1,1,124,0,2.499144," ","integrate(x^3*(d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{24 i \, a c^{5} d x^{5} + 6 \, {\left(5 \, a - i \, b\right)} c^{4} d x^{4} - 10 \, b c^{3} d x^{3} + 12 i \, b c^{2} d x^{2} + 30 \, b c d x - 27 i \, b d \log\left(\frac{c x + i}{c}\right) + 3 i \, b d \log\left(\frac{c x - i}{c}\right) - {\left(12 \, b c^{5} d x^{5} - 15 i \, b c^{4} d x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{120 \, c^{4}}"," ",0,"1/120*(24*I*a*c^5*d*x^5 + 6*(5*a - I*b)*c^4*d*x^4 - 10*b*c^3*d*x^3 + 12*I*b*c^2*d*x^2 + 30*b*c*d*x - 27*I*b*d*log((c*x + I)/c) + 3*I*b*d*log((c*x - I)/c) - (12*b*c^5*d*x^5 - 15*I*b*c^4*d*x^4)*log(-(c*x + I)/(c*x - I)))/c^4","A",0
2,1,113,0,0.873699," ","integrate(x^2*(d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{6 i \, a c^{4} d x^{4} + 2 \, {\left(4 \, a - i \, b\right)} c^{3} d x^{3} - 4 \, b c^{2} d x^{2} + 6 i \, b c d x + 7 \, b d \log\left(\frac{c x + i}{c}\right) + b d \log\left(\frac{c x - i}{c}\right) - {\left(3 \, b c^{4} d x^{4} - 4 i \, b c^{3} d x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{24 \, c^{3}}"," ",0,"1/24*(6*I*a*c^4*d*x^4 + 2*(4*a - I*b)*c^3*d*x^3 - 4*b*c^2*d*x^2 + 6*I*b*c*d*x + 7*b*d*log((c*x + I)/c) + b*d*log((c*x - I)/c) - (3*b*c^4*d*x^4 - 4*I*b*c^3*d*x^3)*log(-(c*x + I)/(c*x - I)))/c^3","A",0
3,1,104,0,1.613776," ","integrate(x*(d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{4 i \, a c^{3} d x^{3} + 2 \, {\left(3 \, a - i \, b\right)} c^{2} d x^{2} - 6 \, b c d x + 5 i \, b d \log\left(\frac{c x + i}{c}\right) - i \, b d \log\left(\frac{c x - i}{c}\right) - {\left(2 \, b c^{3} d x^{3} - 3 i \, b c^{2} d x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{12 \, c^{2}}"," ",0,"1/12*(4*I*a*c^3*d*x^3 + 2*(3*a - I*b)*c^2*d*x^2 - 6*b*c*d*x + 5*I*b*d*log((c*x + I)/c) - I*b*d*log((c*x - I)/c) - (2*b*c^3*d*x^3 - 3*I*b*c^2*d*x^2)*log(-(c*x + I)/(c*x - I)))/c^2","A",0
4,1,89,0,0.667802," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{2 i \, a c^{2} d x^{2} + 2 \, {\left(2 \, a - i \, b\right)} c d x - 3 \, b d \log\left(\frac{c x + i}{c}\right) - b d \log\left(\frac{c x - i}{c}\right) - {\left(b c^{2} d x^{2} - 2 i \, b c d x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, c}"," ",0,"1/4*(2*I*a*c^2*d*x^2 + 2*(2*a - I*b)*c*d*x - 3*b*d*log((c*x + I)/c) - b*d*log((c*x - I)/c) - (b*c^2*d*x^2 - 2*I*b*c*d*x)*log(-(c*x + I)/(c*x - I)))/c","B",0
5,0,0,0,0.467903," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 i \, a c d x + 2 \, a d - {\left(b c d x - i \, b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*(2*I*a*c*d*x + 2*a*d - (b*c*d*x - I*b*d)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
6,0,0,0,0.555495," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 i \, a c d x + 2 \, a d - {\left(b c d x - i \, b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{2}}, x\right)"," ",0,"integral(1/2*(2*I*a*c*d*x + 2*a*d - (b*c*d*x - I*b*d)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
7,1,100,0,0.437763," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","\frac{4 i \, b c^{2} d x^{2} \log\left(x\right) - 3 i \, b c^{2} d x^{2} \log\left(\frac{c x + i}{c}\right) - i \, b c^{2} d x^{2} \log\left(\frac{c x - i}{c}\right) + {\left(-4 i \, a - 2 \, b\right)} c d x - 2 \, a d + {\left(2 \, b c d x - i \, b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{2}}"," ",0,"1/4*(4*I*b*c^2*d*x^2*log(x) - 3*I*b*c^2*d*x^2*log((c*x + I)/c) - I*b*c^2*d*x^2*log((c*x - I)/c) + (-4*I*a - 2*b)*c*d*x - 2*a*d + (2*b*c*d*x - I*b*d)*log(-(c*x + I)/(c*x - I)))/x^2","A",0
8,1,111,0,0.444581," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","-\frac{4 \, b c^{3} d x^{3} \log\left(x\right) - 5 \, b c^{3} d x^{3} \log\left(\frac{c x + i}{c}\right) + b c^{3} d x^{3} \log\left(\frac{c x - i}{c}\right) + 6 i \, b c^{2} d x^{2} - {\left(-6 i \, a - 2 \, b\right)} c d x + 4 \, a d - {\left(3 \, b c d x - 2 i \, b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{12 \, x^{3}}"," ",0,"-1/12*(4*b*c^3*d*x^3*log(x) - 5*b*c^3*d*x^3*log((c*x + I)/c) + b*c^3*d*x^3*log((c*x - I)/c) + 6*I*b*c^2*d*x^2 - (-6*I*a - 2*b)*c*d*x + 4*a*d - (3*b*c*d*x - 2*I*b*d)*log(-(c*x + I)/(c*x - I)))/x^3","A",0
9,1,120,0,0.439862," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","\frac{-8 i \, b c^{4} d x^{4} \log\left(x\right) + 7 i \, b c^{4} d x^{4} \log\left(\frac{c x + i}{c}\right) + i \, b c^{4} d x^{4} \log\left(\frac{c x - i}{c}\right) + 6 \, b c^{3} d x^{3} - 4 i \, b c^{2} d x^{2} + {\left(-8 i \, a - 2 \, b\right)} c d x - 6 \, a d + {\left(4 \, b c d x - 3 i \, b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{24 \, x^{4}}"," ",0,"1/24*(-8*I*b*c^4*d*x^4*log(x) + 7*I*b*c^4*d*x^4*log((c*x + I)/c) + I*b*c^4*d*x^4*log((c*x - I)/c) + 6*b*c^3*d*x^3 - 4*I*b*c^2*d*x^2 + (-8*I*a - 2*b)*c*d*x - 6*a*d + (4*b*c*d*x - 3*I*b*d)*log(-(c*x + I)/(c*x - I)))/x^4","A",0
10,1,172,0,0.460285," ","integrate(x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","-\frac{60 \, a c^{6} d^{2} x^{6} - {\left(144 i \, a + 12 \, b\right)} c^{5} d^{2} x^{5} - 18 \, {\left(5 \, a - 2 i \, b\right)} c^{4} d^{2} x^{4} + 50 \, b c^{3} d^{2} x^{3} - 72 i \, b c^{2} d^{2} x^{2} - 150 \, b c d^{2} x + 147 i \, b d^{2} \log\left(\frac{c x + i}{c}\right) - 3 i \, b d^{2} \log\left(\frac{c x - i}{c}\right) - {\left(-30 i \, b c^{6} d^{2} x^{6} - 72 \, b c^{5} d^{2} x^{5} + 45 i \, b c^{4} d^{2} x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{360 \, c^{4}}"," ",0,"-1/360*(60*a*c^6*d^2*x^6 - (144*I*a + 12*b)*c^5*d^2*x^5 - 18*(5*a - 2*I*b)*c^4*d^2*x^4 + 50*b*c^3*d^2*x^3 - 72*I*b*c^2*d^2*x^2 - 150*b*c*d^2*x + 147*I*b*d^2*log((c*x + I)/c) - 3*I*b*d^2*log((c*x - I)/c) - (-30*I*b*c^6*d^2*x^6 - 72*b*c^5*d^2*x^5 + 45*I*b*c^4*d^2*x^4)*log(-(c*x + I)/(c*x - I)))/c^4","A",0
11,1,160,0,0.440804," ","integrate(x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","-\frac{12 \, a c^{5} d^{2} x^{5} - {\left(30 i \, a + 3 \, b\right)} c^{4} d^{2} x^{4} - 10 \, {\left(2 \, a - i \, b\right)} c^{3} d^{2} x^{3} + 16 \, b c^{2} d^{2} x^{2} - 30 i \, b c d^{2} x - 31 \, b d^{2} \log\left(\frac{c x + i}{c}\right) - b d^{2} \log\left(\frac{c x - i}{c}\right) - {\left(-6 i \, b c^{5} d^{2} x^{5} - 15 \, b c^{4} d^{2} x^{4} + 10 i \, b c^{3} d^{2} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, c^{3}}"," ",0,"-1/60*(12*a*c^5*d^2*x^5 - (30*I*a + 3*b)*c^4*d^2*x^4 - 10*(2*a - I*b)*c^3*d^2*x^3 + 16*b*c^2*d^2*x^2 - 30*I*b*c*d^2*x - 31*b*d^2*log((c*x + I)/c) - b*d^2*log((c*x - I)/c) - (-6*I*b*c^5*d^2*x^5 - 15*b*c^4*d^2*x^4 + 10*I*b*c^3*d^2*x^3)*log(-(c*x + I)/(c*x - I)))/c^3","A",0
12,1,148,0,0.455276," ","integrate(x*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","-\frac{6 \, a c^{4} d^{2} x^{4} - {\left(16 i \, a + 2 \, b\right)} c^{3} d^{2} x^{3} - 4 \, {\left(3 \, a - 2 i \, b\right)} c^{2} d^{2} x^{2} + 18 \, b c d^{2} x - 17 i \, b d^{2} \log\left(\frac{c x + i}{c}\right) + i \, b d^{2} \log\left(\frac{c x - i}{c}\right) - {\left(-3 i \, b c^{4} d^{2} x^{4} - 8 \, b c^{3} d^{2} x^{3} + 6 i \, b c^{2} d^{2} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{24 \, c^{2}}"," ",0,"-1/24*(6*a*c^4*d^2*x^4 - (16*I*a + 2*b)*c^3*d^2*x^3 - 4*(3*a - 2*I*b)*c^2*d^2*x^2 + 18*b*c*d^2*x - 17*I*b*d^2*log((c*x + I)/c) + I*b*d^2*log((c*x - I)/c) - (-3*I*b*c^4*d^2*x^4 - 8*b*c^3*d^2*x^3 + 6*I*b*c^2*d^2*x^2)*log(-(c*x + I)/(c*x - I)))/c^2","A",0
13,1,127,0,0.457388," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","-\frac{2 \, a c^{3} d^{2} x^{3} - {\left(6 i \, a + b\right)} c^{2} d^{2} x^{2} - 6 \, {\left(a - i \, b\right)} c d^{2} x + 7 \, b d^{2} \log\left(\frac{c x + i}{c}\right) + b d^{2} \log\left(\frac{c x - i}{c}\right) - {\left(-i \, b c^{3} d^{2} x^{3} - 3 \, b c^{2} d^{2} x^{2} + 3 i \, b c d^{2} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{6 \, c}"," ",0,"-1/6*(2*a*c^3*d^2*x^3 - (6*I*a + b)*c^2*d^2*x^2 - 6*(a - I*b)*c*d^2*x + 7*b*d^2*log((c*x + I)/c) + b*d^2*log((c*x - I)/c) - (-I*b*c^3*d^2*x^3 - 3*b*c^2*d^2*x^2 + 3*I*b*c*d^2*x)*log(-(c*x + I)/(c*x - I)))/c","A",0
14,0,0,0,0.488339," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, a c^{2} d^{2} x^{2} - 4 i \, a c d^{2} x - 2 \, a d^{2} - {\left(-i \, b c^{2} d^{2} x^{2} - 2 \, b c d^{2} x + i \, b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*(2*a*c^2*d^2*x^2 - 4*I*a*c*d^2*x - 2*a*d^2 - (-I*b*c^2*d^2*x^2 - 2*b*c*d^2*x + I*b*d^2)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
15,0,0,0,0.451099," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, a c^{2} d^{2} x^{2} - 4 i \, a c d^{2} x - 2 \, a d^{2} - {\left(-i \, b c^{2} d^{2} x^{2} - 2 \, b c d^{2} x + i \, b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{2}}, x\right)"," ",0,"integral(-1/2*(2*a*c^2*d^2*x^2 - 4*I*a*c*d^2*x - 2*a*d^2 - (-I*b*c^2*d^2*x^2 - 2*b*c*d^2*x + I*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
16,0,0,0,0.421745," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 \, a c^{2} d^{2} x^{2} - 4 i \, a c d^{2} x - 2 \, a d^{2} - {\left(-i \, b c^{2} d^{2} x^{2} - 2 \, b c d^{2} x + i \, b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{3}}, x\right)"," ",0,"integral(-1/2*(2*a*c^2*d^2*x^2 - 4*I*a*c*d^2*x - 2*a*d^2 - (-I*b*c^2*d^2*x^2 - 2*b*c*d^2*x + I*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^3, x)","F",0
17,1,144,0,0.444107," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","-\frac{8 \, b c^{3} d^{2} x^{3} \log\left(x\right) - 7 \, b c^{3} d^{2} x^{3} \log\left(\frac{c x + i}{c}\right) - b c^{3} d^{2} x^{3} \log\left(\frac{c x - i}{c}\right) - 6 \, {\left(a - i \, b\right)} c^{2} d^{2} x^{2} - {\left(-6 i \, a - b\right)} c d^{2} x + 2 \, a d^{2} - {\left(3 i \, b c^{2} d^{2} x^{2} + 3 \, b c d^{2} x - i \, b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{6 \, x^{3}}"," ",0,"-1/6*(8*b*c^3*d^2*x^3*log(x) - 7*b*c^3*d^2*x^3*log((c*x + I)/c) - b*c^3*d^2*x^3*log((c*x - I)/c) - 6*(a - I*b)*c^2*d^2*x^2 - (-6*I*a - b)*c*d^2*x + 2*a*d^2 - (3*I*b*c^2*d^2*x^2 + 3*b*c*d^2*x - I*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^3","A",0
18,1,156,0,0.486392," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","\frac{-16 i \, b c^{4} d^{2} x^{4} \log\left(x\right) + 17 i \, b c^{4} d^{2} x^{4} \log\left(\frac{c x + i}{c}\right) - i \, b c^{4} d^{2} x^{4} \log\left(\frac{c x - i}{c}\right) + 18 \, b c^{3} d^{2} x^{3} + 4 \, {\left(3 \, a - 2 i \, b\right)} c^{2} d^{2} x^{2} + {\left(-16 i \, a - 2 \, b\right)} c d^{2} x - 6 \, a d^{2} + {\left(6 i \, b c^{2} d^{2} x^{2} + 8 \, b c d^{2} x - 3 i \, b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{24 \, x^{4}}"," ",0,"1/24*(-16*I*b*c^4*d^2*x^4*log(x) + 17*I*b*c^4*d^2*x^4*log((c*x + I)/c) - I*b*c^4*d^2*x^4*log((c*x - I)/c) + 18*b*c^3*d^2*x^3 + 4*(3*a - 2*I*b)*c^2*d^2*x^2 + (-16*I*a - 2*b)*c*d^2*x - 6*a*d^2 + (6*I*b*c^2*d^2*x^2 + 8*b*c*d^2*x - 3*I*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^4","A",0
19,1,168,0,0.451103," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","\frac{32 \, b c^{5} d^{2} x^{5} \log\left(x\right) - 31 \, b c^{5} d^{2} x^{5} \log\left(\frac{c x + i}{c}\right) - b c^{5} d^{2} x^{5} \log\left(\frac{c x - i}{c}\right) + 30 i \, b c^{4} d^{2} x^{4} + 16 \, b c^{3} d^{2} x^{3} + 10 \, {\left(2 \, a - i \, b\right)} c^{2} d^{2} x^{2} + {\left(-30 i \, a - 3 \, b\right)} c d^{2} x - 12 \, a d^{2} + {\left(10 i \, b c^{2} d^{2} x^{2} + 15 \, b c d^{2} x - 6 i \, b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, x^{5}}"," ",0,"1/60*(32*b*c^5*d^2*x^5*log(x) - 31*b*c^5*d^2*x^5*log((c*x + I)/c) - b*c^5*d^2*x^5*log((c*x - I)/c) + 30*I*b*c^4*d^2*x^4 + 16*b*c^3*d^2*x^3 + 10*(2*a - I*b)*c^2*d^2*x^2 + (-30*I*a - 3*b)*c*d^2*x - 12*a*d^2 + (10*I*b*c^2*d^2*x^2 + 15*b*c*d^2*x - 6*I*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^5","A",0
20,1,200,0,0.453614," ","integrate(x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{-120 i \, a c^{7} d^{3} x^{7} - 20 \, {\left(21 \, a - i \, b\right)} c^{6} d^{3} x^{6} + {\left(504 i \, a + 84 \, b\right)} c^{5} d^{3} x^{5} + 6 \, {\left(35 \, a - 26 i \, b\right)} c^{4} d^{3} x^{4} - 210 \, b c^{3} d^{3} x^{3} + 312 i \, b c^{2} d^{3} x^{2} + 630 \, b c d^{3} x - 627 i \, b d^{3} \log\left(\frac{c x + i}{c}\right) + 3 i \, b d^{3} \log\left(\frac{c x - i}{c}\right) + {\left(60 \, b c^{7} d^{3} x^{7} - 210 i \, b c^{6} d^{3} x^{6} - 252 \, b c^{5} d^{3} x^{5} + 105 i \, b c^{4} d^{3} x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{840 \, c^{4}}"," ",0,"1/840*(-120*I*a*c^7*d^3*x^7 - 20*(21*a - I*b)*c^6*d^3*x^6 + (504*I*a + 84*b)*c^5*d^3*x^5 + 6*(35*a - 26*I*b)*c^4*d^3*x^4 - 210*b*c^3*d^3*x^3 + 312*I*b*c^2*d^3*x^2 + 630*b*c*d^3*x - 627*I*b*d^3*log((c*x + I)/c) + 3*I*b*d^3*log((c*x - I)/c) + (60*b*c^7*d^3*x^7 - 210*I*b*c^6*d^3*x^6 - 252*b*c^5*d^3*x^5 + 105*I*b*c^4*d^3*x^4)*log(-(c*x + I)/(c*x - I)))/c^4","A",0
21,1,188,0,0.437655," ","integrate(x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{-60 i \, a c^{6} d^{3} x^{6} - 12 \, {\left(18 \, a - i \, b\right)} c^{5} d^{3} x^{5} + {\left(270 i \, a + 54 \, b\right)} c^{4} d^{3} x^{4} + 10 \, {\left(12 \, a - 11 i \, b\right)} c^{3} d^{3} x^{3} - 168 \, b c^{2} d^{3} x^{2} + 330 i \, b c d^{3} x + 333 \, b d^{3} \log\left(\frac{c x + i}{c}\right) + 3 \, b d^{3} \log\left(\frac{c x - i}{c}\right) + {\left(30 \, b c^{6} d^{3} x^{6} - 108 i \, b c^{5} d^{3} x^{5} - 135 \, b c^{4} d^{3} x^{4} + 60 i \, b c^{3} d^{3} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{360 \, c^{3}}"," ",0,"1/360*(-60*I*a*c^6*d^3*x^6 - 12*(18*a - I*b)*c^5*d^3*x^5 + (270*I*a + 54*b)*c^4*d^3*x^4 + 10*(12*a - 11*I*b)*c^3*d^3*x^3 - 168*b*c^2*d^3*x^2 + 330*I*b*c*d^3*x + 333*b*d^3*log((c*x + I)/c) + 3*b*d^3*log((c*x - I)/c) + (30*b*c^6*d^3*x^6 - 108*I*b*c^5*d^3*x^5 - 135*b*c^4*d^3*x^4 + 60*I*b*c^3*d^3*x^3)*log(-(c*x + I)/(c*x - I)))/c^3","A",0
22,1,176,0,0.443325," ","integrate(x*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{-8 i \, a c^{5} d^{3} x^{5} - 2 \, {\left(15 \, a - i \, b\right)} c^{4} d^{3} x^{4} + {\left(40 i \, a + 10 \, b\right)} c^{3} d^{3} x^{3} + 4 \, {\left(5 \, a - 6 i \, b\right)} c^{2} d^{3} x^{2} - 50 \, b c d^{3} x + 49 i \, b d^{3} \log\left(\frac{c x + i}{c}\right) - i \, b d^{3} \log\left(\frac{c x - i}{c}\right) + {\left(4 \, b c^{5} d^{3} x^{5} - 15 i \, b c^{4} d^{3} x^{4} - 20 \, b c^{3} d^{3} x^{3} + 10 i \, b c^{2} d^{3} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{40 \, c^{2}}"," ",0,"1/40*(-8*I*a*c^5*d^3*x^5 - 2*(15*a - I*b)*c^4*d^3*x^4 + (40*I*a + 10*b)*c^3*d^3*x^3 + 4*(5*a - 6*I*b)*c^2*d^3*x^2 - 50*b*c*d^3*x + 49*I*b*d^3*log((c*x + I)/c) - I*b*d^3*log((c*x - I)/c) + (4*b*c^5*d^3*x^5 - 15*I*b*c^4*d^3*x^4 - 20*b*c^3*d^3*x^3 + 10*I*b*c^2*d^3*x^2)*log(-(c*x + I)/(c*x - I)))/c^2","A",0
23,1,160,0,0.432595," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{-6 i \, a c^{4} d^{3} x^{4} - 2 \, {\left(12 \, a - i \, b\right)} c^{3} d^{3} x^{3} + {\left(36 i \, a + 12 \, b\right)} c^{2} d^{3} x^{2} + 6 \, {\left(4 \, a - 7 i \, b\right)} c d^{3} x - 45 \, b d^{3} \log\left(\frac{c x + i}{c}\right) - 3 \, b d^{3} \log\left(\frac{c x - i}{c}\right) + {\left(3 \, b c^{4} d^{3} x^{4} - 12 i \, b c^{3} d^{3} x^{3} - 18 \, b c^{2} d^{3} x^{2} + 12 i \, b c d^{3} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{24 \, c}"," ",0,"1/24*(-6*I*a*c^4*d^3*x^4 - 2*(12*a - I*b)*c^3*d^3*x^3 + (36*I*a + 12*b)*c^2*d^3*x^2 + 6*(4*a - 7*I*b)*c*d^3*x - 45*b*d^3*log((c*x + I)/c) - 3*b*d^3*log((c*x - I)/c) + (3*b*c^4*d^3*x^4 - 12*I*b*c^3*d^3*x^3 - 18*b*c^2*d^3*x^2 + 12*I*b*c*d^3*x)*log(-(c*x + I)/(c*x - I)))/c","A",0
24,0,0,0,0.433960," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-2 i \, a c^{3} d^{3} x^{3} - 6 \, a c^{2} d^{3} x^{2} + 6 i \, a c d^{3} x + 2 \, a d^{3} + {\left(b c^{3} d^{3} x^{3} - 3 i \, b c^{2} d^{3} x^{2} - 3 \, b c d^{3} x + i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*(-2*I*a*c^3*d^3*x^3 - 6*a*c^2*d^3*x^2 + 6*I*a*c*d^3*x + 2*a*d^3 + (b*c^3*d^3*x^3 - 3*I*b*c^2*d^3*x^2 - 3*b*c*d^3*x + I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
25,0,0,0,0.612021," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-2 i \, a c^{3} d^{3} x^{3} - 6 \, a c^{2} d^{3} x^{2} + 6 i \, a c d^{3} x + 2 \, a d^{3} + {\left(b c^{3} d^{3} x^{3} - 3 i \, b c^{2} d^{3} x^{2} - 3 \, b c d^{3} x + i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{2}}, x\right)"," ",0,"integral(1/2*(-2*I*a*c^3*d^3*x^3 - 6*a*c^2*d^3*x^2 + 6*I*a*c*d^3*x + 2*a*d^3 + (b*c^3*d^3*x^3 - 3*I*b*c^2*d^3*x^2 - 3*b*c*d^3*x + I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
26,0,0,0,0.576315," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-2 i \, a c^{3} d^{3} x^{3} - 6 \, a c^{2} d^{3} x^{2} + 6 i \, a c d^{3} x + 2 \, a d^{3} + {\left(b c^{3} d^{3} x^{3} - 3 i \, b c^{2} d^{3} x^{2} - 3 \, b c d^{3} x + i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{3}}, x\right)"," ",0,"integral(1/2*(-2*I*a*c^3*d^3*x^3 - 6*a*c^2*d^3*x^2 + 6*I*a*c*d^3*x + 2*a*d^3 + (b*c^3*d^3*x^3 - 3*I*b*c^2*d^3*x^2 - 3*b*c*d^3*x + I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^3, x)","F",0
27,0,0,0,0.460957," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-2 i \, a c^{3} d^{3} x^{3} - 6 \, a c^{2} d^{3} x^{2} + 6 i \, a c d^{3} x + 2 \, a d^{3} + {\left(b c^{3} d^{3} x^{3} - 3 i \, b c^{2} d^{3} x^{2} - 3 \, b c d^{3} x + i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{4}}, x\right)"," ",0,"integral(1/2*(-2*I*a*c^3*d^3*x^3 - 6*a*c^2*d^3*x^2 + 6*I*a*c*d^3*x + 2*a*d^3 + (b*c^3*d^3*x^3 - 3*I*b*c^2*d^3*x^2 - 3*b*c*d^3*x + I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^4, x)","F",0
28,1,174,0,0.494903," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","\frac{-48 i \, b c^{4} d^{3} x^{4} \log\left(x\right) + 45 i \, b c^{4} d^{3} x^{4} \log\left(\frac{c x + i}{c}\right) + 3 i \, b c^{4} d^{3} x^{4} \log\left(\frac{c x - i}{c}\right) + {\left(24 i \, a + 42 \, b\right)} c^{3} d^{3} x^{3} + 12 \, {\left(3 \, a - i \, b\right)} c^{2} d^{3} x^{2} + {\left(-24 i \, a - 2 \, b\right)} c d^{3} x - 6 \, a d^{3} - {\left(12 \, b c^{3} d^{3} x^{3} - 18 i \, b c^{2} d^{3} x^{2} - 12 \, b c d^{3} x + 3 i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{24 \, x^{4}}"," ",0,"1/24*(-48*I*b*c^4*d^3*x^4*log(x) + 45*I*b*c^4*d^3*x^4*log((c*x + I)/c) + 3*I*b*c^4*d^3*x^4*log((c*x - I)/c) + (24*I*a + 42*b)*c^3*d^3*x^3 + 12*(3*a - I*b)*c^2*d^3*x^2 + (-24*I*a - 2*b)*c*d^3*x - 6*a*d^3 - (12*b*c^3*d^3*x^3 - 18*I*b*c^2*d^3*x^2 - 12*b*c*d^3*x + 3*I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^4","B",0
29,1,185,0,0.531261," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","\frac{48 \, b c^{5} d^{3} x^{5} \log\left(x\right) - 49 \, b c^{5} d^{3} x^{5} \log\left(\frac{c x + i}{c}\right) + b c^{5} d^{3} x^{5} \log\left(\frac{c x - i}{c}\right) + 50 i \, b c^{4} d^{3} x^{4} + {\left(20 i \, a + 24 \, b\right)} c^{3} d^{3} x^{3} + 10 \, {\left(4 \, a - i \, b\right)} c^{2} d^{3} x^{2} + {\left(-30 i \, a - 2 \, b\right)} c d^{3} x - 8 \, a d^{3} - {\left(10 \, b c^{3} d^{3} x^{3} - 20 i \, b c^{2} d^{3} x^{2} - 15 \, b c d^{3} x + 4 i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{40 \, x^{5}}"," ",0,"1/40*(48*b*c^5*d^3*x^5*log(x) - 49*b*c^5*d^3*x^5*log((c*x + I)/c) + b*c^5*d^3*x^5*log((c*x - I)/c) + 50*I*b*c^4*d^3*x^4 + (20*I*a + 24*b)*c^3*d^3*x^3 + 10*(4*a - I*b)*c^2*d^3*x^2 + (-30*I*a - 2*b)*c*d^3*x - 8*a*d^3 - (10*b*c^3*d^3*x^3 - 20*I*b*c^2*d^3*x^2 - 15*b*c*d^3*x + 4*I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^5","A",0
30,1,198,0,0.546470," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^7,x, algorithm=""fricas"")","\frac{336 i \, b c^{6} d^{3} x^{6} \log\left(x\right) - 333 i \, b c^{6} d^{3} x^{6} \log\left(\frac{c x + i}{c}\right) - 3 i \, b c^{6} d^{3} x^{6} \log\left(\frac{c x - i}{c}\right) - 330 \, b c^{5} d^{3} x^{5} + 168 i \, b c^{4} d^{3} x^{4} + {\left(120 i \, a + 110 \, b\right)} c^{3} d^{3} x^{3} + 54 \, {\left(5 \, a - i \, b\right)} c^{2} d^{3} x^{2} + {\left(-216 i \, a - 12 \, b\right)} c d^{3} x - 60 \, a d^{3} - {\left(60 \, b c^{3} d^{3} x^{3} - 135 i \, b c^{2} d^{3} x^{2} - 108 \, b c d^{3} x + 30 i \, b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{360 \, x^{6}}"," ",0,"1/360*(336*I*b*c^6*d^3*x^6*log(x) - 333*I*b*c^6*d^3*x^6*log((c*x + I)/c) - 3*I*b*c^6*d^3*x^6*log((c*x - I)/c) - 330*b*c^5*d^3*x^5 + 168*I*b*c^4*d^3*x^4 + (120*I*a + 110*b)*c^3*d^3*x^3 + 54*(5*a - I*b)*c^2*d^3*x^2 + (-216*I*a - 12*b)*c*d^3*x - 60*a*d^3 - (60*b*c^3*d^3*x^3 - 135*I*b*c^2*d^3*x^2 - 108*b*c*d^3*x + 30*I*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^6","A",0
31,1,229,0,0.501166," ","integrate(x^3*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{210 \, a c^{8} d^{4} x^{8} + {\left(-960 i \, a - 30 \, b\right)} c^{7} d^{4} x^{7} - 80 \, {\left(21 \, a - 2 i \, b\right)} c^{6} d^{4} x^{6} + {\left(1344 i \, a + 378 \, b\right)} c^{5} d^{4} x^{5} + 12 \, {\left(35 \, a - 48 i \, b\right)} c^{4} d^{4} x^{4} - 770 \, b c^{3} d^{4} x^{3} + 1152 i \, b c^{2} d^{4} x^{2} + 2310 \, b c d^{4} x - 2307 i \, b d^{4} \log\left(\frac{c x + i}{c}\right) + 3 i \, b d^{4} \log\left(\frac{c x - i}{c}\right) + {\left(105 i \, b c^{8} d^{4} x^{8} + 480 \, b c^{7} d^{4} x^{7} - 840 i \, b c^{6} d^{4} x^{6} - 672 \, b c^{5} d^{4} x^{5} + 210 i \, b c^{4} d^{4} x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{1680 \, c^{4}}"," ",0,"1/1680*(210*a*c^8*d^4*x^8 + (-960*I*a - 30*b)*c^7*d^4*x^7 - 80*(21*a - 2*I*b)*c^6*d^4*x^6 + (1344*I*a + 378*b)*c^5*d^4*x^5 + 12*(35*a - 48*I*b)*c^4*d^4*x^4 - 770*b*c^3*d^4*x^3 + 1152*I*b*c^2*d^4*x^2 + 2310*b*c*d^4*x - 2307*I*b*d^4*log((c*x + I)/c) + 3*I*b*d^4*log((c*x - I)/c) + (105*I*b*c^8*d^4*x^8 + 480*b*c^7*d^4*x^7 - 840*I*b*c^6*d^4*x^6 - 672*b*c^5*d^4*x^5 + 210*I*b*c^4*d^4*x^4)*log(-(c*x + I)/(c*x - I)))/c^4","A",0
32,1,217,0,0.453434," ","integrate(x^2*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{180 \, a c^{7} d^{4} x^{7} + {\left(-840 i \, a - 30 \, b\right)} c^{6} d^{4} x^{6} - 168 \, {\left(9 \, a - i \, b\right)} c^{5} d^{4} x^{5} + {\left(1260 i \, a + 423 \, b\right)} c^{4} d^{4} x^{4} + 140 \, {\left(3 \, a - 5 i \, b\right)} c^{3} d^{4} x^{3} - 1056 \, b c^{2} d^{4} x^{2} + 2100 i \, b c d^{4} x + 2106 \, b d^{4} \log\left(\frac{c x + i}{c}\right) + 6 \, b d^{4} \log\left(\frac{c x - i}{c}\right) + {\left(90 i \, b c^{7} d^{4} x^{7} + 420 \, b c^{6} d^{4} x^{6} - 756 i \, b c^{5} d^{4} x^{5} - 630 \, b c^{4} d^{4} x^{4} + 210 i \, b c^{3} d^{4} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{1260 \, c^{3}}"," ",0,"1/1260*(180*a*c^7*d^4*x^7 + (-840*I*a - 30*b)*c^6*d^4*x^6 - 168*(9*a - I*b)*c^5*d^4*x^5 + (1260*I*a + 423*b)*c^4*d^4*x^4 + 140*(3*a - 5*I*b)*c^3*d^4*x^3 - 1056*b*c^2*d^4*x^2 + 2100*I*b*c*d^4*x + 2106*b*d^4*log((c*x + I)/c) + 6*b*d^4*log((c*x - I)/c) + (90*I*b*c^7*d^4*x^7 + 420*b*c^6*d^4*x^6 - 756*I*b*c^5*d^4*x^5 - 630*b*c^4*d^4*x^4 + 210*I*b*c^3*d^4*x^3)*log(-(c*x + I)/(c*x - I)))/c^3","A",0
33,1,205,0,1.362159," ","integrate(x*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{30 \, a c^{6} d^{4} x^{6} + {\left(-144 i \, a - 6 \, b\right)} c^{5} d^{4} x^{5} - 18 \, {\left(15 \, a - 2 i \, b\right)} c^{4} d^{4} x^{4} + {\left(240 i \, a + 100 \, b\right)} c^{3} d^{4} x^{3} + 6 \, {\left(15 \, a - 32 i \, b\right)} c^{2} d^{4} x^{2} - 390 \, b c d^{4} x + 387 i \, b d^{4} \log\left(\frac{c x + i}{c}\right) - 3 i \, b d^{4} \log\left(\frac{c x - i}{c}\right) + {\left(15 i \, b c^{6} d^{4} x^{6} + 72 \, b c^{5} d^{4} x^{5} - 135 i \, b c^{4} d^{4} x^{4} - 120 \, b c^{3} d^{4} x^{3} + 45 i \, b c^{2} d^{4} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{180 \, c^{2}}"," ",0,"1/180*(30*a*c^6*d^4*x^6 + (-144*I*a - 6*b)*c^5*d^4*x^5 - 18*(15*a - 2*I*b)*c^4*d^4*x^4 + (240*I*a + 100*b)*c^3*d^4*x^3 + 6*(15*a - 32*I*b)*c^2*d^4*x^2 - 390*b*c*d^4*x + 387*I*b*d^4*log((c*x + I)/c) - 3*I*b*d^4*log((c*x - I)/c) + (15*I*b*c^6*d^4*x^6 + 72*b*c^5*d^4*x^5 - 135*I*b*c^4*d^4*x^4 - 120*b*c^3*d^4*x^3 + 45*I*b*c^2*d^4*x^2)*log(-(c*x + I)/(c*x - I)))/c^2","A",0
34,1,187,0,0.613869," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{12 \, a c^{5} d^{4} x^{5} + {\left(-60 i \, a - 3 \, b\right)} c^{4} d^{4} x^{4} - 20 \, {\left(6 \, a - i \, b\right)} c^{3} d^{4} x^{3} + {\left(120 i \, a + 66 \, b\right)} c^{2} d^{4} x^{2} + 60 \, {\left(a - 3 i \, b\right)} c d^{4} x - 186 \, b d^{4} \log\left(\frac{c x + i}{c}\right) - 6 \, b d^{4} \log\left(\frac{c x - i}{c}\right) + {\left(6 i \, b c^{5} d^{4} x^{5} + 30 \, b c^{4} d^{4} x^{4} - 60 i \, b c^{3} d^{4} x^{3} - 60 \, b c^{2} d^{4} x^{2} + 30 i \, b c d^{4} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, c}"," ",0,"1/60*(12*a*c^5*d^4*x^5 + (-60*I*a - 3*b)*c^4*d^4*x^4 - 20*(6*a - I*b)*c^3*d^4*x^3 + (120*I*a + 66*b)*c^2*d^4*x^2 + 60*(a - 3*I*b)*c*d^4*x - 186*b*d^4*log((c*x + I)/c) - 6*b*d^4*log((c*x - I)/c) + (6*I*b*c^5*d^4*x^5 + 30*b*c^4*d^4*x^4 - 60*I*b*c^3*d^4*x^3 - 60*b*c^2*d^4*x^2 + 30*I*b*c*d^4*x)*log(-(c*x + I)/(c*x - I)))/c","A",0
35,0,0,0,0.474529," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a c^{4} d^{4} x^{4} - 8 i \, a c^{3} d^{4} x^{3} - 12 \, a c^{2} d^{4} x^{2} + 8 i \, a c d^{4} x + 2 \, a d^{4} + {\left(i \, b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} - 6 i \, b c^{2} d^{4} x^{2} - 4 \, b c d^{4} x + i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*(2*a*c^4*d^4*x^4 - 8*I*a*c^3*d^4*x^3 - 12*a*c^2*d^4*x^2 + 8*I*a*c*d^4*x + 2*a*d^4 + (I*b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 - 6*I*b*c^2*d^4*x^2 - 4*b*c*d^4*x + I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
36,0,0,0,0.462571," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a c^{4} d^{4} x^{4} - 8 i \, a c^{3} d^{4} x^{3} - 12 \, a c^{2} d^{4} x^{2} + 8 i \, a c d^{4} x + 2 \, a d^{4} + {\left(i \, b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} - 6 i \, b c^{2} d^{4} x^{2} - 4 \, b c d^{4} x + i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{2}}, x\right)"," ",0,"integral(1/2*(2*a*c^4*d^4*x^4 - 8*I*a*c^3*d^4*x^3 - 12*a*c^2*d^4*x^2 + 8*I*a*c*d^4*x + 2*a*d^4 + (I*b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 - 6*I*b*c^2*d^4*x^2 - 4*b*c*d^4*x + I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
37,0,0,0,0.449665," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a c^{4} d^{4} x^{4} - 8 i \, a c^{3} d^{4} x^{3} - 12 \, a c^{2} d^{4} x^{2} + 8 i \, a c d^{4} x + 2 \, a d^{4} + {\left(i \, b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} - 6 i \, b c^{2} d^{4} x^{2} - 4 \, b c d^{4} x + i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{3}}, x\right)"," ",0,"integral(1/2*(2*a*c^4*d^4*x^4 - 8*I*a*c^3*d^4*x^3 - 12*a*c^2*d^4*x^2 + 8*I*a*c*d^4*x + 2*a*d^4 + (I*b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 - 6*I*b*c^2*d^4*x^2 - 4*b*c*d^4*x + I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^3, x)","F",0
38,0,0,0,0.441341," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a c^{4} d^{4} x^{4} - 8 i \, a c^{3} d^{4} x^{3} - 12 \, a c^{2} d^{4} x^{2} + 8 i \, a c d^{4} x + 2 \, a d^{4} + {\left(i \, b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} - 6 i \, b c^{2} d^{4} x^{2} - 4 \, b c d^{4} x + i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{4}}, x\right)"," ",0,"integral(1/2*(2*a*c^4*d^4*x^4 - 8*I*a*c^3*d^4*x^3 - 12*a*c^2*d^4*x^2 + 8*I*a*c*d^4*x + 2*a*d^4 + (I*b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 - 6*I*b*c^2*d^4*x^2 - 4*b*c*d^4*x + I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^4, x)","F",0
39,0,0,0,0.439851," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a c^{4} d^{4} x^{4} - 8 i \, a c^{3} d^{4} x^{3} - 12 \, a c^{2} d^{4} x^{2} + 8 i \, a c d^{4} x + 2 \, a d^{4} + {\left(i \, b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} - 6 i \, b c^{2} d^{4} x^{2} - 4 \, b c d^{4} x + i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, x^{5}}, x\right)"," ",0,"integral(1/2*(2*a*c^4*d^4*x^4 - 8*I*a*c^3*d^4*x^3 - 12*a*c^2*d^4*x^2 + 8*I*a*c*d^4*x + 2*a*d^4 + (I*b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 - 6*I*b*c^2*d^4*x^2 - 4*b*c*d^4*x + I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^5, x)","F",0
40,1,201,0,0.508391," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","\frac{192 \, b c^{5} d^{4} x^{5} \log\left(x\right) - 186 \, b c^{5} d^{4} x^{5} \log\left(\frac{c x + i}{c}\right) - 6 \, b c^{5} d^{4} x^{5} \log\left(\frac{c x - i}{c}\right) - 60 \, {\left(a - 3 i \, b\right)} c^{4} d^{4} x^{4} + {\left(120 i \, a + 66 \, b\right)} c^{3} d^{4} x^{3} + 20 \, {\left(6 \, a - i \, b\right)} c^{2} d^{4} x^{2} + {\left(-60 i \, a - 3 \, b\right)} c d^{4} x - 12 \, a d^{4} + {\left(-30 i \, b c^{4} d^{4} x^{4} - 60 \, b c^{3} d^{4} x^{3} + 60 i \, b c^{2} d^{4} x^{2} + 30 \, b c d^{4} x - 6 i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, x^{5}}"," ",0,"1/60*(192*b*c^5*d^4*x^5*log(x) - 186*b*c^5*d^4*x^5*log((c*x + I)/c) - 6*b*c^5*d^4*x^5*log((c*x - I)/c) - 60*(a - 3*I*b)*c^4*d^4*x^4 + (120*I*a + 66*b)*c^3*d^4*x^3 + 20*(6*a - I*b)*c^2*d^4*x^2 + (-60*I*a - 3*b)*c*d^4*x - 12*a*d^4 + (-30*I*b*c^4*d^4*x^4 - 60*b*c^3*d^4*x^3 + 60*I*b*c^2*d^4*x^2 + 30*b*c*d^4*x - 6*I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^5","B",0
41,1,215,0,0.463753," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^7,x, algorithm=""fricas"")","\frac{384 i \, b c^{6} d^{4} x^{6} \log\left(x\right) - 387 i \, b c^{6} d^{4} x^{6} \log\left(\frac{c x + i}{c}\right) + 3 i \, b c^{6} d^{4} x^{6} \log\left(\frac{c x - i}{c}\right) - 390 \, b c^{5} d^{4} x^{5} - 6 \, {\left(15 \, a - 32 i \, b\right)} c^{4} d^{4} x^{4} + {\left(240 i \, a + 100 \, b\right)} c^{3} d^{4} x^{3} + 18 \, {\left(15 \, a - 2 i \, b\right)} c^{2} d^{4} x^{2} + {\left(-144 i \, a - 6 \, b\right)} c d^{4} x - 30 \, a d^{4} + {\left(-45 i \, b c^{4} d^{4} x^{4} - 120 \, b c^{3} d^{4} x^{3} + 135 i \, b c^{2} d^{4} x^{2} + 72 \, b c d^{4} x - 15 i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{180 \, x^{6}}"," ",0,"1/180*(384*I*b*c^6*d^4*x^6*log(x) - 387*I*b*c^6*d^4*x^6*log((c*x + I)/c) + 3*I*b*c^6*d^4*x^6*log((c*x - I)/c) - 390*b*c^5*d^4*x^5 - 6*(15*a - 32*I*b)*c^4*d^4*x^4 + (240*I*a + 100*b)*c^3*d^4*x^3 + 18*(15*a - 2*I*b)*c^2*d^4*x^2 + (-144*I*a - 6*b)*c*d^4*x - 30*a*d^4 + (-45*I*b*c^4*d^4*x^4 - 120*b*c^3*d^4*x^3 + 135*I*b*c^2*d^4*x^2 + 72*b*c*d^4*x - 15*I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^6","A",0
42,1,230,0,0.540289," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^8,x, algorithm=""fricas"")","-\frac{2112 \, b c^{7} d^{4} x^{7} \log\left(x\right) - 2106 \, b c^{7} d^{4} x^{7} \log\left(\frac{c x + i}{c}\right) - 6 \, b c^{7} d^{4} x^{7} \log\left(\frac{c x - i}{c}\right) + 2100 i \, b c^{6} d^{4} x^{6} + 1056 \, b c^{5} d^{4} x^{5} + 140 \, {\left(3 \, a - 5 i \, b\right)} c^{4} d^{4} x^{4} - {\left(1260 i \, a + 423 \, b\right)} c^{3} d^{4} x^{3} - 168 \, {\left(9 \, a - i \, b\right)} c^{2} d^{4} x^{2} - {\left(-840 i \, a - 30 \, b\right)} c d^{4} x + 180 \, a d^{4} - {\left(-210 i \, b c^{4} d^{4} x^{4} - 630 \, b c^{3} d^{4} x^{3} + 756 i \, b c^{2} d^{4} x^{2} + 420 \, b c d^{4} x - 90 i \, b d^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{1260 \, x^{7}}"," ",0,"-1/1260*(2112*b*c^7*d^4*x^7*log(x) - 2106*b*c^7*d^4*x^7*log((c*x + I)/c) - 6*b*c^7*d^4*x^7*log((c*x - I)/c) + 2100*I*b*c^6*d^4*x^6 + 1056*b*c^5*d^4*x^5 + 140*(3*a - 5*I*b)*c^4*d^4*x^4 - (1260*I*a + 423*b)*c^3*d^4*x^3 - 168*(9*a - I*b)*c^2*d^4*x^2 - (-840*I*a - 30*b)*c*d^4*x + 180*a*d^4 - (-210*I*b*c^4*d^4*x^4 - 630*b*c^3*d^4*x^3 + 756*I*b*c^2*d^4*x^2 + 420*b*c*d^4*x - 90*I*b*d^4)*log(-(c*x + I)/(c*x - I)))/x^7","A",0
43,0,0,0,0.430433," ","integrate(x^3*(a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a x^{3}}{2 \, c d x - 2 i \, d}, x\right)"," ",0,"integral((b*x^3*log(-(c*x + I)/(c*x - I)) - 2*I*a*x^3)/(2*c*d*x - 2*I*d), x)","F",0
44,0,0,0,0.485316," ","integrate(x^2*(a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a x^{2}}{2 \, c d x - 2 i \, d}, x\right)"," ",0,"integral((b*x^2*log(-(c*x + I)/(c*x - I)) - 2*I*a*x^2)/(2*c*d*x - 2*I*d), x)","F",0
45,0,0,0,0.530230," ","integrate(x*(a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a x}{2 \, c d x - 2 i \, d}, x\right)"," ",0,"integral((b*x*log(-(c*x + I)/(c*x - I)) - 2*I*a*x)/(2*c*d*x - 2*I*d), x)","F",0
46,0,0,0,0.507551," ","integrate((a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c d x - 2 i \, d}, x\right)"," ",0,"integral((b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c*d*x - 2*I*d), x)","F",0
47,1,43,0,0.552806," ","integrate((a+b*arctan(c*x))/x/(d+I*c*d*x),x, algorithm=""fricas"")","\frac{-i \, b {\rm Li}_2\left(\frac{c x + i}{c x - i} + 1\right) + 2 \, a \log\left(x\right) - 2 \, a \log\left(\frac{c x - i}{c}\right)}{2 \, d}"," ",0,"1/2*(-I*b*dilog((c*x + I)/(c*x - I) + 1) + 2*a*log(x) - 2*a*log((c*x - I)/c))/d","A",0
48,0,0,0,0.525807," ","integrate((a+b*arctan(c*x))/x^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c d x^{3} - 2 i \, d x^{2}}, x\right)"," ",0,"integral((b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c*d*x^3 - 2*I*d*x^2), x)","F",0
49,0,0,0,0.533749," ","integrate((a+b*arctan(c*x))/x^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c d x^{4} - 2 i \, d x^{3}}, x\right)"," ",0,"integral((b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c*d*x^4 - 2*I*d*x^3), x)","F",0
50,0,0,0,0.474136," ","integrate((a+b*arctan(c*x))/x^4/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c d x^{5} - 2 i \, d x^{4}}, x\right)"," ",0,"integral((b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c*d*x^5 - 2*I*d*x^4), x)","F",0
51,0,0,0,0.427713," ","integrate(x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b x^{3} \log\left(-\frac{c x + i}{c x - i}\right) - 2 \, a x^{3}}{2 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/2*(-I*b*x^3*log(-(c*x + I)/(c*x - I)) - 2*a*x^3)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
52,0,0,0,0.437702," ","integrate(x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) - 2 \, a x^{2}}{2 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/2*(-I*b*x^2*log(-(c*x + I)/(c*x - I)) - 2*a*x^2)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
53,0,0,0,0.423524," ","integrate(x*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b x \log\left(-\frac{c x + i}{c x - i}\right) - 2 \, a x}{2 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/2*(-I*b*x*log(-(c*x + I)/(c*x - I)) - 2*a*x)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
54,1,50,0,0.485059," ","integrate((a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""fricas"")","\frac{{\left(b c x + i \, b\right)} \log\left(-\frac{c x + i}{c x - i}\right) + 4 \, a - 2 i \, b}{4 \, c^{2} d^{2} x - 4 i \, c d^{2}}"," ",0,"((b*c*x + I*b)*log(-(c*x + I)/(c*x - I)) + 4*a - 2*I*b)/(4*c^2*d^2*x - 4*I*c*d^2)","A",0
55,0,0,0,0.434056," ","integrate((a+b*arctan(c*x))/x/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b \log\left(-\frac{c x + i}{c x - i}\right) - 2 \, a}{2 \, {\left(c^{2} d^{2} x^{3} - 2 i \, c d^{2} x^{2} - d^{2} x\right)}}, x\right)"," ",0,"integral(1/2*(-I*b*log(-(c*x + I)/(c*x - I)) - 2*a)/(c^2*d^2*x^3 - 2*I*c*d^2*x^2 - d^2*x), x)","F",0
56,0,0,0,0.463588," ","integrate((a+b*arctan(c*x))/x^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b \log\left(-\frac{c x + i}{c x - i}\right) - 2 \, a}{2 \, {\left(c^{2} d^{2} x^{4} - 2 i \, c d^{2} x^{3} - d^{2} x^{2}\right)}}, x\right)"," ",0,"integral(1/2*(-I*b*log(-(c*x + I)/(c*x - I)) - 2*a)/(c^2*d^2*x^4 - 2*I*c*d^2*x^3 - d^2*x^2), x)","F",0
57,0,0,0,0.432486," ","integrate((a+b*arctan(c*x))/x^3/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b \log\left(-\frac{c x + i}{c x - i}\right) - 2 \, a}{2 \, {\left(c^{2} d^{2} x^{5} - 2 i \, c d^{2} x^{4} - d^{2} x^{3}\right)}}, x\right)"," ",0,"integral(1/2*(-I*b*log(-(c*x + I)/(c*x - I)) - 2*a)/(c^2*d^2*x^5 - 2*I*c*d^2*x^4 - d^2*x^3), x)","F",0
58,0,0,0,0.477823," ","integrate(x^4*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{4} \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a x^{4}}{2 \, c^{3} d^{3} x^{3} - 6 i \, c^{2} d^{3} x^{2} - 6 \, c d^{3} x + 2 i \, d^{3}}, x\right)"," ",0,"integral(-(b*x^4*log(-(c*x + I)/(c*x - I)) - 2*I*a*x^4)/(2*c^3*d^3*x^3 - 6*I*c^2*d^3*x^2 - 6*c*d^3*x + 2*I*d^3), x)","F",0
59,0,0,0,0.437099," ","integrate(x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{3} \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a x^{3}}{2 \, c^{3} d^{3} x^{3} - 6 i \, c^{2} d^{3} x^{2} - 6 \, c d^{3} x + 2 i \, d^{3}}, x\right)"," ",0,"integral(-(b*x^3*log(-(c*x + I)/(c*x - I)) - 2*I*a*x^3)/(2*c^3*d^3*x^3 - 6*I*c^2*d^3*x^2 - 6*c*d^3*x + 2*I*d^3), x)","F",0
60,0,0,0,0.494052," ","integrate(x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a x^{2}}{2 \, c^{3} d^{3} x^{3} - 6 i \, c^{2} d^{3} x^{2} - 6 \, c d^{3} x + 2 i \, d^{3}}, x\right)"," ",0,"integral(-(b*x^2*log(-(c*x + I)/(c*x - I)) - 2*I*a*x^2)/(2*c^3*d^3*x^3 - 6*I*c^2*d^3*x^2 - 6*c*d^3*x + 2*I*d^3), x)","F",0
61,1,83,0,0.605036," ","integrate(x*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""fricas"")","\frac{{\left(-16 i \, a - 6 \, b\right)} c x + {\left(-3 i \, b c^{2} x^{2} + 2 \, b c x - i \, b\right)} \log\left(-\frac{c x + i}{c x - i}\right) - 8 \, a + 4 i \, b}{16 \, {\left(c^{4} d^{3} x^{2} - 2 i \, c^{3} d^{3} x - c^{2} d^{3}\right)}}"," ",0,"1/16*((-16*I*a - 6*b)*c*x + (-3*I*b*c^2*x^2 + 2*b*c*x - I*b)*log(-(c*x + I)/(c*x - I)) - 8*a + 4*I*b)/(c^4*d^3*x^2 - 2*I*c^3*d^3*x - c^2*d^3)","A",0
62,1,75,0,0.469767," ","integrate((a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""fricas"")","\frac{-2 i \, b c x + {\left(b c^{2} x^{2} - 2 i \, b c x + 3 \, b\right)} \log\left(-\frac{c x + i}{c x - i}\right) - 8 i \, a - 4 \, b}{16 \, {\left(c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}\right)}}"," ",0,"1/16*(-2*I*b*c*x + (b*c^2*x^2 - 2*I*b*c*x + 3*b)*log(-(c*x + I)/(c*x - I)) - 8*I*a - 4*b)/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3)","A",0
63,0,0,0,0.474251," ","integrate((a+b*arctan(c*x))/x/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c^{3} d^{3} x^{4} - 6 i \, c^{2} d^{3} x^{3} - 6 \, c d^{3} x^{2} + 2 i \, d^{3} x}, x\right)"," ",0,"integral(-(b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c^3*d^3*x^4 - 6*I*c^2*d^3*x^3 - 6*c*d^3*x^2 + 2*I*d^3*x), x)","F",0
64,0,0,0,0.453385," ","integrate((a+b*arctan(c*x))/x^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c^{3} d^{3} x^{5} - 6 i \, c^{2} d^{3} x^{4} - 6 \, c d^{3} x^{3} + 2 i \, d^{3} x^{2}}, x\right)"," ",0,"integral(-(b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c^3*d^3*x^5 - 6*I*c^2*d^3*x^4 - 6*c*d^3*x^3 + 2*I*d^3*x^2), x)","F",0
65,0,0,0,0.427509," ","integrate((a+b*arctan(c*x))/x^3/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \log\left(-\frac{c x + i}{c x - i}\right) - 2 i \, a}{2 \, c^{3} d^{3} x^{6} - 6 i \, c^{2} d^{3} x^{5} - 6 \, c d^{3} x^{4} + 2 i \, d^{3} x^{3}}, x\right)"," ",0,"integral(-(b*log(-(c*x + I)/(c*x - I)) - 2*I*a)/(2*c^3*d^3*x^6 - 6*I*c^2*d^3*x^5 - 6*c*d^3*x^4 + 2*I*d^3*x^3), x)","F",0
66,1,93,0,0.428614," ","integrate((a+b*arctan(c*x))/(1+I*c*x)^4,x, algorithm=""fricas"")","\frac{-6 i \, b c^{2} x^{2} - 18 \, b c x + {\left(3 \, b c^{3} x^{3} - 9 i \, b c^{2} x^{2} - 9 \, b c x - 21 i \, b\right)} \log\left(-\frac{c x + i}{c x - i}\right) - 48 \, a + 20 i \, b}{144 \, c^{4} x^{3} - 432 i \, c^{3} x^{2} - 432 \, c^{2} x + 144 i \, c}"," ",0,"(-6*I*b*c^2*x^2 - 18*b*c*x + (3*b*c^3*x^3 - 9*I*b*c^2*x^2 - 9*b*c*x - 21*I*b)*log(-(c*x + I)/(c*x - I)) - 48*a + 20*I*b)/(144*c^4*x^3 - 432*I*c^3*x^2 - 432*c^2*x + 144*I*c)","A",0
67,1,21,0,0.467974," ","integrate(arctan(a*x)/(c*x+I*a*c*x^2),x, algorithm=""fricas"")","-\frac{i \, {\rm Li}_2\left(\frac{a x + i}{a x - i} + 1\right)}{2 \, c}"," ",0,"-1/2*I*dilog((a*x + I)/(a*x - I) + 1)/c","A",0
68,0,0,0,0.452107," ","integrate(x^3*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{80} \, {\left(-4 i \, b^{2} c d x^{5} - 5 \, b^{2} d x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{20 i \, a^{2} c^{3} d x^{6} + 20 \, a^{2} c^{2} d x^{5} + 20 i \, a^{2} c d x^{4} + 20 \, a^{2} d x^{3} - {\left(20 \, a b c^{3} d x^{6} + 4 \, {\left(-5 i \, a b - b^{2}\right)} c^{2} d x^{5} + {\left(20 \, a b + 5 i \, b^{2}\right)} c d x^{4} - 20 i \, a b d x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{20 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/80*(-4*I*b^2*c*d*x^5 - 5*b^2*d*x^4)*log(-(c*x + I)/(c*x - I))^2 + integral(1/20*(20*I*a^2*c^3*d*x^6 + 20*a^2*c^2*d*x^5 + 20*I*a^2*c*d*x^4 + 20*a^2*d*x^3 - (20*a*b*c^3*d*x^6 + 4*(-5*I*a*b - b^2)*c^2*d*x^5 + (20*a*b + 5*I*b^2)*c*d*x^4 - 20*I*a*b*d*x^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
69,0,0,0,0.466908," ","integrate(x^2*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{48} \, {\left(-3 i \, b^{2} c d x^{4} - 4 \, b^{2} d x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{12 i \, a^{2} c^{3} d x^{5} + 12 \, a^{2} c^{2} d x^{4} + 12 i \, a^{2} c d x^{3} + 12 \, a^{2} d x^{2} - {\left(12 \, a b c^{3} d x^{5} + 3 \, {\left(-4 i \, a b - b^{2}\right)} c^{2} d x^{4} + {\left(12 \, a b + 4 i \, b^{2}\right)} c d x^{3} - 12 i \, a b d x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{12 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/48*(-3*I*b^2*c*d*x^4 - 4*b^2*d*x^3)*log(-(c*x + I)/(c*x - I))^2 + integral(1/12*(12*I*a^2*c^3*d*x^5 + 12*a^2*c^2*d*x^4 + 12*I*a^2*c*d*x^3 + 12*a^2*d*x^2 - (12*a*b*c^3*d*x^5 + 3*(-4*I*a*b - b^2)*c^2*d*x^4 + (12*a*b + 4*I*b^2)*c*d*x^3 - 12*I*a*b*d*x^2)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
70,0,0,0,0.541716," ","integrate(x*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{24} \, {\left(-2 i \, b^{2} c d x^{3} - 3 \, b^{2} d x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{6 i \, a^{2} c^{3} d x^{4} + 6 \, a^{2} c^{2} d x^{3} + 6 i \, a^{2} c d x^{2} + 6 \, a^{2} d x - {\left(6 \, a b c^{3} d x^{4} + 2 \, {\left(-3 i \, a b - b^{2}\right)} c^{2} d x^{3} + {\left(6 \, a b + 3 i \, b^{2}\right)} c d x^{2} - 6 i \, a b d x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{6 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/24*(-2*I*b^2*c*d*x^3 - 3*b^2*d*x^2)*log(-(c*x + I)/(c*x - I))^2 + integral(1/6*(6*I*a^2*c^3*d*x^4 + 6*a^2*c^2*d*x^3 + 6*I*a^2*c*d*x^2 + 6*a^2*d*x - (6*a*b*c^3*d*x^4 + 2*(-3*I*a*b - b^2)*c^2*d*x^3 + (6*a*b + 3*I*b^2)*c*d*x^2 - 6*I*a*b*d*x)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
71,0,0,0,0.464081," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{8} \, {\left(-i \, b^{2} c d x^{2} - 2 \, b^{2} d x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{2 i \, a^{2} c^{3} d x^{3} + 2 \, a^{2} c^{2} d x^{2} + 2 i \, a^{2} c d x + 2 \, a^{2} d - {\left(2 \, a b c^{3} d x^{3} - {\left(2 i \, a b + b^{2}\right)} c^{2} d x^{2} + {\left(2 \, a b + 2 i \, b^{2}\right)} c d x - 2 i \, a b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/8*(-I*b^2*c*d*x^2 - 2*b^2*d*x)*log(-(c*x + I)/(c*x - I))^2 + integral(1/2*(2*I*a^2*c^3*d*x^3 + 2*a^2*c^2*d*x^2 + 2*I*a^2*c*d*x + 2*a^2*d - (2*a*b*c^3*d*x^3 - (2*I*a*b + b^2)*c^2*d*x^2 + (2*a*b + 2*I*b^2)*c*d*x - 2*I*a*b*d)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
72,0,0,0,0.473341," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 i \, a^{2} c d x + 4 \, a^{2} d + {\left(-i \, b^{2} c d x - b^{2} d\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(4 \, a b c d x - 4 i \, a b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x}, x\right)"," ",0,"integral(1/4*(4*I*a^2*c*d*x + 4*a^2*d + (-I*b^2*c*d*x - b^2*d)*log(-(c*x + I)/(c*x - I))^2 - (4*a*b*c*d*x - 4*I*a*b*d)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
73,0,0,0,0.469277," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 i \, a^{2} c d x + 4 \, a^{2} d + {\left(-i \, b^{2} c d x - b^{2} d\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(4 \, a b c d x - 4 i \, a b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{2}}, x\right)"," ",0,"integral(1/4*(4*I*a^2*c*d*x + 4*a^2*d + (-I*b^2*c*d*x - b^2*d)*log(-(c*x + I)/(c*x - I))^2 - (4*a*b*c*d*x - 4*I*a*b*d)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
74,0,0,0,0.446980," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^3,x, algorithm=""fricas"")","\frac{8 \, x^{2} {\rm integral}\left(\frac{2 i \, a^{2} c^{3} d x^{3} + 2 \, a^{2} c^{2} d x^{2} + 2 i \, a^{2} c d x + 2 \, a^{2} d - {\left(2 \, a b c^{3} d x^{3} + 2 \, {\left(-i \, a b + b^{2}\right)} c^{2} d x^{2} + {\left(2 \, a b - i \, b^{2}\right)} c d x - 2 i \, a b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{2 \, {\left(c^{2} x^{5} + x^{3}\right)}}, x\right) + {\left(2 i \, b^{2} c d x + b^{2} d\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2}}{8 \, x^{2}}"," ",0,"1/8*(8*x^2*integral(1/2*(2*I*a^2*c^3*d*x^3 + 2*a^2*c^2*d*x^2 + 2*I*a^2*c*d*x + 2*a^2*d - (2*a*b*c^3*d*x^3 + 2*(-I*a*b + b^2)*c^2*d*x^2 + (2*a*b - I*b^2)*c*d*x - 2*I*a*b*d)*log(-(c*x + I)/(c*x - I)))/(c^2*x^5 + x^3), x) + (2*I*b^2*c*d*x + b^2*d)*log(-(c*x + I)/(c*x - I))^2)/x^2","F",0
75,0,0,0,0.635561," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^4,x, algorithm=""fricas"")","\frac{24 \, x^{3} {\rm integral}\left(\frac{6 i \, a^{2} c^{3} d x^{3} + 6 \, a^{2} c^{2} d x^{2} + 6 i \, a^{2} c d x + 6 \, a^{2} d - {\left(6 \, a b c^{3} d x^{3} + 3 \, {\left(-2 i \, a b + b^{2}\right)} c^{2} d x^{2} + {\left(6 \, a b - 2 i \, b^{2}\right)} c d x - 6 i \, a b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{6 \, {\left(c^{2} x^{6} + x^{4}\right)}}, x\right) + {\left(3 i \, b^{2} c d x + 2 \, b^{2} d\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2}}{24 \, x^{3}}"," ",0,"1/24*(24*x^3*integral(1/6*(6*I*a^2*c^3*d*x^3 + 6*a^2*c^2*d*x^2 + 6*I*a^2*c*d*x + 6*a^2*d - (6*a*b*c^3*d*x^3 + 3*(-2*I*a*b + b^2)*c^2*d*x^2 + (6*a*b - 2*I*b^2)*c*d*x - 6*I*a*b*d)*log(-(c*x + I)/(c*x - I)))/(c^2*x^6 + x^4), x) + (3*I*b^2*c*d*x + 2*b^2*d)*log(-(c*x + I)/(c*x - I))^2)/x^3","F",0
76,0,0,0,0.454150," ","integrate(x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{240} \, {\left(10 \, b^{2} c^{2} d^{2} x^{6} - 24 i \, b^{2} c d^{2} x^{5} - 15 \, b^{2} d^{2} x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(-\frac{60 \, a^{2} c^{4} d^{2} x^{7} - 120 i \, a^{2} c^{3} d^{2} x^{6} - 120 i \, a^{2} c d^{2} x^{4} - 60 \, a^{2} d^{2} x^{3} - {\left(-60 i \, a b c^{4} d^{2} x^{7} - {\left(120 \, a b - 10 i \, b^{2}\right)} c^{3} d^{2} x^{6} + 24 \, b^{2} c^{2} d^{2} x^{5} - {\left(120 \, a b + 15 i \, b^{2}\right)} c d^{2} x^{4} + 60 i \, a b d^{2} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/240*(10*b^2*c^2*d^2*x^6 - 24*I*b^2*c*d^2*x^5 - 15*b^2*d^2*x^4)*log(-(c*x + I)/(c*x - I))^2 + integral(-1/60*(60*a^2*c^4*d^2*x^7 - 120*I*a^2*c^3*d^2*x^6 - 120*I*a^2*c*d^2*x^4 - 60*a^2*d^2*x^3 - (-60*I*a*b*c^4*d^2*x^7 - (120*a*b - 10*I*b^2)*c^3*d^2*x^6 + 24*b^2*c^2*d^2*x^5 - (120*a*b + 15*I*b^2)*c*d^2*x^4 + 60*I*a*b*d^2*x^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
77,0,0,0,0.603581," ","integrate(x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{120} \, {\left(6 \, b^{2} c^{2} d^{2} x^{5} - 15 i \, b^{2} c d^{2} x^{4} - 10 \, b^{2} d^{2} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(-\frac{30 \, a^{2} c^{4} d^{2} x^{6} - 60 i \, a^{2} c^{3} d^{2} x^{5} - 60 i \, a^{2} c d^{2} x^{3} - 30 \, a^{2} d^{2} x^{2} - {\left(-30 i \, a b c^{4} d^{2} x^{6} - {\left(60 \, a b - 6 i \, b^{2}\right)} c^{3} d^{2} x^{5} + 15 \, b^{2} c^{2} d^{2} x^{4} - {\left(60 \, a b + 10 i \, b^{2}\right)} c d^{2} x^{3} + 30 i \, a b d^{2} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{30 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/120*(6*b^2*c^2*d^2*x^5 - 15*I*b^2*c*d^2*x^4 - 10*b^2*d^2*x^3)*log(-(c*x + I)/(c*x - I))^2 + integral(-1/30*(30*a^2*c^4*d^2*x^6 - 60*I*a^2*c^3*d^2*x^5 - 60*I*a^2*c*d^2*x^3 - 30*a^2*d^2*x^2 - (-30*I*a*b*c^4*d^2*x^6 - (60*a*b - 6*I*b^2)*c^3*d^2*x^5 + 15*b^2*c^2*d^2*x^4 - (60*a*b + 10*I*b^2)*c*d^2*x^3 + 30*I*a*b*d^2*x^2)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
78,0,0,0,0.508360," ","integrate(x*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{48} \, {\left(3 \, b^{2} c^{2} d^{2} x^{4} - 8 i \, b^{2} c d^{2} x^{3} - 6 \, b^{2} d^{2} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(-\frac{12 \, a^{2} c^{4} d^{2} x^{5} - 24 i \, a^{2} c^{3} d^{2} x^{4} - 24 i \, a^{2} c d^{2} x^{2} - 12 \, a^{2} d^{2} x - {\left(-12 i \, a b c^{4} d^{2} x^{5} - {\left(24 \, a b - 3 i \, b^{2}\right)} c^{3} d^{2} x^{4} + 8 \, b^{2} c^{2} d^{2} x^{3} - {\left(24 \, a b + 6 i \, b^{2}\right)} c d^{2} x^{2} + 12 i \, a b d^{2} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{12 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/48*(3*b^2*c^2*d^2*x^4 - 8*I*b^2*c*d^2*x^3 - 6*b^2*d^2*x^2)*log(-(c*x + I)/(c*x - I))^2 + integral(-1/12*(12*a^2*c^4*d^2*x^5 - 24*I*a^2*c^3*d^2*x^4 - 24*I*a^2*c*d^2*x^2 - 12*a^2*d^2*x - (-12*I*a*b*c^4*d^2*x^5 - (24*a*b - 3*I*b^2)*c^3*d^2*x^4 + 8*b^2*c^2*d^2*x^3 - (24*a*b + 6*I*b^2)*c*d^2*x^2 + 12*I*a*b*d^2*x)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
79,0,0,0,1.376612," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{12} \, {\left(b^{2} c^{2} d^{2} x^{3} - 3 i \, b^{2} c d^{2} x^{2} - 3 \, b^{2} d^{2} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(-\frac{3 \, a^{2} c^{4} d^{2} x^{4} - 6 i \, a^{2} c^{3} d^{2} x^{3} - 6 i \, a^{2} c d^{2} x - 3 \, a^{2} d^{2} - {\left(-3 i \, a b c^{4} d^{2} x^{4} - {\left(6 \, a b - i \, b^{2}\right)} c^{3} d^{2} x^{3} + 3 \, b^{2} c^{2} d^{2} x^{2} - {\left(6 \, a b + 3 i \, b^{2}\right)} c d^{2} x + 3 i \, a b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{3 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/12*(b^2*c^2*d^2*x^3 - 3*I*b^2*c*d^2*x^2 - 3*b^2*d^2*x)*log(-(c*x + I)/(c*x - I))^2 + integral(-1/3*(3*a^2*c^4*d^2*x^4 - 6*I*a^2*c^3*d^2*x^3 - 6*I*a^2*c*d^2*x - 3*a^2*d^2 - (-3*I*a*b*c^4*d^2*x^4 - (6*a*b - I*b^2)*c^3*d^2*x^3 + 3*b^2*c^2*d^2*x^2 - (6*a*b + 3*I*b^2)*c*d^2*x + 3*I*a*b*d^2)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
80,0,0,0,0.501128," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{4 \, a^{2} c^{2} d^{2} x^{2} - 8 i \, a^{2} c d^{2} x - 4 \, a^{2} d^{2} - {\left(b^{2} c^{2} d^{2} x^{2} - 2 i \, b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(-4 i \, a b c^{2} d^{2} x^{2} - 8 \, a b c d^{2} x + 4 i \, a b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x}, x\right)"," ",0,"integral(-1/4*(4*a^2*c^2*d^2*x^2 - 8*I*a^2*c*d^2*x - 4*a^2*d^2 - (b^2*c^2*d^2*x^2 - 2*I*b^2*c*d^2*x - b^2*d^2)*log(-(c*x + I)/(c*x - I))^2 - (-4*I*a*b*c^2*d^2*x^2 - 8*a*b*c*d^2*x + 4*I*a*b*d^2)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
81,0,0,0,0.593613," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{4 \, a^{2} c^{2} d^{2} x^{2} - 8 i \, a^{2} c d^{2} x - 4 \, a^{2} d^{2} - {\left(b^{2} c^{2} d^{2} x^{2} - 2 i \, b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(-4 i \, a b c^{2} d^{2} x^{2} - 8 \, a b c d^{2} x + 4 i \, a b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{2}}, x\right)"," ",0,"integral(-1/4*(4*a^2*c^2*d^2*x^2 - 8*I*a^2*c*d^2*x - 4*a^2*d^2 - (b^2*c^2*d^2*x^2 - 2*I*b^2*c*d^2*x - b^2*d^2)*log(-(c*x + I)/(c*x - I))^2 - (-4*I*a*b*c^2*d^2*x^2 - 8*a*b*c*d^2*x + 4*I*a*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
82,0,0,0,0.442739," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{4 \, a^{2} c^{2} d^{2} x^{2} - 8 i \, a^{2} c d^{2} x - 4 \, a^{2} d^{2} - {\left(b^{2} c^{2} d^{2} x^{2} - 2 i \, b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(-4 i \, a b c^{2} d^{2} x^{2} - 8 \, a b c d^{2} x + 4 i \, a b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{3}}, x\right)"," ",0,"integral(-1/4*(4*a^2*c^2*d^2*x^2 - 8*I*a^2*c*d^2*x - 4*a^2*d^2 - (b^2*c^2*d^2*x^2 - 2*I*b^2*c*d^2*x - b^2*d^2)*log(-(c*x + I)/(c*x - I))^2 - (-4*I*a*b*c^2*d^2*x^2 - 8*a*b*c*d^2*x + 4*I*a*b*d^2)*log(-(c*x + I)/(c*x - I)))/x^3, x)","F",0
83,0,0,0,0.457547," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^4,x, algorithm=""fricas"")","\frac{12 \, x^{3} {\rm integral}\left(-\frac{3 \, a^{2} c^{4} d^{2} x^{4} - 6 i \, a^{2} c^{3} d^{2} x^{3} - 6 i \, a^{2} c d^{2} x - 3 \, a^{2} d^{2} - {\left(-3 i \, a b c^{4} d^{2} x^{4} - {\left(6 \, a b + 3 i \, b^{2}\right)} c^{3} d^{2} x^{3} - 3 \, b^{2} c^{2} d^{2} x^{2} - {\left(6 \, a b - i \, b^{2}\right)} c d^{2} x + 3 i \, a b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{3 \, {\left(c^{2} x^{6} + x^{4}\right)}}, x\right) - {\left(3 \, b^{2} c^{2} d^{2} x^{2} - 3 i \, b^{2} c d^{2} x - b^{2} d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2}}{12 \, x^{3}}"," ",0,"1/12*(12*x^3*integral(-1/3*(3*a^2*c^4*d^2*x^4 - 6*I*a^2*c^3*d^2*x^3 - 6*I*a^2*c*d^2*x - 3*a^2*d^2 - (-3*I*a*b*c^4*d^2*x^4 - (6*a*b + 3*I*b^2)*c^3*d^2*x^3 - 3*b^2*c^2*d^2*x^2 - (6*a*b - I*b^2)*c*d^2*x + 3*I*a*b*d^2)*log(-(c*x + I)/(c*x - I)))/(c^2*x^6 + x^4), x) - (3*b^2*c^2*d^2*x^2 - 3*I*b^2*c*d^2*x - b^2*d^2)*log(-(c*x + I)/(c*x - I))^2)/x^3","F",0
84,0,0,0,0.761746," ","integrate(x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{560} \, {\left(20 i \, b^{2} c^{3} d^{3} x^{7} + 70 \, b^{2} c^{2} d^{3} x^{6} - 84 i \, b^{2} c d^{3} x^{5} - 35 \, b^{2} d^{3} x^{4}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{-140 i \, a^{2} c^{5} d^{3} x^{8} - 420 \, a^{2} c^{4} d^{3} x^{7} + 280 i \, a^{2} c^{3} d^{3} x^{6} - 280 \, a^{2} c^{2} d^{3} x^{5} + 420 i \, a^{2} c d^{3} x^{4} + 140 \, a^{2} d^{3} x^{3} + {\left(140 \, a b c^{5} d^{3} x^{8} - 20 \, {\left(21 i \, a b + b^{2}\right)} c^{4} d^{3} x^{7} - {\left(280 \, a b - 70 i \, b^{2}\right)} c^{3} d^{3} x^{6} - 28 \, {\left(10 i \, a b - 3 \, b^{2}\right)} c^{2} d^{3} x^{5} - {\left(420 \, a b + 35 i \, b^{2}\right)} c d^{3} x^{4} + 140 i \, a b d^{3} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{140 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/560*(20*I*b^2*c^3*d^3*x^7 + 70*b^2*c^2*d^3*x^6 - 84*I*b^2*c*d^3*x^5 - 35*b^2*d^3*x^4)*log(-(c*x + I)/(c*x - I))^2 + integral(1/140*(-140*I*a^2*c^5*d^3*x^8 - 420*a^2*c^4*d^3*x^7 + 280*I*a^2*c^3*d^3*x^6 - 280*a^2*c^2*d^3*x^5 + 420*I*a^2*c*d^3*x^4 + 140*a^2*d^3*x^3 + (140*a*b*c^5*d^3*x^8 - 20*(21*I*a*b + b^2)*c^4*d^3*x^7 - (280*a*b - 70*I*b^2)*c^3*d^3*x^6 - 28*(10*I*a*b - 3*b^2)*c^2*d^3*x^5 - (420*a*b + 35*I*b^2)*c*d^3*x^4 + 140*I*a*b*d^3*x^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
85,0,0,0,0.460124," ","integrate(x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{240} \, {\left(10 i \, b^{2} c^{3} d^{3} x^{6} + 36 \, b^{2} c^{2} d^{3} x^{5} - 45 i \, b^{2} c d^{3} x^{4} - 20 \, b^{2} d^{3} x^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{-60 i \, a^{2} c^{5} d^{3} x^{7} - 180 \, a^{2} c^{4} d^{3} x^{6} + 120 i \, a^{2} c^{3} d^{3} x^{5} - 120 \, a^{2} c^{2} d^{3} x^{4} + 180 i \, a^{2} c d^{3} x^{3} + 60 \, a^{2} d^{3} x^{2} + {\left(60 \, a b c^{5} d^{3} x^{7} - 10 \, {\left(18 i \, a b + b^{2}\right)} c^{4} d^{3} x^{6} - {\left(120 \, a b - 36 i \, b^{2}\right)} c^{3} d^{3} x^{5} - 15 \, {\left(8 i \, a b - 3 \, b^{2}\right)} c^{2} d^{3} x^{4} - {\left(180 \, a b + 20 i \, b^{2}\right)} c d^{3} x^{3} + 60 i \, a b d^{3} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/240*(10*I*b^2*c^3*d^3*x^6 + 36*b^2*c^2*d^3*x^5 - 45*I*b^2*c*d^3*x^4 - 20*b^2*d^3*x^3)*log(-(c*x + I)/(c*x - I))^2 + integral(1/60*(-60*I*a^2*c^5*d^3*x^7 - 180*a^2*c^4*d^3*x^6 + 120*I*a^2*c^3*d^3*x^5 - 120*a^2*c^2*d^3*x^4 + 180*I*a^2*c*d^3*x^3 + 60*a^2*d^3*x^2 + (60*a*b*c^5*d^3*x^7 - 10*(18*I*a*b + b^2)*c^4*d^3*x^6 - (120*a*b - 36*I*b^2)*c^3*d^3*x^5 - 15*(8*I*a*b - 3*b^2)*c^2*d^3*x^4 - (180*a*b + 20*I*b^2)*c*d^3*x^3 + 60*I*a*b*d^3*x^2)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
86,0,0,0,0.446212," ","integrate(x*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{80} \, {\left(4 i \, b^{2} c^{3} d^{3} x^{5} + 15 \, b^{2} c^{2} d^{3} x^{4} - 20 i \, b^{2} c d^{3} x^{3} - 10 \, b^{2} d^{3} x^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{-20 i \, a^{2} c^{5} d^{3} x^{6} - 60 \, a^{2} c^{4} d^{3} x^{5} + 40 i \, a^{2} c^{3} d^{3} x^{4} - 40 \, a^{2} c^{2} d^{3} x^{3} + 60 i \, a^{2} c d^{3} x^{2} + 20 \, a^{2} d^{3} x + {\left(20 \, a b c^{5} d^{3} x^{6} - 4 \, {\left(15 i \, a b + b^{2}\right)} c^{4} d^{3} x^{5} - {\left(40 \, a b - 15 i \, b^{2}\right)} c^{3} d^{3} x^{4} - 20 \, {\left(2 i \, a b - b^{2}\right)} c^{2} d^{3} x^{3} - {\left(60 \, a b + 10 i \, b^{2}\right)} c d^{3} x^{2} + 20 i \, a b d^{3} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{20 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/80*(4*I*b^2*c^3*d^3*x^5 + 15*b^2*c^2*d^3*x^4 - 20*I*b^2*c*d^3*x^3 - 10*b^2*d^3*x^2)*log(-(c*x + I)/(c*x - I))^2 + integral(1/20*(-20*I*a^2*c^5*d^3*x^6 - 60*a^2*c^4*d^3*x^5 + 40*I*a^2*c^3*d^3*x^4 - 40*a^2*c^2*d^3*x^3 + 60*I*a^2*c*d^3*x^2 + 20*a^2*d^3*x + (20*a*b*c^5*d^3*x^6 - 4*(15*I*a*b + b^2)*c^4*d^3*x^5 - (40*a*b - 15*I*b^2)*c^3*d^3*x^4 - 20*(2*I*a*b - b^2)*c^2*d^3*x^3 - (60*a*b + 10*I*b^2)*c*d^3*x^2 + 20*I*a*b*d^3*x)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
87,0,0,0,0.504690," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{1}{16} \, {\left(i \, b^{2} c^{3} d^{3} x^{4} + 4 \, b^{2} c^{2} d^{3} x^{3} - 6 i \, b^{2} c d^{3} x^{2} - 4 \, b^{2} d^{3} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\rm integral}\left(\frac{-4 i \, a^{2} c^{5} d^{3} x^{5} - 12 \, a^{2} c^{4} d^{3} x^{4} + 8 i \, a^{2} c^{3} d^{3} x^{3} - 8 \, a^{2} c^{2} d^{3} x^{2} + 12 i \, a^{2} c d^{3} x + 4 \, a^{2} d^{3} + {\left(4 \, a b c^{5} d^{3} x^{5} + {\left(-12 i \, a b - b^{2}\right)} c^{4} d^{3} x^{4} - {\left(8 \, a b - 4 i \, b^{2}\right)} c^{3} d^{3} x^{3} - 2 \, {\left(4 i \, a b - 3 \, b^{2}\right)} c^{2} d^{3} x^{2} - {\left(12 \, a b + 4 i \, b^{2}\right)} c d^{3} x + 4 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/16*(I*b^2*c^3*d^3*x^4 + 4*b^2*c^2*d^3*x^3 - 6*I*b^2*c*d^3*x^2 - 4*b^2*d^3*x)*log(-(c*x + I)/(c*x - I))^2 + integral(1/4*(-4*I*a^2*c^5*d^3*x^5 - 12*a^2*c^4*d^3*x^4 + 8*I*a^2*c^3*d^3*x^3 - 8*a^2*c^2*d^3*x^2 + 12*I*a^2*c*d^3*x + 4*a^2*d^3 + (4*a*b*c^5*d^3*x^5 + (-12*I*a*b - b^2)*c^4*d^3*x^4 - (8*a*b - 4*I*b^2)*c^3*d^3*x^3 - 2*(4*I*a*b - 3*b^2)*c^2*d^3*x^2 - (12*a*b + 4*I*b^2)*c*d^3*x + 4*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
88,0,0,0,0.432977," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-4 i \, a^{2} c^{3} d^{3} x^{3} - 12 \, a^{2} c^{2} d^{3} x^{2} + 12 i \, a^{2} c d^{3} x + 4 \, a^{2} d^{3} + {\left(i \, b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} - 3 i \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\left(4 \, a b c^{3} d^{3} x^{3} - 12 i \, a b c^{2} d^{3} x^{2} - 12 \, a b c d^{3} x + 4 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x}, x\right)"," ",0,"integral(1/4*(-4*I*a^2*c^3*d^3*x^3 - 12*a^2*c^2*d^3*x^2 + 12*I*a^2*c*d^3*x + 4*a^2*d^3 + (I*b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 - 3*I*b^2*c*d^3*x - b^2*d^3)*log(-(c*x + I)/(c*x - I))^2 + (4*a*b*c^3*d^3*x^3 - 12*I*a*b*c^2*d^3*x^2 - 12*a*b*c*d^3*x + 4*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/x, x)","F",0
89,0,0,0,0.614332," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-4 i \, a^{2} c^{3} d^{3} x^{3} - 12 \, a^{2} c^{2} d^{3} x^{2} + 12 i \, a^{2} c d^{3} x + 4 \, a^{2} d^{3} + {\left(i \, b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} - 3 i \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\left(4 \, a b c^{3} d^{3} x^{3} - 12 i \, a b c^{2} d^{3} x^{2} - 12 \, a b c d^{3} x + 4 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{2}}, x\right)"," ",0,"integral(1/4*(-4*I*a^2*c^3*d^3*x^3 - 12*a^2*c^2*d^3*x^2 + 12*I*a^2*c*d^3*x + 4*a^2*d^3 + (I*b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 - 3*I*b^2*c*d^3*x - b^2*d^3)*log(-(c*x + I)/(c*x - I))^2 + (4*a*b*c^3*d^3*x^3 - 12*I*a*b*c^2*d^3*x^2 - 12*a*b*c*d^3*x + 4*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^2, x)","F",0
90,0,0,0,0.427953," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-4 i \, a^{2} c^{3} d^{3} x^{3} - 12 \, a^{2} c^{2} d^{3} x^{2} + 12 i \, a^{2} c d^{3} x + 4 \, a^{2} d^{3} + {\left(i \, b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} - 3 i \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\left(4 \, a b c^{3} d^{3} x^{3} - 12 i \, a b c^{2} d^{3} x^{2} - 12 \, a b c d^{3} x + 4 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{3}}, x\right)"," ",0,"integral(1/4*(-4*I*a^2*c^3*d^3*x^3 - 12*a^2*c^2*d^3*x^2 + 12*I*a^2*c*d^3*x + 4*a^2*d^3 + (I*b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 - 3*I*b^2*c*d^3*x - b^2*d^3)*log(-(c*x + I)/(c*x - I))^2 + (4*a*b*c^3*d^3*x^3 - 12*I*a*b*c^2*d^3*x^2 - 12*a*b*c*d^3*x + 4*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^3, x)","F",0
91,0,0,0,0.434605," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-4 i \, a^{2} c^{3} d^{3} x^{3} - 12 \, a^{2} c^{2} d^{3} x^{2} + 12 i \, a^{2} c d^{3} x + 4 \, a^{2} d^{3} + {\left(i \, b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} - 3 i \, b^{2} c d^{3} x - b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\left(4 \, a b c^{3} d^{3} x^{3} - 12 i \, a b c^{2} d^{3} x^{2} - 12 \, a b c d^{3} x + 4 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, x^{4}}, x\right)"," ",0,"integral(1/4*(-4*I*a^2*c^3*d^3*x^3 - 12*a^2*c^2*d^3*x^2 + 12*I*a^2*c*d^3*x + 4*a^2*d^3 + (I*b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 - 3*I*b^2*c*d^3*x - b^2*d^3)*log(-(c*x + I)/(c*x - I))^2 + (4*a*b*c^3*d^3*x^3 - 12*I*a*b*c^2*d^3*x^2 - 12*a*b*c*d^3*x + 4*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/x^4, x)","F",0
92,0,0,0,0.619301," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^5,x, algorithm=""fricas"")","\frac{16 \, x^{4} {\rm integral}\left(\frac{-4 i \, a^{2} c^{5} d^{3} x^{5} - 12 \, a^{2} c^{4} d^{3} x^{4} + 8 i \, a^{2} c^{3} d^{3} x^{3} - 8 \, a^{2} c^{2} d^{3} x^{2} + 12 i \, a^{2} c d^{3} x + 4 \, a^{2} d^{3} + {\left(4 \, a b c^{5} d^{3} x^{5} - 4 \, {\left(3 i \, a b - b^{2}\right)} c^{4} d^{3} x^{4} - {\left(8 \, a b + 6 i \, b^{2}\right)} c^{3} d^{3} x^{3} - 4 \, {\left(2 i \, a b + b^{2}\right)} c^{2} d^{3} x^{2} - {\left(12 \, a b - i \, b^{2}\right)} c d^{3} x + 4 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, {\left(c^{2} x^{7} + x^{5}\right)}}, x\right) + {\left(-4 i \, b^{2} c^{3} d^{3} x^{3} - 6 \, b^{2} c^{2} d^{3} x^{2} + 4 i \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2}}{16 \, x^{4}}"," ",0,"1/16*(16*x^4*integral(1/4*(-4*I*a^2*c^5*d^3*x^5 - 12*a^2*c^4*d^3*x^4 + 8*I*a^2*c^3*d^3*x^3 - 8*a^2*c^2*d^3*x^2 + 12*I*a^2*c*d^3*x + 4*a^2*d^3 + (4*a*b*c^5*d^3*x^5 - 4*(3*I*a*b - b^2)*c^4*d^3*x^4 - (8*a*b + 6*I*b^2)*c^3*d^3*x^3 - 4*(2*I*a*b + b^2)*c^2*d^3*x^2 - (12*a*b - I*b^2)*c*d^3*x + 4*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^7 + x^5), x) + (-4*I*b^2*c^3*d^3*x^3 - 6*b^2*c^2*d^3*x^2 + 4*I*b^2*c*d^3*x + b^2*d^3)*log(-(c*x + I)/(c*x - I))^2)/x^4","F",0
93,0,0,0,0.471024," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^6,x, algorithm=""fricas"")","\frac{80 \, x^{5} {\rm integral}\left(\frac{-20 i \, a^{2} c^{5} d^{3} x^{5} - 60 \, a^{2} c^{4} d^{3} x^{4} + 40 i \, a^{2} c^{3} d^{3} x^{3} - 40 \, a^{2} c^{2} d^{3} x^{2} + 60 i \, a^{2} c d^{3} x + 20 \, a^{2} d^{3} + {\left(20 \, a b c^{5} d^{3} x^{5} - 10 \, {\left(6 i \, a b - b^{2}\right)} c^{4} d^{3} x^{4} - {\left(40 \, a b + 20 i \, b^{2}\right)} c^{3} d^{3} x^{3} - 5 \, {\left(8 i \, a b + 3 \, b^{2}\right)} c^{2} d^{3} x^{2} - {\left(60 \, a b - 4 i \, b^{2}\right)} c d^{3} x + 20 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{20 \, {\left(c^{2} x^{8} + x^{6}\right)}}, x\right) + {\left(-10 i \, b^{2} c^{3} d^{3} x^{3} - 20 \, b^{2} c^{2} d^{3} x^{2} + 15 i \, b^{2} c d^{3} x + 4 \, b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2}}{80 \, x^{5}}"," ",0,"1/80*(80*x^5*integral(1/20*(-20*I*a^2*c^5*d^3*x^5 - 60*a^2*c^4*d^3*x^4 + 40*I*a^2*c^3*d^3*x^3 - 40*a^2*c^2*d^3*x^2 + 60*I*a^2*c*d^3*x + 20*a^2*d^3 + (20*a*b*c^5*d^3*x^5 - 10*(6*I*a*b - b^2)*c^4*d^3*x^4 - (40*a*b + 20*I*b^2)*c^3*d^3*x^3 - 5*(8*I*a*b + 3*b^2)*c^2*d^3*x^2 - (60*a*b - 4*I*b^2)*c*d^3*x + 20*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^8 + x^6), x) + (-10*I*b^2*c^3*d^3*x^3 - 20*b^2*c^2*d^3*x^2 + 15*I*b^2*c*d^3*x + 4*b^2*d^3)*log(-(c*x + I)/(c*x - I))^2)/x^5","F",0
94,0,0,0,0.974158," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^7,x, algorithm=""fricas"")","\frac{240 \, x^{6} {\rm integral}\left(\frac{-60 i \, a^{2} c^{5} d^{3} x^{5} - 180 \, a^{2} c^{4} d^{3} x^{4} + 120 i \, a^{2} c^{3} d^{3} x^{3} - 120 \, a^{2} c^{2} d^{3} x^{2} + 180 i \, a^{2} c d^{3} x + 60 \, a^{2} d^{3} + {\left(60 \, a b c^{5} d^{3} x^{5} - 20 \, {\left(9 i \, a b - b^{2}\right)} c^{4} d^{3} x^{4} - {\left(120 \, a b + 45 i \, b^{2}\right)} c^{3} d^{3} x^{3} - 12 \, {\left(10 i \, a b + 3 \, b^{2}\right)} c^{2} d^{3} x^{2} - {\left(180 \, a b - 10 i \, b^{2}\right)} c d^{3} x + 60 i \, a b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{60 \, {\left(c^{2} x^{9} + x^{7}\right)}}, x\right) + {\left(-20 i \, b^{2} c^{3} d^{3} x^{3} - 45 \, b^{2} c^{2} d^{3} x^{2} + 36 i \, b^{2} c d^{3} x + 10 \, b^{2} d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2}}{240 \, x^{6}}"," ",0,"1/240*(240*x^6*integral(1/60*(-60*I*a^2*c^5*d^3*x^5 - 180*a^2*c^4*d^3*x^4 + 120*I*a^2*c^3*d^3*x^3 - 120*a^2*c^2*d^3*x^2 + 180*I*a^2*c*d^3*x + 60*a^2*d^3 + (60*a*b*c^5*d^3*x^5 - 20*(9*I*a*b - b^2)*c^4*d^3*x^4 - (120*a*b + 45*I*b^2)*c^3*d^3*x^3 - 12*(10*I*a*b + 3*b^2)*c^2*d^3*x^2 - (180*a*b - 10*I*b^2)*c*d^3*x + 60*I*a*b*d^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^9 + x^7), x) + (-20*I*b^2*c^3*d^3*x^3 - 45*b^2*c^2*d^3*x^2 + 36*I*b^2*c*d^3*x + 10*b^2*d^3)*log(-(c*x + I)/(c*x - I))^2)/x^6","F",0
95,0,0,0,0.732404," ","integrate(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} x^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b x^{3} \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2} x^{3}}{4 \, c d x - 4 i \, d}, x\right)"," ",0,"integral((I*b^2*x^3*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*x^3*log(-(c*x + I)/(c*x - I)) - 4*I*a^2*x^3)/(4*c*d*x - 4*I*d), x)","F",0
96,0,0,0,0.780926," ","integrate(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} x^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2} x^{2}}{4 \, c d x - 4 i \, d}, x\right)"," ",0,"integral((I*b^2*x^2*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*x^2*log(-(c*x + I)/(c*x - I)) - 4*I*a^2*x^2)/(4*c*d*x - 4*I*d), x)","F",0
97,0,0,0,0.551690," ","integrate(x*(a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} x \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b x \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2} x}{4 \, c d x - 4 i \, d}, x\right)"," ",0,"integral((I*b^2*x*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*x*log(-(c*x + I)/(c*x - I)) - 4*I*a^2*x)/(4*c*d*x - 4*I*d), x)","F",0
98,0,0,0,0.864545," ","integrate((a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2}}{4 \, c d x - 4 i \, d}, x\right)"," ",0,"integral((I*b^2*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*log(-(c*x + I)/(c*x - I)) - 4*I*a^2)/(4*c*d*x - 4*I*d), x)","F",0
99,0,0,0,0.478573," ","integrate((a+b*arctan(c*x))^2/x/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2}}{4 \, c d x^{2} - 4 i \, d x}, x\right)"," ",0,"integral((I*b^2*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*log(-(c*x + I)/(c*x - I)) - 4*I*a^2)/(4*c*d*x^2 - 4*I*d*x), x)","F",0
100,0,0,0,0.429101," ","integrate((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2}}{4 \, c d x^{3} - 4 i \, d x^{2}}, x\right)"," ",0,"integral((I*b^2*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*log(-(c*x + I)/(c*x - I)) - 4*I*a^2)/(4*c*d*x^3 - 4*I*d*x^2), x)","F",0
101,0,0,0,0.659088," ","integrate((a+b*arctan(c*x))^2/x^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2}}{4 \, c d x^{4} - 4 i \, d x^{3}}, x\right)"," ",0,"integral((I*b^2*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*log(-(c*x + I)/(c*x - I)) - 4*I*a^2)/(4*c*d*x^4 - 4*I*d*x^3), x)","F",0
102,0,0,0,1.037289," ","integrate((a+b*arctan(c*x))^2/x^4/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 i \, a^{2}}{4 \, c d x^{5} - 4 i \, d x^{4}}, x\right)"," ",0,"integral((I*b^2*log(-(c*x + I)/(c*x - I))^2 + 4*a*b*log(-(c*x + I)/(c*x - I)) - 4*I*a^2)/(4*c*d*x^5 - 4*I*d*x^4), x)","F",0
103,0,0,0,0.428980," ","integrate(x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{4} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b x^{4} \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2} x^{4}}{4 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/4*(b^2*x^4*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*x^4*log(-(c*x + I)/(c*x - I)) - 4*a^2*x^4)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
104,0,0,0,0.428066," ","integrate(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b x^{3} \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2} x^{3}}{4 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/4*(b^2*x^3*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*x^3*log(-(c*x + I)/(c*x - I)) - 4*a^2*x^3)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
105,0,0,0,0.637729," ","integrate(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2} x^{2}}{4 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/4*(b^2*x^2*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*x^2*log(-(c*x + I)/(c*x - I)) - 4*a^2*x^2)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
106,0,0,0,0.510799," ","integrate(x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b x \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2} x}{4 \, {\left(c^{2} d^{2} x^{2} - 2 i \, c d^{2} x - d^{2}\right)}}, x\right)"," ",0,"integral(1/4*(b^2*x*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*x*log(-(c*x + I)/(c*x - I)) - 4*a^2*x)/(c^2*d^2*x^2 - 2*I*c*d^2*x - d^2), x)","F",0
107,1,104,0,0.470917," ","integrate((a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","\frac{{\left(i \, b^{2} c x - b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 8 \, a^{2} - 8 i \, a b - 4 \, b^{2} + {\left({\left(4 \, a b - 2 i \, b^{2}\right)} c x + 4 i \, a b + 2 \, b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{8 \, c^{2} d^{2} x - 8 i \, c d^{2}}"," ",0,"((I*b^2*c*x - b^2)*log(-(c*x + I)/(c*x - I))^2 + 8*a^2 - 8*I*a*b - 4*b^2 + ((4*a*b - 2*I*b^2)*c*x + 4*I*a*b + 2*b^2)*log(-(c*x + I)/(c*x - I)))/(8*c^2*d^2*x - 8*I*c*d^2)","A",0
108,0,0,0,0.458951," ","integrate((a+b*arctan(c*x))^2/x/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2}}{4 \, {\left(c^{2} d^{2} x^{3} - 2 i \, c d^{2} x^{2} - d^{2} x\right)}}, x\right)"," ",0,"integral(1/4*(b^2*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*log(-(c*x + I)/(c*x - I)) - 4*a^2)/(c^2*d^2*x^3 - 2*I*c*d^2*x^2 - d^2*x), x)","F",0
109,0,0,0,0.539471," ","integrate((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2}}{4 \, {\left(c^{2} d^{2} x^{4} - 2 i \, c d^{2} x^{3} - d^{2} x^{2}\right)}}, x\right)"," ",0,"integral(1/4*(b^2*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*log(-(c*x + I)/(c*x - I)) - 4*a^2)/(c^2*d^2*x^4 - 2*I*c*d^2*x^3 - d^2*x^2), x)","F",0
110,0,0,0,0.630601," ","integrate((a+b*arctan(c*x))^2/x^3/(d+I*c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 i \, a b \log\left(-\frac{c x + i}{c x - i}\right) - 4 \, a^{2}}{4 \, {\left(c^{2} d^{2} x^{5} - 2 i \, c d^{2} x^{4} - d^{2} x^{3}\right)}}, x\right)"," ",0,"integral(1/4*(b^2*log(-(c*x + I)/(c*x - I))^2 - 4*I*a*b*log(-(c*x + I)/(c*x - I)) - 4*a^2)/(c^2*d^2*x^5 - 2*I*c*d^2*x^4 - d^2*x^3), x)","F",0
111,0,0,0,0.491374," ","integrate(x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b^{2} x^{4} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 \, a b x^{4} \log\left(-\frac{c x + i}{c x - i}\right) + 4 i \, a^{2} x^{4}}{4 \, c^{3} d^{3} x^{3} - 12 i \, c^{2} d^{3} x^{2} - 12 \, c d^{3} x + 4 i \, d^{3}}, x\right)"," ",0,"integral((-I*b^2*x^4*log(-(c*x + I)/(c*x - I))^2 - 4*a*b*x^4*log(-(c*x + I)/(c*x - I)) + 4*I*a^2*x^4)/(4*c^3*d^3*x^3 - 12*I*c^2*d^3*x^2 - 12*c*d^3*x + 4*I*d^3), x)","F",0
112,0,0,0,0.611621," ","integrate(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b^{2} x^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 \, a b x^{3} \log\left(-\frac{c x + i}{c x - i}\right) + 4 i \, a^{2} x^{3}}{4 \, c^{3} d^{3} x^{3} - 12 i \, c^{2} d^{3} x^{2} - 12 \, c d^{3} x + 4 i \, d^{3}}, x\right)"," ",0,"integral((-I*b^2*x^3*log(-(c*x + I)/(c*x - I))^2 - 4*a*b*x^3*log(-(c*x + I)/(c*x - I)) + 4*I*a^2*x^3)/(4*c^3*d^3*x^3 - 12*I*c^2*d^3*x^2 - 12*c*d^3*x + 4*I*d^3), x)","F",0
113,0,0,0,0.598629," ","integrate(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b^{2} x^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 \, a b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) + 4 i \, a^{2} x^{2}}{4 \, c^{3} d^{3} x^{3} - 12 i \, c^{2} d^{3} x^{2} - 12 \, c d^{3} x + 4 i \, d^{3}}, x\right)"," ",0,"integral((-I*b^2*x^2*log(-(c*x + I)/(c*x - I))^2 - 4*a*b*x^2*log(-(c*x + I)/(c*x - I)) + 4*I*a^2*x^2)/(4*c^3*d^3*x^3 - 12*I*c^2*d^3*x^2 - 12*c*d^3*x + 4*I*d^3), x)","F",0
114,1,161,0,1.419754," ","integrate(x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","\frac{{\left(-32 i \, a^{2} - 24 \, a b + 10 i \, b^{2}\right)} c x + {\left(3 \, b^{2} c^{2} x^{2} + 2 i \, b^{2} c x + b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 16 \, a^{2} + 16 i \, a b + 8 \, b^{2} + {\left({\left(-12 i \, a b - 5 \, b^{2}\right)} c^{2} x^{2} + {\left(8 \, a b - 2 i \, b^{2}\right)} c x - 4 i \, a b - 3 \, b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{32 \, {\left(c^{4} d^{3} x^{2} - 2 i \, c^{3} d^{3} x - c^{2} d^{3}\right)}}"," ",0,"1/32*((-32*I*a^2 - 24*a*b + 10*I*b^2)*c*x + (3*b^2*c^2*x^2 + 2*I*b^2*c*x + b^2)*log(-(c*x + I)/(c*x - I))^2 - 16*a^2 + 16*I*a*b + 8*b^2 + ((-12*I*a*b - 5*b^2)*c^2*x^2 + (8*a*b - 2*I*b^2)*c*x - 4*I*a*b - 3*b^2)*log(-(c*x + I)/(c*x - I)))/(c^4*d^3*x^2 - 2*I*c^3*d^3*x - c^2*d^3)","A",0
115,1,158,0,0.622908," ","integrate((a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 i \, a b + 3 \, b^{2}\right)} c x - {\left(i \, b^{2} c^{2} x^{2} + 2 \, b^{2} c x + 3 i \, b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 16 i \, a^{2} + 16 \, a b - 8 i \, b^{2} - {\left({\left(4 \, a b - 3 i \, b^{2}\right)} c^{2} x^{2} - 2 \, {\left(4 i \, a b + b^{2}\right)} c x + 12 \, a b - 5 i \, b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{32 \, {\left(c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}\right)}}"," ",0,"-1/32*(2*(4*I*a*b + 3*b^2)*c*x - (I*b^2*c^2*x^2 + 2*b^2*c*x + 3*I*b^2)*log(-(c*x + I)/(c*x - I))^2 + 16*I*a^2 + 16*a*b - 8*I*b^2 - ((4*a*b - 3*I*b^2)*c^2*x^2 - 2*(4*I*a*b + b^2)*c*x + 12*a*b - 5*I*b^2)*log(-(c*x + I)/(c*x - I)))/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3)","A",0
116,0,0,0,0.621778," ","integrate((a+b*arctan(c*x))^2/x/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) + 4 i \, a^{2}}{4 \, c^{3} d^{3} x^{4} - 12 i \, c^{2} d^{3} x^{3} - 12 \, c d^{3} x^{2} + 4 i \, d^{3} x}, x\right)"," ",0,"integral((-I*b^2*log(-(c*x + I)/(c*x - I))^2 - 4*a*b*log(-(c*x + I)/(c*x - I)) + 4*I*a^2)/(4*c^3*d^3*x^4 - 12*I*c^2*d^3*x^3 - 12*c*d^3*x^2 + 4*I*d^3*x), x)","F",0
117,0,0,0,0.666439," ","integrate((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 4 \, a b \log\left(-\frac{c x + i}{c x - i}\right) + 4 i \, a^{2}}{4 \, c^{3} d^{3} x^{5} - 12 i \, c^{2} d^{3} x^{4} - 12 \, c d^{3} x^{3} + 4 i \, d^{3} x^{2}}, x\right)"," ",0,"integral((-I*b^2*log(-(c*x + I)/(c*x - I))^2 - 4*a*b*log(-(c*x + I)/(c*x - I)) + 4*I*a^2)/(4*c^3*d^3*x^5 - 12*I*c^2*d^3*x^4 - 12*c*d^3*x^3 + 4*I*d^3*x^2), x)","F",0
118,1,206,0,0.799828," ","integrate((a+b*arctan(c*x))^2/(1+I*c*x)^4,x, algorithm=""fricas"")","-\frac{6 \, {\left(12 i \, a b + 11 \, b^{2}\right)} c^{2} x^{2} + {\left(216 \, a b - 162 i \, b^{2}\right)} c x - {\left(9 i \, b^{2} c^{3} x^{3} + 27 \, b^{2} c^{2} x^{2} - 27 i \, b^{2} c x + 63 \, b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + 288 \, a^{2} - 240 i \, a b - 112 \, b^{2} - {\left({\left(36 \, a b - 33 i \, b^{2}\right)} c^{3} x^{3} - 9 \, {\left(12 i \, a b + 7 \, b^{2}\right)} c^{2} x^{2} - {\left(108 \, a b + 9 i \, b^{2}\right)} c x - 252 i \, a b - 87 \, b^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{864 \, c^{4} x^{3} - 2592 i \, c^{3} x^{2} - 2592 \, c^{2} x + 864 i \, c}"," ",0,"-(6*(12*I*a*b + 11*b^2)*c^2*x^2 + (216*a*b - 162*I*b^2)*c*x - (9*I*b^2*c^3*x^3 + 27*b^2*c^2*x^2 - 27*I*b^2*c*x + 63*b^2)*log(-(c*x + I)/(c*x - I))^2 + 288*a^2 - 240*I*a*b - 112*b^2 - ((36*a*b - 33*I*b^2)*c^3*x^3 - 9*(12*I*a*b + 7*b^2)*c^2*x^2 - (108*a*b + 9*I*b^2)*c*x - 252*I*a*b - 87*b^2)*log(-(c*x + I)/(c*x - I)))/(864*c^4*x^3 - 2592*I*c^3*x^2 - 2592*c^2*x + 864*I*c)","A",0
119,0,0,0,0.480558," ","integrate(arctan(a*x)^2/(c*x-I*a*c*x^2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{i \, \log\left(-\frac{a x + i}{a x - i}\right)^{2}}{4 \, {\left(a c x^{2} + i \, c x\right)}}, x\right)"," ",0,"integral(-1/4*I*log(-(a*x + I)/(a*x - I))^2/(a*c*x^2 + I*c*x), x)","F",0
120,0,0,0,0.680352," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","-\frac{1}{32} \, {\left(b^{3} c^{3} d^{3} x^{4} - 4 i \, b^{3} c^{2} d^{3} x^{3} - 6 \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} d^{3} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{3} + {\rm integral}\left(\frac{-16 i \, a^{3} c^{5} d^{3} x^{5} - 48 \, a^{3} c^{4} d^{3} x^{4} + 32 i \, a^{3} c^{3} d^{3} x^{3} - 32 \, a^{3} c^{2} d^{3} x^{2} + 48 i \, a^{3} c d^{3} x + 16 \, a^{3} d^{3} + {\left(12 i \, a b^{2} c^{5} d^{3} x^{5} + {\left(36 \, a b^{2} - 3 i \, b^{3}\right)} c^{4} d^{3} x^{4} - 12 \, {\left(2 i \, a b^{2} + b^{3}\right)} c^{3} d^{3} x^{3} + {\left(24 \, a b^{2} + 18 i \, b^{3}\right)} c^{2} d^{3} x^{2} - 12 \, a b^{2} d^{3} - 12 \, {\left(3 i \, a b^{2} - b^{3}\right)} c d^{3} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\left(24 \, a^{2} b c^{5} d^{3} x^{5} - 72 i \, a^{2} b c^{4} d^{3} x^{4} - 48 \, a^{2} b c^{3} d^{3} x^{3} - 48 i \, a^{2} b c^{2} d^{3} x^{2} - 72 \, a^{2} b c d^{3} x + 24 i \, a^{2} b d^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"-1/32*(b^3*c^3*d^3*x^4 - 4*I*b^3*c^2*d^3*x^3 - 6*b^3*c*d^3*x^2 + 4*I*b^3*d^3*x)*log(-(c*x + I)/(c*x - I))^3 + integral(1/16*(-16*I*a^3*c^5*d^3*x^5 - 48*a^3*c^4*d^3*x^4 + 32*I*a^3*c^3*d^3*x^3 - 32*a^3*c^2*d^3*x^2 + 48*I*a^3*c*d^3*x + 16*a^3*d^3 + (12*I*a*b^2*c^5*d^3*x^5 + (36*a*b^2 - 3*I*b^3)*c^4*d^3*x^4 - 12*(2*I*a*b^2 + b^3)*c^3*d^3*x^3 + (24*a*b^2 + 18*I*b^3)*c^2*d^3*x^2 - 12*a*b^2*d^3 - 12*(3*I*a*b^2 - b^3)*c*d^3*x)*log(-(c*x + I)/(c*x - I))^2 + (24*a^2*b*c^5*d^3*x^5 - 72*I*a^2*b*c^4*d^3*x^4 - 48*a^2*b*c^3*d^3*x^3 - 48*I*a^2*b*c^2*d^3*x^2 - 72*a^2*b*c*d^3*x + 24*I*a^2*b*d^3)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
121,0,0,0,0.574665," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","\frac{1}{24} \, {\left(i \, b^{3} c^{2} d^{2} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 3 i \, b^{3} d^{2} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{3} + {\rm integral}\left(-\frac{4 \, a^{3} c^{4} d^{2} x^{4} - 8 i \, a^{3} c^{3} d^{2} x^{3} - 8 i \, a^{3} c d^{2} x - 4 \, a^{3} d^{2} - {\left(3 \, a b^{2} c^{4} d^{2} x^{4} + 3 i \, b^{3} c^{2} d^{2} x^{2} + {\left(-6 i \, a b^{2} - b^{3}\right)} c^{3} d^{2} x^{3} - 3 \, a b^{2} d^{2} - 3 \, {\left(2 i \, a b^{2} - b^{3}\right)} c d^{2} x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(-6 i \, a^{2} b c^{4} d^{2} x^{4} - 12 \, a^{2} b c^{3} d^{2} x^{3} - 12 \, a^{2} b c d^{2} x + 6 i \, a^{2} b d^{2}\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{4 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/24*(I*b^3*c^2*d^2*x^3 + 3*b^3*c*d^2*x^2 - 3*I*b^3*d^2*x)*log(-(c*x + I)/(c*x - I))^3 + integral(-1/4*(4*a^3*c^4*d^2*x^4 - 8*I*a^3*c^3*d^2*x^3 - 8*I*a^3*c*d^2*x - 4*a^3*d^2 - (3*a*b^2*c^4*d^2*x^4 + 3*I*b^3*c^2*d^2*x^2 + (-6*I*a*b^2 - b^3)*c^3*d^2*x^3 - 3*a*b^2*d^2 - 3*(2*I*a*b^2 - b^3)*c*d^2*x)*log(-(c*x + I)/(c*x - I))^2 - (-6*I*a^2*b*c^4*d^2*x^4 - 12*a^2*b*c^3*d^2*x^3 - 12*a^2*b*c*d^2*x + 6*I*a^2*b*d^2)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
122,0,0,0,0.545262," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","\frac{1}{16} \, {\left(b^{3} c d x^{2} - 2 i \, b^{3} d x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{3} + {\rm integral}\left(\frac{8 i \, a^{3} c^{3} d x^{3} + 8 \, a^{3} c^{2} d x^{2} + 8 i \, a^{3} c d x + 8 \, a^{3} d + {\left(-6 i \, a b^{2} c^{3} d x^{3} - {\left(6 \, a b^{2} - 3 i \, b^{3}\right)} c^{2} d x^{2} - 6 \, a b^{2} d - 6 \, {\left(i \, a b^{2} - b^{3}\right)} c d x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(12 \, a^{2} b c^{3} d x^{3} - 12 i \, a^{2} b c^{2} d x^{2} + 12 \, a^{2} b c d x - 12 i \, a^{2} b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{8 \, {\left(c^{2} x^{2} + 1\right)}}, x\right)"," ",0,"1/16*(b^3*c*d*x^2 - 2*I*b^3*d*x)*log(-(c*x + I)/(c*x - I))^3 + integral(1/8*(8*I*a^3*c^3*d*x^3 + 8*a^3*c^2*d*x^2 + 8*I*a^3*c*d*x + 8*a^3*d + (-6*I*a*b^2*c^3*d*x^3 - (6*a*b^2 - 3*I*b^3)*c^2*d*x^2 - 6*a*b^2*d - 6*(I*a*b^2 - b^3)*c*d*x)*log(-(c*x + I)/(c*x - I))^2 - (12*a^2*b*c^3*d*x^3 - 12*I*a^2*b*c^2*d*x^2 + 12*a^2*b*c*d*x - 12*I*a^2*b*d)*log(-(c*x + I)/(c*x - I)))/(c^2*x^2 + 1), x)","F",0
123,0,0,0,0.654253," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3}}{8 \, c d x - 8 i \, d}, x\right)"," ",0,"integral(-(b^3*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*log(-(c*x + I)/(c*x - I)) + 8*I*a^3)/(8*c*d*x - 8*I*d), x)","F",0
124,1,176,0,0.671919," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x)^2,x, algorithm=""fricas"")","-\frac{{\left(b^{3} c x + i \, b^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 16 \, a^{3} + 24 i \, a^{2} b + 24 \, a b^{2} - 12 i \, b^{3} + {\left(6 \, a b^{2} - 3 i \, b^{3} + 3 \, {\left(-2 i \, a b^{2} - b^{3}\right)} c x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(12 i \, a^{2} b + 12 \, a b^{2} - 6 i \, b^{3} + 6 \, {\left(2 \, a^{2} b - 2 i \, a b^{2} - b^{3}\right)} c x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{16 \, c^{2} d^{2} x - 16 i \, c d^{2}}"," ",0,"-((b^3*c*x + I*b^3)*log(-(c*x + I)/(c*x - I))^3 - 16*a^3 + 24*I*a^2*b + 24*a*b^2 - 12*I*b^3 + (6*a*b^2 - 3*I*b^3 + 3*(-2*I*a*b^2 - b^3)*c*x)*log(-(c*x + I)/(c*x - I))^2 - (12*I*a^2*b + 12*a*b^2 - 6*I*b^3 + 6*(2*a^2*b - 2*I*a*b^2 - b^3)*c*x)*log(-(c*x + I)/(c*x - I)))/(16*c^2*d^2*x - 16*I*c*d^2)","A",0
125,1,265,0,0.879155," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x)^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, b^{3} c^{2} x^{2} - 4 i \, b^{3} c x + 6 \, b^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{3} + 64 i \, a^{3} + 96 \, a^{2} b - 96 i \, a b^{2} - 48 \, b^{3} - {\left(-48 i \, a^{2} b - 72 \, a b^{2} + 42 i \, b^{3}\right)} c x + {\left(3 \, {\left(-4 i \, a b^{2} - 3 \, b^{3}\right)} c^{2} x^{2} - 36 i \, a b^{2} - 15 \, b^{3} - {\left(24 \, a b^{2} - 6 i \, b^{3}\right)} c x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - {\left(3 \, {\left(8 \, a^{2} b - 12 i \, a b^{2} - 7 \, b^{3}\right)} c^{2} x^{2} + 72 \, a^{2} b - 60 i \, a b^{2} - 27 \, b^{3} + {\left(-48 i \, a^{2} b - 24 \, a b^{2} + 6 i \, b^{3}\right)} c x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{128 \, {\left(c^{3} d^{3} x^{2} - 2 i \, c^{2} d^{3} x - c d^{3}\right)}}"," ",0,"-1/128*((2*b^3*c^2*x^2 - 4*I*b^3*c*x + 6*b^3)*log(-(c*x + I)/(c*x - I))^3 + 64*I*a^3 + 96*a^2*b - 96*I*a*b^2 - 48*b^3 - (-48*I*a^2*b - 72*a*b^2 + 42*I*b^3)*c*x + (3*(-4*I*a*b^2 - 3*b^3)*c^2*x^2 - 36*I*a*b^2 - 15*b^3 - (24*a*b^2 - 6*I*b^3)*c*x)*log(-(c*x + I)/(c*x - I))^2 - (3*(8*a^2*b - 12*I*a*b^2 - 7*b^3)*c^2*x^2 + 72*a^2*b - 60*I*a*b^2 - 27*b^3 + (-48*I*a^2*b - 24*a*b^2 + 6*I*b^3)*c*x)*log(-(c*x + I)/(c*x - I)))/(c^3*d^3*x^2 - 2*I*c^2*d^3*x - c*d^3)","A",0
126,1,359,0,0.532601," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x)^4,x, algorithm=""fricas"")","\frac{{\left(-432 i \, a^{2} b - 792 \, a b^{2} + 510 i \, b^{3}\right)} c^{2} x^{2} - {\left(18 \, b^{3} c^{3} x^{3} - 54 i \, b^{3} c^{2} x^{2} - 54 \, b^{3} c x - 126 i \, b^{3}\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 1152 \, a^{3} + 1440 i \, a^{2} b + 1344 \, a b^{2} - 656 i \, b^{3} - 162 \, {\left(8 \, a^{2} b - 12 i \, a b^{2} - 7 \, b^{3}\right)} c x - {\left(9 \, {\left(-12 i \, a b^{2} - 11 \, b^{3}\right)} c^{3} x^{3} - {\left(324 \, a b^{2} - 189 i \, b^{3}\right)} c^{2} x^{2} - 756 \, a b^{2} + 261 i \, b^{3} + 27 \, {\left(12 i \, a b^{2} - b^{3}\right)} c x\right)} \log\left(-\frac{c x + i}{c x - i}\right)^{2} + {\left(3 \, {\left(72 \, a^{2} b - 132 i \, a b^{2} - 85 \, b^{3}\right)} c^{3} x^{3} + {\left(-648 i \, a^{2} b - 756 \, a b^{2} + 369 i \, b^{3}\right)} c^{2} x^{2} - 1512 i \, a^{2} b - 1044 \, a b^{2} + 417 i \, b^{3} - 9 \, {\left(72 \, a^{2} b + 12 i \, a b^{2} + 23 \, b^{3}\right)} c x\right)} \log\left(-\frac{c x + i}{c x - i}\right)}{3456 \, c^{4} d^{4} x^{3} - 10368 i \, c^{3} d^{4} x^{2} - 10368 \, c^{2} d^{4} x + 3456 i \, c d^{4}}"," ",0,"((-432*I*a^2*b - 792*a*b^2 + 510*I*b^3)*c^2*x^2 - (18*b^3*c^3*x^3 - 54*I*b^3*c^2*x^2 - 54*b^3*c*x - 126*I*b^3)*log(-(c*x + I)/(c*x - I))^3 - 1152*a^3 + 1440*I*a^2*b + 1344*a*b^2 - 656*I*b^3 - 162*(8*a^2*b - 12*I*a*b^2 - 7*b^3)*c*x - (9*(-12*I*a*b^2 - 11*b^3)*c^3*x^3 - (324*a*b^2 - 189*I*b^3)*c^2*x^2 - 756*a*b^2 + 261*I*b^3 + 27*(12*I*a*b^2 - b^3)*c*x)*log(-(c*x + I)/(c*x - I))^2 + (3*(72*a^2*b - 132*I*a*b^2 - 85*b^3)*c^3*x^3 + (-648*I*a^2*b - 756*a*b^2 + 369*I*b^3)*c^2*x^2 - 1512*I*a^2*b - 1044*a*b^2 + 417*I*b^3 - 9*(72*a^2*b + 12*I*a*b^2 + 23*b^3)*c*x)*log(-(c*x + I)/(c*x - I)))/(3456*c^4*d^4*x^3 - 10368*I*c^3*d^4*x^2 - 10368*c^2*d^4*x + 3456*I*c*d^4)","A",0
127,0,0,0,0.500316," ","integrate(x^2*(a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} x^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} x^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b x^{2} \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3} x^{2}}{8 \, c d x - 8 i \, d}, x\right)"," ",0,"integral(-(b^3*x^2*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*x^2*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*x^2*log(-(c*x + I)/(c*x - I)) + 8*I*a^3*x^2)/(8*c*d*x - 8*I*d), x)","F",0
128,0,0,0,1.331186," ","integrate(x*(a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} x \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} x \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b x \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3} x}{8 \, c d x - 8 i \, d}, x\right)"," ",0,"integral(-(b^3*x*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*x*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*x*log(-(c*x + I)/(c*x - I)) + 8*I*a^3*x)/(8*c*d*x - 8*I*d), x)","F",0
129,0,0,0,1.088144," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3}}{8 \, c d x - 8 i \, d}, x\right)"," ",0,"integral(-(b^3*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*log(-(c*x + I)/(c*x - I)) + 8*I*a^3)/(8*c*d*x - 8*I*d), x)","F",0
130,0,0,0,0.569150," ","integrate((a+b*arctan(c*x))^3/x/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3}}{8 \, c d x^{2} - 8 i \, d x}, x\right)"," ",0,"integral(-(b^3*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*log(-(c*x + I)/(c*x - I)) + 8*I*a^3)/(8*c*d*x^2 - 8*I*d*x), x)","F",0
131,0,0,0,0.571245," ","integrate((a+b*arctan(c*x))^3/x^2/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3}}{8 \, c d x^{3} - 8 i \, d x^{2}}, x\right)"," ",0,"integral(-(b^3*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*log(-(c*x + I)/(c*x - I)) + 8*I*a^3)/(8*c*d*x^3 - 8*I*d*x^2), x)","F",0
132,0,0,0,0.792053," ","integrate((a+b*arctan(c*x))^3/x^3/(d+I*c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \log\left(-\frac{c x + i}{c x - i}\right)^{3} - 6 i \, a b^{2} \log\left(-\frac{c x + i}{c x - i}\right)^{2} - 12 \, a^{2} b \log\left(-\frac{c x + i}{c x - i}\right) + 8 i \, a^{3}}{8 \, c d x^{4} - 8 i \, d x^{3}}, x\right)"," ",0,"integral(-(b^3*log(-(c*x + I)/(c*x - I))^3 - 6*I*a*b^2*log(-(c*x + I)/(c*x - I))^2 - 12*a^2*b*log(-(c*x + I)/(c*x - I)) + 8*I*a^3)/(8*c*d*x^4 - 8*I*d*x^3), x)","F",0
133,0,0,0,0.577639," ","integrate(1/(d+I*c*d*x)/(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2}{-2 i \, a c d x - 2 \, a d + {\left(b c d x - i \, b d\right)} \log\left(-\frac{c x + i}{c x - i}\right)}, x\right)"," ",0,"integral(-2/(-2*I*a*c*d*x - 2*a*d + (b*c*d*x - I*b*d)*log(-(c*x + I)/(c*x - I))), x)","F",0
134,0,0,0,0.722909," ","integrate(x^3*(a+b*arctan(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arctan\left(c x\right) + a x^{3}}{e x + d}, x\right)"," ",0,"integral((b*x^3*arctan(c*x) + a*x^3)/(e*x + d), x)","F",0
135,0,0,0,0.529953," ","integrate(x^2*(a+b*arctan(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arctan\left(c x\right) + a x^{2}}{e x + d}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)/(e*x + d), x)","F",0
136,0,0,0,0.504300," ","integrate(x*(a+b*arctan(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \arctan\left(c x\right) + a x}{e x + d}, x\right)"," ",0,"integral((b*x*arctan(c*x) + a*x)/(e*x + d), x)","F",0
137,0,0,0,0.761864," ","integrate((a+b*arctan(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x + d), x)","F",0
138,0,0,0,1.688041," ","integrate((a+b*arctan(c*x))/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{2} + d x}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^2 + d*x), x)","F",0
139,0,0,0,0.814811," ","integrate((a+b*arctan(c*x))/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^3 + d*x^2), x)","F",0
140,0,0,0,0.686794," ","integrate((a+b*arctan(c*x))/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^4 + d*x^3), x)","F",0
141,0,0,0,0.584652," ","integrate(x^3*(a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \arctan\left(c x\right)^{2} + 2 \, a b x^{3} \arctan\left(c x\right) + a^{2} x^{3}}{e x + d}, x\right)"," ",0,"integral((b^2*x^3*arctan(c*x)^2 + 2*a*b*x^3*arctan(c*x) + a^2*x^3)/(e*x + d), x)","F",0
142,0,0,0,0.602125," ","integrate(x^2*(a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \arctan\left(c x\right)^{2} + 2 \, a b x^{2} \arctan\left(c x\right) + a^{2} x^{2}}{e x + d}, x\right)"," ",0,"integral((b^2*x^2*arctan(c*x)^2 + 2*a*b*x^2*arctan(c*x) + a^2*x^2)/(e*x + d), x)","F",0
143,0,0,0,0.517966," ","integrate(x*(a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \arctan\left(c x\right)^{2} + 2 \, a b x \arctan\left(c x\right) + a^{2} x}{e x + d}, x\right)"," ",0,"integral((b^2*x*arctan(c*x)^2 + 2*a*b*x*arctan(c*x) + a^2*x)/(e*x + d), x)","F",0
144,0,0,0,0.927108," ","integrate((a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x + d}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x + d), x)","F",0
145,0,0,0,0.627813," ","integrate((a+b*arctan(c*x))^2/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{2} + d x}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^2 + d*x), x)","F",0
146,0,0,0,1.287872," ","integrate((a+b*arctan(c*x))^2/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^3 + d*x^2), x)","F",0
147,0,0,0,0.408893," ","integrate((a+b*arctan(c*x))^2/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^4 + d*x^3), x)","F",0
148,0,0,0,0.668829," ","integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a e x + a d + {\left(b e x + b d\right)} \arctan\left(c x\right)}, x\right)"," ",0,"integral(1/(a*e*x + a*d + (b*e*x + b*d)*arctan(c*x)), x)","F",0
149,1,57,0,0.951299," ","integrate(x^3*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""fricas"")","-\frac{6 \, a^{5} c x^{5} + 5 \, a^{3} c x^{3} - 15 \, a c x - 15 \, {\left(2 \, a^{6} c x^{6} + 3 \, a^{4} c x^{4} - c\right)} \arctan\left(a x\right)}{180 \, a^{4}}"," ",0,"-1/180*(6*a^5*c*x^5 + 5*a^3*c*x^3 - 15*a*c*x - 15*(2*a^6*c*x^6 + 3*a^4*c*x^4 - c)*arctan(a*x))/a^4","A",0
150,1,62,0,0.680609," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""fricas"")","-\frac{3 \, a^{4} c x^{4} + 4 \, a^{2} c x^{2} - 4 \, {\left(3 \, a^{5} c x^{5} + 5 \, a^{3} c x^{3}\right)} \arctan\left(a x\right) - 4 \, c \log\left(a^{2} x^{2} + 1\right)}{60 \, a^{3}}"," ",0,"-1/60*(3*a^4*c*x^4 + 4*a^2*c*x^2 - 4*(3*a^5*c*x^5 + 5*a^3*c*x^3)*arctan(a*x) - 4*c*log(a^2*x^2 + 1))/a^3","A",0
151,1,44,0,0.609916," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""fricas"")","-\frac{a^{3} c x^{3} + 3 \, a c x - 3 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{12 \, a^{2}}"," ",0,"-1/12*(a^3*c*x^3 + 3*a*c*x - 3*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x))/a^2","A",0
152,1,47,0,1.012876," ","integrate((a^2*c*x^2+c)*arctan(a*x),x, algorithm=""fricas"")","-\frac{a^{2} c x^{2} - 2 \, {\left(a^{3} c x^{3} + 3 \, a c x\right)} \arctan\left(a x\right) + 2 \, c \log\left(a^{2} x^{2} + 1\right)}{6 \, a}"," ",0,"-1/6*(a^2*c*x^2 - 2*(a^3*c*x^3 + 3*a*c*x)*arctan(a*x) + 2*c*log(a^2*x^2 + 1))/a","A",0
153,0,0,0,0.496751," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{x}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)/x, x)","F",0
154,1,45,0,0.475814," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x^2,x, algorithm=""fricas"")","-\frac{a c x \log\left(a^{2} x^{2} + 1\right) - a c x \log\left(x\right) - {\left(a^{2} c x^{2} - c\right)} \arctan\left(a x\right)}{x}"," ",0,"-(a*c*x*log(a^2*x^2 + 1) - a*c*x*log(x) - (a^2*c*x^2 - c)*arctan(a*x))/x","A",0
155,0,0,0,0.472424," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)/x^3, x)","F",0
156,1,57,0,0.496065," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x^4,x, algorithm=""fricas"")","-\frac{2 \, a^{3} c x^{3} \log\left(a^{2} x^{2} + 1\right) - 4 \, a^{3} c x^{3} \log\left(x\right) + a c x + 2 \, {\left(3 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{6 \, x^{3}}"," ",0,"-1/6*(2*a^3*c*x^3*log(a^2*x^2 + 1) - 4*a^3*c*x^3*log(x) + a*c*x + 2*(3*a^2*c*x^2 + c)*arctan(a*x))/x^3","A",0
157,1,91,0,0.473460," ","integrate(x^3*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""fricas"")","-\frac{9 \, a^{7} c^{2} x^{7} + 21 \, a^{5} c^{2} x^{5} + 7 \, a^{3} c^{2} x^{3} - 21 \, a c^{2} x - 21 \, {\left(3 \, a^{8} c^{2} x^{8} + 8 \, a^{6} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{4} - c^{2}\right)} \arctan\left(a x\right)}{504 \, a^{4}}"," ",0,"-1/504*(9*a^7*c^2*x^7 + 21*a^5*c^2*x^5 + 7*a^3*c^2*x^3 - 21*a*c^2*x - 21*(3*a^8*c^2*x^8 + 8*a^6*c^2*x^6 + 6*a^4*c^2*x^4 - c^2)*arctan(a*x))/a^4","A",0
158,1,94,0,0.444625," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""fricas"")","-\frac{10 \, a^{6} c^{2} x^{6} + 27 \, a^{4} c^{2} x^{4} + 16 \, a^{2} c^{2} x^{2} - 16 \, c^{2} \log\left(a^{2} x^{2} + 1\right) - 4 \, {\left(15 \, a^{7} c^{2} x^{7} + 42 \, a^{5} c^{2} x^{5} + 35 \, a^{3} c^{2} x^{3}\right)} \arctan\left(a x\right)}{420 \, a^{3}}"," ",0,"-1/420*(10*a^6*c^2*x^6 + 27*a^4*c^2*x^4 + 16*a^2*c^2*x^2 - 16*c^2*log(a^2*x^2 + 1) - 4*(15*a^7*c^2*x^7 + 42*a^5*c^2*x^5 + 35*a^3*c^2*x^3)*arctan(a*x))/a^3","A",0
159,1,77,0,0.473881," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""fricas"")","-\frac{3 \, a^{5} c^{2} x^{5} + 10 \, a^{3} c^{2} x^{3} + 15 \, a c^{2} x - 15 \, {\left(a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}{90 \, a^{2}}"," ",0,"-1/90*(3*a^5*c^2*x^5 + 10*a^3*c^2*x^3 + 15*a*c^2*x - 15*(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*arctan(a*x))/a^2","A",0
160,1,79,0,0.476364," ","integrate((a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""fricas"")","-\frac{3 \, a^{4} c^{2} x^{4} + 14 \, a^{2} c^{2} x^{2} + 16 \, c^{2} \log\left(a^{2} x^{2} + 1\right) - 4 \, {\left(3 \, a^{5} c^{2} x^{5} + 10 \, a^{3} c^{2} x^{3} + 15 \, a c^{2} x\right)} \arctan\left(a x\right)}{60 \, a}"," ",0,"-1/60*(3*a^4*c^2*x^4 + 14*a^2*c^2*x^2 + 16*c^2*log(a^2*x^2 + 1) - 4*(3*a^5*c^2*x^5 + 10*a^3*c^2*x^3 + 15*a*c^2*x)*arctan(a*x))/a","A",0
161,0,0,0,0.443234," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}{x}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)/x, x)","F",0
162,1,75,0,0.679191," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x^2,x, algorithm=""fricas"")","-\frac{a^{3} c^{2} x^{3} + 8 \, a c^{2} x \log\left(a^{2} x^{2} + 1\right) - 6 \, a c^{2} x \log\left(x\right) - 2 \, {\left(a^{4} c^{2} x^{4} + 6 \, a^{2} c^{2} x^{2} - 3 \, c^{2}\right)} \arctan\left(a x\right)}{6 \, x}"," ",0,"-1/6*(a^3*c^2*x^3 + 8*a*c^2*x*log(a^2*x^2 + 1) - 6*a*c^2*x*log(x) - 2*(a^4*c^2*x^4 + 6*a^2*c^2*x^2 - 3*c^2)*arctan(a*x))/x","A",0
163,0,0,0,0.542384," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)/x^3, x)","F",0
164,1,80,0,0.634716," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x^4,x, algorithm=""fricas"")","-\frac{8 \, a^{3} c^{2} x^{3} \log\left(a^{2} x^{2} + 1\right) - 10 \, a^{3} c^{2} x^{3} \log\left(x\right) + a c^{2} x - 2 \, {\left(3 \, a^{4} c^{2} x^{4} - 6 \, a^{2} c^{2} x^{2} - c^{2}\right)} \arctan\left(a x\right)}{6 \, x^{3}}"," ",0,"-1/6*(8*a^3*c^2*x^3*log(a^2*x^2 + 1) - 10*a^3*c^2*x^3*log(x) + a*c^2*x - 2*(3*a^4*c^2*x^4 - 6*a^2*c^2*x^2 - c^2)*arctan(a*x))/x^3","A",0
165,1,113,0,0.568431," ","integrate(x^3*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""fricas"")","-\frac{140 \, a^{9} c^{3} x^{9} + 495 \, a^{7} c^{3} x^{7} + 567 \, a^{5} c^{3} x^{5} + 105 \, a^{3} c^{3} x^{3} - 315 \, a c^{3} x - 315 \, {\left(4 \, a^{10} c^{3} x^{10} + 15 \, a^{8} c^{3} x^{8} + 20 \, a^{6} c^{3} x^{6} + 10 \, a^{4} c^{3} x^{4} - c^{3}\right)} \arctan\left(a x\right)}{12600 \, a^{4}}"," ",0,"-1/12600*(140*a^9*c^3*x^9 + 495*a^7*c^3*x^7 + 567*a^5*c^3*x^5 + 105*a^3*c^3*x^3 - 315*a*c^3*x - 315*(4*a^10*c^3*x^10 + 15*a^8*c^3*x^8 + 20*a^6*c^3*x^6 + 10*a^4*c^3*x^4 - c^3)*arctan(a*x))/a^4","A",0
166,1,116,0,0.496529," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""fricas"")","-\frac{105 \, a^{8} c^{3} x^{8} + 400 \, a^{6} c^{3} x^{6} + 534 \, a^{4} c^{3} x^{4} + 192 \, a^{2} c^{3} x^{2} - 192 \, c^{3} \log\left(a^{2} x^{2} + 1\right) - 24 \, {\left(35 \, a^{9} c^{3} x^{9} + 135 \, a^{7} c^{3} x^{7} + 189 \, a^{5} c^{3} x^{5} + 105 \, a^{3} c^{3} x^{3}\right)} \arctan\left(a x\right)}{7560 \, a^{3}}"," ",0,"-1/7560*(105*a^8*c^3*x^8 + 400*a^6*c^3*x^6 + 534*a^4*c^3*x^4 + 192*a^2*c^3*x^2 - 192*c^3*log(a^2*x^2 + 1) - 24*(35*a^9*c^3*x^9 + 135*a^7*c^3*x^7 + 189*a^5*c^3*x^5 + 105*a^3*c^3*x^3)*arctan(a*x))/a^3","A",0
167,1,99,0,0.611698," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""fricas"")","-\frac{5 \, a^{7} c^{3} x^{7} + 21 \, a^{5} c^{3} x^{5} + 35 \, a^{3} c^{3} x^{3} + 35 \, a c^{3} x - 35 \, {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}{280 \, a^{2}}"," ",0,"-1/280*(5*a^7*c^3*x^7 + 21*a^5*c^3*x^5 + 35*a^3*c^3*x^3 + 35*a*c^3*x - 35*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*arctan(a*x))/a^2","A",0
168,1,101,0,0.570808," ","integrate((a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""fricas"")","-\frac{5 \, a^{6} c^{3} x^{6} + 24 \, a^{4} c^{3} x^{4} + 57 \, a^{2} c^{3} x^{2} + 48 \, c^{3} \log\left(a^{2} x^{2} + 1\right) - 6 \, {\left(5 \, a^{7} c^{3} x^{7} + 21 \, a^{5} c^{3} x^{5} + 35 \, a^{3} c^{3} x^{3} + 35 \, a c^{3} x\right)} \arctan\left(a x\right)}{210 \, a}"," ",0,"-1/210*(5*a^6*c^3*x^6 + 24*a^4*c^3*x^4 + 57*a^2*c^3*x^2 + 48*c^3*log(a^2*x^2 + 1) - 6*(5*a^7*c^3*x^7 + 21*a^5*c^3*x^5 + 35*a^3*c^3*x^3 + 35*a*c^3*x)*arctan(a*x))/a","A",0
169,0,0,0,0.626266," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}{x}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)/x, x)","F",0
170,1,97,0,0.527781," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x^2,x, algorithm=""fricas"")","-\frac{a^{5} c^{3} x^{5} + 8 \, a^{3} c^{3} x^{3} + 32 \, a c^{3} x \log\left(a^{2} x^{2} + 1\right) - 20 \, a c^{3} x \log\left(x\right) - 4 \, {\left(a^{6} c^{3} x^{6} + 5 \, a^{4} c^{3} x^{4} + 15 \, a^{2} c^{3} x^{2} - 5 \, c^{3}\right)} \arctan\left(a x\right)}{20 \, x}"," ",0,"-1/20*(a^5*c^3*x^5 + 8*a^3*c^3*x^3 + 32*a*c^3*x*log(a^2*x^2 + 1) - 20*a*c^3*x*log(x) - 4*(a^6*c^3*x^6 + 5*a^4*c^3*x^4 + 15*a^2*c^3*x^2 - 5*c^3)*arctan(a*x))/x","A",0
171,0,0,0,0.586613," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)/x^3, x)","F",0
172,1,100,0,0.501414," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x^4,x, algorithm=""fricas"")","-\frac{a^{5} c^{3} x^{5} + 16 \, a^{3} c^{3} x^{3} \log\left(a^{2} x^{2} + 1\right) - 16 \, a^{3} c^{3} x^{3} \log\left(x\right) + a c^{3} x - 2 \, {\left(a^{6} c^{3} x^{6} + 9 \, a^{4} c^{3} x^{4} - 9 \, a^{2} c^{3} x^{2} - c^{3}\right)} \arctan\left(a x\right)}{6 \, x^{3}}"," ",0,"-1/6*(a^5*c^3*x^5 + 16*a^3*c^3*x^3*log(a^2*x^2 + 1) - 16*a^3*c^3*x^3*log(x) + a*c^3*x - 2*(a^6*c^3*x^6 + 9*a^4*c^3*x^4 - 9*a^2*c^3*x^2 - c^3)*arctan(a*x))/x^3","A",0
173,1,54,0,0.450627," ","integrate(x^4*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{a^{2} x^{2} - 2 \, {\left(a^{3} x^{3} - 3 \, a x\right)} \arctan\left(a x\right) - 3 \, \arctan\left(a x\right)^{2} - 4 \, \log\left(a^{2} x^{2} + 1\right)}{6 \, a^{5} c}"," ",0,"-1/6*(a^2*x^2 - 2*(a^3*x^3 - 3*a*x)*arctan(a*x) - 3*arctan(a*x)^2 - 4*log(a^2*x^2 + 1))/(a^5*c)","A",0
174,0,0,0,0.478475," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^3*arctan(a*x)/(a^2*c*x^2 + c), x)","F",0
175,1,37,0,0.461662," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{2 \, a x \arctan\left(a x\right) - \arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right)}{2 \, a^{3} c}"," ",0,"1/2*(2*a*x*arctan(a*x) - arctan(a*x)^2 - log(a^2*x^2 + 1))/(a^3*c)","A",0
176,0,0,0,0.528325," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(a x\right)}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x*arctan(a*x)/(a^2*c*x^2 + c), x)","F",0
177,1,14,0,0.468841," ","integrate(arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{\arctan\left(a x\right)^{2}}{2 \, a c}"," ",0,"1/2*arctan(a*x)^2/(a*c)","A",0
178,0,0,0,0.490826," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(arctan(a*x)/(a^2*c*x^3 + c*x), x)","F",0
179,1,43,0,0.677928," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","-\frac{a x \arctan\left(a x\right)^{2} + a x \log\left(a^{2} x^{2} + 1\right) - 2 \, a x \log\left(x\right) + 2 \, \arctan\left(a x\right)}{2 \, c x}"," ",0,"-1/2*(a*x*arctan(a*x)^2 + a*x*log(a^2*x^2 + 1) - 2*a*x*log(x) + 2*arctan(a*x))/(c*x)","A",0
180,0,0,0,0.489462," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(arctan(a*x)/(a^2*c*x^5 + c*x^3), x)","F",0
181,1,71,0,0.463321," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{3 \, a^{3} x^{3} \arctan\left(a x\right)^{2} + 4 \, a^{3} x^{3} \log\left(a^{2} x^{2} + 1\right) - 8 \, a^{3} x^{3} \log\left(x\right) - a x + 2 \, {\left(3 \, a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{6 \, c x^{3}}"," ",0,"1/6*(3*a^3*x^3*arctan(a*x)^2 + 4*a^3*x^3*log(a^2*x^2 + 1) - 8*a^3*x^3*log(x) - a*x + 2*(3*a^2*x^2 - 1)*arctan(a*x))/(c*x^3)","A",0
182,0,0,0,0.460108," ","integrate(x^5*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5} \arctan\left(a x\right)}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^5*arctan(a*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
183,1,81,0,0.533999," ","integrate(x^4*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 2 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right) + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a^{2} x^{2} + 1\right) - 1}{4 \, {\left(a^{7} c^{2} x^{2} + a^{5} c^{2}\right)}}"," ",0,"-1/4*(3*(a^2*x^2 + 1)*arctan(a*x)^2 - 2*(2*a^3*x^3 + 3*a*x)*arctan(a*x) + 2*(a^2*x^2 + 1)*log(a^2*x^2 + 1) - 1)/(a^7*c^2*x^2 + a^5*c^2)","A",0
184,0,0,0,0.413166," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^3*arctan(a*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
185,1,49,0,0.521487," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{2 \, a x \arctan\left(a x\right) - {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 1}{4 \, {\left(a^{5} c^{2} x^{2} + a^{3} c^{2}\right)}}"," ",0,"-1/4*(2*a*x*arctan(a*x) - (a^2*x^2 + 1)*arctan(a*x)^2 + 1)/(a^5*c^2*x^2 + a^3*c^2)","A",0
186,1,40,0,0.502678," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{a x + {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{4 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}"," ",0,"1/4*(a*x + (a^2*x^2 - 1)*arctan(a*x))/(a^4*c^2*x^2 + a^2*c^2)","A",0
187,1,46,0,0.529130," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{2 \, a x \arctan\left(a x\right) + {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 1}{4 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/4*(2*a*x*arctan(a*x) + (a^2*x^2 + 1)*arctan(a*x)^2 + 1)/(a^3*c^2*x^2 + a*c^2)","A",0
188,0,0,0,0.477231," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(arctan(a*x)/(a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x), x)","F",0
189,1,97,0,0.487259," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{3} x^{3} + a x\right)} \arctan\left(a x\right)^{2} + a x + 2 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right) + 2 \, {\left(a^{3} x^{3} + a x\right)} \log\left(a^{2} x^{2} + 1\right) - 4 \, {\left(a^{3} x^{3} + a x\right)} \log\left(x\right)}{4 \, {\left(a^{2} c^{2} x^{3} + c^{2} x\right)}}"," ",0,"-1/4*(3*(a^3*x^3 + a*x)*arctan(a*x)^2 + a*x + 2*(3*a^2*x^2 + 2)*arctan(a*x) + 2*(a^3*x^3 + a*x)*log(a^2*x^2 + 1) - 4*(a^3*x^3 + a*x)*log(x))/(a^2*c^2*x^3 + c^2*x)","A",0
190,0,0,0,0.504755," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}}, x\right)"," ",0,"integral(arctan(a*x)/(a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3), x)","F",0
191,1,127,0,0.506727," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} + 15 \, {\left(a^{5} x^{5} + a^{3} x^{3}\right)} \arctan\left(a x\right)^{2} - 2 \, a x + 2 \, {\left(15 \, a^{4} x^{4} + 10 \, a^{2} x^{2} - 2\right)} \arctan\left(a x\right) + 14 \, {\left(a^{5} x^{5} + a^{3} x^{3}\right)} \log\left(a^{2} x^{2} + 1\right) - 28 \, {\left(a^{5} x^{5} + a^{3} x^{3}\right)} \log\left(x\right)}{12 \, {\left(a^{2} c^{2} x^{5} + c^{2} x^{3}\right)}}"," ",0,"1/12*(a^3*x^3 + 15*(a^5*x^5 + a^3*x^3)*arctan(a*x)^2 - 2*a*x + 2*(15*a^4*x^4 + 10*a^2*x^2 - 2)*arctan(a*x) + 14*(a^5*x^5 + a^3*x^3)*log(a^2*x^2 + 1) - 28*(a^5*x^5 + a^3*x^3)*log(x))/(a^2*c^2*x^5 + c^2*x^3)","A",0
192,1,69,0,0.609839," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{5 \, a^{3} x^{3} + 3 \, a x + {\left(5 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 3\right)} \arctan\left(a x\right)}{32 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/32*(5*a^3*x^3 + 3*a*x + (5*a^4*x^4 - 6*a^2*x^2 - 3)*arctan(a*x))/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
193,1,83,0,0.470925," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \arctan\left(a x\right)}{16 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"1/16*(a^2*x^2 + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 2*(a^3*x^3 - a*x)*arctan(a*x))/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)","A",0
194,1,69,0,0.630105," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{3 \, a^{3} x^{3} + 5 \, a x + {\left(3 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 5\right)} \arctan\left(a x\right)}{32 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/32*(3*a^3*x^3 + 5*a*x + (3*a^4*x^4 + 6*a^2*x^2 - 5)*arctan(a*x))/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
195,1,85,0,0.457070," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 2 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \arctan\left(a x\right) + 4}{16 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/16*(3*a^2*x^2 + 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 2*(3*a^3*x^3 + 5*a*x)*arctan(a*x) + 4)/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
196,0,0,0,0.573121," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}, x\right)"," ",0,"integral(arctan(a*x)/(a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x), x)","F",0
197,1,149,0,0.586834," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{7 \, a^{3} x^{3} + 15 \, {\left(a^{5} x^{5} + 2 \, a^{3} x^{3} + a x\right)} \arctan\left(a x\right)^{2} + 8 \, a x + 2 \, {\left(15 \, a^{4} x^{4} + 25 \, a^{2} x^{2} + 8\right)} \arctan\left(a x\right) + 8 \, {\left(a^{5} x^{5} + 2 \, a^{3} x^{3} + a x\right)} \log\left(a^{2} x^{2} + 1\right) - 16 \, {\left(a^{5} x^{5} + 2 \, a^{3} x^{3} + a x\right)} \log\left(x\right)}{16 \, {\left(a^{4} c^{3} x^{5} + 2 \, a^{2} c^{3} x^{3} + c^{3} x\right)}}"," ",0,"-1/16*(7*a^3*x^3 + 15*(a^5*x^5 + 2*a^3*x^3 + a*x)*arctan(a*x)^2 + 8*a*x + 2*(15*a^4*x^4 + 25*a^2*x^2 + 8)*arctan(a*x) + 8*(a^5*x^5 + 2*a^3*x^3 + a*x)*log(a^2*x^2 + 1) - 16*(a^5*x^5 + 2*a^3*x^3 + a*x)*log(x))/(a^4*c^3*x^5 + 2*a^2*c^3*x^3 + c^3*x)","A",0
198,0,0,0,0.531182," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}}, x\right)"," ",0,"integral(arctan(a*x)/(a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3), x)","F",0
199,1,179,0,0.681368," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{25 \, a^{5} x^{5} + 20 \, a^{3} x^{3} + 105 \, {\left(a^{7} x^{7} + 2 \, a^{5} x^{5} + a^{3} x^{3}\right)} \arctan\left(a x\right)^{2} - 8 \, a x + 2 \, {\left(105 \, a^{6} x^{6} + 175 \, a^{4} x^{4} + 56 \, a^{2} x^{2} - 8\right)} \arctan\left(a x\right) + 80 \, {\left(a^{7} x^{7} + 2 \, a^{5} x^{5} + a^{3} x^{3}\right)} \log\left(a^{2} x^{2} + 1\right) - 160 \, {\left(a^{7} x^{7} + 2 \, a^{5} x^{5} + a^{3} x^{3}\right)} \log\left(x\right)}{48 \, {\left(a^{4} c^{3} x^{7} + 2 \, a^{2} c^{3} x^{5} + c^{3} x^{3}\right)}}"," ",0,"1/48*(25*a^5*x^5 + 20*a^3*x^3 + 105*(a^7*x^7 + 2*a^5*x^5 + a^3*x^3)*arctan(a*x)^2 - 8*a*x + 2*(105*a^6*x^6 + 175*a^4*x^4 + 56*a^2*x^2 - 8)*arctan(a*x) + 80*(a^7*x^7 + 2*a^5*x^5 + a^3*x^3)*log(a^2*x^2 + 1) - 160*(a^7*x^7 + 2*a^5*x^5 + a^3*x^3)*log(x))/(a^4*c^3*x^7 + 2*a^2*c^3*x^5 + c^3*x^3)","A",0
200,1,94,0,0.593144," ","integrate(x^3*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a^{3} x^{3} - 5 \, a x - 8 \, {\left(3 \, a^{4} x^{4} + a^{2} x^{2} - 2\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c} - 11 \, \sqrt{c} \log\left(-2 \, a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right)}{240 \, a^{4}}"," ",0,"-1/240*(2*(6*a^3*x^3 - 5*a*x - 8*(3*a^4*x^4 + a^2*x^2 - 2)*arctan(a*x))*sqrt(a^2*c*x^2 + c) - 11*sqrt(c)*log(-2*a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c))/a^4","A",0
201,0,0,0,0.534694," ","integrate(x^2*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right), x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x), x)","F",0
202,1,77,0,0.589374," ","integrate(x*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a^{2} c x^{2} + c} {\left(a x - 2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} - \sqrt{c} \log\left(-2 \, a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right)}{12 \, a^{2}}"," ",0,"-1/12*(2*sqrt(a^2*c*x^2 + c)*(a*x - 2*(a^2*x^2 + 1)*arctan(a*x)) - sqrt(c)*log(-2*a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c))/a^2","A",0
203,0,0,0,0.645093," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right), x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x), x)","F",0
204,0,0,0,0.598396," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/x, x)","F",0
205,0,0,0,0.739465," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^2, x)","F",0
206,0,0,0,0.738835," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^3, x)","F",0
207,1,84,0,0.788558," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{a^{3} \sqrt{c} x^{3} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{a^{2} c x^{2} + c} {\left(a x + 2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)}}{12 \, x^{3}}"," ",0,"1/12*(a^3*sqrt(c)*x^3*log(-(a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(a^2*c*x^2 + c)*(a*x + 2*(a^2*x^2 + 1)*arctan(a*x)))/x^3","A",0
208,1,118,0,0.750632," ","integrate(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""fricas"")","\frac{51 \, c^{\frac{3}{2}} \log\left(-2 \, a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right) - 2 \, {\left(40 \, a^{5} c x^{5} + 46 \, a^{3} c x^{3} - 45 \, a c x - 48 \, {\left(5 \, a^{6} c x^{6} + 8 \, a^{4} c x^{4} + a^{2} c x^{2} - 2 \, c\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{3360 \, a^{4}}"," ",0,"1/3360*(51*c^(3/2)*log(-2*a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c) - 2*(40*a^5*c*x^5 + 46*a^3*c*x^3 - 45*a*c*x - 48*(5*a^6*c*x^6 + 8*a^4*c*x^4 + a^2*c*x^2 - 2*c)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/a^4","A",0
209,0,0,0,0.572352," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{4} + c x^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right), x\right)"," ",0,"integral((a^2*c*x^4 + c*x^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x), x)","F",0
210,1,98,0,0.717500," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""fricas"")","\frac{3 \, c^{\frac{3}{2}} \log\left(-2 \, a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right) - 2 \, {\left(2 \, a^{3} c x^{3} + 5 \, a c x - 8 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{80 \, a^{2}}"," ",0,"1/80*(3*c^(3/2)*log(-2*a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c) - 2*(2*a^3*c*x^3 + 5*a*c*x - 8*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/a^2","A",0
211,0,0,0,0.770288," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right), x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x), x)","F",0
212,0,0,0,0.670306," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x, x)","F",0
213,0,0,0,0.579007," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x^2, x)","F",0
214,0,0,0,0.642576," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x^3, x)","F",0
215,0,0,0,0.497905," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{4}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x^4, x)","F",0
216,1,154,0,0.557907," ","integrate(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""fricas"")","\frac{345 \, c^{\frac{5}{2}} \log\left(-2 \, a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right) - 2 \, {\left(336 \, a^{7} c^{2} x^{7} + 824 \, a^{5} c^{2} x^{5} + 410 \, a^{3} c^{2} x^{3} - 423 \, a c^{2} x - 384 \, {\left(7 \, a^{8} c^{2} x^{8} + 19 \, a^{6} c^{2} x^{6} + 15 \, a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2} - 2 \, c^{2}\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{48384 \, a^{4}}"," ",0,"1/48384*(345*c^(5/2)*log(-2*a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c) - 2*(336*a^7*c^2*x^7 + 824*a^5*c^2*x^5 + 410*a^3*c^2*x^3 - 423*a*c^2*x - 384*(7*a^8*c^2*x^8 + 19*a^6*c^2*x^6 + 15*a^4*c^2*x^4 + a^2*c^2*x^2 - 2*c^2)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/a^4","A",0
217,0,0,0,0.727897," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right), x\right)"," ",0,"integral((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x), x)","F",0
218,1,130,0,0.622128," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""fricas"")","\frac{15 \, c^{\frac{5}{2}} \log\left(-2 \, a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right) - 2 \, {\left(8 \, a^{5} c^{2} x^{5} + 26 \, a^{3} c^{2} x^{3} + 33 \, a c^{2} x - 48 \, {\left(a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{672 \, a^{2}}"," ",0,"1/672*(15*c^(5/2)*log(-2*a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c) - 2*(8*a^5*c^2*x^5 + 26*a^3*c^2*x^3 + 33*a*c^2*x - 48*(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/a^2","A",0
219,0,0,0,0.810221," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right), x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x), x)","F",0
220,0,0,0,0.624490," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)/x, x)","F",0
221,0,0,0,0.520144," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^2, x)","F",0
222,0,0,0,1.053450," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^3, x)","F",0
223,0,0,0,0.599578," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{4}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^4, x)","F",0
224,1,80,0,0.663196," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a^{2} c x^{2} + c} {\left(a x - 2 \, {\left(a^{2} x^{2} - 2\right)} \arctan\left(a x\right)\right)} - 5 \, \sqrt{c} \log\left(-2 \, a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right)}{12 \, a^{4} c}"," ",0,"-1/12*(2*sqrt(a^2*c*x^2 + c)*(a*x - 2*(a^2*x^2 - 2)*arctan(a*x)) - 5*sqrt(c)*log(-2*a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c))/(a^4*c)","A",0
225,0,0,0,0.470055," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^2*arctan(a*x)/sqrt(a^2*c*x^2 + c), x)","F",0
226,1,64,0,0.563091," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right) + \sqrt{c} \log\left(-2 \, a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right)}{2 \, a^{2} c}"," ",0,"1/2*(2*sqrt(a^2*c*x^2 + c)*arctan(a*x) + sqrt(c)*log(-2*a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c))/(a^2*c)","A",0
227,0,0,0,0.763343," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(arctan(a*x)/sqrt(a^2*c*x^2 + c), x)","F",0
228,0,0,0,0.504483," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/(a^2*c*x^3 + c*x), x)","F",0
229,1,68,0,0.597853," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{a \sqrt{c} x \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{2 \, c x}"," ",0,"1/2*(a*sqrt(c)*x*log(-(a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(a^2*c*x^2 + c)*arctan(a*x))/(c*x)","A",0
230,0,0,0,0.448952," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/(a^2*c*x^5 + c*x^3), x)","F",0
231,1,89,0,0.646321," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{5 \, a^{3} \sqrt{c} x^{3} \log\left(-\frac{a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{a^{2} c x^{2} + c} {\left(a x - 2 \, {\left(2 \, a^{2} x^{2} - 1\right)} \arctan\left(a x\right)\right)}}{12 \, c x^{3}}"," ",0,"1/12*(5*a^3*sqrt(c)*x^3*log(-(a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(a^2*c*x^2 + c)*(a*x - 2*(2*a^2*x^2 - 1)*arctan(a*x)))/(c*x^3)","A",0
232,1,102,0,0.624269," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 1\right)} \sqrt{c} \log\left(-2 \, a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right) - 2 \, \sqrt{a^{2} c x^{2} + c} {\left(a x - {\left(a^{2} x^{2} + 2\right)} \arctan\left(a x\right)\right)}}{2 \, {\left(a^{6} c^{2} x^{2} + a^{4} c^{2}\right)}}"," ",0,"1/2*((a^2*x^2 + 1)*sqrt(c)*log(-2*a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c) - 2*sqrt(a^2*c*x^2 + c)*(a*x - (a^2*x^2 + 2)*arctan(a*x)))/(a^6*c^2*x^2 + a^4*c^2)","A",0
233,0,0,0,0.533978," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
234,1,43,0,0.623930," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x - \arctan\left(a x\right)\right)}}{a^{4} c^{2} x^{2} + a^{2} c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(a*x - arctan(a*x))/(a^4*c^2*x^2 + a^2*c^2)","A",0
235,1,40,0,1.192377," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x \arctan\left(a x\right) + 1\right)}}{a^{3} c^{2} x^{2} + a c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(a*x*arctan(a*x) + 1)/(a^3*c^2*x^2 + a*c^2)","A",0
236,0,0,0,0.690096," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/(a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x), x)","F",0
237,1,104,0,0.706243," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{3} x^{3} + a x\right)} \sqrt{c} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{a^{2} c x^{2} + c} {\left(a x + {\left(2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)}}{2 \, {\left(a^{2} c^{2} x^{3} + c^{2} x\right)}}"," ",0,"1/2*((a^3*x^3 + a*x)*sqrt(c)*log(-(a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(a^2*c*x^2 + c)*(a*x + (2*a^2*x^2 + 1)*arctan(a*x)))/(a^2*c^2*x^3 + c^2*x)","A",0
238,0,0,0,0.617726," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/(a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3), x)","F",0
239,1,129,0,0.633754," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{11 \, {\left(a^{5} x^{5} + a^{3} x^{3}\right)} \sqrt{c} \log\left(-\frac{a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(5 \, a^{3} x^{3} - a x + 2 \, {\left(8 \, a^{4} x^{4} + 4 \, a^{2} x^{2} - 1\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{12 \, {\left(a^{2} c^{2} x^{5} + c^{2} x^{3}\right)}}"," ",0,"1/12*(11*(a^5*x^5 + a^3*x^3)*sqrt(c)*log(-(a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(5*a^3*x^3 - a*x + 2*(8*a^4*x^4 + 4*a^2*x^2 - 1)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/(a^2*c^2*x^5 + c^2*x^3)","A",0
240,1,140,0,0.532318," ","integrate(x^5*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{9 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \sqrt{c} \log\left(-2 \, a^{2} c x^{2} + 2 \, \sqrt{a^{2} c x^{2} + c} a \sqrt{c} x - c\right) - 2 \, {\left(16 \, a^{3} x^{3} + 15 \, a x - 3 \, {\left(3 \, a^{4} x^{4} + 12 \, a^{2} x^{2} + 8\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{18 \, {\left(a^{10} c^{3} x^{4} + 2 \, a^{8} c^{3} x^{2} + a^{6} c^{3}\right)}}"," ",0,"1/18*(9*(a^4*x^4 + 2*a^2*x^2 + 1)*sqrt(c)*log(-2*a^2*c*x^2 + 2*sqrt(a^2*c*x^2 + c)*a*sqrt(c)*x - c) - 2*(16*a^3*x^3 + 15*a*x - 3*(3*a^4*x^4 + 12*a^2*x^2 + 8)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/(a^10*c^3*x^4 + 2*a^8*c^3*x^2 + a^6*c^3)","A",0
241,0,0,0,0.570215," ","integrate(x^4*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{4} \arctan\left(a x\right)}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^4*arctan(a*x)/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
242,1,74,0,0.787854," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(7 \, a^{3} x^{3} + 6 \, a x - 3 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{9 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/9*(7*a^3*x^3 + 6*a*x - 3*(3*a^2*x^2 + 2)*arctan(a*x))*sqrt(a^2*c*x^2 + c)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
243,1,67,0,0.571227," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} x^{3} \arctan\left(a x\right) + 3 \, a^{2} x^{2} + 2\right)} \sqrt{a^{2} c x^{2} + c}}{9 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"1/9*(3*a^3*x^3*arctan(a*x) + 3*a^2*x^2 + 2)*sqrt(a^2*c*x^2 + c)/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)","A",0
244,1,64,0,0.507190," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} x^{3} + 3 \, a x - 3 \, \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{9 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/9*(2*a^3*x^3 + 3*a*x - 3*arctan(a*x))*sqrt(a^2*c*x^2 + c)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
245,1,72,0,0.736776," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(6 \, a^{2} x^{2} + 3 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right) + 7\right)}}{9 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/9*sqrt(a^2*c*x^2 + c)*(6*a^2*x^2 + 3*(2*a^3*x^3 + 3*a*x)*arctan(a*x) + 7)/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
246,0,0,0,0.685436," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)/(a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x), x)","F",0
247,1,142,0,0.585680," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{9 \, {\left(a^{5} x^{5} + 2 \, a^{3} x^{3} + a x\right)} \sqrt{c} \log\left(-\frac{a^{2} c x^{2} - 2 \, \sqrt{a^{2} c x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(15 \, a^{3} x^{3} + 16 \, a x + 3 \, {\left(8 \, a^{4} x^{4} + 12 \, a^{2} x^{2} + 3\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{18 \, {\left(a^{4} c^{3} x^{5} + 2 \, a^{2} c^{3} x^{3} + c^{3} x\right)}}"," ",0,"1/18*(9*(a^5*x^5 + 2*a^3*x^3 + a*x)*sqrt(c)*log(-(a^2*c*x^2 - 2*sqrt(a^2*c*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(15*a^3*x^3 + 16*a*x + 3*(8*a^4*x^4 + 12*a^2*x^2 + 3)*arctan(a*x))*sqrt(a^2*c*x^2 + c))/(a^4*c^3*x^5 + 2*a^2*c^3*x^3 + c^3*x)","A",0
248,0,0,0,1.290329," ","integrate(x^m*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m} \arctan\left(a x\right), x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m*arctan(a*x), x)","F",0
249,0,0,0,0.615210," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m} \arctan\left(a x\right), x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m*arctan(a*x), x)","F",0
250,0,0,0,1.192612," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} \arctan\left(a x\right), x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*arctan(a*x), x)","F",0
251,0,0,0,1.006819," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*arctan(a*x)/(a^2*c*x^2 + c), x)","F",0
252,0,0,0,0.516172," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*arctan(a*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
253,0,0,0,0.536302," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right), x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x), x)","F",0
254,0,0,0,0.586576," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right), x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x), x)","F",0
255,0,0,0,0.563687," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right), x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x), x)","F",0
256,0,0,0,0.543492," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*arctan(a*x)/sqrt(a^2*c*x^2 + c), x)","F",0
257,0,0,0,0.726874," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
258,1,97,0,1.339828," ","integrate(x^3*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} c x^{4} - a^{2} c x^{2} + 15 \, {\left(2 \, a^{6} c x^{6} + 3 \, a^{4} c x^{4} - c\right)} \arctan\left(a x\right)^{2} - 2 \, {\left(6 \, a^{5} c x^{5} + 5 \, a^{3} c x^{3} - 15 \, a c x\right)} \arctan\left(a x\right) - 14 \, c \log\left(a^{2} x^{2} + 1\right)}{180 \, a^{4}}"," ",0,"1/180*(3*a^4*c*x^4 - a^2*c*x^2 + 15*(2*a^6*c*x^6 + 3*a^4*c*x^4 - c)*arctan(a*x)^2 - 2*(6*a^5*c*x^5 + 5*a^3*c*x^3 - 15*a*c*x)*arctan(a*x) - 14*c*log(a^2*x^2 + 1))/a^4","A",0
259,0,0,0,0.548455," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^4 + c*x^2)*arctan(a*x)^2, x)","F",0
260,1,74,0,0.591724," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""fricas"")","\frac{a^{2} c x^{2} + 3 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2} - 2 \, {\left(a^{3} c x^{3} + 3 \, a c x\right)} \arctan\left(a x\right) + 2 \, c \log\left(a^{2} x^{2} + 1\right)}{12 \, a^{2}}"," ",0,"1/12*(a^2*c*x^2 + 3*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x)^2 - 2*(a^3*c*x^3 + 3*a*c*x)*arctan(a*x) + 2*c*log(a^2*x^2 + 1))/a^2","A",0
261,0,0,0,1.280067," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
262,0,0,0,0.635467," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^2/x, x)","F",0
263,0,0,0,0.497549," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^2/x^2, x)","F",0
264,0,0,0,0.710264," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^2/x^3, x)","F",0
265,0,0,0,0.689798," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^2/x^4, x)","F",0
266,1,148,0,0.625329," ","integrate(x^3*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{6} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{4} - 5 \, a^{2} c^{2} x^{2} + 21 \, {\left(3 \, a^{8} c^{2} x^{8} + 8 \, a^{6} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{4} - c^{2}\right)} \arctan\left(a x\right)^{2} - 16 \, c^{2} \log\left(a^{2} x^{2} + 1\right) - 2 \, {\left(9 \, a^{7} c^{2} x^{7} + 21 \, a^{5} c^{2} x^{5} + 7 \, a^{3} c^{2} x^{3} - 21 \, a c^{2} x\right)} \arctan\left(a x\right)}{504 \, a^{4}}"," ",0,"1/504*(3*a^6*c^2*x^6 + 6*a^4*c^2*x^4 - 5*a^2*c^2*x^2 + 21*(3*a^8*c^2*x^8 + 8*a^6*c^2*x^6 + 6*a^4*c^2*x^4 - c^2)*arctan(a*x)^2 - 16*c^2*log(a^2*x^2 + 1) - 2*(9*a^7*c^2*x^7 + 21*a^5*c^2*x^5 + 7*a^3*c^2*x^3 - 21*a*c^2*x)*arctan(a*x))/a^4","A",0
267,0,0,0,0.611913," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^2, x)","F",0
268,1,123,0,0.642384," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} c^{2} x^{4} + 14 \, a^{2} c^{2} x^{2} + 30 \, {\left(a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2} + 16 \, c^{2} \log\left(a^{2} x^{2} + 1\right) - 4 \, {\left(3 \, a^{5} c^{2} x^{5} + 10 \, a^{3} c^{2} x^{3} + 15 \, a c^{2} x\right)} \arctan\left(a x\right)}{180 \, a^{2}}"," ",0,"1/180*(3*a^4*c^2*x^4 + 14*a^2*c^2*x^2 + 30*(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*arctan(a*x)^2 + 16*c^2*log(a^2*x^2 + 1) - 4*(3*a^5*c^2*x^5 + 10*a^3*c^2*x^3 + 15*a*c^2*x)*arctan(a*x))/a^2","A",0
269,0,0,0,0.700566," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2, x)","F",0
270,0,0,0,0.531684," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2/x, x)","F",0
271,0,0,0,0.802347," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2/x^2, x)","F",0
272,0,0,0,1.027810," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2/x^3, x)","F",0
273,0,0,0,0.664429," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2/x^4, x)","F",0
274,1,181,0,0.679626," ","integrate(x^3*(a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""fricas"")","\frac{105 \, a^{8} c^{3} x^{8} + 355 \, a^{6} c^{3} x^{6} + 318 \, a^{4} c^{3} x^{4} - 321 \, a^{2} c^{3} x^{2} - 624 \, c^{3} \log\left(a^{2} x^{2} + 1\right) + 945 \, {\left(4 \, a^{10} c^{3} x^{10} + 15 \, a^{8} c^{3} x^{8} + 20 \, a^{6} c^{3} x^{6} + 10 \, a^{4} c^{3} x^{4} - c^{3}\right)} \arctan\left(a x\right)^{2} - 6 \, {\left(140 \, a^{9} c^{3} x^{9} + 495 \, a^{7} c^{3} x^{7} + 567 \, a^{5} c^{3} x^{5} + 105 \, a^{3} c^{3} x^{3} - 315 \, a c^{3} x\right)} \arctan\left(a x\right)}{37800 \, a^{4}}"," ",0,"1/37800*(105*a^8*c^3*x^8 + 355*a^6*c^3*x^6 + 318*a^4*c^3*x^4 - 321*a^2*c^3*x^2 - 624*c^3*log(a^2*x^2 + 1) + 945*(4*a^10*c^3*x^10 + 15*a^8*c^3*x^8 + 20*a^6*c^3*x^6 + 10*a^4*c^3*x^4 - c^3)*arctan(a*x)^2 - 6*(140*a^9*c^3*x^9 + 495*a^7*c^3*x^7 + 567*a^5*c^3*x^5 + 105*a^3*c^3*x^3 - 315*a*c^3*x)*arctan(a*x))/a^4","A",0
275,0,0,0,0.775384," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^2, x)","F",0
276,1,156,0,0.663108," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""fricas"")","\frac{5 \, a^{6} c^{3} x^{6} + 24 \, a^{4} c^{3} x^{4} + 57 \, a^{2} c^{3} x^{2} + 48 \, c^{3} \log\left(a^{2} x^{2} + 1\right) + 105 \, {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2} - 6 \, {\left(5 \, a^{7} c^{3} x^{7} + 21 \, a^{5} c^{3} x^{5} + 35 \, a^{3} c^{3} x^{3} + 35 \, a c^{3} x\right)} \arctan\left(a x\right)}{840 \, a^{2}}"," ",0,"1/840*(5*a^6*c^3*x^6 + 24*a^4*c^3*x^4 + 57*a^2*c^3*x^2 + 48*c^3*log(a^2*x^2 + 1) + 105*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*arctan(a*x)^2 - 6*(5*a^7*c^3*x^7 + 21*a^5*c^3*x^5 + 35*a^3*c^3*x^3 + 35*a*c^3*x)*arctan(a*x))/a^2","A",0
277,0,0,0,0.422201," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2, x)","F",0
278,0,0,0,0.417856," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2/x, x)","F",0
279,0,0,0,0.428430," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2/x^2, x)","F",0
280,0,0,0,0.424997," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2/x^3, x)","F",0
281,0,0,0,0.549910," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2/x^4, x)","F",0
282,0,0,0,3.172204," ","integrate(x^4*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^4*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
283,0,0,0,0.580617," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^3*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
284,0,0,0,0.763868," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^2*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
285,0,0,0,0.525157," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
286,1,14,0,0.671596," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{\arctan\left(a x\right)^{3}}{3 \, a c}"," ",0,"1/3*arctan(a*x)^3/(a*c)","A",0
287,0,0,0,0.592540," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^2*c*x^3 + c*x), x)","F",0
288,0,0,0,0.446383," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{2} c x^{4} + c x^{2}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^2*c*x^4 + c*x^2), x)","F",0
289,0,0,0,0.649387," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^2*c*x^5 + c*x^3), x)","F",0
290,0,0,0,0.669387," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{2} c x^{6} + c x^{4}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^2*c*x^6 + c*x^4), x)","F",0
291,0,0,0,0.601708," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^3*arctan(a*x)^2/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
292,1,69,0,1.220144," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{6 \, a x \arctan\left(a x\right)^{2} - 2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x - 3 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{12 \, {\left(a^{5} c^{2} x^{2} + a^{3} c^{2}\right)}}"," ",0,"-1/12*(6*a*x*arctan(a*x)^2 - 2*(a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x - 3*(a^2*x^2 - 1)*arctan(a*x))/(a^5*c^2*x^2 + a^3*c^2)","A",0
293,1,48,0,0.580512," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{2 \, a x \arctan\left(a x\right) + {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)^{2} + 1}{4 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}"," ",0,"1/4*(2*a*x*arctan(a*x) + (a^2*x^2 - 1)*arctan(a*x)^2 + 1)/(a^4*c^2*x^2 + a^2*c^2)","A",0
294,1,67,0,0.545090," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{6 \, a x \arctan\left(a x\right)^{2} + 2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x - 3 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{12 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/12*(6*a*x*arctan(a*x)^2 + 2*(a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x - 3*(a^2*x^2 - 1)*arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
295,0,0,0,0.665584," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x), x)","F",0
296,0,0,0,0.585702," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2), x)","F",0
297,0,0,0,0.426181," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3), x)","F",0
298,0,0,0,1.053309," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4), x)","F",0
299,1,87,0,0.646823," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{5 \, a^{2} x^{2} + {\left(5 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 3\right)} \arctan\left(a x\right)^{2} + 2 \, {\left(5 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right) + 4}{32 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/32*(5*a^2*x^2 + (5*a^4*x^4 - 6*a^2*x^2 - 3)*arctan(a*x)^2 + 2*(5*a^3*x^3 + 3*a*x)*arctan(a*x) + 4)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
300,1,114,0,0.723556," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 24 \, {\left(a^{3} x^{3} - a x\right)} \arctan\left(a x\right)^{2} - 3 \, a x + 3 \, {\left(a^{4} x^{4} - 6 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{192 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"-1/192*(3*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 - 24*(a^3*x^3 - a*x)*arctan(a*x)^2 - 3*a*x + 3*(a^4*x^4 - 6*a^2*x^2 + 1)*arctan(a*x))/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)","A",0
301,1,87,0,0.670527," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} x^{2} + {\left(3 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 5\right)} \arctan\left(a x\right)^{2} + 2 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \arctan\left(a x\right) + 4}{32 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/32*(3*a^2*x^2 + (3*a^4*x^4 + 6*a^2*x^2 - 5)*arctan(a*x)^2 + 2*(3*a^3*x^3 + 5*a*x)*arctan(a*x) + 4)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
302,1,113,0,0.692908," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{15 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 8 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \arctan\left(a x\right)^{2} + 17 \, a x + {\left(15 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 17\right)} \arctan\left(a x\right)}{64 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/64*(15*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 - 8*(3*a^3*x^3 + 5*a*x)*arctan(a*x)^2 + 17*a*x + (15*a^4*x^4 + 6*a^2*x^2 - 17)*arctan(a*x))/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
303,0,0,0,0.669730," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x), x)","F",0
304,0,0,0,0.685827," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2), x)","F",0
305,0,0,0,0.609455," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3), x)","F",0
306,0,0,0,0.677260," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{10} + 3 \, a^{4} c^{3} x^{8} + 3 \, a^{2} c^{3} x^{6} + c^{3} x^{4}}, x\right)"," ",0,"integral(arctan(a*x)^2/(a^6*c^3*x^10 + 3*a^4*c^3*x^8 + 3*a^2*c^3*x^6 + c^3*x^4), x)","F",0
307,0,0,0,0.740571," ","integrate(x^3*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^2, x)","F",0
308,0,0,0,0.738376," ","integrate(x^2*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^2, x)","F",0
309,0,0,0,0.740660," ","integrate(x*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)^2, x)","F",0
310,0,0,0,0.525528," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
311,0,0,0,1.566946," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x, x)","F",0
312,0,0,0,0.702318," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^2, x)","F",0
313,0,0,0,1.529538," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^3, x)","F",0
314,0,0,0,0.573553," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^4, x)","F",0
315,0,0,0,0.691875," ","integrate(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{5} + c x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^5 + c*x^3)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
316,0,0,0,0.756868," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{4} + c x^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^4 + c*x^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
317,0,0,0,0.781735," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{3} + c x\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
318,0,0,0,0.769626," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2, x)","F",0
319,0,0,0,1.495183," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x, x)","F",0
320,0,0,0,1.992371," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x^2, x)","F",0
321,0,0,0,1.997571," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x^3, x)","F",0
322,0,0,0,0.741105," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x^4, x)","F",0
323,0,0,0,0.594455," ","integrate(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
324,0,0,0,0.593148," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
325,0,0,0,1.320890," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
326,0,0,0,0.963603," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
327,0,0,0,0.621985," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x, x)","F",0
328,0,0,0,0.557509," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^2, x)","F",0
329,0,0,0,0.561865," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^3, x)","F",0
330,0,0,0,0.724943," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^4, x)","F",0
331,0,0,0,0.710061," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^3*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
332,0,0,0,0.592879," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^2*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
333,0,0,0,2.003593," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
334,0,0,0,0.655871," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
335,0,0,0,0.785023," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^2*c*x^3 + c*x), x)","F",0
336,0,0,0,0.624227," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{2} c x^{4} + c x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^2*c*x^4 + c*x^2), x)","F",0
337,0,0,0,1.253170," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^2*c*x^5 + c*x^3), x)","F",0
338,0,0,0,0.654671," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{2} c x^{6} + c x^{4}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^2*c*x^6 + c*x^4), x)","F",0
339,0,0,0,0.617185," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^2/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
340,0,0,0,0.921587," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^2/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
341,1,51,0,0.871381," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(2 \, a x \arctan\left(a x\right) - \arctan\left(a x\right)^{2} + 2\right)}}{a^{4} c^{2} x^{2} + a^{2} c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(2*a*x*arctan(a*x) - arctan(a*x)^2 + 2)/(a^4*c^2*x^2 + a^2*c^2)","A",0
342,1,51,0,0.669119," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x \arctan\left(a x\right)^{2} - 2 \, a x + 2 \, \arctan\left(a x\right)\right)}}{a^{3} c^{2} x^{2} + a c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(a*x*arctan(a*x)^2 - 2*a*x + 2*arctan(a*x))/(a^3*c^2*x^2 + a*c^2)","A",0
343,0,0,0,0.661733," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x), x)","F",0
344,0,0,0,0.695473," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2), x)","F",0
345,0,0,0,0.568816," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3), x)","F",0
346,0,0,0,0.619421," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4), x)","F",0
347,0,0,0,0.515661," ","integrate(x^5*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{5} \arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^5*arctan(a*x)^2/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
348,0,0,0,0.629600," ","integrate(x^4*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{4} \arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^4*arctan(a*x)^2/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
349,1,92,0,0.737005," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(42 \, a^{2} x^{2} - 9 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)^{2} + 6 \, {\left(7 \, a^{3} x^{3} + 6 \, a x\right)} \arctan\left(a x\right) + 40\right)}}{27 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/27*sqrt(a^2*c*x^2 + c)*(42*a^2*x^2 - 9*(3*a^2*x^2 + 2)*arctan(a*x)^2 + 6*(7*a^3*x^3 + 6*a*x)*arctan(a*x) + 40)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
350,1,88,0,0.479383," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(9 \, a^{3} x^{3} \arctan\left(a x\right)^{2} - 14 \, a^{3} x^{3} - 12 \, a x + 6 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{27 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"1/27*(9*a^3*x^3*arctan(a*x)^2 - 14*a^3*x^3 - 12*a*x + 6*(3*a^2*x^2 + 2)*arctan(a*x))*sqrt(a^2*c*x^2 + c)/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)","A",0
351,1,82,0,0.706085," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(12 \, a^{2} x^{2} + 6 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right) - 9 \, \arctan\left(a x\right)^{2} + 14\right)}}{27 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/27*sqrt(a^2*c*x^2 + c)*(12*a^2*x^2 + 6*(2*a^3*x^3 + 3*a*x)*arctan(a*x) - 9*arctan(a*x)^2 + 14)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
352,1,93,0,0.683831," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(40 \, a^{3} x^{3} - 9 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right)^{2} + 42 \, a x - 6 \, {\left(6 \, a^{2} x^{2} + 7\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{27 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/27*(40*a^3*x^3 - 9*(2*a^3*x^3 + 3*a*x)*arctan(a*x)^2 + 42*a*x - 6*(6*a^2*x^2 + 7)*arctan(a*x))*sqrt(a^2*c*x^2 + c)/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
353,0,0,0,0.775878," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x), x)","F",0
354,0,0,0,0.578271," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/(a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2), x)","F",0
355,0,0,0,0.703661," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m*arctan(a*x)^2, x)","F",0
356,0,0,0,0.551748," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*arctan(a*x)^2, x)","F",0
357,0,0,0,0.601545," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
358,0,0,0,0.548193," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^2/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
359,0,0,0,0.670302," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x)^2, x)","F",0
360,0,0,0,0.681122," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^2, x)","F",0
361,0,0,0,0.678511," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
362,0,0,0,0.665053," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{2}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^2/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
363,0,0,0,0.743194," ","integrate(x^3*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{5} + c x^{3}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^5 + c*x^3)*arctan(a*x)^3, x)","F",0
364,0,0,0,0.549943," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^4 + c*x^2)*arctan(a*x)^3, x)","F",0
365,0,0,0,0.684966," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)*arctan(a*x)^3, x)","F",0
366,0,0,0,0.787028," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
367,0,0,0,0.693242," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^3/x, x)","F",0
368,0,0,0,0.592637," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^3/x^2, x)","F",0
369,0,0,0,0.671381," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^3/x^3, x)","F",0
370,0,0,0,0.766823," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*arctan(a*x)^3/x^4, x)","F",0
371,0,0,0,0.550594," ","integrate(x^3*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*arctan(a*x)^3, x)","F",0
372,0,0,0,0.546808," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^3, x)","F",0
373,0,0,0,0.664943," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)^3, x)","F",0
374,0,0,0,0.740273," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3, x)","F",0
375,0,0,0,0.780679," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3/x, x)","F",0
376,0,0,0,0.729423," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3/x^2, x)","F",0
377,0,0,0,0.842311," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3/x^3, x)","F",0
378,0,0,0,0.729655," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3/x^4, x)","F",0
379,0,0,0,0.580633," ","integrate(x^3*(a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3)*arctan(a*x)^3, x)","F",0
380,0,0,0,0.577517," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^3, x)","F",0
381,0,0,0,0.566005," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)^3, x)","F",0
382,0,0,0,0.779579," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3, x)","F",0
383,0,0,0,0.529898," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3/x, x)","F",0
384,0,0,0,0.609450," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3/x^2, x)","F",0
385,0,0,0,0.572829," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3/x^3, x)","F",0
386,0,0,0,0.421193," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3/x^4, x)","F",0
387,0,0,0,0.660707," ","integrate(x^4*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^4*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
388,0,0,0,0.737871," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^3*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
389,0,0,0,0.558638," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^2*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
390,0,0,0,0.539428," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
391,1,14,0,0.614367," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{\arctan\left(a x\right)^{4}}{4 \, a c}"," ",0,"1/4*arctan(a*x)^4/(a*c)","A",0
392,0,0,0,0.577641," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^2*c*x^3 + c*x), x)","F",0
393,0,0,0,0.432289," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{2} c x^{4} + c x^{2}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^2*c*x^4 + c*x^2), x)","F",0
394,0,0,0,0.487272," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^2*c*x^5 + c*x^3), x)","F",0
395,0,0,0,0.882450," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{2} c x^{6} + c x^{4}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^2*c*x^6 + c*x^4), x)","F",0
396,0,0,0,0.694674," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^3*arctan(a*x)^3/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
397,1,76,0,0.735159," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","-\frac{4 \, a x \arctan\left(a x\right)^{3} - {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} - 6 \, a x \arctan\left(a x\right) - 3 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)^{2} - 3}{8 \, {\left(a^{5} c^{2} x^{2} + a^{3} c^{2}\right)}}"," ",0,"-1/8*(4*a*x*arctan(a*x)^3 - (a^2*x^2 + 1)*arctan(a*x)^4 - 6*a*x*arctan(a*x) - 3*(a^2*x^2 - 1)*arctan(a*x)^2 - 3)/(a^5*c^2*x^2 + a^3*c^2)","A",0
398,1,69,0,0.640146," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{6 \, a x \arctan\left(a x\right)^{2} + 2 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x - 3 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{8 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}"," ",0,"1/8*(6*a*x*arctan(a*x)^2 + 2*(a^2*x^2 - 1)*arctan(a*x)^3 - 3*a*x - 3*(a^2*x^2 - 1)*arctan(a*x))/(a^4*c^2*x^2 + a^2*c^2)","A",0
399,1,73,0,1.059906," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, a x \arctan\left(a x\right)^{3} + {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} - 6 \, a x \arctan\left(a x\right) - 3 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)^{2} - 3}{8 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)}}"," ",0,"1/8*(4*a*x*arctan(a*x)^3 + (a^2*x^2 + 1)*arctan(a*x)^4 - 6*a*x*arctan(a*x) - 3*(a^2*x^2 - 1)*arctan(a*x)^2 - 3)/(a^3*c^2*x^2 + a*c^2)","A",0
400,0,0,0,0.720221," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x), x)","F",0
401,0,0,0,0.640630," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2), x)","F",0
402,0,0,0,0.603352," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3), x)","F",0
403,0,0,0,0.631353," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4), x)","F",0
404,1,117,0,0.818117," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{51 \, a^{3} x^{3} - 8 \, {\left(5 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 3\right)} \arctan\left(a x\right)^{3} - 24 \, {\left(5 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right)^{2} + 45 \, a x + 3 \, {\left(17 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 15\right)} \arctan\left(a x\right)}{256 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"-1/256*(51*a^3*x^3 - 8*(5*a^4*x^4 - 6*a^2*x^2 - 3)*arctan(a*x)^3 - 24*(5*a^3*x^3 + 3*a*x)*arctan(a*x)^2 + 45*a*x + 3*(17*a^4*x^4 - 6*a^2*x^2 - 15)*arctan(a*x))/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
405,1,130,0,0.658265," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} - 3 \, a^{2} x^{2} + 16 \, {\left(a^{3} x^{3} - a x\right)} \arctan\left(a x\right)^{3} - 3 \, {\left(a^{4} x^{4} - 6 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 6 \, {\left(a^{3} x^{3} - a x\right)} \arctan\left(a x\right)}{128 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"1/128*(4*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^4 - 3*a^2*x^2 + 16*(a^3*x^3 - a*x)*arctan(a*x)^3 - 3*(a^4*x^4 - 6*a^2*x^2 + 1)*arctan(a*x)^2 - 6*(a^3*x^3 - a*x)*arctan(a*x))/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)","A",0
406,1,117,0,0.430444," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","-\frac{45 \, a^{3} x^{3} - 8 \, {\left(3 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 5\right)} \arctan\left(a x\right)^{3} - 24 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \arctan\left(a x\right)^{2} + 51 \, a x + 3 \, {\left(15 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 17\right)} \arctan\left(a x\right)}{256 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"-1/256*(45*a^3*x^3 - 8*(3*a^4*x^4 + 6*a^2*x^2 - 5)*arctan(a*x)^3 - 24*(3*a^3*x^3 + 5*a*x)*arctan(a*x)^2 + 51*a*x + 3*(15*a^4*x^4 + 6*a^2*x^2 - 17)*arctan(a*x))/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
407,1,132,0,0.966280," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} - 45 \, a^{2} x^{2} + 16 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \arctan\left(a x\right)^{3} - 3 \, {\left(15 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 17\right)} \arctan\left(a x\right)^{2} - 6 \, {\left(15 \, a^{3} x^{3} + 17 \, a x\right)} \arctan\left(a x\right) - 48}{128 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/128*(12*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^4 - 45*a^2*x^2 + 16*(3*a^3*x^3 + 5*a*x)*arctan(a*x)^3 - 3*(15*a^4*x^4 + 6*a^2*x^2 - 17)*arctan(a*x)^2 - 6*(15*a^3*x^3 + 17*a*x)*arctan(a*x) - 48)/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
408,0,0,0,0.515783," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x), x)","F",0
409,0,0,0,0.779211," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2), x)","F",0
410,0,0,0,0.513857," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3), x)","F",0
411,0,0,0,1.158402," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{10} + 3 \, a^{4} c^{3} x^{8} + 3 \, a^{2} c^{3} x^{6} + c^{3} x^{4}}, x\right)"," ",0,"integral(arctan(a*x)^3/(a^6*c^3*x^10 + 3*a^4*c^3*x^8 + 3*a^2*c^3*x^6 + c^3*x^4), x)","F",0
412,0,0,0,0.922720," ","integrate(x^3*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^3, x)","F",0
413,0,0,0,0.835763," ","integrate(x^2*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^3, x)","F",0
414,0,0,0,0.547614," ","integrate(x*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)^3, x)","F",0
415,0,0,0,0.620845," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
416,0,0,0,0.490911," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x, x)","F",0
417,0,0,0,0.478106," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^2, x)","F",0
418,0,0,0,0.704780," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^3, x)","F",0
419,0,0,0,0.544585," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^4, x)","F",0
420,0,0,0,0.720585," ","integrate(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{5} + c x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^5 + c*x^3)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
421,0,0,0,0.543402," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{4} + c x^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^4 + c*x^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
422,0,0,0,0.607084," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{3} + c x\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
423,0,0,0,1.204136," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3, x)","F",0
424,0,0,0,0.589730," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x, x)","F",0
425,0,0,0,0.730107," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x^2, x)","F",0
426,0,0,0,0.633725," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x^3, x)","F",0
427,0,0,0,0.700283," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x^4, x)","F",0
428,0,0,0,0.665201," ","integrate(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
429,0,0,0,0.446939," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
430,0,0,0,0.509619," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
431,0,0,0,0.544099," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
432,0,0,0,0.506520," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x, x)","F",0
433,0,0,0,0.574667," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^2, x)","F",0
434,0,0,0,0.581501," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^3, x)","F",0
435,0,0,0,0.753532," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^4, x)","F",0
436,0,0,0,0.738738," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^3*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
437,0,0,0,0.491631," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^2*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
438,0,0,0,0.464971," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
439,0,0,0,0.544564," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
440,0,0,0,0.453576," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{2} c x^{3} + c x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^2*c*x^3 + c*x), x)","F",0
441,0,0,0,0.437319," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{2} c x^{4} + c x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^2*c*x^4 + c*x^2), x)","F",0
442,0,0,0,0.491641," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{2} c x^{5} + c x^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^2*c*x^5 + c*x^3), x)","F",0
443,0,0,0,0.482311," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{2} c x^{6} + c x^{4}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^2*c*x^6 + c*x^4), x)","F",0
444,0,0,0,0.441880," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^3/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
445,0,0,0,0.420784," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^3/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
446,1,62,0,0.417304," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(3 \, a x \arctan\left(a x\right)^{2} - \arctan\left(a x\right)^{3} - 6 \, a x + 6 \, \arctan\left(a x\right)\right)}}{a^{4} c^{2} x^{2} + a^{2} c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(3*a*x*arctan(a*x)^2 - arctan(a*x)^3 - 6*a*x + 6*arctan(a*x))/(a^4*c^2*x^2 + a^2*c^2)","A",0
447,1,58,0,0.412950," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} c x^{2} + c} {\left(a x \arctan\left(a x\right)^{3} - 6 \, a x \arctan\left(a x\right) + 3 \, \arctan\left(a x\right)^{2} - 6\right)}}{a^{3} c^{2} x^{2} + a c^{2}}"," ",0,"sqrt(a^2*c*x^2 + c)*(a*x*arctan(a*x)^3 - 6*a*x*arctan(a*x) + 3*arctan(a*x)^2 - 6)/(a^3*c^2*x^2 + a*c^2)","A",0
448,0,0,0,0.603954," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x), x)","F",0
449,0,0,0,0.442191," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2), x)","F",0
450,0,0,0,0.488500," ","integrate(x^5*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{5} \arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^5*arctan(a*x)^3/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
451,0,0,0,0.410122," ","integrate(x^4*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{4} \arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^4*arctan(a*x)^3/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
452,1,113,0,0.412899," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(122 \, a^{3} x^{3} + 9 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)^{3} - 9 \, {\left(7 \, a^{3} x^{3} + 6 \, a x\right)} \arctan\left(a x\right)^{2} + 120 \, a x - 6 \, {\left(21 \, a^{2} x^{2} + 20\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{27 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"-1/27*(122*a^3*x^3 + 9*(3*a^2*x^2 + 2)*arctan(a*x)^3 - 9*(7*a^3*x^3 + 6*a*x)*arctan(a*x)^2 + 120*a*x - 6*(21*a^2*x^2 + 20)*arctan(a*x))*sqrt(a^2*c*x^2 + c)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
453,1,106,0,0.423800," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(9 \, a^{3} x^{3} \arctan\left(a x\right)^{3} - 42 \, a^{2} x^{2} + 9 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)^{2} - 6 \, {\left(7 \, a^{3} x^{3} + 6 \, a x\right)} \arctan\left(a x\right) - 40\right)} \sqrt{a^{2} c x^{2} + c}}{27 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}}"," ",0,"1/27*(9*a^3*x^3*arctan(a*x)^3 - 42*a^2*x^2 + 9*(3*a^2*x^2 + 2)*arctan(a*x)^2 - 6*(7*a^3*x^3 + 6*a*x)*arctan(a*x) - 40)*sqrt(a^2*c*x^2 + c)/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)","A",0
454,1,103,0,0.408053," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(40 \, a^{3} x^{3} - 9 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right)^{2} + 9 \, \arctan\left(a x\right)^{3} + 42 \, a x - 6 \, {\left(6 \, a^{2} x^{2} + 7\right)} \arctan\left(a x\right)\right)} \sqrt{a^{2} c x^{2} + c}}{27 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"-1/27*(40*a^3*x^3 - 9*(2*a^3*x^3 + 3*a*x)*arctan(a*x)^2 + 9*arctan(a*x)^3 + 42*a*x - 6*(6*a^2*x^2 + 7)*arctan(a*x))*sqrt(a^2*c*x^2 + c)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
455,1,111,0,0.418744," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{a^{2} c x^{2} + c} {\left(120 \, a^{2} x^{2} - 9 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arctan\left(a x\right)^{3} - 9 \, {\left(6 \, a^{2} x^{2} + 7\right)} \arctan\left(a x\right)^{2} + 6 \, {\left(20 \, a^{3} x^{3} + 21 \, a x\right)} \arctan\left(a x\right) + 122\right)}}{27 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"-1/27*sqrt(a^2*c*x^2 + c)*(120*a^2*x^2 - 9*(2*a^3*x^3 + 3*a*x)*arctan(a*x)^3 - 9*(6*a^2*x^2 + 7)*arctan(a*x)^2 + 6*(20*a^3*x^3 + 21*a*x)*arctan(a*x) + 122)/(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)","A",0
456,0,0,0,0.410465," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x), x)","F",0
457,0,0,0,0.435039," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/(a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2), x)","F",0
458,0,0,0,0.409044," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m*arctan(a*x)^3, x)","F",0
459,0,0,0,0.513550," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*arctan(a*x)^3, x)","F",0
460,0,0,0,0.443310," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
461,0,0,0,0.415167," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^3/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
462,0,0,0,0.415233," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x)^3, x)","F",0
463,0,0,0,0.411774," ","integrate(x^m*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^3, x)","F",0
464,0,0,0,0.418933," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
465,0,0,0,0.414615," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{3}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^3/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
466,0,0,0,0.413008," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{3} + c x}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)/arctan(a*x), x)","F",0
467,0,0,0,0.389216," ","integrate((a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{2} + c}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)/arctan(a*x), x)","F",0
468,0,0,0,0.402178," ","integrate((a^2*c*x^2+c)/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{2} + c}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)/(x*arctan(a*x)), x)","F",0
469,0,0,0,0.392267," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)/arctan(a*x), x)","F",0
470,0,0,0,0.406517," ","integrate((a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)/arctan(a*x), x)","F",0
471,0,0,0,0.388420," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)/(x*arctan(a*x)), x)","F",0
472,0,0,0,0.398204," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)/arctan(a*x), x)","F",0
473,0,0,0,0.391491," ","integrate((a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)/arctan(a*x), x)","F",0
474,0,0,0,0.403392," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)/(x*arctan(a*x)), x)","F",0
475,0,0,0,0.394624," ","integrate(x^2/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^2/((a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
476,0,0,0,0.398932," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x/((a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
477,1,12,0,0.396040," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","\frac{\log\left(\arctan\left(a x\right)\right)}{a c}"," ",0,"log(arctan(a*x))/(a*c)","A",0
478,0,0,0,0.398776," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/((a^2*c*x^3 + c*x)*arctan(a*x)), x)","F",0
479,0,0,0,0.391879," ","integrate(1/x^2/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/((a^2*c*x^4 + c*x^2)*arctan(a*x)), x)","F",0
480,0,0,0,0.392601," ","integrate(x^4/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^4/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
481,0,0,0,0.394279," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^3/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
482,1,74,0,0.442497," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","\frac{2 \, \log\left(\arctan\left(a x\right)\right) - \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{4 \, a^{3} c^{2}}"," ",0,"1/4*(2*log(arctan(a*x)) - log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a^3*c^2)","C",0
483,1,67,0,0.397315," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","\frac{i \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - i \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{4 \, a^{2} c^{2}}"," ",0,"1/4*(I*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - I*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a^2*c^2)","C",0
484,1,70,0,0.406986," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","\frac{2 \, \log\left(\arctan\left(a x\right)\right) + \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{4 \, a c^{2}}"," ",0,"1/4*(2*log(arctan(a*x)) + log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a*c^2)","C",0
485,0,0,0,0.391439," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)), x)","F",0
486,0,0,0,0.387621," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)), x)","F",0
487,0,0,0,0.394518," ","integrate(x^6/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^6/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
488,0,0,0,0.398917," ","integrate(x^5/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^5/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
489,1,174,0,0.556488," ","integrate(x^4/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","\frac{6 \, \log\left(\arctan\left(a x\right)\right) + \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - 4 \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 4 \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{16 \, a^{5} c^{3}}"," ",0,"1/16*(6*log(arctan(a*x)) + log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - 4*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - 4*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a^5*c^3)","C",0
490,1,171,0,0.578327," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","\frac{-i \, \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + i \, \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + 2 i \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2 i \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{16 \, a^{4} c^{3}}"," ",0,"1/16*(-I*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + I*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + 2*I*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2*I*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a^4*c^3)","C",0
491,1,120,0,0.470514," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","\frac{2 \, \log\left(\arctan\left(a x\right)\right) - \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right)}{16 \, a^{3} c^{3}}"," ",0,"1/16*(2*log(arctan(a*x)) - log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)))/(a^3*c^3)","C",0
492,1,171,0,0.443138," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","\frac{i \, \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - i \, \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + 2 i \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2 i \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{16 \, a^{2} c^{3}}"," ",0,"1/16*(I*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - I*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + 2*I*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2*I*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a^2*c^3)","C",0
493,1,174,0,0.459679," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","\frac{6 \, \log\left(\arctan\left(a x\right)\right) + \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + 4 \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + 4 \, \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{16 \, a c^{3}}"," ",0,"1/16*(6*log(arctan(a*x)) + log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + 4*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + 4*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/(a*c^3)","C",0
494,0,0,0,0.419433," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)), x)","F",0
495,0,0,0,0.401406," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)), x)","F",0
496,0,0,0,0.406950," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{\arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/arctan(a*x), x)","F",0
497,0,0,0,0.423238," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/arctan(a*x), x)","F",0
498,0,0,0,0.402286," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)), x)","F",0
499,0,0,0,0.403025," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{3} + c x\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)*sqrt(a^2*c*x^2 + c)/arctan(a*x), x)","F",0
500,0,0,0,0.397934," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)/arctan(a*x), x)","F",0
501,0,0,0,0.444091," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)/(x*arctan(a*x)), x)","F",0
502,0,0,0,0.440092," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*sqrt(a^2*c*x^2 + c)/arctan(a*x), x)","F",0
503,0,0,0,0.417673," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)/arctan(a*x), x)","F",0
504,0,0,0,1.346404," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)), x)","F",0
505,0,0,0,0.420943," ","integrate(x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x/(sqrt(a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
506,0,0,0,0.412129," ","integrate(1/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/(sqrt(a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
507,0,0,0,0.446946," ","integrate(1/x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^2*c*x^3 + c*x)*arctan(a*x)), x)","F",0
508,0,0,0,0.434838," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
509,0,0,0,0.454442," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
510,0,0,0,0.456817," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
511,0,0,0,0.432753," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
512,0,0,0,0.462250," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)), x)","F",0
513,0,0,0,0.439891," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)), x)","F",0
514,0,0,0,0.410142," ","integrate(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{5}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^5/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
515,0,0,0,0.437166," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{4}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^4/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
516,0,0,0,0.525952," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
517,0,0,0,0.534241," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
518,0,0,0,0.721575," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
519,0,0,0,0.546013," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
520,0,0,0,0.581109," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)), x)","F",0
521,0,0,0,0.505209," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)), x)","F",0
522,0,0,0,0.412806," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m/arctan(a*x), x)","F",0
523,0,0,0,0.553267," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m/arctan(a*x), x)","F",0
524,0,0,0,0.628861," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m/arctan(a*x), x)","F",0
525,0,0,0,0.680571," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^m/((a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
526,0,0,0,0.631660," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
527,0,0,0,0.561345," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
528,0,0,0,0.462307," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x), x)","F",0
529,0,0,0,0.587630," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x), x)","F",0
530,0,0,0,0.513542," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x), x)","F",0
531,0,0,0,0.572251," ","integrate(x^m/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}, x\right)"," ",0,"integral(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
532,0,0,0,0.598787," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x)","F",0
533,0,0,0,0.652589," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x)","F",0
534,0,0,0,0.514020," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{3} + c x}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)/arctan(a*x)^2, x)","F",0
535,0,0,0,0.451147," ","integrate((a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{2} + c}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)/arctan(a*x)^2, x)","F",0
536,0,0,0,0.415845," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{2} + c}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)/(x*arctan(a*x)^2), x)","F",0
537,0,0,0,0.435672," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)/arctan(a*x)^2, x)","F",0
538,0,0,0,0.424769," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)/arctan(a*x)^2, x)","F",0
539,0,0,0,0.420329," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)/(x*arctan(a*x)^2), x)","F",0
540,0,0,0,0.423668," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)/arctan(a*x)^2, x)","F",0
541,0,0,0,0.417021," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)/arctan(a*x)^2, x)","F",0
542,0,0,0,0.409477," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)/(x*arctan(a*x)^2), x)","F",0
543,0,0,0,0.400085," ","integrate(x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^3/((a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
544,0,0,0,0.409071," ","integrate(x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^2/((a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
545,0,0,0,0.388575," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x/((a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
546,1,14,0,0.375783," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","-\frac{1}{a c \arctan\left(a x\right)}"," ",0,"-1/(a*c*arctan(a*x))","A",0
547,0,0,0,0.389969," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^2*c*x^3 + c*x)*arctan(a*x)^2), x)","F",0
548,0,0,0,0.388730," ","integrate(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^2*c*x^4 + c*x^2)*arctan(a*x)^2), x)","F",0
549,0,0,0,0.391270," ","integrate(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{5} + c x^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^2*c*x^5 + c*x^3)*arctan(a*x)^2), x)","F",0
550,0,0,0,0.399585," ","integrate(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{6} + c x^{4}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^2*c*x^6 + c*x^4)*arctan(a*x)^2), x)","F",0
551,0,0,0,0.468796," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^3/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
552,1,123,0,0.459415," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} x^{2} - {\left(i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - {\left(-i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{2 \, {\left(a^{5} c^{2} x^{2} + a^{3} c^{2}\right)} \arctan\left(a x\right)}"," ",0,"-1/2*(2*a^2*x^2 - (I*a^2*x^2 + I)*arctan(a*x)*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - (-I*a^2*x^2 - I)*arctan(a*x)*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/((a^5*c^2*x^2 + a^3*c^2)*arctan(a*x))","C",0
553,1,115,0,0.447347," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2 \, a x}{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right)}"," ",0,"1/2*((a^2*x^2 + 1)*arctan(a*x)*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (a^2*x^2 + 1)*arctan(a*x)*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2*a*x)/((a^4*c^2*x^2 + a^2*c^2)*arctan(a*x))","C",0
554,1,112,0,0.511373," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2}{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)}"," ",0,"1/2*((-I*a^2*x^2 - I)*arctan(a*x)*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (I*a^2*x^2 + I)*arctan(a*x)*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2)/((a^3*c^2*x^2 + a*c^2)*arctan(a*x))","C",0
555,0,0,0,0.429336," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)^2), x)","F",0
556,0,0,0,0.480892," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^2), x)","F",0
557,0,0,0,0.437979," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*arctan(a*x)^2), x)","F",0
558,0,0,0,0.462927," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4)*arctan(a*x)^2), x)","F",0
559,1,292,0,0.470160," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","-\frac{4 \, a^{3} x^{3} + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right)}{4 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)} \arctan\left(a x\right)}"," ",0,"-1/4*(4*a^3*x^3 + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)))/((a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)*arctan(a*x))","C",0
560,1,196,0,0.506521," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} - {\left(i \, a^{4} x^{4} + 2 i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - {\left(-i \, a^{4} x^{4} - 2 i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right)}{4 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)} \arctan\left(a x\right)}"," ",0,"-1/4*(4*a^2*x^2 - (I*a^4*x^4 + 2*I*a^2*x^2 + I)*arctan(a*x)*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - (-I*a^4*x^4 - 2*I*a^2*x^2 - I)*arctan(a*x)*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)))/((a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)*arctan(a*x))","C",0
561,1,286,0,0.463547," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","\frac{{\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 4 \, a x}{4 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \arctan\left(a x\right)}"," ",0,"1/4*((a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 4*a*x)/((a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x))","C",0
562,1,285,0,0.494612," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, a^{4} x^{4} - 2 i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(i \, a^{4} x^{4} + 2 i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(-2 i \, a^{4} x^{4} - 4 i \, a^{2} x^{2} - 2 i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(2 i \, a^{4} x^{4} + 4 i \, a^{2} x^{2} + 2 i\right)} \arctan\left(a x\right) \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 4}{4 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)}"," ",0,"1/4*((-I*a^4*x^4 - 2*I*a^2*x^2 - I)*arctan(a*x)*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (I*a^4*x^4 + 2*I*a^2*x^2 + I)*arctan(a*x)*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (-2*I*a^4*x^4 - 4*I*a^2*x^2 - 2*I)*arctan(a*x)*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (2*I*a^4*x^4 + 4*I*a^2*x^2 + 2*I)*arctan(a*x)*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 4)/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x))","C",0
563,0,0,0,0.443596," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)^2), x)","F",0
564,0,0,0,0.444271," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^2), x)","F",0
565,0,0,0,0.417553," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3)*arctan(a*x)^2), x)","F",0
566,0,0,0,0.442719," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{10} + 3 \, a^{4} c^{3} x^{8} + 3 \, a^{2} c^{3} x^{6} + c^{3} x^{4}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^10 + 3*a^4*c^3*x^8 + 3*a^2*c^3*x^6 + c^3*x^4)*arctan(a*x)^2), x)","F",0
567,0,0,0,0.434767," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/arctan(a*x)^2, x)","F",0
568,0,0,0,0.452841," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/arctan(a*x)^2, x)","F",0
569,0,0,0,0.445660," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)^2), x)","F",0
570,0,0,0,0.410495," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{3} + c x\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)*sqrt(a^2*c*x^2 + c)/arctan(a*x)^2, x)","F",0
571,0,0,0,0.397747," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)/arctan(a*x)^2, x)","F",0
572,0,0,0,0.395420," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)/(x*arctan(a*x)^2), x)","F",0
573,0,0,0,0.428641," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*sqrt(a^2*c*x^2 + c)/arctan(a*x)^2, x)","F",0
574,0,0,0,0.472055," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)/arctan(a*x)^2, x)","F",0
575,0,0,0,0.464158," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)^2), x)","F",0
576,0,0,0,0.531904," ","integrate(x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
577,0,0,0,0.432928," ","integrate(1/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
578,0,0,0,0.466939," ","integrate(1/x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^2*c*x^3 + c*x)*arctan(a*x)^2), x)","F",0
579,0,0,0,0.636740," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
580,0,0,0,0.496156," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
581,0,0,0,0.540953," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
582,0,0,0,0.429221," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
583,0,0,0,0.596671," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)^2), x)","F",0
584,0,0,0,0.570187," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^2), x)","F",0
585,0,0,0,0.460862," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*arctan(a*x)^2), x)","F",0
586,0,0,0,0.440281," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4)*arctan(a*x)^2), x)","F",0
587,0,0,0,0.423185," ","integrate(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{5}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^5/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
588,0,0,0,0.403599," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{4}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^4/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
589,0,0,0,0.407083," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
590,0,0,0,0.415605," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
591,0,0,0,0.460810," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
592,0,0,0,0.484598," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
593,0,0,0,0.536858," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)^2), x)","F",0
594,0,0,0,0.506114," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^2), x)","F",0
595,0,0,0,0.425221," ","integrate(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3)*arctan(a*x)^2), x)","F",0
596,0,0,0,0.440529," ","integrate(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{10} + 3 \, a^{4} c^{3} x^{8} + 3 \, a^{2} c^{3} x^{6} + c^{3} x^{4}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^10 + 3*a^4*c^3*x^8 + 3*a^2*c^3*x^6 + c^3*x^4)*arctan(a*x)^2), x)","F",0
597,0,0,0,0.439025," ","integrate((f*x)^(1/2)/(c^2*d*x^2+d)^2/(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{f x}}{a^{2} c^{4} d^{2} x^{4} + 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} + 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} + 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arctan\left(c x\right)}, x\right)"," ",0,"integral(sqrt(f*x)/(a^2*c^4*d^2*x^4 + 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 + 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*c^4*d^2*x^4 + 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan(c*x)), x)","F",0
598,0,0,0,0.422247," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m/arctan(a*x)^2, x)","F",0
599,0,0,0,0.530421," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m/arctan(a*x)^2, x)","F",0
600,0,0,0,0.533406," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m/arctan(a*x)^2, x)","F",0
601,0,0,0,0.481097," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^m/((a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
602,0,0,0,0.415970," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
603,0,0,0,0.406522," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
604,0,0,0,0.400582," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^2, x)","F",0
605,0,0,0,0.456598," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x)^2, x)","F",0
606,0,0,0,0.463239," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^2, x)","F",0
607,0,0,0,0.491016," ","integrate(x^m/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
608,0,0,0,0.478972," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^2), x)","F",0
609,0,0,0,0.438323," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^2), x)","F",0
610,0,0,0,0.449453," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{3} + c x}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)/arctan(a*x)^3, x)","F",0
611,0,0,0,0.461469," ","integrate((a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{2} + c}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)/arctan(a*x)^3, x)","F",0
612,0,0,0,0.434846," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c x^{2} + c}{x \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)/(x*arctan(a*x)^3), x)","F",0
613,0,0,0,0.467839," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)/arctan(a*x)^3, x)","F",0
614,0,0,0,0.398258," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)/arctan(a*x)^3, x)","F",0
615,0,0,0,0.387413," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}{x \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)/(x*arctan(a*x)^3), x)","F",0
616,0,0,0,0.402492," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)/arctan(a*x)^3, x)","F",0
617,0,0,0,0.391365," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)/arctan(a*x)^3, x)","F",0
618,0,0,0,0.389837," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}{x \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)/(x*arctan(a*x)^3), x)","F",0
619,0,0,0,0.402545," ","integrate(x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^3/((a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
620,0,0,0,0.394862," ","integrate(x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^2/((a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
621,0,0,0,0.404384," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x/((a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
622,1,14,0,0.378671," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","-\frac{1}{2 \, a c \arctan\left(a x\right)^{2}}"," ",0,"-1/2/(a*c*arctan(a*x)^2)","A",0
623,0,0,0,0.387064," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^2*c*x^3 + c*x)*arctan(a*x)^3), x)","F",0
624,0,0,0,0.391135," ","integrate(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^2*c*x^4 + c*x^2)*arctan(a*x)^3), x)","F",0
625,0,0,0,0.407561," ","integrate(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{5} + c x^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^2*c*x^5 + c*x^3)*arctan(a*x)^3), x)","F",0
626,0,0,0,0.388686," ","integrate(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} c x^{6} + c x^{4}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^2*c*x^6 + c*x^4)*arctan(a*x)^3), x)","F",0
627,0,0,0,0.397784," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^3/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
628,1,132,0,0.493031," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} - {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + 2 \, a x \arctan\left(a x\right)}{2 \, {\left(a^{5} c^{2} x^{2} + a^{3} c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^2*x^2 - (a^2*x^2 + 1)*arctan(a*x)^2*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - (a^2*x^2 + 1)*arctan(a*x)^2*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) + 2*a*x*arctan(a*x))/((a^5*c^2*x^2 + a^3*c^2)*arctan(a*x)^2)","C",0
629,1,135,0,0.404611," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","\frac{{\left(-i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - a x + {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*((-I*a^2*x^2 - I)*arctan(a*x)^2*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (I*a^2*x^2 + I)*arctan(a*x)^2*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - a*x + (a^2*x^2 - 1)*arctan(a*x))/((a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2)","C",0
630,1,122,0,0.414752," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2 \, a x \arctan\left(a x\right) + 1}{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*((a^2*x^2 + 1)*arctan(a*x)^2*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (a^2*x^2 + 1)*arctan(a*x)^2*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2*a*x*arctan(a*x) + 1)/((a^3*c^2*x^2 + a*c^2)*arctan(a*x)^2)","C",0
631,0,0,0,1.080908," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)^3), x)","F",0
632,0,0,0,0.494801," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^3), x)","F",0
633,0,0,0,0.589582," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*arctan(a*x)^3), x)","F",0
634,0,0,0,0.578188," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4)*arctan(a*x)^3), x)","F",0
635,1,328,0,0.418384," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} x^{3} - {\left(2 i \, a^{4} x^{4} + 4 i \, a^{2} x^{2} + 2 i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - {\left(-2 i \, a^{4} x^{4} - 4 i \, a^{2} x^{2} - 2 i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - {\left(-i \, a^{4} x^{4} - 2 i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - {\left(i \, a^{4} x^{4} + 2 i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2 \, {\left(a^{4} x^{4} - 3 \, a^{2} x^{2}\right)} \arctan\left(a x\right)}{4 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/4*(2*a^3*x^3 - (2*I*a^4*x^4 + 4*I*a^2*x^2 + 2*I)*arctan(a*x)^2*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - (-2*I*a^4*x^4 - 4*I*a^2*x^2 - 2*I)*arctan(a*x)^2*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - (-I*a^4*x^4 - 2*I*a^2*x^2 - I)*arctan(a*x)^2*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) - (I*a^4*x^4 + 2*I*a^2*x^2 + I)*arctan(a*x)^2*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2*(a^4*x^4 - 3*a^2*x^2)*arctan(a*x))/((a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)*arctan(a*x)^2)","C",0
636,1,215,0,0.521456," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - 2 \, {\left(a^{3} x^{3} - a x\right)} \arctan\left(a x\right)}{2 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^2*x^2 - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) - 2*(a^3*x^3 - a*x)*arctan(a*x))/((a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3)*arctan(a*x)^2)","C",0
637,1,314,0,0.430191," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","\frac{{\left(-2 i \, a^{4} x^{4} - 4 i \, a^{2} x^{2} - 2 i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(2 i \, a^{4} x^{4} + 4 i \, a^{2} x^{2} + 2 i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(-i \, a^{4} x^{4} - 2 i \, a^{2} x^{2} - i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(i \, a^{4} x^{4} + 2 i \, a^{2} x^{2} + i\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 2 \, a x + 2 \, {\left(3 \, a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{4 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/4*((-2*I*a^4*x^4 - 4*I*a^2*x^2 - 2*I)*arctan(a*x)^2*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (2*I*a^4*x^4 + 4*I*a^2*x^2 + 2*I)*arctan(a*x)^2*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (-I*a^4*x^4 - 2*I*a^2*x^2 - I)*arctan(a*x)^2*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (I*a^4*x^4 + 2*I*a^2*x^2 + I)*arctan(a*x)^2*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 2*a*x + 2*(3*a^2*x^2 - 1)*arctan(a*x))/((a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2)","C",0
638,1,297,0,0.460226," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} + 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} - 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(\frac{a^{4} x^{4} - 4 i \, a^{3} x^{3} - 6 \, a^{2} x^{2} + 4 i \, a x + 1}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} + 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) + {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} \operatorname{log\_integral}\left(-\frac{a^{2} x^{2} - 2 i \, a x - 1}{a^{2} x^{2} + 1}\right) - 4 \, a x \arctan\left(a x\right) + 1}{2 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*((a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2*log_integral((a^4*x^4 + 4*I*a^3*x^3 - 6*a^2*x^2 - 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2*log_integral((a^4*x^4 - 4*I*a^3*x^3 - 6*a^2*x^2 + 4*I*a*x + 1)/(a^4*x^4 + 2*a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2*log_integral(-(a^2*x^2 + 2*I*a*x - 1)/(a^2*x^2 + 1)) + (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2*log_integral(-(a^2*x^2 - 2*I*a*x - 1)/(a^2*x^2 + 1)) - 4*a*x*arctan(a*x) + 1)/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x)^2)","C",0
639,0,0,0,0.434411," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)^3), x)","F",0
640,0,0,0,0.414157," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^3), x)","F",0
641,0,0,0,0.400607," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{9} + 3 \, a^{4} c^{3} x^{7} + 3 \, a^{2} c^{3} x^{5} + c^{3} x^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^9 + 3*a^4*c^3*x^7 + 3*a^2*c^3*x^5 + c^3*x^3)*arctan(a*x)^3), x)","F",0
642,0,0,0,0.627426," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{6} c^{3} x^{10} + 3 \, a^{4} c^{3} x^{8} + 3 \, a^{2} c^{3} x^{6} + c^{3} x^{4}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^6*c^3*x^10 + 3*a^4*c^3*x^8 + 3*a^2*c^3*x^6 + c^3*x^4)*arctan(a*x)^3), x)","F",0
643,1,14,0,0.453225," ","integrate(x^3/(a^2*x^2+1)/arctan(a*x)^3-3/2*x^2/a/arctan(a*x)^2,x, algorithm=""fricas"")","-\frac{x^{3}}{2 \, a \arctan\left(a x\right)^{2}}"," ",0,"-1/2*x^3/(a*arctan(a*x)^2)","A",0
644,0,0,0,0.464267," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/arctan(a*x)^3, x)","F",0
645,0,0,0,0.427260," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/arctan(a*x)^3, x)","F",0
646,0,0,0,0.396507," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)^3), x)","F",0
647,0,0,0,0.392863," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{3} + c x\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^3 + c*x)*sqrt(a^2*c*x^2 + c)/arctan(a*x)^3, x)","F",0
648,0,0,0,0.386966," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)/arctan(a*x)^3, x)","F",0
649,0,0,0,0.582611," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{x \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)/(x*arctan(a*x)^3), x)","F",0
650,0,0,0,1.316458," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*sqrt(a^2*c*x^2 + c)/arctan(a*x)^3, x)","F",0
651,0,0,0,1.580482," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)/arctan(a*x)^3, x)","F",0
652,0,0,0,1.397583," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)^3), x)","F",0
653,0,0,0,1.097253," ","integrate(x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
654,0,0,0,0.506588," ","integrate(1/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
655,0,0,0,0.858728," ","integrate(1/x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{2} c x^{3} + c x\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^2*c*x^3 + c*x)*arctan(a*x)^3), x)","F",0
656,0,0,0,0.568940," ","integrate(1/x^2/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^2*c*x^4 + c*x^2)*arctan(a*x)^3), x)","F",0
657,0,0,0,0.436639," ","integrate(1/x^3/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{2} c x^{5} + c x^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^2*c*x^5 + c*x^3)*arctan(a*x)^3), x)","F",0
658,0,0,0,0.435514," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
659,0,0,0,0.425048," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
660,0,0,0,0.462753," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
661,0,0,0,0.468613," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
662,0,0,0,0.460831," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{5} + 2 \, a^{2} c^{2} x^{3} + c^{2} x\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^5 + 2*a^2*c^2*x^3 + c^2*x)*arctan(a*x)^3), x)","F",0
663,0,0,0,0.523800," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{6} + 2 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^6 + 2*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^3), x)","F",0
664,0,0,0,0.453528," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{7} + 2 \, a^{2} c^{2} x^{5} + c^{2} x^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^7 + 2*a^2*c^2*x^5 + c^2*x^3)*arctan(a*x)^3), x)","F",0
665,0,0,0,0.535801," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{4} c^{2} x^{8} + 2 \, a^{2} c^{2} x^{6} + c^{2} x^{4}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^4*c^2*x^8 + 2*a^2*c^2*x^6 + c^2*x^4)*arctan(a*x)^3), x)","F",0
666,0,0,0,0.444678," ","integrate(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{5}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^5/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
667,0,0,0,0.479681," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{4}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^4/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
668,0,0,0,0.438778," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{3}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^3/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
669,0,0,0,0.413999," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{2}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^2/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
670,0,0,0,0.488798," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
671,0,0,0,0.500422," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
672,0,0,0,0.451914," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{7} + 3 \, a^{4} c^{3} x^{5} + 3 \, a^{2} c^{3} x^{3} + c^{3} x\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^7 + 3*a^4*c^3*x^5 + 3*a^2*c^3*x^3 + c^3*x)*arctan(a*x)^3), x)","F",0
673,0,0,0,0.562935," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c}}{{\left(a^{6} c^{3} x^{8} + 3 \, a^{4} c^{3} x^{6} + 3 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)/((a^6*c^3*x^8 + 3*a^4*c^3*x^6 + 3*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^3), x)","F",0
674,0,0,0,0.650672," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m/arctan(a*x)^3, x)","F",0
675,0,0,0,0.639178," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m/arctan(a*x)^3, x)","F",0
676,0,0,0,0.467134," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m/arctan(a*x)^3, x)","F",0
677,0,0,0,0.513021," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^m/((a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
678,0,0,0,0.613647," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
679,0,0,0,0.444000," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
680,0,0,0,0.799936," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^3, x)","F",0
681,0,0,0,0.484503," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x)^3, x)","F",0
682,0,0,0,0.446719," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^3, x)","F",0
683,0,0,0,0.578395," ","integrate(x^m/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
684,0,0,0,0.576817," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^3), x)","F",0
685,0,0,0,0.451219," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^3), x)","F",0
686,0,0,0,0.437061," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} \sqrt{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*sqrt(arctan(a*x)), x)","F",0
687,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
688,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
689,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
690,0,0,0,0.479309," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m} \sqrt{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m*sqrt(arctan(a*x)), x)","F",0
691,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
692,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
693,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
694,0,0,0,0.440820," ","integrate(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m} \sqrt{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m*sqrt(arctan(a*x)), x)","F",0
695,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
696,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
697,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
698,0,0,0,0.563153," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \sqrt{\arctan\left(a x\right)}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*sqrt(arctan(a*x))/(a^2*c*x^2 + c), x)","F",0
699,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
700,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
701,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
702,1,14,0,0.396906," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(a x\right)^{\frac{3}{2}}}{3 \, a c}"," ",0,"2/3*arctan(a*x)^(3/2)/(a*c)","A",0
703,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
704,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
705,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
706,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
707,0,0,0,0.438356," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \sqrt{\arctan\left(a x\right)}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*sqrt(arctan(a*x))/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
708,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
709,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
710,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
711,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
712,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
713,0,0,0,0.468251," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \sqrt{\arctan\left(a x\right)}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(x^m*sqrt(arctan(a*x))/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
714,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
715,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
716,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
717,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
718,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
719,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
720,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
721,0,0,0,0.453563," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{m} \sqrt{\arctan\left(a x\right)}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*sqrt(arctan(a*x)), x)","F",0
722,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
723,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
724,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
725,0,0,0,0.627259," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \sqrt{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m*sqrt(arctan(a*x)), x)","F",0
726,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
727,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
728,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
729,0,0,0,0.455012," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m} \sqrt{\arctan\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m*sqrt(arctan(a*x)), x)","F",0
730,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
731,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
732,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
733,0,0,0,0.615060," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \sqrt{\arctan\left(a x\right)}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*sqrt(arctan(a*x))/sqrt(a^2*c*x^2 + c), x)","F",0
734,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
735,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
736,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
737,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
738,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
739,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
740,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
741,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
742,0,0,0,0.502069," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \sqrt{\arctan\left(a x\right)}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*sqrt(arctan(a*x))/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
743,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
744,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
745,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
746,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
747,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
748,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
749,0,0,0,0.535917," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \sqrt{\arctan\left(a x\right)}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*sqrt(arctan(a*x))/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
750,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
751,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
752,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
753,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
754,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
755,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
756,0,0,0,0.498693," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*arctan(a*x)^(3/2), x)","F",0
757,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
758,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
759,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
760,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
761,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
762,0,0,0,0.491934," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m*arctan(a*x)^(3/2), x)","F",0
763,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
764,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
765,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
766,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
767,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
768,0,0,0,0.496022," ","integrate(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m*arctan(a*x)^(3/2), x)","F",0
769,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
770,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
771,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
772,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
773,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
774,0,0,0,0.470319," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{3}{2}}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2 + c), x)","F",0
775,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
776,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
777,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
778,1,14,0,0.428113," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(a x\right)^{\frac{5}{2}}}{5 \, a c}"," ",0,"2/5*arctan(a*x)^(5/2)/(a*c)","A",0
779,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
780,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
781,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
782,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
783,0,0,0,0.579572," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{3}{2}}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(3/2)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
784,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
785,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
786,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
787,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
788,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
789,0,0,0,0.469735," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{3}{2}}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(3/2)/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
790,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
791,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
792,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
793,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
794,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
795,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
796,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
797,0,0,0,0.598593," ","integrate(x^m*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(3/2), x)","F",0
798,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
799,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
800,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
801,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
802,0,0,0,0.474602," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x)^(3/2), x)","F",0
803,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
804,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
805,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
806,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
807,0,0,0,0.794292," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(3/2), x)","F",0
808,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
809,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
810,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
811,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
812,0,0,0,0.989370," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{3}{2}}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(3/2)/sqrt(a^2*c*x^2 + c), x)","F",0
813,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
814,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
815,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
816,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
817,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
818,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
819,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
820,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
821,0,0,0,0.925129," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(3/2)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
822,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
823,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
824,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
825,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
826,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
827,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
828,0,0,0,0.545460," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{3}{2}}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(3/2)/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
829,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
830,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
831,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
832,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
833,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
834,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
835,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
836,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
837,0,0,0,0.464436," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m*arctan(a*x)^(5/2), x)","F",0
838,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
839,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
840,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
841,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
842,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
843,0,0,0,0.570552," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m*arctan(a*x)^(5/2), x)","F",0
844,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
845,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
846,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
847,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
848,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
849,0,0,0,0.529520," ","integrate(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m*arctan(a*x)^(5/2), x)","F",0
850,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
851,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
852,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
853,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
854,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
855,0,0,0,0.478067," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{5}{2}}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2 + c), x)","F",0
856,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
857,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
858,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
859,1,14,0,0.471802," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(a x\right)^{\frac{7}{2}}}{7 \, a c}"," ",0,"2/7*arctan(a*x)^(7/2)/(a*c)","A",0
860,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
861,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
862,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
863,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
864,0,0,0,0.432642," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{5}{2}}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(5/2)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
865,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
866,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
867,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
868,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
869,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
870,0,0,0,0.446752," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{5}{2}}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(5/2)/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
871,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
872,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
873,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
874,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
875,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
876,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
877,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
878,0,0,0,0.491094," ","integrate(x^m*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(5/2), x)","F",0
879,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
880,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
881,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
882,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
883,0,0,0,0.467422," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x)^(5/2), x)","F",0
884,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
885,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
886,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
887,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
888,0,0,0,0.581083," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(5/2), x)","F",0
889,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
890,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
891,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
892,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
893,0,0,0,0.500975," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \arctan\left(a x\right)^{\frac{5}{2}}}{\sqrt{a^{2} c x^{2} + c}}, x\right)"," ",0,"integral(x^m*arctan(a*x)^(5/2)/sqrt(a^2*c*x^2 + c), x)","F",0
894,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
895,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
896,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
897,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
898,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
899,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
900,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
901,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
902,0,0,0,0.431946," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(5/2)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2), x)","F",0
903,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
904,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
905,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
906,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
907,0,0,0,0.430734," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{\frac{5}{2}}}{a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^(5/2)/(a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3), x)","F",0
908,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
909,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
910,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
911,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
912,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
913,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
914,0,0,0,0.416669," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m/sqrt(arctan(a*x)), x)","F",0
915,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
916,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
917,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
918,0,0,0,0.461074," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m}}{\sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m/sqrt(arctan(a*x)), x)","F",0
919,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
920,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
921,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
922,0,0,0,0.519768," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m}}{\sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m/sqrt(arctan(a*x)), x)","F",0
923,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
924,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
925,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
926,0,0,0,0.560273," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(x^m/((a^2*c*x^2 + c)*sqrt(arctan(a*x))), x)","F",0
927,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
928,1,14,0,0.430935," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\arctan\left(a x\right)}}{a c}"," ",0,"2*sqrt(arctan(a*x))/(a*c)","A",0
929,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
930,0,0,0,0.500732," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(arctan(a*x))), x)","F",0
931,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
932,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
933,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
934,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
935,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
936,0,0,0,0.493706," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*sqrt(arctan(a*x))), x)","F",0
937,-2,0,0,0.000000," ","integrate(x^5/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
938,-2,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
939,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
940,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
941,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
942,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
943,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
944,0,0,0,0.470277," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/sqrt(arctan(a*x)), x)","F",0
945,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
946,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
947,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
948,0,0,0,0.421204," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m/sqrt(arctan(a*x)), x)","F",0
949,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
950,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
951,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
952,0,0,0,0.447631," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m}}{\sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m/sqrt(arctan(a*x)), x)","F",0
953,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
954,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
955,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
956,0,0,0,0.536888," ","integrate(x^m/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(x^m/(sqrt(a^2*c*x^2 + c)*sqrt(arctan(a*x))), x)","F",0
957,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
958,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
959,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
960,0,0,0,0.479249," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(arctan(a*x))), x)","F",0
961,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
962,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
963,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
964,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
965,0,0,0,0.531150," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \sqrt{\arctan\left(a x\right)}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*sqrt(arctan(a*x))), x)","F",0
966,-2,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
967,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
968,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
969,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
970,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
971,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
972,0,0,0,0.454444," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m/arctan(a*x)^(3/2), x)","F",0
973,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
974,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
975,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
976,0,0,0,0.553078," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m}}{\arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m/arctan(a*x)^(3/2), x)","F",0
977,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
978,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
979,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
980,0,0,0,0.529816," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m}}{\arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m/arctan(a*x)^(3/2), x)","F",0
981,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
982,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
983,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
984,0,0,0,2.707958," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^m/((a^2*c*x^2 + c)*arctan(a*x)^(3/2)), x)","F",0
985,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
986,1,14,0,0.665243," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","-\frac{2}{a c \sqrt{\arctan\left(a x\right)}}"," ",0,"-2/(a*c*sqrt(arctan(a*x)))","A",0
987,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
988,0,0,0,0.504568," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^(3/2)), x)","F",0
989,-2,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
990,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
991,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
992,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
993,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
994,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
995,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
996,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
997,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
998,0,0,0,0.432959," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^(3/2)), x)","F",0
999,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1000,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1001,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1002,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1003,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1004,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1005,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1006,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1007,0,0,0,0.435052," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^(3/2), x)","F",0
1008,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1009,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1010,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1011,0,0,0,0.437949," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x)^(3/2), x)","F",0
1012,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1013,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1014,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1015,0,0,0,0.436041," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^(3/2), x)","F",0
1016,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1017,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1018,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1019,0,0,0,0.442536," ","integrate(x^m/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^(3/2)), x)","F",0
1020,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1021,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1022,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1023,-2,0,0,0.000000," ","integrate(1/x^2/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1024,0,0,0,0.475624," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^(3/2)), x)","F",0
1025,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1026,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1027,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1028,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1029,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1030,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1031,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1032,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1033,0,0,0,0.453013," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^(3/2)), x)","F",0
1034,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1035,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1036,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1037,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1038,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1039,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1040,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1041,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1042,0,0,0,0.502792," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)*x^m/arctan(a*x)^(5/2), x)","F",0
1043,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1044,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1045,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1046,0,0,0,0.512625," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} x^{m}}{\arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*x^m/arctan(a*x)^(5/2), x)","F",0
1047,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1048,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1049,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1050,0,0,0,0.801672," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} x^{m}}{\arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*x^m/arctan(a*x)^(5/2), x)","F",0
1051,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1052,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1053,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1054,0,0,0,0.575890," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(x^m/((a^2*c*x^2 + c)*arctan(a*x)^(5/2)), x)","F",0
1055,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1056,1,14,0,0.488138," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","-\frac{2}{3 \, a c \arctan\left(a x\right)^{\frac{3}{2}}}"," ",0,"-2/3/(a*c*arctan(a*x)^(3/2))","A",0
1057,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1058,0,0,0,0.492558," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^(5/2)), x)","F",0
1059,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1060,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1061,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1062,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1063,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1064,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1065,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1066,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1067,0,0,0,0.475609," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^(5/2)), x)","F",0
1068,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1069,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1070,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1071,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1072,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1073,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1074,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1075,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1076,0,0,0,0.491681," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^(5/2), x)","F",0
1077,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1078,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1079,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1080,0,0,0,0.566168," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x)^(5/2), x)","F",0
1081,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1082,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1083,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1084,0,0,0,0.498466," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^(5/2), x)","F",0
1085,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1086,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1087,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1088,0,0,0,0.446086," ","integrate(x^m/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^(5/2)), x)","F",0
1089,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1090,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1091,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1092,-2,0,0,0.000000," ","integrate(1/x^2/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1093,0,0,0,0.498521," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)^(5/2)), x)","F",0
1094,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1095,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1096,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1097,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1098,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1099,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1100,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1101,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1102,0,0,0,0.495560," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(a^2*c*x^2 + c)*x^m/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)^(5/2)), x)","F",0
1103,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1104,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1105,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1106,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1107,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1108,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1109,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1110,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
1111,0,0,0,0.549345," ","integrate(x*arctan(a*x)^n/(a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \arctan\left(a x\right)^{n}}{a^{2} c x^{2} + c}, x\right)"," ",0,"integral(x*arctan(a*x)^n/(a^2*c*x^2 + c), x)","F",0
1112,1,21,0,0.596900," ","integrate(arctan(a*x)^n/(a^2*c*x^2+c),x, algorithm=""fricas"")","\frac{\arctan\left(a x\right)^{n} \arctan\left(a x\right)}{a c n + a c}"," ",0,"arctan(a*x)^n*arctan(a*x)/(a*c*n + a*c)","A",0
1113,0,0,0,0.494016," ","integrate((f*x)^m*(c^2*d*x^2+d)^q*(a+b*arctan(c*x))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} d x^{2} + d\right)}^{q} \left(f x\right)^{m} {\left(b \arctan\left(c x\right) + a\right)}^{p}, x\right)"," ",0,"integral((c^2*d*x^2 + d)^q*(f*x)^m*(b*arctan(c*x) + a)^p, x)","F",0
1114,1,110,0,0.448345," ","integrate(x^3*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{30 \, a c^{6} e x^{6} + 45 \, a c^{6} d x^{4} - 6 \, b c^{5} e x^{5} - 5 \, {\left(3 \, b c^{5} d - 2 \, b c^{3} e\right)} x^{3} + 15 \, {\left(3 \, b c^{3} d - 2 \, b c e\right)} x + 15 \, {\left(2 \, b c^{6} e x^{6} + 3 \, b c^{6} d x^{4} - 3 \, b c^{2} d + 2 \, b e\right)} \arctan\left(c x\right)}{180 \, c^{6}}"," ",0,"1/180*(30*a*c^6*e*x^6 + 45*a*c^6*d*x^4 - 6*b*c^5*e*x^5 - 5*(3*b*c^5*d - 2*b*c^3*e)*x^3 + 15*(3*b*c^3*d - 2*b*c*e)*x + 15*(2*b*c^6*e*x^6 + 3*b*c^6*d*x^4 - 3*b*c^2*d + 2*b*e)*arctan(c*x))/c^6","A",0
1115,1,107,0,0.480999," ","integrate(x^2*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{12 \, a c^{5} e x^{5} + 20 \, a c^{5} d x^{3} - 3 \, b c^{4} e x^{4} - 2 \, {\left(5 \, b c^{4} d - 3 \, b c^{2} e\right)} x^{2} + 4 \, {\left(3 \, b c^{5} e x^{5} + 5 \, b c^{5} d x^{3}\right)} \arctan\left(c x\right) + 2 \, {\left(5 \, b c^{2} d - 3 \, b e\right)} \log\left(c^{2} x^{2} + 1\right)}{60 \, c^{5}}"," ",0,"1/60*(12*a*c^5*e*x^5 + 20*a*c^5*d*x^3 - 3*b*c^4*e*x^4 - 2*(5*b*c^4*d - 3*b*c^2*e)*x^2 + 4*(3*b*c^5*e*x^5 + 5*b*c^5*d*x^3)*arctan(c*x) + 2*(5*b*c^2*d - 3*b*e)*log(c^2*x^2 + 1))/c^5","A",0
1116,1,89,0,0.478447," ","integrate(x*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} e x^{4} + 6 \, a c^{4} d x^{2} - b c^{3} e x^{3} - 3 \, {\left(2 \, b c^{3} d - b c e\right)} x + 3 \, {\left(b c^{4} e x^{4} + 2 \, b c^{4} d x^{2} + 2 \, b c^{2} d - b e\right)} \arctan\left(c x\right)}{12 \, c^{4}}"," ",0,"1/12*(3*a*c^4*e*x^4 + 6*a*c^4*d*x^2 - b*c^3*e*x^3 - 3*(2*b*c^3*d - b*c*e)*x + 3*(b*c^4*e*x^4 + 2*b*c^4*d*x^2 + 2*b*c^2*d - b*e)*arctan(c*x))/c^4","A",0
1117,1,82,0,0.460537," ","integrate((e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} e x^{3} + 6 \, a c^{3} d x - b c^{2} e x^{2} + 2 \, {\left(b c^{3} e x^{3} + 3 \, b c^{3} d x\right)} \arctan\left(c x\right) - {\left(3 \, b c^{2} d - b e\right)} \log\left(c^{2} x^{2} + 1\right)}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*e*x^3 + 6*a*c^3*d*x - b*c^2*e*x^2 + 2*(b*c^3*e*x^3 + 3*b*c^3*d*x)*arctan(c*x) - (3*b*c^2*d - b*e)*log(c^2*x^2 + 1))/c^3","A",0
1118,0,0,0,0.429618," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))/x, x)","F",0
1119,1,74,0,0.490628," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","\frac{2 \, b c^{2} d x \log\left(x\right) + 2 \, a c e x^{2} - 2 \, a c d - {\left(b c^{2} d + b e\right)} x \log\left(c^{2} x^{2} + 1\right) + 2 \, {\left(b c e x^{2} - b c d\right)} \arctan\left(c x\right)}{2 \, c x}"," ",0,"1/2*(2*b*c^2*d*x*log(x) + 2*a*c*e*x^2 - 2*a*c*d - (b*c^2*d + b*e)*x*log(c^2*x^2 + 1) + 2*(b*c*e*x^2 - b*c*d)*arctan(c*x))/(c*x)","A",0
1120,0,0,0,0.413324," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))/x^3, x)","F",0
1121,1,85,0,0.425101," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","\frac{{\left(b c^{3} d - 3 \, b c e\right)} x^{3} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(b c^{3} d - 3 \, b c e\right)} x^{3} \log\left(x\right) - b c d x - 6 \, a e x^{2} - 2 \, a d - 2 \, {\left(3 \, b e x^{2} + b d\right)} \arctan\left(c x\right)}{6 \, x^{3}}"," ",0,"1/6*((b*c^3*d - 3*b*c*e)*x^3*log(c^2*x^2 + 1) - 2*(b*c^3*d - 3*b*c*e)*x^3*log(x) - b*c*d*x - 6*a*e*x^2 - 2*a*d - 2*(3*b*e*x^2 + b*d)*arctan(c*x))/x^3","A",0
1122,1,75,0,0.476915," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","-\frac{b c d x + 6 \, a e x^{2} - 3 \, {\left(b c^{3} d - 2 \, b c e\right)} x^{3} + 3 \, a d - 3 \, {\left({\left(b c^{4} d - 2 \, b c^{2} e\right)} x^{4} - 2 \, b e x^{2} - b d\right)} \arctan\left(c x\right)}{12 \, x^{4}}"," ",0,"-1/12*(b*c*d*x + 6*a*e*x^2 - 3*(b*c^3*d - 2*b*c*e)*x^3 + 3*a*d - 3*((b*c^4*d - 2*b*c^2*e)*x^4 - 2*b*e*x^2 - b*d)*arctan(c*x))/x^4","A",0
1123,1,111,0,0.445455," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b c^{5} d - 5 \, b c^{3} e\right)} x^{5} \log\left(c^{2} x^{2} + 1\right) - 4 \, {\left(3 \, b c^{5} d - 5 \, b c^{3} e\right)} x^{5} \log\left(x\right) + 3 \, b c d x + 20 \, a e x^{2} - 2 \, {\left(3 \, b c^{3} d - 5 \, b c e\right)} x^{3} + 12 \, a d + 4 \, {\left(5 \, b e x^{2} + 3 \, b d\right)} \arctan\left(c x\right)}{60 \, x^{5}}"," ",0,"-1/60*(2*(3*b*c^5*d - 5*b*c^3*e)*x^5*log(c^2*x^2 + 1) - 4*(3*b*c^5*d - 5*b*c^3*e)*x^5*log(x) + 3*b*c*d*x + 20*a*e*x^2 - 2*(3*b*c^3*d - 5*b*c*e)*x^3 + 12*a*d + 4*(5*b*e*x^2 + 3*b*d)*arctan(c*x))/x^5","A",0
1124,1,98,0,0.409854," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^7,x, algorithm=""fricas"")","-\frac{15 \, {\left(2 \, b c^{5} d - 3 \, b c^{3} e\right)} x^{5} + 6 \, b c d x + 45 \, a e x^{2} - 5 \, {\left(2 \, b c^{3} d - 3 \, b c e\right)} x^{3} + 30 \, a d + 15 \, {\left({\left(2 \, b c^{6} d - 3 \, b c^{4} e\right)} x^{6} + 3 \, b e x^{2} + 2 \, b d\right)} \arctan\left(c x\right)}{180 \, x^{6}}"," ",0,"-1/180*(15*(2*b*c^5*d - 3*b*c^3*e)*x^5 + 6*b*c*d*x + 45*a*e*x^2 - 5*(2*b*c^3*d - 3*b*c*e)*x^3 + 30*a*d + 15*((2*b*c^6*d - 3*b*c^4*e)*x^6 + 3*b*e*x^2 + 2*b*d)*arctan(c*x))/x^6","A",0
1125,1,201,0,0.421295," ","integrate(x^3*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{315 \, a c^{8} e^{2} x^{8} + 840 \, a c^{8} d e x^{6} - 45 \, b c^{7} e^{2} x^{7} + 630 \, a c^{8} d^{2} x^{4} - 21 \, {\left(8 \, b c^{7} d e - 3 \, b c^{5} e^{2}\right)} x^{5} - 35 \, {\left(6 \, b c^{7} d^{2} - 8 \, b c^{5} d e + 3 \, b c^{3} e^{2}\right)} x^{3} + 105 \, {\left(6 \, b c^{5} d^{2} - 8 \, b c^{3} d e + 3 \, b c e^{2}\right)} x + 105 \, {\left(3 \, b c^{8} e^{2} x^{8} + 8 \, b c^{8} d e x^{6} + 6 \, b c^{8} d^{2} x^{4} - 6 \, b c^{4} d^{2} + 8 \, b c^{2} d e - 3 \, b e^{2}\right)} \arctan\left(c x\right)}{2520 \, c^{8}}"," ",0,"1/2520*(315*a*c^8*e^2*x^8 + 840*a*c^8*d*e*x^6 - 45*b*c^7*e^2*x^7 + 630*a*c^8*d^2*x^4 - 21*(8*b*c^7*d*e - 3*b*c^5*e^2)*x^5 - 35*(6*b*c^7*d^2 - 8*b*c^5*d*e + 3*b*c^3*e^2)*x^3 + 105*(6*b*c^5*d^2 - 8*b*c^3*d*e + 3*b*c*e^2)*x + 105*(3*b*c^8*e^2*x^8 + 8*b*c^8*d*e*x^6 + 6*b*c^8*d^2*x^4 - 6*b*c^4*d^2 + 8*b*c^2*d*e - 3*b*e^2)*arctan(c*x))/c^8","A",0
1126,1,186,0,0.418810," ","integrate(x^2*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{60 \, a c^{7} e^{2} x^{7} + 168 \, a c^{7} d e x^{5} - 10 \, b c^{6} e^{2} x^{6} + 140 \, a c^{7} d^{2} x^{3} - 3 \, {\left(14 \, b c^{6} d e - 5 \, b c^{4} e^{2}\right)} x^{4} - 2 \, {\left(35 \, b c^{6} d^{2} - 42 \, b c^{4} d e + 15 \, b c^{2} e^{2}\right)} x^{2} + 4 \, {\left(15 \, b c^{7} e^{2} x^{7} + 42 \, b c^{7} d e x^{5} + 35 \, b c^{7} d^{2} x^{3}\right)} \arctan\left(c x\right) + 2 \, {\left(35 \, b c^{4} d^{2} - 42 \, b c^{2} d e + 15 \, b e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{420 \, c^{7}}"," ",0,"1/420*(60*a*c^7*e^2*x^7 + 168*a*c^7*d*e*x^5 - 10*b*c^6*e^2*x^6 + 140*a*c^7*d^2*x^3 - 3*(14*b*c^6*d*e - 5*b*c^4*e^2)*x^4 - 2*(35*b*c^6*d^2 - 42*b*c^4*d*e + 15*b*c^2*e^2)*x^2 + 4*(15*b*c^7*e^2*x^7 + 42*b*c^7*d*e*x^5 + 35*b*c^7*d^2*x^3)*arctan(c*x) + 2*(35*b*c^4*d^2 - 42*b*c^2*d*e + 15*b*e^2)*log(c^2*x^2 + 1))/c^7","A",0
1127,1,166,0,0.428314," ","integrate(x*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{15 \, a c^{6} e^{2} x^{6} + 45 \, a c^{6} d e x^{4} - 3 \, b c^{5} e^{2} x^{5} + 45 \, a c^{6} d^{2} x^{2} - 5 \, {\left(3 \, b c^{5} d e - b c^{3} e^{2}\right)} x^{3} - 15 \, {\left(3 \, b c^{5} d^{2} - 3 \, b c^{3} d e + b c e^{2}\right)} x + 15 \, {\left(b c^{6} e^{2} x^{6} + 3 \, b c^{6} d e x^{4} + 3 \, b c^{6} d^{2} x^{2} + 3 \, b c^{4} d^{2} - 3 \, b c^{2} d e + b e^{2}\right)} \arctan\left(c x\right)}{90 \, c^{6}}"," ",0,"1/90*(15*a*c^6*e^2*x^6 + 45*a*c^6*d*e*x^4 - 3*b*c^5*e^2*x^5 + 45*a*c^6*d^2*x^2 - 5*(3*b*c^5*d*e - b*c^3*e^2)*x^3 - 15*(3*b*c^5*d^2 - 3*b*c^3*d*e + b*c*e^2)*x + 15*(b*c^6*e^2*x^6 + 3*b*c^6*d*e*x^4 + 3*b*c^6*d^2*x^2 + 3*b*c^4*d^2 - 3*b*c^2*d*e + b*e^2)*arctan(c*x))/c^6","A",0
1128,1,150,0,0.520886," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{12 \, a c^{5} e^{2} x^{5} + 40 \, a c^{5} d e x^{3} - 3 \, b c^{4} e^{2} x^{4} + 60 \, a c^{5} d^{2} x - 2 \, {\left(10 \, b c^{4} d e - 3 \, b c^{2} e^{2}\right)} x^{2} + 4 \, {\left(3 \, b c^{5} e^{2} x^{5} + 10 \, b c^{5} d e x^{3} + 15 \, b c^{5} d^{2} x\right)} \arctan\left(c x\right) - 2 \, {\left(15 \, b c^{4} d^{2} - 10 \, b c^{2} d e + 3 \, b e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{60 \, c^{5}}"," ",0,"1/60*(12*a*c^5*e^2*x^5 + 40*a*c^5*d*e*x^3 - 3*b*c^4*e^2*x^4 + 60*a*c^5*d^2*x - 2*(10*b*c^4*d*e - 3*b*c^2*e^2)*x^2 + 4*(3*b*c^5*e^2*x^5 + 10*b*c^5*d*e*x^3 + 15*b*c^5*d^2*x)*arctan(c*x) - 2*(15*b*c^4*d^2 - 10*b*c^2*d*e + 3*b*e^2)*log(c^2*x^2 + 1))/c^5","A",0
1129,0,0,0,0.671632," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))/x, x)","F",0
1130,1,140,0,0.455500," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","\frac{2 \, a c^{3} e^{2} x^{4} + 6 \, b c^{4} d^{2} x \log\left(x\right) + 12 \, a c^{3} d e x^{2} - b c^{2} e^{2} x^{3} - 6 \, a c^{3} d^{2} - {\left(3 \, b c^{4} d^{2} + 6 \, b c^{2} d e - b e^{2}\right)} x \log\left(c^{2} x^{2} + 1\right) + 2 \, {\left(b c^{3} e^{2} x^{4} + 6 \, b c^{3} d e x^{2} - 3 \, b c^{3} d^{2}\right)} \arctan\left(c x\right)}{6 \, c^{3} x}"," ",0,"1/6*(2*a*c^3*e^2*x^4 + 6*b*c^4*d^2*x*log(x) + 12*a*c^3*d*e*x^2 - b*c^2*e^2*x^3 - 6*a*c^3*d^2 - (3*b*c^4*d^2 + 6*b*c^2*d*e - b*e^2)*x*log(c^2*x^2 + 1) + 2*(b*c^3*e^2*x^4 + 6*b*c^3*d*e*x^2 - 3*b*c^3*d^2)*arctan(c*x))/(c^3*x)","A",0
1131,0,0,0,0.452095," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))/x^3, x)","F",0
1132,1,139,0,0.434784," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","\frac{6 \, a c e^{2} x^{4} - b c^{2} d^{2} x - 12 \, a c d e x^{2} + {\left(b c^{4} d^{2} - 6 \, b c^{2} d e - 3 \, b e^{2}\right)} x^{3} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(b c^{4} d^{2} - 6 \, b c^{2} d e\right)} x^{3} \log\left(x\right) - 2 \, a c d^{2} + 2 \, {\left(3 \, b c e^{2} x^{4} - 6 \, b c d e x^{2} - b c d^{2}\right)} \arctan\left(c x\right)}{6 \, c x^{3}}"," ",0,"1/6*(6*a*c*e^2*x^4 - b*c^2*d^2*x - 12*a*c*d*e*x^2 + (b*c^4*d^2 - 6*b*c^2*d*e - 3*b*e^2)*x^3*log(c^2*x^2 + 1) - 2*(b*c^4*d^2 - 6*b*c^2*d*e)*x^3*log(x) - 2*a*c*d^2 + 2*(3*b*c*e^2*x^4 - 6*b*c*d*e*x^2 - b*c*d^2)*arctan(c*x))/(c*x^3)","A",0
1133,0,0,0,0.427175," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)}{x^{5}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))/x^5, x)","F",0
1134,1,160,0,0.503081," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","-\frac{60 \, a e^{2} x^{4} + 2 \, {\left(3 \, b c^{5} d^{2} - 10 \, b c^{3} d e + 15 \, b c e^{2}\right)} x^{5} \log\left(c^{2} x^{2} + 1\right) - 4 \, {\left(3 \, b c^{5} d^{2} - 10 \, b c^{3} d e + 15 \, b c e^{2}\right)} x^{5} \log\left(x\right) + 3 \, b c d^{2} x + 40 \, a d e x^{2} - 2 \, {\left(3 \, b c^{3} d^{2} - 10 \, b c d e\right)} x^{3} + 12 \, a d^{2} + 4 \, {\left(15 \, b e^{2} x^{4} + 10 \, b d e x^{2} + 3 \, b d^{2}\right)} \arctan\left(c x\right)}{60 \, x^{5}}"," ",0,"-1/60*(60*a*e^2*x^4 + 2*(3*b*c^5*d^2 - 10*b*c^3*d*e + 15*b*c*e^2)*x^5*log(c^2*x^2 + 1) - 4*(3*b*c^5*d^2 - 10*b*c^3*d*e + 15*b*c*e^2)*x^5*log(x) + 3*b*c*d^2*x + 40*a*d*e*x^2 - 2*(3*b*c^3*d^2 - 10*b*c*d*e)*x^3 + 12*a*d^2 + 4*(15*b*e^2*x^4 + 10*b*d*e*x^2 + 3*b*d^2)*arctan(c*x))/x^5","A",0
1135,1,145,0,0.450768," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^7,x, algorithm=""fricas"")","-\frac{45 \, a e^{2} x^{4} + 15 \, {\left(b c^{5} d^{2} - 3 \, b c^{3} d e + 3 \, b c e^{2}\right)} x^{5} + 3 \, b c d^{2} x + 45 \, a d e x^{2} - 5 \, {\left(b c^{3} d^{2} - 3 \, b c d e\right)} x^{3} + 15 \, a d^{2} + 15 \, {\left(3 \, b e^{2} x^{4} + {\left(b c^{6} d^{2} - 3 \, b c^{4} d e + 3 \, b c^{2} e^{2}\right)} x^{6} + 3 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)}{90 \, x^{6}}"," ",0,"-1/90*(45*a*e^2*x^4 + 15*(b*c^5*d^2 - 3*b*c^3*d*e + 3*b*c*e^2)*x^5 + 3*b*c*d^2*x + 45*a*d*e*x^2 - 5*(b*c^3*d^2 - 3*b*c*d*e)*x^3 + 15*a*d^2 + 15*(3*b*e^2*x^4 + (b*c^6*d^2 - 3*b*c^4*d*e + 3*b*c^2*e^2)*x^6 + 3*b*d*e*x^2 + b*d^2)*arctan(c*x))/x^6","A",0
1136,1,194,0,0.447950," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^8,x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b c^{7} d^{2} - 42 \, b c^{5} d e + 35 \, b c^{3} e^{2}\right)} x^{7} \log\left(c^{2} x^{2} + 1\right) - 4 \, {\left(15 \, b c^{7} d^{2} - 42 \, b c^{5} d e + 35 \, b c^{3} e^{2}\right)} x^{7} \log\left(x\right) - 140 \, a e^{2} x^{4} - 2 \, {\left(15 \, b c^{5} d^{2} - 42 \, b c^{3} d e + 35 \, b c e^{2}\right)} x^{5} - 10 \, b c d^{2} x - 168 \, a d e x^{2} + 3 \, {\left(5 \, b c^{3} d^{2} - 14 \, b c d e\right)} x^{3} - 60 \, a d^{2} - 4 \, {\left(35 \, b e^{2} x^{4} + 42 \, b d e x^{2} + 15 \, b d^{2}\right)} \arctan\left(c x\right)}{420 \, x^{7}}"," ",0,"1/420*(2*(15*b*c^7*d^2 - 42*b*c^5*d*e + 35*b*c^3*e^2)*x^7*log(c^2*x^2 + 1) - 4*(15*b*c^7*d^2 - 42*b*c^5*d*e + 35*b*c^3*e^2)*x^7*log(x) - 140*a*e^2*x^4 - 2*(15*b*c^5*d^2 - 42*b*c^3*d*e + 35*b*c*e^2)*x^5 - 10*b*c*d^2*x - 168*a*d*e*x^2 + 3*(5*b*c^3*d^2 - 14*b*c*d*e)*x^3 - 60*a*d^2 - 4*(35*b*e^2*x^4 + 42*b*d*e*x^2 + 15*b*d^2)*arctan(c*x))/x^7","A",0
1137,1,304,0,0.463055," ","integrate(x^3*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{1260 \, a c^{10} e^{3} x^{10} + 4725 \, a c^{10} d e^{2} x^{8} - 140 \, b c^{9} e^{3} x^{9} + 6300 \, a c^{10} d^{2} e x^{6} + 3150 \, a c^{10} d^{3} x^{4} - 45 \, {\left(15 \, b c^{9} d e^{2} - 4 \, b c^{7} e^{3}\right)} x^{7} - 63 \, {\left(20 \, b c^{9} d^{2} e - 15 \, b c^{7} d e^{2} + 4 \, b c^{5} e^{3}\right)} x^{5} - 105 \, {\left(10 \, b c^{9} d^{3} - 20 \, b c^{7} d^{2} e + 15 \, b c^{5} d e^{2} - 4 \, b c^{3} e^{3}\right)} x^{3} + 315 \, {\left(10 \, b c^{7} d^{3} - 20 \, b c^{5} d^{2} e + 15 \, b c^{3} d e^{2} - 4 \, b c e^{3}\right)} x + 315 \, {\left(4 \, b c^{10} e^{3} x^{10} + 15 \, b c^{10} d e^{2} x^{8} + 20 \, b c^{10} d^{2} e x^{6} + 10 \, b c^{10} d^{3} x^{4} - 10 \, b c^{6} d^{3} + 20 \, b c^{4} d^{2} e - 15 \, b c^{2} d e^{2} + 4 \, b e^{3}\right)} \arctan\left(c x\right)}{12600 \, c^{10}}"," ",0,"1/12600*(1260*a*c^10*e^3*x^10 + 4725*a*c^10*d*e^2*x^8 - 140*b*c^9*e^3*x^9 + 6300*a*c^10*d^2*e*x^6 + 3150*a*c^10*d^3*x^4 - 45*(15*b*c^9*d*e^2 - 4*b*c^7*e^3)*x^7 - 63*(20*b*c^9*d^2*e - 15*b*c^7*d*e^2 + 4*b*c^5*e^3)*x^5 - 105*(10*b*c^9*d^3 - 20*b*c^7*d^2*e + 15*b*c^5*d*e^2 - 4*b*c^3*e^3)*x^3 + 315*(10*b*c^7*d^3 - 20*b*c^5*d^2*e + 15*b*c^3*d*e^2 - 4*b*c*e^3)*x + 315*(4*b*c^10*e^3*x^10 + 15*b*c^10*d*e^2*x^8 + 20*b*c^10*d^2*e*x^6 + 10*b*c^10*d^3*x^4 - 10*b*c^6*d^3 + 20*b*c^4*d^2*e - 15*b*c^2*d*e^2 + 4*b*e^3)*arctan(c*x))/c^10","A",0
1138,1,277,0,0.477599," ","integrate(x^2*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{840 \, a c^{9} e^{3} x^{9} + 3240 \, a c^{9} d e^{2} x^{7} - 105 \, b c^{8} e^{3} x^{8} + 4536 \, a c^{9} d^{2} e x^{5} + 2520 \, a c^{9} d^{3} x^{3} - 20 \, {\left(27 \, b c^{8} d e^{2} - 7 \, b c^{6} e^{3}\right)} x^{6} - 6 \, {\left(189 \, b c^{8} d^{2} e - 135 \, b c^{6} d e^{2} + 35 \, b c^{4} e^{3}\right)} x^{4} - 12 \, {\left(105 \, b c^{8} d^{3} - 189 \, b c^{6} d^{2} e + 135 \, b c^{4} d e^{2} - 35 \, b c^{2} e^{3}\right)} x^{2} + 24 \, {\left(35 \, b c^{9} e^{3} x^{9} + 135 \, b c^{9} d e^{2} x^{7} + 189 \, b c^{9} d^{2} e x^{5} + 105 \, b c^{9} d^{3} x^{3}\right)} \arctan\left(c x\right) + 12 \, {\left(105 \, b c^{6} d^{3} - 189 \, b c^{4} d^{2} e + 135 \, b c^{2} d e^{2} - 35 \, b e^{3}\right)} \log\left(c^{2} x^{2} + 1\right)}{7560 \, c^{9}}"," ",0,"1/7560*(840*a*c^9*e^3*x^9 + 3240*a*c^9*d*e^2*x^7 - 105*b*c^8*e^3*x^8 + 4536*a*c^9*d^2*e*x^5 + 2520*a*c^9*d^3*x^3 - 20*(27*b*c^8*d*e^2 - 7*b*c^6*e^3)*x^6 - 6*(189*b*c^8*d^2*e - 135*b*c^6*d*e^2 + 35*b*c^4*e^3)*x^4 - 12*(105*b*c^8*d^3 - 189*b*c^6*d^2*e + 135*b*c^4*d*e^2 - 35*b*c^2*e^3)*x^2 + 24*(35*b*c^9*e^3*x^9 + 135*b*c^9*d*e^2*x^7 + 189*b*c^9*d^2*e*x^5 + 105*b*c^9*d^3*x^3)*arctan(c*x) + 12*(105*b*c^6*d^3 - 189*b*c^4*d^2*e + 135*b*c^2*d*e^2 - 35*b*e^3)*log(c^2*x^2 + 1))/c^9","A",0
1139,1,258,0,0.480512," ","integrate(x*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{105 \, a c^{8} e^{3} x^{8} + 420 \, a c^{8} d e^{2} x^{6} - 15 \, b c^{7} e^{3} x^{7} + 630 \, a c^{8} d^{2} e x^{4} + 420 \, a c^{8} d^{3} x^{2} - 21 \, {\left(4 \, b c^{7} d e^{2} - b c^{5} e^{3}\right)} x^{5} - 35 \, {\left(6 \, b c^{7} d^{2} e - 4 \, b c^{5} d e^{2} + b c^{3} e^{3}\right)} x^{3} - 105 \, {\left(4 \, b c^{7} d^{3} - 6 \, b c^{5} d^{2} e + 4 \, b c^{3} d e^{2} - b c e^{3}\right)} x + 105 \, {\left(b c^{8} e^{3} x^{8} + 4 \, b c^{8} d e^{2} x^{6} + 6 \, b c^{8} d^{2} e x^{4} + 4 \, b c^{8} d^{3} x^{2} + 4 \, b c^{6} d^{3} - 6 \, b c^{4} d^{2} e + 4 \, b c^{2} d e^{2} - b e^{3}\right)} \arctan\left(c x\right)}{840 \, c^{8}}"," ",0,"1/840*(105*a*c^8*e^3*x^8 + 420*a*c^8*d*e^2*x^6 - 15*b*c^7*e^3*x^7 + 630*a*c^8*d^2*e*x^4 + 420*a*c^8*d^3*x^2 - 21*(4*b*c^7*d*e^2 - b*c^5*e^3)*x^5 - 35*(6*b*c^7*d^2*e - 4*b*c^5*d*e^2 + b*c^3*e^3)*x^3 - 105*(4*b*c^7*d^3 - 6*b*c^5*d^2*e + 4*b*c^3*d*e^2 - b*c*e^3)*x + 105*(b*c^8*e^3*x^8 + 4*b*c^8*d*e^2*x^6 + 6*b*c^8*d^2*e*x^4 + 4*b*c^8*d^3*x^2 + 4*b*c^6*d^3 - 6*b*c^4*d^2*e + 4*b*c^2*d*e^2 - b*e^3)*arctan(c*x))/c^8","A",0
1140,1,229,0,0.510201," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{60 \, a c^{7} e^{3} x^{7} + 252 \, a c^{7} d e^{2} x^{5} - 10 \, b c^{6} e^{3} x^{6} + 420 \, a c^{7} d^{2} e x^{3} + 420 \, a c^{7} d^{3} x - 3 \, {\left(21 \, b c^{6} d e^{2} - 5 \, b c^{4} e^{3}\right)} x^{4} - 6 \, {\left(35 \, b c^{6} d^{2} e - 21 \, b c^{4} d e^{2} + 5 \, b c^{2} e^{3}\right)} x^{2} + 12 \, {\left(5 \, b c^{7} e^{3} x^{7} + 21 \, b c^{7} d e^{2} x^{5} + 35 \, b c^{7} d^{2} e x^{3} + 35 \, b c^{7} d^{3} x\right)} \arctan\left(c x\right) - 6 \, {\left(35 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e + 21 \, b c^{2} d e^{2} - 5 \, b e^{3}\right)} \log\left(c^{2} x^{2} + 1\right)}{420 \, c^{7}}"," ",0,"1/420*(60*a*c^7*e^3*x^7 + 252*a*c^7*d*e^2*x^5 - 10*b*c^6*e^3*x^6 + 420*a*c^7*d^2*e*x^3 + 420*a*c^7*d^3*x - 3*(21*b*c^6*d*e^2 - 5*b*c^4*e^3)*x^4 - 6*(35*b*c^6*d^2*e - 21*b*c^4*d*e^2 + 5*b*c^2*e^3)*x^2 + 12*(5*b*c^7*e^3*x^7 + 21*b*c^7*d*e^2*x^5 + 35*b*c^7*d^2*e*x^3 + 35*b*c^7*d^3*x)*arctan(c*x) - 6*(35*b*c^6*d^3 - 35*b*c^4*d^2*e + 21*b*c^2*d*e^2 - 5*b*e^3)*log(c^2*x^2 + 1))/c^7","A",0
1141,0,0,0,0.473660," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arctan(c*x))/x, x)","F",0
1142,1,206,0,0.628364," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","\frac{4 \, a c^{5} e^{3} x^{6} + 20 \, a c^{5} d e^{2} x^{4} - b c^{4} e^{3} x^{5} + 20 \, b c^{6} d^{3} x \log\left(x\right) + 60 \, a c^{5} d^{2} e x^{2} - 20 \, a c^{5} d^{3} - 2 \, {\left(5 \, b c^{4} d e^{2} - b c^{2} e^{3}\right)} x^{3} - 2 \, {\left(5 \, b c^{6} d^{3} + 15 \, b c^{4} d^{2} e - 5 \, b c^{2} d e^{2} + b e^{3}\right)} x \log\left(c^{2} x^{2} + 1\right) + 4 \, {\left(b c^{5} e^{3} x^{6} + 5 \, b c^{5} d e^{2} x^{4} + 15 \, b c^{5} d^{2} e x^{2} - 5 \, b c^{5} d^{3}\right)} \arctan\left(c x\right)}{20 \, c^{5} x}"," ",0,"1/20*(4*a*c^5*e^3*x^6 + 20*a*c^5*d*e^2*x^4 - b*c^4*e^3*x^5 + 20*b*c^6*d^3*x*log(x) + 60*a*c^5*d^2*e*x^2 - 20*a*c^5*d^3 - 2*(5*b*c^4*d*e^2 - b*c^2*e^3)*x^3 - 2*(5*b*c^6*d^3 + 15*b*c^4*d^2*e - 5*b*c^2*d*e^2 + b*e^3)*x*log(c^2*x^2 + 1) + 4*(b*c^5*e^3*x^6 + 5*b*c^5*d*e^2*x^4 + 15*b*c^5*d^2*e*x^2 - 5*b*c^5*d^3)*arctan(c*x))/(c^5*x)","A",0
1143,0,0,0,0.493926," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arctan(c*x))/x^3, x)","F",0
1144,1,205,0,0.464650," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","\frac{2 \, a c^{3} e^{3} x^{6} + 18 \, a c^{3} d e^{2} x^{4} - b c^{2} e^{3} x^{5} - b c^{4} d^{3} x - 18 \, a c^{3} d^{2} e x^{2} - 2 \, a c^{3} d^{3} + {\left(b c^{6} d^{3} - 9 \, b c^{4} d^{2} e - 9 \, b c^{2} d e^{2} + b e^{3}\right)} x^{3} \log\left(c^{2} x^{2} + 1\right) - 2 \, {\left(b c^{6} d^{3} - 9 \, b c^{4} d^{2} e\right)} x^{3} \log\left(x\right) + 2 \, {\left(b c^{3} e^{3} x^{6} + 9 \, b c^{3} d e^{2} x^{4} - 9 \, b c^{3} d^{2} e x^{2} - b c^{3} d^{3}\right)} \arctan\left(c x\right)}{6 \, c^{3} x^{3}}"," ",0,"1/6*(2*a*c^3*e^3*x^6 + 18*a*c^3*d*e^2*x^4 - b*c^2*e^3*x^5 - b*c^4*d^3*x - 18*a*c^3*d^2*e*x^2 - 2*a*c^3*d^3 + (b*c^6*d^3 - 9*b*c^4*d^2*e - 9*b*c^2*d*e^2 + b*e^3)*x^3*log(c^2*x^2 + 1) - 2*(b*c^6*d^3 - 9*b*c^4*d^2*e)*x^3*log(x) + 2*(b*c^3*e^3*x^6 + 9*b*c^3*d*e^2*x^4 - 9*b*c^3*d^2*e*x^2 - b*c^3*d^3)*arctan(c*x))/(c^3*x^3)","A",0
1145,0,0,0,0.429812," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x\right)}{x^{5}}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arctan(c*x))/x^5, x)","F",0
1146,1,214,0,0.481272," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","\frac{20 \, a c e^{3} x^{6} - 60 \, a c d e^{2} x^{4} - b c^{2} d^{3} x - 20 \, a c d^{2} e x^{2} - 2 \, {\left(b c^{6} d^{3} - 5 \, b c^{4} d^{2} e + 15 \, b c^{2} d e^{2} + 5 \, b e^{3}\right)} x^{5} \log\left(c^{2} x^{2} + 1\right) + 4 \, {\left(b c^{6} d^{3} - 5 \, b c^{4} d^{2} e + 15 \, b c^{2} d e^{2}\right)} x^{5} \log\left(x\right) - 4 \, a c d^{3} + 2 \, {\left(b c^{4} d^{3} - 5 \, b c^{2} d^{2} e\right)} x^{3} + 4 \, {\left(5 \, b c e^{3} x^{6} - 15 \, b c d e^{2} x^{4} - 5 \, b c d^{2} e x^{2} - b c d^{3}\right)} \arctan\left(c x\right)}{20 \, c x^{5}}"," ",0,"1/20*(20*a*c*e^3*x^6 - 60*a*c*d*e^2*x^4 - b*c^2*d^3*x - 20*a*c*d^2*e*x^2 - 2*(b*c^6*d^3 - 5*b*c^4*d^2*e + 15*b*c^2*d*e^2 + 5*b*e^3)*x^5*log(c^2*x^2 + 1) + 4*(b*c^6*d^3 - 5*b*c^4*d^2*e + 15*b*c^2*d*e^2)*x^5*log(x) - 4*a*c*d^3 + 2*(b*c^4*d^3 - 5*b*c^2*d^2*e)*x^3 + 4*(5*b*c*e^3*x^6 - 15*b*c*d*e^2*x^4 - 5*b*c*d^2*e*x^2 - b*c*d^3)*arctan(c*x))/(c*x^5)","A",0
1147,0,0,0,0.461333," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x\right)}{x^{7}}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arctan(c*x))/x^7, x)","F",0
1148,1,243,0,0.497480," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^8,x, algorithm=""fricas"")","-\frac{420 \, a e^{3} x^{6} - 6 \, {\left(5 \, b c^{7} d^{3} - 21 \, b c^{5} d^{2} e + 35 \, b c^{3} d e^{2} - 35 \, b c e^{3}\right)} x^{7} \log\left(c^{2} x^{2} + 1\right) + 12 \, {\left(5 \, b c^{7} d^{3} - 21 \, b c^{5} d^{2} e + 35 \, b c^{3} d e^{2} - 35 \, b c e^{3}\right)} x^{7} \log\left(x\right) + 420 \, a d e^{2} x^{4} + 10 \, b c d^{3} x + 252 \, a d^{2} e x^{2} + 6 \, {\left(5 \, b c^{5} d^{3} - 21 \, b c^{3} d^{2} e + 35 \, b c d e^{2}\right)} x^{5} + 60 \, a d^{3} - 3 \, {\left(5 \, b c^{3} d^{3} - 21 \, b c d^{2} e\right)} x^{3} + 12 \, {\left(35 \, b e^{3} x^{6} + 35 \, b d e^{2} x^{4} + 21 \, b d^{2} e x^{2} + 5 \, b d^{3}\right)} \arctan\left(c x\right)}{420 \, x^{7}}"," ",0,"-1/420*(420*a*e^3*x^6 - 6*(5*b*c^7*d^3 - 21*b*c^5*d^2*e + 35*b*c^3*d*e^2 - 35*b*c*e^3)*x^7*log(c^2*x^2 + 1) + 12*(5*b*c^7*d^3 - 21*b*c^5*d^2*e + 35*b*c^3*d*e^2 - 35*b*c*e^3)*x^7*log(x) + 420*a*d*e^2*x^4 + 10*b*c*d^3*x + 252*a*d^2*e*x^2 + 6*(5*b*c^5*d^3 - 21*b*c^3*d^2*e + 35*b*c*d*e^2)*x^5 + 60*a*d^3 - 3*(5*b*c^3*d^3 - 21*b*c*d^2*e)*x^3 + 12*(35*b*e^3*x^6 + 35*b*d*e^2*x^4 + 21*b*d^2*e*x^2 + 5*b*d^3)*arctan(c*x))/x^7","A",0
1149,1,228,0,0.434801," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^9,x, algorithm=""fricas"")","-\frac{420 \, a e^{3} x^{6} + 630 \, a d e^{2} x^{4} - 105 \, {\left(b c^{7} d^{3} - 4 \, b c^{5} d^{2} e + 6 \, b c^{3} d e^{2} - 4 \, b c e^{3}\right)} x^{7} + 15 \, b c d^{3} x + 420 \, a d^{2} e x^{2} + 35 \, {\left(b c^{5} d^{3} - 4 \, b c^{3} d^{2} e + 6 \, b c d e^{2}\right)} x^{5} + 105 \, a d^{3} - 21 \, {\left(b c^{3} d^{3} - 4 \, b c d^{2} e\right)} x^{3} + 105 \, {\left(4 \, b e^{3} x^{6} - {\left(b c^{8} d^{3} - 4 \, b c^{6} d^{2} e + 6 \, b c^{4} d e^{2} - 4 \, b c^{2} e^{3}\right)} x^{8} + 6 \, b d e^{2} x^{4} + 4 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x\right)}{840 \, x^{8}}"," ",0,"-1/840*(420*a*e^3*x^6 + 630*a*d*e^2*x^4 - 105*(b*c^7*d^3 - 4*b*c^5*d^2*e + 6*b*c^3*d*e^2 - 4*b*c*e^3)*x^7 + 15*b*c*d^3*x + 420*a*d^2*e*x^2 + 35*(b*c^5*d^3 - 4*b*c^3*d^2*e + 6*b*c*d*e^2)*x^5 + 105*a*d^3 - 21*(b*c^3*d^3 - 4*b*c*d^2*e)*x^3 + 105*(4*b*e^3*x^6 - (b*c^8*d^3 - 4*b*c^6*d^2*e + 6*b*c^4*d*e^2 - 4*b*c^2*e^3)*x^8 + 6*b*d*e^2*x^4 + 4*b*d^2*e*x^2 + b*d^3)*arctan(c*x))/x^8","A",0
1150,1,237,0,0.509381," ","integrate((d*x^2+c)^4*arctan(a*x),x, algorithm=""fricas"")","-\frac{105 \, a^{8} d^{4} x^{8} + 20 \, {\left(36 \, a^{8} c d^{3} - 7 \, a^{6} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{8} c^{2} d^{2} - 180 \, a^{6} c d^{3} + 35 \, a^{4} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{8} c^{3} d - 378 \, a^{6} c^{2} d^{2} + 180 \, a^{4} c d^{3} - 35 \, a^{2} d^{4}\right)} x^{2} - 24 \, {\left(35 \, a^{9} d^{4} x^{9} + 180 \, a^{9} c d^{3} x^{7} + 378 \, a^{9} c^{2} d^{2} x^{5} + 420 \, a^{9} c^{3} d x^{3} + 315 \, a^{9} c^{4} x\right)} \arctan\left(a x\right) + 12 \, {\left(315 \, a^{8} c^{4} - 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} - 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a^{2} x^{2} + 1\right)}{7560 \, a^{9}}"," ",0,"-1/7560*(105*a^8*d^4*x^8 + 20*(36*a^8*c*d^3 - 7*a^6*d^4)*x^6 + 6*(378*a^8*c^2*d^2 - 180*a^6*c*d^3 + 35*a^4*d^4)*x^4 + 12*(420*a^8*c^3*d - 378*a^6*c^2*d^2 + 180*a^4*c*d^3 - 35*a^2*d^4)*x^2 - 24*(35*a^9*d^4*x^9 + 180*a^9*c*d^3*x^7 + 378*a^9*c^2*d^2*x^5 + 420*a^9*c^3*d*x^3 + 315*a^9*c^4*x)*arctan(a*x) + 12*(315*a^8*c^4 - 420*a^6*c^3*d + 378*a^4*c^2*d^2 - 180*a^2*c*d^3 + 35*d^4)*log(a^2*x^2 + 1))/a^9","A",0
1151,0,0,0,0.490325," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arctan\left(c x\right) + a x^{3}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^3*arctan(c*x) + a*x^3)/(e*x^2 + d), x)","F",0
1152,0,0,0,0.445009," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \arctan\left(c x\right) + a x}{e x^{2} + d}, x\right)"," ",0,"integral((b*x*arctan(c*x) + a*x)/(e*x^2 + d), x)","F",0
1153,0,0,0,0.496782," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{3} + d x}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^3 + d*x), x)","F",0
1154,0,0,0,0.409560," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{5} + d x^{3}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^5 + d*x^3), x)","F",0
1155,0,0,0,0.402628," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arctan\left(c x\right) + a x^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)/(e*x^2 + d), x)","F",0
1156,0,0,0,0.403258," ","integrate((a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{2} + d}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^2 + d), x)","F",0
1157,0,0,0,0.434648," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e*x^4 + d*x^2), x)","F",0
1158,0,0,0,0.452748," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arctan\left(c x\right) + a x^{3}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^3*arctan(c*x) + a*x^3)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1159,1,234,0,0.528590," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a c^{2} d^{2} - 2 \, a d e - {\left(b c e x^{2} + b c d\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 2 \, {\left(b c^{2} d e x^{2} + b d e\right)} \arctan\left(c x\right)}{4 \, {\left(c^{2} d^{3} e - d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - d e^{3}\right)} x^{2}\right)}}, -\frac{a c^{2} d^{2} - a d e + {\left(b c e x^{2} + b c d\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(b c^{2} d e x^{2} + b d e\right)} \arctan\left(c x\right)}{2 \, {\left(c^{2} d^{3} e - d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - d e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*c^2*d^2 - 2*a*d*e - (b*c*e*x^2 + b*c*d)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 2*(b*c^2*d*e*x^2 + b*d*e)*arctan(c*x))/(c^2*d^3*e - d^2*e^2 + (c^2*d^2*e^2 - d*e^3)*x^2), -1/2*(a*c^2*d^2 - a*d*e + (b*c*e*x^2 + b*c*d)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - (b*c^2*d*e*x^2 + b*d*e)*arctan(c*x))/(c^2*d^3*e - d^2*e^2 + (c^2*d^2*e^2 - d*e^3)*x^2)]","A",0
1160,0,0,0,0.407441," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
1161,0,0,0,0.406384," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
1162,0,0,0,0.453587," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arctan\left(c x\right) + a x^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1163,0,0,0,0.459119," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1164,0,0,0,0.553714," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
1165,0,0,0,0.450643," ","integrate(x^5*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{5} \arctan\left(c x\right) + a x^{5}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^5*arctan(c*x) + a*x^5)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1166,1,697,0,0.590906," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{4} d^{4} - 8 \, a c^{2} d^{3} e + 4 \, a d^{2} e^{2} - 2 \, {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + 8 \, {\left(a c^{4} d^{3} e - 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} - {\left(b c^{3} d^{3} - 3 \, b c d^{2} e + {\left(b c^{3} d e^{2} - 3 \, b c e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e - 3 \, b c d e^{2}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 2 \, {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x + 4 \, {\left(2 \, b d e^{3} x^{2} + b d^{2} e^{2} - {\left(b c^{4} d^{2} e^{2} - 2 \, b c^{2} d e^{3}\right)} x^{4}\right)} \arctan\left(c x\right)}{16 \, {\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4} + {\left(c^{4} d^{3} e^{4} - 2 \, c^{2} d^{2} e^{5} + d e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{3} - 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{2}\right)}}, -\frac{2 \, a c^{4} d^{4} - 4 \, a c^{2} d^{3} e + 2 \, a d^{2} e^{2} - {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + 4 \, {\left(a c^{4} d^{3} e - 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} + {\left(b c^{3} d^{3} - 3 \, b c d^{2} e + {\left(b c^{3} d e^{2} - 3 \, b c e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e - 3 \, b c d e^{2}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x + 2 \, {\left(2 \, b d e^{3} x^{2} + b d^{2} e^{2} - {\left(b c^{4} d^{2} e^{2} - 2 \, b c^{2} d e^{3}\right)} x^{4}\right)} \arctan\left(c x\right)}{8 \, {\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4} + {\left(c^{4} d^{3} e^{4} - 2 \, c^{2} d^{2} e^{5} + d e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{3} - 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(4*a*c^4*d^4 - 8*a*c^2*d^3*e + 4*a*d^2*e^2 - 2*(b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + 8*(a*c^4*d^3*e - 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 - (b*c^3*d^3 - 3*b*c*d^2*e + (b*c^3*d*e^2 - 3*b*c*e^3)*x^4 + 2*(b*c^3*d^2*e - 3*b*c*d*e^2)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 2*(b*c^3*d^3*e - b*c*d^2*e^2)*x + 4*(2*b*d*e^3*x^2 + b*d^2*e^2 - (b*c^4*d^2*e^2 - 2*b*c^2*d*e^3)*x^4)*arctan(c*x))/(c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4 + (c^4*d^3*e^4 - 2*c^2*d^2*e^5 + d*e^6)*x^4 + 2*(c^4*d^4*e^3 - 2*c^2*d^3*e^4 + d^2*e^5)*x^2), -1/8*(2*a*c^4*d^4 - 4*a*c^2*d^3*e + 2*a*d^2*e^2 - (b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + 4*(a*c^4*d^3*e - 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 + (b*c^3*d^3 - 3*b*c*d^2*e + (b*c^3*d*e^2 - 3*b*c*e^3)*x^4 + 2*(b*c^3*d^2*e - 3*b*c*d*e^2)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - (b*c^3*d^3*e - b*c*d^2*e^2)*x + 2*(2*b*d*e^3*x^2 + b*d^2*e^2 - (b*c^4*d^2*e^2 - 2*b*c^2*d*e^3)*x^4)*arctan(c*x))/(c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4 + (c^4*d^3*e^4 - 2*c^2*d^2*e^5 + d*e^6)*x^4 + 2*(c^4*d^4*e^3 - 2*c^2*d^3*e^4 + d^2*e^5)*x^2)]","B",0
1167,1,637,0,0.675099," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{4} d^{4} - 8 \, a c^{2} d^{3} e + 4 \, a d^{2} e^{2} + 2 \, {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} - {\left(3 \, b c^{3} d^{3} - b c d^{2} e + {\left(3 \, b c^{3} d e^{2} - b c e^{3}\right)} x^{4} + 2 \, {\left(3 \, b c^{3} d^{2} e - b c d e^{2}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x - 4 \, {\left(b c^{4} d^{2} e^{2} x^{4} + 2 \, b c^{4} d^{3} e x^{2} + 2 \, b c^{2} d^{3} e - b d^{2} e^{2}\right)} \arctan\left(c x\right)}{16 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3} + {\left(c^{4} d^{4} e^{3} - 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{2}\right)}}, -\frac{2 \, a c^{4} d^{4} - 4 \, a c^{2} d^{3} e + 2 \, a d^{2} e^{2} + {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + {\left(3 \, b c^{3} d^{3} - b c d^{2} e + {\left(3 \, b c^{3} d e^{2} - b c e^{3}\right)} x^{4} + 2 \, {\left(3 \, b c^{3} d^{2} e - b c d e^{2}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x - 2 \, {\left(b c^{4} d^{2} e^{2} x^{4} + 2 \, b c^{4} d^{3} e x^{2} + 2 \, b c^{2} d^{3} e - b d^{2} e^{2}\right)} \arctan\left(c x\right)}{8 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3} + {\left(c^{4} d^{4} e^{3} - 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(4*a*c^4*d^4 - 8*a*c^2*d^3*e + 4*a*d^2*e^2 + 2*(b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 - (3*b*c^3*d^3 - b*c*d^2*e + (3*b*c^3*d*e^2 - b*c*e^3)*x^4 + 2*(3*b*c^3*d^2*e - b*c*d*e^2)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(b*c^3*d^3*e - b*c*d^2*e^2)*x - 4*(b*c^4*d^2*e^2*x^4 + 2*b*c^4*d^3*e*x^2 + 2*b*c^2*d^3*e - b*d^2*e^2)*arctan(c*x))/(c^4*d^6*e - 2*c^2*d^5*e^2 + d^4*e^3 + (c^4*d^4*e^3 - 2*c^2*d^3*e^4 + d^2*e^5)*x^4 + 2*(c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4)*x^2), -1/8*(2*a*c^4*d^4 - 4*a*c^2*d^3*e + 2*a*d^2*e^2 + (b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + (3*b*c^3*d^3 - b*c*d^2*e + (3*b*c^3*d*e^2 - b*c*e^3)*x^4 + 2*(3*b*c^3*d^2*e - b*c*d*e^2)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (b*c^3*d^3*e - b*c*d^2*e^2)*x - 2*(b*c^4*d^2*e^2*x^4 + 2*b*c^4*d^3*e*x^2 + 2*b*c^2*d^3*e - b*d^2*e^2)*arctan(c*x))/(c^4*d^6*e - 2*c^2*d^5*e^2 + d^4*e^3 + (c^4*d^4*e^3 - 2*c^2*d^3*e^4 + d^2*e^5)*x^4 + 2*(c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4)*x^2)]","B",0
1168,0,0,0,0.461119," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
1169,0,0,0,0.405740," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
1170,0,0,0,0.417785," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arctan\left(c x\right) + a x^{2}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1171,0,0,0,0.401986," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1172,0,0,0,0.408099," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{e^{3} x^{8} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{4} + d^{3} x^{2}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/(e^3*x^8 + 3*d*e^2*x^6 + 3*d^2*e*x^4 + d^3*x^2), x)","F",0
1173,1,1200,0,3.800038," ","integrate(x^3*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\left[-\frac{{\left(15 \, b c^{4} d^{2} + 20 \, b c^{2} d e - 24 \, b e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 4 \, {\left(2 \, b c^{4} d^{2} + b c^{2} d e - 3 \, b e^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 2 \, {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 6 \, b c^{4} e^{2} x^{3} - 16 \, a c^{5} d^{2} - {\left(7 \, b c^{4} d e - 12 \, b c^{2} e^{2}\right)} x + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{2}}, \frac{8 \, {\left(2 \, b c^{4} d^{2} + b c^{2} d e - 3 \, b e^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(15 \, b c^{4} d^{2} + 20 \, b c^{2} d e - 24 \, b e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 6 \, b c^{4} e^{2} x^{3} - 16 \, a c^{5} d^{2} - {\left(7 \, b c^{4} d e - 12 \, b c^{2} e^{2}\right)} x + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{2}}, -\frac{{\left(15 \, b c^{4} d^{2} + 20 \, b c^{2} d e - 24 \, b e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + 2 \, {\left(2 \, b c^{4} d^{2} + b c^{2} d e - 3 \, b e^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 6 \, b c^{4} e^{2} x^{3} - 16 \, a c^{5} d^{2} - {\left(7 \, b c^{4} d e - 12 \, b c^{2} e^{2}\right)} x + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{120 \, c^{5} e^{2}}, \frac{4 \, {\left(2 \, b c^{4} d^{2} + b c^{2} d e - 3 \, b e^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(15 \, b c^{4} d^{2} + 20 \, b c^{2} d e - 24 \, b e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 6 \, b c^{4} e^{2} x^{3} - 16 \, a c^{5} d^{2} - {\left(7 \, b c^{4} d e - 12 \, b c^{2} e^{2}\right)} x + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{120 \, c^{5} e^{2}}\right]"," ",0,"[-1/240*((15*b*c^4*d^2 + 20*b*c^2*d*e - 24*b*e^2)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 4*(2*b*c^4*d^2 + b*c^2*d*e - 3*b*e^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 2*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 6*b*c^4*e^2*x^3 - 16*a*c^5*d^2 - (7*b*c^4*d*e - 12*b*c^2*e^2)*x + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e^2), 1/240*(8*(2*b*c^4*d^2 + b*c^2*d*e - 3*b*e^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (15*b*c^4*d^2 + 20*b*c^2*d*e - 24*b*e^2)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 6*b*c^4*e^2*x^3 - 16*a*c^5*d^2 - (7*b*c^4*d*e - 12*b*c^2*e^2)*x + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e^2), -1/120*((15*b*c^4*d^2 + 20*b*c^2*d*e - 24*b*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + 2*(2*b*c^4*d^2 + b*c^2*d*e - 3*b*e^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - (24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 6*b*c^4*e^2*x^3 - 16*a*c^5*d^2 - (7*b*c^4*d*e - 12*b*c^2*e^2)*x + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e^2), 1/120*(4*(2*b*c^4*d^2 + b*c^2*d*e - 3*b*e^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (15*b*c^4*d^2 + 20*b*c^2*d*e - 24*b*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 6*b*c^4*e^2*x^3 - 16*a*c^5*d^2 - (7*b*c^4*d*e - 12*b*c^2*e^2)*x + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e^2)]","A",0
1174,0,0,0,0.424791," ","integrate(x^2*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} \arctan\left(c x\right) + a x^{2}\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)*sqrt(e*x^2 + d), x)","F",0
1175,1,879,0,1.096563," ","integrate(x*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b c^{2} d - 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + {\left(b c^{2} d - b e\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 2 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}, -\frac{2 \, {\left(b c^{2} d - b e\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) + {\left(3 \, b c^{2} d - 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}, \frac{2 \, {\left(3 \, b c^{2} d - 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(b c^{2} d - b e\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}, -\frac{{\left(b c^{2} d - b e\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(3 \, b c^{2} d - 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, c^{3} e}\right]"," ",0,"[-1/12*((3*b*c^2*d - 2*b*e)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + (b*c^2*d - b*e)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 2*(2*a*c^3*e*x^2 + 2*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 + b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e), -1/12*(2*(b*c^2*d - b*e)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) + (3*b*c^2*d - 2*b*e)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*(2*a*c^3*e*x^2 + 2*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 + b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e), 1/12*(2*(3*b*c^2*d - 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (b*c^2*d - b*e)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(2*a*c^3*e*x^2 + 2*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 + b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e), -1/6*((b*c^2*d - b*e)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (3*b*c^2*d - 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (2*a*c^3*e*x^2 + 2*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 + b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e)]","A",0
1176,0,0,0,0.439578," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a), x)","F",0
1177,0,0,0,0.408693," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/x, x)","F",0
1178,0,0,0,0.421501," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/x^2, x)","F",0
1179,0,0,0,0.409120," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/x^3, x)","F",0
1180,1,858,0,0.605063," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","\left[-\frac{{\left(b c^{2} d - b e\right)} \sqrt{c^{2} d - e} x^{3} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(2 \, b c^{3} d - 3 \, b c e\right)} \sqrt{d} x^{3} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(b c d x + 2 \, a e x^{2} + 2 \, a d + 2 \, {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, d x^{3}}, -\frac{2 \, {\left(b c^{2} d - b e\right)} \sqrt{-c^{2} d + e} x^{3} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c^{3} d - 3 \, b c e\right)} \sqrt{d} x^{3} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(b c d x + 2 \, a e x^{2} + 2 \, a d + 2 \, {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, d x^{3}}, -\frac{2 \, {\left(2 \, b c^{3} d - 3 \, b c e\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left(b c^{2} d - b e\right)} \sqrt{c^{2} d - e} x^{3} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(b c d x + 2 \, a e x^{2} + 2 \, a d + 2 \, {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, d x^{3}}, -\frac{{\left(b c^{2} d - b e\right)} \sqrt{-c^{2} d + e} x^{3} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c^{3} d - 3 \, b c e\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left(b c d x + 2 \, a e x^{2} + 2 \, a d + 2 \, {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, d x^{3}}\right]"," ",0,"[-1/12*((b*c^2*d - b*e)*sqrt(c^2*d - e)*x^3*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (2*b*c^3*d - 3*b*c*e)*sqrt(d)*x^3*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(b*c*d*x + 2*a*e*x^2 + 2*a*d + 2*(b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^3), -1/12*(2*(b*c^2*d - b*e)*sqrt(-c^2*d + e)*x^3*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (2*b*c^3*d - 3*b*c*e)*sqrt(d)*x^3*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(b*c*d*x + 2*a*e*x^2 + 2*a*d + 2*(b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^3), -1/12*(2*(2*b*c^3*d - 3*b*c*e)*sqrt(-d)*x^3*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + (b*c^2*d - b*e)*sqrt(c^2*d - e)*x^3*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(b*c*d*x + 2*a*e*x^2 + 2*a*d + 2*(b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^3), -1/6*((b*c^2*d - b*e)*sqrt(-c^2*d + e)*x^3*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (2*b*c^3*d - 3*b*c*e)*sqrt(-d)*x^3*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + (b*c*d*x + 2*a*e*x^2 + 2*a*d + 2*(b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^3)]","A",0
1181,0,0,0,0.460567," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{x^{5}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/x^5, x)","F",0
1182,1,1156,0,1.085553," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, b c^{4} d^{2} - b c^{2} d e - 2 \, b e^{2}\right)} \sqrt{c^{2} d - e} x^{5} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(24 \, b c^{5} d^{2} - 20 \, b c^{3} d e - 15 \, b c e^{2}\right)} \sqrt{d} x^{5} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) - 2 \, {\left(16 \, a e^{2} x^{4} - 6 \, b c d^{2} x - 8 \, a d e x^{2} + {\left(12 \, b c^{3} d^{2} - 7 \, b c d e\right)} x^{3} - 24 \, a d^{2} + 8 \, {\left(2 \, b e^{2} x^{4} - b d e x^{2} - 3 \, b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{240 \, d^{2} x^{5}}, \frac{8 \, {\left(3 \, b c^{4} d^{2} - b c^{2} d e - 2 \, b e^{2}\right)} \sqrt{-c^{2} d + e} x^{5} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - {\left(24 \, b c^{5} d^{2} - 20 \, b c^{3} d e - 15 \, b c e^{2}\right)} \sqrt{d} x^{5} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(16 \, a e^{2} x^{4} - 6 \, b c d^{2} x - 8 \, a d e x^{2} + {\left(12 \, b c^{3} d^{2} - 7 \, b c d e\right)} x^{3} - 24 \, a d^{2} + 8 \, {\left(2 \, b e^{2} x^{4} - b d e x^{2} - 3 \, b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{240 \, d^{2} x^{5}}, \frac{{\left(24 \, b c^{5} d^{2} - 20 \, b c^{3} d e - 15 \, b c e^{2}\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - 2 \, {\left(3 \, b c^{4} d^{2} - b c^{2} d e - 2 \, b e^{2}\right)} \sqrt{c^{2} d - e} x^{5} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(16 \, a e^{2} x^{4} - 6 \, b c d^{2} x - 8 \, a d e x^{2} + {\left(12 \, b c^{3} d^{2} - 7 \, b c d e\right)} x^{3} - 24 \, a d^{2} + 8 \, {\left(2 \, b e^{2} x^{4} - b d e x^{2} - 3 \, b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{120 \, d^{2} x^{5}}, \frac{4 \, {\left(3 \, b c^{4} d^{2} - b c^{2} d e - 2 \, b e^{2}\right)} \sqrt{-c^{2} d + e} x^{5} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(24 \, b c^{5} d^{2} - 20 \, b c^{3} d e - 15 \, b c e^{2}\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left(16 \, a e^{2} x^{4} - 6 \, b c d^{2} x - 8 \, a d e x^{2} + {\left(12 \, b c^{3} d^{2} - 7 \, b c d e\right)} x^{3} - 24 \, a d^{2} + 8 \, {\left(2 \, b e^{2} x^{4} - b d e x^{2} - 3 \, b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{120 \, d^{2} x^{5}}\right]"," ",0,"[-1/240*(4*(3*b*c^4*d^2 - b*c^2*d*e - 2*b*e^2)*sqrt(c^2*d - e)*x^5*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (24*b*c^5*d^2 - 20*b*c^3*d*e - 15*b*c*e^2)*sqrt(d)*x^5*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) - 2*(16*a*e^2*x^4 - 6*b*c*d^2*x - 8*a*d*e*x^2 + (12*b*c^3*d^2 - 7*b*c*d*e)*x^3 - 24*a*d^2 + 8*(2*b*e^2*x^4 - b*d*e*x^2 - 3*b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^5), 1/240*(8*(3*b*c^4*d^2 - b*c^2*d*e - 2*b*e^2)*sqrt(-c^2*d + e)*x^5*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - (24*b*c^5*d^2 - 20*b*c^3*d*e - 15*b*c*e^2)*sqrt(d)*x^5*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(16*a*e^2*x^4 - 6*b*c*d^2*x - 8*a*d*e*x^2 + (12*b*c^3*d^2 - 7*b*c*d*e)*x^3 - 24*a*d^2 + 8*(2*b*e^2*x^4 - b*d*e*x^2 - 3*b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^5), 1/120*((24*b*c^5*d^2 - 20*b*c^3*d*e - 15*b*c*e^2)*sqrt(-d)*x^5*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - 2*(3*b*c^4*d^2 - b*c^2*d*e - 2*b*e^2)*sqrt(c^2*d - e)*x^5*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (16*a*e^2*x^4 - 6*b*c*d^2*x - 8*a*d*e*x^2 + (12*b*c^3*d^2 - 7*b*c*d*e)*x^3 - 24*a*d^2 + 8*(2*b*e^2*x^4 - b*d*e*x^2 - 3*b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^5), 1/120*(4*(3*b*c^4*d^2 - b*c^2*d*e - 2*b*e^2)*sqrt(-c^2*d + e)*x^5*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (24*b*c^5*d^2 - 20*b*c^3*d*e - 15*b*c*e^2)*sqrt(-d)*x^5*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + (16*a*e^2*x^4 - 6*b*c*d^2*x - 8*a*d*e*x^2 + (12*b*c^3*d^2 - 7*b*c*d*e)*x^3 - 24*a*d^2 + 8*(2*b*e^2*x^4 - b*d*e*x^2 - 3*b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^5)]","A",0
1183,1,1566,0,14.789485," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b c^{6} d^{3} + 70 \, b c^{4} d^{2} e - 168 \, b c^{2} d e^{2} + 80 \, b e^{3}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 24 \, {\left(2 \, b c^{6} d^{3} + b c^{4} d^{2} e - 8 \, b c^{2} d e^{2} + 5 \, b e^{3}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} - 40 \, b c^{6} e^{3} x^{5} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - 2 \, {\left(53 \, b c^{6} d e^{2} - 30 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(19 \, b c^{6} d^{2} e - 74 \, b c^{4} d e^{2} + 40 \, b c^{2} e^{3}\right)} x + 48 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{2}}, \frac{48 \, {\left(2 \, b c^{6} d^{3} + b c^{4} d^{2} e - 8 \, b c^{2} d e^{2} + 5 \, b e^{3}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) + 3 \, {\left(35 \, b c^{6} d^{3} + 70 \, b c^{4} d^{2} e - 168 \, b c^{2} d e^{2} + 80 \, b e^{3}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} - 40 \, b c^{6} e^{3} x^{5} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - 2 \, {\left(53 \, b c^{6} d e^{2} - 30 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(19 \, b c^{6} d^{2} e - 74 \, b c^{4} d e^{2} + 40 \, b c^{2} e^{3}\right)} x + 48 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{2}}, -\frac{3 \, {\left(35 \, b c^{6} d^{3} + 70 \, b c^{4} d^{2} e - 168 \, b c^{2} d e^{2} + 80 \, b e^{3}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - 12 \, {\left(2 \, b c^{6} d^{3} + b c^{4} d^{2} e - 8 \, b c^{2} d e^{2} + 5 \, b e^{3}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} - 40 \, b c^{6} e^{3} x^{5} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - 2 \, {\left(53 \, b c^{6} d e^{2} - 30 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(19 \, b c^{6} d^{2} e - 74 \, b c^{4} d e^{2} + 40 \, b c^{2} e^{3}\right)} x + 48 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{1680 \, c^{7} e^{2}}, \frac{24 \, {\left(2 \, b c^{6} d^{3} + b c^{4} d^{2} e - 8 \, b c^{2} d e^{2} + 5 \, b e^{3}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 3 \, {\left(35 \, b c^{6} d^{3} + 70 \, b c^{4} d^{2} e - 168 \, b c^{2} d e^{2} + 80 \, b e^{3}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} - 40 \, b c^{6} e^{3} x^{5} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - 2 \, {\left(53 \, b c^{6} d e^{2} - 30 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(19 \, b c^{6} d^{2} e - 74 \, b c^{4} d e^{2} + 40 \, b c^{2} e^{3}\right)} x + 48 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{1680 \, c^{7} e^{2}}\right]"," ",0,"[1/3360*(3*(35*b*c^6*d^3 + 70*b*c^4*d^2*e - 168*b*c^2*d*e^2 + 80*b*e^3)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 24*(2*b*c^6*d^3 + b*c^4*d^2*e - 8*b*c^2*d*e^2 + 5*b*e^3)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 - 40*b*c^6*e^3*x^5 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - 2*(53*b*c^6*d*e^2 - 30*b*c^4*e^3)*x^3 - 3*(19*b*c^6*d^2*e - 74*b*c^4*d*e^2 + 40*b*c^2*e^3)*x + 48*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e^2), 1/3360*(48*(2*b*c^6*d^3 + b*c^4*d^2*e - 8*b*c^2*d*e^2 + 5*b*e^3)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) + 3*(35*b*c^6*d^3 + 70*b*c^4*d^2*e - 168*b*c^2*d*e^2 + 80*b*e^3)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 - 40*b*c^6*e^3*x^5 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - 2*(53*b*c^6*d*e^2 - 30*b*c^4*e^3)*x^3 - 3*(19*b*c^6*d^2*e - 74*b*c^4*d*e^2 + 40*b*c^2*e^3)*x + 48*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e^2), -1/1680*(3*(35*b*c^6*d^3 + 70*b*c^4*d^2*e - 168*b*c^2*d*e^2 + 80*b*e^3)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 12*(2*b*c^6*d^3 + b*c^4*d^2*e - 8*b*c^2*d*e^2 + 5*b*e^3)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - (240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 - 40*b*c^6*e^3*x^5 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - 2*(53*b*c^6*d*e^2 - 30*b*c^4*e^3)*x^3 - 3*(19*b*c^6*d^2*e - 74*b*c^4*d*e^2 + 40*b*c^2*e^3)*x + 48*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e^2), 1/1680*(24*(2*b*c^6*d^3 + b*c^4*d^2*e - 8*b*c^2*d*e^2 + 5*b*e^3)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 3*(35*b*c^6*d^3 + 70*b*c^4*d^2*e - 168*b*c^2*d*e^2 + 80*b*e^3)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 - 40*b*c^6*e^3*x^5 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - 2*(53*b*c^6*d*e^2 - 30*b*c^4*e^3)*x^3 - 3*(19*b*c^6*d^2*e - 74*b*c^4*d*e^2 + 40*b*c^2*e^3)*x + 48*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e^2)]","A",0
1184,0,0,0,0.414798," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{4} + a d x^{2} + {\left(b e x^{4} + b d x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((a*e*x^4 + a*d*x^2 + (b*e*x^4 + b*d*x^2)*arctan(c*x))*sqrt(e*x^2 + d), x)","F",0
1185,1,1192,0,3.632272," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, b c^{4} d^{2} - 20 \, b c^{2} d e + 8 \, b e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 4 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} - 2 \, b c^{4} e^{2} x^{3} + 8 \, a c^{5} d^{2} - {\left(9 \, b c^{4} d e - 4 \, b c^{2} e^{2}\right)} x + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{80 \, c^{5} e}, -\frac{8 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(15 \, b c^{4} d^{2} - 20 \, b c^{2} d e + 8 \, b e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} - 2 \, b c^{4} e^{2} x^{3} + 8 \, a c^{5} d^{2} - {\left(9 \, b c^{4} d e - 4 \, b c^{2} e^{2}\right)} x + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{80 \, c^{5} e}, \frac{{\left(15 \, b c^{4} d^{2} - 20 \, b c^{2} d e + 8 \, b e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + 2 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} - 2 \, b c^{4} e^{2} x^{3} + 8 \, a c^{5} d^{2} - {\left(9 \, b c^{4} d e - 4 \, b c^{2} e^{2}\right)} x + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{40 \, c^{5} e}, -\frac{4 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(15 \, b c^{4} d^{2} - 20 \, b c^{2} d e + 8 \, b e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} - 2 \, b c^{4} e^{2} x^{3} + 8 \, a c^{5} d^{2} - {\left(9 \, b c^{4} d e - 4 \, b c^{2} e^{2}\right)} x + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{40 \, c^{5} e}\right]"," ",0,"[1/80*((15*b*c^4*d^2 - 20*b*c^2*d*e + 8*b*e^2)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 4*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 - 2*b*c^4*e^2*x^3 + 8*a*c^5*d^2 - (9*b*c^4*d*e - 4*b*c^2*e^2)*x + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e), -1/80*(8*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (15*b*c^4*d^2 - 20*b*c^2*d*e + 8*b*e^2)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 - 2*b*c^4*e^2*x^3 + 8*a*c^5*d^2 - (9*b*c^4*d*e - 4*b*c^2*e^2)*x + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e), 1/40*((15*b*c^4*d^2 - 20*b*c^2*d*e + 8*b*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + 2*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 - 2*b*c^4*e^2*x^3 + 8*a*c^5*d^2 - (9*b*c^4*d*e - 4*b*c^2*e^2)*x + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e), -1/40*(4*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (15*b*c^4*d^2 - 20*b*c^2*d*e + 8*b*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 - 2*b*c^4*e^2*x^3 + 8*a*c^5*d^2 - (9*b*c^4*d*e - 4*b*c^2*e^2)*x + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^5*e)]","A",0
1186,0,0,0,0.411788," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d), x)","F",0
1187,0,0,0,0.470544," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d)/x, x)","F",0
1188,0,0,0,0.453994," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d)/x^2, x)","F",0
1189,0,0,0,0.428699," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d)/x^3, x)","F",0
1190,0,0,0,0.503252," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d)/x^4, x)","F",0
1191,0,0,0,0.546034," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{5}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d)/x^5, x)","F",0
1192,1,1145,0,1.265715," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{c^{2} d - e} x^{5} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(8 \, b c^{5} d^{2} - 20 \, b c^{3} d e + 15 \, b c e^{2}\right)} \sqrt{d} x^{5} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) - 2 \, {\left(8 \, a e^{2} x^{4} + 2 \, b c d^{2} x + 16 \, a d e x^{2} - {\left(4 \, b c^{3} d^{2} - 9 \, b c d e\right)} x^{3} + 8 \, a d^{2} + 8 \, {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{80 \, d x^{5}}, \frac{8 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{-c^{2} d + e} x^{5} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(8 \, b c^{5} d^{2} - 20 \, b c^{3} d e + 15 \, b c e^{2}\right)} \sqrt{d} x^{5} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) - 2 \, {\left(8 \, a e^{2} x^{4} + 2 \, b c d^{2} x + 16 \, a d e x^{2} - {\left(4 \, b c^{3} d^{2} - 9 \, b c d e\right)} x^{3} + 8 \, a d^{2} + 8 \, {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{80 \, d x^{5}}, \frac{{\left(8 \, b c^{5} d^{2} - 20 \, b c^{3} d e + 15 \, b c e^{2}\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + 2 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{c^{2} d - e} x^{5} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - {\left(8 \, a e^{2} x^{4} + 2 \, b c d^{2} x + 16 \, a d e x^{2} - {\left(4 \, b c^{3} d^{2} - 9 \, b c d e\right)} x^{3} + 8 \, a d^{2} + 8 \, {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{40 \, d x^{5}}, \frac{4 \, {\left(b c^{4} d^{2} - 2 \, b c^{2} d e + b e^{2}\right)} \sqrt{-c^{2} d + e} x^{5} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(8 \, b c^{5} d^{2} - 20 \, b c^{3} d e + 15 \, b c e^{2}\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - {\left(8 \, a e^{2} x^{4} + 2 \, b c d^{2} x + 16 \, a d e x^{2} - {\left(4 \, b c^{3} d^{2} - 9 \, b c d e\right)} x^{3} + 8 \, a d^{2} + 8 \, {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{40 \, d x^{5}}\right]"," ",0,"[1/80*(4*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(c^2*d - e)*x^5*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (8*b*c^5*d^2 - 20*b*c^3*d*e + 15*b*c*e^2)*sqrt(d)*x^5*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) - 2*(8*a*e^2*x^4 + 2*b*c*d^2*x + 16*a*d*e*x^2 - (4*b*c^3*d^2 - 9*b*c*d*e)*x^3 + 8*a*d^2 + 8*(b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^5), 1/80*(8*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(-c^2*d + e)*x^5*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (8*b*c^5*d^2 - 20*b*c^3*d*e + 15*b*c*e^2)*sqrt(d)*x^5*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) - 2*(8*a*e^2*x^4 + 2*b*c*d^2*x + 16*a*d*e*x^2 - (4*b*c^3*d^2 - 9*b*c*d*e)*x^3 + 8*a*d^2 + 8*(b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^5), 1/40*((8*b*c^5*d^2 - 20*b*c^3*d*e + 15*b*c*e^2)*sqrt(-d)*x^5*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + 2*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(c^2*d - e)*x^5*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - (8*a*e^2*x^4 + 2*b*c*d^2*x + 16*a*d*e*x^2 - (4*b*c^3*d^2 - 9*b*c*d*e)*x^3 + 8*a*d^2 + 8*(b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^5), 1/40*(4*(b*c^4*d^2 - 2*b*c^2*d*e + b*e^2)*sqrt(-c^2*d + e)*x^5*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (8*b*c^5*d^2 - 20*b*c^3*d*e + 15*b*c*e^2)*sqrt(-d)*x^5*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - (8*a*e^2*x^4 + 2*b*c*d^2*x + 16*a*d*e*x^2 - (4*b*c^3*d^2 - 9*b*c*d*e)*x^3 + 8*a*d^2 + 8*(b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d))/(d*x^5)]","A",0
1193,1,1978,0,49.890607," ","integrate(x^3*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(315 \, b c^{8} d^{4} + 840 \, b c^{6} d^{3} e - 3024 \, b c^{4} d^{2} e^{2} + 2880 \, b c^{2} d e^{3} - 896 \, b e^{4}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 192 \, {\left(2 \, b c^{8} d^{4} + b c^{6} d^{3} e - 15 \, b c^{4} d^{2} e^{2} + 19 \, b c^{2} d e^{3} - 7 \, b e^{4}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 2 \, {\left(2688 \, a c^{9} e^{4} x^{8} + 7296 \, a c^{9} d e^{3} x^{6} - 336 \, b c^{8} e^{4} x^{7} + 5760 \, a c^{9} d^{2} e^{2} x^{4} + 384 \, a c^{9} d^{3} e x^{2} - 768 \, a c^{9} d^{4} - 8 \, {\left(159 \, b c^{8} d e^{3} - 56 \, b c^{6} e^{4}\right)} x^{5} - 2 \, {\left(837 \, b c^{8} d^{2} e^{2} - 968 \, b c^{6} d e^{3} + 336 \, b c^{4} e^{4}\right)} x^{3} - 3 \, {\left(187 \, b c^{8} d^{3} e - 1208 \, b c^{6} d^{2} e^{2} + 1328 \, b c^{4} d e^{3} - 448 \, b c^{2} e^{4}\right)} x + 384 \, {\left(7 \, b c^{9} e^{4} x^{8} + 19 \, b c^{9} d e^{3} x^{6} + 15 \, b c^{9} d^{2} e^{2} x^{4} + b c^{9} d^{3} e x^{2} - 2 \, b c^{9} d^{4}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{48384 \, c^{9} e^{2}}, \frac{384 \, {\left(2 \, b c^{8} d^{4} + b c^{6} d^{3} e - 15 \, b c^{4} d^{2} e^{2} + 19 \, b c^{2} d e^{3} - 7 \, b e^{4}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 3 \, {\left(315 \, b c^{8} d^{4} + 840 \, b c^{6} d^{3} e - 3024 \, b c^{4} d^{2} e^{2} + 2880 \, b c^{2} d e^{3} - 896 \, b e^{4}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(2688 \, a c^{9} e^{4} x^{8} + 7296 \, a c^{9} d e^{3} x^{6} - 336 \, b c^{8} e^{4} x^{7} + 5760 \, a c^{9} d^{2} e^{2} x^{4} + 384 \, a c^{9} d^{3} e x^{2} - 768 \, a c^{9} d^{4} - 8 \, {\left(159 \, b c^{8} d e^{3} - 56 \, b c^{6} e^{4}\right)} x^{5} - 2 \, {\left(837 \, b c^{8} d^{2} e^{2} - 968 \, b c^{6} d e^{3} + 336 \, b c^{4} e^{4}\right)} x^{3} - 3 \, {\left(187 \, b c^{8} d^{3} e - 1208 \, b c^{6} d^{2} e^{2} + 1328 \, b c^{4} d e^{3} - 448 \, b c^{2} e^{4}\right)} x + 384 \, {\left(7 \, b c^{9} e^{4} x^{8} + 19 \, b c^{9} d e^{3} x^{6} + 15 \, b c^{9} d^{2} e^{2} x^{4} + b c^{9} d^{3} e x^{2} - 2 \, b c^{9} d^{4}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{48384 \, c^{9} e^{2}}, -\frac{3 \, {\left(315 \, b c^{8} d^{4} + 840 \, b c^{6} d^{3} e - 3024 \, b c^{4} d^{2} e^{2} + 2880 \, b c^{2} d e^{3} - 896 \, b e^{4}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + 96 \, {\left(2 \, b c^{8} d^{4} + b c^{6} d^{3} e - 15 \, b c^{4} d^{2} e^{2} + 19 \, b c^{2} d e^{3} - 7 \, b e^{4}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - {\left(2688 \, a c^{9} e^{4} x^{8} + 7296 \, a c^{9} d e^{3} x^{6} - 336 \, b c^{8} e^{4} x^{7} + 5760 \, a c^{9} d^{2} e^{2} x^{4} + 384 \, a c^{9} d^{3} e x^{2} - 768 \, a c^{9} d^{4} - 8 \, {\left(159 \, b c^{8} d e^{3} - 56 \, b c^{6} e^{4}\right)} x^{5} - 2 \, {\left(837 \, b c^{8} d^{2} e^{2} - 968 \, b c^{6} d e^{3} + 336 \, b c^{4} e^{4}\right)} x^{3} - 3 \, {\left(187 \, b c^{8} d^{3} e - 1208 \, b c^{6} d^{2} e^{2} + 1328 \, b c^{4} d e^{3} - 448 \, b c^{2} e^{4}\right)} x + 384 \, {\left(7 \, b c^{9} e^{4} x^{8} + 19 \, b c^{9} d e^{3} x^{6} + 15 \, b c^{9} d^{2} e^{2} x^{4} + b c^{9} d^{3} e x^{2} - 2 \, b c^{9} d^{4}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{24192 \, c^{9} e^{2}}, \frac{192 \, {\left(2 \, b c^{8} d^{4} + b c^{6} d^{3} e - 15 \, b c^{4} d^{2} e^{2} + 19 \, b c^{2} d e^{3} - 7 \, b e^{4}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 3 \, {\left(315 \, b c^{8} d^{4} + 840 \, b c^{6} d^{3} e - 3024 \, b c^{4} d^{2} e^{2} + 2880 \, b c^{2} d e^{3} - 896 \, b e^{4}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(2688 \, a c^{9} e^{4} x^{8} + 7296 \, a c^{9} d e^{3} x^{6} - 336 \, b c^{8} e^{4} x^{7} + 5760 \, a c^{9} d^{2} e^{2} x^{4} + 384 \, a c^{9} d^{3} e x^{2} - 768 \, a c^{9} d^{4} - 8 \, {\left(159 \, b c^{8} d e^{3} - 56 \, b c^{6} e^{4}\right)} x^{5} - 2 \, {\left(837 \, b c^{8} d^{2} e^{2} - 968 \, b c^{6} d e^{3} + 336 \, b c^{4} e^{4}\right)} x^{3} - 3 \, {\left(187 \, b c^{8} d^{3} e - 1208 \, b c^{6} d^{2} e^{2} + 1328 \, b c^{4} d e^{3} - 448 \, b c^{2} e^{4}\right)} x + 384 \, {\left(7 \, b c^{9} e^{4} x^{8} + 19 \, b c^{9} d e^{3} x^{6} + 15 \, b c^{9} d^{2} e^{2} x^{4} + b c^{9} d^{3} e x^{2} - 2 \, b c^{9} d^{4}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{24192 \, c^{9} e^{2}}\right]"," ",0,"[-1/48384*(3*(315*b*c^8*d^4 + 840*b*c^6*d^3*e - 3024*b*c^4*d^2*e^2 + 2880*b*c^2*d*e^3 - 896*b*e^4)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 192*(2*b*c^8*d^4 + b*c^6*d^3*e - 15*b*c^4*d^2*e^2 + 19*b*c^2*d*e^3 - 7*b*e^4)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 2*(2688*a*c^9*e^4*x^8 + 7296*a*c^9*d*e^3*x^6 - 336*b*c^8*e^4*x^7 + 5760*a*c^9*d^2*e^2*x^4 + 384*a*c^9*d^3*e*x^2 - 768*a*c^9*d^4 - 8*(159*b*c^8*d*e^3 - 56*b*c^6*e^4)*x^5 - 2*(837*b*c^8*d^2*e^2 - 968*b*c^6*d*e^3 + 336*b*c^4*e^4)*x^3 - 3*(187*b*c^8*d^3*e - 1208*b*c^6*d^2*e^2 + 1328*b*c^4*d*e^3 - 448*b*c^2*e^4)*x + 384*(7*b*c^9*e^4*x^8 + 19*b*c^9*d*e^3*x^6 + 15*b*c^9*d^2*e^2*x^4 + b*c^9*d^3*e*x^2 - 2*b*c^9*d^4)*arctan(c*x))*sqrt(e*x^2 + d))/(c^9*e^2), 1/48384*(384*(2*b*c^8*d^4 + b*c^6*d^3*e - 15*b*c^4*d^2*e^2 + 19*b*c^2*d*e^3 - 7*b*e^4)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 3*(315*b*c^8*d^4 + 840*b*c^6*d^3*e - 3024*b*c^4*d^2*e^2 + 2880*b*c^2*d*e^3 - 896*b*e^4)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(2688*a*c^9*e^4*x^8 + 7296*a*c^9*d*e^3*x^6 - 336*b*c^8*e^4*x^7 + 5760*a*c^9*d^2*e^2*x^4 + 384*a*c^9*d^3*e*x^2 - 768*a*c^9*d^4 - 8*(159*b*c^8*d*e^3 - 56*b*c^6*e^4)*x^5 - 2*(837*b*c^8*d^2*e^2 - 968*b*c^6*d*e^3 + 336*b*c^4*e^4)*x^3 - 3*(187*b*c^8*d^3*e - 1208*b*c^6*d^2*e^2 + 1328*b*c^4*d*e^3 - 448*b*c^2*e^4)*x + 384*(7*b*c^9*e^4*x^8 + 19*b*c^9*d*e^3*x^6 + 15*b*c^9*d^2*e^2*x^4 + b*c^9*d^3*e*x^2 - 2*b*c^9*d^4)*arctan(c*x))*sqrt(e*x^2 + d))/(c^9*e^2), -1/24192*(3*(315*b*c^8*d^4 + 840*b*c^6*d^3*e - 3024*b*c^4*d^2*e^2 + 2880*b*c^2*d*e^3 - 896*b*e^4)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + 96*(2*b*c^8*d^4 + b*c^6*d^3*e - 15*b*c^4*d^2*e^2 + 19*b*c^2*d*e^3 - 7*b*e^4)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - (2688*a*c^9*e^4*x^8 + 7296*a*c^9*d*e^3*x^6 - 336*b*c^8*e^4*x^7 + 5760*a*c^9*d^2*e^2*x^4 + 384*a*c^9*d^3*e*x^2 - 768*a*c^9*d^4 - 8*(159*b*c^8*d*e^3 - 56*b*c^6*e^4)*x^5 - 2*(837*b*c^8*d^2*e^2 - 968*b*c^6*d*e^3 + 336*b*c^4*e^4)*x^3 - 3*(187*b*c^8*d^3*e - 1208*b*c^6*d^2*e^2 + 1328*b*c^4*d*e^3 - 448*b*c^2*e^4)*x + 384*(7*b*c^9*e^4*x^8 + 19*b*c^9*d*e^3*x^6 + 15*b*c^9*d^2*e^2*x^4 + b*c^9*d^3*e*x^2 - 2*b*c^9*d^4)*arctan(c*x))*sqrt(e*x^2 + d))/(c^9*e^2), 1/24192*(192*(2*b*c^8*d^4 + b*c^6*d^3*e - 15*b*c^4*d^2*e^2 + 19*b*c^2*d*e^3 - 7*b*e^4)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 3*(315*b*c^8*d^4 + 840*b*c^6*d^3*e - 3024*b*c^4*d^2*e^2 + 2880*b*c^2*d*e^3 - 896*b*e^4)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (2688*a*c^9*e^4*x^8 + 7296*a*c^9*d*e^3*x^6 - 336*b*c^8*e^4*x^7 + 5760*a*c^9*d^2*e^2*x^4 + 384*a*c^9*d^3*e*x^2 - 768*a*c^9*d^4 - 8*(159*b*c^8*d*e^3 - 56*b*c^6*e^4)*x^5 - 2*(837*b*c^8*d^2*e^2 - 968*b*c^6*d*e^3 + 336*b*c^4*e^4)*x^3 - 3*(187*b*c^8*d^3*e - 1208*b*c^6*d^2*e^2 + 1328*b*c^4*d*e^3 - 448*b*c^2*e^4)*x + 384*(7*b*c^9*e^4*x^8 + 19*b*c^9*d*e^3*x^6 + 15*b*c^9*d^2*e^2*x^4 + b*c^9*d^3*e*x^2 - 2*b*c^9*d^4)*arctan(c*x))*sqrt(e*x^2 + d))/(c^9*e^2)]","A",0
1194,0,0,0,0.568720," ","integrate(x^2*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} x^{6} + 2 \, a d e x^{4} + a d^{2} x^{2} + {\left(b e^{2} x^{6} + 2 \, b d e x^{4} + b d^{2} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((a*e^2*x^6 + 2*a*d*e*x^4 + a*d^2*x^2 + (b*e^2*x^6 + 2*b*d*e*x^4 + b*d^2*x^2)*arctan(c*x))*sqrt(e*x^2 + d), x)","F",0
1195,1,1562,0,15.581743," ","integrate(x*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(35 \, b c^{6} d^{3} - 70 \, b c^{4} d^{2} e + 56 \, b c^{2} d e^{2} - 16 \, b e^{3}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 24 \, {\left(b c^{6} d^{3} - 3 \, b c^{4} d^{2} e + 3 \, b c^{2} d e^{2} - b e^{3}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 2 \, {\left(48 \, a c^{7} e^{3} x^{6} + 144 \, a c^{7} d e^{2} x^{4} - 8 \, b c^{6} e^{3} x^{5} + 144 \, a c^{7} d^{2} e x^{2} + 48 \, a c^{7} d^{3} - 2 \, {\left(19 \, b c^{6} d e^{2} - 6 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(29 \, b c^{6} d^{2} e - 26 \, b c^{4} d e^{2} + 8 \, b c^{2} e^{3}\right)} x + 48 \, {\left(b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} + 3 \, b c^{7} d^{2} e x^{2} + b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{672 \, c^{7} e}, -\frac{48 \, {\left(b c^{6} d^{3} - 3 \, b c^{4} d^{2} e + 3 \, b c^{2} d e^{2} - b e^{3}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) + 3 \, {\left(35 \, b c^{6} d^{3} - 70 \, b c^{4} d^{2} e + 56 \, b c^{2} d e^{2} - 16 \, b e^{3}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, {\left(48 \, a c^{7} e^{3} x^{6} + 144 \, a c^{7} d e^{2} x^{4} - 8 \, b c^{6} e^{3} x^{5} + 144 \, a c^{7} d^{2} e x^{2} + 48 \, a c^{7} d^{3} - 2 \, {\left(19 \, b c^{6} d e^{2} - 6 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(29 \, b c^{6} d^{2} e - 26 \, b c^{4} d e^{2} + 8 \, b c^{2} e^{3}\right)} x + 48 \, {\left(b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} + 3 \, b c^{7} d^{2} e x^{2} + b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{672 \, c^{7} e}, \frac{3 \, {\left(35 \, b c^{6} d^{3} - 70 \, b c^{4} d^{2} e + 56 \, b c^{2} d e^{2} - 16 \, b e^{3}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - 12 \, {\left(b c^{6} d^{3} - 3 \, b c^{4} d^{2} e + 3 \, b c^{2} d e^{2} - b e^{3}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(48 \, a c^{7} e^{3} x^{6} + 144 \, a c^{7} d e^{2} x^{4} - 8 \, b c^{6} e^{3} x^{5} + 144 \, a c^{7} d^{2} e x^{2} + 48 \, a c^{7} d^{3} - 2 \, {\left(19 \, b c^{6} d e^{2} - 6 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(29 \, b c^{6} d^{2} e - 26 \, b c^{4} d e^{2} + 8 \, b c^{2} e^{3}\right)} x + 48 \, {\left(b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} + 3 \, b c^{7} d^{2} e x^{2} + b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{336 \, c^{7} e}, -\frac{24 \, {\left(b c^{6} d^{3} - 3 \, b c^{4} d^{2} e + 3 \, b c^{2} d e^{2} - b e^{3}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 3 \, {\left(35 \, b c^{6} d^{3} - 70 \, b c^{4} d^{2} e + 56 \, b c^{2} d e^{2} - 16 \, b e^{3}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(48 \, a c^{7} e^{3} x^{6} + 144 \, a c^{7} d e^{2} x^{4} - 8 \, b c^{6} e^{3} x^{5} + 144 \, a c^{7} d^{2} e x^{2} + 48 \, a c^{7} d^{3} - 2 \, {\left(19 \, b c^{6} d e^{2} - 6 \, b c^{4} e^{3}\right)} x^{3} - 3 \, {\left(29 \, b c^{6} d^{2} e - 26 \, b c^{4} d e^{2} + 8 \, b c^{2} e^{3}\right)} x + 48 \, {\left(b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} + 3 \, b c^{7} d^{2} e x^{2} + b c^{7} d^{3}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{336 \, c^{7} e}\right]"," ",0,"[-1/672*(3*(35*b*c^6*d^3 - 70*b*c^4*d^2*e + 56*b*c^2*d*e^2 - 16*b*e^3)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 24*(b*c^6*d^3 - 3*b*c^4*d^2*e + 3*b*c^2*d*e^2 - b*e^3)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 2*(48*a*c^7*e^3*x^6 + 144*a*c^7*d*e^2*x^4 - 8*b*c^6*e^3*x^5 + 144*a*c^7*d^2*e*x^2 + 48*a*c^7*d^3 - 2*(19*b*c^6*d*e^2 - 6*b*c^4*e^3)*x^3 - 3*(29*b*c^6*d^2*e - 26*b*c^4*d*e^2 + 8*b*c^2*e^3)*x + 48*(b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 + 3*b*c^7*d^2*e*x^2 + b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e), -1/672*(48*(b*c^6*d^3 - 3*b*c^4*d^2*e + 3*b*c^2*d*e^2 - b*e^3)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) + 3*(35*b*c^6*d^3 - 70*b*c^4*d^2*e + 56*b*c^2*d*e^2 - 16*b*e^3)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*(48*a*c^7*e^3*x^6 + 144*a*c^7*d*e^2*x^4 - 8*b*c^6*e^3*x^5 + 144*a*c^7*d^2*e*x^2 + 48*a*c^7*d^3 - 2*(19*b*c^6*d*e^2 - 6*b*c^4*e^3)*x^3 - 3*(29*b*c^6*d^2*e - 26*b*c^4*d*e^2 + 8*b*c^2*e^3)*x + 48*(b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 + 3*b*c^7*d^2*e*x^2 + b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e), 1/336*(3*(35*b*c^6*d^3 - 70*b*c^4*d^2*e + 56*b*c^2*d*e^2 - 16*b*e^3)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 12*(b*c^6*d^3 - 3*b*c^4*d^2*e + 3*b*c^2*d*e^2 - b*e^3)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (48*a*c^7*e^3*x^6 + 144*a*c^7*d*e^2*x^4 - 8*b*c^6*e^3*x^5 + 144*a*c^7*d^2*e*x^2 + 48*a*c^7*d^3 - 2*(19*b*c^6*d*e^2 - 6*b*c^4*e^3)*x^3 - 3*(29*b*c^6*d^2*e - 26*b*c^4*d*e^2 + 8*b*c^2*e^3)*x + 48*(b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 + 3*b*c^7*d^2*e*x^2 + b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e), -1/336*(24*(b*c^6*d^3 - 3*b*c^4*d^2*e + 3*b*c^2*d*e^2 - b*e^3)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 3*(35*b*c^6*d^3 - 70*b*c^4*d^2*e + 56*b*c^2*d*e^2 - 16*b*e^3)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (48*a*c^7*e^3*x^6 + 144*a*c^7*d*e^2*x^4 - 8*b*c^6*e^3*x^5 + 144*a*c^7*d^2*e*x^2 + 48*a*c^7*d^3 - 2*(19*b*c^6*d*e^2 - 6*b*c^4*e^3)*x^3 - 3*(29*b*c^6*d^2*e - 26*b*c^4*d*e^2 + 8*b*c^2*e^3)*x + 48*(b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 + 3*b*c^7*d^2*e*x^2 + b*c^7*d^3)*arctan(c*x))*sqrt(e*x^2 + d))/(c^7*e)]","A",0
1196,0,0,0,0.430197," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d), x)","F",0
1197,0,0,0,0.438401," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d)/x, x)","F",0
1198,0,0,0,0.476889," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d)/x^2, x)","F",0
1199,0,0,0,0.462783," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d)/x^3, x)","F",0
1200,0,0,0,0.460521," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d)/x^4, x)","F",0
1201,1,882,0,1.344403," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b c^{2} d + 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + {\left(2 \, b c^{2} d + b e\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}, \frac{2 \, {\left(2 \, b c^{2} d + b e\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) + {\left(3 \, b c^{2} d + 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}, -\frac{2 \, {\left(3 \, b c^{2} d + 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(2 \, b c^{2} d + b e\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 2 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}, \frac{{\left(2 \, b c^{2} d + b e\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(3 \, b c^{2} d + 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - b c^{2} e x + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, c^{3} e^{2}}\right]"," ",0,"[1/12*((3*b*c^2*d + 2*b*e)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + (2*b*c^2*d + b*e)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(2*a*c^3*e*x^2 - 4*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e^2), 1/12*(2*(2*b*c^2*d + b*e)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) + (3*b*c^2*d + 2*b*e)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(2*a*c^3*e*x^2 - 4*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e^2), -1/12*(2*(3*b*c^2*d + 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (2*b*c^2*d + b*e)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 2*(2*a*c^3*e*x^2 - 4*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e^2), 1/6*((2*b*c^2*d + b*e)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (3*b*c^2*d + 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (2*a*c^3*e*x^2 - 4*a*c^3*d - b*c^2*e*x + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*e^2)]","A",0
1202,0,0,0,0.461819," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arctan\left(c x\right) + a x^{2}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)/sqrt(e*x^2 + d), x)","F",0
1203,1,647,0,0.665815," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + \sqrt{-c^{2} d + e} b \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, \sqrt{e x^{2} + d} {\left(b c \arctan\left(c x\right) + a c\right)}}{4 \, c e}, -\frac{\sqrt{c^{2} d - e} b \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - b \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, \sqrt{e x^{2} + d} {\left(b c \arctan\left(c x\right) + a c\right)}}{2 \, c e}, \frac{4 \, b \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + \sqrt{-c^{2} d + e} b \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, \sqrt{e x^{2} + d} {\left(b c \arctan\left(c x\right) + a c\right)}}{4 \, c e}, -\frac{\sqrt{c^{2} d - e} b \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 2 \, b \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - 2 \, \sqrt{e x^{2} + d} {\left(b c \arctan\left(c x\right) + a c\right)}}{2 \, c e}\right]"," ",0,"[1/4*(2*b*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + sqrt(-c^2*d + e)*b*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*sqrt(e*x^2 + d)*(b*c*arctan(c*x) + a*c))/(c*e), -1/2*(sqrt(c^2*d - e)*b*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - b*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*sqrt(e*x^2 + d)*(b*c*arctan(c*x) + a*c))/(c*e), 1/4*(4*b*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + sqrt(-c^2*d + e)*b*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*sqrt(e*x^2 + d)*(b*c*arctan(c*x) + a*c))/(c*e), -1/2*(sqrt(c^2*d - e)*b*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 2*b*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 2*sqrt(e*x^2 + d)*(b*c*arctan(c*x) + a*c))/(c*e)]","A",0
1204,0,0,0,0.431426," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/sqrt(e*x^2 + d), x)","F",0
1205,0,0,0,0.425573," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{e x^{3} + d x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/(e*x^3 + d*x), x)","F",0
1206,1,660,0,0.532681," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c \sqrt{d} x \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + \sqrt{c^{2} d - e} b x \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, \sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{4 \, d x}, \frac{b c \sqrt{d} x \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + \sqrt{-c^{2} d + e} b x \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - 2 \, \sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{2 \, d x}, \frac{4 \, b c \sqrt{-d} x \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + \sqrt{c^{2} d - e} b x \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, \sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{4 \, d x}, \frac{2 \, b c \sqrt{-d} x \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + \sqrt{-c^{2} d + e} b x \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - 2 \, \sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{2 \, d x}\right]"," ",0,"[1/4*(2*b*c*sqrt(d)*x*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + sqrt(c^2*d - e)*b*x*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*sqrt(e*x^2 + d)*(b*arctan(c*x) + a))/(d*x), 1/2*(b*c*sqrt(d)*x*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + sqrt(-c^2*d + e)*b*x*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*sqrt(e*x^2 + d)*(b*arctan(c*x) + a))/(d*x), 1/4*(4*b*c*sqrt(-d)*x*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + sqrt(c^2*d - e)*b*x*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*sqrt(e*x^2 + d)*(b*arctan(c*x) + a))/(d*x), 1/2*(2*b*c*sqrt(-d)*x*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + sqrt(-c^2*d + e)*b*x*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*sqrt(e*x^2 + d)*(b*arctan(c*x) + a))/(d*x)]","A",0
1207,0,0,0,0.469740," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{e x^{5} + d x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/(e*x^5 + d*x^3), x)","F",0
1208,1,868,0,0.619303," ","integrate((a+b*arctan(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{2} d + 2 \, b e\right)} \sqrt{c^{2} d - e} x^{3} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + {\left(2 \, b c^{3} d + 3 \, b c e\right)} \sqrt{d} x^{3} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) - 2 \, {\left(b c d x - 4 \, a e x^{2} + 2 \, a d - 2 \, {\left(2 \, b e x^{2} - b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, d^{2} x^{3}}, -\frac{2 \, {\left(b c^{2} d + 2 \, b e\right)} \sqrt{-c^{2} d + e} x^{3} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - {\left(2 \, b c^{3} d + 3 \, b c e\right)} \sqrt{d} x^{3} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(b c d x - 4 \, a e x^{2} + 2 \, a d - 2 \, {\left(2 \, b e x^{2} - b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, d^{2} x^{3}}, -\frac{2 \, {\left(2 \, b c^{3} d + 3 \, b c e\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - {\left(b c^{2} d + 2 \, b e\right)} \sqrt{c^{2} d - e} x^{3} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(b c d x - 4 \, a e x^{2} + 2 \, a d - 2 \, {\left(2 \, b e x^{2} - b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, d^{2} x^{3}}, -\frac{{\left(b c^{2} d + 2 \, b e\right)} \sqrt{-c^{2} d + e} x^{3} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c^{3} d + 3 \, b c e\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left(b c d x - 4 \, a e x^{2} + 2 \, a d - 2 \, {\left(2 \, b e x^{2} - b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, d^{2} x^{3}}\right]"," ",0,"[1/12*((b*c^2*d + 2*b*e)*sqrt(c^2*d - e)*x^3*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + (2*b*c^3*d + 3*b*c*e)*sqrt(d)*x^3*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) - 2*(b*c*d*x - 4*a*e*x^2 + 2*a*d - 2*(2*b*e*x^2 - b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^3), -1/12*(2*(b*c^2*d + 2*b*e)*sqrt(-c^2*d + e)*x^3*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - (2*b*c^3*d + 3*b*c*e)*sqrt(d)*x^3*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(b*c*d*x - 4*a*e*x^2 + 2*a*d - 2*(2*b*e*x^2 - b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^3), -1/12*(2*(2*b*c^3*d + 3*b*c*e)*sqrt(-d)*x^3*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - (b*c^2*d + 2*b*e)*sqrt(c^2*d - e)*x^3*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(b*c*d*x - 4*a*e*x^2 + 2*a*d - 2*(2*b*e*x^2 - b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^3), -1/6*((b*c^2*d + 2*b*e)*sqrt(-c^2*d + e)*x^3*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (2*b*c^3*d + 3*b*c*e)*sqrt(-d)*x^3*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + (b*c*d*x - 4*a*e*x^2 + 2*a*d - 2*(2*b*e*x^2 - b*d)*arctan(c*x))*sqrt(e*x^2 + d))/(d^2*x^3)]","A",0
1209,1,1291,0,0.887617," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c^{2} d^{2} - b d e + {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + {\left(2 \, b c^{2} d^{2} - b d e + {\left(2 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, {\left(2 \, a c^{3} d^{2} - 2 \, a c d e + {\left(a c^{3} d e - a c e^{2}\right)} x^{2} + {\left(2 \, b c^{3} d^{2} - 2 \, b c d e + {\left(b c^{3} d e - b c e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{4 \, {\left(c^{3} d^{2} e^{2} - c d e^{3} + {\left(c^{3} d e^{3} - c e^{4}\right)} x^{2}\right)}}, -\frac{{\left(2 \, b c^{2} d^{2} - b d e + {\left(2 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - {\left(b c^{2} d^{2} - b d e + {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, {\left(2 \, a c^{3} d^{2} - 2 \, a c d e + {\left(a c^{3} d e - a c e^{2}\right)} x^{2} + {\left(2 \, b c^{3} d^{2} - 2 \, b c d e + {\left(b c^{3} d e - b c e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} e^{2} - c d e^{3} + {\left(c^{3} d e^{3} - c e^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left(b c^{2} d^{2} - b d e + {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(2 \, b c^{2} d^{2} - b d e + {\left(2 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, {\left(2 \, a c^{3} d^{2} - 2 \, a c d e + {\left(a c^{3} d e - a c e^{2}\right)} x^{2} + {\left(2 \, b c^{3} d^{2} - 2 \, b c d e + {\left(b c^{3} d e - b c e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{4 \, {\left(c^{3} d^{2} e^{2} - c d e^{3} + {\left(c^{3} d e^{3} - c e^{4}\right)} x^{2}\right)}}, -\frac{{\left(2 \, b c^{2} d^{2} - b d e + {\left(2 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 2 \, {\left(b c^{2} d^{2} - b d e + {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - 2 \, {\left(2 \, a c^{3} d^{2} - 2 \, a c d e + {\left(a c^{3} d e - a c e^{2}\right)} x^{2} + {\left(2 \, b c^{3} d^{2} - 2 \, b c d e + {\left(b c^{3} d e - b c e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} e^{2} - c d e^{3} + {\left(c^{3} d e^{3} - c e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(b*c^2*d^2 - b*d*e + (b*c^2*d*e - b*e^2)*x^2)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + (2*b*c^2*d^2 - b*d*e + (2*b*c^2*d*e - b*e^2)*x^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*(2*a*c^3*d^2 - 2*a*c*d*e + (a*c^3*d*e - a*c*e^2)*x^2 + (2*b*c^3*d^2 - 2*b*c*d*e + (b*c^3*d*e - b*c*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*d^2*e^2 - c*d*e^3 + (c^3*d*e^3 - c*e^4)*x^2), -1/2*((2*b*c^2*d^2 - b*d*e + (2*b*c^2*d*e - b*e^2)*x^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - (b*c^2*d^2 - b*d*e + (b*c^2*d*e - b*e^2)*x^2)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*(2*a*c^3*d^2 - 2*a*c*d*e + (a*c^3*d*e - a*c*e^2)*x^2 + (2*b*c^3*d^2 - 2*b*c*d*e + (b*c^3*d*e - b*c*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*d^2*e^2 - c*d*e^3 + (c^3*d*e^3 - c*e^4)*x^2), 1/4*(4*(b*c^2*d^2 - b*d*e + (b*c^2*d*e - b*e^2)*x^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (2*b*c^2*d^2 - b*d*e + (2*b*c^2*d*e - b*e^2)*x^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*(2*a*c^3*d^2 - 2*a*c*d*e + (a*c^3*d*e - a*c*e^2)*x^2 + (2*b*c^3*d^2 - 2*b*c*d*e + (b*c^3*d*e - b*c*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*d^2*e^2 - c*d*e^3 + (c^3*d*e^3 - c*e^4)*x^2), -1/2*((2*b*c^2*d^2 - b*d*e + (2*b*c^2*d*e - b*e^2)*x^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 2*(b*c^2*d^2 - b*d*e + (b*c^2*d*e - b*e^2)*x^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - 2*(2*a*c^3*d^2 - 2*a*c*d*e + (a*c^3*d*e - a*c*e^2)*x^2 + (2*b*c^3*d^2 - 2*b*c*d*e + (b*c^3*d*e - b*c*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^3*d^2*e^2 - c*d*e^3 + (c^3*d*e^3 - c*e^4)*x^2)]","B",0
1210,0,0,0,0.451182," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} \arctan\left(c x\right) + a x^{2}\right)} \sqrt{e x^{2} + d}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^2*arctan(c*x) + a*x^2)*sqrt(e*x^2 + d)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1211,1,379,0,0.528354," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c e x^{2} + b c d\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, {\left(a c^{2} d - a e + {\left(b c^{2} d - b e\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{4 \, {\left(c^{2} d^{2} e - d e^{2} + {\left(c^{2} d e^{2} - e^{3}\right)} x^{2}\right)}}, \frac{{\left(b c e x^{2} + b c d\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 2 \, {\left(a c^{2} d - a e + {\left(b c^{2} d - b e\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{2 \, {\left(c^{2} d^{2} e - d e^{2} + {\left(c^{2} d e^{2} - e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((b*c*e*x^2 + b*c*d)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*(a*c^2*d - a*e + (b*c^2*d - b*e)*arctan(c*x))*sqrt(e*x^2 + d))/(c^2*d^2*e - d*e^2 + (c^2*d*e^2 - e^3)*x^2), 1/2*((b*c*e*x^2 + b*c*d)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 2*(a*c^2*d - a*e + (b*c^2*d - b*e)*arctan(c*x))*sqrt(e*x^2 + d))/(c^2*d^2*e - d*e^2 + (c^2*d*e^2 - e^3)*x^2)]","B",0
1212,1,388,0,0.537334," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b e x^{2} + b d\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, \sqrt{e x^{2} + d} {\left({\left(b c^{2} d - b e\right)} x \arctan\left(c x\right) + {\left(a c^{2} d - a e\right)} x\right)}}{4 \, {\left(c^{2} d^{3} - d^{2} e + {\left(c^{2} d^{2} e - d e^{2}\right)} x^{2}\right)}}, \frac{{\left(b e x^{2} + b d\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, \sqrt{e x^{2} + d} {\left({\left(b c^{2} d - b e\right)} x \arctan\left(c x\right) + {\left(a c^{2} d - a e\right)} x\right)}}{2 \, {\left(c^{2} d^{3} - d^{2} e + {\left(c^{2} d^{2} e - d e^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*((b*e*x^2 + b*d)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*sqrt(e*x^2 + d)*((b*c^2*d - b*e)*x*arctan(c*x) + (a*c^2*d - a*e)*x))/(c^2*d^3 - d^2*e + (c^2*d^2*e - d*e^2)*x^2), 1/2*((b*e*x^2 + b*d)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*sqrt(e*x^2 + d)*((b*c^2*d - b*e)*x*arctan(c*x) + (a*c^2*d - a*e)*x))/(c^2*d^3 - d^2*e + (c^2*d^2*e - d*e^2)*x^2)]","B",0
1213,0,0,0,0.472919," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
1214,1,1317,0,0.696352," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b c^{2} d e - 2 \, b e^{2}\right)} x^{3} + {\left(b c^{2} d^{2} - 2 \, b d e\right)} x\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 2 \, {\left({\left(b c^{3} d e - b c e^{2}\right)} x^{3} + {\left(b c^{3} d^{2} - b c d e\right)} x\right)} \sqrt{d} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 4 \, {\left(a c^{2} d^{2} - a d e + 2 \, {\left(a c^{2} d e - a e^{2}\right)} x^{2} + {\left(b c^{2} d^{2} - b d e + 2 \, {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{4 \, {\left({\left(c^{2} d^{3} e - d^{2} e^{2}\right)} x^{3} + {\left(c^{2} d^{4} - d^{3} e\right)} x\right)}}, \frac{{\left({\left(b c^{2} d e - 2 \, b e^{2}\right)} x^{3} + {\left(b c^{2} d^{2} - 2 \, b d e\right)} x\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left({\left(b c^{3} d e - b c e^{2}\right)} x^{3} + {\left(b c^{3} d^{2} - b c d e\right)} x\right)} \sqrt{d} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) - 2 \, {\left(a c^{2} d^{2} - a d e + 2 \, {\left(a c^{2} d e - a e^{2}\right)} x^{2} + {\left(b c^{2} d^{2} - b d e + 2 \, {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d^{3} e - d^{2} e^{2}\right)} x^{3} + {\left(c^{2} d^{4} - d^{3} e\right)} x\right)}}, \frac{4 \, {\left({\left(b c^{3} d e - b c e^{2}\right)} x^{3} + {\left(b c^{3} d^{2} - b c d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - {\left({\left(b c^{2} d e - 2 \, b e^{2}\right)} x^{3} + {\left(b c^{2} d^{2} - 2 \, b d e\right)} x\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, {\left(a c^{2} d^{2} - a d e + 2 \, {\left(a c^{2} d e - a e^{2}\right)} x^{2} + {\left(b c^{2} d^{2} - b d e + 2 \, {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{4 \, {\left({\left(c^{2} d^{3} e - d^{2} e^{2}\right)} x^{3} + {\left(c^{2} d^{4} - d^{3} e\right)} x\right)}}, \frac{{\left({\left(b c^{2} d e - 2 \, b e^{2}\right)} x^{3} + {\left(b c^{2} d^{2} - 2 \, b d e\right)} x\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left({\left(b c^{3} d e - b c e^{2}\right)} x^{3} + {\left(b c^{3} d^{2} - b c d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - 2 \, {\left(a c^{2} d^{2} - a d e + 2 \, {\left(a c^{2} d e - a e^{2}\right)} x^{2} + {\left(b c^{2} d^{2} - b d e + 2 \, {\left(b c^{2} d e - b e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d^{3} e - d^{2} e^{2}\right)} x^{3} + {\left(c^{2} d^{4} - d^{3} e\right)} x\right)}}\right]"," ",0,"[-1/4*(((b*c^2*d*e - 2*b*e^2)*x^3 + (b*c^2*d^2 - 2*b*d*e)*x)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 2*((b*c^3*d*e - b*c*e^2)*x^3 + (b*c^3*d^2 - b*c*d*e)*x)*sqrt(d)*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 4*(a*c^2*d^2 - a*d*e + 2*(a*c^2*d*e - a*e^2)*x^2 + (b*c^2*d^2 - b*d*e + 2*(b*c^2*d*e - b*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^3*e - d^2*e^2)*x^3 + (c^2*d^4 - d^3*e)*x), 1/2*(((b*c^2*d*e - 2*b*e^2)*x^3 + (b*c^2*d^2 - 2*b*d*e)*x)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + ((b*c^3*d*e - b*c*e^2)*x^3 + (b*c^3*d^2 - b*c*d*e)*x)*sqrt(d)*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) - 2*(a*c^2*d^2 - a*d*e + 2*(a*c^2*d*e - a*e^2)*x^2 + (b*c^2*d^2 - b*d*e + 2*(b*c^2*d*e - b*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^3*e - d^2*e^2)*x^3 + (c^2*d^4 - d^3*e)*x), 1/4*(4*((b*c^3*d*e - b*c*e^2)*x^3 + (b*c^3*d^2 - b*c*d*e)*x)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - ((b*c^2*d*e - 2*b*e^2)*x^3 + (b*c^2*d^2 - 2*b*d*e)*x)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*(a*c^2*d^2 - a*d*e + 2*(a*c^2*d*e - a*e^2)*x^2 + (b*c^2*d^2 - b*d*e + 2*(b*c^2*d*e - b*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^3*e - d^2*e^2)*x^3 + (c^2*d^4 - d^3*e)*x), 1/2*(((b*c^2*d*e - 2*b*e^2)*x^3 + (b*c^2*d^2 - 2*b*d*e)*x)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*((b*c^3*d*e - b*c*e^2)*x^3 + (b*c^3*d^2 - b*c*d*e)*x)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - 2*(a*c^2*d^2 - a*d*e + 2*(a*c^2*d*e - a*e^2)*x^2 + (b*c^2*d^2 - b*d*e + 2*(b*c^2*d*e - b*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^3*e - d^2*e^2)*x^3 + (c^2*d^4 - d^3*e)*x)]","B",0
1215,0,0,0,0.436459," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
1216,1,1920,0,0.900733," ","integrate((a+b*arctan(c*x))/x^4/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b c^{4} d^{2} e + 4 \, b c^{2} d e^{2} - 8 \, b e^{3}\right)} x^{5} + {\left(b c^{4} d^{3} + 4 \, b c^{2} d^{2} e - 8 \, b d e^{2}\right)} x^{3}\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - {\left({\left(2 \, b c^{5} d^{2} e + 7 \, b c^{3} d e^{2} - 9 \, b c e^{3}\right)} x^{5} + {\left(2 \, b c^{5} d^{3} + 7 \, b c^{3} d^{2} e - 9 \, b c d e^{2}\right)} x^{3}\right)} \sqrt{d} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, a c^{2} d^{3} - 16 \, {\left(a c^{2} d e^{2} - a e^{3}\right)} x^{4} - 2 \, a d^{2} e + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{3} - 8 \, {\left(a c^{2} d^{2} e - a d e^{2}\right)} x^{2} + {\left(b c^{3} d^{3} - b c d^{2} e\right)} x + 2 \, {\left(b c^{2} d^{3} - 8 \, {\left(b c^{2} d e^{2} - b e^{3}\right)} x^{4} - b d^{2} e - 4 \, {\left(b c^{2} d^{2} e - b d e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{2} d^{4} e - d^{3} e^{2}\right)} x^{5} + {\left(c^{2} d^{5} - d^{4} e\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(b c^{4} d^{2} e + 4 \, b c^{2} d e^{2} - 8 \, b e^{3}\right)} x^{5} + {\left(b c^{4} d^{3} + 4 \, b c^{2} d^{2} e - 8 \, b d e^{2}\right)} x^{3}\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - {\left({\left(2 \, b c^{5} d^{2} e + 7 \, b c^{3} d e^{2} - 9 \, b c e^{3}\right)} x^{5} + {\left(2 \, b c^{5} d^{3} + 7 \, b c^{3} d^{2} e - 9 \, b c d e^{2}\right)} x^{3}\right)} \sqrt{d} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, a c^{2} d^{3} - 16 \, {\left(a c^{2} d e^{2} - a e^{3}\right)} x^{4} - 2 \, a d^{2} e + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{3} - 8 \, {\left(a c^{2} d^{2} e - a d e^{2}\right)} x^{2} + {\left(b c^{3} d^{3} - b c d^{2} e\right)} x + 2 \, {\left(b c^{2} d^{3} - 8 \, {\left(b c^{2} d e^{2} - b e^{3}\right)} x^{4} - b d^{2} e - 4 \, {\left(b c^{2} d^{2} e - b d e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{2} d^{4} e - d^{3} e^{2}\right)} x^{5} + {\left(c^{2} d^{5} - d^{4} e\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(2 \, b c^{5} d^{2} e + 7 \, b c^{3} d e^{2} - 9 \, b c e^{3}\right)} x^{5} + {\left(2 \, b c^{5} d^{3} + 7 \, b c^{3} d^{2} e - 9 \, b c d e^{2}\right)} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left({\left(b c^{4} d^{2} e + 4 \, b c^{2} d e^{2} - 8 \, b e^{3}\right)} x^{5} + {\left(b c^{4} d^{3} + 4 \, b c^{2} d^{2} e - 8 \, b d e^{2}\right)} x^{3}\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(2 \, a c^{2} d^{3} - 16 \, {\left(a c^{2} d e^{2} - a e^{3}\right)} x^{4} - 2 \, a d^{2} e + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{3} - 8 \, {\left(a c^{2} d^{2} e - a d e^{2}\right)} x^{2} + {\left(b c^{3} d^{3} - b c d^{2} e\right)} x + 2 \, {\left(b c^{2} d^{3} - 8 \, {\left(b c^{2} d e^{2} - b e^{3}\right)} x^{4} - b d^{2} e - 4 \, {\left(b c^{2} d^{2} e - b d e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{2} d^{4} e - d^{3} e^{2}\right)} x^{5} + {\left(c^{2} d^{5} - d^{4} e\right)} x^{3}\right)}}, -\frac{{\left({\left(b c^{4} d^{2} e + 4 \, b c^{2} d e^{2} - 8 \, b e^{3}\right)} x^{5} + {\left(b c^{4} d^{3} + 4 \, b c^{2} d^{2} e - 8 \, b d e^{2}\right)} x^{3}\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left({\left(2 \, b c^{5} d^{2} e + 7 \, b c^{3} d e^{2} - 9 \, b c e^{3}\right)} x^{5} + {\left(2 \, b c^{5} d^{3} + 7 \, b c^{3} d^{2} e - 9 \, b c d e^{2}\right)} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left(2 \, a c^{2} d^{3} - 16 \, {\left(a c^{2} d e^{2} - a e^{3}\right)} x^{4} - 2 \, a d^{2} e + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{3} - 8 \, {\left(a c^{2} d^{2} e - a d e^{2}\right)} x^{2} + {\left(b c^{3} d^{3} - b c d^{2} e\right)} x + 2 \, {\left(b c^{2} d^{3} - 8 \, {\left(b c^{2} d e^{2} - b e^{3}\right)} x^{4} - b d^{2} e - 4 \, {\left(b c^{2} d^{2} e - b d e^{2}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left({\left(c^{2} d^{4} e - d^{3} e^{2}\right)} x^{5} + {\left(c^{2} d^{5} - d^{4} e\right)} x^{3}\right)}}\right]"," ",0,"[-1/12*(((b*c^4*d^2*e + 4*b*c^2*d*e^2 - 8*b*e^3)*x^5 + (b*c^4*d^3 + 4*b*c^2*d^2*e - 8*b*d*e^2)*x^3)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - ((2*b*c^5*d^2*e + 7*b*c^3*d*e^2 - 9*b*c*e^3)*x^5 + (2*b*c^5*d^3 + 7*b*c^3*d^2*e - 9*b*c*d*e^2)*x^3)*sqrt(d)*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(2*a*c^2*d^3 - 16*(a*c^2*d*e^2 - a*e^3)*x^4 - 2*a*d^2*e + (b*c^3*d^2*e - b*c*d*e^2)*x^3 - 8*(a*c^2*d^2*e - a*d*e^2)*x^2 + (b*c^3*d^3 - b*c*d^2*e)*x + 2*(b*c^2*d^3 - 8*(b*c^2*d*e^2 - b*e^3)*x^4 - b*d^2*e - 4*(b*c^2*d^2*e - b*d*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^4*e - d^3*e^2)*x^5 + (c^2*d^5 - d^4*e)*x^3), -1/12*(2*((b*c^4*d^2*e + 4*b*c^2*d*e^2 - 8*b*e^3)*x^5 + (b*c^4*d^3 + 4*b*c^2*d^2*e - 8*b*d*e^2)*x^3)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - ((2*b*c^5*d^2*e + 7*b*c^3*d*e^2 - 9*b*c*e^3)*x^5 + (2*b*c^5*d^3 + 7*b*c^3*d^2*e - 9*b*c*d*e^2)*x^3)*sqrt(d)*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(2*a*c^2*d^3 - 16*(a*c^2*d*e^2 - a*e^3)*x^4 - 2*a*d^2*e + (b*c^3*d^2*e - b*c*d*e^2)*x^3 - 8*(a*c^2*d^2*e - a*d*e^2)*x^2 + (b*c^3*d^3 - b*c*d^2*e)*x + 2*(b*c^2*d^3 - 8*(b*c^2*d*e^2 - b*e^3)*x^4 - b*d^2*e - 4*(b*c^2*d^2*e - b*d*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^4*e - d^3*e^2)*x^5 + (c^2*d^5 - d^4*e)*x^3), -1/12*(2*((2*b*c^5*d^2*e + 7*b*c^3*d*e^2 - 9*b*c*e^3)*x^5 + (2*b*c^5*d^3 + 7*b*c^3*d^2*e - 9*b*c*d*e^2)*x^3)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + ((b*c^4*d^2*e + 4*b*c^2*d*e^2 - 8*b*e^3)*x^5 + (b*c^4*d^3 + 4*b*c^2*d^2*e - 8*b*d*e^2)*x^3)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(2*a*c^2*d^3 - 16*(a*c^2*d*e^2 - a*e^3)*x^4 - 2*a*d^2*e + (b*c^3*d^2*e - b*c*d*e^2)*x^3 - 8*(a*c^2*d^2*e - a*d*e^2)*x^2 + (b*c^3*d^3 - b*c*d^2*e)*x + 2*(b*c^2*d^3 - 8*(b*c^2*d*e^2 - b*e^3)*x^4 - b*d^2*e - 4*(b*c^2*d^2*e - b*d*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^4*e - d^3*e^2)*x^5 + (c^2*d^5 - d^4*e)*x^3), -1/6*(((b*c^4*d^2*e + 4*b*c^2*d*e^2 - 8*b*e^3)*x^5 + (b*c^4*d^3 + 4*b*c^2*d^2*e - 8*b*d*e^2)*x^3)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + ((2*b*c^5*d^2*e + 7*b*c^3*d*e^2 - 9*b*c*e^3)*x^5 + (2*b*c^5*d^3 + 7*b*c^3*d^2*e - 9*b*c*d*e^2)*x^3)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + (2*a*c^2*d^3 - 16*(a*c^2*d*e^2 - a*e^3)*x^4 - 2*a*d^2*e + (b*c^3*d^2*e - b*c*d*e^2)*x^3 - 8*(a*c^2*d^2*e - a*d*e^2)*x^2 + (b*c^3*d^3 - b*c*d^2*e)*x + 2*(b*c^2*d^3 - 8*(b*c^2*d*e^2 - b*e^3)*x^4 - b*d^2*e - 4*(b*c^2*d^2*e - b*d*e^2)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^2*d^4*e - d^3*e^2)*x^5 + (c^2*d^5 - d^4*e)*x^3)]","B",0
1217,0,0,0,0.431384," ","integrate(x^4*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} \arctan\left(c x\right) + a x^{4}\right)} \sqrt{e x^{2} + d}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^4*arctan(c*x) + a*x^4)*sqrt(e*x^2 + d)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1218,1,863,0,0.972820," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, b c^{3} d^{3} - 3 \, b c d^{2} e + {\left(2 \, b c^{3} d e^{2} - 3 \, b c e^{3}\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d^{2} e - 3 \, b c d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} - 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 4 \, {\left(2 \, a c^{4} d^{3} - 4 \, a c^{2} d^{2} e + 2 \, a d e^{2} - {\left(b c^{3} d e^{2} - b c e^{3}\right)} x^{3} + 3 \, {\left(a c^{4} d^{2} e - 2 \, a c^{2} d e^{2} + a e^{3}\right)} x^{2} - {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x + {\left(2 \, b c^{4} d^{3} - 4 \, b c^{2} d^{2} e + 2 \, b d e^{2} + 3 \, {\left(b c^{4} d^{2} e - 2 \, b c^{2} d e^{2} + b e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4} + {\left(c^{4} d^{2} e^{4} - 2 \, c^{2} d e^{5} + e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{3} e^{3} - 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{2}\right)}}, \frac{{\left(2 \, b c^{3} d^{3} - 3 \, b c d^{2} e + {\left(2 \, b c^{3} d e^{2} - 3 \, b c e^{3}\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d^{2} e - 3 \, b c d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 2 \, {\left(2 \, a c^{4} d^{3} - 4 \, a c^{2} d^{2} e + 2 \, a d e^{2} - {\left(b c^{3} d e^{2} - b c e^{3}\right)} x^{3} + 3 \, {\left(a c^{4} d^{2} e - 2 \, a c^{2} d e^{2} + a e^{3}\right)} x^{2} - {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x + {\left(2 \, b c^{4} d^{3} - 4 \, b c^{2} d^{2} e + 2 \, b d e^{2} + 3 \, {\left(b c^{4} d^{2} e - 2 \, b c^{2} d e^{2} + b e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4} + {\left(c^{4} d^{2} e^{4} - 2 \, c^{2} d e^{5} + e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{3} e^{3} - 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/12*((2*b*c^3*d^3 - 3*b*c*d^2*e + (2*b*c^3*d*e^2 - 3*b*c*e^3)*x^4 + 2*(2*b*c^3*d^2*e - 3*b*c*d*e^2)*x^2)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 - 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 4*(2*a*c^4*d^3 - 4*a*c^2*d^2*e + 2*a*d*e^2 - (b*c^3*d*e^2 - b*c*e^3)*x^3 + 3*(a*c^4*d^2*e - 2*a*c^2*d*e^2 + a*e^3)*x^2 - (b*c^3*d^2*e - b*c*d*e^2)*x + (2*b*c^4*d^3 - 4*b*c^2*d^2*e + 2*b*d*e^2 + 3*(b*c^4*d^2*e - 2*b*c^2*d*e^2 + b*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4 + (c^4*d^2*e^4 - 2*c^2*d*e^5 + e^6)*x^4 + 2*(c^4*d^3*e^3 - 2*c^2*d^2*e^4 + d*e^5)*x^2), 1/6*((2*b*c^3*d^3 - 3*b*c*d^2*e + (2*b*c^3*d*e^2 - 3*b*c*e^3)*x^4 + 2*(2*b*c^3*d^2*e - 3*b*c*d*e^2)*x^2)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 2*(2*a*c^4*d^3 - 4*a*c^2*d^2*e + 2*a*d*e^2 - (b*c^3*d*e^2 - b*c*e^3)*x^3 + 3*(a*c^4*d^2*e - 2*a*c^2*d*e^2 + a*e^3)*x^2 - (b*c^3*d^2*e - b*c*d*e^2)*x + (2*b*c^4*d^3 - 4*b*c^2*d^2*e + 2*b*d*e^2 + 3*(b*c^4*d^2*e - 2*b*c^2*d*e^2 + b*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4 + (c^4*d^2*e^4 - 2*c^2*d*e^5 + e^6)*x^4 + 2*(c^4*d^3*e^3 - 2*c^2*d^2*e^4 + d*e^5)*x^2)]","B",0
1219,1,676,0,0.758198," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b e^{3} x^{4} + 2 \, b d e^{2} x^{2} + b d^{2} e\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, {\left(b c^{3} d^{3} - b c d^{2} e + {\left(b c^{4} d^{2} e - 2 \, b c^{2} d e^{2} + b e^{3}\right)} x^{3} \arctan\left(c x\right) + {\left(a c^{4} d^{2} e - 2 \, a c^{2} d e^{2} + a e^{3}\right)} x^{3} + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{4} e^{2} + d^{3} e^{3} + {\left(c^{4} d^{3} e^{3} - 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{2}\right)}}, -\frac{{\left(b e^{3} x^{4} + 2 \, b d e^{2} x^{2} + b d^{2} e\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(b c^{3} d^{3} - b c d^{2} e + {\left(b c^{4} d^{2} e - 2 \, b c^{2} d e^{2} + b e^{3}\right)} x^{3} \arctan\left(c x\right) + {\left(a c^{4} d^{2} e - 2 \, a c^{2} d e^{2} + a e^{3}\right)} x^{3} + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{4} e^{2} + d^{3} e^{3} + {\left(c^{4} d^{3} e^{3} - 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/12*((b*e^3*x^4 + 2*b*d*e^2*x^2 + b*d^2*e)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*(b*c^3*d^3 - b*c*d^2*e + (b*c^4*d^2*e - 2*b*c^2*d*e^2 + b*e^3)*x^3*arctan(c*x) + (a*c^4*d^2*e - 2*a*c^2*d*e^2 + a*e^3)*x^3 + (b*c^3*d^2*e - b*c*d*e^2)*x^2)*sqrt(e*x^2 + d))/(c^4*d^5*e - 2*c^2*d^4*e^2 + d^3*e^3 + (c^4*d^3*e^3 - 2*c^2*d^2*e^4 + d*e^5)*x^4 + 2*(c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4)*x^2), -1/6*((b*e^3*x^4 + 2*b*d*e^2*x^2 + b*d^2*e)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*(b*c^3*d^3 - b*c*d^2*e + (b*c^4*d^2*e - 2*b*c^2*d*e^2 + b*e^3)*x^3*arctan(c*x) + (a*c^4*d^2*e - 2*a*c^2*d*e^2 + a*e^3)*x^3 + (b*c^3*d^2*e - b*c*d*e^2)*x^2)*sqrt(e*x^2 + d))/(c^4*d^5*e - 2*c^2*d^4*e^2 + d^3*e^3 + (c^4*d^3*e^3 - 2*c^2*d^2*e^4 + d*e^5)*x^4 + 2*(c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4)*x^2)]","B",0
1220,1,679,0,0.888914," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{3} d e^{2} x^{4} + 2 \, b c^{3} d^{2} e x^{2} + b c^{3} d^{3}\right)} \sqrt{-c^{2} d + e} \log\left(\frac{{\left(c^{4} d^{2} - 8 \, c^{2} d e + 8 \, e^{2}\right)} x^{4} - 2 \, {\left(3 \, c^{2} d^{2} - 4 \, d e\right)} x^{2} + 4 \, {\left({\left(c^{2} d - 2 \, e\right)} x^{3} - d x\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d} + d^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, {\left(a c^{4} d^{3} - 2 \, a c^{2} d^{2} e + a d e^{2} + {\left(b c^{3} d e^{2} - b c e^{3}\right)} x^{3} + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x + {\left(b c^{4} d^{3} - 2 \, b c^{2} d^{2} e + b d e^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{4} e^{2} + d^{3} e^{3} + {\left(c^{4} d^{3} e^{3} - 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{2}\right)}}, \frac{{\left(b c^{3} d e^{2} x^{4} + 2 \, b c^{3} d^{2} e x^{2} + b c^{3} d^{3}\right)} \sqrt{c^{2} d - e} \arctan\left(\frac{\sqrt{c^{2} d - e} {\left({\left(c^{2} d - 2 \, e\right)} x^{2} - d\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(c^{2} d e - e^{2}\right)} x^{3} + {\left(c^{2} d^{2} - d e\right)} x\right)}}\right) - 2 \, {\left(a c^{4} d^{3} - 2 \, a c^{2} d^{2} e + a d e^{2} + {\left(b c^{3} d e^{2} - b c e^{3}\right)} x^{3} + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x + {\left(b c^{4} d^{3} - 2 \, b c^{2} d^{2} e + b d e^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{4} e^{2} + d^{3} e^{3} + {\left(c^{4} d^{3} e^{3} - 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*((b*c^3*d*e^2*x^4 + 2*b*c^3*d^2*e*x^2 + b*c^3*d^3)*sqrt(-c^2*d + e)*log(((c^4*d^2 - 8*c^2*d*e + 8*e^2)*x^4 - 2*(3*c^2*d^2 - 4*d*e)*x^2 + 4*((c^2*d - 2*e)*x^3 - d*x)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d) + d^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*(a*c^4*d^3 - 2*a*c^2*d^2*e + a*d*e^2 + (b*c^3*d*e^2 - b*c*e^3)*x^3 + (b*c^3*d^2*e - b*c*d*e^2)*x + (b*c^4*d^3 - 2*b*c^2*d^2*e + b*d*e^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^4*d^5*e - 2*c^2*d^4*e^2 + d^3*e^3 + (c^4*d^3*e^3 - 2*c^2*d^2*e^4 + d*e^5)*x^4 + 2*(c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4)*x^2), 1/6*((b*c^3*d*e^2*x^4 + 2*b*c^3*d^2*e*x^2 + b*c^3*d^3)*sqrt(c^2*d - e)*arctan(1/2*sqrt(c^2*d - e)*((c^2*d - 2*e)*x^2 - d)*sqrt(e*x^2 + d)/((c^2*d*e - e^2)*x^3 + (c^2*d^2 - d*e)*x)) - 2*(a*c^4*d^3 - 2*a*c^2*d^2*e + a*d*e^2 + (b*c^3*d*e^2 - b*c*e^3)*x^3 + (b*c^3*d^2*e - b*c*d*e^2)*x + (b*c^4*d^3 - 2*b*c^2*d^2*e + b*d*e^2)*arctan(c*x))*sqrt(e*x^2 + d))/(c^4*d^5*e - 2*c^2*d^4*e^2 + d^3*e^3 + (c^4*d^3*e^3 - 2*c^2*d^2*e^4 + d*e^5)*x^4 + 2*(c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4)*x^2)]","B",0
1221,1,864,0,0.989899," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b c^{2} d^{3} + {\left(3 \, b c^{2} d e^{2} - 2 \, b e^{3}\right)} x^{4} - 2 \, b d^{2} e + 2 \, {\left(3 \, b c^{2} d^{2} e - 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, {\left(b c^{3} d^{3} - b c d^{2} e - 2 \, {\left(a c^{4} d^{2} e - 2 \, a c^{2} d e^{2} + a e^{3}\right)} x^{3} + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{2} - 3 \, {\left(a c^{4} d^{3} - 2 \, a c^{2} d^{2} e + a d e^{2}\right)} x - {\left(2 \, {\left(b c^{4} d^{2} e - 2 \, b c^{2} d e^{2} + b e^{3}\right)} x^{3} + 3 \, {\left(b c^{4} d^{3} - 2 \, b c^{2} d^{2} e + b d e^{2}\right)} x\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{4} d^{6} - 2 \, c^{2} d^{5} e + d^{4} e^{2} + {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{4} e^{2} + d^{3} e^{3}\right)} x^{2}\right)}}, \frac{{\left(3 \, b c^{2} d^{3} + {\left(3 \, b c^{2} d e^{2} - 2 \, b e^{3}\right)} x^{4} - 2 \, b d^{2} e + 2 \, {\left(3 \, b c^{2} d^{2} e - 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(b c^{3} d^{3} - b c d^{2} e - 2 \, {\left(a c^{4} d^{2} e - 2 \, a c^{2} d e^{2} + a e^{3}\right)} x^{3} + {\left(b c^{3} d^{2} e - b c d e^{2}\right)} x^{2} - 3 \, {\left(a c^{4} d^{3} - 2 \, a c^{2} d^{2} e + a d e^{2}\right)} x - {\left(2 \, {\left(b c^{4} d^{2} e - 2 \, b c^{2} d e^{2} + b e^{3}\right)} x^{3} + 3 \, {\left(b c^{4} d^{3} - 2 \, b c^{2} d^{2} e + b d e^{2}\right)} x\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{4} d^{6} - 2 \, c^{2} d^{5} e + d^{4} e^{2} + {\left(c^{4} d^{4} e^{2} - 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e - 2 \, c^{2} d^{4} e^{2} + d^{3} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*((3*b*c^2*d^3 + (3*b*c^2*d*e^2 - 2*b*e^3)*x^4 - 2*b*d^2*e + 2*(3*b*c^2*d^2*e - 2*b*d*e^2)*x^2)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*(b*c^3*d^3 - b*c*d^2*e - 2*(a*c^4*d^2*e - 2*a*c^2*d*e^2 + a*e^3)*x^3 + (b*c^3*d^2*e - b*c*d*e^2)*x^2 - 3*(a*c^4*d^3 - 2*a*c^2*d^2*e + a*d*e^2)*x - (2*(b*c^4*d^2*e - 2*b*c^2*d*e^2 + b*e^3)*x^3 + 3*(b*c^4*d^3 - 2*b*c^2*d^2*e + b*d*e^2)*x)*arctan(c*x))*sqrt(e*x^2 + d))/(c^4*d^6 - 2*c^2*d^5*e + d^4*e^2 + (c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4)*x^4 + 2*(c^4*d^5*e - 2*c^2*d^4*e^2 + d^3*e^3)*x^2), 1/6*((3*b*c^2*d^3 + (3*b*c^2*d*e^2 - 2*b*e^3)*x^4 - 2*b*d^2*e + 2*(3*b*c^2*d^2*e - 2*b*d*e^2)*x^2)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*(b*c^3*d^3 - b*c*d^2*e - 2*(a*c^4*d^2*e - 2*a*c^2*d*e^2 + a*e^3)*x^3 + (b*c^3*d^2*e - b*c*d*e^2)*x^2 - 3*(a*c^4*d^3 - 2*a*c^2*d^2*e + a*d*e^2)*x - (2*(b*c^4*d^2*e - 2*b*c^2*d*e^2 + b*e^3)*x^3 + 3*(b*c^4*d^3 - 2*b*c^2*d^2*e + b*d*e^2)*x)*arctan(c*x))*sqrt(e*x^2 + d))/(c^4*d^6 - 2*c^2*d^5*e + d^4*e^2 + (c^4*d^4*e^2 - 2*c^2*d^3*e^3 + d^2*e^4)*x^4 + 2*(c^4*d^5*e - 2*c^2*d^4*e^2 + d^3*e^3)*x^2)]","B",0
1222,0,0,0,0.428192," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
1223,1,2714,0,2.143999," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, b c^{4} d^{2} e^{2} - 12 \, b c^{2} d e^{3} + 8 \, b e^{4}\right)} x^{5} + 2 \, {\left(3 \, b c^{4} d^{3} e - 12 \, b c^{2} d^{2} e^{2} + 8 \, b d e^{3}\right)} x^{3} + {\left(3 \, b c^{4} d^{4} - 12 \, b c^{2} d^{3} e + 8 \, b d^{2} e^{2}\right)} x\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 6 \, {\left({\left(b c^{5} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + b c e^{4}\right)} x^{5} + 2 \, {\left(b c^{5} d^{3} e - 2 \, b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{5} d^{4} - 2 \, b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{d} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 4 \, {\left(3 \, a c^{4} d^{4} - 6 \, a c^{2} d^{3} e + 3 \, a d^{2} e^{2} + 8 \, {\left(a c^{4} d^{2} e^{2} - 2 \, a c^{2} d e^{3} + a e^{4}\right)} x^{4} - {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + 12 \, {\left(a c^{4} d^{3} e - 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} - {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x + {\left(3 \, b c^{4} d^{4} - 6 \, b c^{2} d^{3} e + 3 \, b d^{2} e^{2} + 8 \, {\left(b c^{4} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 12 \, {\left(b c^{4} d^{3} e - 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{5} + 2 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3}\right)} x^{3} + {\left(c^{4} d^{7} - 2 \, c^{2} d^{6} e + d^{5} e^{2}\right)} x\right)}}, \frac{{\left({\left(3 \, b c^{4} d^{2} e^{2} - 12 \, b c^{2} d e^{3} + 8 \, b e^{4}\right)} x^{5} + 2 \, {\left(3 \, b c^{4} d^{3} e - 12 \, b c^{2} d^{2} e^{2} + 8 \, b d e^{3}\right)} x^{3} + {\left(3 \, b c^{4} d^{4} - 12 \, b c^{2} d^{3} e + 8 \, b d^{2} e^{2}\right)} x\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 3 \, {\left({\left(b c^{5} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + b c e^{4}\right)} x^{5} + 2 \, {\left(b c^{5} d^{3} e - 2 \, b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{5} d^{4} - 2 \, b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{d} \log\left(-\frac{e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) - 2 \, {\left(3 \, a c^{4} d^{4} - 6 \, a c^{2} d^{3} e + 3 \, a d^{2} e^{2} + 8 \, {\left(a c^{4} d^{2} e^{2} - 2 \, a c^{2} d e^{3} + a e^{4}\right)} x^{4} - {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + 12 \, {\left(a c^{4} d^{3} e - 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} - {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x + {\left(3 \, b c^{4} d^{4} - 6 \, b c^{2} d^{3} e + 3 \, b d^{2} e^{2} + 8 \, {\left(b c^{4} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 12 \, {\left(b c^{4} d^{3} e - 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left({\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{5} + 2 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3}\right)} x^{3} + {\left(c^{4} d^{7} - 2 \, c^{2} d^{6} e + d^{5} e^{2}\right)} x\right)}}, \frac{12 \, {\left({\left(b c^{5} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + b c e^{4}\right)} x^{5} + 2 \, {\left(b c^{5} d^{3} e - 2 \, b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{5} d^{4} - 2 \, b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - {\left({\left(3 \, b c^{4} d^{2} e^{2} - 12 \, b c^{2} d e^{3} + 8 \, b e^{4}\right)} x^{5} + 2 \, {\left(3 \, b c^{4} d^{3} e - 12 \, b c^{2} d^{2} e^{2} + 8 \, b d e^{3}\right)} x^{3} + {\left(3 \, b c^{4} d^{4} - 12 \, b c^{2} d^{3} e + 8 \, b d^{2} e^{2}\right)} x\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} - 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - 4 \, {\left(3 \, a c^{4} d^{4} - 6 \, a c^{2} d^{3} e + 3 \, a d^{2} e^{2} + 8 \, {\left(a c^{4} d^{2} e^{2} - 2 \, a c^{2} d e^{3} + a e^{4}\right)} x^{4} - {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + 12 \, {\left(a c^{4} d^{3} e - 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} - {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x + {\left(3 \, b c^{4} d^{4} - 6 \, b c^{2} d^{3} e + 3 \, b d^{2} e^{2} + 8 \, {\left(b c^{4} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 12 \, {\left(b c^{4} d^{3} e - 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{5} + 2 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3}\right)} x^{3} + {\left(c^{4} d^{7} - 2 \, c^{2} d^{6} e + d^{5} e^{2}\right)} x\right)}}, \frac{{\left({\left(3 \, b c^{4} d^{2} e^{2} - 12 \, b c^{2} d e^{3} + 8 \, b e^{4}\right)} x^{5} + 2 \, {\left(3 \, b c^{4} d^{3} e - 12 \, b c^{2} d^{2} e^{2} + 8 \, b d e^{3}\right)} x^{3} + {\left(3 \, b c^{4} d^{4} - 12 \, b c^{2} d^{3} e + 8 \, b d^{2} e^{2}\right)} x\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 6 \, {\left({\left(b c^{5} d^{2} e^{2} - 2 \, b c^{3} d e^{3} + b c e^{4}\right)} x^{5} + 2 \, {\left(b c^{5} d^{3} e - 2 \, b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{5} d^{4} - 2 \, b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) - 2 \, {\left(3 \, a c^{4} d^{4} - 6 \, a c^{2} d^{3} e + 3 \, a d^{2} e^{2} + 8 \, {\left(a c^{4} d^{2} e^{2} - 2 \, a c^{2} d e^{3} + a e^{4}\right)} x^{4} - {\left(b c^{3} d^{2} e^{2} - b c d e^{3}\right)} x^{3} + 12 \, {\left(a c^{4} d^{3} e - 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} - {\left(b c^{3} d^{3} e - b c d^{2} e^{2}\right)} x + {\left(3 \, b c^{4} d^{4} - 6 \, b c^{2} d^{3} e + 3 \, b d^{2} e^{2} + 8 \, {\left(b c^{4} d^{2} e^{2} - 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 12 \, {\left(b c^{4} d^{3} e - 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left({\left(c^{4} d^{5} e^{2} - 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{5} + 2 \, {\left(c^{4} d^{6} e - 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3}\right)} x^{3} + {\left(c^{4} d^{7} - 2 \, c^{2} d^{6} e + d^{5} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/12*(((3*b*c^4*d^2*e^2 - 12*b*c^2*d*e^3 + 8*b*e^4)*x^5 + 2*(3*b*c^4*d^3*e - 12*b*c^2*d^2*e^2 + 8*b*d*e^3)*x^3 + (3*b*c^4*d^4 - 12*b*c^2*d^3*e + 8*b*d^2*e^2)*x)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 6*((b*c^5*d^2*e^2 - 2*b*c^3*d*e^3 + b*c*e^4)*x^5 + 2*(b*c^5*d^3*e - 2*b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^5*d^4 - 2*b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(d)*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 4*(3*a*c^4*d^4 - 6*a*c^2*d^3*e + 3*a*d^2*e^2 + 8*(a*c^4*d^2*e^2 - 2*a*c^2*d*e^3 + a*e^4)*x^4 - (b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + 12*(a*c^4*d^3*e - 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 - (b*c^3*d^3*e - b*c*d^2*e^2)*x + (3*b*c^4*d^4 - 6*b*c^2*d^3*e + 3*b*d^2*e^2 + 8*(b*c^4*d^2*e^2 - 2*b*c^2*d*e^3 + b*e^4)*x^4 + 12*(b*c^4*d^3*e - 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4)*x^5 + 2*(c^4*d^6*e - 2*c^2*d^5*e^2 + d^4*e^3)*x^3 + (c^4*d^7 - 2*c^2*d^6*e + d^5*e^2)*x), 1/6*(((3*b*c^4*d^2*e^2 - 12*b*c^2*d*e^3 + 8*b*e^4)*x^5 + 2*(3*b*c^4*d^3*e - 12*b*c^2*d^2*e^2 + 8*b*d*e^3)*x^3 + (3*b*c^4*d^4 - 12*b*c^2*d^3*e + 8*b*d^2*e^2)*x)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 3*((b*c^5*d^2*e^2 - 2*b*c^3*d*e^3 + b*c*e^4)*x^5 + 2*(b*c^5*d^3*e - 2*b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^5*d^4 - 2*b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(d)*log(-(e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) - 2*(3*a*c^4*d^4 - 6*a*c^2*d^3*e + 3*a*d^2*e^2 + 8*(a*c^4*d^2*e^2 - 2*a*c^2*d*e^3 + a*e^4)*x^4 - (b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + 12*(a*c^4*d^3*e - 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 - (b*c^3*d^3*e - b*c*d^2*e^2)*x + (3*b*c^4*d^4 - 6*b*c^2*d^3*e + 3*b*d^2*e^2 + 8*(b*c^4*d^2*e^2 - 2*b*c^2*d*e^3 + b*e^4)*x^4 + 12*(b*c^4*d^3*e - 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4)*x^5 + 2*(c^4*d^6*e - 2*c^2*d^5*e^2 + d^4*e^3)*x^3 + (c^4*d^7 - 2*c^2*d^6*e + d^5*e^2)*x), 1/12*(12*((b*c^5*d^2*e^2 - 2*b*c^3*d*e^3 + b*c*e^4)*x^5 + 2*(b*c^5*d^3*e - 2*b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^5*d^4 - 2*b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - ((3*b*c^4*d^2*e^2 - 12*b*c^2*d*e^3 + 8*b*e^4)*x^5 + 2*(3*b*c^4*d^3*e - 12*b*c^2*d^2*e^2 + 8*b*d*e^3)*x^3 + (3*b*c^4*d^4 - 12*b*c^2*d^3*e + 8*b*d^2*e^2)*x)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 - 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - 4*(3*a*c^4*d^4 - 6*a*c^2*d^3*e + 3*a*d^2*e^2 + 8*(a*c^4*d^2*e^2 - 2*a*c^2*d*e^3 + a*e^4)*x^4 - (b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + 12*(a*c^4*d^3*e - 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 - (b*c^3*d^3*e - b*c*d^2*e^2)*x + (3*b*c^4*d^4 - 6*b*c^2*d^3*e + 3*b*d^2*e^2 + 8*(b*c^4*d^2*e^2 - 2*b*c^2*d*e^3 + b*e^4)*x^4 + 12*(b*c^4*d^3*e - 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4)*x^5 + 2*(c^4*d^6*e - 2*c^2*d^5*e^2 + d^4*e^3)*x^3 + (c^4*d^7 - 2*c^2*d^6*e + d^5*e^2)*x), 1/6*(((3*b*c^4*d^2*e^2 - 12*b*c^2*d*e^3 + 8*b*e^4)*x^5 + 2*(3*b*c^4*d^3*e - 12*b*c^2*d^2*e^2 + 8*b*d*e^3)*x^3 + (3*b*c^4*d^4 - 12*b*c^2*d^3*e + 8*b*d^2*e^2)*x)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 6*((b*c^5*d^2*e^2 - 2*b*c^3*d*e^3 + b*c*e^4)*x^5 + 2*(b*c^5*d^3*e - 2*b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^5*d^4 - 2*b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) - 2*(3*a*c^4*d^4 - 6*a*c^2*d^3*e + 3*a*d^2*e^2 + 8*(a*c^4*d^2*e^2 - 2*a*c^2*d*e^3 + a*e^4)*x^4 - (b*c^3*d^2*e^2 - b*c*d*e^3)*x^3 + 12*(a*c^4*d^3*e - 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 - (b*c^3*d^3*e - b*c*d^2*e^2)*x + (3*b*c^4*d^4 - 6*b*c^2*d^3*e + 3*b*d^2*e^2 + 8*(b*c^4*d^2*e^2 - 2*b*c^2*d*e^3 + b*e^4)*x^4 + 12*(b*c^4*d^3*e - 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^5*e^2 - 2*c^2*d^4*e^3 + d^3*e^4)*x^5 + 2*(c^4*d^6*e - 2*c^2*d^5*e^2 + d^4*e^3)*x^3 + (c^4*d^7 - 2*c^2*d^6*e + d^5*e^2)*x)]","B",0
1224,0,0,0,0.427863," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)}}{e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
1225,1,3460,0,3.206433," ","integrate((a+b*arctan(c*x))/x^4/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b c^{6} d^{3} e^{2} + 6 \, b c^{4} d^{2} e^{3} - 24 \, b c^{2} d e^{4} + 16 \, b e^{5}\right)} x^{7} + 2 \, {\left(b c^{6} d^{4} e + 6 \, b c^{4} d^{3} e^{2} - 24 \, b c^{2} d^{2} e^{3} + 16 \, b d e^{4}\right)} x^{5} + {\left(b c^{6} d^{5} + 6 \, b c^{4} d^{4} e - 24 \, b c^{2} d^{3} e^{2} + 16 \, b d^{2} e^{3}\right)} x^{3}\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) - {\left({\left(2 \, b c^{7} d^{3} e^{2} + 11 \, b c^{5} d^{2} e^{3} - 28 \, b c^{3} d e^{4} + 15 \, b c e^{5}\right)} x^{7} + 2 \, {\left(2 \, b c^{7} d^{4} e + 11 \, b c^{5} d^{3} e^{2} - 28 \, b c^{3} d^{2} e^{3} + 15 \, b c d e^{4}\right)} x^{5} + {\left(2 \, b c^{7} d^{5} + 11 \, b c^{5} d^{4} e - 28 \, b c^{3} d^{3} e^{2} + 15 \, b c d^{2} e^{3}\right)} x^{3}\right)} \sqrt{d} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, a c^{4} d^{5} - 4 \, a c^{2} d^{4} e - 32 \, {\left(a c^{4} d^{2} e^{3} - 2 \, a c^{2} d e^{4} + a e^{5}\right)} x^{6} + 2 \, a d^{3} e^{2} + {\left(b c^{5} d^{3} e^{2} - b c d e^{4}\right)} x^{5} - 48 \, {\left(a c^{4} d^{3} e^{2} - 2 \, a c^{2} d^{2} e^{3} + a d e^{4}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} e - b c^{3} d^{3} e^{2}\right)} x^{3} - 12 \, {\left(a c^{4} d^{4} e - 2 \, a c^{2} d^{3} e^{2} + a d^{2} e^{3}\right)} x^{2} + {\left(b c^{5} d^{5} - 2 \, b c^{3} d^{4} e + b c d^{3} e^{2}\right)} x + 2 \, {\left(b c^{4} d^{5} - 2 \, b c^{2} d^{4} e - 16 \, {\left(b c^{4} d^{2} e^{3} - 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{6} + b d^{3} e^{2} - 24 \, {\left(b c^{4} d^{3} e^{2} - 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{4} - 6 \, {\left(b c^{4} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{4} d^{6} e^{2} - 2 \, c^{2} d^{5} e^{3} + d^{4} e^{4}\right)} x^{7} + 2 \, {\left(c^{4} d^{7} e - 2 \, c^{2} d^{6} e^{2} + d^{5} e^{3}\right)} x^{5} + {\left(c^{4} d^{8} - 2 \, c^{2} d^{7} e + d^{6} e^{2}\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(b c^{6} d^{3} e^{2} + 6 \, b c^{4} d^{2} e^{3} - 24 \, b c^{2} d e^{4} + 16 \, b e^{5}\right)} x^{7} + 2 \, {\left(b c^{6} d^{4} e + 6 \, b c^{4} d^{3} e^{2} - 24 \, b c^{2} d^{2} e^{3} + 16 \, b d e^{4}\right)} x^{5} + {\left(b c^{6} d^{5} + 6 \, b c^{4} d^{4} e - 24 \, b c^{2} d^{3} e^{2} + 16 \, b d^{2} e^{3}\right)} x^{3}\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - {\left({\left(2 \, b c^{7} d^{3} e^{2} + 11 \, b c^{5} d^{2} e^{3} - 28 \, b c^{3} d e^{4} + 15 \, b c e^{5}\right)} x^{7} + 2 \, {\left(2 \, b c^{7} d^{4} e + 11 \, b c^{5} d^{3} e^{2} - 28 \, b c^{3} d^{2} e^{3} + 15 \, b c d e^{4}\right)} x^{5} + {\left(2 \, b c^{7} d^{5} + 11 \, b c^{5} d^{4} e - 28 \, b c^{3} d^{3} e^{2} + 15 \, b c d^{2} e^{3}\right)} x^{3}\right)} \sqrt{d} \log\left(-\frac{e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{d} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, a c^{4} d^{5} - 4 \, a c^{2} d^{4} e - 32 \, {\left(a c^{4} d^{2} e^{3} - 2 \, a c^{2} d e^{4} + a e^{5}\right)} x^{6} + 2 \, a d^{3} e^{2} + {\left(b c^{5} d^{3} e^{2} - b c d e^{4}\right)} x^{5} - 48 \, {\left(a c^{4} d^{3} e^{2} - 2 \, a c^{2} d^{2} e^{3} + a d e^{4}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} e - b c^{3} d^{3} e^{2}\right)} x^{3} - 12 \, {\left(a c^{4} d^{4} e - 2 \, a c^{2} d^{3} e^{2} + a d^{2} e^{3}\right)} x^{2} + {\left(b c^{5} d^{5} - 2 \, b c^{3} d^{4} e + b c d^{3} e^{2}\right)} x + 2 \, {\left(b c^{4} d^{5} - 2 \, b c^{2} d^{4} e - 16 \, {\left(b c^{4} d^{2} e^{3} - 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{6} + b d^{3} e^{2} - 24 \, {\left(b c^{4} d^{3} e^{2} - 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{4} - 6 \, {\left(b c^{4} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{4} d^{6} e^{2} - 2 \, c^{2} d^{5} e^{3} + d^{4} e^{4}\right)} x^{7} + 2 \, {\left(c^{4} d^{7} e - 2 \, c^{2} d^{6} e^{2} + d^{5} e^{3}\right)} x^{5} + {\left(c^{4} d^{8} - 2 \, c^{2} d^{7} e + d^{6} e^{2}\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(2 \, b c^{7} d^{3} e^{2} + 11 \, b c^{5} d^{2} e^{3} - 28 \, b c^{3} d e^{4} + 15 \, b c e^{5}\right)} x^{7} + 2 \, {\left(2 \, b c^{7} d^{4} e + 11 \, b c^{5} d^{3} e^{2} - 28 \, b c^{3} d^{2} e^{3} + 15 \, b c d e^{4}\right)} x^{5} + {\left(2 \, b c^{7} d^{5} + 11 \, b c^{5} d^{4} e - 28 \, b c^{3} d^{3} e^{2} + 15 \, b c d^{2} e^{3}\right)} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left({\left(b c^{6} d^{3} e^{2} + 6 \, b c^{4} d^{2} e^{3} - 24 \, b c^{2} d e^{4} + 16 \, b e^{5}\right)} x^{7} + 2 \, {\left(b c^{6} d^{4} e + 6 \, b c^{4} d^{3} e^{2} - 24 \, b c^{2} d^{2} e^{3} + 16 \, b d e^{4}\right)} x^{5} + {\left(b c^{6} d^{5} + 6 \, b c^{4} d^{4} e - 24 \, b c^{2} d^{3} e^{2} + 16 \, b d^{2} e^{3}\right)} x^{3}\right)} \sqrt{c^{2} d - e} \log\left(\frac{c^{4} e^{2} x^{4} + 8 \, c^{4} d^{2} - 8 \, c^{2} d e + 2 \, {\left(4 \, c^{4} d e - 3 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} e x^{2} + 2 \, c^{3} d - c e\right)} \sqrt{c^{2} d - e} \sqrt{e x^{2} + d} + e^{2}}{c^{4} x^{4} + 2 \, c^{2} x^{2} + 1}\right) + 2 \, {\left(2 \, a c^{4} d^{5} - 4 \, a c^{2} d^{4} e - 32 \, {\left(a c^{4} d^{2} e^{3} - 2 \, a c^{2} d e^{4} + a e^{5}\right)} x^{6} + 2 \, a d^{3} e^{2} + {\left(b c^{5} d^{3} e^{2} - b c d e^{4}\right)} x^{5} - 48 \, {\left(a c^{4} d^{3} e^{2} - 2 \, a c^{2} d^{2} e^{3} + a d e^{4}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} e - b c^{3} d^{3} e^{2}\right)} x^{3} - 12 \, {\left(a c^{4} d^{4} e - 2 \, a c^{2} d^{3} e^{2} + a d^{2} e^{3}\right)} x^{2} + {\left(b c^{5} d^{5} - 2 \, b c^{3} d^{4} e + b c d^{3} e^{2}\right)} x + 2 \, {\left(b c^{4} d^{5} - 2 \, b c^{2} d^{4} e - 16 \, {\left(b c^{4} d^{2} e^{3} - 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{6} + b d^{3} e^{2} - 24 \, {\left(b c^{4} d^{3} e^{2} - 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{4} - 6 \, {\left(b c^{4} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, {\left({\left(c^{4} d^{6} e^{2} - 2 \, c^{2} d^{5} e^{3} + d^{4} e^{4}\right)} x^{7} + 2 \, {\left(c^{4} d^{7} e - 2 \, c^{2} d^{6} e^{2} + d^{5} e^{3}\right)} x^{5} + {\left(c^{4} d^{8} - 2 \, c^{2} d^{7} e + d^{6} e^{2}\right)} x^{3}\right)}}, -\frac{{\left({\left(b c^{6} d^{3} e^{2} + 6 \, b c^{4} d^{2} e^{3} - 24 \, b c^{2} d e^{4} + 16 \, b e^{5}\right)} x^{7} + 2 \, {\left(b c^{6} d^{4} e + 6 \, b c^{4} d^{3} e^{2} - 24 \, b c^{2} d^{2} e^{3} + 16 \, b d e^{4}\right)} x^{5} + {\left(b c^{6} d^{5} + 6 \, b c^{4} d^{4} e - 24 \, b c^{2} d^{3} e^{2} + 16 \, b d^{2} e^{3}\right)} x^{3}\right)} \sqrt{-c^{2} d + e} \arctan\left(-\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d - e\right)} \sqrt{-c^{2} d + e} \sqrt{e x^{2} + d}}{2 \, {\left(c^{3} d^{2} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left({\left(2 \, b c^{7} d^{3} e^{2} + 11 \, b c^{5} d^{2} e^{3} - 28 \, b c^{3} d e^{4} + 15 \, b c e^{5}\right)} x^{7} + 2 \, {\left(2 \, b c^{7} d^{4} e + 11 \, b c^{5} d^{3} e^{2} - 28 \, b c^{3} d^{2} e^{3} + 15 \, b c d e^{4}\right)} x^{5} + {\left(2 \, b c^{7} d^{5} + 11 \, b c^{5} d^{4} e - 28 \, b c^{3} d^{3} e^{2} + 15 \, b c d^{2} e^{3}\right)} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d}}{\sqrt{e x^{2} + d}}\right) + {\left(2 \, a c^{4} d^{5} - 4 \, a c^{2} d^{4} e - 32 \, {\left(a c^{4} d^{2} e^{3} - 2 \, a c^{2} d e^{4} + a e^{5}\right)} x^{6} + 2 \, a d^{3} e^{2} + {\left(b c^{5} d^{3} e^{2} - b c d e^{4}\right)} x^{5} - 48 \, {\left(a c^{4} d^{3} e^{2} - 2 \, a c^{2} d^{2} e^{3} + a d e^{4}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} e - b c^{3} d^{3} e^{2}\right)} x^{3} - 12 \, {\left(a c^{4} d^{4} e - 2 \, a c^{2} d^{3} e^{2} + a d^{2} e^{3}\right)} x^{2} + {\left(b c^{5} d^{5} - 2 \, b c^{3} d^{4} e + b c d^{3} e^{2}\right)} x + 2 \, {\left(b c^{4} d^{5} - 2 \, b c^{2} d^{4} e - 16 \, {\left(b c^{4} d^{2} e^{3} - 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{6} + b d^{3} e^{2} - 24 \, {\left(b c^{4} d^{3} e^{2} - 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{4} - 6 \, {\left(b c^{4} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d}}{6 \, {\left({\left(c^{4} d^{6} e^{2} - 2 \, c^{2} d^{5} e^{3} + d^{4} e^{4}\right)} x^{7} + 2 \, {\left(c^{4} d^{7} e - 2 \, c^{2} d^{6} e^{2} + d^{5} e^{3}\right)} x^{5} + {\left(c^{4} d^{8} - 2 \, c^{2} d^{7} e + d^{6} e^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/12*(((b*c^6*d^3*e^2 + 6*b*c^4*d^2*e^3 - 24*b*c^2*d*e^4 + 16*b*e^5)*x^7 + 2*(b*c^6*d^4*e + 6*b*c^4*d^3*e^2 - 24*b*c^2*d^2*e^3 + 16*b*d*e^4)*x^5 + (b*c^6*d^5 + 6*b*c^4*d^4*e - 24*b*c^2*d^3*e^2 + 16*b*d^2*e^3)*x^3)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) - ((2*b*c^7*d^3*e^2 + 11*b*c^5*d^2*e^3 - 28*b*c^3*d*e^4 + 15*b*c*e^5)*x^7 + 2*(2*b*c^7*d^4*e + 11*b*c^5*d^3*e^2 - 28*b*c^3*d^2*e^3 + 15*b*c*d*e^4)*x^5 + (2*b*c^7*d^5 + 11*b*c^5*d^4*e - 28*b*c^3*d^3*e^2 + 15*b*c*d^2*e^3)*x^3)*sqrt(d)*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(2*a*c^4*d^5 - 4*a*c^2*d^4*e - 32*(a*c^4*d^2*e^3 - 2*a*c^2*d*e^4 + a*e^5)*x^6 + 2*a*d^3*e^2 + (b*c^5*d^3*e^2 - b*c*d*e^4)*x^5 - 48*(a*c^4*d^3*e^2 - 2*a*c^2*d^2*e^3 + a*d*e^4)*x^4 + 2*(b*c^5*d^4*e - b*c^3*d^3*e^2)*x^3 - 12*(a*c^4*d^4*e - 2*a*c^2*d^3*e^2 + a*d^2*e^3)*x^2 + (b*c^5*d^5 - 2*b*c^3*d^4*e + b*c*d^3*e^2)*x + 2*(b*c^4*d^5 - 2*b*c^2*d^4*e - 16*(b*c^4*d^2*e^3 - 2*b*c^2*d*e^4 + b*e^5)*x^6 + b*d^3*e^2 - 24*(b*c^4*d^3*e^2 - 2*b*c^2*d^2*e^3 + b*d*e^4)*x^4 - 6*(b*c^4*d^4*e - 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^6*e^2 - 2*c^2*d^5*e^3 + d^4*e^4)*x^7 + 2*(c^4*d^7*e - 2*c^2*d^6*e^2 + d^5*e^3)*x^5 + (c^4*d^8 - 2*c^2*d^7*e + d^6*e^2)*x^3), -1/12*(2*((b*c^6*d^3*e^2 + 6*b*c^4*d^2*e^3 - 24*b*c^2*d*e^4 + 16*b*e^5)*x^7 + 2*(b*c^6*d^4*e + 6*b*c^4*d^3*e^2 - 24*b*c^2*d^2*e^3 + 16*b*d*e^4)*x^5 + (b*c^6*d^5 + 6*b*c^4*d^4*e - 24*b*c^2*d^3*e^2 + 16*b*d^2*e^3)*x^3)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - ((2*b*c^7*d^3*e^2 + 11*b*c^5*d^2*e^3 - 28*b*c^3*d*e^4 + 15*b*c*e^5)*x^7 + 2*(2*b*c^7*d^4*e + 11*b*c^5*d^3*e^2 - 28*b*c^3*d^2*e^3 + 15*b*c*d*e^4)*x^5 + (2*b*c^7*d^5 + 11*b*c^5*d^4*e - 28*b*c^3*d^3*e^2 + 15*b*c*d^2*e^3)*x^3)*sqrt(d)*log(-(e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(d) + 2*d)/x^2) + 2*(2*a*c^4*d^5 - 4*a*c^2*d^4*e - 32*(a*c^4*d^2*e^3 - 2*a*c^2*d*e^4 + a*e^5)*x^6 + 2*a*d^3*e^2 + (b*c^5*d^3*e^2 - b*c*d*e^4)*x^5 - 48*(a*c^4*d^3*e^2 - 2*a*c^2*d^2*e^3 + a*d*e^4)*x^4 + 2*(b*c^5*d^4*e - b*c^3*d^3*e^2)*x^3 - 12*(a*c^4*d^4*e - 2*a*c^2*d^3*e^2 + a*d^2*e^3)*x^2 + (b*c^5*d^5 - 2*b*c^3*d^4*e + b*c*d^3*e^2)*x + 2*(b*c^4*d^5 - 2*b*c^2*d^4*e - 16*(b*c^4*d^2*e^3 - 2*b*c^2*d*e^4 + b*e^5)*x^6 + b*d^3*e^2 - 24*(b*c^4*d^3*e^2 - 2*b*c^2*d^2*e^3 + b*d*e^4)*x^4 - 6*(b*c^4*d^4*e - 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^6*e^2 - 2*c^2*d^5*e^3 + d^4*e^4)*x^7 + 2*(c^4*d^7*e - 2*c^2*d^6*e^2 + d^5*e^3)*x^5 + (c^4*d^8 - 2*c^2*d^7*e + d^6*e^2)*x^3), -1/12*(2*((2*b*c^7*d^3*e^2 + 11*b*c^5*d^2*e^3 - 28*b*c^3*d*e^4 + 15*b*c*e^5)*x^7 + 2*(2*b*c^7*d^4*e + 11*b*c^5*d^3*e^2 - 28*b*c^3*d^2*e^3 + 15*b*c*d*e^4)*x^5 + (2*b*c^7*d^5 + 11*b*c^5*d^4*e - 28*b*c^3*d^3*e^2 + 15*b*c*d^2*e^3)*x^3)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + ((b*c^6*d^3*e^2 + 6*b*c^4*d^2*e^3 - 24*b*c^2*d*e^4 + 16*b*e^5)*x^7 + 2*(b*c^6*d^4*e + 6*b*c^4*d^3*e^2 - 24*b*c^2*d^2*e^3 + 16*b*d*e^4)*x^5 + (b*c^6*d^5 + 6*b*c^4*d^4*e - 24*b*c^2*d^3*e^2 + 16*b*d^2*e^3)*x^3)*sqrt(c^2*d - e)*log((c^4*e^2*x^4 + 8*c^4*d^2 - 8*c^2*d*e + 2*(4*c^4*d*e - 3*c^2*e^2)*x^2 + 4*(c^3*e*x^2 + 2*c^3*d - c*e)*sqrt(c^2*d - e)*sqrt(e*x^2 + d) + e^2)/(c^4*x^4 + 2*c^2*x^2 + 1)) + 2*(2*a*c^4*d^5 - 4*a*c^2*d^4*e - 32*(a*c^4*d^2*e^3 - 2*a*c^2*d*e^4 + a*e^5)*x^6 + 2*a*d^3*e^2 + (b*c^5*d^3*e^2 - b*c*d*e^4)*x^5 - 48*(a*c^4*d^3*e^2 - 2*a*c^2*d^2*e^3 + a*d*e^4)*x^4 + 2*(b*c^5*d^4*e - b*c^3*d^3*e^2)*x^3 - 12*(a*c^4*d^4*e - 2*a*c^2*d^3*e^2 + a*d^2*e^3)*x^2 + (b*c^5*d^5 - 2*b*c^3*d^4*e + b*c*d^3*e^2)*x + 2*(b*c^4*d^5 - 2*b*c^2*d^4*e - 16*(b*c^4*d^2*e^3 - 2*b*c^2*d*e^4 + b*e^5)*x^6 + b*d^3*e^2 - 24*(b*c^4*d^3*e^2 - 2*b*c^2*d^2*e^3 + b*d*e^4)*x^4 - 6*(b*c^4*d^4*e - 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^6*e^2 - 2*c^2*d^5*e^3 + d^4*e^4)*x^7 + 2*(c^4*d^7*e - 2*c^2*d^6*e^2 + d^5*e^3)*x^5 + (c^4*d^8 - 2*c^2*d^7*e + d^6*e^2)*x^3), -1/6*(((b*c^6*d^3*e^2 + 6*b*c^4*d^2*e^3 - 24*b*c^2*d*e^4 + 16*b*e^5)*x^7 + 2*(b*c^6*d^4*e + 6*b*c^4*d^3*e^2 - 24*b*c^2*d^2*e^3 + 16*b*d*e^4)*x^5 + (b*c^6*d^5 + 6*b*c^4*d^4*e - 24*b*c^2*d^3*e^2 + 16*b*d^2*e^3)*x^3)*sqrt(-c^2*d + e)*arctan(-1/2*(c^2*e*x^2 + 2*c^2*d - e)*sqrt(-c^2*d + e)*sqrt(e*x^2 + d)/(c^3*d^2 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + ((2*b*c^7*d^3*e^2 + 11*b*c^5*d^2*e^3 - 28*b*c^3*d*e^4 + 15*b*c*e^5)*x^7 + 2*(2*b*c^7*d^4*e + 11*b*c^5*d^3*e^2 - 28*b*c^3*d^2*e^3 + 15*b*c*d*e^4)*x^5 + (2*b*c^7*d^5 + 11*b*c^5*d^4*e - 28*b*c^3*d^3*e^2 + 15*b*c*d^2*e^3)*x^3)*sqrt(-d)*arctan(sqrt(-d)/sqrt(e*x^2 + d)) + (2*a*c^4*d^5 - 4*a*c^2*d^4*e - 32*(a*c^4*d^2*e^3 - 2*a*c^2*d*e^4 + a*e^5)*x^6 + 2*a*d^3*e^2 + (b*c^5*d^3*e^2 - b*c*d*e^4)*x^5 - 48*(a*c^4*d^3*e^2 - 2*a*c^2*d^2*e^3 + a*d*e^4)*x^4 + 2*(b*c^5*d^4*e - b*c^3*d^3*e^2)*x^3 - 12*(a*c^4*d^4*e - 2*a*c^2*d^3*e^2 + a*d^2*e^3)*x^2 + (b*c^5*d^5 - 2*b*c^3*d^4*e + b*c*d^3*e^2)*x + 2*(b*c^4*d^5 - 2*b*c^2*d^4*e - 16*(b*c^4*d^2*e^3 - 2*b*c^2*d*e^4 + b*e^5)*x^6 + b*d^3*e^2 - 24*(b*c^4*d^3*e^2 - 2*b*c^2*d^2*e^3 + b*d*e^4)*x^4 - 6*(b*c^4*d^4*e - 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x^2)*arctan(c*x))*sqrt(e*x^2 + d))/((c^4*d^6*e^2 - 2*c^2*d^5*e^3 + d^4*e^4)*x^7 + 2*(c^4*d^7*e - 2*c^2*d^6*e^2 + d^5*e^3)*x^5 + (c^4*d^8 - 2*c^2*d^7*e + d^6*e^2)*x^3)]","B",0
1226,1,1280,0,0.568678," ","integrate(arctan(a*x)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, a^{4} c^{5} - 20 \, a^{2} c^{4} d + {\left(15 \, a^{4} c^{2} d^{3} - 20 \, a^{2} c d^{4} + 8 \, d^{5}\right)} x^{6} + 8 \, c^{3} d^{2} + 3 \, {\left(15 \, a^{4} c^{3} d^{2} - 20 \, a^{2} c^{2} d^{3} + 8 \, c d^{4}\right)} x^{4} + 3 \, {\left(15 \, a^{4} c^{4} d - 20 \, a^{2} c^{3} d^{2} + 8 \, c^{2} d^{3}\right)} x^{2}\right)} \sqrt{a^{2} c - d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} - 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d - 3 \, a^{2} d^{2}\right)} x^{2} + 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c - a d\right)} \sqrt{a^{2} c - d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - 4 \, {\left(8 \, a^{5} c^{5} - 13 \, a^{3} c^{4} d + 5 \, a c^{3} d^{2} + {\left(7 \, a^{5} c^{3} d^{2} - 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 3 \, {\left(5 \, a^{5} c^{4} d - 8 \, a^{3} c^{3} d^{2} + 3 \, a c^{2} d^{3}\right)} x^{2} - {\left(8 \, {\left(a^{6} c^{3} d^{2} - 3 \, a^{4} c^{2} d^{3} + 3 \, a^{2} c d^{4} - d^{5}\right)} x^{5} + 20 \, {\left(a^{6} c^{4} d - 3 \, a^{4} c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3} - c d^{4}\right)} x^{3} + 15 \, {\left(a^{6} c^{5} - 3 \, a^{4} c^{4} d + 3 \, a^{2} c^{3} d^{2} - c^{2} d^{3}\right)} x\right)} \arctan\left(a x\right)\right)} \sqrt{d x^{2} + c}}{60 \, {\left(a^{6} c^{9} - 3 \, a^{4} c^{8} d + 3 \, a^{2} c^{7} d^{2} - c^{6} d^{3} + {\left(a^{6} c^{6} d^{3} - 3 \, a^{4} c^{5} d^{4} + 3 \, a^{2} c^{4} d^{5} - c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{6} c^{7} d^{2} - 3 \, a^{4} c^{6} d^{3} + 3 \, a^{2} c^{5} d^{4} - c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{6} c^{8} d - 3 \, a^{4} c^{7} d^{2} + 3 \, a^{2} c^{6} d^{3} - c^{5} d^{4}\right)} x^{2}\right)}}, \frac{{\left(15 \, a^{4} c^{5} - 20 \, a^{2} c^{4} d + {\left(15 \, a^{4} c^{2} d^{3} - 20 \, a^{2} c d^{4} + 8 \, d^{5}\right)} x^{6} + 8 \, c^{3} d^{2} + 3 \, {\left(15 \, a^{4} c^{3} d^{2} - 20 \, a^{2} c^{2} d^{3} + 8 \, c d^{4}\right)} x^{4} + 3 \, {\left(15 \, a^{4} c^{4} d - 20 \, a^{2} c^{3} d^{2} + 8 \, c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a^{2} c + d} \arctan\left(-\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c - d\right)} \sqrt{-a^{2} c + d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} - a c d + {\left(a^{3} c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(8 \, a^{5} c^{5} - 13 \, a^{3} c^{4} d + 5 \, a c^{3} d^{2} + {\left(7 \, a^{5} c^{3} d^{2} - 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 3 \, {\left(5 \, a^{5} c^{4} d - 8 \, a^{3} c^{3} d^{2} + 3 \, a c^{2} d^{3}\right)} x^{2} - {\left(8 \, {\left(a^{6} c^{3} d^{2} - 3 \, a^{4} c^{2} d^{3} + 3 \, a^{2} c d^{4} - d^{5}\right)} x^{5} + 20 \, {\left(a^{6} c^{4} d - 3 \, a^{4} c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3} - c d^{4}\right)} x^{3} + 15 \, {\left(a^{6} c^{5} - 3 \, a^{4} c^{4} d + 3 \, a^{2} c^{3} d^{2} - c^{2} d^{3}\right)} x\right)} \arctan\left(a x\right)\right)} \sqrt{d x^{2} + c}}{30 \, {\left(a^{6} c^{9} - 3 \, a^{4} c^{8} d + 3 \, a^{2} c^{7} d^{2} - c^{6} d^{3} + {\left(a^{6} c^{6} d^{3} - 3 \, a^{4} c^{5} d^{4} + 3 \, a^{2} c^{4} d^{5} - c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{6} c^{7} d^{2} - 3 \, a^{4} c^{6} d^{3} + 3 \, a^{2} c^{5} d^{4} - c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{6} c^{8} d - 3 \, a^{4} c^{7} d^{2} + 3 \, a^{2} c^{6} d^{3} - c^{5} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/60*((15*a^4*c^5 - 20*a^2*c^4*d + (15*a^4*c^2*d^3 - 20*a^2*c*d^4 + 8*d^5)*x^6 + 8*c^3*d^2 + 3*(15*a^4*c^3*d^2 - 20*a^2*c^2*d^3 + 8*c*d^4)*x^4 + 3*(15*a^4*c^4*d - 20*a^2*c^3*d^2 + 8*c^2*d^3)*x^2)*sqrt(a^2*c - d)*log((a^4*d^2*x^4 + 8*a^4*c^2 - 8*a^2*c*d + 2*(4*a^4*c*d - 3*a^2*d^2)*x^2 + 4*(a^3*d*x^2 + 2*a^3*c - a*d)*sqrt(a^2*c - d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 + 2*a^2*x^2 + 1)) - 4*(8*a^5*c^5 - 13*a^3*c^4*d + 5*a*c^3*d^2 + (7*a^5*c^3*d^2 - 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 3*(5*a^5*c^4*d - 8*a^3*c^3*d^2 + 3*a*c^2*d^3)*x^2 - (8*(a^6*c^3*d^2 - 3*a^4*c^2*d^3 + 3*a^2*c*d^4 - d^5)*x^5 + 20*(a^6*c^4*d - 3*a^4*c^3*d^2 + 3*a^2*c^2*d^3 - c*d^4)*x^3 + 15*(a^6*c^5 - 3*a^4*c^4*d + 3*a^2*c^3*d^2 - c^2*d^3)*x)*arctan(a*x))*sqrt(d*x^2 + c))/(a^6*c^9 - 3*a^4*c^8*d + 3*a^2*c^7*d^2 - c^6*d^3 + (a^6*c^6*d^3 - 3*a^4*c^5*d^4 + 3*a^2*c^4*d^5 - c^3*d^6)*x^6 + 3*(a^6*c^7*d^2 - 3*a^4*c^6*d^3 + 3*a^2*c^5*d^4 - c^4*d^5)*x^4 + 3*(a^6*c^8*d - 3*a^4*c^7*d^2 + 3*a^2*c^6*d^3 - c^5*d^4)*x^2), 1/30*((15*a^4*c^5 - 20*a^2*c^4*d + (15*a^4*c^2*d^3 - 20*a^2*c*d^4 + 8*d^5)*x^6 + 8*c^3*d^2 + 3*(15*a^4*c^3*d^2 - 20*a^2*c^2*d^3 + 8*c*d^4)*x^4 + 3*(15*a^4*c^4*d - 20*a^2*c^3*d^2 + 8*c^2*d^3)*x^2)*sqrt(-a^2*c + d)*arctan(-1/2*(a^2*d*x^2 + 2*a^2*c - d)*sqrt(-a^2*c + d)*sqrt(d*x^2 + c)/(a^3*c^2 - a*c*d + (a^3*c*d - a*d^2)*x^2)) - 2*(8*a^5*c^5 - 13*a^3*c^4*d + 5*a*c^3*d^2 + (7*a^5*c^3*d^2 - 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 3*(5*a^5*c^4*d - 8*a^3*c^3*d^2 + 3*a*c^2*d^3)*x^2 - (8*(a^6*c^3*d^2 - 3*a^4*c^2*d^3 + 3*a^2*c*d^4 - d^5)*x^5 + 20*(a^6*c^4*d - 3*a^4*c^3*d^2 + 3*a^2*c^2*d^3 - c*d^4)*x^3 + 15*(a^6*c^5 - 3*a^4*c^4*d + 3*a^2*c^3*d^2 - c^2*d^3)*x)*arctan(a*x))*sqrt(d*x^2 + c))/(a^6*c^9 - 3*a^4*c^8*d + 3*a^2*c^7*d^2 - c^6*d^3 + (a^6*c^6*d^3 - 3*a^4*c^5*d^4 + 3*a^2*c^4*d^5 - c^3*d^6)*x^6 + 3*(a^6*c^7*d^2 - 3*a^4*c^6*d^3 + 3*a^2*c^5*d^4 - c^4*d^5)*x^4 + 3*(a^6*c^8*d - 3*a^4*c^7*d^2 + 3*a^2*c^6*d^3 - c^5*d^4)*x^2)]","B",0
1227,1,1986,0,1.235671," ","integrate(arctan(a*x)/(d*x^2+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, a^{6} c^{7} - 70 \, a^{4} c^{6} d + 56 \, a^{2} c^{5} d^{2} + {\left(35 \, a^{6} c^{3} d^{4} - 70 \, a^{4} c^{2} d^{5} + 56 \, a^{2} c d^{6} - 16 \, d^{7}\right)} x^{8} - 16 \, c^{4} d^{3} + 4 \, {\left(35 \, a^{6} c^{4} d^{3} - 70 \, a^{4} c^{3} d^{4} + 56 \, a^{2} c^{2} d^{5} - 16 \, c d^{6}\right)} x^{6} + 6 \, {\left(35 \, a^{6} c^{5} d^{2} - 70 \, a^{4} c^{4} d^{3} + 56 \, a^{2} c^{3} d^{4} - 16 \, c^{2} d^{5}\right)} x^{4} + 4 \, {\left(35 \, a^{6} c^{6} d - 70 \, a^{4} c^{5} d^{2} + 56 \, a^{2} c^{4} d^{3} - 16 \, c^{3} d^{4}\right)} x^{2}\right)} \sqrt{a^{2} c - d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} - 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d - 3 \, a^{2} d^{2}\right)} x^{2} + 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c - a d\right)} \sqrt{a^{2} c - d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} + 2 \, a^{2} x^{2} + 1}\right) - 4 \, {\left(71 \, a^{7} c^{7} - 160 \, a^{5} c^{6} d + 122 \, a^{3} c^{5} d^{2} - 33 \, a c^{4} d^{3} + 3 \, {\left(19 \, a^{7} c^{4} d^{3} - 41 \, a^{5} c^{3} d^{4} + 30 \, a^{3} c^{2} d^{5} - 8 \, a c d^{6}\right)} x^{6} + {\left(182 \, a^{7} c^{5} d^{2} - 397 \, a^{5} c^{4} d^{3} + 293 \, a^{3} c^{3} d^{4} - 78 \, a c^{2} d^{5}\right)} x^{4} + {\left(196 \, a^{7} c^{6} d - 434 \, a^{5} c^{5} d^{2} + 325 \, a^{3} c^{4} d^{3} - 87 \, a c^{3} d^{4}\right)} x^{2} - 3 \, {\left(16 \, {\left(a^{8} c^{4} d^{3} - 4 \, a^{6} c^{3} d^{4} + 6 \, a^{4} c^{2} d^{5} - 4 \, a^{2} c d^{6} + d^{7}\right)} x^{7} + 56 \, {\left(a^{8} c^{5} d^{2} - 4 \, a^{6} c^{4} d^{3} + 6 \, a^{4} c^{3} d^{4} - 4 \, a^{2} c^{2} d^{5} + c d^{6}\right)} x^{5} + 70 \, {\left(a^{8} c^{6} d - 4 \, a^{6} c^{5} d^{2} + 6 \, a^{4} c^{4} d^{3} - 4 \, a^{2} c^{3} d^{4} + c^{2} d^{5}\right)} x^{3} + 35 \, {\left(a^{8} c^{7} - 4 \, a^{6} c^{6} d + 6 \, a^{4} c^{5} d^{2} - 4 \, a^{2} c^{4} d^{3} + c^{3} d^{4}\right)} x\right)} \arctan\left(a x\right)\right)} \sqrt{d x^{2} + c}}{420 \, {\left(a^{8} c^{12} - 4 \, a^{6} c^{11} d + 6 \, a^{4} c^{10} d^{2} - 4 \, a^{2} c^{9} d^{3} + c^{8} d^{4} + {\left(a^{8} c^{8} d^{4} - 4 \, a^{6} c^{7} d^{5} + 6 \, a^{4} c^{6} d^{6} - 4 \, a^{2} c^{5} d^{7} + c^{4} d^{8}\right)} x^{8} + 4 \, {\left(a^{8} c^{9} d^{3} - 4 \, a^{6} c^{8} d^{4} + 6 \, a^{4} c^{7} d^{5} - 4 \, a^{2} c^{6} d^{6} + c^{5} d^{7}\right)} x^{6} + 6 \, {\left(a^{8} c^{10} d^{2} - 4 \, a^{6} c^{9} d^{3} + 6 \, a^{4} c^{8} d^{4} - 4 \, a^{2} c^{7} d^{5} + c^{6} d^{6}\right)} x^{4} + 4 \, {\left(a^{8} c^{11} d - 4 \, a^{6} c^{10} d^{2} + 6 \, a^{4} c^{9} d^{3} - 4 \, a^{2} c^{8} d^{4} + c^{7} d^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left(35 \, a^{6} c^{7} - 70 \, a^{4} c^{6} d + 56 \, a^{2} c^{5} d^{2} + {\left(35 \, a^{6} c^{3} d^{4} - 70 \, a^{4} c^{2} d^{5} + 56 \, a^{2} c d^{6} - 16 \, d^{7}\right)} x^{8} - 16 \, c^{4} d^{3} + 4 \, {\left(35 \, a^{6} c^{4} d^{3} - 70 \, a^{4} c^{3} d^{4} + 56 \, a^{2} c^{2} d^{5} - 16 \, c d^{6}\right)} x^{6} + 6 \, {\left(35 \, a^{6} c^{5} d^{2} - 70 \, a^{4} c^{4} d^{3} + 56 \, a^{2} c^{3} d^{4} - 16 \, c^{2} d^{5}\right)} x^{4} + 4 \, {\left(35 \, a^{6} c^{6} d - 70 \, a^{4} c^{5} d^{2} + 56 \, a^{2} c^{4} d^{3} - 16 \, c^{3} d^{4}\right)} x^{2}\right)} \sqrt{-a^{2} c + d} \arctan\left(-\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c - d\right)} \sqrt{-a^{2} c + d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} - a c d + {\left(a^{3} c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(71 \, a^{7} c^{7} - 160 \, a^{5} c^{6} d + 122 \, a^{3} c^{5} d^{2} - 33 \, a c^{4} d^{3} + 3 \, {\left(19 \, a^{7} c^{4} d^{3} - 41 \, a^{5} c^{3} d^{4} + 30 \, a^{3} c^{2} d^{5} - 8 \, a c d^{6}\right)} x^{6} + {\left(182 \, a^{7} c^{5} d^{2} - 397 \, a^{5} c^{4} d^{3} + 293 \, a^{3} c^{3} d^{4} - 78 \, a c^{2} d^{5}\right)} x^{4} + {\left(196 \, a^{7} c^{6} d - 434 \, a^{5} c^{5} d^{2} + 325 \, a^{3} c^{4} d^{3} - 87 \, a c^{3} d^{4}\right)} x^{2} - 3 \, {\left(16 \, {\left(a^{8} c^{4} d^{3} - 4 \, a^{6} c^{3} d^{4} + 6 \, a^{4} c^{2} d^{5} - 4 \, a^{2} c d^{6} + d^{7}\right)} x^{7} + 56 \, {\left(a^{8} c^{5} d^{2} - 4 \, a^{6} c^{4} d^{3} + 6 \, a^{4} c^{3} d^{4} - 4 \, a^{2} c^{2} d^{5} + c d^{6}\right)} x^{5} + 70 \, {\left(a^{8} c^{6} d - 4 \, a^{6} c^{5} d^{2} + 6 \, a^{4} c^{4} d^{3} - 4 \, a^{2} c^{3} d^{4} + c^{2} d^{5}\right)} x^{3} + 35 \, {\left(a^{8} c^{7} - 4 \, a^{6} c^{6} d + 6 \, a^{4} c^{5} d^{2} - 4 \, a^{2} c^{4} d^{3} + c^{3} d^{4}\right)} x\right)} \arctan\left(a x\right)\right)} \sqrt{d x^{2} + c}}{210 \, {\left(a^{8} c^{12} - 4 \, a^{6} c^{11} d + 6 \, a^{4} c^{10} d^{2} - 4 \, a^{2} c^{9} d^{3} + c^{8} d^{4} + {\left(a^{8} c^{8} d^{4} - 4 \, a^{6} c^{7} d^{5} + 6 \, a^{4} c^{6} d^{6} - 4 \, a^{2} c^{5} d^{7} + c^{4} d^{8}\right)} x^{8} + 4 \, {\left(a^{8} c^{9} d^{3} - 4 \, a^{6} c^{8} d^{4} + 6 \, a^{4} c^{7} d^{5} - 4 \, a^{2} c^{6} d^{6} + c^{5} d^{7}\right)} x^{6} + 6 \, {\left(a^{8} c^{10} d^{2} - 4 \, a^{6} c^{9} d^{3} + 6 \, a^{4} c^{8} d^{4} - 4 \, a^{2} c^{7} d^{5} + c^{6} d^{6}\right)} x^{4} + 4 \, {\left(a^{8} c^{11} d - 4 \, a^{6} c^{10} d^{2} + 6 \, a^{4} c^{9} d^{3} - 4 \, a^{2} c^{8} d^{4} + c^{7} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/420*(3*(35*a^6*c^7 - 70*a^4*c^6*d + 56*a^2*c^5*d^2 + (35*a^6*c^3*d^4 - 70*a^4*c^2*d^5 + 56*a^2*c*d^6 - 16*d^7)*x^8 - 16*c^4*d^3 + 4*(35*a^6*c^4*d^3 - 70*a^4*c^3*d^4 + 56*a^2*c^2*d^5 - 16*c*d^6)*x^6 + 6*(35*a^6*c^5*d^2 - 70*a^4*c^4*d^3 + 56*a^2*c^3*d^4 - 16*c^2*d^5)*x^4 + 4*(35*a^6*c^6*d - 70*a^4*c^5*d^2 + 56*a^2*c^4*d^3 - 16*c^3*d^4)*x^2)*sqrt(a^2*c - d)*log((a^4*d^2*x^4 + 8*a^4*c^2 - 8*a^2*c*d + 2*(4*a^4*c*d - 3*a^2*d^2)*x^2 + 4*(a^3*d*x^2 + 2*a^3*c - a*d)*sqrt(a^2*c - d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 + 2*a^2*x^2 + 1)) - 4*(71*a^7*c^7 - 160*a^5*c^6*d + 122*a^3*c^5*d^2 - 33*a*c^4*d^3 + 3*(19*a^7*c^4*d^3 - 41*a^5*c^3*d^4 + 30*a^3*c^2*d^5 - 8*a*c*d^6)*x^6 + (182*a^7*c^5*d^2 - 397*a^5*c^4*d^3 + 293*a^3*c^3*d^4 - 78*a*c^2*d^5)*x^4 + (196*a^7*c^6*d - 434*a^5*c^5*d^2 + 325*a^3*c^4*d^3 - 87*a*c^3*d^4)*x^2 - 3*(16*(a^8*c^4*d^3 - 4*a^6*c^3*d^4 + 6*a^4*c^2*d^5 - 4*a^2*c*d^6 + d^7)*x^7 + 56*(a^8*c^5*d^2 - 4*a^6*c^4*d^3 + 6*a^4*c^3*d^4 - 4*a^2*c^2*d^5 + c*d^6)*x^5 + 70*(a^8*c^6*d - 4*a^6*c^5*d^2 + 6*a^4*c^4*d^3 - 4*a^2*c^3*d^4 + c^2*d^5)*x^3 + 35*(a^8*c^7 - 4*a^6*c^6*d + 6*a^4*c^5*d^2 - 4*a^2*c^4*d^3 + c^3*d^4)*x)*arctan(a*x))*sqrt(d*x^2 + c))/(a^8*c^12 - 4*a^6*c^11*d + 6*a^4*c^10*d^2 - 4*a^2*c^9*d^3 + c^8*d^4 + (a^8*c^8*d^4 - 4*a^6*c^7*d^5 + 6*a^4*c^6*d^6 - 4*a^2*c^5*d^7 + c^4*d^8)*x^8 + 4*(a^8*c^9*d^3 - 4*a^6*c^8*d^4 + 6*a^4*c^7*d^5 - 4*a^2*c^6*d^6 + c^5*d^7)*x^6 + 6*(a^8*c^10*d^2 - 4*a^6*c^9*d^3 + 6*a^4*c^8*d^4 - 4*a^2*c^7*d^5 + c^6*d^6)*x^4 + 4*(a^8*c^11*d - 4*a^6*c^10*d^2 + 6*a^4*c^9*d^3 - 4*a^2*c^8*d^4 + c^7*d^5)*x^2), 1/210*(3*(35*a^6*c^7 - 70*a^4*c^6*d + 56*a^2*c^5*d^2 + (35*a^6*c^3*d^4 - 70*a^4*c^2*d^5 + 56*a^2*c*d^6 - 16*d^7)*x^8 - 16*c^4*d^3 + 4*(35*a^6*c^4*d^3 - 70*a^4*c^3*d^4 + 56*a^2*c^2*d^5 - 16*c*d^6)*x^6 + 6*(35*a^6*c^5*d^2 - 70*a^4*c^4*d^3 + 56*a^2*c^3*d^4 - 16*c^2*d^5)*x^4 + 4*(35*a^6*c^6*d - 70*a^4*c^5*d^2 + 56*a^2*c^4*d^3 - 16*c^3*d^4)*x^2)*sqrt(-a^2*c + d)*arctan(-1/2*(a^2*d*x^2 + 2*a^2*c - d)*sqrt(-a^2*c + d)*sqrt(d*x^2 + c)/(a^3*c^2 - a*c*d + (a^3*c*d - a*d^2)*x^2)) - 2*(71*a^7*c^7 - 160*a^5*c^6*d + 122*a^3*c^5*d^2 - 33*a*c^4*d^3 + 3*(19*a^7*c^4*d^3 - 41*a^5*c^3*d^4 + 30*a^3*c^2*d^5 - 8*a*c*d^6)*x^6 + (182*a^7*c^5*d^2 - 397*a^5*c^4*d^3 + 293*a^3*c^3*d^4 - 78*a*c^2*d^5)*x^4 + (196*a^7*c^6*d - 434*a^5*c^5*d^2 + 325*a^3*c^4*d^3 - 87*a*c^3*d^4)*x^2 - 3*(16*(a^8*c^4*d^3 - 4*a^6*c^3*d^4 + 6*a^4*c^2*d^5 - 4*a^2*c*d^6 + d^7)*x^7 + 56*(a^8*c^5*d^2 - 4*a^6*c^4*d^3 + 6*a^4*c^3*d^4 - 4*a^2*c^2*d^5 + c*d^6)*x^5 + 70*(a^8*c^6*d - 4*a^6*c^5*d^2 + 6*a^4*c^4*d^3 - 4*a^2*c^3*d^4 + c^2*d^5)*x^3 + 35*(a^8*c^7 - 4*a^6*c^6*d + 6*a^4*c^5*d^2 - 4*a^2*c^4*d^3 + c^3*d^4)*x)*arctan(a*x))*sqrt(d*x^2 + c))/(a^8*c^12 - 4*a^6*c^11*d + 6*a^4*c^10*d^2 - 4*a^2*c^9*d^3 + c^8*d^4 + (a^8*c^8*d^4 - 4*a^6*c^7*d^5 + 6*a^4*c^6*d^6 - 4*a^2*c^5*d^7 + c^4*d^8)*x^8 + 4*(a^8*c^9*d^3 - 4*a^6*c^8*d^4 + 6*a^4*c^7*d^5 - 4*a^2*c^6*d^6 + c^5*d^7)*x^6 + 6*(a^8*c^10*d^2 - 4*a^6*c^9*d^3 + 6*a^4*c^8*d^4 - 4*a^2*c^7*d^5 + c^6*d^6)*x^4 + 4*(a^8*c^11*d - 4*a^6*c^10*d^2 + 6*a^4*c^9*d^3 - 4*a^2*c^8*d^4 + c^7*d^5)*x^2)]","B",0
1228,0,0,0,0.494092," ","integrate(x^m*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arctan(c*x))*x^m, x)","F",0
1229,0,0,0,0.430194," ","integrate(x^m*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*x^m, x)","F",0
1230,0,0,0,0.497589," ","integrate(x^m*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*x^m, x)","F",0
1231,0,0,0,0.418284," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{e x^{2} + d}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*x^m/(e*x^2 + d), x)","F",0
1232,0,0,0,0.510931," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*x^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1233,0,0,0,0.446998," ","integrate(x^m*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d} x^{m}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan(c*x))*sqrt(e*x^2 + d)*x^m, x)","F",0
1234,0,0,0,0.510364," ","integrate(x^m*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arctan\left(c x\right)\right)} \sqrt{e x^{2} + d} x^{m}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arctan(c*x))*sqrt(e*x^2 + d)*x^m, x)","F",0
1235,0,0,0,0.520179," ","integrate(x^m*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)} x^{m}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)*x^m, x)","F",0
1236,0,0,0,0.766207," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*x^m/sqrt(e*x^2 + d), x)","F",0
1237,0,0,0,0.697966," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)} x^{m}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)*x^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1238,0,0,0,0.540351," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)} x^{m}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)*x^m/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1239,0,0,0,0.515604," ","integrate(x^m*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{m}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^m, x)","F",0
1240,0,0,0,0.435279," ","integrate(x^(-2-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 2}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 2), x)","F",0
1241,0,0,0,0.563134," ","integrate(x^(-3-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 3}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 3), x)","F",0
1242,0,0,0,0.659788," ","integrate(x^(-4-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 4}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 4), x)","F",0
1243,0,0,0,0.547640," ","integrate(x^(-5-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 5}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 5), x)","F",0
1244,0,0,0,0.429888," ","integrate(x^(-6-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 6}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 6), x)","F",0
1245,0,0,0,0.446146," ","integrate(x^(-7-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 7}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 7), x)","F",0
1246,0,0,0,0.444649," ","integrate(x^(-8-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 8}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 8), x)","F",0
1247,1,289,0,0.476747," ","integrate(x^3*(e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{30 \, a^{2} c^{6} e x^{6} - 12 \, a b c^{5} e x^{5} + 3 \, {\left(15 \, a^{2} c^{6} d + b^{2} c^{4} e\right)} x^{4} - 10 \, {\left(3 \, a b c^{5} d - 2 \, a b c^{3} e\right)} x^{3} + {\left(15 \, b^{2} c^{4} d - 16 \, b^{2} c^{2} e\right)} x^{2} + 15 \, {\left(2 \, b^{2} c^{6} e x^{6} + 3 \, b^{2} c^{6} d x^{4} - 3 \, b^{2} c^{2} d + 2 \, b^{2} e\right)} \arctan\left(c x\right)^{2} + 30 \, {\left(3 \, a b c^{3} d - 2 \, a b c e\right)} x + 2 \, {\left(30 \, a b c^{6} e x^{6} + 45 \, a b c^{6} d x^{4} - 6 \, b^{2} c^{5} e x^{5} - 45 \, a b c^{2} d - 5 \, {\left(3 \, b^{2} c^{5} d - 2 \, b^{2} c^{3} e\right)} x^{3} + 30 \, a b e + 15 \, {\left(3 \, b^{2} c^{3} d - 2 \, b^{2} c e\right)} x\right)} \arctan\left(c x\right) - 2 \, {\left(30 \, b^{2} c^{2} d - 23 \, b^{2} e\right)} \log\left(c^{2} x^{2} + 1\right)}{180 \, c^{6}}"," ",0,"1/180*(30*a^2*c^6*e*x^6 - 12*a*b*c^5*e*x^5 + 3*(15*a^2*c^6*d + b^2*c^4*e)*x^4 - 10*(3*a*b*c^5*d - 2*a*b*c^3*e)*x^3 + (15*b^2*c^4*d - 16*b^2*c^2*e)*x^2 + 15*(2*b^2*c^6*e*x^6 + 3*b^2*c^6*d*x^4 - 3*b^2*c^2*d + 2*b^2*e)*arctan(c*x)^2 + 30*(3*a*b*c^3*d - 2*a*b*c*e)*x + 2*(30*a*b*c^6*e*x^6 + 45*a*b*c^6*d*x^4 - 6*b^2*c^5*e*x^5 - 45*a*b*c^2*d - 5*(3*b^2*c^5*d - 2*b^2*c^3*e)*x^3 + 30*a*b*e + 15*(3*b^2*c^3*d - 2*b^2*c*e)*x)*arctan(c*x) - 2*(30*b^2*c^2*d - 23*b^2*e)*log(c^2*x^2 + 1))/c^6","A",0
1248,0,0,0,0.435112," ","integrate(x^2*(e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e x^{4} + a^{2} d x^{2} + {\left(b^{2} e x^{4} + b^{2} d x^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e x^{4} + a b d x^{2}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e*x^4 + a^2*d*x^2 + (b^2*e*x^4 + b^2*d*x^2)*arctan(c*x)^2 + 2*(a*b*e*x^4 + a*b*d*x^2)*arctan(c*x), x)","F",0
1249,1,218,0,0.468219," ","integrate(x*(e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} c^{4} e x^{4} - 2 \, a b c^{3} e x^{3} + {\left(6 \, a^{2} c^{4} d + b^{2} c^{2} e\right)} x^{2} + 3 \, {\left(b^{2} c^{4} e x^{4} + 2 \, b^{2} c^{4} d x^{2} + 2 \, b^{2} c^{2} d - b^{2} e\right)} \arctan\left(c x\right)^{2} - 6 \, {\left(2 \, a b c^{3} d - a b c e\right)} x + 2 \, {\left(3 \, a b c^{4} e x^{4} + 6 \, a b c^{4} d x^{2} - b^{2} c^{3} e x^{3} + 6 \, a b c^{2} d - 3 \, a b e - 3 \, {\left(2 \, b^{2} c^{3} d - b^{2} c e\right)} x\right)} \arctan\left(c x\right) + 2 \, {\left(3 \, b^{2} c^{2} d - 2 \, b^{2} e\right)} \log\left(c^{2} x^{2} + 1\right)}{12 \, c^{4}}"," ",0,"1/12*(3*a^2*c^4*e*x^4 - 2*a*b*c^3*e*x^3 + (6*a^2*c^4*d + b^2*c^2*e)*x^2 + 3*(b^2*c^4*e*x^4 + 2*b^2*c^4*d*x^2 + 2*b^2*c^2*d - b^2*e)*arctan(c*x)^2 - 6*(2*a*b*c^3*d - a*b*c*e)*x + 2*(3*a*b*c^4*e*x^4 + 6*a*b*c^4*d*x^2 - b^2*c^3*e*x^3 + 6*a*b*c^2*d - 3*a*b*e - 3*(2*b^2*c^3*d - b^2*c*e)*x)*arctan(c*x) + 2*(3*b^2*c^2*d - 2*b^2*e)*log(c^2*x^2 + 1))/c^4","A",0
1250,0,0,0,0.446193," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e x^{2} + a^{2} d + {\left(b^{2} e x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e x^{2} + a b d\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e*x^2 + a^2*d + (b^2*e*x^2 + b^2*d)*arctan(c*x)^2 + 2*(a*b*e*x^2 + a*b*d)*arctan(c*x), x)","F",0
1251,0,0,0,0.410556," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} e x^{2} + a^{2} d + {\left(b^{2} e x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e x^{2} + a b d\right)} \arctan\left(c x\right)}{x}, x\right)"," ",0,"integral((a^2*e*x^2 + a^2*d + (b^2*e*x^2 + b^2*d)*arctan(c*x)^2 + 2*(a*b*e*x^2 + a*b*d)*arctan(c*x))/x, x)","F",0
1252,0,0,0,0.459196," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} e x^{2} + a^{2} d + {\left(b^{2} e x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e x^{2} + a b d\right)} \arctan\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*e*x^2 + a^2*d + (b^2*e*x^2 + b^2*d)*arctan(c*x)^2 + 2*(a*b*e*x^2 + a*b*d)*arctan(c*x))/x^2, x)","F",0
1253,0,0,0,0.504238," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} e x^{2} + a^{2} d + {\left(b^{2} e x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e x^{2} + a b d\right)} \arctan\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*e*x^2 + a^2*d + (b^2*e*x^2 + b^2*d)*arctan(c*x)^2 + 2*(a*b*e*x^2 + a*b*d)*arctan(c*x))/x^3, x)","F",0
1254,1,530,0,0.551521," ","integrate(x^3*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{315 \, a^{2} c^{8} e^{2} x^{8} - 90 \, a b c^{7} e^{2} x^{7} + 15 \, {\left(56 \, a^{2} c^{8} d e + b^{2} c^{6} e^{2}\right)} x^{6} - 42 \, {\left(8 \, a b c^{7} d e - 3 \, a b c^{5} e^{2}\right)} x^{5} + 6 \, {\left(105 \, a^{2} c^{8} d^{2} + 14 \, b^{2} c^{6} d e - 9 \, b^{2} c^{4} e^{2}\right)} x^{4} - 70 \, {\left(6 \, a b c^{7} d^{2} - 8 \, a b c^{5} d e + 3 \, a b c^{3} e^{2}\right)} x^{3} + {\left(210 \, b^{2} c^{6} d^{2} - 448 \, b^{2} c^{4} d e + 213 \, b^{2} c^{2} e^{2}\right)} x^{2} + 105 \, {\left(3 \, b^{2} c^{8} e^{2} x^{8} + 8 \, b^{2} c^{8} d e x^{6} + 6 \, b^{2} c^{8} d^{2} x^{4} - 6 \, b^{2} c^{4} d^{2} + 8 \, b^{2} c^{2} d e - 3 \, b^{2} e^{2}\right)} \arctan\left(c x\right)^{2} + 210 \, {\left(6 \, a b c^{5} d^{2} - 8 \, a b c^{3} d e + 3 \, a b c e^{2}\right)} x + 2 \, {\left(315 \, a b c^{8} e^{2} x^{8} + 840 \, a b c^{8} d e x^{6} - 45 \, b^{2} c^{7} e^{2} x^{7} + 630 \, a b c^{8} d^{2} x^{4} - 630 \, a b c^{4} d^{2} + 840 \, a b c^{2} d e - 21 \, {\left(8 \, b^{2} c^{7} d e - 3 \, b^{2} c^{5} e^{2}\right)} x^{5} - 315 \, a b e^{2} - 35 \, {\left(6 \, b^{2} c^{7} d^{2} - 8 \, b^{2} c^{5} d e + 3 \, b^{2} c^{3} e^{2}\right)} x^{3} + 105 \, {\left(6 \, b^{2} c^{5} d^{2} - 8 \, b^{2} c^{3} d e + 3 \, b^{2} c e^{2}\right)} x\right)} \arctan\left(c x\right) - 8 \, {\left(105 \, b^{2} c^{4} d^{2} - 161 \, b^{2} c^{2} d e + 66 \, b^{2} e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{2520 \, c^{8}}"," ",0,"1/2520*(315*a^2*c^8*e^2*x^8 - 90*a*b*c^7*e^2*x^7 + 15*(56*a^2*c^8*d*e + b^2*c^6*e^2)*x^6 - 42*(8*a*b*c^7*d*e - 3*a*b*c^5*e^2)*x^5 + 6*(105*a^2*c^8*d^2 + 14*b^2*c^6*d*e - 9*b^2*c^4*e^2)*x^4 - 70*(6*a*b*c^7*d^2 - 8*a*b*c^5*d*e + 3*a*b*c^3*e^2)*x^3 + (210*b^2*c^6*d^2 - 448*b^2*c^4*d*e + 213*b^2*c^2*e^2)*x^2 + 105*(3*b^2*c^8*e^2*x^8 + 8*b^2*c^8*d*e*x^6 + 6*b^2*c^8*d^2*x^4 - 6*b^2*c^4*d^2 + 8*b^2*c^2*d*e - 3*b^2*e^2)*arctan(c*x)^2 + 210*(6*a*b*c^5*d^2 - 8*a*b*c^3*d*e + 3*a*b*c*e^2)*x + 2*(315*a*b*c^8*e^2*x^8 + 840*a*b*c^8*d*e*x^6 - 45*b^2*c^7*e^2*x^7 + 630*a*b*c^8*d^2*x^4 - 630*a*b*c^4*d^2 + 840*a*b*c^2*d*e - 21*(8*b^2*c^7*d*e - 3*b^2*c^5*e^2)*x^5 - 315*a*b*e^2 - 35*(6*b^2*c^7*d^2 - 8*b^2*c^5*d*e + 3*b^2*c^3*e^2)*x^3 + 105*(6*b^2*c^5*d^2 - 8*b^2*c^3*d*e + 3*b^2*c*e^2)*x)*arctan(c*x) - 8*(105*b^2*c^4*d^2 - 161*b^2*c^2*d*e + 66*b^2*e^2)*log(c^2*x^2 + 1))/c^8","A",0
1255,0,0,0,0.437388," ","integrate(x^2*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e^{2} x^{6} + 2 \, a^{2} d e x^{4} + a^{2} d^{2} x^{2} + {\left(b^{2} e^{2} x^{6} + 2 \, b^{2} d e x^{4} + b^{2} d^{2} x^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{6} + 2 \, a b d e x^{4} + a b d^{2} x^{2}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e^2*x^6 + 2*a^2*d*e*x^4 + a^2*d^2*x^2 + (b^2*e^2*x^6 + 2*b^2*d*e*x^4 + b^2*d^2*x^2)*arctan(c*x)^2 + 2*(a*b*e^2*x^6 + 2*a*b*d*e*x^4 + a*b*d^2*x^2)*arctan(c*x), x)","F",0
1256,1,416,0,0.548774," ","integrate(x*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{30 \, a^{2} c^{6} e^{2} x^{6} - 12 \, a b c^{5} e^{2} x^{5} + 3 \, {\left(30 \, a^{2} c^{6} d e + b^{2} c^{4} e^{2}\right)} x^{4} - 20 \, {\left(3 \, a b c^{5} d e - a b c^{3} e^{2}\right)} x^{3} + 2 \, {\left(45 \, a^{2} c^{6} d^{2} + 15 \, b^{2} c^{4} d e - 8 \, b^{2} c^{2} e^{2}\right)} x^{2} + 30 \, {\left(b^{2} c^{6} e^{2} x^{6} + 3 \, b^{2} c^{6} d e x^{4} + 3 \, b^{2} c^{6} d^{2} x^{2} + 3 \, b^{2} c^{4} d^{2} - 3 \, b^{2} c^{2} d e + b^{2} e^{2}\right)} \arctan\left(c x\right)^{2} - 60 \, {\left(3 \, a b c^{5} d^{2} - 3 \, a b c^{3} d e + a b c e^{2}\right)} x + 4 \, {\left(15 \, a b c^{6} e^{2} x^{6} + 45 \, a b c^{6} d e x^{4} - 3 \, b^{2} c^{5} e^{2} x^{5} + 45 \, a b c^{6} d^{2} x^{2} + 45 \, a b c^{4} d^{2} - 45 \, a b c^{2} d e + 15 \, a b e^{2} - 5 \, {\left(3 \, b^{2} c^{5} d e - b^{2} c^{3} e^{2}\right)} x^{3} - 15 \, {\left(3 \, b^{2} c^{5} d^{2} - 3 \, b^{2} c^{3} d e + b^{2} c e^{2}\right)} x\right)} \arctan\left(c x\right) + 2 \, {\left(45 \, b^{2} c^{4} d^{2} - 60 \, b^{2} c^{2} d e + 23 \, b^{2} e^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{180 \, c^{6}}"," ",0,"1/180*(30*a^2*c^6*e^2*x^6 - 12*a*b*c^5*e^2*x^5 + 3*(30*a^2*c^6*d*e + b^2*c^4*e^2)*x^4 - 20*(3*a*b*c^5*d*e - a*b*c^3*e^2)*x^3 + 2*(45*a^2*c^6*d^2 + 15*b^2*c^4*d*e - 8*b^2*c^2*e^2)*x^2 + 30*(b^2*c^6*e^2*x^6 + 3*b^2*c^6*d*e*x^4 + 3*b^2*c^6*d^2*x^2 + 3*b^2*c^4*d^2 - 3*b^2*c^2*d*e + b^2*e^2)*arctan(c*x)^2 - 60*(3*a*b*c^5*d^2 - 3*a*b*c^3*d*e + a*b*c*e^2)*x + 4*(15*a*b*c^6*e^2*x^6 + 45*a*b*c^6*d*e*x^4 - 3*b^2*c^5*e^2*x^5 + 45*a*b*c^6*d^2*x^2 + 45*a*b*c^4*d^2 - 45*a*b*c^2*d*e + 15*a*b*e^2 - 5*(3*b^2*c^5*d*e - b^2*c^3*e^2)*x^3 - 15*(3*b^2*c^5*d^2 - 3*b^2*c^3*d*e + b^2*c*e^2)*x)*arctan(c*x) + 2*(45*b^2*c^4*d^2 - 60*b^2*c^2*d*e + 23*b^2*e^2)*log(c^2*x^2 + 1))/c^6","A",0
1257,0,0,0,0.466331," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left(b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right)} \arctan\left(c x\right), x\right)"," ",0,"integral(a^2*e^2*x^4 + 2*a^2*d*e*x^2 + a^2*d^2 + (b^2*e^2*x^4 + 2*b^2*d*e*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*e^2*x^4 + 2*a*b*d*e*x^2 + a*b*d^2)*arctan(c*x), x)","F",0
1258,0,0,0,0.472019," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left(b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right)} \arctan\left(c x\right)}{x}, x\right)"," ",0,"integral((a^2*e^2*x^4 + 2*a^2*d*e*x^2 + a^2*d^2 + (b^2*e^2*x^4 + 2*b^2*d*e*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*e^2*x^4 + 2*a*b*d*e*x^2 + a*b*d^2)*arctan(c*x))/x, x)","F",0
1259,0,0,0,0.417354," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left(b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right)} \arctan\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*e^2*x^4 + 2*a^2*d*e*x^2 + a^2*d^2 + (b^2*e^2*x^4 + 2*b^2*d*e*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*e^2*x^4 + 2*a*b*d*e*x^2 + a*b*d^2)*arctan(c*x))/x^2, x)","F",0
1260,0,0,0,0.442839," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left(b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right)} \arctan\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*e^2*x^4 + 2*a^2*d*e*x^2 + a^2*d^2 + (b^2*e^2*x^4 + 2*b^2*d*e*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*e^2*x^4 + 2*a*b*d*e*x^2 + a*b*d^2)*arctan(c*x))/x^3, x)","F",0
1261,0,0,0,0.637567," ","integrate(x^3*(a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \arctan\left(c x\right)^{2} + 2 \, a b x^{3} \arctan\left(c x\right) + a^{2} x^{3}}{e x^{2} + d}, x\right)"," ",0,"integral((b^2*x^3*arctan(c*x)^2 + 2*a*b*x^3*arctan(c*x) + a^2*x^3)/(e*x^2 + d), x)","F",0
1262,0,0,0,0.438581," ","integrate(x^2*(a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \arctan\left(c x\right)^{2} + 2 \, a b x^{2} \arctan\left(c x\right) + a^{2} x^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b^2*x^2*arctan(c*x)^2 + 2*a*b*x^2*arctan(c*x) + a^2*x^2)/(e*x^2 + d), x)","F",0
1263,0,0,0,0.481381," ","integrate(x*(a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \arctan\left(c x\right)^{2} + 2 \, a b x \arctan\left(c x\right) + a^{2} x}{e x^{2} + d}, x\right)"," ",0,"integral((b^2*x*arctan(c*x)^2 + 2*a*b*x*arctan(c*x) + a^2*x)/(e*x^2 + d), x)","F",0
1264,0,0,0,0.460056," ","integrate((a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^2 + d), x)","F",0
1265,0,0,0,0.404964," ","integrate((a+b*arctan(c*x))^2/x/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{3} + d x}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^3 + d*x), x)","F",0
1266,0,0,0,0.454183," ","integrate((a+b*arctan(c*x))^2/x^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^4 + d*x^2), x)","F",0
1267,0,0,0,0.635078," ","integrate((a+b*arctan(c*x))^2/x^3/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e x^{5} + d x^{3}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e*x^5 + d*x^3), x)","F",0
1268,0,0,0,0.397624," ","integrate(x^3*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \arctan\left(c x\right)^{2} + 2 \, a b x^{3} \arctan\left(c x\right) + a^{2} x^{3}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^3*arctan(c*x)^2 + 2*a*b*x^3*arctan(c*x) + a^2*x^3)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1269,0,0,0,0.460048," ","integrate(x^2*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \arctan\left(c x\right)^{2} + 2 \, a b x^{2} \arctan\left(c x\right) + a^{2} x^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^2*arctan(c*x)^2 + 2*a*b*x^2*arctan(c*x) + a^2*x^2)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1270,0,0,0,0.433005," ","integrate(x*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \arctan\left(c x\right)^{2} + 2 \, a b x \arctan\left(c x\right) + a^{2} x}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x*arctan(c*x)^2 + 2*a*b*x*arctan(c*x) + a^2*x)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1271,0,0,0,0.580147," ","integrate((a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1272,0,0,0,0.401268," ","integrate((a+b*arctan(c*x))^2/x/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
1273,0,0,0,0.419904," ","integrate((a+b*arctan(c*x))^2/x^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
1274,0,0,0,0.398564," ","integrate((a+b*arctan(c*x))^2/x^3/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
1275,1,72,0,0.391619," ","integrate(x^4*arctan(x)*log(x^2+1),x, algorithm=""fricas"")","\frac{9}{200} \, x^{4} - \frac{77}{300} \, x^{2} - \frac{2}{75} \, {\left(3 \, x^{5} - 5 \, x^{3} + 15 \, x\right)} \arctan\left(x\right) + \frac{1}{5} \, \arctan\left(x\right)^{2} + \frac{1}{300} \, {\left(60 \, x^{5} \arctan\left(x\right) - 15 \, x^{4} + 30 \, x^{2} + 137\right)} \log\left(x^{2} + 1\right) - \frac{1}{20} \, \log\left(x^{2} + 1\right)^{2}"," ",0,"9/200*x^4 - 77/300*x^2 - 2/75*(3*x^5 - 5*x^3 + 15*x)*arctan(x) + 1/5*arctan(x)^2 + 1/300*(60*x^5*arctan(x) - 15*x^4 + 30*x^2 + 137)*log(x^2 + 1) - 1/20*log(x^2 + 1)^2","A",0
1276,1,49,0,0.391167," ","integrate(x^3*arctan(x)*log(x^2+1),x, algorithm=""fricas"")","\frac{7}{72} \, x^{3} - \frac{1}{24} \, {\left(3 \, x^{4} - 6 \, x^{2} - 25\right)} \arctan\left(x\right) - \frac{1}{12} \, {\left(x^{3} - 3 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) - 3 \, x\right)} \log\left(x^{2} + 1\right) - \frac{25}{24} \, x"," ",0,"7/72*x^3 - 1/24*(3*x^4 - 6*x^2 - 25)*arctan(x) - 1/12*(x^3 - 3*(x^4 - 1)*arctan(x) - 3*x)*log(x^2 + 1) - 25/24*x","A",0
1277,1,55,0,0.396125," ","integrate(x^2*arctan(x)*log(x^2+1),x, algorithm=""fricas"")","\frac{5}{18} \, x^{2} - \frac{2}{9} \, {\left(x^{3} - 3 \, x\right)} \arctan\left(x\right) - \frac{1}{3} \, \arctan\left(x\right)^{2} + \frac{1}{18} \, {\left(6 \, x^{3} \arctan\left(x\right) - 3 \, x^{2} - 11\right)} \log\left(x^{2} + 1\right) + \frac{1}{12} \, \log\left(x^{2} + 1\right)^{2}"," ",0,"5/18*x^2 - 2/9*(x^3 - 3*x)*arctan(x) - 1/3*arctan(x)^2 + 1/18*(6*x^3*arctan(x) - 3*x^2 - 11)*log(x^2 + 1) + 1/12*log(x^2 + 1)^2","A",0
1278,1,33,0,0.390900," ","integrate(x*arctan(x)*log(x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x^{2} + 3\right)} \arctan\left(x\right) + \frac{1}{2} \, {\left({\left(x^{2} + 1\right)} \arctan\left(x\right) - x\right)} \log\left(x^{2} + 1\right) + \frac{3}{2} \, x"," ",0,"-1/2*(x^2 + 3)*arctan(x) + 1/2*((x^2 + 1)*arctan(x) - x)*log(x^2 + 1) + 3/2*x","A",0
1279,1,33,0,0.389921," ","integrate(arctan(x)*log(x^2+1),x, algorithm=""fricas"")","-2 \, x \arctan\left(x\right) + \arctan\left(x\right)^{2} + {\left(x \arctan\left(x\right) + 1\right)} \log\left(x^{2} + 1\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right)^{2}"," ",0,"-2*x*arctan(x) + arctan(x)^2 + (x*arctan(x) + 1)*log(x^2 + 1) - 1/4*log(x^2 + 1)^2","A",0
1280,0,0,0,0.398069," ","integrate(arctan(x)*log(x^2+1)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x}, x\right)"," ",0,"integral(arctan(x)*log(x^2 + 1)/x, x)","F",0
1281,0,0,0,0.496533," ","integrate(arctan(x)*log(x^2+1)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x^{2}}, x\right)"," ",0,"integral(arctan(x)*log(x^2 + 1)/x^2, x)","F",0
1282,0,0,0,0.423682," ","integrate(arctan(x)*log(x^2+1)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x^{3}}, x\right)"," ",0,"integral(arctan(x)*log(x^2 + 1)/x^3, x)","F",0
1283,0,0,0,0.433732," ","integrate(arctan(x)*log(x^2+1)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x^{4}}, x\right)"," ",0,"integral(arctan(x)*log(x^2 + 1)/x^4, x)","F",0
1284,0,0,0,0.432426," ","integrate(arctan(x)*log(x^2+1)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x^{5}}, x\right)"," ",0,"integral(arctan(x)*log(x^2 + 1)/x^5, x)","F",0
1285,0,0,0,0.595616," ","integrate(arctan(x)*log(x^2+1)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x^{6}}, x\right)"," ",0,"integral(arctan(x)*log(x^2 + 1)/x^6, x)","F",0
1286,1,220,0,0.558765," ","integrate(x^4*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""fricas"")","\frac{80 \, a c^{3} e x^{3} + 24 \, {\left(5 \, a c^{5} d - 2 \, a c^{5} e\right)} x^{5} - 3 \, {\left(10 \, b c^{4} d - 9 \, b c^{4} e\right)} x^{4} - 240 \, a c e x + 120 \, b e \arctan\left(c x\right)^{2} - 30 \, b e \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(30 \, b c^{2} d - 77 \, b c^{2} e\right)} x^{2} + 8 \, {\left(10 \, b c^{3} e x^{3} + 3 \, {\left(5 \, b c^{5} d - 2 \, b c^{5} e\right)} x^{5} - 30 \, b c e x + 30 \, a e\right)} \arctan\left(c x\right) + 2 \, {\left(60 \, b c^{5} e x^{5} \arctan\left(c x\right) + 60 \, a c^{5} e x^{5} - 15 \, b c^{4} e x^{4} + 30 \, b c^{2} e x^{2} - 30 \, b d + 137 \, b e\right)} \log\left(c^{2} x^{2} + 1\right)}{600 \, c^{5}}"," ",0,"1/600*(80*a*c^3*e*x^3 + 24*(5*a*c^5*d - 2*a*c^5*e)*x^5 - 3*(10*b*c^4*d - 9*b*c^4*e)*x^4 - 240*a*c*e*x + 120*b*e*arctan(c*x)^2 - 30*b*e*log(c^2*x^2 + 1)^2 + 2*(30*b*c^2*d - 77*b*c^2*e)*x^2 + 8*(10*b*c^3*e*x^3 + 3*(5*b*c^5*d - 2*b*c^5*e)*x^5 - 30*b*c*e*x + 30*a*e)*arctan(c*x) + 2*(60*b*c^5*e*x^5*arctan(c*x) + 60*a*c^5*e*x^5 - 15*b*c^4*e*x^4 + 30*b*c^2*e*x^2 - 30*b*d + 137*b*e)*log(c^2*x^2 + 1))/c^5","A",0
1287,1,178,0,0.477262," ","integrate(x^3*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""fricas"")","\frac{18 \, a c^{2} e x^{2} + 9 \, {\left(2 \, a c^{4} d - a c^{4} e\right)} x^{4} - {\left(6 \, b c^{3} d - 7 \, b c^{3} e\right)} x^{3} + 3 \, {\left(6 \, b c d - 25 \, b c e\right)} x + 3 \, {\left(6 \, b c^{2} e x^{2} + 3 \, {\left(2 \, b c^{4} d - b c^{4} e\right)} x^{4} - 6 \, b d + 25 \, b e\right)} \arctan\left(c x\right) + 6 \, {\left(3 \, a c^{4} e x^{4} - b c^{3} e x^{3} + 3 \, b c e x - 3 \, a e + 3 \, {\left(b c^{4} e x^{4} - b e\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{72 \, c^{4}}"," ",0,"1/72*(18*a*c^2*e*x^2 + 9*(2*a*c^4*d - a*c^4*e)*x^4 - (6*b*c^3*d - 7*b*c^3*e)*x^3 + 3*(6*b*c*d - 25*b*c*e)*x + 3*(6*b*c^2*e*x^2 + 3*(2*b*c^4*d - b*c^4*e)*x^4 - 6*b*d + 25*b*e)*arctan(c*x) + 6*(3*a*c^4*e*x^4 - b*c^3*e*x^3 + 3*b*c*e*x - 3*a*e + 3*(b*c^4*e*x^4 - b*e)*arctan(c*x))*log(c^2*x^2 + 1))/c^4","A",0
1288,1,169,0,0.456340," ","integrate(x^2*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""fricas"")","\frac{24 \, a c e x + 4 \, {\left(3 \, a c^{3} d - 2 \, a c^{3} e\right)} x^{3} - 12 \, b e \arctan\left(c x\right)^{2} + 3 \, b e \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(3 \, b c^{2} d - 5 \, b c^{2} e\right)} x^{2} + 4 \, {\left(6 \, b c e x + {\left(3 \, b c^{3} d - 2 \, b c^{3} e\right)} x^{3} - 6 \, a e\right)} \arctan\left(c x\right) + 2 \, {\left(6 \, b c^{3} e x^{3} \arctan\left(c x\right) + 6 \, a c^{3} e x^{3} - 3 \, b c^{2} e x^{2} + 3 \, b d - 11 \, b e\right)} \log\left(c^{2} x^{2} + 1\right)}{36 \, c^{3}}"," ",0,"1/36*(24*a*c*e*x + 4*(3*a*c^3*d - 2*a*c^3*e)*x^3 - 12*b*e*arctan(c*x)^2 + 3*b*e*log(c^2*x^2 + 1)^2 - 2*(3*b*c^2*d - 5*b*c^2*e)*x^2 + 4*(6*b*c*e*x + (3*b*c^3*d - 2*b*c^3*e)*x^3 - 6*a*e)*arctan(c*x) + 2*(6*b*c^3*e*x^3*arctan(c*x) + 6*a*c^3*e*x^3 - 3*b*c^2*e*x^2 + 3*b*d - 11*b*e)*log(c^2*x^2 + 1))/c^3","A",0
1289,1,116,0,0.420650," ","integrate(x*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""fricas"")","\frac{{\left(a c^{2} d - a c^{2} e\right)} x^{2} - {\left(b c d - 3 \, b c e\right)} x + {\left({\left(b c^{2} d - b c^{2} e\right)} x^{2} + b d - 3 \, b e\right)} \arctan\left(c x\right) + {\left(a c^{2} e x^{2} - b c e x + a e + {\left(b c^{2} e x^{2} + b e\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{2 \, c^{2}}"," ",0,"1/2*((a*c^2*d - a*c^2*e)*x^2 - (b*c*d - 3*b*c*e)*x + ((b*c^2*d - b*c^2*e)*x^2 + b*d - 3*b*e)*arctan(c*x) + (a*c^2*e*x^2 - b*c*e*x + a*e + (b*c^2*e*x^2 + b*e)*arctan(c*x))*log(c^2*x^2 + 1))/c^2","A",0
1290,1,105,0,0.458097," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""fricas"")","\frac{4 \, b e \arctan\left(c x\right)^{2} - b e \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(a c d - 2 \, a c e\right)} x + 4 \, {\left(2 \, a e + {\left(b c d - 2 \, b c e\right)} x\right)} \arctan\left(c x\right) + 2 \, {\left(2 \, b c e x \arctan\left(c x\right) + 2 \, a c e x - b d + 2 \, b e\right)} \log\left(c^{2} x^{2} + 1\right)}{4 \, c}"," ",0,"1/4*(4*b*e*arctan(c*x)^2 - b*e*log(c^2*x^2 + 1)^2 + 4*(a*c*d - 2*a*c*e)*x + 4*(2*a*e + (b*c*d - 2*b*c*e)*x)*arctan(c*x) + 2*(2*b*c*e*x*arctan(c*x) + 2*a*c*e*x - b*d + 2*b*e)*log(c^2*x^2 + 1))/c","A",0
1291,0,0,0,0.496393," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)}{x}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x, x)","F",0
1292,0,0,0,0.423063," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{2}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x^2, x)","F",0
1293,0,0,0,0.425939," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{3}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x^3, x)","F",0
1294,0,0,0,0.600870," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{4}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x^4, x)","F",0
1295,0,0,0,0.533729," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{5}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x^5, x)","F",0
1296,0,0,0,0.494089," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{6}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x^6, x)","F",0
1297,0,0,0,0.584985," ","integrate(x*(a+b*arctan(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""fricas"")","{\rm integral}\left(b d x \arctan\left(c x\right) + a d x + {\left(b e x \arctan\left(c x\right) + a e x\right)} \log\left(g x^{2} + f\right), x\right)"," ",0,"integral(b*d*x*arctan(c*x) + a*d*x + (b*e*x*arctan(c*x) + a*e*x)*log(g*x^2 + f), x)","F",0
1298,0,0,0,0.428505," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""fricas"")","{\rm integral}\left(b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right), x\right)"," ",0,"integral(b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(g*x^2 + f), x)","F",0
1299,0,0,0,0.613723," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(g*x^2 + f))/x, x)","F",0
1300,0,0,0,0.451691," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x^{2}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(g*x^2 + f))/x^2, x)","F",0
1301,0,0,0,0.495909," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \arctan\left(c x\right) + a d + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x^{3}}, x\right)"," ",0,"integral((b*d*arctan(c*x) + a*d + (b*e*arctan(c*x) + a*e)*log(g*x^2 + f))/x^3, x)","F",0
