1,0,0,0,0.000000," ","integrate(arcsec(a*x^5)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arcsec(a*x^5)/x, x)","F",0
2,1,152,0,0.134372," ","integrate(x^3*arcsec(x^(1/2)),x, algorithm=""giac"")","-\frac{1}{3584} \, x^{\frac{7}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{7} - \frac{7}{2560} \, x^{\frac{5}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{5} + \frac{1}{4} \, x^{4} \arccos\left(\frac{1}{\sqrt{x}}\right) - \frac{7}{512} \, x^{\frac{3}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{3} - \frac{35}{512} \, \sqrt{x} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)} + \frac{1225 \, x^{3} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{6} + 245 \, x^{2} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{4} + 49 \, x {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{2} + 5}{17920 \, x^{\frac{7}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{7}}"," ",0,"-1/3584*x^(7/2)*(sqrt(-1/x + 1) - 1)^7 - 7/2560*x^(5/2)*(sqrt(-1/x + 1) - 1)^5 + 1/4*x^4*arccos(1/sqrt(x)) - 7/512*x^(3/2)*(sqrt(-1/x + 1) - 1)^3 - 35/512*sqrt(x)*(sqrt(-1/x + 1) - 1) + 1/17920*(1225*x^3*(sqrt(-1/x + 1) - 1)^6 + 245*x^2*(sqrt(-1/x + 1) - 1)^4 + 49*x*(sqrt(-1/x + 1) - 1)^2 + 5)/(x^(7/2)*(sqrt(-1/x + 1) - 1)^7)","B",0
3,1,116,0,0.137659," ","integrate(x^2*arcsec(x^(1/2)),x, algorithm=""giac"")","-\frac{1}{480} \, x^{\frac{5}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{5} - \frac{5}{288} \, x^{\frac{3}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{3} + \frac{1}{3} \, x^{3} \arccos\left(\frac{1}{\sqrt{x}}\right) - \frac{5}{48} \, \sqrt{x} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)} + \frac{150 \, x^{2} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{4} + 25 \, x {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{2} + 3}{1440 \, x^{\frac{5}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{5}}"," ",0,"-1/480*x^(5/2)*(sqrt(-1/x + 1) - 1)^5 - 5/288*x^(3/2)*(sqrt(-1/x + 1) - 1)^3 + 1/3*x^3*arccos(1/sqrt(x)) - 5/48*sqrt(x)*(sqrt(-1/x + 1) - 1) + 1/1440*(150*x^2*(sqrt(-1/x + 1) - 1)^4 + 25*x*(sqrt(-1/x + 1) - 1)^2 + 3)/(x^(5/2)*(sqrt(-1/x + 1) - 1)^5)","B",0
4,1,80,0,0.149909," ","integrate(x*arcsec(x^(1/2)),x, algorithm=""giac"")","-\frac{1}{48} \, x^{\frac{3}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{3} + \frac{1}{2} \, x^{2} \arccos\left(\frac{1}{\sqrt{x}}\right) - \frac{3}{16} \, \sqrt{x} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)} + \frac{9 \, x {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{2} + 1}{48 \, x^{\frac{3}{2}} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}^{3}}"," ",0,"-1/48*x^(3/2)*(sqrt(-1/x + 1) - 1)^3 + 1/2*x^2*arccos(1/sqrt(x)) - 3/16*sqrt(x)*(sqrt(-1/x + 1) - 1) + 1/48*(9*x*(sqrt(-1/x + 1) - 1)^2 + 1)/(x^(3/2)*(sqrt(-1/x + 1) - 1)^3)","B",0
5,1,41,0,0.127056," ","integrate(arcsec(x^(1/2)),x, algorithm=""giac"")","x \arccos\left(\frac{1}{\sqrt{x}}\right) - \frac{1}{2} \, \sqrt{x} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)} + \frac{1}{2 \, \sqrt{x} {\left(\sqrt{-\frac{1}{x} + 1} - 1\right)}}"," ",0,"x*arccos(1/sqrt(x)) - 1/2*sqrt(x)*(sqrt(-1/x + 1) - 1) + 1/2/(sqrt(x)*(sqrt(-1/x + 1) - 1))","B",0
6,0,0,0,0.000000," ","integrate(arcsec(x^(1/2))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arcsec(sqrt(x))/x, x)","F",0
7,1,30,0,0.127883," ","integrate(arcsec(x^(1/2))/x^2,x, algorithm=""giac"")","\frac{\sqrt{-\frac{1}{x} + 1}}{2 \, \sqrt{x}} - \frac{\arccos\left(\frac{1}{\sqrt{x}}\right)}{x} + \frac{1}{2} \, \arccos\left(\frac{1}{\sqrt{x}}\right)"," ",0,"1/2*sqrt(-1/x + 1)/sqrt(x) - arccos(1/sqrt(x))/x + 1/2*arccos(1/sqrt(x))","A",0
8,1,44,0,0.142139," ","integrate(arcsec(x^(1/2))/x^3,x, algorithm=""giac"")","\frac{3 \, \sqrt{-\frac{1}{x} + 1}}{16 \, \sqrt{x}} + \frac{\sqrt{-\frac{1}{x} + 1}}{8 \, x^{\frac{3}{2}}} - \frac{\arccos\left(\frac{1}{\sqrt{x}}\right)}{2 \, x^{2}} + \frac{3}{16} \, \arccos\left(\frac{1}{\sqrt{x}}\right)"," ",0,"3/16*sqrt(-1/x + 1)/sqrt(x) + 1/8*sqrt(-1/x + 1)/x^(3/2) - 1/2*arccos(1/sqrt(x))/x^2 + 3/16*arccos(1/sqrt(x))","A",0
9,1,58,0,0.147939," ","integrate(arcsec(x^(1/2))/x^4,x, algorithm=""giac"")","\frac{5 \, \sqrt{-\frac{1}{x} + 1}}{48 \, \sqrt{x}} + \frac{5 \, \sqrt{-\frac{1}{x} + 1}}{72 \, x^{\frac{3}{2}}} + \frac{\sqrt{-\frac{1}{x} + 1}}{18 \, x^{\frac{5}{2}}} - \frac{\arccos\left(\frac{1}{\sqrt{x}}\right)}{3 \, x^{3}} + \frac{5}{48} \, \arccos\left(\frac{1}{\sqrt{x}}\right)"," ",0,"5/48*sqrt(-1/x + 1)/sqrt(x) + 5/72*sqrt(-1/x + 1)/x^(3/2) + 1/18*sqrt(-1/x + 1)/x^(5/2) - 1/3*arccos(1/sqrt(x))/x^3 + 5/48*arccos(1/sqrt(x))","A",0
10,1,47,0,0.136408," ","integrate(x^2*arcsec(a/x),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} \arccos\left(\frac{x}{a}\right) - \frac{2}{9} \, a^{3} \sqrt{-\frac{x^{2}}{a^{2}} + 1} - \frac{1}{9} \, a x^{2} \sqrt{-\frac{x^{2}}{a^{2}} + 1}"," ",0,"1/3*x^3*arccos(x/a) - 2/9*a^3*sqrt(-x^2/a^2 + 1) - 1/9*a*x^2*sqrt(-x^2/a^2 + 1)","A",0
11,1,39,0,0.121900," ","integrate(x*arcsec(a/x),x, algorithm=""giac"")","-\frac{1}{4} \, a^{2} \arccos\left(\frac{x}{a}\right) + \frac{1}{2} \, x^{2} \arccos\left(\frac{x}{a}\right) - \frac{1}{4} \, a x \sqrt{-\frac{x^{2}}{a^{2}} + 1}"," ",0,"-1/4*a^2*arccos(x/a) + 1/2*x^2*arccos(x/a) - 1/4*a*x*sqrt(-x^2/a^2 + 1)","A",0
12,1,28,0,0.127343," ","integrate(arcsec(a/x),x, algorithm=""giac"")","a {\left(\frac{x \arccos\left(\frac{x}{a}\right)}{a} - \sqrt{-\frac{x^{2}}{a^{2}} + 1}\right)}"," ",0,"a*(x*arccos(x/a)/a - sqrt(-x^2/a^2 + 1))","A",0
13,0,0,0,0.000000," ","integrate(arcsec(a/x)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(\frac{a}{x}\right)}{x}\,{d x}"," ",0,"integrate(arcsec(a/x)/x, x)","F",0
14,1,61,0,0.141277," ","integrate(arcsec(a/x)/x^2,x, algorithm=""giac"")","\frac{a {\left(\frac{\log\left({\left| a + \sqrt{a^{2} - x^{2}} \right|}\right)}{a} - \frac{\log\left({\left| -a + \sqrt{a^{2} - x^{2}} \right|}\right)}{a}\right)}}{2 \, {\left| a \right|}} - \frac{\arccos\left(\frac{x}{a}\right)}{x}"," ",0,"1/2*a*(log(abs(a + sqrt(a^2 - x^2)))/a - log(abs(-a + sqrt(a^2 - x^2)))/a)/abs(a) - arccos(x/a)/x","B",0
15,1,61,0,0.175541," ","integrate(arcsec(a/x)/x^3,x, algorithm=""giac"")","\frac{a {\left(\frac{a + \sqrt{a^{2} - x^{2}}}{a^{2} x} - \frac{x}{{\left(a + \sqrt{a^{2} - x^{2}}\right)} a^{2}}\right)}}{4 \, {\left| a \right|}} - \frac{\arccos\left(\frac{x}{a}\right)}{2 \, x^{2}}"," ",0,"1/4*a*((a + sqrt(a^2 - x^2))/(a^2*x) - x/((a + sqrt(a^2 - x^2))*a^2))/abs(a) - 1/2*arccos(x/a)/x^2","A",0
16,1,80,0,0.124670," ","integrate(arcsec(a/x)/x^4,x, algorithm=""giac"")","\frac{a {\left(\frac{\log\left({\left| a + \sqrt{a^{2} - x^{2}} \right|}\right)}{a^{3}} - \frac{\log\left({\left| -a + \sqrt{a^{2} - x^{2}} \right|}\right)}{a^{3}} + \frac{2 \, \sqrt{a^{2} - x^{2}}}{a^{2} x^{2}}\right)}}{12 \, {\left| a \right|}} - \frac{\arccos\left(\frac{x}{a}\right)}{3 \, x^{3}}"," ",0,"1/12*a*(log(abs(a + sqrt(a^2 - x^2)))/a^3 - log(abs(-a + sqrt(a^2 - x^2)))/a^3 + 2*sqrt(a^2 - x^2)/(a^2*x^2))/abs(a) - 1/3*arccos(x/a)/x^3","A",0
17,0,0,0,0.000000," ","integrate(arcsec(a*x^n)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(a x^{n}\right)}{x}\,{d x}"," ",0,"integrate(arcsec(a*x^n)/x, x)","F",0
18,1,409,0,0.180362," ","integrate(x^4*arcsec(b*x+a),x, algorithm=""giac"")","-\frac{1}{960} \, b {\left(\frac{192 \, {\left(b x + a\right)}^{5} {\left(\frac{5 \, a}{b x + a} - \frac{10 \, a^{2}}{{\left(b x + a\right)}^{2}} + \frac{10 \, a^{3}}{{\left(b x + a\right)}^{3}} - \frac{5 \, a^{4}}{{\left(b x + a\right)}^{4}} - 1\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{b^{6}} - \frac{3 \, {\left(b x + a\right)}^{4} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{4} + 40 \, {\left(b x + a\right)}^{3} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{3} + 240 \, {\left(b x + a\right)}^{2} a^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 960 \, {\left(b x + a\right)} a^{3} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 24 \, {\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 360 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 24 \, {\left(40 \, a^{4} + 40 \, a^{2} + 3\right)} \log\left(-{\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} {\left| b x + a \right|}\right) - \frac{120 \, {\left(8 \, a^{3} + 3 \, a\right)} {\left(b x + a\right)}^{3} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{3} + 24 \, {\left(10 \, a^{2} + 1\right)} {\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 40 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 3}{{\left(b x + a\right)}^{4} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{4}}}{b^{6}}\right)}"," ",0,"-1/960*b*(192*(b*x + a)^5*(5*a/(b*x + a) - 10*a^2/(b*x + a)^2 + 10*a^3/(b*x + a)^3 - 5*a^4/(b*x + a)^4 - 1)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/b^6 - (3*(b*x + a)^4*(sqrt(-1/(b*x + a)^2 + 1) - 1)^4 + 40*(b*x + a)^3*a*(sqrt(-1/(b*x + a)^2 + 1) - 1)^3 + 240*(b*x + a)^2*a^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 960*(b*x + a)*a^3*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 24*(b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 360*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 24*(40*a^4 + 40*a^2 + 3)*log(-(sqrt(-1/(b*x + a)^2 + 1) - 1)*abs(b*x + a)) - (120*(8*a^3 + 3*a)*(b*x + a)^3*(sqrt(-1/(b*x + a)^2 + 1) - 1)^3 + 24*(10*a^2 + 1)*(b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 40*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 3)/((b*x + a)^4*(sqrt(-1/(b*x + a)^2 + 1) - 1)^4))/b^6)","B",0
19,1,299,0,0.187212," ","integrate(x^3*arcsec(b*x+a),x, algorithm=""giac"")","-\frac{1}{96} \, b {\left(\frac{24 \, {\left(b x + a\right)}^{4} {\left(\frac{4 \, a}{b x + a} - \frac{6 \, a^{2}}{{\left(b x + a\right)}^{2}} + \frac{4 \, a^{3}}{{\left(b x + a\right)}^{3}} - 1\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{b^{5}} + \frac{{\left(b x + a\right)}^{3} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{3} + 12 \, {\left(b x + a\right)}^{2} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 72 \, {\left(b x + a\right)} a^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 9 \, {\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 48 \, {\left(2 \, a^{3} + a\right)} \log\left(-{\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} {\left| b x + a \right|}\right) - \frac{9 \, {\left(8 \, a^{2} + 1\right)} {\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 12 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 1}{{\left(b x + a\right)}^{3} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{3}}}{b^{5}}\right)}"," ",0,"-1/96*b*(24*(b*x + a)^4*(4*a/(b*x + a) - 6*a^2/(b*x + a)^2 + 4*a^3/(b*x + a)^3 - 1)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/b^5 + ((b*x + a)^3*(sqrt(-1/(b*x + a)^2 + 1) - 1)^3 + 12*(b*x + a)^2*a*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 72*(b*x + a)*a^2*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 9*(b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 48*(2*a^3 + a)*log(-(sqrt(-1/(b*x + a)^2 + 1) - 1)*abs(b*x + a)) - (9*(8*a^2 + 1)*(b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 12*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 1)/((b*x + a)^3*(sqrt(-1/(b*x + a)^2 + 1) - 1)^3))/b^5)","B",0
20,1,204,0,0.170423," ","integrate(x^2*arcsec(b*x+a),x, algorithm=""giac"")","-\frac{1}{24} \, b {\left(\frac{8 \, {\left(b x + a\right)}^{3} {\left(\frac{3 \, a}{b x + a} - \frac{3 \, a^{2}}{{\left(b x + a\right)}^{2}} - 1\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{b^{4}} - \frac{{\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 12 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 4 \, {\left(6 \, a^{2} + 1\right)} \log\left(-{\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} {\left| b x + a \right|}\right) - \frac{12 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 1}{{\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2}}}{b^{4}}\right)}"," ",0,"-1/24*b*(8*(b*x + a)^3*(3*a/(b*x + a) - 3*a^2/(b*x + a)^2 - 1)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/b^4 - ((b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 12*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 4*(6*a^2 + 1)*log(-(sqrt(-1/(b*x + a)^2 + 1) - 1)*abs(b*x + a)) - (12*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 1)/((b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2))/b^4)","B",0
21,1,133,0,0.155820," ","integrate(x*arcsec(b*x+a),x, algorithm=""giac"")","-\frac{1}{4} \, b {\left(\frac{2 \, {\left(b x + a\right)}^{2} {\left(\frac{2 \, a}{b x + a} - 1\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{b^{3}} + \frac{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 4 \, a \log\left(-{\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} {\left| b x + a \right|}\right) - \frac{1}{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}}}{b^{3}}\right)}"," ",0,"-1/4*b*(2*(b*x + a)^2*(2*a/(b*x + a) - 1)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/b^3 + ((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 4*a*log(-(sqrt(-1/(b*x + a)^2 + 1) - 1)*abs(b*x + a)) - 1/((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1)))/b^3)","A",0
22,1,82,0,0.170743," ","integrate(arcsec(b*x+a),x, algorithm=""giac"")","\frac{1}{2} \, b {\left(\frac{2 \, {\left(b x + a\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{b^{2}} - \frac{\log\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} + 1\right)}{b^{2}}\right)}"," ",0,"1/2*b*(2*(b*x + a)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/b^2 - (log(sqrt(-1/(b*x + a)^2 + 1) + 1) - log(-sqrt(-1/(b*x + a)^2 + 1) + 1))/b^2)","B",0
23,0,0,0,0.000000," ","integrate(arcsec(b*x+a)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arcsec(b*x + a)/x, x)","F",0
24,1,94,0,0.192765," ","integrate(arcsec(b*x+a)/x^2,x, algorithm=""giac"")","b {\left(\frac{2 \, \arctan\left(\frac{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + a}{\sqrt{-a^{2} + 1}}\right)}{\sqrt{-a^{2} + 1} a} + \frac{\arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{a {\left(\frac{a}{b x + a} - 1\right)}}\right)}"," ",0,"b*(2*arctan(((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1) + a)/sqrt(-a^2 + 1))/(sqrt(-a^2 + 1)*a) + arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/(a*(a/(b*x + a) - 1)))","A",0
25,1,216,0,0.221444," ","integrate(arcsec(b*x+a)/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, b {\left(\frac{2 \, {\left(2 \, a^{2} b - b\right)} \arctan\left(\frac{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + a}{\sqrt{-a^{2} + 1}}\right)}{{\left(a^{4} - a^{2}\right)} \sqrt{-a^{2} + 1}} + \frac{2 \, {\left({\left(b x + a\right)} a b {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + b\right)}}{{\left({\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 2 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 1\right)} {\left(a^{3} - a\right)}} + \frac{{\left(\frac{2 \, a b}{b x + a} - b\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{a^{2} {\left(\frac{a}{b x + a} - 1\right)}^{2}}\right)}"," ",0,"-1/2*b*(2*(2*a^2*b - b)*arctan(((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1) + a)/sqrt(-a^2 + 1))/((a^4 - a^2)*sqrt(-a^2 + 1)) + 2*((b*x + a)*a*b*(sqrt(-1/(b*x + a)^2 + 1) - 1) + b)/(((b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 2*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 1)*(a^3 - a)) + (2*a*b/(b*x + a) - b)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/(a^2*(a/(b*x + a) - 1)^2))","B",0
26,1,451,0,0.222901," ","integrate(arcsec(b*x+a)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, b {\left(\frac{{\left(6 \, a^{4} b^{2} - 5 \, a^{2} b^{2} + 2 \, b^{2}\right)} \arctan\left(\frac{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + a}{\sqrt{-a^{2} + 1}}\right)}{{\left(a^{7} - 2 \, a^{5} + a^{3}\right)} \sqrt{-a^{2} + 1}} + \frac{4 \, {\left(b x + a\right)}^{3} a^{3} b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{3} + 10 \, {\left(b x + a\right)}^{2} a^{4} b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} - {\left(b x + a\right)}^{3} a b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{3} + {\left(b x + a\right)}^{2} a^{2} b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 16 \, {\left(b x + a\right)} a^{3} b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} - 2 \, {\left(b x + a\right)}^{2} b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} - 7 \, {\left(b x + a\right)} a b^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 5 \, a^{2} b^{2} - 2 \, b^{2}}{{\left(a^{6} - 2 \, a^{4} + a^{2}\right)} {\left({\left(b x + a\right)}^{2} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}^{2} + 2 \, {\left(b x + a\right)} a {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} + 1\right)}^{2}} - \frac{{\left(\frac{3 \, a b^{2}}{b x + a} - \frac{3 \, a^{2} b^{2}}{{\left(b x + a\right)}^{2}} - b^{2}\right)} \arccos\left(-\frac{1}{{\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a}\right)}{a^{3} {\left(\frac{a}{b x + a} - 1\right)}^{3}}\right)}"," ",0,"1/3*b*((6*a^4*b^2 - 5*a^2*b^2 + 2*b^2)*arctan(((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1) + a)/sqrt(-a^2 + 1))/((a^7 - 2*a^5 + a^3)*sqrt(-a^2 + 1)) + (4*(b*x + a)^3*a^3*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^3 + 10*(b*x + a)^2*a^4*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 - (b*x + a)^3*a*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^3 + (b*x + a)^2*a^2*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 16*(b*x + a)*a^3*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1) - 2*(b*x + a)^2*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 - 7*(b*x + a)*a*b^2*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 5*a^2*b^2 - 2*b^2)/((a^6 - 2*a^4 + a^2)*((b*x + a)^2*(sqrt(-1/(b*x + a)^2 + 1) - 1)^2 + 2*(b*x + a)*a*(sqrt(-1/(b*x + a)^2 + 1) - 1) + 1)^2) - (3*a*b^2/(b*x + a) - 3*a^2*b^2/(b*x + a)^2 - b^2)*arccos(-1/((b*x + a)*(a/(b*x + a) - 1) - a))/(a^3*(a/(b*x + a) - 1)^3))","B",0
27,-2,0,0,0.000000," ","integrate(x^3*arcsec(b*x+a)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(a+b*x)]Simplification assuming t_nostep near 0Simplification assuming t_nostep near 0Evaluation time: 0.59sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
28,0,0,0,0.000000," ","integrate(x^2*arcsec(b*x+a)^2,x, algorithm=""giac"")","\int x^{2} \operatorname{arcsec}\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^2*arcsec(b*x + a)^2, x)","F",0
29,0,0,0,0.000000," ","integrate(x*arcsec(b*x+a)^2,x, algorithm=""giac"")","\int x \operatorname{arcsec}\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x*arcsec(b*x + a)^2, x)","F",0
30,0,0,0,0.000000," ","integrate(arcsec(b*x+a)^2,x, algorithm=""giac"")","\int \operatorname{arcsec}\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(arcsec(b*x + a)^2, x)","F",0
31,0,0,0,0.000000," ","integrate(arcsec(b*x+a)^2/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arcsec(b*x + a)^2/x, x)","F",0
32,0,0,0,0.000000," ","integrate(arcsec(b*x+a)^2/x^2,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(b x + a\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(arcsec(b*x + a)^2/x^2, x)","F",0
33,0,0,0,0.000000," ","integrate(x^2*arcsec(b*x+a)^3,x, algorithm=""giac"")","\int x^{2} \operatorname{arcsec}\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(x^2*arcsec(b*x + a)^3, x)","F",0
34,0,0,0,0.000000," ","integrate(x*arcsec(b*x+a)^3,x, algorithm=""giac"")","\int x \operatorname{arcsec}\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(x*arcsec(b*x + a)^3, x)","F",0
35,0,0,0,0.000000," ","integrate(arcsec(b*x+a)^3,x, algorithm=""giac"")","\int \operatorname{arcsec}\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(arcsec(b*x + a)^3, x)","F",0
36,0,0,0,0.000000," ","integrate(arcsec(b*x+a)^3/x,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(arcsec(b*x + a)^3/x, x)","F",0
37,0,0,0,0.000000," ","integrate(arcsec(b*x+a)^3/x^2,x, algorithm=""giac"")","\int \frac{\operatorname{arcsec}\left(b x + a\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate(arcsec(b*x + a)^3/x^2, x)","F",0
38,1,100,0,0.377165," ","integrate(x*(a+b*arcsec(d*x^2+c)),x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + \frac{1}{4} \, b d {\left(\frac{2 \, {\left(d x^{2} + c\right)} \arccos\left(-\frac{1}{{\left(d x^{2} + c\right)} {\left(\frac{c}{d x^{2} + c} - 1\right)} - c}\right)}{d^{2}} - \frac{\log\left(\sqrt{-\frac{1}{{\left(d x^{2} + c\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(d x^{2} + c\right)}^{2}} + 1} + 1\right)}{d^{2}}\right)}"," ",0,"1/2*a*x^2 + 1/4*b*d*(2*(d*x^2 + c)*arccos(-1/((d*x^2 + c)*(c/(d*x^2 + c) - 1) - c))/d^2 - (log(sqrt(-1/(d*x^2 + c)^2 + 1) + 1) - log(-sqrt(-1/(d*x^2 + c)^2 + 1) + 1))/d^2)","A",0
39,1,100,0,0.400779," ","integrate(x^2*(a+b*arcsec(d*x^3+c)),x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, b d {\left(\frac{2 \, {\left(d x^{3} + c\right)} \arccos\left(-\frac{1}{{\left(d x^{3} + c\right)} {\left(\frac{c}{d x^{3} + c} - 1\right)} - c}\right)}{d^{2}} - \frac{\log\left(\sqrt{-\frac{1}{{\left(d x^{3} + c\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(d x^{3} + c\right)}^{2}} + 1} + 1\right)}{d^{2}}\right)}"," ",0,"1/3*a*x^3 + 1/6*b*d*(2*(d*x^3 + c)*arccos(-1/((d*x^3 + c)*(c/(d*x^3 + c) - 1) - c))/d^2 - (log(sqrt(-1/(d*x^3 + c)^2 + 1) + 1) - log(-sqrt(-1/(d*x^3 + c)^2 + 1) + 1))/d^2)","A",0
40,1,100,0,0.382406," ","integrate(x^3*(a+b*arcsec(d*x^4+c)),x, algorithm=""giac"")","\frac{1}{4} \, a x^{4} + \frac{1}{8} \, b d {\left(\frac{2 \, {\left(d x^{4} + c\right)} \arccos\left(-\frac{1}{{\left(d x^{4} + c\right)} {\left(\frac{c}{d x^{4} + c} - 1\right)} - c}\right)}{d^{2}} - \frac{\log\left(\sqrt{-\frac{1}{{\left(d x^{4} + c\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(d x^{4} + c\right)}^{2}} + 1} + 1\right)}{d^{2}}\right)}"," ",0,"1/4*a*x^4 + 1/8*b*d*(2*(d*x^4 + c)*arccos(-1/((d*x^4 + c)*(c/(d*x^4 + c) - 1) - c))/d^2 - (log(sqrt(-1/(d*x^4 + c)^2 + 1) + 1) - log(-sqrt(-1/(d*x^4 + c)^2 + 1) + 1))/d^2)","A",0
41,1,75,0,0.279417," ","integrate(x^(-1+n)*arcsec(a+b*x^n),x, algorithm=""giac"")","\frac{b {\left(\frac{2 \, {\left(b x^{n} + a\right)} \arccos\left(\frac{1}{b x^{n} + a}\right)}{b^{2}} - \frac{\log\left(\sqrt{-\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1} + 1\right)}{b^{2}}\right)}}{2 \, n}"," ",0,"1/2*b*(2*(b*x^n + a)*arccos(1/(b*x^n + a))/b^2 - (log(sqrt(-1/(b*x^n + a)^2 + 1) + 1) - log(-sqrt(-1/(b*x^n + a)^2 + 1) + 1))/b^2)/n","A",0
42,0,0,0,0.000000," ","integrate(arcsec(c*exp(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arcsec}\left(c e^{\left(b x + a\right)}\right)\,{d x}"," ",0,"integrate(arcsec(c*e^(b*x + a)), x)","F",0
43,0,0,0,0.000000," ","integrate(exp(arcsec(a*x))*x^2,x, algorithm=""giac"")","\int x^{2} e^{\left(\operatorname{arcsec}\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^2*e^(arcsec(a*x)), x)","F",0
44,0,0,0,0.000000," ","integrate(exp(arcsec(a*x))*x,x, algorithm=""giac"")","\int x e^{\left(\operatorname{arcsec}\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x*e^(arcsec(a*x)), x)","F",0
45,0,0,0,0.000000," ","integrate(exp(arcsec(a*x)),x, algorithm=""giac"")","\int e^{\left(\operatorname{arcsec}\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(arcsec(a*x)), x)","F",0
46,0,0,0,0.000000," ","integrate(exp(arcsec(a*x))/x,x, algorithm=""giac"")","\int \frac{e^{\left(\operatorname{arcsec}\left(a x\right)\right)}}{x}\,{d x}"," ",0,"integrate(e^(arcsec(a*x))/x, x)","F",0
47,1,51,0,0.204849," ","integrate(exp(arcsec(a*x))/x^2,x, algorithm=""giac"")","\frac{1}{2} \, a \sqrt{-\frac{1}{a^{2} x^{2}} + 1} e^{\left(\frac{1}{2} \, \pi - \arcsin\left(\frac{1}{a x}\right)\right)} - \frac{e^{\left(\frac{1}{2} \, \pi - \arcsin\left(\frac{1}{a x}\right)\right)}}{2 \, x}"," ",0,"1/2*a*sqrt(-1/(a^2*x^2) + 1)*e^(1/2*pi - arcsin(1/(a*x))) - 1/2*e^(1/2*pi - arcsin(1/(a*x)))/x","A",0
48,0,0,0,0.000000," ","integrate(exp(arcsec(a*x))/x^3,x, algorithm=""giac"")","\int \frac{e^{\left(\operatorname{arcsec}\left(a x\right)\right)}}{x^{3}}\,{d x}"," ",0,"integrate(e^(arcsec(a*x))/x^3, x)","F",0
49,0,0,0,0.000000," ","integrate(exp(arcsec(a*x))/x^4,x, algorithm=""giac"")","\int \frac{e^{\left(\operatorname{arcsec}\left(a x\right)\right)}}{x^{4}}\,{d x}"," ",0,"integrate(e^(arcsec(a*x))/x^4, x)","F",0
50,1,115,0,0.590810," ","integrate(arcsec(b*x+a)/(a*d/b+d*x),x, algorithm=""giac"")","-\frac{1}{4} \, b^{2} {\left(\frac{2 \, {\left(b x + a\right)}^{2} \arccos\left(\frac{1}{{\left({\left(b x + a\right)} {\left(\frac{a}{b x + a} - 1\right)} - a\right)} {\left(\frac{a}{b x + a} - 1\right)} + a}\right)}{b^{3} d} - \frac{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)} - \frac{1}{{\left(b x + a\right)} {\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} - 1\right)}}}{b^{3} d}\right)}"," ",0,"-1/4*b^2*(2*(b*x + a)^2*arccos(1/(((b*x + a)*(a/(b*x + a) - 1) - a)*(a/(b*x + a) - 1) + a))/(b^3*d) - ((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1) - 1/((b*x + a)*(sqrt(-1/(b*x + a)^2 + 1) - 1)))/(b^3*d))","A",0
