\left(x\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(x\right)\right)} - \frac{11 \, \sqrt{2} \log\left(-\sqrt{-\tan\left(x\right)^{2} + 1} + 1\right)}{16 \, \mathrm{sgn}\left(\tan\left(x\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(x\right)\right)} + \frac{\log\left(\frac{\sqrt{2} - \sqrt{-\tan\left(x\right)^{2} + 1}}{\sqrt{2} + \sqrt{-\tan\left(x\right)^{2} + 1}}\right)}{\mathrm{sgn}\left(\tan\left(x\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(x\right)\right)} - \frac{\sqrt{2} \sqrt{-\tan\left(x\right)^{2} + 1}}{8 \, \mathrm{sgn}\left(\tan\left(x\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(x\right)\right) \tan\left(x\right)^{2}}"," ",0,"-1/12*sqrt(2)*(2*(-tan(x)^2 + 1)^(3/2) + 3*sqrt(-tan(x)^2 + 1))/(sgn(tan(x)^2 - 1)*sgn(tan(x))) + 11/16*sqrt(2)*log(sqrt(-tan(x)^2 + 1) + 1)/(sgn(tan(x)^2 - 1)*sgn(tan(x))) - 11/16*sqrt(2)*log(-sqrt(-tan(x)^2 + 1) + 1)/(sgn(tan(x)^2 - 1)*sgn(tan(x))) + log((sqrt(2) - sqrt(-tan(x)^2 + 1))/(sqrt(2) + sqrt(-tan(x)^2 + 1)))/(sgn(tan(x)^2 - 1)*sgn(tan(x))) - 1/8*sqrt(2)*sqrt(-tan(x)^2 + 1)/(sgn(tan(x)^2 - 1)*sgn(tan(x))*tan(x)^2)","B",0
448,0,0,0,0.000000," ","integrate(tan(x)/(a^3-b^3*cos(x)^n)^(4/3),x, algorithm=""giac"")","\int \frac{\tan\left(x\right)}{{\left(-b^{3} \cos\left(x\right)^{n} + a^{3}\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(tan(x)/(-b^3*cos(x)^n + a^3)^(4/3), x)","F",0
449,1,146,0,1.244353," ","integrate((1+2*cos(x)^9)^(5/6)*tan(x),x, algorithm=""giac"")","-\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| {\left(2 \, \cos\left(x\right)^{9} + 1\right)}^{\frac{1}{6}} - 1 \right|}\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(abs((2*cos(x)^9 + 1)^(1/6) - 1))","B",0
450,1,37,0,0.909144," ","integrate(cot(x)*sin(x)^9/(2-5*sin(x)^3)^(4/3),x, algorithm=""giac"")","-\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
451,1,25,0,0.875161," ","integrate(tan(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x, algorithm=""giac"")","-\frac{3}{32} \, {\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{2}{3}} - \frac{3}{16} \, {\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}}"," ",0,"-3/32*(-8*tan(x)^2 + 1)^(2/3) - 3/16*(-8*tan(x)^2 + 1)^(1/3)","A",0
452,1,40,0,0.843452," ","integrate(cot(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{2}{3}} + {\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \log\left({\left| {\left(-8 \, \tan\left(x\right)^{2} + 1\right)}^{\frac{1}{3}} - 1 \right|}\right)"," ",0,"-1/2*log((-8*tan(x)^2 + 1)^(2/3) + (-8*tan(x)^2 + 1)^(1/3) + 1) + log(abs((-8*tan(x)^2 + 1)^(1/3) - 1))","A",0
453,0,0,0,0.000000," ","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=""giac"")","\int \frac{{\left(5 \, \cos\left(x\right)^{2} - \sqrt{5 \, \sin\left(x\right)^{2} - 1}\right)} \tan\left(x\right)}{{\left(5 \, \sin\left(x\right)^{2} - 1\right)}^{\frac{1}{4}} {\left(\sqrt{5 \, \sin\left(x\right)^{2} - 1} + 2\right)}}\,{d x}"," ",0,"integrate((5*cos(x)^2 - sqrt(5*sin(x)^2 - 1))*tan(x)/((5*sin(x)^2 - 1)^(1/4)*(sqrt(5*sin(x)^2 - 1) + 2)), x)","F",0
454,1,25,0,0.636169," ","integrate(cos(x)^4*cos(2*x)^(2/3)*tan(x),x, algorithm=""giac"")","-\frac{3}{64} \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)}^{\frac{8}{3}} - \frac{3}{40} \, {\left(2 \, \cos\left(x\right)^{2} - 1\right)}^{\frac{5}{3}}"," ",0,"-3/64*(2*cos(x)^2 - 1)^(8/3) - 3/40*(2*cos(x)^2 - 1)^(5/3)","A",0
455,1,120,0,0.680683," ","integrate(sin(x)^6*tan(x)/cos(2*x)^(3/4),x, algorithm=""giac"")","\frac{1}{36} \, \cos\left(2 \, x\right)^{\frac{9}{4}} - \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \cos\left(2 \, x\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{2} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \cos\left(2 \, x\right)^{\frac{1}{4}}\right)}\right) - \frac{1}{4} \, \sqrt{2} \log\left(\sqrt{2} \cos\left(2 \, x\right)^{\frac{1}{4}} + \sqrt{\cos\left(2 \, x\right)} + 1\right) + \frac{1}{4} \, \sqrt{2} \log\left(-\sqrt{2} \cos\left(2 \, x\right)^{\frac{1}{4}} + \sqrt{\cos\left(2 \, x\right)} + 1\right) - \frac{1}{5} \, \cos\left(2 \, x\right)^{\frac{5}{4}} + \frac{7}{4} \, \cos\left(2 \, x\right)^{\frac{1}{4}}"," ",0,"1/36*cos(2*x)^(9/4) - 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*cos(2*x)^(1/4))) - 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*cos(2*x)^(1/4))) - 1/4*sqrt(2)*log(sqrt(2)*cos(2*x)^(1/4) + sqrt(cos(2*x)) + 1) + 1/4*sqrt(2)*log(-sqrt(2)*cos(2*x)^(1/4) + sqrt(cos(2*x)) + 1) - 1/5*cos(2*x)^(5/4) + 7/4*cos(2*x)^(1/4)","A",0
456,1,85,0,0.773977," ","integrate((tan(x)*tan(2*x))^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} {\left({\left(\sqrt{2} \log\left(\sqrt{2} + \sqrt{-\tan\left(x\right)^{2} + 1}\right) - \sqrt{2} \log\left(\sqrt{2} - \sqrt{-\tan\left(x\right)^{2} + 1}\right)\right)} \mathrm{sgn}\left(\tan\left(x\right)^{2} - 1\right) \mathrm{sgn}\left(\tan\left(x\right)\right) + {\left(\sqrt{2} \log\left(\sqrt{2} + 1\right) - \sqrt{2} \log\left(\sqrt{2} - 1\right)\right)} \mathrm{sgn}\left(\tan\left(x\right)\right)\right)}"," ",0,"1/4*sqrt(2)*((sqrt(2)*log(sqrt(2) + sqrt(-tan(x)^2 + 1)) - sqrt(2)*log(sqrt(2) - sqrt(-tan(x)^2 + 1)))*sgn(tan(x)^2 - 1)*sgn(tan(x)) + (sqrt(2)*log(sqrt(2) + 1) - sqrt(2)*log(sqrt(2) - 1))*sgn(tan(x)))","B",0
457,1,138,0,0.834234," ","integrate((cot(2*x)/cot(x))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\pi - \sqrt{2} \arctan\left(-i\right) - \sqrt{2} \arctan\left(\sqrt{2}\right) - i \, \log\left(2 \, \sqrt{2} + 3\right)\right)} \mathrm{sgn}\left(\sin\left(2 \, x\right)\right) - \frac{\sqrt{2} {\left(-i \, \sqrt{2} \log\left(2 i \, \sqrt{2} + 3 i\right) - 2 \, \arctan\left(-i\right)\right)} \mathrm{sgn}\left(\cos\left(x\right)\right) + 2 \, {\left(\sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} {\left(\frac{3 \, {\left(2 \, \sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1} - 1\right)}}{4 \, \cos\left(x\right)^{2} - 3} - 1\right)}\right) + \arcsin\left(4 \, \cos\left(x\right)^{2} - 3\right)\right)} \mathrm{sgn}\left(\cos\left(x\right)\right)}{4 \, \mathrm{sgn}\left(\cos\left(x\right)\right) \mathrm{sgn}\left(\sin\left(2 \, x\right)\right)}"," ",0,"1/2*(pi - sqrt(2)*arctan(-I) - sqrt(2)*arctan(sqrt(2)) - I*log(2*sqrt(2) + 3))*sgn(sin(2*x)) - 1/4*(sqrt(2)*(-I*sqrt(2)*log(2*I*sqrt(2) + 3*I) - 2*arctan(-I))*sgn(cos(x)) + 2*(sqrt(2)*arctan(1/4*sqrt(2)*(3*(2*sqrt(2)*sqrt(-2*cos(x)^4 + 3*cos(x)^2 - 1) - 1)/(4*cos(x)^2 - 3) - 1)) + arcsin(4*cos(x)^2 - 3))*sgn(cos(x)))/(sgn(cos(x))*sgn(sin(2*x)))","C",0
458,1,32,0,0.591281," ","integrate(1/x^5/(x^2+5),x, algorithm=""giac"")","-\frac{3 \, x^{4} - 10 \, x^{2} + 25}{500 \, x^{4}} - \frac{1}{250} \, \log\left(x^{2} + 5\right) + \frac{1}{250} \, \log\left(x^{2}\right)"," ",0,"-1/500*(3*x^4 - 10*x^2 + 25)/x^4 - 1/250*log(x^2 + 5) + 1/250*log(x^2)","A",0
459,1,30,0,0.576275," ","integrate(1/x^6/(x^2+5),x, algorithm=""giac"")","-\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
460,1,42,0,0.610101," ","integrate(1/x/(x^2-4)^4,x, algorithm=""giac"")","\frac{11 \, x^{6} - 156 \, x^{4} + 768 \, x^{2} - 1408}{3072 \, {\left(x^{2} - 4\right)}^{3}} + \frac{1}{512} \, \log\left(x^{2}\right) - \frac{1}{512} \, \log\left({\left| x^{2} - 4 \right|}\right)"," ",0,"1/3072*(11*x^6 - 156*x^4 + 768*x^2 - 1408)/(x^2 - 4)^3 + 1/512*log(x^2) - 1/512*log(abs(x^2 - 4))","A",0
461,1,35,0,0.613954," ","integrate(1/x/(x^2-2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{x^{2} - 2}\right) + \frac{3 \, x^{2} - 8}{12 \, {\left(x^{2} - 2\right)}^{\frac{3}{2}}}"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(x^2 - 2)) + 1/12*(3*x^2 - 8)/(x^2 - 2)^(3/2)","A",0
462,1,46,0,0.626691," ","integrate((x^2-10)^(5/2)/x,x, algorithm=""giac"")","\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} \arctan\left(\frac{1}{10} \, \sqrt{10} \sqrt{x^{2} - 10}\right) + 100 \, \sqrt{x^{2} - 10}"," ",0,"1/5*(x^2 - 10)^(5/2) - 10/3*(x^2 - 10)^(3/2) - 100*sqrt(10)*arctan(1/10*sqrt(10)*sqrt(x^2 - 10)) + 100*sqrt(x^2 - 10)","A",0
463,1,14,0,0.583103," ","integrate(x^(1+2*n),x, algorithm=""giac"")","\frac{x^{2 \, n + 2}}{2 \, {\left(n + 1\right)}}"," ",0,"1/2*x^(2*n + 2)/(n + 1)","A",0
464,1,36,0,0.603539," ","integrate(x^7/(x^2-5)^3,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - \frac{5 \, {\left(9 \, x^{4} - 60 \, x^{2} + 100\right)}}{4 \, {\left(x^{2} - 5\right)}^{2}} + \frac{15}{2} \, \log\left({\left| x^{2} - 5 \right|}\right)"," ",0,"1/2*x^2 - 5/4*(9*x^4 - 60*x^2 + 100)/(x^2 - 5)^2 + 15/2*log(abs(x^2 - 5))","A",0
465,1,21,0,0.584178," ","integrate((3*x^5-4*x^3)/(x^2-1)^5,x, algorithm=""giac"")","-\frac{18 \, x^{4} - 28 \, x^{2} + 7}{24 \, {\left(x^{2} - 1\right)}^{4}}"," ",0,"-1/24*(18*x^4 - 28*x^2 + 7)/(x^2 - 1)^4","A",0
466,1,19,0,0.604115," ","integrate(x^3*(x^2+1)^(9/14),x, algorithm=""giac"")","\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
467,1,26,0,0.606830," ","integrate(x^5/(x^2-4)^(13/6),x, algorithm=""giac"")","\frac{3}{5} \, {\left(x^{2} - 4\right)}^{\frac{5}{6}} - \frac{24 \, {\left(7 \, x^{2} - 26\right)}}{7 \, {\left(x^{2} - 4\right)}^{\frac{7}{6}}}"," ",0,"3/5*(x^2 - 4)^(5/6) - 24/7*(7*x^2 - 26)/(x^2 - 4)^(7/6)","A",0
468,1,19,0,0.625930," ","integrate(1/(2*x^2+1)^(5/2),x, algorithm=""giac"")","\frac{{\left(4 \, x^{2} + 3\right)} x}{3 \, {\left(2 \, x^{2} + 1\right)}^{\frac{3}{2}}}"," ",0,"1/3*(4*x^2 + 3)*x/(2*x^2 + 1)^(3/2)","A",0
469,1,21,0,0.661847," ","integrate(1/(x^2-2*x-1)^(5/2),x, algorithm=""giac"")","\frac{{\left(x - 3\right)} x^{2} + 2}{6 \, {\left(x^{2} - 2 \, x - 1\right)}^{\frac{3}{2}}}"," ",0,"1/6*((x - 3)*x^2 + 2)/(x^2 - 2*x - 1)^(3/2)","A",0
470,1,62,0,0.653393," ","integrate(1/x^4/(x^2-8)^(3/2),x, algorithm=""giac"")","-\frac{x}{512 \, \sqrt{x^{2} - 8}} - \frac{3 \, {\left(x - \sqrt{x^{2} - 8}\right)}^{4} + 96 \, {\left(x - \sqrt{x^{2} - 8}\right)}^{2} + 320}{96 \, {\left({\left(x - \sqrt{x^{2} - 8}\right)}^{2} + 8\right)}^{3}}"," ",0,"-1/512*x/sqrt(x^2 - 8) - 1/96*(3*(x - sqrt(x^2 - 8))^4 + 96*(x - sqrt(x^2 - 8))^2 + 320)/((x - sqrt(x^2 - 8))^2 + 8)^3","A",0
471,1,16,0,0.626740," ","integrate((x^2+5)^2/x^(13/3),x, algorithm=""giac"")","\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
472,1,58,0,0.617552," ","integrate(1/x^7/(x^2+1)^3,x, algorithm=""giac"")","-\frac{30 \, x^{4} + 68 \, x^{2} + 39}{4 \, {\left(x^{2} + 1\right)}^{2}} + \frac{110 \, x^{6} - 36 \, x^{4} + 9 \, x^{2} - 2}{12 \, x^{6}} + 5 \, \log\left(x^{2} + 1\right) - 5 \, \log\left(x^{2}\right)"," ",0,"-1/4*(30*x^4 + 68*x^2 + 39)/(x^2 + 1)^2 + 1/12*(110*x^6 - 36*x^4 + 9*x^2 - 2)/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=""giac"")","\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
474,1,98,0,0.798288," ","integrate(x^4/(-x^2+10^(1/2))^(9/2),x, algorithm=""giac"")","-\frac{16 \, {\left(7 \, {\left(\frac{x}{\sqrt{-x^{2} + \sqrt{10}} - 10^{\frac{1}{4}}} - \frac{\sqrt{-x^{2} + \sqrt{10}} - 10^{\frac{1}{4}}}{x}\right)}^{2} + 20\right)}}{175 \, {\left(\frac{x}{\sqrt{-x^{2} + \sqrt{10}} - 10^{\frac{1}{4}}} - \frac{\sqrt{-x^{2} + \sqrt{10}} - 10^{\frac{1}{4}}}{x}\right)}^{7}}"," ",0,"-16/175*(7*(x/(sqrt(-x^2 + sqrt(10)) - 10^(1/4)) - (sqrt(-x^2 + sqrt(10)) - 10^(1/4))/x)^2 + 20)/(x/(sqrt(-x^2 + sqrt(10)) - 10^(1/4)) - (sqrt(-x^2 + sqrt(10)) - 10^(1/4))/x)^7","B",0
475,1,29,0,0.655273," ","integrate(x^2/(-x^2+3)^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} + 3} x}{x^{2} - 3} - \arcsin\left(\frac{1}{3} \, \sqrt{3} x\right)"," ",0,"-sqrt(-x^2 + 3)*x/(x^2 - 3) - arcsin(1/3*sqrt(3)*x)","A",0
476,1,77,0,0.659019," ","integrate((-x^2+25)^(3/2)/x^4,x, algorithm=""giac"")","-\frac{x^{3} {\left(\frac{15 \, {\left(\sqrt{-x^{2} + 25} - 5\right)}^{2}}{x^{2}} - 1\right)}}{24 \, {\left(\sqrt{-x^{2} + 25} - 5\right)}^{3}} + \frac{5 \, {\left(\sqrt{-x^{2} + 25} - 5\right)}}{8 \, x} - \frac{{\left(\sqrt{-x^{2} + 25} - 5\right)}^{3}}{24 \, x^{3}} + \arcsin\left(\frac{1}{5} \, x\right)"," ",0,"-1/24*x^3*(15*(sqrt(-x^2 + 25) - 5)^2/x^2 - 1)/(sqrt(-x^2 + 25) - 5)^3 + 5/8*(sqrt(-x^2 + 25) - 5)/x - 1/24*(sqrt(-x^2 + 25) - 5)^3/x^3 + arcsin(1/5*x)","B",0
477,1,35,0,0.661221," ","integrate(1/(-2*x^2+1)^(7/2),x, algorithm=""giac"")","-\frac{{\left(8 \, {\left(4 \, x^{2} - 5\right)} x^{2} + 15\right)} \sqrt{-2 \, x^{2} + 1} x}{15 \, {\left(2 \, x^{2} - 1\right)}^{3}}"," ",0,"-1/15*(8*(4*x^2 - 5)*x^2 + 15)*sqrt(-2*x^2 + 1)*x/(2*x^2 - 1)^3","A",0
478,1,35,0,0.651669," ","integrate(1/(-x^2+6*x-7)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left({\left(x - 9\right)} x + 24\right)} x - 18\right)} \sqrt{-x^{2} + 6 \, x - 7}}{6 \, {\left(x^{2} - 6 \, x + 7\right)}^{2}}"," ",0,"-1/6*(((x - 9)*x + 24)*x - 18)*sqrt(-x^2 + 6*x - 7)/(x^2 - 6*x + 7)^2","A",0
479,1,32,0,0.610864," ","integrate((-2*x^2-2*x+1)^3,x, algorithm=""giac"")","-\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
480,1,29,0,0.583299," ","integrate((-1+5*x)*(x^2-x-1)^2,x, algorithm=""giac"")","\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
481,1,27,0,0.699620," ","integrate((1+3*x)/(2*x^2-8*x+1)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(4 \, {\left(x - 6\right)} x + 27\right)} x - 1}{42 \, {\left(2 \, x^{2} - 8 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"1/42*(2*(4*(x - 6)*x + 27)*x - 1)/(2*x^2 - 8*x + 1)^(3/2)","A",0
482,1,41,0,0.657159," ","integrate((8*x^3-8*x-1)/(-4*x^2+2*x+1)^(5/2),x, algorithm=""giac"")","\frac{{\left(4 \, {\left(2 \, {\left(61 \, x - 27\right)} x - 39\right)} x - 27\right)} \sqrt{-4 \, x^{2} + 2 \, x + 1}}{75 \, {\left(4 \, x^{2} - 2 \, x - 1\right)}^{2}}"," ",0,"1/75*(4*(2*(61*x - 27)*x - 39)*x - 27)*sqrt(-4*x^2 + 2*x + 1)/(4*x^2 - 2*x - 1)^2","A",0
483,1,55,0,0.584862," ","integrate(x^2*cos(x)^5,x, algorithm=""giac"")","\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
484,1,49,0,0.613895," ","integrate(x^3*sin(x)^3,x, algorithm=""giac"")","\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
485,1,66,0,0.591641," ","integrate(x^2*sin(x)^6,x, algorithm=""giac"")","\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
486,1,35,0,0.619064," ","integrate(x^2*cos(x)*sin(x)^2,x, algorithm=""giac"")","-\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
487,1,206,0,0.704450," ","integrate(x*cos(x)^4/sin(x)^2,x, algorithm=""giac"")","-\frac{6 \, x^{2} \tan\left(\frac{1}{2} \, x\right)^{5} - 4 \, x \tan\left(\frac{1}{2} \, x\right)^{6} - 4 \, \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, x\right)^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{5} + 12 \, x^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 12 \, x \tan\left(\frac{1}{2} \, x\right)^{4} + \tan\left(\frac{1}{2} \, x\right)^{5} - 8 \, \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, x\right)^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, x^{2} \tan\left(\frac{1}{2} \, x\right) + 12 \, x \tan\left(\frac{1}{2} \, x\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, x\right)^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right) + 4 \, x + \tan\left(\frac{1}{2} \, x\right)}{8 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{5} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)\right)}}"," ",0,"-1/8*(6*x^2*tan(1/2*x)^5 - 4*x*tan(1/2*x)^6 - 4*log(16*tan(1/2*x)^2/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^5 + 12*x^2*tan(1/2*x)^3 - 12*x*tan(1/2*x)^4 + tan(1/2*x)^5 - 8*log(16*tan(1/2*x)^2/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^3 + 6*x^2*tan(1/2*x) + 12*x*tan(1/2*x)^2 - 6*tan(1/2*x)^3 - 4*log(16*tan(1/2*x)^2/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x) + 4*x + tan(1/2*x))/(tan(1/2*x)^5 + 2*tan(1/2*x)^3 + tan(1/2*x))","B",0
488,1,341,0,1.216283," ","integrate(x*sin(x)^3/cos(x)^4,x, algorithm=""giac"")","\frac{8 \, x \tan\left(\frac{1}{2} \, x\right)^{6} + 5 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{6} - 5 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{6} - 24 \, x \tan\left(\frac{1}{2} \, x\right)^{4} - 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, \tan\left(\frac{1}{2} \, x\right)^{5} - 24 \, x \tan\left(\frac{1}{2} \, x\right)^{2} + 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} - 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 8 \, x - 5 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 5 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 4 \, \tan\left(\frac{1}{2} \, x\right)}{12 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{6} - 3 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}}"," ",0,"1/12*(8*x*tan(1/2*x)^6 + 5*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6 - 5*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6 - 24*x*tan(1/2*x)^4 - 15*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4 + 15*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4 - 4*tan(1/2*x)^5 - 24*x*tan(1/2*x)^2 + 15*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - 15*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 8*x - 5*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) + 5*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) + 4*tan(1/2*x))/(tan(1/2*x)^6 - 3*tan(1/2*x)^4 + 3*tan(1/2*x)^2 - 1)","B",0
489,1,53,0,0.596806," ","integrate(x*sin(x)/cos(x)^3,x, algorithm=""giac"")","\frac{x \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, x \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + x - 2 \, \tan\left(\frac{1}{2} \, x\right)}{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}"," ",0,"1/2*(x*tan(1/2*x)^4 + 2*x*tan(1/2*x)^2 + 2*tan(1/2*x)^3 + x - 2*tan(1/2*x))/(tan(1/2*x)^4 - 2*tan(1/2*x)^2 + 1)","B",0
490,0,0,0,0.000000," ","integrate(x*sin(x)^3/cos(x),x, algorithm=""giac"")","\int \frac{x \sin\left(x\right)^{3}}{\cos\left(x\right)}\,{d x}"," ",0,"integrate(x*sin(x)^3/cos(x), x)","F",0
491,0,0,0,0.000000," ","integrate(x*sin(x)^3/cos(x)^3,x, algorithm=""giac"")","\int \frac{x \sin\left(x\right)^{3}}{\cos\left(x\right)^{3}}\,{d x}"," ",0,"integrate(x*sin(x)^3/cos(x)^3, x)","F",0
492,1,10,0,0.625102," ","integrate((2*x+sin(2*x))/(cos(x)+x*sin(x))^2,x, algorithm=""giac"")","-\frac{2}{x \tan\left(x\right) + 1}"," ",0,"-2/(x*tan(x) + 1)","A",0
493,1,39,0,0.627966," ","integrate(x^2/(x*cos(x)-sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, x \tan\left(\frac{1}{2} \, x\right) - \tan\left(\frac{1}{2} \, x\right)^{2} + 1}{x \tan\left(\frac{1}{2} \, x\right)^{2} - x + 2 \, \tan\left(\frac{1}{2} \, x\right)}"," ",0,"-(2*x*tan(1/2*x) - tan(1/2*x)^2 + 1)/(x*tan(1/2*x)^2 - x + 2*tan(1/2*x))","A",0
494,1,325,0,0.680887," ","integrate(a^(m*x)*b^(n*x),x, algorithm=""giac"")","2 \, {\left(\frac{2 \, {\left(m \log\left({\left| a \right|}\right) + n \log\left({\left| b \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi m x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi n x \mathrm{sgn}\left(b\right) + \frac{1}{2} \, \pi m x + \frac{1}{2} \, \pi n x\right)}{{\left(\pi m \mathrm{sgn}\left(a\right) + \pi n \mathrm{sgn}\left(b\right) - \pi m - \pi n\right)}^{2} + 4 \, {\left(m \log\left({\left| a \right|}\right) + n \log\left({\left| b \right|}\right)\right)}^{2}} - \frac{{\left(\pi m \mathrm{sgn}\left(a\right) + \pi n \mathrm{sgn}\left(b\right) - \pi m - \pi n\right)} \sin\left(-\frac{1}{2} \, \pi m x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi n x \mathrm{sgn}\left(b\right) + \frac{1}{2} \, \pi m x + \frac{1}{2} \, \pi n x\right)}{{\left(\pi m \mathrm{sgn}\left(a\right) + \pi n \mathrm{sgn}\left(b\right) - \pi m - \pi n\right)}^{2} + 4 \, {\left(m \log\left({\left| a \right|}\right) + n \log\left({\left| b \right|}\right)\right)}^{2}}\right)} e^{\left({\left(m \log\left({\left| a \right|}\right) + n \log\left({\left| b \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{2 i \, e^{\left(\frac{1}{2} i \, \pi m x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi n x \mathrm{sgn}\left(b\right) - \frac{1}{2} i \, \pi m x - \frac{1}{2} i \, \pi n x\right)}}{i \, \pi m \mathrm{sgn}\left(a\right) + i \, \pi n \mathrm{sgn}\left(b\right) - i \, \pi m - i \, \pi n + 2 \, m \log\left({\left| a \right|}\right) + 2 \, n \log\left({\left| b \right|}\right)} + \frac{2 i \, e^{\left(-\frac{1}{2} i \, \pi m x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi n x \mathrm{sgn}\left(b\right) + \frac{1}{2} i \, \pi m x + \frac{1}{2} i \, \pi n x\right)}}{-i \, \pi m \mathrm{sgn}\left(a\right) - i \, \pi n \mathrm{sgn}\left(b\right) + i \, \pi m + i \, \pi n + 2 \, m \log\left({\left| a \right|}\right) + 2 \, n \log\left({\left| b \right|}\right)}\right)} e^{\left({\left(m \log\left({\left| a \right|}\right) + n \log\left({\left| b \right|}\right)\right)} x\right)}"," ",0,"2*(2*(m*log(abs(a)) + n*log(abs(b)))*cos(-1/2*pi*m*x*sgn(a) - 1/2*pi*n*x*sgn(b) + 1/2*pi*m*x + 1/2*pi*n*x)/((pi*m*sgn(a) + pi*n*sgn(b) - pi*m - pi*n)^2 + 4*(m*log(abs(a)) + n*log(abs(b)))^2) - (pi*m*sgn(a) + pi*n*sgn(b) - pi*m - pi*n)*sin(-1/2*pi*m*x*sgn(a) - 1/2*pi*n*x*sgn(b) + 1/2*pi*m*x + 1/2*pi*n*x)/((pi*m*sgn(a) + pi*n*sgn(b) - pi*m - pi*n)^2 + 4*(m*log(abs(a)) + n*log(abs(b)))^2))*e^((m*log(abs(a)) + n*log(abs(b)))*x) - 1/2*I*(-2*I*e^(1/2*I*pi*m*x*sgn(a) + 1/2*I*pi*n*x*sgn(b) - 1/2*I*pi*m*x - 1/2*I*pi*n*x)/(I*pi*m*sgn(a) + I*pi*n*sgn(b) - I*pi*m - I*pi*n + 2*m*log(abs(a)) + 2*n*log(abs(b))) + 2*I*e^(-1/2*I*pi*m*x*sgn(a) - 1/2*I*pi*n*x*sgn(b) + 1/2*I*pi*m*x + 1/2*I*pi*n*x)/(-I*pi*m*sgn(a) - I*pi*n*sgn(b) + I*pi*m + I*pi*n + 2*m*log(abs(a)) + 2*n*log(abs(b))))*e^((m*log(abs(a)) + n*log(abs(b)))*x)","C",0
495,1,436,0,0.936733," ","integrate((a^x-b^x)^2/(a^x)/(b^x),x, algorithm=""giac"")","2 \, {\left(\frac{2 \, {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi x \mathrm{sgn}\left(b\right)\right)}{{\left(\pi \mathrm{sgn}\left(a\right) - \pi \mathrm{sgn}\left(b\right)\right)}^{2} + 4 \, {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}^{2}} - \frac{{\left(\pi \mathrm{sgn}\left(a\right) - \pi \mathrm{sgn}\left(b\right)\right)} \sin\left(-\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi x \mathrm{sgn}\left(b\right)\right)}{{\left(\pi \mathrm{sgn}\left(a\right) - \pi \mathrm{sgn}\left(b\right)\right)}^{2} + 4 \, {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}^{2}}\right)} e^{\left(x {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}\right)} - \frac{1}{2} i \, {\left(-\frac{2 i \, e^{\left(\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi x \mathrm{sgn}\left(b\right)\right)}}{i \, \pi \mathrm{sgn}\left(a\right) - i \, \pi \mathrm{sgn}\left(b\right) + 2 \, \log\left({\left| a \right|}\right) - 2 \, \log\left({\left| b \right|}\right)} + \frac{2 i \, e^{\left(-\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi x \mathrm{sgn}\left(b\right)\right)}}{-i \, \pi \mathrm{sgn}\left(a\right) + i \, \pi \mathrm{sgn}\left(b\right) + 2 \, \log\left({\left| a \right|}\right) - 2 \, \log\left({\left| b \right|}\right)}\right)} e^{\left(x {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}\right)} - 2 \, {\left(\frac{2 \, {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)} \cos\left(\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi x \mathrm{sgn}\left(b\right)\right)}{{\left(\pi \mathrm{sgn}\left(a\right) - \pi \mathrm{sgn}\left(b\right)\right)}^{2} + 4 \, {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}^{2}} - \frac{{\left(\pi \mathrm{sgn}\left(a\right) - \pi \mathrm{sgn}\left(b\right)\right)} \sin\left(\frac{1}{2} \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi x \mathrm{sgn}\left(b\right)\right)}{{\left(\pi \mathrm{sgn}\left(a\right) - \pi \mathrm{sgn}\left(b\right)\right)}^{2} + 4 \, {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}^{2}}\right)} e^{\left(-x {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}\right)} - \frac{1}{2} i \, {\left(\frac{2 i \, e^{\left(\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi x \mathrm{sgn}\left(b\right)\right)}}{i \, \pi \mathrm{sgn}\left(a\right) - i \, \pi \mathrm{sgn}\left(b\right) - 2 \, \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| b \right|}\right)} - \frac{2 i \, e^{\left(-\frac{1}{2} i \, \pi x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi x \mathrm{sgn}\left(b\right)\right)}}{-i \, \pi \mathrm{sgn}\left(a\right) + i \, \pi \mathrm{sgn}\left(b\right) - 2 \, \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| b \right|}\right)}\right)} e^{\left(-x {\left(\log\left({\left| a \right|}\right) - \log\left({\left| b \right|}\right)\right)}\right)} - 2 \, x"," ",0,"2*(2*(log(abs(a)) - log(abs(b)))*cos(-1/2*pi*x*sgn(a) + 1/2*pi*x*sgn(b))/((pi*sgn(a) - pi*sgn(b))^2 + 4*(log(abs(a)) - log(abs(b)))^2) - (pi*sgn(a) - pi*sgn(b))*sin(-1/2*pi*x*sgn(a) + 1/2*pi*x*sgn(b))/((pi*sgn(a) - pi*sgn(b))^2 + 4*(log(abs(a)) - log(abs(b)))^2))*e^(x*(log(abs(a)) - log(abs(b)))) - 1/2*I*(-2*I*e^(1/2*I*pi*x*sgn(a) - 1/2*I*pi*x*sgn(b))/(I*pi*sgn(a) - I*pi*sgn(b) + 2*log(abs(a)) - 2*log(abs(b))) + 2*I*e^(-1/2*I*pi*x*sgn(a) + 1/2*I*pi*x*sgn(b))/(-I*pi*sgn(a) + I*pi*sgn(b) + 2*log(abs(a)) - 2*log(abs(b))))*e^(x*(log(abs(a)) - log(abs(b)))) - 2*(2*(log(abs(a)) - log(abs(b)))*cos(1/2*pi*x*sgn(a) - 1/2*pi*x*sgn(b))/((pi*sgn(a) - pi*sgn(b))^2 + 4*(log(abs(a)) - log(abs(b)))^2) - (pi*sgn(a) - pi*sgn(b))*sin(1/2*pi*x*sgn(a) - 1/2*pi*x*sgn(b))/((pi*sgn(a) - pi*sgn(b))^2 + 4*(log(abs(a)) - log(abs(b)))^2))*e^(-x*(log(abs(a)) - log(abs(b)))) - 1/2*I*(2*I*e^(1/2*I*pi*x*sgn(a) - 1/2*I*pi*x*sgn(b))/(I*pi*sgn(a) - I*pi*sgn(b) - 2*log(abs(a)) + 2*log(abs(b))) - 2*I*e^(-1/2*I*pi*x*sgn(a) + 1/2*I*pi*x*sgn(b))/(-I*pi*sgn(a) + I*pi*sgn(b) - 2*log(abs(a)) + 2*log(abs(b))))*e^(-x*(log(abs(a)) - log(abs(b)))) - 2*x","C",0
496,1,7,0,0.600787," ","integrate(-1/exp(x)+exp(x),x, algorithm=""giac"")","e^{\left(-x\right)} + e^{x}"," ",0,"e^(-x) + e^x","A",0
497,1,24,0,0.580363," ","integrate((-1/exp(x)+exp(x))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, e^{\left(2 \, x\right)} - 1\right)} e^{\left(-2 \, x\right)} - 2 \, x + \frac{1}{2} \, e^{\left(2 \, x\right)}"," ",0,"1/2*(2*e^(2*x) - 1)*e^(-2*x) - 2*x + 1/2*e^(2*x)","A",0
498,1,25,0,0.618381," ","integrate((-1/exp(x)+exp(x))^3,x, algorithm=""giac"")","-\frac{1}{3} \, {\left(9 \, e^{\left(2 \, x\right)} - 1\right)} e^{\left(-3 \, x\right)} + \frac{1}{3} \, e^{\left(3 \, x\right)} - 3 \, e^{x}"," ",0,"-1/3*(9*e^(2*x) - 1)*e^(-3*x) + 1/3*e^(3*x) - 3*e^x","A",0
499,1,36,0,0.588501," ","integrate((-1/exp(x)+exp(x))^4,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(18 \, e^{\left(4 \, x\right)} - 8 \, e^{\left(2 \, x\right)} + 1\right)} e^{\left(-4 \, x\right)} + 6 \, x + \frac{1}{4} \, e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)}"," ",0,"-1/4*(18*e^(4*x) - 8*e^(2*x) + 1)*e^(-4*x) + 6*x + 1/4*e^(4*x) - 2*e^(2*x)","A",0
500,0,0,0,0.000000," ","integrate((-1/exp(x)+exp(x))^n,x, algorithm=""giac"")","\int {\left(-e^{\left(-x\right)} + e^{x}\right)}^{n}\,{d x}"," ",0,"integrate((-e^(-x) + e^x)^n, x)","F",0
501,1,46,0,0.601164," ","integrate((1/(a^(4*x))-a^(2*x))^3,x, algorithm=""giac"")","-\frac{2 \, a^{6 \, x} + \frac{9 \, a^{12 \, x} - 6 \, a^{6 \, x} + 1}{a^{12 \, x}} - 6 \, \log\left(a^{6 \, x}\right)}{12 \, \log\left(a\right)}"," ",0,"-1/12*(2*a^(6*x) + (9*a^(12*x) - 6*a^(6*x) + 1)/a^(12*x) - 6*log(a^(6*x)))/log(a)","A",0
502,1,27,0,0.628781," ","integrate(a^(k*x)+a^(l*x),x, algorithm=""giac"")","\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
503,1,691,0,0.733927," ","integrate((a^(k*x)+a^(l*x))^2,x, algorithm=""giac"")","{\left(\frac{2 \, k \cos\left(-\pi k x \mathrm{sgn}\left(a\right) + \pi k x\right) \log\left({\left| a \right|}\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)} \sin\left(-\pi k x \mathrm{sgn}\left(a\right) + \pi k x\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}}\right)} {\left| a \right|}^{2 \, k x} + {\left(\frac{2 \, l \cos\left(-\pi l x \mathrm{sgn}\left(a\right) + \pi l x\right) \log\left({\left| a \right|}\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}} - \frac{{\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)} \sin\left(-\pi l x \mathrm{sgn}\left(a\right) + \pi l x\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}}\right)} {\left| a \right|}^{2 \, l x} - \frac{1}{2} i \, {\left| a \right|}^{2 \, k x} {\left(-\frac{i \, e^{\left(i \, \pi k x \mathrm{sgn}\left(a\right) - i \, \pi k x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi k + 2 \, k \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-i \, \pi k x \mathrm{sgn}\left(a\right) + i \, \pi k x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi k + 2 \, k \log\left({\left| a \right|}\right)}\right)} - \frac{1}{2} i \, {\left| a \right|}^{2 \, l x} {\left(-\frac{i \, e^{\left(i \, \pi l x \mathrm{sgn}\left(a\right) - i \, \pi l x\right)}}{i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi l + 2 \, l \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-i \, \pi l x \mathrm{sgn}\left(a\right) + i \, \pi l x\right)}}{-i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi l + 2 \, l \log\left({\left| a \right|}\right)}\right)} + 4 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)} \sin\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{4 i \, e^{\left(\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi k x - \frac{1}{2} i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} + \frac{4 i \, e^{\left(-\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi k x + \frac{1}{2} i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)}"," ",0,"(2*k*cos(-pi*k*x*sgn(a) + pi*k*x)*log(abs(a))/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2) - (pi*k*sgn(a) - pi*k)*sin(-pi*k*x*sgn(a) + pi*k*x)/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2))*abs(a)^(2*k*x) + (2*l*cos(-pi*l*x*sgn(a) + pi*l*x)*log(abs(a))/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2) - (pi*l*sgn(a) - pi*l)*sin(-pi*l*x*sgn(a) + pi*l*x)/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2))*abs(a)^(2*l*x) - 1/2*I*abs(a)^(2*k*x)*(-I*e^(I*pi*k*x*sgn(a) - I*pi*k*x)/(I*pi*k*sgn(a) - I*pi*k + 2*k*log(abs(a))) + I*e^(-I*pi*k*x*sgn(a) + I*pi*k*x)/(-I*pi*k*sgn(a) + I*pi*k + 2*k*log(abs(a)))) - 1/2*I*abs(a)^(2*l*x)*(-I*e^(I*pi*l*x*sgn(a) - I*pi*l*x)/(I*pi*l*sgn(a) - I*pi*l + 2*l*log(abs(a))) + I*e^(-I*pi*l*x*sgn(a) + I*pi*l*x)/(-I*pi*l*sgn(a) + I*pi*l + 2*l*log(abs(a)))) + 4*(2*(k*log(abs(a)) + l*log(abs(a)))*cos(-1/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 1/2*pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2) - (pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)*sin(-1/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 1/2*pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2))*e^((k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(-4*I*e^(1/2*I*pi*k*x*sgn(a) + 1/2*I*pi*l*x*sgn(a) - 1/2*I*pi*k*x - 1/2*I*pi*l*x)/(I*pi*k*sgn(a) + I*pi*l*sgn(a) - I*pi*k - I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))) + 4*I*e^(-1/2*I*pi*k*x*sgn(a) - 1/2*I*pi*l*x*sgn(a) + 1/2*I*pi*k*x + 1/2*I*pi*l*x)/(-I*pi*k*sgn(a) - I*pi*l*sgn(a) + I*pi*k + I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))))*e^((k*log(abs(a)) + l*log(abs(a)))*x)","C",0
504,1,1033,0,0.820602," ","integrate((a^(k*x)+a^(l*x))^3,x, algorithm=""giac"")","\frac{2}{3} \, {\left(\frac{2 \, k \cos\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x\right) \log\left({\left| a \right|}\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)} \sin\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}}\right)} {\left| a \right|}^{3 \, k x} + \frac{2}{3} \, {\left(\frac{2 \, l \cos\left(-\frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi l x\right) \log\left({\left| a \right|}\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}} - \frac{{\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)} \sin\left(-\frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi l x\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}}\right)} {\left| a \right|}^{3 \, l x} - \frac{1}{2} i \, {\left| a \right|}^{3 \, k x} {\left(-\frac{2 i \, e^{\left(\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi k x\right)}}{3 i \, \pi k \mathrm{sgn}\left(a\right) - 3 i \, \pi k + 6 \, k \log\left({\left| a \right|}\right)} + \frac{2 i \, e^{\left(-\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi k x\right)}}{-3 i \, \pi k \mathrm{sgn}\left(a\right) + 3 i \, \pi k + 6 \, k \log\left({\left| a \right|}\right)}\right)} - \frac{1}{2} i \, {\left| a \right|}^{3 \, l x} {\left(-\frac{2 i \, e^{\left(\frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi l x\right)}}{3 i \, \pi l \mathrm{sgn}\left(a\right) - 3 i \, \pi l + 6 \, l \log\left({\left| a \right|}\right)} + \frac{2 i \, e^{\left(-\frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi l x\right)}}{-3 i \, \pi l \mathrm{sgn}\left(a\right) + 3 i \, \pi l + 6 \, l \log\left({\left| a \right|}\right)}\right)} + 6 \, {\left(\frac{2 \, {\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(2 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 2 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(2 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 2 \, \pi k - \pi l\right)} \sin\left(-\pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(2 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 2 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{6 i \, e^{\left(i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - i \, \pi k x - \frac{1}{2} i \, \pi l x\right)}}{2 i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - 2 i \, \pi k - i \, \pi l + 4 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} + \frac{6 i \, e^{\left(-i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + i \, \pi k x + \frac{1}{2} i \, \pi l x\right)}}{-2 i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + 2 i \, \pi k + i \, \pi l + 4 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} + 6 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 2 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 2 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + 2 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 2 \, \pi l\right)} \sin\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 2 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 2 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{6 i \, e^{\left(\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi k x - i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + 2 i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - 2 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 4 \, l \log\left({\left| a \right|}\right)} + \frac{6 i \, e^{\left(-\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi k x + i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - 2 i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + 2 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 4 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)} x\right)}"," ",0,"2/3*(2*k*cos(-3/2*pi*k*x*sgn(a) + 3/2*pi*k*x)*log(abs(a))/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2) - (pi*k*sgn(a) - pi*k)*sin(-3/2*pi*k*x*sgn(a) + 3/2*pi*k*x)/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2))*abs(a)^(3*k*x) + 2/3*(2*l*cos(-3/2*pi*l*x*sgn(a) + 3/2*pi*l*x)*log(abs(a))/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2) - (pi*l*sgn(a) - pi*l)*sin(-3/2*pi*l*x*sgn(a) + 3/2*pi*l*x)/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2))*abs(a)^(3*l*x) - 1/2*I*abs(a)^(3*k*x)*(-2*I*e^(3/2*I*pi*k*x*sgn(a) - 3/2*I*pi*k*x)/(3*I*pi*k*sgn(a) - 3*I*pi*k + 6*k*log(abs(a))) + 2*I*e^(-3/2*I*pi*k*x*sgn(a) + 3/2*I*pi*k*x)/(-3*I*pi*k*sgn(a) + 3*I*pi*k + 6*k*log(abs(a)))) - 1/2*I*abs(a)^(3*l*x)*(-2*I*e^(3/2*I*pi*l*x*sgn(a) - 3/2*I*pi*l*x)/(3*I*pi*l*sgn(a) - 3*I*pi*l + 6*l*log(abs(a))) + 2*I*e^(-3/2*I*pi*l*x*sgn(a) + 3/2*I*pi*l*x)/(-3*I*pi*l*sgn(a) + 3*I*pi*l + 6*l*log(abs(a)))) + 6*(2*(2*k*log(abs(a)) + l*log(abs(a)))*cos(-pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + pi*k*x + 1/2*pi*l*x)/((2*pi*k*sgn(a) + pi*l*sgn(a) - 2*pi*k - pi*l)^2 + 4*(2*k*log(abs(a)) + l*log(abs(a)))^2) - (2*pi*k*sgn(a) + pi*l*sgn(a) - 2*pi*k - pi*l)*sin(-pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + pi*k*x + 1/2*pi*l*x)/((2*pi*k*sgn(a) + pi*l*sgn(a) - 2*pi*k - pi*l)^2 + 4*(2*k*log(abs(a)) + l*log(abs(a)))^2))*e^((2*k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(-6*I*e^(I*pi*k*x*sgn(a) + 1/2*I*pi*l*x*sgn(a) - I*pi*k*x - 1/2*I*pi*l*x)/(2*I*pi*k*sgn(a) + I*pi*l*sgn(a) - 2*I*pi*k - I*pi*l + 4*k*log(abs(a)) + 2*l*log(abs(a))) + 6*I*e^(-I*pi*k*x*sgn(a) - 1/2*I*pi*l*x*sgn(a) + I*pi*k*x + 1/2*I*pi*l*x)/(-2*I*pi*k*sgn(a) - I*pi*l*sgn(a) + 2*I*pi*k + I*pi*l + 4*k*log(abs(a)) + 2*l*log(abs(a))))*e^((2*k*log(abs(a)) + l*log(abs(a)))*x) + 6*(2*(k*log(abs(a)) + 2*l*log(abs(a)))*cos(-1/2*pi*k*x*sgn(a) - pi*l*x*sgn(a) + 1/2*pi*k*x + pi*l*x)/((pi*k*sgn(a) + 2*pi*l*sgn(a) - pi*k - 2*pi*l)^2 + 4*(k*log(abs(a)) + 2*l*log(abs(a)))^2) - (pi*k*sgn(a) + 2*pi*l*sgn(a) - pi*k - 2*pi*l)*sin(-1/2*pi*k*x*sgn(a) - pi*l*x*sgn(a) + 1/2*pi*k*x + pi*l*x)/((pi*k*sgn(a) + 2*pi*l*sgn(a) - pi*k - 2*pi*l)^2 + 4*(k*log(abs(a)) + 2*l*log(abs(a)))^2))*e^((k*log(abs(a)) + 2*l*log(abs(a)))*x) - 1/2*I*(-6*I*e^(1/2*I*pi*k*x*sgn(a) + I*pi*l*x*sgn(a) - 1/2*I*pi*k*x - I*pi*l*x)/(I*pi*k*sgn(a) + 2*I*pi*l*sgn(a) - I*pi*k - 2*I*pi*l + 2*k*log(abs(a)) + 4*l*log(abs(a))) + 6*I*e^(-1/2*I*pi*k*x*sgn(a) - I*pi*l*x*sgn(a) + 1/2*I*pi*k*x + I*pi*l*x)/(-I*pi*k*sgn(a) - 2*I*pi*l*sgn(a) + I*pi*k + 2*I*pi*l + 2*k*log(abs(a)) + 4*l*log(abs(a))))*e^((k*log(abs(a)) + 2*l*log(abs(a)))*x)","C",0
505,1,1359,0,0.935021," ","integrate((a^(k*x)+a^(l*x))^4,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, k \cos\left(-2 \, \pi k x \mathrm{sgn}\left(a\right) + 2 \, \pi k x\right) \log\left({\left| a \right|}\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)} \sin\left(-2 \, \pi k x \mathrm{sgn}\left(a\right) + 2 \, \pi k x\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}}\right)} {\left| a \right|}^{4 \, k x} + \frac{1}{2} \, {\left(\frac{2 \, l \cos\left(-2 \, \pi l x \mathrm{sgn}\left(a\right) + 2 \, \pi l x\right) \log\left({\left| a \right|}\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}} - \frac{{\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)} \sin\left(-2 \, \pi l x \mathrm{sgn}\left(a\right) + 2 \, \pi l x\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}}\right)} {\left| a \right|}^{4 \, l x} - \frac{1}{2} i \, {\left| a \right|}^{4 \, k x} {\left(-\frac{i \, e^{\left(2 i \, \pi k x \mathrm{sgn}\left(a\right) - 2 i \, \pi k x\right)}}{2 i \, \pi k \mathrm{sgn}\left(a\right) - 2 i \, \pi k + 4 \, k \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-2 i \, \pi k x \mathrm{sgn}\left(a\right) + 2 i \, \pi k x\right)}}{-2 i \, \pi k \mathrm{sgn}\left(a\right) + 2 i \, \pi k + 4 \, k \log\left({\left| a \right|}\right)}\right)} - \frac{1}{2} i \, {\left| a \right|}^{4 \, l x} {\left(-\frac{i \, e^{\left(2 i \, \pi l x \mathrm{sgn}\left(a\right) - 2 i \, \pi l x\right)}}{2 i \, \pi l \mathrm{sgn}\left(a\right) - 2 i \, \pi l + 4 \, l \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-2 i \, \pi l x \mathrm{sgn}\left(a\right) + 2 i \, \pi l x\right)}}{-2 i \, \pi l \mathrm{sgn}\left(a\right) + 2 i \, \pi l + 4 \, l \log\left({\left| a \right|}\right)}\right)} + 8 \, {\left(\frac{2 \, {\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(3 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 3 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(3 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 3 \, \pi k - \pi l\right)} \sin\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(3 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 3 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{8 i \, e^{\left(\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi k x - \frac{1}{2} i \, \pi l x\right)}}{3 i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - 3 i \, \pi k - i \, \pi l + 6 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} + \frac{8 i \, e^{\left(-\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi k x + \frac{1}{2} i \, \pi l x\right)}}{-3 i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + 3 i \, \pi k + i \, \pi l + 6 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} + 8 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{3}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 3 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 3 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + 3 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 3 \, \pi l\right)} \sin\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{3}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 3 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 3 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{8 i \, e^{\left(\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi k x - \frac{3}{2} i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + 3 i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - 3 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 6 \, l \log\left({\left| a \right|}\right)} + \frac{8 i \, e^{\left(-\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi k x + \frac{3}{2} i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - 3 i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + 3 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 6 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)} x\right)} + 6 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)} \sin\left(-\pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left(2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{6 i \, e^{\left(i \, \pi k x \mathrm{sgn}\left(a\right) + i \, \pi l x \mathrm{sgn}\left(a\right) - i \, \pi k x - i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} + \frac{6 i \, e^{\left(-i \, \pi k x \mathrm{sgn}\left(a\right) - i \, \pi l x \mathrm{sgn}\left(a\right) + i \, \pi k x + i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left(2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)}"," ",0,"1/2*(2*k*cos(-2*pi*k*x*sgn(a) + 2*pi*k*x)*log(abs(a))/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2) - (pi*k*sgn(a) - pi*k)*sin(-2*pi*k*x*sgn(a) + 2*pi*k*x)/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2))*abs(a)^(4*k*x) + 1/2*(2*l*cos(-2*pi*l*x*sgn(a) + 2*pi*l*x)*log(abs(a))/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2) - (pi*l*sgn(a) - pi*l)*sin(-2*pi*l*x*sgn(a) + 2*pi*l*x)/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2))*abs(a)^(4*l*x) - 1/2*I*abs(a)^(4*k*x)*(-I*e^(2*I*pi*k*x*sgn(a) - 2*I*pi*k*x)/(2*I*pi*k*sgn(a) - 2*I*pi*k + 4*k*log(abs(a))) + I*e^(-2*I*pi*k*x*sgn(a) + 2*I*pi*k*x)/(-2*I*pi*k*sgn(a) + 2*I*pi*k + 4*k*log(abs(a)))) - 1/2*I*abs(a)^(4*l*x)*(-I*e^(2*I*pi*l*x*sgn(a) - 2*I*pi*l*x)/(2*I*pi*l*sgn(a) - 2*I*pi*l + 4*l*log(abs(a))) + I*e^(-2*I*pi*l*x*sgn(a) + 2*I*pi*l*x)/(-2*I*pi*l*sgn(a) + 2*I*pi*l + 4*l*log(abs(a)))) + 8*(2*(3*k*log(abs(a)) + l*log(abs(a)))*cos(-3/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 3/2*pi*k*x + 1/2*pi*l*x)/((3*pi*k*sgn(a) + pi*l*sgn(a) - 3*pi*k - pi*l)^2 + 4*(3*k*log(abs(a)) + l*log(abs(a)))^2) - (3*pi*k*sgn(a) + pi*l*sgn(a) - 3*pi*k - pi*l)*sin(-3/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 3/2*pi*k*x + 1/2*pi*l*x)/((3*pi*k*sgn(a) + pi*l*sgn(a) - 3*pi*k - pi*l)^2 + 4*(3*k*log(abs(a)) + l*log(abs(a)))^2))*e^((3*k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(-8*I*e^(3/2*I*pi*k*x*sgn(a) + 1/2*I*pi*l*x*sgn(a) - 3/2*I*pi*k*x - 1/2*I*pi*l*x)/(3*I*pi*k*sgn(a) + I*pi*l*sgn(a) - 3*I*pi*k - I*pi*l + 6*k*log(abs(a)) + 2*l*log(abs(a))) + 8*I*e^(-3/2*I*pi*k*x*sgn(a) - 1/2*I*pi*l*x*sgn(a) + 3/2*I*pi*k*x + 1/2*I*pi*l*x)/(-3*I*pi*k*sgn(a) - I*pi*l*sgn(a) + 3*I*pi*k + I*pi*l + 6*k*log(abs(a)) + 2*l*log(abs(a))))*e^((3*k*log(abs(a)) + l*log(abs(a)))*x) + 8*(2*(k*log(abs(a)) + 3*l*log(abs(a)))*cos(-1/2*pi*k*x*sgn(a) - 3/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 3/2*pi*l*x)/((pi*k*sgn(a) + 3*pi*l*sgn(a) - pi*k - 3*pi*l)^2 + 4*(k*log(abs(a)) + 3*l*log(abs(a)))^2) - (pi*k*sgn(a) + 3*pi*l*sgn(a) - pi*k - 3*pi*l)*sin(-1/2*pi*k*x*sgn(a) - 3/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 3/2*pi*l*x)/((pi*k*sgn(a) + 3*pi*l*sgn(a) - pi*k - 3*pi*l)^2 + 4*(k*log(abs(a)) + 3*l*log(abs(a)))^2))*e^((k*log(abs(a)) + 3*l*log(abs(a)))*x) - 1/2*I*(-8*I*e^(1/2*I*pi*k*x*sgn(a) + 3/2*I*pi*l*x*sgn(a) - 1/2*I*pi*k*x - 3/2*I*pi*l*x)/(I*pi*k*sgn(a) + 3*I*pi*l*sgn(a) - I*pi*k - 3*I*pi*l + 2*k*log(abs(a)) + 6*l*log(abs(a))) + 8*I*e^(-1/2*I*pi*k*x*sgn(a) - 3/2*I*pi*l*x*sgn(a) + 1/2*I*pi*k*x + 3/2*I*pi*l*x)/(-I*pi*k*sgn(a) - 3*I*pi*l*sgn(a) + I*pi*k + 3*I*pi*l + 2*k*log(abs(a)) + 6*l*log(abs(a))))*e^((k*log(abs(a)) + 3*l*log(abs(a)))*x) + 6*(2*(k*log(abs(a)) + l*log(abs(a)))*cos(-pi*k*x*sgn(a) - pi*l*x*sgn(a) + pi*k*x + pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2) - (pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)*sin(-pi*k*x*sgn(a) - pi*l*x*sgn(a) + pi*k*x + pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2))*e^(2*(k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(-6*I*e^(I*pi*k*x*sgn(a) + I*pi*l*x*sgn(a) - I*pi*k*x - I*pi*l*x)/(I*pi*k*sgn(a) + I*pi*l*sgn(a) - I*pi*k - I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))) + 6*I*e^(-I*pi*k*x*sgn(a) - I*pi*l*x*sgn(a) + I*pi*k*x + I*pi*l*x)/(-I*pi*k*sgn(a) - I*pi*l*sgn(a) + I*pi*k + I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))))*e^(2*(k*log(abs(a)) + l*log(abs(a)))*x)","C",0
506,0,0,0,0.000000," ","integrate((a^(k*x)+a^(l*x))^n,x, algorithm=""giac"")","\int {\left(a^{k x} + a^{l x}\right)}^{n}\,{d x}"," ",0,"integrate((a^(k*x) + a^(l*x))^n, x)","F",0
507,1,28,0,0.584010," ","integrate(a^(k*x)-a^(l*x),x, algorithm=""giac"")","\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
508,1,691,0,0.751383," ","integrate((a^(k*x)-a^(l*x))^2,x, algorithm=""giac"")","{\left(\frac{2 \, k \cos\left(-\pi k x \mathrm{sgn}\left(a\right) + \pi k x\right) \log\left({\left| a \right|}\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)} \sin\left(-\pi k x \mathrm{sgn}\left(a\right) + \pi k x\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}}\right)} {\left| a \right|}^{2 \, k x} + {\left(\frac{2 \, l \cos\left(-\pi l x \mathrm{sgn}\left(a\right) + \pi l x\right) \log\left({\left| a \right|}\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}} - \frac{{\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)} \sin\left(-\pi l x \mathrm{sgn}\left(a\right) + \pi l x\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}}\right)} {\left| a \right|}^{2 \, l x} - \frac{1}{2} i \, {\left| a \right|}^{2 \, k x} {\left(-\frac{i \, e^{\left(i \, \pi k x \mathrm{sgn}\left(a\right) - i \, \pi k x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi k + 2 \, k \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-i \, \pi k x \mathrm{sgn}\left(a\right) + i \, \pi k x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi k + 2 \, k \log\left({\left| a \right|}\right)}\right)} - \frac{1}{2} i \, {\left| a \right|}^{2 \, l x} {\left(-\frac{i \, e^{\left(i \, \pi l x \mathrm{sgn}\left(a\right) - i \, \pi l x\right)}}{i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi l + 2 \, l \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-i \, \pi l x \mathrm{sgn}\left(a\right) + i \, \pi l x\right)}}{-i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi l + 2 \, l \log\left({\left| a \right|}\right)}\right)} - 4 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)} \sin\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(\frac{4 i \, e^{\left(\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi k x - \frac{1}{2} i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} - \frac{4 i \, e^{\left(-\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi k x + \frac{1}{2} i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)}"," ",0,"(2*k*cos(-pi*k*x*sgn(a) + pi*k*x)*log(abs(a))/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2) - (pi*k*sgn(a) - pi*k)*sin(-pi*k*x*sgn(a) + pi*k*x)/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2))*abs(a)^(2*k*x) + (2*l*cos(-pi*l*x*sgn(a) + pi*l*x)*log(abs(a))/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2) - (pi*l*sgn(a) - pi*l)*sin(-pi*l*x*sgn(a) + pi*l*x)/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2))*abs(a)^(2*l*x) - 1/2*I*abs(a)^(2*k*x)*(-I*e^(I*pi*k*x*sgn(a) - I*pi*k*x)/(I*pi*k*sgn(a) - I*pi*k + 2*k*log(abs(a))) + I*e^(-I*pi*k*x*sgn(a) + I*pi*k*x)/(-I*pi*k*sgn(a) + I*pi*k + 2*k*log(abs(a)))) - 1/2*I*abs(a)^(2*l*x)*(-I*e^(I*pi*l*x*sgn(a) - I*pi*l*x)/(I*pi*l*sgn(a) - I*pi*l + 2*l*log(abs(a))) + I*e^(-I*pi*l*x*sgn(a) + I*pi*l*x)/(-I*pi*l*sgn(a) + I*pi*l + 2*l*log(abs(a)))) - 4*(2*(k*log(abs(a)) + l*log(abs(a)))*cos(-1/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 1/2*pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2) - (pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)*sin(-1/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 1/2*pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2))*e^((k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(4*I*e^(1/2*I*pi*k*x*sgn(a) + 1/2*I*pi*l*x*sgn(a) - 1/2*I*pi*k*x - 1/2*I*pi*l*x)/(I*pi*k*sgn(a) + I*pi*l*sgn(a) - I*pi*k - I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))) - 4*I*e^(-1/2*I*pi*k*x*sgn(a) - 1/2*I*pi*l*x*sgn(a) + 1/2*I*pi*k*x + 1/2*I*pi*l*x)/(-I*pi*k*sgn(a) - I*pi*l*sgn(a) + I*pi*k + I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))))*e^((k*log(abs(a)) + l*log(abs(a)))*x)","C",0
509,1,1033,0,1.281807," ","integrate((a^(k*x)-a^(l*x))^3,x, algorithm=""giac"")","\frac{2}{3} \, {\left(\frac{2 \, k \cos\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x\right) \log\left({\left| a \right|}\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)} \sin\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}}\right)} {\left| a \right|}^{3 \, k x} - \frac{2}{3} \, {\left(\frac{2 \, l \cos\left(-\frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi l x\right) \log\left({\left| a \right|}\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}} - \frac{{\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)} \sin\left(-\frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi l x\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}}\right)} {\left| a \right|}^{3 \, l x} - \frac{1}{2} i \, {\left| a \right|}^{3 \, k x} {\left(-\frac{2 i \, e^{\left(\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi k x\right)}}{3 i \, \pi k \mathrm{sgn}\left(a\right) - 3 i \, \pi k + 6 \, k \log\left({\left| a \right|}\right)} + \frac{2 i \, e^{\left(-\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi k x\right)}}{-3 i \, \pi k \mathrm{sgn}\left(a\right) + 3 i \, \pi k + 6 \, k \log\left({\left| a \right|}\right)}\right)} - \frac{1}{2} i \, {\left| a \right|}^{3 \, l x} {\left(\frac{2 i \, e^{\left(\frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi l x\right)}}{3 i \, \pi l \mathrm{sgn}\left(a\right) - 3 i \, \pi l + 6 \, l \log\left({\left| a \right|}\right)} - \frac{2 i \, e^{\left(-\frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi l x\right)}}{-3 i \, \pi l \mathrm{sgn}\left(a\right) + 3 i \, \pi l + 6 \, l \log\left({\left| a \right|}\right)}\right)} - 6 \, {\left(\frac{2 \, {\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(2 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 2 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(2 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 2 \, \pi k - \pi l\right)} \sin\left(-\pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(2 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 2 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(\frac{6 i \, e^{\left(i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - i \, \pi k x - \frac{1}{2} i \, \pi l x\right)}}{2 i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - 2 i \, \pi k - i \, \pi l + 4 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} - \frac{6 i \, e^{\left(-i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + i \, \pi k x + \frac{1}{2} i \, \pi l x\right)}}{-2 i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + 2 i \, \pi k + i \, \pi l + 4 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(2 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} + 6 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 2 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 2 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + 2 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 2 \, \pi l\right)} \sin\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 2 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 2 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{6 i \, e^{\left(\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi k x - i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + 2 i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - 2 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 4 \, l \log\left({\left| a \right|}\right)} + \frac{6 i \, e^{\left(-\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi k x + i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - 2 i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + 2 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 4 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)\right)} x\right)}"," ",0,"2/3*(2*k*cos(-3/2*pi*k*x*sgn(a) + 3/2*pi*k*x)*log(abs(a))/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2) - (pi*k*sgn(a) - pi*k)*sin(-3/2*pi*k*x*sgn(a) + 3/2*pi*k*x)/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2))*abs(a)^(3*k*x) - 2/3*(2*l*cos(-3/2*pi*l*x*sgn(a) + 3/2*pi*l*x)*log(abs(a))/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2) - (pi*l*sgn(a) - pi*l)*sin(-3/2*pi*l*x*sgn(a) + 3/2*pi*l*x)/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2))*abs(a)^(3*l*x) - 1/2*I*abs(a)^(3*k*x)*(-2*I*e^(3/2*I*pi*k*x*sgn(a) - 3/2*I*pi*k*x)/(3*I*pi*k*sgn(a) - 3*I*pi*k + 6*k*log(abs(a))) + 2*I*e^(-3/2*I*pi*k*x*sgn(a) + 3/2*I*pi*k*x)/(-3*I*pi*k*sgn(a) + 3*I*pi*k + 6*k*log(abs(a)))) - 1/2*I*abs(a)^(3*l*x)*(2*I*e^(3/2*I*pi*l*x*sgn(a) - 3/2*I*pi*l*x)/(3*I*pi*l*sgn(a) - 3*I*pi*l + 6*l*log(abs(a))) - 2*I*e^(-3/2*I*pi*l*x*sgn(a) + 3/2*I*pi*l*x)/(-3*I*pi*l*sgn(a) + 3*I*pi*l + 6*l*log(abs(a)))) - 6*(2*(2*k*log(abs(a)) + l*log(abs(a)))*cos(-pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + pi*k*x + 1/2*pi*l*x)/((2*pi*k*sgn(a) + pi*l*sgn(a) - 2*pi*k - pi*l)^2 + 4*(2*k*log(abs(a)) + l*log(abs(a)))^2) - (2*pi*k*sgn(a) + pi*l*sgn(a) - 2*pi*k - pi*l)*sin(-pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + pi*k*x + 1/2*pi*l*x)/((2*pi*k*sgn(a) + pi*l*sgn(a) - 2*pi*k - pi*l)^2 + 4*(2*k*log(abs(a)) + l*log(abs(a)))^2))*e^((2*k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(6*I*e^(I*pi*k*x*sgn(a) + 1/2*I*pi*l*x*sgn(a) - I*pi*k*x - 1/2*I*pi*l*x)/(2*I*pi*k*sgn(a) + I*pi*l*sgn(a) - 2*I*pi*k - I*pi*l + 4*k*log(abs(a)) + 2*l*log(abs(a))) - 6*I*e^(-I*pi*k*x*sgn(a) - 1/2*I*pi*l*x*sgn(a) + I*pi*k*x + 1/2*I*pi*l*x)/(-2*I*pi*k*sgn(a) - I*pi*l*sgn(a) + 2*I*pi*k + I*pi*l + 4*k*log(abs(a)) + 2*l*log(abs(a))))*e^((2*k*log(abs(a)) + l*log(abs(a)))*x) + 6*(2*(k*log(abs(a)) + 2*l*log(abs(a)))*cos(-1/2*pi*k*x*sgn(a) - pi*l*x*sgn(a) + 1/2*pi*k*x + pi*l*x)/((pi*k*sgn(a) + 2*pi*l*sgn(a) - pi*k - 2*pi*l)^2 + 4*(k*log(abs(a)) + 2*l*log(abs(a)))^2) - (pi*k*sgn(a) + 2*pi*l*sgn(a) - pi*k - 2*pi*l)*sin(-1/2*pi*k*x*sgn(a) - pi*l*x*sgn(a) + 1/2*pi*k*x + pi*l*x)/((pi*k*sgn(a) + 2*pi*l*sgn(a) - pi*k - 2*pi*l)^2 + 4*(k*log(abs(a)) + 2*l*log(abs(a)))^2))*e^((k*log(abs(a)) + 2*l*log(abs(a)))*x) - 1/2*I*(-6*I*e^(1/2*I*pi*k*x*sgn(a) + I*pi*l*x*sgn(a) - 1/2*I*pi*k*x - I*pi*l*x)/(I*pi*k*sgn(a) + 2*I*pi*l*sgn(a) - I*pi*k - 2*I*pi*l + 2*k*log(abs(a)) + 4*l*log(abs(a))) + 6*I*e^(-1/2*I*pi*k*x*sgn(a) - I*pi*l*x*sgn(a) + 1/2*I*pi*k*x + I*pi*l*x)/(-I*pi*k*sgn(a) - 2*I*pi*l*sgn(a) + I*pi*k + 2*I*pi*l + 2*k*log(abs(a)) + 4*l*log(abs(a))))*e^((k*log(abs(a)) + 2*l*log(abs(a)))*x)","C",0
510,1,1359,0,1.212764," ","integrate((a^(k*x)-a^(l*x))^4,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, k \cos\left(-2 \, \pi k x \mathrm{sgn}\left(a\right) + 2 \, \pi k x\right) \log\left({\left| a \right|}\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)} \sin\left(-2 \, \pi k x \mathrm{sgn}\left(a\right) + 2 \, \pi k x\right)}{4 \, k^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi k \mathrm{sgn}\left(a\right) - \pi k\right)}^{2}}\right)} {\left| a \right|}^{4 \, k x} + \frac{1}{2} \, {\left(\frac{2 \, l \cos\left(-2 \, \pi l x \mathrm{sgn}\left(a\right) + 2 \, \pi l x\right) \log\left({\left| a \right|}\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}} - \frac{{\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)} \sin\left(-2 \, \pi l x \mathrm{sgn}\left(a\right) + 2 \, \pi l x\right)}{4 \, l^{2} \log\left({\left| a \right|}\right)^{2} + {\left(\pi l \mathrm{sgn}\left(a\right) - \pi l\right)}^{2}}\right)} {\left| a \right|}^{4 \, l x} - \frac{1}{2} i \, {\left| a \right|}^{4 \, k x} {\left(-\frac{i \, e^{\left(2 i \, \pi k x \mathrm{sgn}\left(a\right) - 2 i \, \pi k x\right)}}{2 i \, \pi k \mathrm{sgn}\left(a\right) - 2 i \, \pi k + 4 \, k \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-2 i \, \pi k x \mathrm{sgn}\left(a\right) + 2 i \, \pi k x\right)}}{-2 i \, \pi k \mathrm{sgn}\left(a\right) + 2 i \, \pi k + 4 \, k \log\left({\left| a \right|}\right)}\right)} - \frac{1}{2} i \, {\left| a \right|}^{4 \, l x} {\left(-\frac{i \, e^{\left(2 i \, \pi l x \mathrm{sgn}\left(a\right) - 2 i \, \pi l x\right)}}{2 i \, \pi l \mathrm{sgn}\left(a\right) - 2 i \, \pi l + 4 \, l \log\left({\left| a \right|}\right)} + \frac{i \, e^{\left(-2 i \, \pi l x \mathrm{sgn}\left(a\right) + 2 i \, \pi l x\right)}}{-2 i \, \pi l \mathrm{sgn}\left(a\right) + 2 i \, \pi l + 4 \, l \log\left({\left| a \right|}\right)}\right)} - 8 \, {\left(\frac{2 \, {\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(3 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 3 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(3 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 3 \, \pi k - \pi l\right)} \sin\left(-\frac{3}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi k x + \frac{1}{2} \, \pi l x\right)}{{\left(3 \, \pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - 3 \, \pi k - \pi l\right)}^{2} + 4 \, {\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(\frac{8 i \, e^{\left(\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi k x - \frac{1}{2} i \, \pi l x\right)}}{3 i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - 3 i \, \pi k - i \, \pi l + 6 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} - \frac{8 i \, e^{\left(-\frac{3}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi k x + \frac{1}{2} i \, \pi l x\right)}}{-3 i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + 3 i \, \pi k + i \, \pi l + 6 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(3 \, k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - 8 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)} \cos\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{3}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 3 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 3 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + 3 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 3 \, \pi l\right)} \sin\left(-\frac{1}{2} \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} \, \pi k x + \frac{3}{2} \, \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + 3 \, \pi l \mathrm{sgn}\left(a\right) - \pi k - 3 \, \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(\frac{8 i \, e^{\left(\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) - \frac{1}{2} i \, \pi k x - \frac{3}{2} i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + 3 i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - 3 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 6 \, l \log\left({\left| a \right|}\right)} - \frac{8 i \, e^{\left(-\frac{1}{2} i \, \pi k x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi l x \mathrm{sgn}\left(a\right) + \frac{1}{2} i \, \pi k x + \frac{3}{2} i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - 3 i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + 3 i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 6 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left({\left(k \log\left({\left| a \right|}\right) + 3 \, l \log\left({\left| a \right|}\right)\right)} x\right)} + 6 \, {\left(\frac{2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} \cos\left(-\pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}} - \frac{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)} \sin\left(-\pi k x \mathrm{sgn}\left(a\right) - \pi l x \mathrm{sgn}\left(a\right) + \pi k x + \pi l x\right)}{{\left(\pi k \mathrm{sgn}\left(a\right) + \pi l \mathrm{sgn}\left(a\right) - \pi k - \pi l\right)}^{2} + 4 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)}^{2}}\right)} e^{\left(2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)} - \frac{1}{2} i \, {\left(-\frac{6 i \, e^{\left(i \, \pi k x \mathrm{sgn}\left(a\right) + i \, \pi l x \mathrm{sgn}\left(a\right) - i \, \pi k x - i \, \pi l x\right)}}{i \, \pi k \mathrm{sgn}\left(a\right) + i \, \pi l \mathrm{sgn}\left(a\right) - i \, \pi k - i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)} + \frac{6 i \, e^{\left(-i \, \pi k x \mathrm{sgn}\left(a\right) - i \, \pi l x \mathrm{sgn}\left(a\right) + i \, \pi k x + i \, \pi l x\right)}}{-i \, \pi k \mathrm{sgn}\left(a\right) - i \, \pi l \mathrm{sgn}\left(a\right) + i \, \pi k + i \, \pi l + 2 \, k \log\left({\left| a \right|}\right) + 2 \, l \log\left({\left| a \right|}\right)}\right)} e^{\left(2 \, {\left(k \log\left({\left| a \right|}\right) + l \log\left({\left| a \right|}\right)\right)} x\right)}"," ",0,"1/2*(2*k*cos(-2*pi*k*x*sgn(a) + 2*pi*k*x)*log(abs(a))/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2) - (pi*k*sgn(a) - pi*k)*sin(-2*pi*k*x*sgn(a) + 2*pi*k*x)/(4*k^2*log(abs(a))^2 + (pi*k*sgn(a) - pi*k)^2))*abs(a)^(4*k*x) + 1/2*(2*l*cos(-2*pi*l*x*sgn(a) + 2*pi*l*x)*log(abs(a))/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2) - (pi*l*sgn(a) - pi*l)*sin(-2*pi*l*x*sgn(a) + 2*pi*l*x)/(4*l^2*log(abs(a))^2 + (pi*l*sgn(a) - pi*l)^2))*abs(a)^(4*l*x) - 1/2*I*abs(a)^(4*k*x)*(-I*e^(2*I*pi*k*x*sgn(a) - 2*I*pi*k*x)/(2*I*pi*k*sgn(a) - 2*I*pi*k + 4*k*log(abs(a))) + I*e^(-2*I*pi*k*x*sgn(a) + 2*I*pi*k*x)/(-2*I*pi*k*sgn(a) + 2*I*pi*k + 4*k*log(abs(a)))) - 1/2*I*abs(a)^(4*l*x)*(-I*e^(2*I*pi*l*x*sgn(a) - 2*I*pi*l*x)/(2*I*pi*l*sgn(a) - 2*I*pi*l + 4*l*log(abs(a))) + I*e^(-2*I*pi*l*x*sgn(a) + 2*I*pi*l*x)/(-2*I*pi*l*sgn(a) + 2*I*pi*l + 4*l*log(abs(a)))) - 8*(2*(3*k*log(abs(a)) + l*log(abs(a)))*cos(-3/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 3/2*pi*k*x + 1/2*pi*l*x)/((3*pi*k*sgn(a) + pi*l*sgn(a) - 3*pi*k - pi*l)^2 + 4*(3*k*log(abs(a)) + l*log(abs(a)))^2) - (3*pi*k*sgn(a) + pi*l*sgn(a) - 3*pi*k - pi*l)*sin(-3/2*pi*k*x*sgn(a) - 1/2*pi*l*x*sgn(a) + 3/2*pi*k*x + 1/2*pi*l*x)/((3*pi*k*sgn(a) + pi*l*sgn(a) - 3*pi*k - pi*l)^2 + 4*(3*k*log(abs(a)) + l*log(abs(a)))^2))*e^((3*k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(8*I*e^(3/2*I*pi*k*x*sgn(a) + 1/2*I*pi*l*x*sgn(a) - 3/2*I*pi*k*x - 1/2*I*pi*l*x)/(3*I*pi*k*sgn(a) + I*pi*l*sgn(a) - 3*I*pi*k - I*pi*l + 6*k*log(abs(a)) + 2*l*log(abs(a))) - 8*I*e^(-3/2*I*pi*k*x*sgn(a) - 1/2*I*pi*l*x*sgn(a) + 3/2*I*pi*k*x + 1/2*I*pi*l*x)/(-3*I*pi*k*sgn(a) - I*pi*l*sgn(a) + 3*I*pi*k + I*pi*l + 6*k*log(abs(a)) + 2*l*log(abs(a))))*e^((3*k*log(abs(a)) + l*log(abs(a)))*x) - 8*(2*(k*log(abs(a)) + 3*l*log(abs(a)))*cos(-1/2*pi*k*x*sgn(a) - 3/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 3/2*pi*l*x)/((pi*k*sgn(a) + 3*pi*l*sgn(a) - pi*k - 3*pi*l)^2 + 4*(k*log(abs(a)) + 3*l*log(abs(a)))^2) - (pi*k*sgn(a) + 3*pi*l*sgn(a) - pi*k - 3*pi*l)*sin(-1/2*pi*k*x*sgn(a) - 3/2*pi*l*x*sgn(a) + 1/2*pi*k*x + 3/2*pi*l*x)/((pi*k*sgn(a) + 3*pi*l*sgn(a) - pi*k - 3*pi*l)^2 + 4*(k*log(abs(a)) + 3*l*log(abs(a)))^2))*e^((k*log(abs(a)) + 3*l*log(abs(a)))*x) - 1/2*I*(8*I*e^(1/2*I*pi*k*x*sgn(a) + 3/2*I*pi*l*x*sgn(a) - 1/2*I*pi*k*x - 3/2*I*pi*l*x)/(I*pi*k*sgn(a) + 3*I*pi*l*sgn(a) - I*pi*k - 3*I*pi*l + 2*k*log(abs(a)) + 6*l*log(abs(a))) - 8*I*e^(-1/2*I*pi*k*x*sgn(a) - 3/2*I*pi*l*x*sgn(a) + 1/2*I*pi*k*x + 3/2*I*pi*l*x)/(-I*pi*k*sgn(a) - 3*I*pi*l*sgn(a) + I*pi*k + 3*I*pi*l + 2*k*log(abs(a)) + 6*l*log(abs(a))))*e^((k*log(abs(a)) + 3*l*log(abs(a)))*x) + 6*(2*(k*log(abs(a)) + l*log(abs(a)))*cos(-pi*k*x*sgn(a) - pi*l*x*sgn(a) + pi*k*x + pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2) - (pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)*sin(-pi*k*x*sgn(a) - pi*l*x*sgn(a) + pi*k*x + pi*l*x)/((pi*k*sgn(a) + pi*l*sgn(a) - pi*k - pi*l)^2 + 4*(k*log(abs(a)) + l*log(abs(a)))^2))*e^(2*(k*log(abs(a)) + l*log(abs(a)))*x) - 1/2*I*(-6*I*e^(I*pi*k*x*sgn(a) + I*pi*l*x*sgn(a) - I*pi*k*x - I*pi*l*x)/(I*pi*k*sgn(a) + I*pi*l*sgn(a) - I*pi*k - I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))) + 6*I*e^(-I*pi*k*x*sgn(a) - I*pi*l*x*sgn(a) + I*pi*k*x + I*pi*l*x)/(-I*pi*k*sgn(a) - I*pi*l*sgn(a) + I*pi*k + I*pi*l + 2*k*log(abs(a)) + 2*l*log(abs(a))))*e^(2*(k*log(abs(a)) + l*log(abs(a)))*x)","C",0
511,0,0,0,0.000000," ","integrate((a^(k*x)-a^(l*x))^n,x, algorithm=""giac"")","\int {\left(a^{k x} - a^{l x}\right)}^{n}\,{d x}"," ",0,"integrate((a^(k*x) - a^(l*x))^n, x)","F",0
512,1,15,0,0.577293," ","integrate(1+a^(m*x),x, algorithm=""giac"")","x + \frac{a^{m x}}{m \log\left(a\right)}"," ",0,"x + a^(m*x)/(m*log(a))","A",0
513,1,30,0,0.582270," ","integrate((1+a^(m*x))^2,x, algorithm=""giac"")","\frac{2 \, m x \log\left({\left| a \right|}\right) + a^{2 \, m x} + 4 \, a^{m x}}{2 \, m \log\left(a\right)}"," ",0,"1/2*(2*m*x*log(abs(a)) + a^(2*m*x) + 4*a^(m*x))/(m*log(a))","A",0
514,1,40,0,0.620409," ","integrate((1+a^(m*x))^3,x, algorithm=""giac"")","\frac{6 \, m x \log\left({\left| a \right|}\right) + 2 \, a^{3 \, m x} + 9 \, a^{2 \, m x} + 18 \, a^{m x}}{6 \, m \log\left(a\right)}"," ",0,"1/6*(6*m*x*log(abs(a)) + 2*a^(3*m*x) + 9*a^(2*m*x) + 18*a^(m*x))/(m*log(a))","A",0
515,1,48,0,0.581615," ","integrate((1+a^(m*x))^4,x, algorithm=""giac"")","\frac{12 \, m x \log\left({\left| a \right|}\right) + 3 \, a^{4 \, m x} + 16 \, a^{3 \, m x} + 36 \, a^{2 \, m x} + 48 \, a^{m x}}{12 \, m \log\left(a\right)}"," ",0,"1/12*(12*m*x*log(abs(a)) + 3*a^(4*m*x) + 16*a^(3*m*x) + 36*a^(2*m*x) + 48*a^(m*x))/(m*log(a))","A",0
516,0,0,0,0.000000," ","integrate((1+a^(m*x))^n,x, algorithm=""giac"")","\int {\left(a^{m x} + 1\right)}^{n}\,{d x}"," ",0,"integrate((a^(m*x) + 1)^n, x)","F",0
517,1,16,0,0.585421," ","integrate(1-a^(m*x),x, algorithm=""giac"")","x - \frac{a^{m x}}{m \log\left(a\right)}"," ",0,"x - a^(m*x)/(m*log(a))","A",0
518,1,30,0,0.605267," ","integrate((1-a^(m*x))^2,x, algorithm=""giac"")","\frac{2 \, m x \log\left({\left| a \right|}\right) + a^{2 \, m x} - 4 \, a^{m x}}{2 \, m \log\left(a\right)}"," ",0,"1/2*(2*m*x*log(abs(a)) + a^(2*m*x) - 4*a^(m*x))/(m*log(a))","A",0
519,1,40,0,0.571712," ","integrate((1-a^(m*x))^3,x, algorithm=""giac"")","\frac{6 \, m x \log\left({\left| a \right|}\right) - 2 \, a^{3 \, m x} + 9 \, a^{2 \, m x} - 18 \, a^{m x}}{6 \, m \log\left(a\right)}"," ",0,"1/6*(6*m*x*log(abs(a)) - 2*a^(3*m*x) + 9*a^(2*m*x) - 18*a^(m*x))/(m*log(a))","A",0
520,1,48,0,0.612833," ","integrate((1-a^(m*x))^4,x, algorithm=""giac"")","\frac{12 \, m x \log\left({\left| a \right|}\right) + 3 \, a^{4 \, m x} - 16 \, a^{3 \, m x} + 36 \, a^{2 \, m x} - 48 \, a^{m x}}{12 \, m \log\left(a\right)}"," ",0,"1/12*(12*m*x*log(abs(a)) + 3*a^(4*m*x) - 16*a^(3*m*x) + 36*a^(2*m*x) - 48*a^(m*x))/(m*log(a))","A",0
521,0,0,0,0.000000," ","integrate((1-a^(m*x))^n,x, algorithm=""giac"")","\int {\left(-a^{m x} + 1\right)}^{n}\,{d x}"," ",0,"integrate((-a^(m*x) + 1)^n, x)","F",0
522,1,26,0,0.577909," ","integrate(1/(b+a*exp(n*x)),x, algorithm=""giac"")","\frac{\frac{n x}{b} - \frac{\log\left({\left| a e^{\left(n x\right)} + b \right|}\right)}{b}}{n}"," ",0,"(n*x/b - log(abs(a*e^(n*x) + b))/b)/n","A",0
523,1,116,0,0.625870," ","integrate(exp(x)/(b+a*exp(3*x)),x, algorithm=""giac"")","-\frac{\left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left({\left| -\left(-\frac{b}{a}\right)^{\frac{1}{3}} + e^{x} \right|}\right)}{3 \, b} + \frac{\sqrt{3} \left(-a^{2} b\right)^{\frac{1}{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 b} + \frac{\left(-a^{2} b\right)^{\frac{1}{3}} \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 b}"," ",0,"-1/3*(-b/a)^(1/3)*log(abs(-(-b/a)^(1/3) + e^x))/b + 1/3*sqrt(3)*(-a^2*b)^(1/3)*arctan(1/3*sqrt(3)*((-b/a)^(1/3) + 2*e^x)/(-b/a)^(1/3))/(a*b) + 1/6*(-a^2*b)^(1/3)*log((-b/a)^(1/3)*e^x + (-b/a)^(2/3) + e^(2*x))/(a*b)","A",0
524,1,11,0,0.573037," ","integrate((-1+exp(x))/(1+exp(x)),x, algorithm=""giac"")","-x + 2 \, \log\left(e^{x} + 1\right)"," ",0,"-x + 2*log(e^x + 1)","A",0
525,1,37,0,0.598692," ","integrate(exp(4*x)/(1-2*exp(2*x)+3*exp(4*x)),x, algorithm=""giac"")","\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
526,1,29,0,0.630122," ","integrate((exp(x)+exp(5*x))/(-1+exp(x)-exp(2*x)+exp(3*x)),x, algorithm=""giac"")","-\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({\left| e^{x} - 1 \right|}\right)"," ",0,"-arctan(e^x) + 1/2*e^(2*x) + e^x - 1/2*log(e^(2*x) + 1) + log(abs(e^x - 1))","A",0
527,1,32,0,0.638616," ","integrate(exp(n*x)*(a+b*exp(n*x))^(r/s),x, algorithm=""giac"")","\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
528,1,57,0,0.592804," ","integrate((1-2*exp(1/3*x))^(1/4),x, algorithm=""giac"")","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| {\left(-2 \, e^{\left(\frac{1}{3} \, x\right)} + 1\right)}^{\frac{1}{4}} - 1 \right|}\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(abs((-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=""giac"")","\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
530,1,18,0,0.582633," ","integrate(exp(x)/(a^2+exp(2*x))^(1/2),x, algorithm=""giac"")","-\log\left(\sqrt{a^{2} + e^{\left(2 \, x\right)}} - e^{x}\right)"," ",0,"-log(sqrt(a^2 + e^(2*x)) - e^x)","A",0
531,1,20,0,0.614777," ","integrate(exp(x)/(-a^2+exp(2*x))^(1/2),x, algorithm=""giac"")","-\log\left(-\sqrt{-a^{2} + e^{\left(2 \, x\right)}} + e^{x}\right)"," ",0,"-log(-sqrt(-a^2 + e^(2*x)) + e^x)","A",0
532,1,48,0,0.818610," ","integrate(exp(3/4*x)/(-2+exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, \log\left({\left| \sqrt{e^{\left(\frac{3}{2} \, x\right)} + e^{\left(\frac{3}{4} \, x\right)} - 2} - e^{\left(\frac{3}{4} \, x\right)} + 4 \right|}\right) + \frac{2}{3} \, \log\left({\left| \sqrt{e^{\left(\frac{3}{2} \, x\right)} + e^{\left(\frac{3}{4} \, x\right)} - 2} - e^{\left(\frac{3}{4} \, x\right)} \right|}\right)"," ",0,"-2/3*log(abs(sqrt(e^(3/2*x) + e^(3/4*x) - 2) - e^(3/4*x) + 4)) + 2/3*log(abs(sqrt(e^(3/2*x) + e^(3/4*x) - 2) - e^(3/4*x)))","A",0
533,0,0,0,0.000000," ","integrate((-3+exp(7*x))^(2/3)/exp(2*x),x, algorithm=""giac"")","\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
534,1,65,0,0.655707," ","integrate(exp(2*x)/(3-exp(1/2*x))^(3/4),x, algorithm=""giac"")","-\frac{8}{13} \, {\left(e^{\left(\frac{1}{2} \, x\right)} - 3\right)}^{3} {\left(-e^{\left(\frac{1}{2} \, x\right)} + 3\right)}^{\frac{1}{4}} - 8 \, {\left(e^{\left(\frac{1}{2} \, x\right)} - 3\right)}^{2} {\left(-e^{\left(\frac{1}{2} \, x\right)} + 3\right)}^{\frac{1}{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)^3*(-e^(1/2*x) + 3)^(1/4) - 8*(e^(1/2*x) - 3)^2*(-e^(1/2*x) + 3)^(1/4) + 216/5*(-e^(1/2*x) + 3)^(5/4) - 216*(-e^(1/2*x) + 3)^(1/4)","A",0
535,1,19,0,0.596379," ","integrate(x^3/exp(1/2*x),x, algorithm=""giac"")","-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
536,1,27,0,0.597785," ","integrate(1/exp(1/2*x)/x^3,x, algorithm=""giac"")","\frac{x^{2} {\rm Ei}\left(-\frac{1}{2} \, x\right) + 2 \, x e^{\left(-\frac{1}{2} \, x\right)} - 4 \, e^{\left(-\frac{1}{2} \, x\right)}}{8 \, x^{2}}"," ",0,"1/8*(x^2*Ei(-1/2*x) + 2*x*e^(-1/2*x) - 4*e^(-1/2*x))/x^2","A",0
537,1,826,0,0.703369," ","integrate(a^(3*x)*x^2,x, algorithm=""giac"")","-\frac{1}{27} \, {\left({\left(\frac{6 \, {\left(3 \, \pi x^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi x^{2} \log\left({\left| a \right|}\right) - \pi x \mathrm{sgn}\left(a\right) + \pi x\right)} {\left(\pi^{3} \mathrm{sgn}\left(a\right) - 3 \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - \pi^{3} + 3 \, \pi \log\left({\left| a \right|}\right)^{2}\right)}}{{\left(\pi^{3} \mathrm{sgn}\left(a\right) - 3 \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - \pi^{3} + 3 \, \pi \log\left({\left| a \right|}\right)^{2}\right)}^{2} + {\left(3 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi^{2} \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| a \right|}\right)^{3}\right)}^{2}} - \frac{{\left(9 \, \pi^{2} x^{2} \mathrm{sgn}\left(a\right) - 9 \, \pi^{2} x^{2} + 18 \, x^{2} \log\left({\left| a \right|}\right)^{2} - 12 \, x \log\left({\left| a \right|}\right) + 4\right)} {\left(3 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi^{2} \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| a \right|}\right)^{3}\right)}}{{\left(\pi^{3} \mathrm{sgn}\left(a\right) - 3 \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - \pi^{3} + 3 \, \pi \log\left({\left| a \right|}\right)^{2}\right)}^{2} + {\left(3 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi^{2} \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| a \right|}\right)^{3}\right)}^{2}}\right)} \cos\left(-\frac{3}{2} \, \pi x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi x\right) - {\left(\frac{{\left(9 \, \pi^{2} x^{2} \mathrm{sgn}\left(a\right) - 9 \, \pi^{2} x^{2} + 18 \, x^{2} \log\left({\left| a \right|}\right)^{2} - 12 \, x \log\left({\left| a \right|}\right) + 4\right)} {\left(\pi^{3} \mathrm{sgn}\left(a\right) - 3 \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - \pi^{3} + 3 \, \pi \log\left({\left| a \right|}\right)^{2}\right)}}{{\left(\pi^{3} \mathrm{sgn}\left(a\right) - 3 \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - \pi^{3} + 3 \, \pi \log\left({\left| a \right|}\right)^{2}\right)}^{2} + {\left(3 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi^{2} \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| a \right|}\right)^{3}\right)}^{2}} + \frac{6 \, {\left(3 \, \pi x^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi x^{2} \log\left({\left| a \right|}\right) - \pi x \mathrm{sgn}\left(a\right) + \pi x\right)} {\left(3 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi^{2} \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| a \right|}\right)^{3}\right)}}{{\left(\pi^{3} \mathrm{sgn}\left(a\right) - 3 \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - \pi^{3} + 3 \, \pi \log\left({\left| a \right|}\right)^{2}\right)}^{2} + {\left(3 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 3 \, \pi^{2} \log\left({\left| a \right|}\right) + 2 \, \log\left({\left| a \right|}\right)^{3}\right)}^{2}}\right)} \sin\left(-\frac{3}{2} \, \pi x \mathrm{sgn}\left(a\right) + \frac{3}{2} \, \pi x\right)\right)} {\left| a \right|}^{3 \, x} + \frac{1}{2} i \, {\left| a \right|}^{3 \, x} {\left(\frac{{\left(36 i \, \pi^{2} x^{2} \mathrm{sgn}\left(a\right) - 72 \, \pi x^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 36 i \, \pi^{2} x^{2} + 72 \, \pi x^{2} \log\left({\left| a \right|}\right) + 72 i \, x^{2} \log\left({\left| a \right|}\right)^{2} + 24 \, \pi x \mathrm{sgn}\left(a\right) - 24 \, \pi x - 48 i \, x \log\left({\left| a \right|}\right) + 16 i\right)} e^{\left(\frac{3}{2} i \, \pi x \mathrm{sgn}\left(a\right) - \frac{3}{2} i \, \pi x\right)}}{-108 i \, \pi^{3} \mathrm{sgn}\left(a\right) + 324 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) + 324 i \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) + 108 i \, \pi^{3} - 324 \, \pi^{2} \log\left({\left| a \right|}\right) - 324 i \, \pi \log\left({\left| a \right|}\right)^{2} + 216 \, \log\left({\left| a \right|}\right)^{3}} - \frac{{\left(36 i \, \pi^{2} x^{2} \mathrm{sgn}\left(a\right) + 72 \, \pi x^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 36 i \, \pi^{2} x^{2} - 72 \, \pi x^{2} \log\left({\left| a \right|}\right) + 72 i \, x^{2} \log\left({\left| a \right|}\right)^{2} - 24 \, \pi x \mathrm{sgn}\left(a\right) + 24 \, \pi x - 48 i \, x \log\left({\left| a \right|}\right) + 16 i\right)} e^{\left(-\frac{3}{2} i \, \pi x \mathrm{sgn}\left(a\right) + \frac{3}{2} i \, \pi x\right)}}{108 i \, \pi^{3} \mathrm{sgn}\left(a\right) + 324 \, \pi^{2} \log\left({\left| a \right|}\right) \mathrm{sgn}\left(a\right) - 324 i \, \pi \log\left({\left| a \right|}\right)^{2} \mathrm{sgn}\left(a\right) - 108 i \, \pi^{3} - 324 \, \pi^{2} \log\left({\left| a \right|}\right) + 324 i \, \pi \log\left({\left| a \right|}\right)^{2} + 216 \, \log\left({\left| a \right|}\right)^{3}}\right)}"," ",0,"-1/27*((6*(3*pi*x^2*log(abs(a))*sgn(a) - 3*pi*x^2*log(abs(a)) - pi*x*sgn(a) + pi*x)*(pi^3*sgn(a) - 3*pi*log(abs(a))^2*sgn(a) - pi^3 + 3*pi*log(abs(a))^2)/((pi^3*sgn(a) - 3*pi*log(abs(a))^2*sgn(a) - pi^3 + 3*pi*log(abs(a))^2)^2 + (3*pi^2*log(abs(a))*sgn(a) - 3*pi^2*log(abs(a)) + 2*log(abs(a))^3)^2) - (9*pi^2*x^2*sgn(a) - 9*pi^2*x^2 + 18*x^2*log(abs(a))^2 - 12*x*log(abs(a)) + 4)*(3*pi^2*log(abs(a))*sgn(a) - 3*pi^2*log(abs(a)) + 2*log(abs(a))^3)/((pi^3*sgn(a) - 3*pi*log(abs(a))^2*sgn(a) - pi^3 + 3*pi*log(abs(a))^2)^2 + (3*pi^2*log(abs(a))*sgn(a) - 3*pi^2*log(abs(a)) + 2*log(abs(a))^3)^2))*cos(-3/2*pi*x*sgn(a) + 3/2*pi*x) - ((9*pi^2*x^2*sgn(a) - 9*pi^2*x^2 + 18*x^2*log(abs(a))^2 - 12*x*log(abs(a)) + 4)*(pi^3*sgn(a) - 3*pi*log(abs(a))^2*sgn(a) - pi^3 + 3*pi*log(abs(a))^2)/((pi^3*sgn(a) - 3*pi*log(abs(a))^2*sgn(a) - pi^3 + 3*pi*log(abs(a))^2)^2 + (3*pi^2*log(abs(a))*sgn(a) - 3*pi^2*log(abs(a)) + 2*log(abs(a))^3)^2) + 6*(3*pi*x^2*log(abs(a))*sgn(a) - 3*pi*x^2*log(abs(a)) - pi*x*sgn(a) + pi*x)*(3*pi^2*log(abs(a))*sgn(a) - 3*pi^2*log(abs(a)) + 2*log(abs(a))^3)/((pi^3*sgn(a) - 3*pi*log(abs(a))^2*sgn(a) - pi^3 + 3*pi*log(abs(a))^2)^2 + (3*pi^2*log(abs(a))*sgn(a) - 3*pi^2*log(abs(a)) + 2*log(abs(a))^3)^2))*sin(-3/2*pi*x*sgn(a) + 3/2*pi*x))*abs(a)^(3*x) + 1/2*I*abs(a)^(3*x)*((36*I*pi^2*x^2*sgn(a) - 72*pi*x^2*log(abs(a))*sgn(a) - 36*I*pi^2*x^2 + 72*pi*x^2*log(abs(a)) + 72*I*x^2*log(abs(a))^2 + 24*pi*x*sgn(a) - 24*pi*x - 48*I*x*log(abs(a)) + 16*I)*e^(3/2*I*pi*x*sgn(a) - 3/2*I*pi*x)/(-108*I*pi^3*sgn(a) + 324*pi^2*log(abs(a))*sgn(a) + 324*I*pi*log(abs(a))^2*sgn(a) + 108*I*pi^3 - 324*pi^2*log(abs(a)) - 324*I*pi*log(abs(a))^2 + 216*log(abs(a))^3) - (36*I*pi^2*x^2*sgn(a) + 72*pi*x^2*log(abs(a))*sgn(a) - 36*I*pi^2*x^2 - 72*pi*x^2*log(abs(a)) + 72*I*x^2*log(abs(a))^2 - 24*pi*x*sgn(a) + 24*pi*x - 48*I*x*log(abs(a)) + 16*I)*e^(-3/2*I*pi*x*sgn(a) + 3/2*I*pi*x)/(108*I*pi^3*sgn(a) + 324*pi^2*log(abs(a))*sgn(a) - 324*I*pi*log(abs(a))^2*sgn(a) - 108*I*pi^3 - 324*pi^2*log(abs(a)) + 324*I*pi*log(abs(a))^2 + 216*log(abs(a))^3))","C",0
538,1,18,0,0.570803," ","integrate(exp(x^2)*x*(x^2+1),x, algorithm=""giac"")","\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
539,1,40,0,0.603603," ","integrate(x/(exp(-x)+exp(x))^2,x, algorithm=""giac"")","\frac{2 \, x e^{\left(2 \, x\right)} - e^{\left(2 \, x\right)} \log\left(e^{\left(2 \, x\right)} + 1\right) - \log\left(e^{\left(2 \, x\right)} + 1\right)}{4 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"1/4*(2*x*e^(2*x) - e^(2*x)*log(e^(2*x) + 1) - log(e^(2*x) + 1))/(e^(2*x) + 1)","A",0
540,0,0,0,0.000000," ","integrate(exp(x)*(-x^2-x+1)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(x^{2} + x - 1\right)} e^{x}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(-(x^2 + x - 1)*e^x/sqrt(-x^2 + 1), x)","F",0
541,1,19,0,0.642881," ","integrate(cos(2*x)/exp(3*x),x, algorithm=""giac"")","-\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
542,1,39,0,0.604028," ","integrate((cos(1/2*x)+sin(1/2*x))/exp(x)^(1/3),x, algorithm=""giac"")","-\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
543,1,39,0,0.629294," ","integrate(cos(3/2*x)/(3^(3*x))^(1/4),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{\cos\left(\frac{3}{2} \, x\right) \log\left(3\right)}{\log\left(3\right)^{2} + 4} - \frac{2 \, \sin\left(\frac{3}{2} \, x\right)}{\log\left(3\right)^{2} + 4}\right)}}{3 \cdot 3^{\frac{3}{4} \, x}}"," ",0,"-4/3*(cos(3/2*x)*log(3)/(log(3)^2 + 4) - 2*sin(3/2*x)/(log(3)^2 + 4))/3^(3/4*x)","A",0
544,1,43,0,0.597492," ","integrate(exp(m*x)*cos(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{m \cos\left(2 \, x\right)}{m^{2} + 4} + \frac{2 \, \sin\left(2 \, x\right)}{m^{2} + 4}\right)} e^{\left(m x\right)} + \frac{e^{\left(m x\right)}}{2 \, m}"," ",0,"1/2*(m*cos(2*x)/(m^2 + 4) + 2*sin(2*x)/(m^2 + 4))*e^(m*x) + 1/2*e^(m*x)/m","A",0
545,1,63,0,0.607954," ","integrate(exp(m*x)*sin(x)^3,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{m \sin\left(3 \, x\right)}{m^{2} + 9} - \frac{3 \, \cos\left(3 \, x\right)}{m^{2} + 9}\right)} e^{\left(m x\right)} + \frac{3}{4} \, {\left(\frac{m \sin\left(x\right)}{m^{2} + 1} - \frac{\cos\left(x\right)}{m^{2} + 1}\right)} e^{\left(m x\right)}"," ",0,"-1/4*(m*sin(3*x)/(m^2 + 9) - 3*cos(3*x)/(m^2 + 9))*e^(m*x) + 3/4*(m*sin(x)/(m^2 + 1) - cos(x)/(m^2 + 1))*e^(m*x)","A",0
546,1,33,0,0.634484," ","integrate(cos(1/3*x)^3/exp(x)^(1/2),x, algorithm=""giac"")","-\frac{9}{26} \, {\left(3 \, \cos\left(\frac{1}{3} \, x\right) - 2 \, \sin\left(\frac{1}{3} \, x\right)\right)} e^{\left(-\frac{1}{2} \, x\right)} - \frac{1}{10} \, {\left(\cos\left(x\right) - 2 \, \sin\left(x\right)\right)} e^{\left(-\frac{1}{2} \, x\right)}"," ",0,"-9/26*(3*cos(1/3*x) - 2*sin(1/3*x))*e^(-1/2*x) - 1/10*(cos(x) - 2*sin(x))*e^(-1/2*x)","A",0
547,1,24,0,0.624410," ","integrate(exp(2*x)*cos(x)^2*sin(x)^2,x, algorithm=""giac"")","-\frac{1}{80} \, {\left(\cos\left(4 \, x\right) + 2 \, \sin\left(4 \, x\right)\right)} e^{\left(2 \, x\right)} + \frac{1}{16} \, e^{\left(2 \, x\right)}"," ",0,"-1/80*(cos(4*x) + 2*sin(4*x))*e^(2*x) + 1/16*e^(2*x)","A",0
548,1,24,0,0.646707," ","integrate(exp(3*x)*cos(3/2*x)^2*sin(3/2*x)^2,x, algorithm=""giac"")","-\frac{1}{120} \, {\left(\cos\left(6 \, x\right) + 2 \, \sin\left(6 \, x\right)\right)} e^{\left(3 \, x\right)} + \frac{1}{24} \, e^{\left(3 \, x\right)}"," ",0,"-1/120*(cos(6*x) + 2*sin(6*x))*e^(3*x) + 1/24*e^(3*x)","A",0
549,0,0,0,0.000000," ","integrate(exp(m*x)*tan(x)^2,x, algorithm=""giac"")","\int e^{\left(m x\right)} \tan\left(x\right)^{2}\,{d x}"," ",0,"integrate(e^(m*x)*tan(x)^2, x)","F",0
550,0,0,0,0.000000," ","integrate(exp(m*x)/sin(x)^2,x, algorithm=""giac"")","\int \frac{e^{\left(m x\right)}}{\sin\left(x\right)^{2}}\,{d x}"," ",0,"integrate(e^(m*x)/sin(x)^2, x)","F",0
551,0,0,0,0.000000," ","integrate(exp(m*x)/cos(x)^3,x, algorithm=""giac"")","\int \frac{e^{\left(m x\right)}}{\cos\left(x\right)^{3}}\,{d x}"," ",0,"integrate(e^(m*x)/cos(x)^3, x)","F",0
552,0,0,0,0.000000," ","integrate(exp(x)/(1+cos(x)),x, algorithm=""giac"")","\int \frac{e^{x}}{\cos\left(x\right) + 1}\,{d x}"," ",0,"integrate(e^x/(cos(x) + 1), x)","F",0
553,0,0,0,0.000000," ","integrate(exp(x)/(1-cos(x)),x, algorithm=""giac"")","\int -\frac{e^{x}}{\cos\left(x\right) - 1}\,{d x}"," ",0,"integrate(-e^x/(cos(x) - 1), x)","F",0
554,0,0,0,0.000000," ","integrate(exp(x)/(1+sin(x)),x, algorithm=""giac"")","\int \frac{e^{x}}{\sin\left(x\right) + 1}\,{d x}"," ",0,"integrate(e^x/(sin(x) + 1), x)","F",0
555,0,0,0,0.000000," ","integrate(exp(x)/(1-sin(x)),x, algorithm=""giac"")","\int -\frac{e^{x}}{\sin\left(x\right) - 1}\,{d x}"," ",0,"integrate(-e^x/(sin(x) - 1), x)","F",0
556,1,10,0,0.642984," ","integrate(exp(x)*(1-sin(x))/(1-cos(x)),x, algorithm=""giac"")","-\frac{e^{x}}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-e^x/tan(1/2*x)","A",0
557,0,0,0,0.000000," ","integrate(exp(x)*(1+sin(x))/(1-cos(x)),x, algorithm=""giac"")","\int -\frac{{\left(\sin\left(x\right) + 1\right)} e^{x}}{\cos\left(x\right) - 1}\,{d x}"," ",0,"integrate(-(sin(x) + 1)*e^x/(cos(x) - 1), x)","F",0
558,1,7,0,0.625001," ","integrate(exp(x)*(1+sin(x))/(1+cos(x)),x, algorithm=""giac"")","e^{x} \tan\left(\frac{1}{2} \, x\right)"," ",0,"e^x*tan(1/2*x)","A",0
559,0,0,0,0.000000," ","integrate(exp(x)*(1-sin(x))/(1+cos(x)),x, algorithm=""giac"")","\int -\frac{{\left(\sin\left(x\right) - 1\right)} e^{x}}{\cos\left(x\right) + 1}\,{d x}"," ",0,"integrate(-(sin(x) - 1)*e^x/(cos(x) + 1), x)","F",0
560,0,0,0,0.000000," ","integrate(exp(x)*(1-cos(x))/(1-sin(x)),x, algorithm=""giac"")","\int \frac{{\left(\cos\left(x\right) - 1\right)} e^{x}}{\sin\left(x\right) - 1}\,{d x}"," ",0,"integrate((cos(x) - 1)*e^x/(sin(x) - 1), x)","F",0
561,1,20,0,0.611543," ","integrate(exp(x)*(1+cos(x))/(1-sin(x)),x, algorithm=""giac"")","-\frac{e^{x} \tan\left(\frac{1}{2} \, x\right) + e^{x}}{\tan\left(\frac{1}{2} \, x\right) - 1}"," ",0,"-(e^x*tan(1/2*x) + e^x)/(tan(1/2*x) - 1)","A",0
562,0,0,0,0.000000," ","integrate(exp(x)*(1+cos(x))/(1+sin(x)),x, algorithm=""giac"")","\int \frac{{\left(\cos\left(x\right) + 1\right)} e^{x}}{\sin\left(x\right) + 1}\,{d x}"," ",0,"integrate((cos(x) + 1)*e^x/(sin(x) + 1), x)","F",0
563,1,21,0,0.628301," ","integrate(exp(x)*(1-cos(x))/(1+sin(x)),x, algorithm=""giac"")","\frac{e^{x} \tan\left(\frac{1}{2} \, x\right) - e^{x}}{\tan\left(\frac{1}{2} \, x\right) + 1}"," ",0,"(e^x*tan(1/2*x) - e^x)/(tan(1/2*x) + 1)","A",0
564,1,15,0,0.624227," ","integrate(exp(x)*x*cos(x),x, algorithm=""giac"")","\frac{1}{2} \, {\left(x \cos\left(x\right) + {\left(x - 1\right)} \sin\left(x\right)\right)} e^{x}"," ",0,"1/2*(x*cos(x) + (x - 1)*sin(x))*e^x","A",0
565,1,25,0,0.600806," ","integrate(exp(x)*x^2*sin(x),x, algorithm=""giac"")","-\frac{1}{2} \, {\left({\left(x^{2} - 2 \, x + 1\right)} \cos\left(x\right) - {\left(x^{2} - 1\right)} \sin\left(x\right)\right)} e^{x}"," ",0,"-1/2*((x^2 - 2*x + 1)*cos(x) - (x^2 - 1)*sin(x))*e^x","A",0
566,1,33,0,0.573269," ","integrate(x^2*sin(x)/exp(3*x),x, algorithm=""giac"")","-\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
567,1,73,0,0.599033," ","integrate(exp(1/2*x)*x^2*cos(x)^3,x, algorithm=""giac"")","\frac{1}{101306} \, {\left({\left(1369 \, x^{2} + 5180 \, x - 856\right)} \cos\left(3 \, x\right) + 6 \, {\left(1369 \, x^{2} - 296 \, x - 264\right)} \sin\left(3 \, x\right)\right)} e^{\left(\frac{1}{2} \, x\right)} + \frac{3}{250} \, {\left({\left(25 \, x^{2} + 60 \, x - 88\right)} \cos\left(x\right) + 2 \, {\left(25 \, x^{2} - 40 \, x - 8\right)} \sin\left(x\right)\right)} e^{\left(\frac{1}{2} \, x\right)}"," ",0,"1/101306*((1369*x^2 + 5180*x - 856)*cos(3*x) + 6*(1369*x^2 - 296*x - 264)*sin(3*x))*e^(1/2*x) + 3/250*((25*x^2 + 60*x - 88)*cos(x) + 2*(25*x^2 - 40*x - 8)*sin(x))*e^(1/2*x)","A",0
568,1,39,0,0.574438," ","integrate(exp(2*x)*x^2*sin(4*x),x, algorithm=""giac"")","-\frac{1}{500} \, {\left(2 \, {\left(50 \, x^{2} - 20 \, x - 1\right)} \cos\left(4 \, x\right) - {\left(50 \, x^{2} + 30 \, x - 11\right)} \sin\left(4 \, x\right)\right)} e^{\left(2 \, x\right)}"," ",0,"-1/500*(2*(50*x^2 - 20*x - 1)*cos(4*x) - (50*x^2 + 30*x - 11)*sin(4*x))*e^(2*x)","A",0
569,1,73,0,0.601305," ","integrate(exp(1/2*x)*x^2*cos(x)*sin(x)^2,x, algorithm=""giac"")","-\frac{1}{101306} \, {\left({\left(1369 \, x^{2} + 5180 \, x - 856\right)} \cos\left(3 \, x\right) + 6 \, {\left(1369 \, x^{2} - 296 \, x - 264\right)} \sin\left(3 \, x\right)\right)} e^{\left(\frac{1}{2} \, x\right)} + \frac{1}{250} \, {\left({\left(25 \, x^{2} + 60 \, x - 88\right)} \cos\left(x\right) + 2 \, {\left(25 \, x^{2} - 40 \, x - 8\right)} \sin\left(x\right)\right)} e^{\left(\frac{1}{2} \, x\right)}"," ",0,"-1/101306*((1369*x^2 + 5180*x - 856)*cos(3*x) + 6*(1369*x^2 - 296*x - 264)*sin(3*x))*e^(1/2*x) + 1/250*((25*x^2 + 60*x - 88)*cos(x) + 2*(25*x^2 - 40*x - 8)*sin(x))*e^(1/2*x)","A",0
570,1,11,0,0.627479," ","integrate(cosh(x),x, algorithm=""giac"")","-\frac{1}{2} \, e^{\left(-x\right)} + \frac{1}{2} \, e^{x}"," ",0,"-1/2*e^(-x) + 1/2*e^x","B",0
571,1,11,0,0.621716," ","integrate(sinh(x),x, algorithm=""giac"")","\frac{1}{2} \, e^{\left(-x\right)} + \frac{1}{2} \, e^{x}"," ",0,"1/2*e^(-x) + 1/2*e^x","B",0
572,1,11,0,0.634197," ","integrate(tanh(x),x, algorithm=""giac"")","-x + \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"-x + log(e^(2*x) + 1)","B",0
573,1,12,0,0.623005," ","integrate(coth(x),x, algorithm=""giac"")","-x + \log\left({\left| e^{\left(2 \, x\right)} - 1 \right|}\right)"," ",0,"-x + log(abs(e^(2*x) - 1))","B",0
574,1,5,0,0.619489," ","integrate(sech(x),x, algorithm=""giac"")","2 \, \arctan\left(e^{x}\right)"," ",0,"2*arctan(e^x)","A",0
575,1,14,0,0.585975," ","integrate(csch(x),x, algorithm=""giac"")","-\log\left(e^{x} + 1\right) + \log\left({\left| e^{x} - 1 \right|}\right)"," ",0,"-log(e^x + 1) + log(abs(e^x - 1))","B",0
576,1,24,0,0.606667," ","integrate(cosh(x)^2,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(2 \, e^{\left(2 \, x\right)} + 1\right)} e^{\left(-2 \, x\right)} + \frac{1}{2} \, x + \frac{1}{8} \, e^{\left(2 \, x\right)}"," ",0,"-1/8*(2*e^(2*x) + 1)*e^(-2*x) + 1/2*x + 1/8*e^(2*x)","B",0
577,1,37,0,0.585062," ","integrate(sinh(x)^5,x, algorithm=""giac"")","\frac{1}{480} \, {\left(150 \, e^{\left(4 \, x\right)} - 25 \, e^{\left(2 \, x\right)} + 3\right)} e^{\left(-5 \, x\right)} + \frac{1}{160} \, e^{\left(5 \, x\right)} - \frac{5}{96} \, e^{\left(3 \, x\right)} + \frac{5}{16} \, e^{x}"," ",0,"1/480*(150*e^(4*x) - 25*e^(2*x) + 3)*e^(-5*x) + 1/160*e^(5*x) - 5/96*e^(3*x) + 5/16*e^x","B",0
578,1,26,0,0.629535," ","integrate(tanh(x)^4,x, algorithm=""giac"")","x + \frac{4 \, {\left(3 \, e^{\left(4 \, x\right)} + 3 \, e^{\left(2 \, x\right)} + 2\right)}}{3 \, {\left(e^{\left(2 \, x\right)} + 1\right)}^{3}}"," ",0,"x + 4/3*(3*e^(4*x) + 3*e^(2*x) + 2)/(e^(2*x) + 1)^3","B",0
579,1,45,0,0.598981," ","integrate(csch(x)^3,x, algorithm=""giac"")","-\frac{e^{\left(-x\right)} + e^{x}}{{\left(e^{\left(-x\right)} + e^{x}\right)}^{2} - 4} + \frac{1}{4} \, \log\left(e^{\left(-x\right)} + e^{x} + 2\right) - \frac{1}{4} \, \log\left(e^{\left(-x\right)} + e^{x} - 2\right)"," ",0,"-(e^(-x) + e^x)/((e^(-x) + e^x)^2 - 4) + 1/4*log(e^(-x) + e^x + 2) - 1/4*log(e^(-x) + e^x - 2)","B",0
580,1,60,0,0.635719," ","integrate(1/cosh(x)^5,x, algorithm=""giac"")","\frac{3}{16} \, \pi - \frac{3 \, {\left(e^{\left(-x\right)} - e^{x}\right)}^{3} + 20 \, e^{\left(-x\right)} - 20 \, e^{x}}{4 \, {\left({\left(e^{\left(-x\right)} - e^{x}\right)}^{2} + 4\right)}^{2}} + \frac{3}{8} \, \arctan\left(\frac{1}{2} \, {\left(e^{\left(2 \, x\right)} - 1\right)} e^{\left(-x\right)}\right)"," ",0,"3/16*pi - 1/4*(3*(e^(-x) - e^x)^3 + 20*e^(-x) - 20*e^x)/((e^(-x) - e^x)^2 + 4)^2 + 3/8*arctan(1/2*(e^(2*x) - 1)*e^(-x))","B",0
581,1,43,0,0.614613," ","integrate(tanh(x)^5/sech(x)^4,x, algorithm=""giac"")","\frac{1}{64} \, {\left(48 \, e^{\left(4 \, x\right)} - 12 \, e^{\left(2 \, x\right)} + 1\right)} e^{\left(-4 \, x\right)} - x + \frac{1}{64} \, e^{\left(4 \, x\right)} - \frac{3}{16} \, e^{\left(2 \, x\right)} + \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"1/64*(48*e^(4*x) - 12*e^(2*x) + 1)*e^(-4*x) - x + 1/64*e^(4*x) - 3/16*e^(2*x) + log(e^(2*x) + 1)","B",0
582,0,0,0,0.000000," ","integrate(sech(x)^(3/4)*tanh(x)^5,x, algorithm=""giac"")","\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
583,1,32,0,0.592397," ","integrate(1/(a+b*cosh(x)),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{b e^{x} + a}{\sqrt{-a^{2} + b^{2}}}\right)}{\sqrt{-a^{2} + b^{2}}}"," ",0,"2*arctan((b*e^x + a)/sqrt(-a^2 + b^2))/sqrt(-a^2 + b^2)","A",0
584,1,14,0,0.606926," ","integrate(1/(1+cosh(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, e^{x} + 1\right)}}{3 \, {\left(e^{x} + 1\right)}^{3}}"," ",0,"-2/3*(3*e^x + 1)/(e^x + 1)^3","A",0
585,1,43,0,0.584769," ","integrate(1/(a+b*tanh(x)),x, algorithm=""giac"")","-\frac{b \log\left({\left| a e^{\left(2 \, x\right)} + b e^{\left(2 \, x\right)} + a - b \right|}\right)}{a^{2} - b^{2}} + \frac{x}{a - b}"," ",0,"-b*log(abs(a*e^(2*x) + b*e^(2*x) + a - b))/(a^2 - b^2) + x/(a - b)","A",0
586,1,79,0,0.603139," ","integrate(1/(a^2+b^2*cosh(x)^2),x, algorithm=""giac"")","\frac{\log\left(\frac{b^{2} e^{\left(2 \, x\right)} + 2 \, a^{2} + b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left| a \right|}}{b^{2} e^{\left(2 \, x\right)} + 2 \, a^{2} + b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left| a \right|}}\right)}{2 \, \sqrt{a^{2} + b^{2}} {\left| a \right|}}"," ",0,"1/2*log((b^2*e^(2*x) + 2*a^2 + b^2 - 2*sqrt(a^2 + b^2)*abs(a))/(b^2*e^(2*x) + 2*a^2 + b^2 + 2*sqrt(a^2 + b^2)*abs(a)))/(sqrt(a^2 + b^2)*abs(a))","B",0
587,1,50,0,0.588361," ","integrate(1/(a^2-b^2*cosh(x)^2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{b^{2} e^{\left(2 \, x\right)} - 2 \, a^{2} + b^{2}}{2 \, \sqrt{-a^{2} + b^{2}} a}\right)}{\sqrt{-a^{2} + b^{2}} a}"," ",0,"-arctan(1/2*(b^2*e^(2*x) - 2*a^2 + b^2)/(sqrt(-a^2 + b^2)*a))/(sqrt(-a^2 + b^2)*a)","A",0
588,1,48,0,0.588440," ","integrate(1/(1-sinh(x)^4),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} + 2 \, e^{\left(2 \, x\right)} - 6 \right|}}{{\left| 4 \, \sqrt{2} + 2 \, e^{\left(2 \, x\right)} - 6 \right|}}\right) - \frac{1}{e^{\left(2 \, x\right)} + 1}"," ",0,"-1/8*sqrt(2)*log(abs(-4*sqrt(2) + 2*e^(2*x) - 6)/abs(4*sqrt(2) + 2*e^(2*x) - 6)) - 1/(e^(2*x) + 1)","B",0
589,1,22,0,0.599285," ","integrate((cosh(x)^3-sinh(x)^3)/(cosh(x)^3+sinh(x)^3),x, algorithm=""giac"")","\frac{4}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} e^{\left(2 \, x\right)}\right) - \frac{1}{6} \, e^{\left(-2 \, x\right)}"," ",0,"4/9*sqrt(3)*arctan(1/3*sqrt(3)*e^(2*x)) - 1/6*e^(-2*x)","A",0
590,1,48,0,0.628780," ","integrate(cosh(x)*cosh(2*x)*cosh(3*x),x, algorithm=""giac"")","-\frac{1}{96} \, {\left(22 \, e^{\left(6 \, x\right)} + 6 \, e^{\left(4 \, x\right)} + 3 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-6 \, x\right)} + \frac{1}{4} \, x + \frac{1}{48} \, e^{\left(6 \, x\right)} + \frac{1}{32} \, e^{\left(4 \, x\right)} + \frac{1}{16} \, e^{\left(2 \, x\right)}"," ",0,"-1/96*(22*e^(6*x) + 6*e^(4*x) + 3*e^(2*x) + 2)*e^(-6*x) + 1/4*x + 1/48*e^(6*x) + 1/32*e^(4*x) + 1/16*e^(2*x)","B",0
591,1,48,0,0.635573," ","integrate(cosh(3/2*x)*sinh(x)*sinh(5/2*x),x, algorithm=""giac"")","\frac{1}{240} \, {\left(137 \, e^{\left(5 \, x\right)} - 15 \, e^{\left(3 \, x\right)} + 10 \, e^{\left(2 \, x\right)} - 6\right)} e^{\left(-5 \, x\right)} - \frac{1}{4} \, x + \frac{1}{40} \, e^{\left(5 \, x\right)} - \frac{1}{24} \, e^{\left(3 \, x\right)} + \frac{1}{16} \, e^{\left(2 \, x\right)}"," ",0,"1/240*(137*e^(5*x) - 15*e^(3*x) + 10*e^(2*x) - 6)*e^(-5*x) - 1/4*x + 1/40*e^(5*x) - 1/24*e^(3*x) + 1/16*e^(2*x)","B",0
592,-2,0,0,0.000000," ","integrate(cosh(x)*(-cosh(2*x)+tanh(x))/(sinh(x)^2+sinh(2*x))/sinh(2*x)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -1/2*(((-i)*pi+sqrt(2)*atan((1+2*i)/(1-i)/sqrt(2))+12*atan(i)+6-6*i)/3/sqrt(2)+2*(-sqrt(2)/(-exp(x)^2+sqrt(exp(x)^4-1)+1)-1/6*atan(1/2*(3*(-exp(x)^2+sqrt(exp(x)^4-1))-1)/sqrt(2))-1/3*ln(exp(x)^2-sqrt(exp(x)^4-1))/sqrt(2)-sqrt(2)*atan(-exp(x)^2+sqrt(exp(x)^4-1))))","F(-2)",0
593,1,40,0,0.733111," ","integrate(sinh(x)/(-9+4*cosh(x)^2)^(5/2),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, e^{\left(2 \, x\right)} - 21\right)} e^{\left(2 \, x\right)} - 21\right)} e^{\left(2 \, x\right)} + 2}{486 \, {\left(e^{\left(4 \, x\right)} - 7 \, e^{\left(2 \, x\right)} + 1\right)}^{\frac{3}{2}}} + \frac{1}{243}"," ",0,"-1/486*(((2*e^(2*x) - 21)*e^(2*x) - 21)*e^(2*x) + 2)/(e^(4*x) - 7*e^(2*x) + 1)^(3/2) + 1/243","A",0
594,0,0,0,0.000000," ","integrate(sinh(x)^2*sinh(2*x)/(1-sinh(x)^2)^(3/2),x, algorithm=""giac"")","\int \frac{\sinh\left(2 \, x\right) \sinh\left(x\right)^{2}}{{\left(-\sinh\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sinh(2*x)*sinh(x)^2/(-sinh(x)^2 + 1)^(3/2), x)","F",0
595,1,58,0,0.660456," ","integrate(cosh(x)/cosh(2*x)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} {\left(\log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)} + 1\right) + \log\left(\sqrt{e^{\left(4 \, x\right)} + 1} - e^{\left(2 \, x\right)}\right) - \log\left(-\sqrt{e^{\left(4 \, x\right)} + 1} + e^{\left(2 \, x\right)} + 1\right)\right)}"," ",0,"-1/4*sqrt(2)*(log(sqrt(e^(4*x) + 1) - e^(2*x) + 1) + log(sqrt(e^(4*x) + 1) - e^(2*x)) - log(-sqrt(e^(4*x) + 1) + e^(2*x) + 1))","B",0
596,1,51,0,0.634118," ","integrate(x*tanh(x)^2,x, algorithm=""giac"")","\frac{x^{2} e^{\left(2 \, x\right)} + x^{2} - 4 \, x e^{\left(2 \, x\right)} + 2 \, e^{\left(2 \, x\right)} \log\left(e^{\left(2 \, x\right)} + 1\right) + 2 \, \log\left(e^{\left(2 \, x\right)} + 1\right)}{2 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"1/2*(x^2*e^(2*x) + x^2 - 4*x*e^(2*x) + 2*e^(2*x)*log(e^(2*x) + 1) + 2*log(e^(2*x) + 1))/(e^(2*x) + 1)","B",0
597,1,53,0,0.587553," ","integrate(x*coth(x)^2,x, algorithm=""giac"")","\frac{x^{2} e^{\left(2 \, x\right)} - x^{2} - 4 \, x e^{\left(2 \, x\right)} + 2 \, e^{\left(2 \, x\right)} \log\left(e^{\left(2 \, x\right)} - 1\right) - 2 \, \log\left(e^{\left(2 \, x\right)} - 1\right)}{2 \, {\left(e^{\left(2 \, x\right)} - 1\right)}}"," ",0,"1/2*(x^2*e^(2*x) - x^2 - 4*x*e^(2*x) + 2*e^(2*x)*log(e^(2*x) - 1) - 2*log(e^(2*x) - 1))/(e^(2*x) - 1)","B",0
598,1,11,0,0.626390," ","integrate((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, x + e^{x} - 2\right)} e^{x}"," ",0,"1/2*(2*x + e^x - 2)*e^x","A",0
599,1,14,0,0.613147," ","integrate((x+cosh(x)+sinh(x))/(1+cosh(x)),x, algorithm=""giac"")","\frac{2 \, {\left(x e^{x} + 1\right)}}{e^{x} + 1}"," ",0,"2*(x*e^x + 1)/(e^x + 1)","A",0
600,1,24,0,0.616930," ","integrate(exp(2*x)/sinh(x)^4,x, algorithm=""giac"")","-\frac{8 \, {\left(3 \, e^{\left(4 \, x\right)} - 3 \, e^{\left(2 \, x\right)} + 1\right)}}{3 \, {\left(e^{\left(2 \, x\right)} - 1\right)}^{3}}"," ",0,"-8/3*(3*e^(4*x) - 3*e^(2*x) + 1)/(e^(2*x) - 1)^3","A",0
601,1,10,0,0.587771," ","integrate(1/exp(2*x)/cosh(x)^4,x, algorithm=""giac"")","-\frac{8}{3 \, {\left(e^{\left(2 \, x\right)} + 1\right)}^{3}}"," ",0,"-8/3/(e^(2*x) + 1)^3","A",0
602,1,6,0,0.593250," ","integrate(exp(x)/(cosh(x)-sinh(x)),x, algorithm=""giac"")","\frac{1}{2} \, e^{\left(2 \, x\right)}"," ",0,"1/2*e^(2*x)","A",0
603,1,16,0,0.577385," ","integrate(exp(m*x)/(cosh(x)+sinh(x)),x, algorithm=""giac"")","\frac{e^{\left(m x\right)}}{m e^{x} - e^{x}}"," ",0,"e^(m*x)/(m*e^x - e^x)","A",0
604,1,1,0,0.594032," ","integrate(exp(x)/(cosh(x)+sinh(x)),x, algorithm=""giac"")","x"," ",0,"x","A",0
605,1,17,0,0.608523," ","integrate(exp(x)/(1-cosh(x)),x, algorithm=""giac"")","\frac{2}{e^{x} - 1} - 2 \, \log\left({\left| e^{x} - 1 \right|}\right)"," ",0,"2/(e^x - 1) - 2*log(abs(e^x - 1))","A",0
606,1,11,0,0.603657," ","integrate(exp(x)*(1+sinh(x))/(1+cosh(x)),x, algorithm=""giac"")","\frac{2}{e^{x} + 1} + e^{x}"," ",0,"2/(e^x + 1) + e^x","A",0
607,1,11,0,0.587214," ","integrate(exp(x)*(1-sinh(x))/(1-cosh(x)),x, algorithm=""giac"")","\frac{2}{e^{x} - 1} + e^{x}"," ",0,"2/(e^x - 1) + e^x","A",0
608,0,0,0,0.000000," ","integrate(x^m*log(x),x, algorithm=""giac"")","\int x^{m} \log\left(x\right)\,{d x}"," ",0,"integrate(x^m*log(x), x)","F",0
609,1,84,0,0.638948," ","integrate(x^m*log(x)^2,x, algorithm=""giac"")","-\frac{2 \, m x x^{m} \log\left(x\right)}{{\left(m^{2} + 2 \, m + 1\right)} {\left(m + 1\right)}} + \frac{x^{m + 1} \log\left(x\right)^{2}}{m + 1} - \frac{2 \, x x^{m} \log\left(x\right)}{{\left(m^{2} + 2 \, m + 1\right)} {\left(m + 1\right)}} + \frac{2 \, x x^{m}}{{\left(m^{2} + 2 \, m + 1\right)} {\left(m + 1\right)}}"," ",0,"-2*m*x*x^m*log(x)/((m^2 + 2*m + 1)*(m + 1)) + x^(m + 1)*log(x)^2/(m + 1) - 2*x*x^m*log(x)/((m^2 + 2*m + 1)*(m + 1)) + 2*x*x^m/((m^2 + 2*m + 1)*(m + 1))","A",0
610,1,22,0,0.634230," ","integrate(log(x)^2/x^(5/2),x, algorithm=""giac"")","-\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
611,1,24,0,0.576727," ","integrate((b*x+a)*log(x),x, algorithm=""giac"")","\frac{1}{2} \, b x^{2} \log\left(x\right) - \frac{1}{4} \, b x^{2} + a x \log\left(x\right) - a x"," ",0,"1/2*b*x^2*log(x) - 1/4*b*x^2 + a*x*log(x) - a*x","A",0
612,1,71,0,0.629314," ","integrate((b*x+a)^3*log(x),x, algorithm=""giac"")","\frac{1}{4} \, b^{3} x^{4} \log\left(x\right) - \frac{1}{16} \, b^{3} x^{4} + a b^{2} x^{3} \log\left(x\right) - \frac{1}{3} \, a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} \log\left(x\right) - \frac{3}{4} \, a^{2} b x^{2} + a^{3} x \log\left(x\right) - a^{3} x"," ",0,"1/4*b^3*x^4*log(x) - 1/16*b^3*x^4 + a*b^2*x^3*log(x) - 1/3*a*b^2*x^3 + 3/2*a^2*b*x^2*log(x) - 3/4*a^2*b*x^2 + a^3*x*log(x) - a^3*x","A",0
613,1,23,0,0.581710," ","integrate(-1-8*log(x)^2+3*log(x)^3,x, algorithm=""giac"")","3 \, x \log\left(x\right)^{3} - 17 \, x \log\left(x\right)^{2} + 34 \, x \log\left(x\right) - 35 \, x"," ",0,"3*x*log(x)^3 - 17*x*log(x)^2 + 34*x*log(x) - 35*x","A",0
614,1,52,0,0.615896," ","integrate((x^4+1)*(1-2*log(x)+log(x)^3),x, algorithm=""giac"")","\frac{1}{5} \, x^{5} \log\left(x\right)^{3} - \frac{3}{25} \, x^{5} \log\left(x\right)^{2} - \frac{44}{125} \, x^{5} \log\left(x\right) + \frac{169}{625} \, x^{5} + x \log\left(x\right)^{3} - 3 \, x \log\left(x\right)^{2} + 4 \, x \log\left(x\right) - 3 \, x"," ",0,"1/5*x^5*log(x)^3 - 3/25*x^5*log(x)^2 - 44/125*x^5*log(x) + 169/625*x^5 + x*log(x)^3 - 3*x*log(x)^2 + 4*x*log(x) - 3*x","A",0
615,0,0,0,0.000000," ","integrate(1/x^3/log(x)^4,x, algorithm=""giac"")","\int \frac{1}{x^{3} \log\left(x\right)^{4}}\,{d x}"," ",0,"integrate(1/(x^3*log(x)^4), x)","F",0
616,0,0,0,0.000000," ","integrate(log(x)/(b*x+a),x, algorithm=""giac"")","\int \frac{\log\left(x\right)}{b x + a}\,{d x}"," ",0,"integrate(log(x)/(b*x + a), x)","F",0
617,1,138,0,0.607461," ","integrate(log(x)/(b*x+a)^2,x, algorithm=""giac"")","b^{2} {\left(\frac{\log\left(\frac{{\left(b x + a\right)}^{2} {\left| b \right|} {\left| \frac{a}{b x + a} - 1 \right|}}{b^{2} {\left| b x + a \right|}}\right)}{a b^{3}} + \frac{\log\left(-\frac{a + \frac{{\left(b x + a\right)} b {\left(\frac{a}{b x + a} - 1\right)} - a b}{b}}{b}\right)}{{\left({\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a\right)} b^{3}} - \frac{\log\left({\left| -{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} + a \right|}\right)}{a b^{3}}\right)}"," ",0,"b^2*(log((b*x + a)^2*abs(b)*abs(a/(b*x + a) - 1)/(b^2*abs(b*x + a)))/(a*b^3) + log(-(a + ((b*x + a)*b*(a/(b*x + a) - 1) - a*b)/b)/b)/(((b*x + a)*(a/(b*x + a) - 1) - a)*b^3) - log(abs(-(b*x + a)*(a/(b*x + a) - 1) + a))/(a*b^3))","B",0
618,1,12,0,0.607718," ","integrate(log(x)^n/x,x, algorithm=""giac"")","\frac{\log\left(x\right)^{n + 1}}{n + 1}"," ",0,"log(x)^(n + 1)/(n + 1)","A",0
619,1,19,0,0.606116," ","integrate((a+b*log(x))^n/x,x, algorithm=""giac"")","\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
620,1,30,0,0.604476," ","integrate(1/x/(a+b*log(x)),x, algorithm=""giac"")","\frac{\log\left(\frac{1}{4} \, \pi^{2} b^{2} {\left(\mathrm{sgn}\left(x\right) - 1\right)}^{2} + {\left(b \log\left({\left| x \right|}\right) + a\right)}^{2}\right)}{2 \, b}"," ",0,"1/2*log(1/4*pi^2*b^2*(sgn(x) - 1)^2 + (b*log(abs(x)) + a)^2)/b","B",0
621,1,22,0,0.628812," ","integrate(1/x/((a+b*log(x))^n),x, algorithm=""giac"")","-\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
622,1,18,0,0.598991," ","integrate(1/x/(a^2+log(x)^2)^(1/2),x, algorithm=""giac"")","-\log\left(\sqrt{a^{2} + \log\left(x\right)^{2}} - \log\left(x\right)\right)"," ",0,"-log(sqrt(a^2 + log(x)^2) - log(x))","A",0
623,-1,0,0,0.000000," ","integrate(1/x/(-a^2+log(x)^2)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,1,10,0,0.772235," ","integrate(1/x/(a^2-log(x)^2)^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{\log\left(x\right)}{a}\right) \mathrm{sgn}\left(a\right)"," ",0,"arcsin(log(x)/a)*sgn(a)","A",0
625,-1,0,0,0.000000," ","integrate(1/x/log(x)/(a^2+log(x)^2)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate(1/x/log(x)/(a^2-log(x)^2)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,1,21,0,1.625911," ","integrate(1/x/log(x)/(-a^2+log(x)^2)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{-a^{2} + \log\left(x\right)^{2}}}{a}\right)}{a}"," ",0,"arctan(sqrt(-a^2 + log(x)^2)/a)/a","A",0
628,1,11,0,1.647175," ","integrate(log(log(x))/x,x, algorithm=""giac"")","\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
629,1,20,0,1.208705," ","integrate(log(log(x))^2/x,x, algorithm=""giac"")","\log\left(x\right) \log\left(\log\left(x\right)\right)^{2} - 2 \, \log\left(x\right) \log\left(\log\left(x\right)\right) + 2 \, \log\left(x\right)"," ",0,"log(x)*log(log(x))^2 - 2*log(x)*log(log(x)) + 2*log(x)","A",0
630,1,29,0,0.790427," ","integrate(log(log(x))^3/x,x, algorithm=""giac"")","\log\left(x\right) \log\left(\log\left(x\right)\right)^{3} - 3 \, \log\left(x\right) \log\left(\log\left(x\right)\right)^{2} + 6 \, \log\left(x\right) \log\left(\log\left(x\right)\right) - 6 \, \log\left(x\right)"," ",0,"log(x)*log(log(x))^3 - 3*log(x)*log(log(x))^2 + 6*log(x)*log(log(x)) - 6*log(x)","A",0
631,1,38,0,0.952270," ","integrate(log(log(x))^4/x,x, algorithm=""giac"")","\log\left(x\right) \log\left(\log\left(x\right)\right)^{4} - 4 \, \log\left(x\right) \log\left(\log\left(x\right)\right)^{3} + 12 \, \log\left(x\right) \log\left(\log\left(x\right)\right)^{2} - 24 \, \log\left(x\right) \log\left(\log\left(x\right)\right) + 24 \, \log\left(x\right)"," ",0,"log(x)*log(log(x))^4 - 4*log(x)*log(log(x))^3 + 12*log(x)*log(log(x))^2 - 24*log(x)*log(log(x)) + 24*log(x)","A",0
632,0,0,0,0.000000," ","integrate(log(log(x))^n/x,x, algorithm=""giac"")","\int \frac{\log\left(\log\left(x\right)\right)^{n}}{x}\,{d x}"," ",0,"integrate(log(log(x))^n/x, x)","F",0
633,1,5,0,0.954717," ","integrate(cot(x)/log(sin(x)),x, algorithm=""giac"")","\log\left({\left| \log\left(\sin\left(x\right)\right) \right|}\right)"," ",0,"log(abs(log(sin(x))))","A",0
634,1,9,0,0.973178," ","integrate((1/cos(x)+cos(x))*tan(x),x, algorithm=""giac"")","\frac{1}{\cos\left(x\right)} - \cos\left(x\right)"," ",0,"1/cos(x) - cos(x)","A",0
635,1,32,0,1.117903," ","integrate(log(cosh(x))*sinh(x),x, algorithm=""giac"")","\frac{1}{2} \, {\left(e^{\left(-x\right)} + e^{x}\right)} \log\left(\frac{1}{2} \, e^{\left(-x\right)} + \frac{1}{2} \, e^{x}\right) - \frac{1}{2} \, e^{\left(-x\right)} - \frac{1}{2} \, e^{x}"," ",0,"1/2*(e^(-x) + e^x)*log(1/2*e^(-x) + 1/2*e^x) - 1/2*e^(-x) - 1/2*e^x","B",0
636,0,0,0,0.000000," ","integrate(log(cosh(x))*tanh(x),x, algorithm=""giac"")","\int \log\left(\cosh\left(x\right)\right) \tanh\left(x\right)\,{d x}"," ",0,"integrate(log(cosh(x))*tanh(x), x)","F",0
637,1,22,0,1.127076," ","integrate(log(x-(x^2+1)^(1/2)),x, algorithm=""giac"")","x \log\left(x - \sqrt{x^{2} + 1}\right) + \sqrt{x^{2} + 1}"," ",0,"x*log(x - sqrt(x^2 + 1)) + sqrt(x^2 + 1)","A",0
638,1,27,0,0.790253," ","integrate(log(-1+x)/x^3,x, algorithm=""giac"")","\frac{1}{2 \, x} - \frac{\log\left(x - 1\right)}{2 \, x^{2}} + \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"1/2/x - 1/2*log(x - 1)/x^2 + 1/2*log(abs(x - 1)) - 1/2*log(abs(x))","A",0
639,1,20,0,0.940959," ","integrate((-1/exp(x)+exp(x))*log(1+exp(2*x)),x, algorithm=""giac"")","{\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
640,1,43,0,0.864869," ","integrate(exp(3/2*x)*log(-1+exp(x)),x, algorithm=""giac"")","\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({\left| e^{\left(\frac{1}{2} \, x\right)} - 1 \right|}\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(abs(e^(1/2*x) - 1))","A",0
641,1,26,0,1.077112," ","integrate(cos(x)^3*log(sin(x)),x, algorithm=""giac"")","-\frac{1}{3} \, \log\left(\sin\left(x\right)\right) \sin\left(x\right)^{3} + \frac{1}{9} \, \sin\left(x\right)^{3} + \log\left(\sin\left(x\right)\right) \sin\left(x\right) - \sin\left(x\right)"," ",0,"-1/3*log(sin(x))*sin(x)^3 + 1/9*sin(x)^3 + log(sin(x))*sin(x) - sin(x)","A",0
642,1,26,0,0.948114," ","integrate(log(tan(x))/cos(x)^4,x, algorithm=""giac"")","\frac{1}{3} \, \log\left(\tan\left(x\right)\right) \tan\left(x\right)^{3} - \frac{1}{9} \, \tan\left(x\right)^{3} + \log\left(\tan\left(x\right)\right) \tan\left(x\right) - \tan\left(x\right)"," ",0,"1/3*log(tan(x))*tan(x)^3 - 1/9*tan(x)^3 + log(tan(x))*tan(x) - tan(x)","A",0
643,1,43,0,0.920613," ","integrate(log(cos(1/2*x))/(1+cos(x)),x, algorithm=""giac"")","-\frac{1}{2} \, x - \frac{2 \, \log\left(\cos\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)}{{\left(x^{2} + 1\right)} {\left(\frac{x^{2} - 1}{x^{2} + 1} - 1\right)}} + \tan\left(\frac{1}{2} \, x\right)"," ",0,"-1/2*x - 2*log(cos(1/2*x))*tan(1/2*x)/((x^2 + 1)*((x^2 - 1)/(x^2 + 1) - 1)) + tan(1/2*x)","A",0
644,1,36,0,1.090041," ","integrate(cos(x)*log(sin(x))/(1+cos(x))^2,x, algorithm=""giac"")","-\frac{1}{18} \, \tan\left(\frac{1}{2} \, x\right)^{3} - \frac{1}{6} \, {\left(\tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, x\right)\right)} \log\left(\sin\left(x\right)\right) - \frac{2}{3} \, x + \frac{5}{6} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"-1/18*tan(1/2*x)^3 - 1/6*(tan(1/2*x)^3 - 3*tan(1/2*x))*log(sin(x)) - 2/3*x + 5/6*tan(1/2*x)","A",0
645,1,104,0,0.988870," ","integrate(arccos(x)^2/x^5,x, algorithm=""giac"")","-\frac{1}{48} \, {\left(\frac{x^{3} {\left(\frac{9 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 1\right)}}{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{3}} - \frac{9 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{3}}{x^{3}}\right)} \arccos\left(x\right) - \frac{2 \, x^{2} + 1}{12 \, x^{2}} - \frac{\arccos\left(x\right)^{2}}{4 \, x^{4}} + \frac{1}{6} \, \log\left(x^{2}\right)"," ",0,"-1/48*(x^3*(9*(sqrt(-x^2 + 1) - 1)^2/x^2 + 1)/(sqrt(-x^2 + 1) - 1)^3 - 9*(sqrt(-x^2 + 1) - 1)/x - (sqrt(-x^2 + 1) - 1)^3/x^3)*arccos(x) - 1/12*(2*x^2 + 1)/x^2 - 1/4*arccos(x)^2/x^4 + 1/6*log(x^2)","B",0
646,1,57,0,0.904217," ","integrate(x^2*arcsin(x)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(x^{2} - 1\right)} x \arcsin\left(x\right)^{2} + \frac{1}{3} \, x \arcsin\left(x\right)^{2} - \frac{2}{9} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} \arcsin\left(x\right) - \frac{2}{27} \, {\left(x^{2} - 1\right)} x + \frac{2}{3} \, \sqrt{-x^{2} + 1} \arcsin\left(x\right) - \frac{14}{27} \, x"," ",0,"1/3*(x^2 - 1)*x*arcsin(x)^2 + 1/3*x*arcsin(x)^2 - 2/9*(-x^2 + 1)^(3/2)*arcsin(x) - 2/27*(x^2 - 1)*x + 2/3*sqrt(-x^2 + 1)*arcsin(x) - 14/27*x","A",0
647,1,41,0,1.087400," ","integrate(x^3*arctan(x)^2,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} \arctan\left(x\right)^{2} - \frac{1}{6} \, x^{3} \arctan\left(x\right) + \frac{1}{12} \, x^{2} + \frac{1}{2} \, x \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 - 1/6*x^3*arctan(x) + 1/12*x^2 + 1/2*x*arctan(x) - 1/4*arctan(x)^2 - 1/3*log(x^2 + 1)","A",0
648,0,0,0,0.000000," ","integrate(arctan(x)^2/x^5,x, algorithm=""giac"")","\int \frac{\arctan\left(x\right)^{2}}{x^{5}}\,{d x}"," ",0,"integrate(arctan(x)^2/x^5, x)","F",0
649,1,106,0,0.960629," ","integrate(x^3*arccsc(x)^2,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} \arcsin\left(\frac{1}{x}\right)^{2} + \frac{1}{12} \, x^{2} {\left(\frac{2}{x^{2}} + 1\right)} + \frac{1}{48} \, {\left(x^{3} {\left(\sqrt{-\frac{1}{x^{2}} + 1} - 1\right)}^{3} + 9 \, x {\left(\sqrt{-\frac{1}{x^{2}} + 1} - 1\right)} - \frac{9 \, x^{2} {\left(\sqrt{-\frac{1}{x^{2}} + 1} - 1\right)}^{2} + 1}{x^{3} {\left(\sqrt{-\frac{1}{x^{2}} + 1} - 1\right)}^{3}}\right)} \arcsin\left(\frac{1}{x}\right) - \frac{1}{6} \, \log\left(\frac{1}{x^{2}}\right)"," ",0,"1/4*x^4*arcsin(1/x)^2 + 1/12*x^2*(2/x^2 + 1) + 1/48*(x^3*(sqrt(-1/x^2 + 1) - 1)^3 + 9*x*(sqrt(-1/x^2 + 1) - 1) - (9*x^2*(sqrt(-1/x^2 + 1) - 1)^2 + 1)/(x^3*(sqrt(-1/x^2 + 1) - 1)^3))*arcsin(1/x) - 1/6*log(x^(-2))","B",0
650,1,137,0,0.983150," ","integrate(arcsec(x)^4/x^5,x, algorithm=""giac"")","\frac{3}{32} \, \arccos\left(\frac{1}{x}\right)^{4} + \frac{3 \, \sqrt{-\frac{1}{x^{2}} + 1} \arccos\left(\frac{1}{x}\right)^{3}}{8 \, x} - \frac{45}{128} \, \arccos\left(\frac{1}{x}\right)^{2} - \frac{45 \, \sqrt{-\frac{1}{x^{2}} + 1} \arccos\left(\frac{1}{x}\right)}{64 \, x} + \frac{\sqrt{-\frac{1}{x^{2}} + 1} \arccos\left(\frac{1}{x}\right)^{3}}{4 \, x^{3}} + \frac{9 \, \arccos\left(\frac{1}{x}\right)^{2}}{16 \, x^{2}} - \frac{\arccos\left(\frac{1}{x}\right)^{4}}{4 \, x^{4}} - \frac{3 \, \sqrt{-\frac{1}{x^{2}} + 1} \arccos\left(\frac{1}{x}\right)}{32 \, x^{3}} - \frac{45}{128 \, x^{2}} + \frac{3 \, \arccos\left(\frac{1}{x}\right)^{2}}{16 \, x^{4}} - \frac{3}{128 \, x^{4}} + \frac{189}{1024}"," ",0,"3/32*arccos(1/x)^4 + 3/8*sqrt(-1/x^2 + 1)*arccos(1/x)^3/x - 45/128*arccos(1/x)^2 - 45/64*sqrt(-1/x^2 + 1)*arccos(1/x)/x + 1/4*sqrt(-1/x^2 + 1)*arccos(1/x)^3/x^3 + 9/16*arccos(1/x)^2/x^2 - 1/4*arccos(1/x)^4/x^4 - 3/32*sqrt(-1/x^2 + 1)*arccos(1/x)/x^3 - 45/128/x^2 + 3/16*arccos(1/x)^2/x^4 - 3/128/x^4 + 189/1024","A",0
651,1,27,0,0.847372," ","integrate(arcsin(x)*(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right) - \frac{1}{4} \, x^{2} + \frac{1}{4} \, \arcsin\left(x\right)^{2} + \frac{1}{8}"," ",0,"1/2*sqrt(-x^2 + 1)*x*arcsin(x) - 1/4*x^2 + 1/4*arcsin(x)^2 + 1/8","A",0
652,1,27,0,1.124194," ","integrate(arccos(x)*(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x \arccos\left(x\right) + \frac{1}{4} \, x^{2} - \frac{1}{4} \, \arccos\left(x\right)^{2} - \frac{1}{8}"," ",0,"1/2*sqrt(-x^2 + 1)*x*arccos(x) + 1/4*x^2 - 1/4*arccos(x)^2 - 1/8","A",0
653,1,22,0,1.163239," ","integrate(x*arccos(x)*(-x^2+1)^(1/2),x, algorithm=""giac"")","\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
654,1,50,0,1.045551," ","integrate((-x^2+1)^(3/2)*arcsin(x),x, algorithm=""giac"")","\frac{1}{4} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} x \arcsin\left(x\right) + \frac{3}{8} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right) + \frac{1}{16} \, {\left(x^{2} - 1\right)}^{2} - \frac{3}{16} \, x^{2} + \frac{3}{16} \, \arcsin\left(x\right)^{2} + \frac{9}{128}"," ",0,"1/4*(-x^2 + 1)^(3/2)*x*arcsin(x) + 3/8*sqrt(-x^2 + 1)*x*arcsin(x) + 1/16*(x^2 - 1)^2 - 3/16*x^2 + 3/16*arcsin(x)^2 + 9/128","A",0
655,1,34,0,0.859340," ","integrate(x*(-x^2+1)^(3/2)*arcsin(x),x, algorithm=""giac"")","\frac{1}{25} \, x^{5} - \frac{1}{5} \, {\left(x^{2} - 1\right)}^{2} \sqrt{-x^{2} + 1} \arcsin\left(x\right) - \frac{2}{15} \, x^{3} + \frac{1}{5} \, x"," ",0,"1/25*x^5 - 1/5*(x^2 - 1)^2*sqrt(-x^2 + 1)*arcsin(x) - 2/15*x^3 + 1/5*x","A",0
656,1,60,0,1.178401," ","integrate(x^3*(-x^2+1)^(3/2)*arccos(x),x, algorithm=""giac"")","-\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)}^{3} \sqrt{-x^{2} + 1} + 7 \, {\left(x^{2} - 1\right)}^{2} \sqrt{-x^{2} + 1}\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)^3*sqrt(-x^2 + 1) + 7*(x^2 - 1)^2*sqrt(-x^2 + 1))*arccos(x) - 2/35*x","A",0
657,0,0,0,0.000000," ","integrate((-x^2+1)^(3/2)*arccos(x)/x,x, algorithm=""giac"")","\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
658,1,135,0,0.987722," ","integrate((-x^2+1)^(3/2)*arcsin(x)/x^6,x, algorithm=""giac"")","-\frac{1}{160} \, {\left(\frac{x^{5} {\left(\frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - \frac{10 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{4}}{x^{4}} - 1\right)}}{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{5}} + \frac{10 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - \frac{5 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{3}}{x^{3}} + \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{5}}{x^{5}}\right)} \arcsin\left(x\right) - \frac{3 \, x^{4} - 4 \, x^{2} + 1}{20 \, x^{4}} + \frac{1}{10} \, \log\left(x^{2}\right)"," ",0,"-1/160*(x^5*(5*(sqrt(-x^2 + 1) - 1)^2/x^2 - 10*(sqrt(-x^2 + 1) - 1)^4/x^4 - 1)/(sqrt(-x^2 + 1) - 1)^5 + 10*(sqrt(-x^2 + 1) - 1)/x - 5*(sqrt(-x^2 + 1) - 1)^3/x^3 + (sqrt(-x^2 + 1) - 1)^5/x^5)*arcsin(x) - 1/20*(3*x^4 - 4*x^2 + 1)/x^4 + 1/10*log(x^2)","B",0
659,1,27,0,1.013632," ","integrate(x^2*arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right) + \frac{1}{4} \, x^{2} + \frac{1}{4} \, \arcsin\left(x\right)^{2} - \frac{1}{8}"," ",0,"-1/2*sqrt(-x^2 + 1)*x*arcsin(x) + 1/4*x^2 + 1/4*arcsin(x)^2 - 1/8","A",0
660,1,50,0,1.405307," ","integrate(x^4*arcsin(x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(-x^{2} + 1\right)}^{\frac{3}{2}} x \arcsin\left(x\right) - \frac{5}{8} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right) + \frac{1}{16} \, {\left(x^{2} - 1\right)}^{2} + \frac{5}{16} \, x^{2} + \frac{3}{16} \, \arcsin\left(x\right)^{2} - \frac{23}{128}"," ",0,"1/4*(-x^2 + 1)^(3/2)*x*arcsin(x) - 5/8*sqrt(-x^2 + 1)*x*arcsin(x) + 1/16*(x^2 - 1)^2 + 5/16*x^2 + 3/16*arcsin(x)^2 - 23/128","A",0
661,1,27,0,1.369921," ","integrate(x*arcsin(x)/(-x^2+1)^(3/2),x, algorithm=""giac"")","\frac{\arcsin\left(x\right)}{\sqrt{-x^{2} + 1}} - \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"arcsin(x)/sqrt(-x^2 + 1) - 1/2*log(abs(x + 1)) + 1/2*log(abs(x - 1))","A",0
662,1,27,0,1.298538," ","integrate(x*arccos(x)/(-x^2+1)^(3/2),x, algorithm=""giac"")","\frac{\arccos\left(x\right)}{\sqrt{-x^{2} + 1}} + \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"arccos(x)/sqrt(-x^2 + 1) + 1/2*log(abs(x + 1)) - 1/2*log(abs(x - 1))","A",0
663,1,54,0,1.375565," ","integrate(arcsin(x)/(-x^2+1)^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, x^{2} - 3\right)} \sqrt{-x^{2} + 1} x \arcsin\left(x\right)}{3 \, {\left(x^{2} - 1\right)}^{2}} - \frac{2 \, x^{2} - 3}{6 \, {\left(x^{2} - 1\right)}} + \frac{1}{3} \, \log\left({\left| x^{2} - 1 \right|}\right)"," ",0,"-1/3*(2*x^2 - 3)*sqrt(-x^2 + 1)*x*arcsin(x)/(x^2 - 1)^2 - 1/6*(2*x^2 - 3)/(x^2 - 1) + 1/3*log(abs(x^2 - 1))","A",0
664,1,40,0,1.346437," ","integrate(x^3*arcsin(x)/(-x^2+1)^(3/2),x, algorithm=""giac"")","{\left(\sqrt{-x^{2} + 1} + \frac{1}{\sqrt{-x^{2} + 1}}\right)} \arcsin\left(x\right) - x - \frac{1}{2} \, \log\left({\left| x + 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"(sqrt(-x^2 + 1) + 1/sqrt(-x^2 + 1))*arcsin(x) - x - 1/2*log(abs(x + 1)) + 1/2*log(abs(x - 1))","A",0
665,0,0,0,0.000000," ","integrate(arcsin(x)/x/(-x^2+1)^(3/2),x, algorithm=""giac"")","\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
666,1,95,0,1.006288," ","integrate(arccos(x)/x^4/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\frac{x^{3} {\left(\frac{9 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 1\right)}}{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{3}} - \frac{9 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}{x} - \frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{3}}{x^{3}}\right)} \arccos\left(x\right) + \frac{2 \, x^{2} + 1}{6 \, x^{2}} - \frac{1}{3} \, \log\left(x^{2}\right)"," ",0,"1/24*(x^3*(9*(sqrt(-x^2 + 1) - 1)^2/x^2 + 1)/(sqrt(-x^2 + 1) - 1)^3 - 9*(sqrt(-x^2 + 1) - 1)/x - (sqrt(-x^2 + 1) - 1)^3/x^3)*arccos(x) + 1/6*(2*x^2 + 1)/x^2 - 1/3*log(x^2)","B",0
667,1,53,0,1.046623," ","integrate(x*arccos(x)^2*(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, x^{3} \arccos\left(x\right) - \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}{3} \, x \arccos\left(x\right) + \frac{14}{27} \, \sqrt{-x^{2} + 1}"," ",0,"2/9*x^3*arccos(x) - 1/3*(-x^2 + 1)^(3/2)*arccos(x)^2 - 2/27*sqrt(-x^2 + 1)*x^2 - 2/3*x*arccos(x) + 14/27*sqrt(-x^2 + 1)","A",0
668,1,60,0,0.972812," ","integrate(x^2*arcsin(x)^3/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right)^{3} + \frac{1}{8} \, \arcsin\left(x\right)^{4} + \frac{3}{4} \, {\left(x^{2} - 1\right)} \arcsin\left(x\right)^{2} + \frac{3}{4} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right) - \frac{3}{8} \, x^{2} + \frac{3}{8} \, \arcsin\left(x\right)^{2} + \frac{3}{16}"," ",0,"-1/2*sqrt(-x^2 + 1)*x*arcsin(x)^3 + 1/8*arcsin(x)^4 + 3/4*(x^2 - 1)*arcsin(x)^2 + 3/4*sqrt(-x^2 + 1)*x*arcsin(x) - 3/8*x^2 + 3/8*arcsin(x)^2 + 3/16","A",0
669,1,26,0,1.064514," ","integrate(x*arctan(x)/(x^2+1)^2,x, algorithm=""giac"")","\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
670,1,34,0,0.886470," ","integrate(x*arctan(x)/(x^2+1)^3,x, algorithm=""giac"")","\frac{3 \, x^{3} + 5 \, x}{32 \, {\left(x^{2} + 1\right)}^{2}} - \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^2 + 1)^2 - 1/4*arctan(x)/(x^2 + 1)^2 + 3/32*arctan(x)","A",0
671,1,19,0,0.900832," ","integrate(x^2*arctan(x)/(x^2+1),x, algorithm=""giac"")","x \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) - 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=""giac"")","\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
673,0,0,0,0.000000," ","integrate(x^2*arctan(x)/(x^2+1)^2,x, algorithm=""giac"")","\int \frac{x^{2} \arctan\left(x\right)}{{\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*arctan(x)/(x^2 + 1)^2, x)","F",0
674,0,0,0,0.000000," ","integrate(x^3*arctan(x)/(x^2+1)^2,x, algorithm=""giac"")","\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=""giac"")","\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
676,1,25,0,0.990895," ","integrate((x^2+1)*arctan(x)/x^2,x, algorithm=""giac"")","{\left(x - \frac{1}{x}\right)} \arctan\left(x\right) - \log\left(x^{2} + 1\right) + \frac{1}{2} \, \log\left(x^{2}\right)"," ",0,"(x - 1/x)*arctan(x) - log(x^2 + 1) + 1/2*log(x^2)","A",0
677,1,31,0,0.945570," ","integrate((x^2+1)*arctan(x)/x^5,x, algorithm=""giac"")","-\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
678,0,0,0,0.000000," ","integrate((x^2+1)^2*arctan(x)/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)}^{2} \arctan\left(x\right)}{x^{5}}\,{d x}"," ",0,"integrate((x^2 + 1)^2*arctan(x)/x^5, x)","F",0
679,0,0,0,0.000000," ","integrate(arctan(x)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{\arctan\left(x\right)}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(arctan(x)/((x^2 + 1)*x^2), x)","F",0
680,0,0,0,0.000000," ","integrate(arctan(x)^2/x^3,x, algorithm=""giac"")","\int \frac{\arctan\left(x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate(arctan(x)^2/x^3, x)","F",0
681,0,0,0,0.000000," ","integrate((x^2+1)*arctan(x)^2/x^5,x, algorithm=""giac"")","\int \frac{{\left(x^{2} + 1\right)} \arctan\left(x\right)^{2}}{x^{5}}\,{d x}"," ",0,"integrate((x^2 + 1)*arctan(x)^2/x^5, x)","F",0
682,0,0,0,0.000000," ","integrate(x^3*arctan(x)^2/(x^2+1)^3,x, algorithm=""giac"")","\int \frac{x^{3} \arctan\left(x\right)^{2}}{{\left(x^{2} + 1\right)}^{3}}\,{d x}"," ",0,"integrate(x^3*arctan(x)^2/(x^2 + 1)^3, x)","F",0
683,0,0,0,0.000000," ","integrate(arcsec(x)*(x^2-1)^(1/2)/x^2,x, algorithm=""giac"")","\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=""giac"")","\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
685,1,75,0,1.163407," ","integrate(arcsec(x)*(x^2-1)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{2 \, \arctan\left(-x + \sqrt{x^{2} - 1}\right)}{3 \, \mathrm{sgn}\left(x\right)} + \frac{2 \, {\left(3 \, {\left(x - \sqrt{x^{2} - 1}\right)}^{4} + 1\right)} \arccos\left(\frac{1}{x}\right)}{3 \, {\left({\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 1\right)}^{3}} + \frac{3 \, x^{2} - 1}{9 \, x^{3} \mathrm{sgn}\left(x\right)}"," ",0,"-2/3*arctan(-x + sqrt(x^2 - 1))/sgn(x) + 2/3*(3*(x - sqrt(x^2 - 1))^4 + 1)*arccos(1/x)/((x - sqrt(x^2 - 1))^2 + 1)^3 + 1/9*(3*x^2 - 1)/(x^3*sgn(x))","B",0
686,1,58,0,0.970333," ","integrate(arcsec(x)/(x^2-1)^(5/2),x, algorithm=""giac"")","\frac{{\left(2 \, x^{2} - 3\right)} x \arccos\left(\frac{1}{x}\right)}{3 \, {\left(x^{2} - 1\right)}^{\frac{3}{2}}} + \frac{5 \, \log\left({\left| x + 1 \right|}\right)}{12 \, \mathrm{sgn}\left(x\right)} - \frac{5 \, \log\left({\left| x - 1 \right|}\right)}{12 \, \mathrm{sgn}\left(x\right)} - \frac{x}{6 \, {\left(x^{2} - 1\right)} \mathrm{sgn}\left(x\right)}"," ",0,"1/3*(2*x^2 - 3)*x*arccos(1/x)/(x^2 - 1)^(3/2) + 5/12*log(abs(x + 1))/sgn(x) - 5/12*log(abs(x - 1))/sgn(x) - 1/6*x/((x^2 - 1)*sgn(x))","A",0
687,1,53,0,1.129369," ","integrate(x^2*arcsec(x)/(x^2-1)^(5/2),x, algorithm=""giac"")","-\frac{x^{3} \arccos\left(\frac{1}{x}\right)}{3 \, {\left(x^{2} - 1\right)}^{\frac{3}{2}}} - \frac{\log\left({\left| x + 1 \right|}\right)}{12 \, \mathrm{sgn}\left(x\right)} + \frac{\log\left({\left| x - 1 \right|}\right)}{12 \, \mathrm{sgn}\left(x\right)} - \frac{x}{6 \, {\left(x^{2} - 1\right)} \mathrm{sgn}\left(x\right)}"," ",0,"-1/3*x^3*arccos(1/x)/(x^2 - 1)^(3/2) - 1/12*log(abs(x + 1))/sgn(x) + 1/12*log(abs(x - 1))/sgn(x) - 1/6*x/((x^2 - 1)*sgn(x))","A",0
688,1,64,0,1.246271," ","integrate(x^3*arcsec(x)/(x^2-1)^(5/2),x, algorithm=""giac"")","-\frac{{\left(3 \, x^{2} - 2\right)} \arccos\left(\frac{1}{x}\right)}{3 \, {\left(x^{2} - 1\right)}^{\frac{3}{2}}} - \frac{\log\left(x^{2}\right)}{3 \, \mathrm{sgn}\left(x\right)} + \frac{\log\left({\left| x^{2} - 1 \right|}\right)}{3 \, \mathrm{sgn}\left(x\right)} - \frac{2 \, x^{2} - 1}{6 \, {\left(x^{2} - 1\right)} \mathrm{sgn}\left(x\right)}"," ",0,"-1/3*(3*x^2 - 2)*arccos(1/x)/(x^2 - 1)^(3/2) - 1/3*log(x^2)/sgn(x) + 1/3*log(abs(x^2 - 1))/sgn(x) - 1/6*(2*x^2 - 1)/((x^2 - 1)*sgn(x))","A",0
689,0,0,0,0.000000," ","integrate(x^6*arcsec(x)/(x^2-1)^(5/2),x, algorithm=""giac"")","\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
690,1,50,0,1.039891," ","integrate(arcsec(x)/x^2/(x^2-1)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arccos\left(\frac{1}{x}\right)}{{\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 1} - \frac{2 \, \arctan\left(-x + \sqrt{x^{2} - 1}\right)}{\mathrm{sgn}\left(x\right)} + \frac{1}{x \mathrm{sgn}\left(x\right)}"," ",0,"2*arccos(1/x)/((x - sqrt(x^2 - 1))^2 + 1) - 2*arctan(-x + sqrt(x^2 - 1))/sgn(x) + 1/(x*sgn(x))","B",0
691,1,105,0,1.185876," ","integrate(arccsc(x)/x^2/(x^2-1)^(5/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\frac{{\left(5 \, x^{2} - 6\right)} x}{{\left(x^{2} - 1\right)}^{\frac{3}{2}}} + \frac{6}{{\left(x - \sqrt{x^{2} - 1}\right)}^{2} + 1}\right)} \arcsin\left(\frac{1}{x}\right) + \frac{2 \, \arctan\left(-x + \sqrt{x^{2} - 1}\right)}{\mathrm{sgn}\left(x\right)} - \frac{11 \, \log\left({\left| x + 1 \right|}\right)}{12 \, \mathrm{sgn}\left(x\right)} + \frac{11 \, \log\left({\left| x - 1 \right|}\right)}{12 \, \mathrm{sgn}\left(x\right)} - \frac{5 \, x^{2} - 6}{6 \, {\left(x^{3} - x\right)} \mathrm{sgn}\left(x\right)}"," ",0,"1/3*((5*x^2 - 6)*x/(x^2 - 1)^(3/2) + 6/((x - sqrt(x^2 - 1))^2 + 1))*arcsin(1/x) + 2*arctan(-x + sqrt(x^2 - 1))/sgn(x) - 11/12*log(abs(x + 1))/sgn(x) + 11/12*log(abs(x - 1))/sgn(x) - 1/6*(5*x^2 - 6)/((x^3 - x)*sgn(x))","A",0
692,0,0,0,0.000000," ","integrate(arccsc(x)^4/x^2/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{\operatorname{arccsc}\left(x\right)^{4}}{\sqrt{x^{2} - 1} x^{2}}\,{d x}"," ",0,"integrate(arccsc(x)^4/(sqrt(x^2 - 1)*x^2), x)","F",0
693,0,0,0,0.000000," ","integrate((x^2-1)^(3/2)*arcsec(x)^2/x^5,x, algorithm=""giac"")","\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
694,0,0,0,0.000000," ","integrate(arcsec(x)^3*(x^2-1)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} - 1} \operatorname{arcsec}\left(x\right)^{3}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(x^2 - 1)*arcsec(x)^3/x^4, x)","F",0
695,0,0,0,0.000000," ","integrate(arcsin(((-a+x)/(a+x))^(1/2)),x, algorithm=""giac"")","\int \arcsin\left(\sqrt{-\frac{a - x}{a + x}}\right)\,{d x}"," ",0,"integrate(arcsin(sqrt(-(a - x)/(a + x))), x)","F",0
696,1,49,0,1.190813," ","integrate(arctan(((-a+x)/(a+x))^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, a \log\left({\left| -x + \sqrt{-a^{2} + x^{2}} \right|}\right) \mathrm{sgn}\left(a + x\right) + x \arctan\left(\frac{\sqrt{-a^{2} + x^{2}} \mathrm{sgn}\left(a + x\right)}{a + x}\right)"," ",0,"1/2*a*log(abs(-x + sqrt(-a^2 + x^2)))*sgn(a + x) + x*arctan(sqrt(-a^2 + x^2)*sgn(a + x)/(a + x))","A",0
697,1,32,0,0.926989," ","integrate(arctan(x)/(1+x)^3,x, algorithm=""giac"")","-\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({\left| x + 1 \right|}\right)"," ",0,"-1/4/(x + 1) - 1/2*arctan(x)/(x + 1)^2 - 1/8*log(x^2 + 1) + 1/4*log(abs(x + 1))","A",0
698,0,0,0,0.000000," ","integrate(-arctan(a-x)/(a+x),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
699,0,0,0,0.000000," ","integrate(arcsin((-x^2+1)^(1/2))/(-x^2+1)^(1/2),x, algorithm=""giac"")","\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
700,1,25,0,1.004050," ","integrate(x*arctan((x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""giac"")","\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
701,1,58,0,0.972310," ","integrate(arcsin(x)/(1-x)^(5/2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{\sqrt{2} - \sqrt{x + 1}}{\sqrt{2} + \sqrt{x + 1}}\right) + \frac{\sqrt{x + 1}}{3 \, {\left(x - 1\right)}} - \frac{2 \, \arcsin\left(x\right)}{3 \, {\left(x - 1\right)} \sqrt{-x + 1}}"," ",0,"1/12*sqrt(2)*log((sqrt(2) - sqrt(x + 1))/(sqrt(2) + sqrt(x + 1))) + 1/3*sqrt(x + 1)/(x - 1) - 2/3*arcsin(x)/((x - 1)*sqrt(-x + 1))","A",0
702,1,228,0,1.746561," ","integrate((-1+x)^(5/2)*arccsc(x),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x - 1\right)}^{\frac{7}{2}} + 21 \, {\left(x - 1\right)}^{\frac{5}{2}} + 35 \, {\left(x - 1\right)}^{\frac{3}{2}} + 35 \, \sqrt{x - 1}\right)} \arcsin\left(\frac{1}{x}\right) - \frac{2}{5} \, {\left(3 \, {\left(x - 1\right)}^{\frac{5}{2}} + 10 \, {\left(x - 1\right)}^{\frac{3}{2}} + 15 \, \sqrt{x - 1}\right)} \arcsin\left(\frac{1}{x}\right) + 2 \, {\left({\left(x - 1\right)}^{\frac{3}{2}} + 3 \, \sqrt{x - 1}\right)} \arcsin\left(\frac{1}{x}\right) - 2 \, \sqrt{x - 1} \arcsin\left(\frac{1}{x}\right) + \frac{4 \, {\left(3 \, {\left(x + 1\right)}^{\frac{5}{2}} - 4 \, {\left(x + 1\right)}^{\frac{3}{2}} + 21 \, \sqrt{x + 1}\right)}}{105 \, \mathrm{sgn}\left({\left(x - 1\right)}^{\frac{3}{2}} + \sqrt{x - 1}\right)} - \frac{4 \, {\left({\left(x + 1\right)}^{\frac{3}{2}} + \sqrt{x + 1}\right)}}{5 \, \mathrm{sgn}\left({\left(x - 1\right)}^{\frac{3}{2}} + \sqrt{x - 1}\right)} + \frac{2 \, \log\left(\sqrt{x + 1} + 1\right)}{7 \, \mathrm{sgn}\left({\left(x - 1\right)}^{\frac{3}{2}} + \sqrt{x - 1}\right)} - \frac{2 \, \log\left(\sqrt{x + 1} - 1\right)}{7 \, \mathrm{sgn}\left({\left(x - 1\right)}^{\frac{3}{2}} + \sqrt{x - 1}\right)} + \frac{4 \, \sqrt{x + 1}}{\mathrm{sgn}\left({\left(x - 1\right)}^{\frac{3}{2}} + \sqrt{x - 1}\right)}"," ",0,"2/35*(5*(x - 1)^(7/2) + 21*(x - 1)^(5/2) + 35*(x - 1)^(3/2) + 35*sqrt(x - 1))*arcsin(1/x) - 2/5*(3*(x - 1)^(5/2) + 10*(x - 1)^(3/2) + 15*sqrt(x - 1))*arcsin(1/x) + 2*((x - 1)^(3/2) + 3*sqrt(x - 1))*arcsin(1/x) - 2*sqrt(x - 1)*arcsin(1/x) + 4/105*(3*(x + 1)^(5/2) - 4*(x + 1)^(3/2) + 21*sqrt(x + 1))/sgn((x - 1)^(3/2) + sqrt(x - 1)) - 4/5*((x + 1)^(3/2) + sqrt(x + 1))/sgn((x - 1)^(3/2) + sqrt(x - 1)) + 2/7*log(sqrt(x + 1) + 1)/sgn((x - 1)^(3/2) + sqrt(x - 1)) - 2/7*log(sqrt(x + 1) - 1)/sgn((x - 1)^(3/2) + sqrt(x - 1)) + 4*sqrt(x + 1)/sgn((x - 1)^(3/2) + sqrt(x - 1))","B",0
703,1,218,0,1.335754," ","integrate(arcsin(sinh(x))*sech(x)^4,x, algorithm=""giac"")","-\frac{16 \, {\left(-8 i \, \sqrt{2} \arctan\left(-i\right) - 3 \, \sqrt{2} + 32 \, \arctan\left(-i\right) - 3 i\right)}}{96 i \, \sqrt{2} - 384} + \frac{\sqrt{2} + \frac{2 \, \sqrt{2} - \sqrt{-e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} - 1}}{e^{\left(2 \, x\right)} - 3}}{6 \, {\left(\frac{\sqrt{2} {\left(2 \, \sqrt{2} - \sqrt{-e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} - 1}\right)}}{e^{\left(2 \, x\right)} - 3} + \frac{{\left(2 \, \sqrt{2} - \sqrt{-e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} - 1}\right)}^{2}}{{\left(e^{\left(2 \, x\right)} - 3\right)}^{2}} + 1\right)}} - \frac{4 \, {\left(3 \, e^{\left(2 \, x\right)} + 1\right)} \arcsin\left(\frac{1}{2} \, {\left(e^{\left(2 \, x\right)} - 1\right)} e^{\left(-x\right)}\right)}{3 \, {\left(e^{\left(2 \, x\right)} + 1\right)}^{3}} - \frac{4}{3} \, \arctan\left(-2 \, \sqrt{2} - \frac{3 \, {\left(2 \, \sqrt{2} - \sqrt{-e^{\left(4 \, x\right)} + 6 \, e^{\left(2 \, x\right)} - 1}\right)}}{e^{\left(2 \, x\right)} - 3}\right)"," ",0,"-16*(-8*I*sqrt(2)*arctan(-I) - 3*sqrt(2) + 32*arctan(-I) - 3*I)/(96*I*sqrt(2) - 384) + 1/6*(sqrt(2) + (2*sqrt(2) - sqrt(-e^(4*x) + 6*e^(2*x) - 1))/(e^(2*x) - 3))/(sqrt(2)*(2*sqrt(2) - sqrt(-e^(4*x) + 6*e^(2*x) - 1))/(e^(2*x) - 3) + (2*sqrt(2) - sqrt(-e^(4*x) + 6*e^(2*x) - 1))^2/(e^(2*x) - 3)^2 + 1) - 4/3*(3*e^(2*x) + 1)*arcsin(1/2*(e^(2*x) - 1)*e^(-x))/(e^(2*x) + 1)^3 - 4/3*arctan(-2*sqrt(2) - 3*(2*sqrt(2) - sqrt(-e^(4*x) + 6*e^(2*x) - 1))/(e^(2*x) - 3))","C",0
704,1,70,0,1.129500," ","integrate(arccot(cosh(x))*cosh(x)/sinh(x)^4,x, algorithm=""giac"")","\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{8 \, \arctan\left(\frac{2}{e^{\left(-x\right)} + e^{x}}\right)}{3 \, {\left(e^{\left(-x\right)} - e^{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) + 8/3*arctan(2/(e^(-x) + e^x))/(e^(-x) - e^x)^3","B",0
705,1,29,0,1.021244," ","integrate(exp(x)*arcsin(tanh(x)),x, algorithm=""giac"")","\arcsin\left(\frac{e^{\left(2 \, x\right)} - 1}{e^{\left(2 \, x\right)} + 1}\right) e^{x} - \log\left(e^{\left(2 \, x\right)} + 1\right)"," ",0,"arcsin((e^(2*x) - 1)/(e^(2*x) + 1))*e^x - log(e^(2*x) + 1)","A",0
