1,0,0,0,0.000000," ","integrate(x^5*(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + 2 \, b \int \frac{x^{5} \cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + x^{5} \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + x^{5} \cos\left(d x^{2} + c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"1/6*a*x^6 + 2*b*integrate((x^5*cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + x^5*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + x^5*cos(d*x^2 + c))/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
2,0,0,0,0.000000," ","integrate(x^4*(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + 2 \, b \int \frac{x^{4} \cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + x^{4} \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + x^{4} \cos\left(d x^{2} + c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"1/5*a*x^5 + 2*b*integrate((x^4*cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + x^4*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + x^4*cos(d*x^2 + c))/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
3,0,0,0,0.000000," ","integrate(x^3*(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + 2 \, b \int \frac{x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + x^{3} \cos\left(d x^{2} + c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"1/4*a*x^4 + 2*b*integrate((x^3*cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + x^3*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + x^3*cos(d*x^2 + c))/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
4,0,0,0,0.000000," ","integrate(x^2*(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + 2 \, b \int \frac{x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + x^{2} \cos\left(d x^{2} + c\right)}{\cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x^{2} + 2 \, c\right) + 1}\,{d x}"," ",0,"1/3*a*x^3 + 2*b*integrate((x^2*cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + x^2*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + x^2*cos(d*x^2 + c))/(cos(2*d*x^2 + 2*c)^2 + sin(2*d*x^2 + 2*c)^2 + 2*cos(2*d*x^2 + 2*c) + 1), x)","F",0
5,1,31,0,0.311423," ","integrate(x*(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{b \log\left(\sec\left(d x^{2} + c\right) + \tan\left(d x^{2} + c\right)\right)}{2 \, d}"," ",0,"1/2*a*x^2 + 1/2*b*log(sec(d*x^2 + c) + tan(d*x^2 + c))/d","A",0
6,0,0,0,0.000000," ","integrate((a+b*sec(d*x^2+c))/x,x, algorithm=""maxima"")","2 \, b \int \frac{\cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + \cos\left(d x^{2} + c\right)}{x \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x \cos\left(2 \, d x^{2} + 2 \, c\right) + x}\,{d x} + a \log\left(x\right)"," ",0,"2*b*integrate((cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + cos(d*x^2 + c))/(x*cos(2*d*x^2 + 2*c)^2 + x*sin(2*d*x^2 + 2*c)^2 + 2*x*cos(2*d*x^2 + 2*c) + x), x) + a*log(x)","F",0
7,0,0,0,0.000000," ","integrate((a+b*sec(d*x^2+c))/x^2,x, algorithm=""maxima"")","2 \, b \int \frac{\cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + \cos\left(d x^{2} + c\right)}{x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{2}}\,{d x} - \frac{a}{x}"," ",0,"2*b*integrate((cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + cos(d*x^2 + c))/(x^2*cos(2*d*x^2 + 2*c)^2 + x^2*sin(2*d*x^2 + 2*c)^2 + 2*x^2*cos(2*d*x^2 + 2*c) + x^2), x) - a/x","F",0
8,0,0,0,0.000000," ","integrate(x^5*(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} x^{6} + \frac{b^{2} x^{4} \sin\left(2 \, d x^{2} + 2 \, c\right) + 4 \, {\left(d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d\right)} \int \frac{a b d x^{5} \cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + a b d x^{5} \cos\left(d x^{2} + c\right) + {\left(a b d x^{5} \sin\left(d x^{2} + c\right) - b^{2} x^{3}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d}\,{d x}}{d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d}"," ",0,"1/6*a^2*x^6 + (b^2*x^4*sin(2*d*x^2 + 2*c) + (d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d)*integrate(4*(a*b*d*x^5*cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + a*b*d*x^5*cos(d*x^2 + c) + (a*b*d*x^5*sin(d*x^2 + c) - b^2*x^3)*sin(2*d*x^2 + 2*c))/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d), x))/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d)","F",0
9,-1,0,0,0.000000," ","integrate(x^4*(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,-1,0,0,0.000000," ","integrate(x^3*(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,-1,0,0,0.000000," ","integrate(x^2*(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,1,96,0,0.820477," ","integrate(x*(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} + \frac{a b \log\left(\sec\left(d x^{2} + c\right) + \tan\left(d x^{2} + c\right)\right)}{d} + \frac{b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)}{d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d x^{2} + 2 \, c\right) + d}"," ",0,"1/2*a^2*x^2 + a*b*log(sec(d*x^2 + c) + tan(d*x^2 + c))/d + b^2*sin(2*d*x^2 + 2*c)/(d*cos(2*d*x^2 + 2*c)^2 + d*sin(2*d*x^2 + 2*c)^2 + 2*d*cos(2*d*x^2 + 2*c) + d)","B",0
13,0,0,0,0.000000," ","integrate((a+b*sec(d*x^2+c))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \frac{b^{2} \sin\left(2 \, d x^{2} + 2 \, c\right) + 2 \, {\left(d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}\right)} \int \frac{2 \, a b d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + 2 \, a b d x^{2} \cos\left(d x^{2} + c\right) + {\left(2 \, a b d x^{2} \sin\left(d x^{2} + c\right) + b^{2}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{3} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{3} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{3}}\,{d x}}{d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + d x^{2}}"," ",0,"a^2*log(x) + (b^2*sin(2*d*x^2 + 2*c) + (d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)*integrate(2*(2*a*b*d*x^2*cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + 2*a*b*d*x^2*cos(d*x^2 + c) + (2*a*b*d*x^2*sin(d*x^2 + c) + b^2)*sin(2*d*x^2 + 2*c))/(d*x^3*cos(2*d*x^2 + 2*c)^2 + d*x^3*sin(2*d*x^2 + 2*c)^2 + 2*d*x^3*cos(2*d*x^2 + 2*c) + d*x^3), x))/(d*x^2*cos(2*d*x^2 + 2*c)^2 + d*x^2*sin(2*d*x^2 + 2*c)^2 + 2*d*x^2*cos(2*d*x^2 + 2*c) + d*x^2)","F",0
14,-1,0,0,0.000000," ","integrate((a+b*sec(d*x^2+c))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,1,2838,0,1.420925," ","integrate(x*sec(b*x^2+a)^7,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, \sin\left(11 \, b x^{2} + 11 \, a\right) + 85 \, \sin\left(9 \, b x^{2} + 9 \, a\right) + 198 \, \sin\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \sin\left(b x^{2} + a\right)\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) - 60 \, {\left(6 \, \sin\left(10 \, b x^{2} + 10 \, a\right) + 15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \cos\left(11 \, b x^{2} + 11 \, a\right) + 24 \, {\left(85 \, \sin\left(9 \, b x^{2} + 9 \, a\right) + 198 \, \sin\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \sin\left(b x^{2} + a\right)\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) - 340 \, {\left(15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \cos\left(9 \, b x^{2} + 9 \, a\right) + 60 \, {\left(198 \, \sin\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \sin\left(b x^{2} + a\right)\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) - 792 \, {\left(20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \cos\left(7 \, b x^{2} + 7 \, a\right) - 80 \, {\left(198 \, \sin\left(5 \, b x^{2} + 5 \, a\right) + 85 \, \sin\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \sin\left(b x^{2} + a\right)\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) + 2376 \, {\left(5 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 2 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \cos\left(5 \, b x^{2} + 5 \, a\right) - 300 \, {\left(17 \, \sin\left(3 \, b x^{2} + 3 \, a\right) + 3 \, \sin\left(b x^{2} + a\right)\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) - 15 \, {\left(2 \, {\left(6 \, \cos\left(10 \, b x^{2} + 10 \, a\right) + 15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) + \cos\left(12 \, b x^{2} + 12 \, a\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) + 36 \, \cos\left(10 \, b x^{2} + 10 \, a\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) + 225 \, \cos\left(8 \, b x^{2} + 8 \, a\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) + 400 \, \cos\left(6 \, b x^{2} + 6 \, a\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) + 225 \, \cos\left(4 \, b x^{2} + 4 \, a\right)^{2} + 36 \, \cos\left(2 \, b x^{2} + 2 \, a\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, b x^{2} + 10 \, a\right) + 15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) + \sin\left(12 \, b x^{2} + 12 \, a\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) + 36 \, \sin\left(10 \, b x^{2} + 10 \, a\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) + 225 \, \sin\left(8 \, b x^{2} + 8 \, a\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, b x^{2} + 4 \, a\right) + 2 \, \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) + 400 \, \sin\left(6 \, b x^{2} + 6 \, a\right)^{2} + 225 \, \sin\left(4 \, b x^{2} + 4 \, a\right)^{2} + 180 \, \sin\left(4 \, b x^{2} + 4 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) + 36 \, \sin\left(2 \, b x^{2} + 2 \, a\right)^{2} + 12 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x^{2} + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x^{2} + 2 \, a\right) + \sin\left(b x^{2} + 2 \, a\right)^{2} + 2 \, \cos\left(b x^{2} + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x^{2} + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x^{2} + 2 \, a\right) + \sin\left(b x^{2} + 2 \, a\right)^{2} - 2 \, \cos\left(b x^{2} + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(15 \, \cos\left(11 \, b x^{2} + 11 \, a\right) + 85 \, \cos\left(9 \, b x^{2} + 9 \, a\right) + 198 \, \cos\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \cos\left(b x^{2} + a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) + 60 \, {\left(6 \, \cos\left(10 \, b x^{2} + 10 \, a\right) + 15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \sin\left(11 \, b x^{2} + 11 \, a\right) - 24 \, {\left(85 \, \cos\left(9 \, b x^{2} + 9 \, a\right) + 198 \, \cos\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \cos\left(b x^{2} + a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) + 340 \, {\left(15 \, \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \sin\left(9 \, b x^{2} + 9 \, a\right) - 60 \, {\left(198 \, \cos\left(7 \, b x^{2} + 7 \, a\right) - 198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) - 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) - 15 \, \cos\left(b x^{2} + a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) + 792 \, {\left(20 \, \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \sin\left(7 \, b x^{2} + 7 \, a\right) + 80 \, {\left(198 \, \cos\left(5 \, b x^{2} + 5 \, a\right) + 85 \, \cos\left(3 \, b x^{2} + 3 \, a\right) + 15 \, \cos\left(b x^{2} + a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) - 792 \, {\left(15 \, \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \sin\left(5 \, b x^{2} + 5 \, a\right) + 300 \, {\left(17 \, \cos\left(3 \, b x^{2} + 3 \, a\right) + 3 \, \cos\left(b x^{2} + a\right)\right)} \sin\left(4 \, b x^{2} + 4 \, a\right) - 340 \, {\left(6 \, \cos\left(2 \, b x^{2} + 2 \, a\right) + 1\right)} \sin\left(3 \, b x^{2} + 3 \, a\right) + 2040 \, \cos\left(3 \, b x^{2} + 3 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) + 360 \, \cos\left(b x^{2} + a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) - 360 \, \cos\left(2 \, b x^{2} + 2 \, a\right) \sin\left(b x^{2} + a\right) - 60 \, \sin\left(b x^{2} + a\right)}{192 \, {\left(b \cos\left(12 \, b x^{2} + 12 \, a\right)^{2} + 36 \, b \cos\left(10 \, b x^{2} + 10 \, a\right)^{2} + 225 \, b \cos\left(8 \, b x^{2} + 8 \, a\right)^{2} + 400 \, b \cos\left(6 \, b x^{2} + 6 \, a\right)^{2} + 225 \, b \cos\left(4 \, b x^{2} + 4 \, a\right)^{2} + 36 \, b \cos\left(2 \, b x^{2} + 2 \, a\right)^{2} + b \sin\left(12 \, b x^{2} + 12 \, a\right)^{2} + 36 \, b \sin\left(10 \, b x^{2} + 10 \, a\right)^{2} + 225 \, b \sin\left(8 \, b x^{2} + 8 \, a\right)^{2} + 400 \, b \sin\left(6 \, b x^{2} + 6 \, a\right)^{2} + 225 \, b \sin\left(4 \, b x^{2} + 4 \, a\right)^{2} + 180 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) \sin\left(2 \, b x^{2} + 2 \, a\right) + 36 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)^{2} + 2 \, {\left(6 \, b \cos\left(10 \, b x^{2} + 10 \, a\right) + 15 \, b \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, b \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(12 \, b x^{2} + 12 \, a\right) + 12 \, {\left(15 \, b \cos\left(8 \, b x^{2} + 8 \, a\right) + 20 \, b \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(10 \, b x^{2} + 10 \, a\right) + 30 \, {\left(20 \, b \cos\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(8 \, b x^{2} + 8 \, a\right) + 40 \, {\left(15 \, b \cos\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(6 \, b x^{2} + 6 \, a\right) + 30 \, {\left(6 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + b\right)} \cos\left(4 \, b x^{2} + 4 \, a\right) + 12 \, b \cos\left(2 \, b x^{2} + 2 \, a\right) + 2 \, {\left(6 \, b \sin\left(10 \, b x^{2} + 10 \, a\right) + 15 \, b \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, b \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(12 \, b x^{2} + 12 \, a\right) + 12 \, {\left(15 \, b \sin\left(8 \, b x^{2} + 8 \, a\right) + 20 \, b \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(10 \, b x^{2} + 10 \, a\right) + 30 \, {\left(20 \, b \sin\left(6 \, b x^{2} + 6 \, a\right) + 15 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) + 6 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(8 \, b x^{2} + 8 \, a\right) + 120 \, {\left(5 \, b \sin\left(4 \, b x^{2} + 4 \, a\right) + 2 \, b \sin\left(2 \, b x^{2} + 2 \, a\right)\right)} \sin\left(6 \, b x^{2} + 6 \, a\right) + b\right)}}"," ",0,"1/192*(4*(15*sin(11*b*x^2 + 11*a) + 85*sin(9*b*x^2 + 9*a) + 198*sin(7*b*x^2 + 7*a) - 198*sin(5*b*x^2 + 5*a) - 85*sin(3*b*x^2 + 3*a) - 15*sin(b*x^2 + a))*cos(12*b*x^2 + 12*a) - 60*(6*sin(10*b*x^2 + 10*a) + 15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*cos(11*b*x^2 + 11*a) + 24*(85*sin(9*b*x^2 + 9*a) + 198*sin(7*b*x^2 + 7*a) - 198*sin(5*b*x^2 + 5*a) - 85*sin(3*b*x^2 + 3*a) - 15*sin(b*x^2 + a))*cos(10*b*x^2 + 10*a) - 340*(15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*cos(9*b*x^2 + 9*a) + 60*(198*sin(7*b*x^2 + 7*a) - 198*sin(5*b*x^2 + 5*a) - 85*sin(3*b*x^2 + 3*a) - 15*sin(b*x^2 + a))*cos(8*b*x^2 + 8*a) - 792*(20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*cos(7*b*x^2 + 7*a) - 80*(198*sin(5*b*x^2 + 5*a) + 85*sin(3*b*x^2 + 3*a) + 15*sin(b*x^2 + a))*cos(6*b*x^2 + 6*a) + 2376*(5*sin(4*b*x^2 + 4*a) + 2*sin(2*b*x^2 + 2*a))*cos(5*b*x^2 + 5*a) - 300*(17*sin(3*b*x^2 + 3*a) + 3*sin(b*x^2 + a))*cos(4*b*x^2 + 4*a) - 15*(2*(6*cos(10*b*x^2 + 10*a) + 15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*cos(12*b*x^2 + 12*a) + cos(12*b*x^2 + 12*a)^2 + 12*(15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*cos(10*b*x^2 + 10*a) + 36*cos(10*b*x^2 + 10*a)^2 + 30*(20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*cos(8*b*x^2 + 8*a) + 225*cos(8*b*x^2 + 8*a)^2 + 40*(15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*cos(6*b*x^2 + 6*a) + 400*cos(6*b*x^2 + 6*a)^2 + 30*(6*cos(2*b*x^2 + 2*a) + 1)*cos(4*b*x^2 + 4*a) + 225*cos(4*b*x^2 + 4*a)^2 + 36*cos(2*b*x^2 + 2*a)^2 + 2*(6*sin(10*b*x^2 + 10*a) + 15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(12*b*x^2 + 12*a) + sin(12*b*x^2 + 12*a)^2 + 12*(15*sin(8*b*x^2 + 8*a) + 20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(10*b*x^2 + 10*a) + 36*sin(10*b*x^2 + 10*a)^2 + 30*(20*sin(6*b*x^2 + 6*a) + 15*sin(4*b*x^2 + 4*a) + 6*sin(2*b*x^2 + 2*a))*sin(8*b*x^2 + 8*a) + 225*sin(8*b*x^2 + 8*a)^2 + 120*(5*sin(4*b*x^2 + 4*a) + 2*sin(2*b*x^2 + 2*a))*sin(6*b*x^2 + 6*a) + 400*sin(6*b*x^2 + 6*a)^2 + 225*sin(4*b*x^2 + 4*a)^2 + 180*sin(4*b*x^2 + 4*a)*sin(2*b*x^2 + 2*a) + 36*sin(2*b*x^2 + 2*a)^2 + 12*cos(2*b*x^2 + 2*a) + 1)*log((cos(b*x^2 + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x^2 + 2*a) + sin(b*x^2 + 2*a)^2 + 2*cos(b*x^2 + 2*a)*sin(a) + sin(a)^2)/(cos(b*x^2 + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x^2 + 2*a) + sin(b*x^2 + 2*a)^2 - 2*cos(b*x^2 + 2*a)*sin(a) + sin(a)^2)) - 4*(15*cos(11*b*x^2 + 11*a) + 85*cos(9*b*x^2 + 9*a) + 198*cos(7*b*x^2 + 7*a) - 198*cos(5*b*x^2 + 5*a) - 85*cos(3*b*x^2 + 3*a) - 15*cos(b*x^2 + a))*sin(12*b*x^2 + 12*a) + 60*(6*cos(10*b*x^2 + 10*a) + 15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*sin(11*b*x^2 + 11*a) - 24*(85*cos(9*b*x^2 + 9*a) + 198*cos(7*b*x^2 + 7*a) - 198*cos(5*b*x^2 + 5*a) - 85*cos(3*b*x^2 + 3*a) - 15*cos(b*x^2 + a))*sin(10*b*x^2 + 10*a) + 340*(15*cos(8*b*x^2 + 8*a) + 20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*sin(9*b*x^2 + 9*a) - 60*(198*cos(7*b*x^2 + 7*a) - 198*cos(5*b*x^2 + 5*a) - 85*cos(3*b*x^2 + 3*a) - 15*cos(b*x^2 + a))*sin(8*b*x^2 + 8*a) + 792*(20*cos(6*b*x^2 + 6*a) + 15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*sin(7*b*x^2 + 7*a) + 80*(198*cos(5*b*x^2 + 5*a) + 85*cos(3*b*x^2 + 3*a) + 15*cos(b*x^2 + a))*sin(6*b*x^2 + 6*a) - 792*(15*cos(4*b*x^2 + 4*a) + 6*cos(2*b*x^2 + 2*a) + 1)*sin(5*b*x^2 + 5*a) + 300*(17*cos(3*b*x^2 + 3*a) + 3*cos(b*x^2 + a))*sin(4*b*x^2 + 4*a) - 340*(6*cos(2*b*x^2 + 2*a) + 1)*sin(3*b*x^2 + 3*a) + 2040*cos(3*b*x^2 + 3*a)*sin(2*b*x^2 + 2*a) + 360*cos(b*x^2 + a)*sin(2*b*x^2 + 2*a) - 360*cos(2*b*x^2 + 2*a)*sin(b*x^2 + a) - 60*sin(b*x^2 + a))/(b*cos(12*b*x^2 + 12*a)^2 + 36*b*cos(10*b*x^2 + 10*a)^2 + 225*b*cos(8*b*x^2 + 8*a)^2 + 400*b*cos(6*b*x^2 + 6*a)^2 + 225*b*cos(4*b*x^2 + 4*a)^2 + 36*b*cos(2*b*x^2 + 2*a)^2 + b*sin(12*b*x^2 + 12*a)^2 + 36*b*sin(10*b*x^2 + 10*a)^2 + 225*b*sin(8*b*x^2 + 8*a)^2 + 400*b*sin(6*b*x^2 + 6*a)^2 + 225*b*sin(4*b*x^2 + 4*a)^2 + 180*b*sin(4*b*x^2 + 4*a)*sin(2*b*x^2 + 2*a) + 36*b*sin(2*b*x^2 + 2*a)^2 + 2*(6*b*cos(10*b*x^2 + 10*a) + 15*b*cos(8*b*x^2 + 8*a) + 20*b*cos(6*b*x^2 + 6*a) + 15*b*cos(4*b*x^2 + 4*a) + 6*b*cos(2*b*x^2 + 2*a) + b)*cos(12*b*x^2 + 12*a) + 12*(15*b*cos(8*b*x^2 + 8*a) + 20*b*cos(6*b*x^2 + 6*a) + 15*b*cos(4*b*x^2 + 4*a) + 6*b*cos(2*b*x^2 + 2*a) + b)*cos(10*b*x^2 + 10*a) + 30*(20*b*cos(6*b*x^2 + 6*a) + 15*b*cos(4*b*x^2 + 4*a) + 6*b*cos(2*b*x^2 + 2*a) + b)*cos(8*b*x^2 + 8*a) + 40*(15*b*cos(4*b*x^2 + 4*a) + 6*b*cos(2*b*x^2 + 2*a) + b)*cos(6*b*x^2 + 6*a) + 30*(6*b*cos(2*b*x^2 + 2*a) + b)*cos(4*b*x^2 + 4*a) + 12*b*cos(2*b*x^2 + 2*a) + 2*(6*b*sin(10*b*x^2 + 10*a) + 15*b*sin(8*b*x^2 + 8*a) + 20*b*sin(6*b*x^2 + 6*a) + 15*b*sin(4*b*x^2 + 4*a) + 6*b*sin(2*b*x^2 + 2*a))*sin(12*b*x^2 + 12*a) + 12*(15*b*sin(8*b*x^2 + 8*a) + 20*b*sin(6*b*x^2 + 6*a) + 15*b*sin(4*b*x^2 + 4*a) + 6*b*sin(2*b*x^2 + 2*a))*sin(10*b*x^2 + 10*a) + 30*(20*b*sin(6*b*x^2 + 6*a) + 15*b*sin(4*b*x^2 + 4*a) + 6*b*sin(2*b*x^2 + 2*a))*sin(8*b*x^2 + 8*a) + 120*(5*b*sin(4*b*x^2 + 4*a) + 2*b*sin(2*b*x^2 + 2*a))*sin(6*b*x^2 + 6*a) + b)","B",0
16,-1,0,0,0.000000," ","integrate(x^5/(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate(x^4/(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-2,0,0,0.000000," ","integrate(x^3/(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
19,-1,0,0,0.000000," ","integrate(x^2/(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,1,7945,0,63.895444," ","integrate(x/(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\frac{\sqrt{-a^{2} + b^{2}} d x^{2} - b \arctan\left(\frac{2 \, {\left(4 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) - 4 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 4 \, {\left(3 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} b - a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} \cos\left(c\right)^{2} - {\left(a^{6} - a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 4 \, {\left({\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3} - 3 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(a^{5} b - a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 4 \, {\left({\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} - {\left({\left(a^{6} - a^{4} b^{2}\right)} \cos\left(c\right)^{2} - {\left(a^{6} - a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 3 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{3} - {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left({\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} - {\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + {\left(a^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} - a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - 4 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) - {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) - 4 \, a^{4} b \cos\left(c\right) \sin\left(c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} + 2 \, {\left(3 \, {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) - {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} - 3 \, {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2} + 2 \, {\left(a^{4} b \cos\left(c\right)^{2} - a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left({\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) + 2 \, {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + 2 \, {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3} + 3 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 4 \, {\left(a^{4} b \cos\left(c\right)^{2} - a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} - {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}\right)}}{a^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{6} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \sin\left(c\right)^{6} - 3 \, {\left(5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) - {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} - 5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) - 6 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 3 \, {\left(5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} + 4 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4} - 6 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left({\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 6 \, {\left(a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + 3 \, a^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{6} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \sin\left(c\right)^{6} + 3 \, {\left(5 \, a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + a^{4} b \cos\left(c\right)^{2} + 5 \, a^{4} b \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 12 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left(5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} - 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - 5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4} + 3 \, {\left(a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left({\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 8 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}}, \frac{a^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{6} - {\left(5 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + {\left(3 \, a^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) - {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} - 5 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(5 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) - 2 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - {\left(5 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left(3 \, a^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} + 12 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) - {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} - 6 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - 5 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4} - 6 \, {\left({\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 12 \, {\left({\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 2 \, {\left({\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) - {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) - 2 \, {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} - {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \sin\left(c\right)^{5} - 6 \, {\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + 4 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{6} - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{6} + {\left(5 \, a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + a^{4} b \cos\left(c\right)^{2} + 5 \, a^{4} b \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} + 2 \, {\left(5 \, a^{3} b^{2} \cos\left(c\right)^{3} + 3 \, a^{3} b^{2} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 4 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, a^{3} b^{2} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(5 \, a^{2} b^{3} \cos\left(c\right)^{4} + 6 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + a^{2} b^{3} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + a^{2} b^{3} \cos\left(c\right)^{4} + 6 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, a^{2} b^{3} \sin\left(c\right)^{4} + 3 \, {\left(a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(a^{3} b^{2} \cos\left(c\right)^{3} + 3 \, a^{3} b^{2} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 8 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) - {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \sin\left(c\right)^{5} + 6 \, {\left(3 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right) + a^{3} b^{2} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 16 \, {\left(a^{2} b^{3} \cos\left(c\right)^{3} \sin\left(c\right) + a^{2} b^{3} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}}{a^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{6} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \sin\left(c\right)^{6} - 3 \, {\left(5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) - {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} - 5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) - 6 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 3 \, {\left(5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} + 4 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4} - 6 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left({\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 6 \, {\left(a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + 3 \, a^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{6} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \sin\left(c\right)^{6} + 3 \, {\left(5 \, a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + a^{4} b \cos\left(c\right)^{2} + 5 \, a^{4} b \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 12 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left(5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} - 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - 5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4} + 3 \, {\left(a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left({\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 8 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}}\right)}{2 \, \sqrt{-a^{2} + b^{2}} a d}"," ",0,"1/2*(sqrt(-a^2 + b^2)*d*x^2 - b*arctan2(2*(4*(a^6 - a^4*b^2)*cos(d*x^2 + 2*c)^4*cos(c)*sin(c) - 4*(a^6 - a^4*b^2)*cos(c)*sin(d*x^2 + 2*c)^4*sin(c) + 4*(3*(a^5*b - a^3*b^3)*cos(c)^2*sin(c) + (a^5*b - a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^3 - 4*((a^5*b - a^3*b^3)*cos(c)^3 + 3*(a^5*b - a^3*b^3)*cos(c)*sin(c)^2 + ((a^6 - a^4*b^2)*cos(c)^2 - (a^6 - a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^3 - 4*((a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)*sin(c)^3 - 3*((a^5*b - a^3*b^3)*cos(c)^2*sin(c) - (a^5*b - a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 4*((a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^4*sin(c) + 2*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^2*sin(c)^3 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 4*((a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^5 + 2*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^3*sin(c)^2 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)*sin(c)^4 - ((a^6 - a^4*b^2)*cos(c)^2 - (a^6 - a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 3*((a^5*b - a^3*b^3)*cos(c)^3 - (a^5*b - a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 + ((a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)^4 - (a^6 - 5*a^4*b^2 + 4*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + (a^5*cos(c)*sin(d*x^2 + 2*c)^5 - a^5*cos(d*x^2 + 2*c)^5*sin(c) - 4*a^4*b*cos(d*x^2 + 2*c)^4*cos(c)*sin(c) - (a^5*cos(d*x^2 + 2*c)*sin(c) - 4*a^4*b*cos(c)*sin(c))*sin(d*x^2 + 2*c)^4 + 2*(3*(a^5 - 2*a^3*b^2)*cos(c)^2*sin(c) + (a^5 - 2*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 2*(a^5*cos(d*x^2 + 2*c)^2*cos(c) - (a^5 - 2*a^3*b^2)*cos(c)^3 - 3*(a^5 - 2*a^3*b^2)*cos(c)*sin(c)^2 + 2*(a^4*b*cos(c)^2 - a^4*b*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^3 + 4*((3*a^4*b - 4*a^2*b^3)*cos(c)^3*sin(c) + (3*a^4*b - 4*a^2*b^3)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 2*(a^5*cos(d*x^2 + 2*c)^3*sin(c) + 2*(3*a^4*b - 4*a^2*b^3)*cos(c)^3*sin(c) + 2*(3*a^4*b - 4*a^2*b^3)*cos(c)*sin(c)^3 + 3*((a^5 - 2*a^3*b^2)*cos(c)^2*sin(c) - (a^5 - 2*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - ((a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^4*sin(c) + 2*(a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^2*sin(c)^3 + (a^5 - 8*a^3*b^2 + 8*a*b^4)*sin(c)^5)*cos(d*x^2 + 2*c) + (a^5*cos(d*x^2 + 2*c)^4*cos(c) + (a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^5 + 2*(a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)*sin(c)^4 + 4*(a^4*b*cos(c)^2 - a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 6*((a^5 - 2*a^3*b^2)*cos(c)^3 - (a^5 - 2*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((3*a^4*b - 4*a^2*b^3)*cos(c)^4 - (3*a^4*b - 4*a^2*b^3)*sin(c)^4)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2))/(a^6*cos(d*x^2 + 2*c)^6 + 6*a^5*b*cos(d*x^2 + 2*c)^5*cos(c) + a^6*sin(d*x^2 + 2*c)^6 + 6*a^5*b*sin(d*x^2 + 2*c)^5*sin(c) - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^6 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^4*sin(c)^2 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^2*sin(c)^4 - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*sin(c)^6 - 3*(5*(a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^6*cos(d*x^2 + 2*c)^2 + 2*a^5*b*cos(d*x^2 + 2*c)*cos(c) - (a^6 - 2*a^4*b^2)*cos(c)^2 - 5*(a^6 - 2*a^4*b^2)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(5*(3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 4*(3*a^5*b*cos(d*x^2 + 2*c)^2*sin(c) - 6*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) - 5*(3*a^5*b - 4*a^3*b^3)*sin(c)^3)*sin(d*x^2 + 2*c)^3 + 3*(5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 3*(a^6*cos(d*x^2 + 2*c)^4 + 4*a^5*b*cos(d*x^2 + 2*c)^3*cos(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + 5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4 - 6*((a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 6*((5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^5 + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^3*sin(c)^2 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 6*(a^5*b*cos(d*x^2 + 2*c)^4*sin(c) - 4*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^4*sin(c) + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^2*sin(c)^3 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*sin(c)^5 - 2*(3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) + (3*a^5*b - 4*a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + 2*(3*a^5*cos(d*x^2 + 2*c)^5*cos(c) + 3*a^5*sin(d*x^2 + 2*c)^5*sin(c) + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^6 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^4*sin(c)^2 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^2*sin(c)^4 + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*sin(c)^6 + 3*(5*a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^5*cos(d*x^2 + 2*c)*cos(c) + a^4*b*cos(c)^2 + 5*a^4*b*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(5*(a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(3*a^5*cos(d*x^2 + 2*c)^2*sin(c) + 12*a^4*b*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) - 5*(a^5 - 4*a^3*b^2)*sin(c)^3)*sin(d*x^2 + 2*c)^3 - 6*(5*(a^4*b - 2*a^2*b^3)*cos(c)^4 + 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 + (a^4*b - 2*a^2*b^3)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 6*(a^5*cos(d*x^2 + 2*c)^3*cos(c) - (a^4*b - 2*a^2*b^3)*cos(c)^4 - 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 - 5*(a^4*b - 2*a^2*b^3)*sin(c)^4 + 3*(a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^2 - ((a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 3*((a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^5 + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 3*(a^5*cos(d*x^2 + 2*c)^4*sin(c) + 8*a^4*b*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^4*sin(c) + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^2*sin(c)^3 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*sin(c)^5 - 2*(3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) + (a^5 - 4*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 16*((a^4*b - 2*a^2*b^3)*cos(c)^3*sin(c) + (a^4*b - 2*a^2*b^3)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2)), (a^6*cos(d*x^2 + 2*c)^6 + 6*a^5*b*cos(d*x^2 + 2*c)^5*cos(c) + a^6*sin(d*x^2 + 2*c)^6 + 6*a^5*b*sin(d*x^2 + 2*c)^5*sin(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^6 + 3*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4*sin(c)^2 + 3*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^4 + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^6 - (5*(a^6 - 4*a^4*b^2)*cos(c)^2 + (a^6 - 4*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + (3*a^6*cos(d*x^2 + 2*c)^2 + 6*a^5*b*cos(d*x^2 + 2*c)*cos(c) - (a^6 - 4*a^4*b^2)*cos(c)^2 - 5*(a^6 - 4*a^4*b^2)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(5*(a^5*b - 2*a^3*b^3)*cos(c)^3 + 3*(a^5*b - 2*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 4*(3*a^5*b*cos(d*x^2 + 2*c)^2*sin(c) - 2*(a^6 - 4*a^4*b^2)*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(a^5*b - 2*a^3*b^3)*cos(c)^2*sin(c) - 5*(a^5*b - 2*a^3*b^3)*sin(c)^3)*sin(d*x^2 + 2*c)^3 - (5*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^4 + 6*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^2*sin(c)^2 + (a^6 + 4*a^4*b^2 - 8*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + (3*a^6*cos(d*x^2 + 2*c)^4 + 12*a^5*b*cos(d*x^2 + 2*c)^3*cos(c) - (a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^4 - 6*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^2*sin(c)^2 - 5*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*sin(c)^4 - 6*((a^6 - 4*a^4*b^2)*cos(c)^2 + (a^6 - 4*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 12*((a^5*b - 2*a^3*b^3)*cos(c)^3 + 3*(a^5*b - 2*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 2*((5*a^5*b - 8*a*b^5)*cos(c)^5 + 2*(5*a^5*b - 8*a*b^5)*cos(c)^3*sin(c)^2 + (5*a^5*b - 8*a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 2*(3*a^5*b*cos(d*x^2 + 2*c)^4*sin(c) - 4*(a^6 - 4*a^4*b^2)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) - (5*a^5*b - 8*a*b^5)*cos(c)^4*sin(c) - 2*(5*a^5*b - 8*a*b^5)*cos(c)^2*sin(c)^3 - (5*a^5*b - 8*a*b^5)*sin(c)^5 - 6*(3*(a^5*b - 2*a^3*b^3)*cos(c)^2*sin(c) + (a^5*b - 2*a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 4*((a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^3*sin(c) + (a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + 4*(a^5*cos(d*x^2 + 2*c)^5*cos(c) + a^5*sin(d*x^2 + 2*c)^5*sin(c) - (a^4*b - 2*a^2*b^3)*cos(c)^6 - 3*(a^4*b - 2*a^2*b^3)*cos(c)^4*sin(c)^2 - 3*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^4 - (a^4*b - 2*a^2*b^3)*sin(c)^6 + (5*a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^4 + (a^5*cos(d*x^2 + 2*c)*cos(c) + a^4*b*cos(c)^2 + 5*a^4*b*sin(c)^2)*sin(d*x^2 + 2*c)^4 + 2*(5*a^3*b^2*cos(c)^3 + 3*a^3*b^2*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(a^5*cos(d*x^2 + 2*c)^2*sin(c) + 4*a^4*b*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 3*a^3*b^2*cos(c)^2*sin(c) + 5*a^3*b^2*sin(c)^3)*sin(d*x^2 + 2*c)^3 + 2*(5*a^2*b^3*cos(c)^4 + 6*a^2*b^3*cos(c)^2*sin(c)^2 + a^2*b^3*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 2*(a^5*cos(d*x^2 + 2*c)^3*cos(c) + a^2*b^3*cos(c)^4 + 6*a^2*b^3*cos(c)^2*sin(c)^2 + 5*a^2*b^3*sin(c)^4 + 3*(a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^2 + 3*(a^3*b^2*cos(c)^3 + 3*a^3*b^2*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - ((a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^5 + 2*(a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + (a^5*cos(d*x^2 + 2*c)^4*sin(c) + 8*a^4*b*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) - (a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^4*sin(c) - 2*(a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^2*sin(c)^3 - (a^5 - 2*a^3*b^2 - 4*a*b^4)*sin(c)^5 + 6*(3*a^3*b^2*cos(c)^2*sin(c) + a^3*b^2*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 16*(a^2*b^3*cos(c)^3*sin(c) + a^2*b^3*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2))/(a^6*cos(d*x^2 + 2*c)^6 + 6*a^5*b*cos(d*x^2 + 2*c)^5*cos(c) + a^6*sin(d*x^2 + 2*c)^6 + 6*a^5*b*sin(d*x^2 + 2*c)^5*sin(c) - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^6 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^4*sin(c)^2 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^2*sin(c)^4 - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*sin(c)^6 - 3*(5*(a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^6*cos(d*x^2 + 2*c)^2 + 2*a^5*b*cos(d*x^2 + 2*c)*cos(c) - (a^6 - 2*a^4*b^2)*cos(c)^2 - 5*(a^6 - 2*a^4*b^2)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(5*(3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 4*(3*a^5*b*cos(d*x^2 + 2*c)^2*sin(c) - 6*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) - 5*(3*a^5*b - 4*a^3*b^3)*sin(c)^3)*sin(d*x^2 + 2*c)^3 + 3*(5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 3*(a^6*cos(d*x^2 + 2*c)^4 + 4*a^5*b*cos(d*x^2 + 2*c)^3*cos(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + 5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4 - 6*((a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 6*((5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^5 + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^3*sin(c)^2 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 6*(a^5*b*cos(d*x^2 + 2*c)^4*sin(c) - 4*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^4*sin(c) + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^2*sin(c)^3 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*sin(c)^5 - 2*(3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) + (3*a^5*b - 4*a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + 2*(3*a^5*cos(d*x^2 + 2*c)^5*cos(c) + 3*a^5*sin(d*x^2 + 2*c)^5*sin(c) + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^6 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^4*sin(c)^2 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^2*sin(c)^4 + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*sin(c)^6 + 3*(5*a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^5*cos(d*x^2 + 2*c)*cos(c) + a^4*b*cos(c)^2 + 5*a^4*b*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(5*(a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(3*a^5*cos(d*x^2 + 2*c)^2*sin(c) + 12*a^4*b*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) - 5*(a^5 - 4*a^3*b^2)*sin(c)^3)*sin(d*x^2 + 2*c)^3 - 6*(5*(a^4*b - 2*a^2*b^3)*cos(c)^4 + 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 + (a^4*b - 2*a^2*b^3)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 6*(a^5*cos(d*x^2 + 2*c)^3*cos(c) - (a^4*b - 2*a^2*b^3)*cos(c)^4 - 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 - 5*(a^4*b - 2*a^2*b^3)*sin(c)^4 + 3*(a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^2 - ((a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 3*((a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^5 + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 3*(a^5*cos(d*x^2 + 2*c)^4*sin(c) + 8*a^4*b*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^4*sin(c) + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^2*sin(c)^3 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*sin(c)^5 - 2*(3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) + (a^5 - 4*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 16*((a^4*b - 2*a^2*b^3)*cos(c)^3*sin(c) + (a^4*b - 2*a^2*b^3)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2))))/(sqrt(-a^2 + b^2)*a*d)","B",0
21,-1,0,0,0.000000," ","integrate(1/x/(a+b*sec(d*x^2+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,0,0,0,0.000000," ","integrate((a+b*sec(d*x^2+c))/x^2,x, algorithm=""maxima"")","2 \, b \int \frac{\cos\left(2 \, d x^{2} + 2 \, c\right) \cos\left(d x^{2} + c\right) + \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + \cos\left(d x^{2} + c\right)}{x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 2 \, x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right) + x^{2}}\,{d x} - \frac{a}{x}"," ",0,"2*b*integrate((cos(2*d*x^2 + 2*c)*cos(d*x^2 + c) + sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + cos(d*x^2 + c))/(x^2*cos(2*d*x^2 + 2*c)^2 + x^2*sin(2*d*x^2 + 2*c)^2 + 2*x^2*cos(2*d*x^2 + 2*c) + x^2), x) - a/x","F",0
23,0,0,0,0.000000," ","integrate(x^5/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{{\left(a^{4} - a^{2} b^{2}\right)} d x^{6} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} d x^{6} \cos\left(d x^{2} + c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} d x^{6} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} d x^{6} \sin\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{3} b - a b^{3}\right)} d x^{6} \cos\left(d x^{2} + c\right) + 6 \, a b^{3} x^{4} \sin\left(d x^{2} + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} d x^{6} + 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d x^{6} \cos\left(d x^{2} + c\right) - 3 \, a b^{3} x^{4} \sin\left(d x^{2} + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} d x^{6}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) - 12 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d \cos\left(d x^{2} + c\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d \sin\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{6} - a^{4} b^{2}\right)} d + 2 \, {\left(2 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{6} - a^{4} b^{2}\right)} d\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)\right)} \int \frac{2 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} d x^{5} \cos\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} d x^{5} \sin\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} d x^{5} \cos\left(d x^{2} + c\right) + 2 \, a b^{3} x^{3} \sin\left(d x^{2} + c\right) + {\left({\left(2 \, a^{3} b - a b^{3}\right)} d x^{5} \cos\left(d x^{2} + c\right) - 2 \, a b^{3} x^{3} \sin\left(d x^{2} + c\right)\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + {\left(2 \, a b^{3} x^{3} \cos\left(d x^{2} + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} d x^{5} \sin\left(d x^{2} + c\right) + 2 \, a^{2} b^{2} x^{3}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{{\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d \cos\left(d x^{2} + c\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d \sin\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{6} - a^{4} b^{2}\right)} d + 2 \, {\left(2 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{6} - a^{4} b^{2}\right)} d\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)}\,{d x} + 2 \, {\left(3 \, a b^{3} x^{4} \cos\left(d x^{2} + c\right) + 2 \, {\left(a^{3} b - a b^{3}\right)} d x^{6} \sin\left(d x^{2} + c\right) + 3 \, a^{2} b^{2} x^{4}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)}{6 \, {\left({\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d \cos\left(d x^{2} + c\right)^{2} + {\left(a^{6} - a^{4} b^{2}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d \sin\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{6} - a^{4} b^{2}\right)} d + 2 \, {\left(2 \, {\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{6} - a^{4} b^{2}\right)} d\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)\right)}}"," ",0,"1/6*((a^4 - a^2*b^2)*d*x^6*cos(2*d*x^2 + 2*c)^2 + 4*(a^2*b^2 - b^4)*d*x^6*cos(d*x^2 + c)^2 + (a^4 - a^2*b^2)*d*x^6*sin(2*d*x^2 + 2*c)^2 + 4*(a^2*b^2 - b^4)*d*x^6*sin(d*x^2 + c)^2 + 4*(a^3*b - a*b^3)*d*x^6*cos(d*x^2 + c) + 6*a*b^3*x^4*sin(d*x^2 + c) + (a^4 - a^2*b^2)*d*x^6 + 2*(2*(a^3*b - a*b^3)*d*x^6*cos(d*x^2 + c) - 3*a*b^3*x^4*sin(d*x^2 + c) + (a^4 - a^2*b^2)*d*x^6)*cos(2*d*x^2 + 2*c) - 6*((a^6 - a^4*b^2)*d*cos(2*d*x^2 + 2*c)^2 + 4*(a^4*b^2 - a^2*b^4)*d*cos(d*x^2 + c)^2 + (a^6 - a^4*b^2)*d*sin(2*d*x^2 + 2*c)^2 + 4*(a^5*b - a^3*b^3)*d*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + 4*(a^4*b^2 - a^2*b^4)*d*sin(d*x^2 + c)^2 + 4*(a^5*b - a^3*b^3)*d*cos(d*x^2 + c) + (a^6 - a^4*b^2)*d + 2*(2*(a^5*b - a^3*b^3)*d*cos(d*x^2 + c) + (a^6 - a^4*b^2)*d)*cos(2*d*x^2 + 2*c))*integrate(2*(2*(2*a^2*b^2 - b^4)*d*x^5*cos(d*x^2 + c)^2 + 2*(2*a^2*b^2 - b^4)*d*x^5*sin(d*x^2 + c)^2 + (2*a^3*b - a*b^3)*d*x^5*cos(d*x^2 + c) + 2*a*b^3*x^3*sin(d*x^2 + c) + ((2*a^3*b - a*b^3)*d*x^5*cos(d*x^2 + c) - 2*a*b^3*x^3*sin(d*x^2 + c))*cos(2*d*x^2 + 2*c) + (2*a*b^3*x^3*cos(d*x^2 + c) + (2*a^3*b - a*b^3)*d*x^5*sin(d*x^2 + c) + 2*a^2*b^2*x^3)*sin(2*d*x^2 + 2*c))/((a^6 - a^4*b^2)*d*cos(2*d*x^2 + 2*c)^2 + 4*(a^4*b^2 - a^2*b^4)*d*cos(d*x^2 + c)^2 + (a^6 - a^4*b^2)*d*sin(2*d*x^2 + 2*c)^2 + 4*(a^5*b - a^3*b^3)*d*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + 4*(a^4*b^2 - a^2*b^4)*d*sin(d*x^2 + c)^2 + 4*(a^5*b - a^3*b^3)*d*cos(d*x^2 + c) + (a^6 - a^4*b^2)*d + 2*(2*(a^5*b - a^3*b^3)*d*cos(d*x^2 + c) + (a^6 - a^4*b^2)*d)*cos(2*d*x^2 + 2*c)), x) + 2*(3*a*b^3*x^4*cos(d*x^2 + c) + 2*(a^3*b - a*b^3)*d*x^6*sin(d*x^2 + c) + 3*a^2*b^2*x^4)*sin(2*d*x^2 + 2*c))/((a^6 - a^4*b^2)*d*cos(2*d*x^2 + 2*c)^2 + 4*(a^4*b^2 - a^2*b^4)*d*cos(d*x^2 + c)^2 + (a^6 - a^4*b^2)*d*sin(2*d*x^2 + 2*c)^2 + 4*(a^5*b - a^3*b^3)*d*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + 4*(a^4*b^2 - a^2*b^4)*d*sin(d*x^2 + c)^2 + 4*(a^5*b - a^3*b^3)*d*cos(d*x^2 + c) + (a^6 - a^4*b^2)*d + 2*(2*(a^5*b - a^3*b^3)*d*cos(d*x^2 + c) + (a^6 - a^4*b^2)*d)*cos(2*d*x^2 + 2*c))","F",0
24,-1,0,0,0.000000," ","integrate(x^4/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-2,0,0,0.000000," ","integrate(x^3/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
26,-1,0,0,0.000000," ","integrate(x^2/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,1,8871,0,66.778454," ","integrate(x/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\frac{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x^{2} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x^{2} \cos\left(d x^{2} + c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x^{2} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x^{2} \sin\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x^{2} + {\left(2 \, a^{4} b - a^{2} b^{3} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + 4 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3} + 2 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right)\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x^{2} + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(\frac{2 \, {\left(4 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) - 4 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 4 \, {\left(3 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} b - a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 4 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2} + {\left({\left(a^{6} - a^{4} b^{2}\right)} \cos\left(c\right)^{2} - {\left(a^{6} - a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 4 \, {\left({\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3} - 3 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(a^{5} b - a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + 4 \, {\left({\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4} - {\left({\left(a^{6} - a^{4} b^{2}\right)} \cos\left(c\right)^{2} - {\left(a^{6} - a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 3 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right)^{3} - {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left({\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} - {\left(a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + {\left(a^{5} \cos\left(c\right) \sin\left(d x^{2} + 2 \, c\right)^{5} - a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - 4 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) \sin\left(c\right) - {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \sin\left(c\right) - 4 \, a^{4} b \cos\left(c\right) \sin\left(c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} + 2 \, {\left(3 \, {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \cos\left(c\right) - {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} - 3 \, {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2} + 2 \, {\left(a^{4} b \cos\left(c\right)^{2} - a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left({\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \sin\left(c\right) + 2 \, {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + 2 \, {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3} + 3 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \sin\left(c\right)^{5}\right)} \cos\left(d x^{2} + 2 \, c\right) + {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \cos\left(c\right) + {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 8 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4} + 4 \, {\left(a^{4} b \cos\left(c\right)^{2} - a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} - {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}\right)}}{a^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{6} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \sin\left(c\right)^{6} - 3 \, {\left(5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) - {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} - 5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) - 6 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 3 \, {\left(5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} + 4 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4} - 6 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left({\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 6 \, {\left(a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + 3 \, a^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{6} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \sin\left(c\right)^{6} + 3 \, {\left(5 \, a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + a^{4} b \cos\left(c\right)^{2} + 5 \, a^{4} b \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 12 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left(5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} - 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - 5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4} + 3 \, {\left(a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left({\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 8 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}}, \frac{a^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{6} + 3 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{6} - {\left(5 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + {\left(3 \, a^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) - {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} - 5 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(5 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) - 2 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - {\left(5 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + {\left(3 \, a^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} + 12 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) - {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} - 6 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - 5 \, {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4} - 6 \, {\left({\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 12 \, {\left({\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - 2 \, {\left({\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) - {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) - 2 \, {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} - {\left(5 \, a^{5} b - 8 \, a b^{5}\right)} \sin\left(c\right)^{5} - 6 \, {\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + 4 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{6} - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{6} + {\left(5 \, a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + a^{4} b \cos\left(c\right)^{2} + 5 \, a^{4} b \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} + 2 \, {\left(5 \, a^{3} b^{2} \cos\left(c\right)^{3} + 3 \, a^{3} b^{2} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 4 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) + 3 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right) + 5 \, a^{3} b^{2} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(5 \, a^{2} b^{3} \cos\left(c\right)^{4} + 6 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + a^{2} b^{3} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + a^{2} b^{3} \cos\left(c\right)^{4} + 6 \, a^{2} b^{3} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, a^{2} b^{3} \sin\left(c\right)^{4} + 3 \, {\left(a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(a^{3} b^{2} \cos\left(c\right)^{3} + 3 \, a^{3} b^{2} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 8 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) - {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \sin\left(c\right)^{5} + 6 \, {\left(3 \, a^{3} b^{2} \cos\left(c\right)^{2} \sin\left(c\right) + a^{3} b^{2} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 16 \, {\left(a^{2} b^{3} \cos\left(c\right)^{3} \sin\left(c\right) + a^{2} b^{3} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}}{a^{6} \cos\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + a^{6} \sin\left(d x^{2} + 2 \, c\right)^{6} + 6 \, a^{5} b \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{6} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} - 3 \, {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} - {\left(a^{6} - 18 \, a^{4} b^{2} + 48 \, a^{2} b^{4} - 32 \, b^{6}\right)} \sin\left(c\right)^{6} - 3 \, {\left(5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{2} + 2 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) - {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} - 5 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 4 \, {\left(5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 4 \, {\left(3 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) - 6 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} + 3 \, {\left(5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left(a^{6} \cos\left(d x^{2} + 2 \, c\right)^{4} + 4 \, a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + 5 \, {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \sin\left(c\right)^{4} - 6 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(c\right)^{2} + {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 4 \, {\left({\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{3} + 3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left({\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{5} + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 6 \, {\left(a^{5} b \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) - 4 \, {\left(a^{6} - 2 \, a^{4} b^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(5 \, a^{5} b - 20 \, a^{3} b^{3} + 16 \, a b^{5}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 4 \, {\left({\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{6} - 8 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right) + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{5} \cos\left(c\right) + 3 \, a^{5} \sin\left(d x^{2} + 2 \, c\right)^{5} \sin\left(c\right) + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{6} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{4} \sin\left(c\right)^{2} + 3 \, {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{4} + {\left(3 \, a^{4} b - 16 \, a^{2} b^{3} + 16 \, b^{5}\right)} \sin\left(c\right)^{6} + 3 \, {\left(5 \, a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{4} + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) + a^{4} b \cos\left(c\right)^{2} + 5 \, a^{4} b \sin\left(c\right)^{2}\right)} \sin\left(d x^{2} + 2 \, c\right)^{4} - 2 \, {\left(5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{5} \cos\left(d x^{2} + 2 \, c\right)^{2} \sin\left(c\right) + 12 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right) \cos\left(c\right) \sin\left(c\right) - 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) - 5 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \sin\left(d x^{2} + 2 \, c\right)^{3} - 6 \, {\left(5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} + 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} + 6 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{4} - 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{2} - 5 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \sin\left(c\right)^{4} + 3 \, {\left(a^{4} b \cos\left(c\right)^{2} + a^{4} b \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - {\left({\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{3} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right) \sin\left(c\right)^{2}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)^{2} + 3 \, {\left({\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{5} + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{3} \sin\left(c\right)^{2} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right) \sin\left(c\right)^{4}\right)} \cos\left(d x^{2} + 2 \, c\right) + 3 \, {\left(a^{5} \cos\left(d x^{2} + 2 \, c\right)^{4} \sin\left(c\right) + 8 \, a^{4} b \cos\left(d x^{2} + 2 \, c\right)^{3} \cos\left(c\right) \sin\left(c\right) + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{4} \sin\left(c\right) + 2 \, {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \cos\left(c\right)^{2} \sin\left(c\right)^{3} + {\left(a^{5} - 12 \, a^{3} b^{2} + 16 \, a b^{4}\right)} \sin\left(c\right)^{5} - 2 \, {\left(3 \, {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \cos\left(c\right)^{2} \sin\left(c\right) + {\left(a^{5} - 4 \, a^{3} b^{2}\right)} \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)^{2} - 16 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right)^{3} \sin\left(c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(c\right) \sin\left(c\right)^{3}\right)} \cos\left(d x^{2} + 2 \, c\right)\right)} \sin\left(d x^{2} + 2 \, c\right)\right)} \sqrt{-a^{2} + b^{2}}}\right) + 2 \, {\left(2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x^{2} - {\left(a^{3} b^{3} - a b^{5}\right)} \sin\left(d x^{2} + c\right)\right)} \cos\left(2 \, d x^{2} + 2 \, c\right) + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x^{2} \sin\left(d x^{2} + c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x^{2} + c\right)\right)} \sin\left(2 \, d x^{2} + 2 \, c\right) + 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} \sin\left(d x^{2} + c\right)}{2 \, {\left({\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} d \cos\left(d x^{2} + c\right)^{2} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right)^{2} + 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \sin\left(2 \, d x^{2} + 2 \, c\right) \sin\left(d x^{2} + c\right) + 4 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} d \sin\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d + 2 \, {\left(2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \cos\left(d x^{2} + c\right) + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d\right)} \cos\left(2 \, d x^{2} + 2 \, c\right)\right)}}"," ",0,"1/2*((a^6 - 2*a^4*b^2 + a^2*b^4)*d*x^2*cos(2*d*x^2 + 2*c)^2 + 4*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x^2*cos(d*x^2 + c)^2 + (a^6 - 2*a^4*b^2 + a^2*b^4)*d*x^2*sin(2*d*x^2 + 2*c)^2 + 4*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x^2*sin(d*x^2 + c)^2 + 4*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x^2*cos(d*x^2 + c) + (a^6 - 2*a^4*b^2 + a^2*b^4)*d*x^2 + (2*a^4*b - a^2*b^3 + (2*a^4*b - a^2*b^3)*cos(2*d*x^2 + 2*c)^2 + 4*(2*a^2*b^3 - b^5)*cos(d*x^2 + c)^2 + (2*a^4*b - a^2*b^3)*sin(2*d*x^2 + 2*c)^2 + 4*(2*a^3*b^2 - a*b^4)*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + 4*(2*a^2*b^3 - b^5)*sin(d*x^2 + c)^2 + 2*(2*a^4*b - a^2*b^3 + 2*(2*a^3*b^2 - a*b^4)*cos(d*x^2 + c))*cos(2*d*x^2 + 2*c) + 4*(2*a^3*b^2 - a*b^4)*cos(d*x^2 + c))*sqrt(-a^2 + b^2)*arctan2(2*(4*(a^6 - a^4*b^2)*cos(d*x^2 + 2*c)^4*cos(c)*sin(c) - 4*(a^6 - a^4*b^2)*cos(c)*sin(d*x^2 + 2*c)^4*sin(c) + 4*(3*(a^5*b - a^3*b^3)*cos(c)^2*sin(c) + (a^5*b - a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^3 - 4*((a^5*b - a^3*b^3)*cos(c)^3 + 3*(a^5*b - a^3*b^3)*cos(c)*sin(c)^2 + ((a^6 - a^4*b^2)*cos(c)^2 - (a^6 - a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^3 - 4*((a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)*sin(c)^3 - 3*((a^5*b - a^3*b^3)*cos(c)^2*sin(c) - (a^5*b - a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 4*((a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^4*sin(c) + 2*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^2*sin(c)^3 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*sin(c)^5)*cos(d*x^2 + 2*c) + 4*((a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^5 + 2*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)^3*sin(c)^2 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(c)*sin(c)^4 - ((a^6 - a^4*b^2)*cos(c)^2 - (a^6 - a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 3*((a^5*b - a^3*b^3)*cos(c)^3 - (a^5*b - a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 + ((a^6 - 5*a^4*b^2 + 4*a^2*b^4)*cos(c)^4 - (a^6 - 5*a^4*b^2 + 4*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + (a^5*cos(c)*sin(d*x^2 + 2*c)^5 - a^5*cos(d*x^2 + 2*c)^5*sin(c) - 4*a^4*b*cos(d*x^2 + 2*c)^4*cos(c)*sin(c) - (a^5*cos(d*x^2 + 2*c)*sin(c) - 4*a^4*b*cos(c)*sin(c))*sin(d*x^2 + 2*c)^4 + 2*(3*(a^5 - 2*a^3*b^2)*cos(c)^2*sin(c) + (a^5 - 2*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c)^3 + 2*(a^5*cos(d*x^2 + 2*c)^2*cos(c) - (a^5 - 2*a^3*b^2)*cos(c)^3 - 3*(a^5 - 2*a^3*b^2)*cos(c)*sin(c)^2 + 2*(a^4*b*cos(c)^2 - a^4*b*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^3 + 4*((3*a^4*b - 4*a^2*b^3)*cos(c)^3*sin(c) + (3*a^4*b - 4*a^2*b^3)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 2*(a^5*cos(d*x^2 + 2*c)^3*sin(c) + 2*(3*a^4*b - 4*a^2*b^3)*cos(c)^3*sin(c) + 2*(3*a^4*b - 4*a^2*b^3)*cos(c)*sin(c)^3 + 3*((a^5 - 2*a^3*b^2)*cos(c)^2*sin(c) - (a^5 - 2*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - ((a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^4*sin(c) + 2*(a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^2*sin(c)^3 + (a^5 - 8*a^3*b^2 + 8*a*b^4)*sin(c)^5)*cos(d*x^2 + 2*c) + (a^5*cos(d*x^2 + 2*c)^4*cos(c) + (a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^5 + 2*(a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 8*a^3*b^2 + 8*a*b^4)*cos(c)*sin(c)^4 + 4*(a^4*b*cos(c)^2 - a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^3 - 6*((a^5 - 2*a^3*b^2)*cos(c)^3 - (a^5 - 2*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((3*a^4*b - 4*a^2*b^3)*cos(c)^4 - (3*a^4*b - 4*a^2*b^3)*sin(c)^4)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2))/(a^6*cos(d*x^2 + 2*c)^6 + 6*a^5*b*cos(d*x^2 + 2*c)^5*cos(c) + a^6*sin(d*x^2 + 2*c)^6 + 6*a^5*b*sin(d*x^2 + 2*c)^5*sin(c) - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^6 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^4*sin(c)^2 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^2*sin(c)^4 - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*sin(c)^6 - 3*(5*(a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^6*cos(d*x^2 + 2*c)^2 + 2*a^5*b*cos(d*x^2 + 2*c)*cos(c) - (a^6 - 2*a^4*b^2)*cos(c)^2 - 5*(a^6 - 2*a^4*b^2)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(5*(3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 4*(3*a^5*b*cos(d*x^2 + 2*c)^2*sin(c) - 6*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) - 5*(3*a^5*b - 4*a^3*b^3)*sin(c)^3)*sin(d*x^2 + 2*c)^3 + 3*(5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 3*(a^6*cos(d*x^2 + 2*c)^4 + 4*a^5*b*cos(d*x^2 + 2*c)^3*cos(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + 5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4 - 6*((a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 6*((5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^5 + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^3*sin(c)^2 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 6*(a^5*b*cos(d*x^2 + 2*c)^4*sin(c) - 4*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^4*sin(c) + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^2*sin(c)^3 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*sin(c)^5 - 2*(3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) + (3*a^5*b - 4*a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + 2*(3*a^5*cos(d*x^2 + 2*c)^5*cos(c) + 3*a^5*sin(d*x^2 + 2*c)^5*sin(c) + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^6 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^4*sin(c)^2 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^2*sin(c)^4 + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*sin(c)^6 + 3*(5*a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^5*cos(d*x^2 + 2*c)*cos(c) + a^4*b*cos(c)^2 + 5*a^4*b*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(5*(a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(3*a^5*cos(d*x^2 + 2*c)^2*sin(c) + 12*a^4*b*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) - 5*(a^5 - 4*a^3*b^2)*sin(c)^3)*sin(d*x^2 + 2*c)^3 - 6*(5*(a^4*b - 2*a^2*b^3)*cos(c)^4 + 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 + (a^4*b - 2*a^2*b^3)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 6*(a^5*cos(d*x^2 + 2*c)^3*cos(c) - (a^4*b - 2*a^2*b^3)*cos(c)^4 - 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 - 5*(a^4*b - 2*a^2*b^3)*sin(c)^4 + 3*(a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^2 - ((a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 3*((a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^5 + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 3*(a^5*cos(d*x^2 + 2*c)^4*sin(c) + 8*a^4*b*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^4*sin(c) + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^2*sin(c)^3 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*sin(c)^5 - 2*(3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) + (a^5 - 4*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 16*((a^4*b - 2*a^2*b^3)*cos(c)^3*sin(c) + (a^4*b - 2*a^2*b^3)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2)), (a^6*cos(d*x^2 + 2*c)^6 + 6*a^5*b*cos(d*x^2 + 2*c)^5*cos(c) + a^6*sin(d*x^2 + 2*c)^6 + 6*a^5*b*sin(d*x^2 + 2*c)^5*sin(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^6 + 3*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4*sin(c)^2 + 3*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^4 + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^6 - (5*(a^6 - 4*a^4*b^2)*cos(c)^2 + (a^6 - 4*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + (3*a^6*cos(d*x^2 + 2*c)^2 + 6*a^5*b*cos(d*x^2 + 2*c)*cos(c) - (a^6 - 4*a^4*b^2)*cos(c)^2 - 5*(a^6 - 4*a^4*b^2)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(5*(a^5*b - 2*a^3*b^3)*cos(c)^3 + 3*(a^5*b - 2*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 4*(3*a^5*b*cos(d*x^2 + 2*c)^2*sin(c) - 2*(a^6 - 4*a^4*b^2)*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(a^5*b - 2*a^3*b^3)*cos(c)^2*sin(c) - 5*(a^5*b - 2*a^3*b^3)*sin(c)^3)*sin(d*x^2 + 2*c)^3 - (5*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^4 + 6*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^2*sin(c)^2 + (a^6 + 4*a^4*b^2 - 8*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + (3*a^6*cos(d*x^2 + 2*c)^4 + 12*a^5*b*cos(d*x^2 + 2*c)^3*cos(c) - (a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^4 - 6*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^2*sin(c)^2 - 5*(a^6 + 4*a^4*b^2 - 8*a^2*b^4)*sin(c)^4 - 6*((a^6 - 4*a^4*b^2)*cos(c)^2 + (a^6 - 4*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 12*((a^5*b - 2*a^3*b^3)*cos(c)^3 + 3*(a^5*b - 2*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - 2*((5*a^5*b - 8*a*b^5)*cos(c)^5 + 2*(5*a^5*b - 8*a*b^5)*cos(c)^3*sin(c)^2 + (5*a^5*b - 8*a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 2*(3*a^5*b*cos(d*x^2 + 2*c)^4*sin(c) - 4*(a^6 - 4*a^4*b^2)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) - (5*a^5*b - 8*a*b^5)*cos(c)^4*sin(c) - 2*(5*a^5*b - 8*a*b^5)*cos(c)^2*sin(c)^3 - (5*a^5*b - 8*a*b^5)*sin(c)^5 - 6*(3*(a^5*b - 2*a^3*b^3)*cos(c)^2*sin(c) + (a^5*b - 2*a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 4*((a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)^3*sin(c) + (a^6 + 4*a^4*b^2 - 8*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + 4*(a^5*cos(d*x^2 + 2*c)^5*cos(c) + a^5*sin(d*x^2 + 2*c)^5*sin(c) - (a^4*b - 2*a^2*b^3)*cos(c)^6 - 3*(a^4*b - 2*a^2*b^3)*cos(c)^4*sin(c)^2 - 3*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^4 - (a^4*b - 2*a^2*b^3)*sin(c)^6 + (5*a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^4 + (a^5*cos(d*x^2 + 2*c)*cos(c) + a^4*b*cos(c)^2 + 5*a^4*b*sin(c)^2)*sin(d*x^2 + 2*c)^4 + 2*(5*a^3*b^2*cos(c)^3 + 3*a^3*b^2*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(a^5*cos(d*x^2 + 2*c)^2*sin(c) + 4*a^4*b*cos(d*x^2 + 2*c)*cos(c)*sin(c) + 3*a^3*b^2*cos(c)^2*sin(c) + 5*a^3*b^2*sin(c)^3)*sin(d*x^2 + 2*c)^3 + 2*(5*a^2*b^3*cos(c)^4 + 6*a^2*b^3*cos(c)^2*sin(c)^2 + a^2*b^3*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 2*(a^5*cos(d*x^2 + 2*c)^3*cos(c) + a^2*b^3*cos(c)^4 + 6*a^2*b^3*cos(c)^2*sin(c)^2 + 5*a^2*b^3*sin(c)^4 + 3*(a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^2 + 3*(a^3*b^2*cos(c)^3 + 3*a^3*b^2*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 - ((a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^5 + 2*(a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + (a^5*cos(d*x^2 + 2*c)^4*sin(c) + 8*a^4*b*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) - (a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^4*sin(c) - 2*(a^5 - 2*a^3*b^2 - 4*a*b^4)*cos(c)^2*sin(c)^3 - (a^5 - 2*a^3*b^2 - 4*a*b^4)*sin(c)^5 + 6*(3*a^3*b^2*cos(c)^2*sin(c) + a^3*b^2*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 16*(a^2*b^3*cos(c)^3*sin(c) + a^2*b^3*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2))/(a^6*cos(d*x^2 + 2*c)^6 + 6*a^5*b*cos(d*x^2 + 2*c)^5*cos(c) + a^6*sin(d*x^2 + 2*c)^6 + 6*a^5*b*sin(d*x^2 + 2*c)^5*sin(c) - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^6 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^4*sin(c)^2 - 3*(a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*cos(c)^2*sin(c)^4 - (a^6 - 18*a^4*b^2 + 48*a^2*b^4 - 32*b^6)*sin(c)^6 - 3*(5*(a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^6*cos(d*x^2 + 2*c)^2 + 2*a^5*b*cos(d*x^2 + 2*c)*cos(c) - (a^6 - 2*a^4*b^2)*cos(c)^2 - 5*(a^6 - 2*a^4*b^2)*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 4*(5*(3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 4*(3*a^5*b*cos(d*x^2 + 2*c)^2*sin(c) - 6*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) - 5*(3*a^5*b - 4*a^3*b^3)*sin(c)^3)*sin(d*x^2 + 2*c)^3 + 3*(5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 3*(a^6*cos(d*x^2 + 2*c)^4 + 4*a^5*b*cos(d*x^2 + 2*c)^3*cos(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^4 + 6*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^2*sin(c)^2 + 5*(a^6 - 8*a^4*b^2 + 8*a^2*b^4)*sin(c)^4 - 6*((a^6 - 2*a^4*b^2)*cos(c)^2 + (a^6 - 2*a^4*b^2)*sin(c)^2)*cos(d*x^2 + 2*c)^2 - 4*((3*a^5*b - 4*a^3*b^3)*cos(c)^3 + 3*(3*a^5*b - 4*a^3*b^3)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 6*((5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^5 + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^3*sin(c)^2 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 6*(a^5*b*cos(d*x^2 + 2*c)^4*sin(c) - 4*(a^6 - 2*a^4*b^2)*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^4*sin(c) + 2*(5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*cos(c)^2*sin(c)^3 + (5*a^5*b - 20*a^3*b^3 + 16*a*b^5)*sin(c)^5 - 2*(3*(3*a^5*b - 4*a^3*b^3)*cos(c)^2*sin(c) + (3*a^5*b - 4*a^3*b^3)*sin(c)^3)*cos(d*x^2 + 2*c)^2 + 4*((a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)^3*sin(c) + (a^6 - 8*a^4*b^2 + 8*a^2*b^4)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c) + 2*(3*a^5*cos(d*x^2 + 2*c)^5*cos(c) + 3*a^5*sin(d*x^2 + 2*c)^5*sin(c) + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^6 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^4*sin(c)^2 + 3*(3*a^4*b - 16*a^2*b^3 + 16*b^5)*cos(c)^2*sin(c)^4 + (3*a^4*b - 16*a^2*b^3 + 16*b^5)*sin(c)^6 + 3*(5*a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^4 + 3*(a^5*cos(d*x^2 + 2*c)*cos(c) + a^4*b*cos(c)^2 + 5*a^4*b*sin(c)^2)*sin(d*x^2 + 2*c)^4 - 2*(5*(a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c)^3 + 2*(3*a^5*cos(d*x^2 + 2*c)^2*sin(c) + 12*a^4*b*cos(d*x^2 + 2*c)*cos(c)*sin(c) - 3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) - 5*(a^5 - 4*a^3*b^2)*sin(c)^3)*sin(d*x^2 + 2*c)^3 - 6*(5*(a^4*b - 2*a^2*b^3)*cos(c)^4 + 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 + (a^4*b - 2*a^2*b^3)*sin(c)^4)*cos(d*x^2 + 2*c)^2 + 6*(a^5*cos(d*x^2 + 2*c)^3*cos(c) - (a^4*b - 2*a^2*b^3)*cos(c)^4 - 6*(a^4*b - 2*a^2*b^3)*cos(c)^2*sin(c)^2 - 5*(a^4*b - 2*a^2*b^3)*sin(c)^4 + 3*(a^4*b*cos(c)^2 + a^4*b*sin(c)^2)*cos(d*x^2 + 2*c)^2 - ((a^5 - 4*a^3*b^2)*cos(c)^3 + 3*(a^5 - 4*a^3*b^2)*cos(c)*sin(c)^2)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c)^2 + 3*((a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^5 + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^3*sin(c)^2 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)*sin(c)^4)*cos(d*x^2 + 2*c) + 3*(a^5*cos(d*x^2 + 2*c)^4*sin(c) + 8*a^4*b*cos(d*x^2 + 2*c)^3*cos(c)*sin(c) + (a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^4*sin(c) + 2*(a^5 - 12*a^3*b^2 + 16*a*b^4)*cos(c)^2*sin(c)^3 + (a^5 - 12*a^3*b^2 + 16*a*b^4)*sin(c)^5 - 2*(3*(a^5 - 4*a^3*b^2)*cos(c)^2*sin(c) + (a^5 - 4*a^3*b^2)*sin(c)^3)*cos(d*x^2 + 2*c)^2 - 16*((a^4*b - 2*a^2*b^3)*cos(c)^3*sin(c) + (a^4*b - 2*a^2*b^3)*cos(c)*sin(c)^3)*cos(d*x^2 + 2*c))*sin(d*x^2 + 2*c))*sqrt(-a^2 + b^2))) + 2*(2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x^2*cos(d*x^2 + c) + (a^6 - 2*a^4*b^2 + a^2*b^4)*d*x^2 - (a^3*b^3 - a*b^5)*sin(d*x^2 + c))*cos(2*d*x^2 + 2*c) + 2*(a^4*b^2 - a^2*b^4 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x^2*sin(d*x^2 + c) + (a^3*b^3 - a*b^5)*cos(d*x^2 + c))*sin(2*d*x^2 + 2*c) + 2*(a^3*b^3 - a*b^5)*sin(d*x^2 + c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(2*d*x^2 + 2*c)^2 + 4*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*d*cos(d*x^2 + c)^2 + (a^8 - 2*a^6*b^2 + a^4*b^4)*d*sin(2*d*x^2 + 2*c)^2 + 4*(a^7*b - 2*a^5*b^3 + a^3*b^5)*d*sin(2*d*x^2 + 2*c)*sin(d*x^2 + c) + 4*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*d*sin(d*x^2 + c)^2 + 4*(a^7*b - 2*a^5*b^3 + a^3*b^5)*d*cos(d*x^2 + c) + (a^8 - 2*a^6*b^2 + a^4*b^4)*d + 2*(2*(a^7*b - 2*a^5*b^3 + a^3*b^5)*d*cos(d*x^2 + c) + (a^8 - 2*a^6*b^2 + a^4*b^4)*d)*cos(2*d*x^2 + 2*c))","B",0
28,-1,0,0,0.000000," ","integrate(1/x/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate(1/x^3/(a+b*sec(d*x^2+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,1,1512,0,1.069614," ","integrate(x^3*(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{8} a - 8 \, {\left(d \sqrt{x} + c\right)}^{7} a c + 28 \, {\left(d \sqrt{x} + c\right)}^{6} a c^{2} - 56 \, {\left(d \sqrt{x} + c\right)}^{5} a c^{3} + 70 \, {\left(d \sqrt{x} + c\right)}^{4} a c^{4} - 56 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{5} + 28 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{6} - 8 \, {\left(d \sqrt{x} + c\right)} a c^{7} - 8 \, b c^{7} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + 4 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{7} b + 14 i \, {\left(d \sqrt{x} + c\right)}^{6} b c - 42 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} + 70 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} - 70 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} + 42 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} - 14 i \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + 4 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{7} b + 14 i \, {\left(d \sqrt{x} + c\right)}^{6} b c - 42 i \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} + 70 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} - 70 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} + 42 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} - 14 i \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + 4 \, {\left(-14 i \, {\left(d \sqrt{x} + c\right)}^{6} b + 84 i \, {\left(d \sqrt{x} + c\right)}^{5} b c - 210 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} + 280 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} - 210 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} + 84 i \, {\left(d \sqrt{x} + c\right)} b c^{5} - 14 i \, b c^{6}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 4 \, {\left(14 i \, {\left(d \sqrt{x} + c\right)}^{6} b - 84 i \, {\left(d \sqrt{x} + c\right)}^{5} b c + 210 i \, {\left(d \sqrt{x} + c\right)}^{4} b c^{2} - 280 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{3} + 210 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{4} - 84 i \, {\left(d \sqrt{x} + c\right)} b c^{5} + 14 i \, b c^{6}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 4 \, {\left({\left(d \sqrt{x} + c\right)}^{7} b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 4 \, {\left({\left(d \sqrt{x} + c\right)}^{7} b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} b c^{6}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + 40320 i \, b {\rm Li}_{8}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 40320 i \, b {\rm Li}_{8}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 40320 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{7}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 40320 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{7}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 4 \, {\left(-5040 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 10080 i \, {\left(d \sqrt{x} + c\right)} b c - 5040 i \, b c^{2}\right)} {\rm Li}_{6}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 4 \, {\left(5040 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 10080 i \, {\left(d \sqrt{x} + c\right)} b c + 5040 i \, b c^{2}\right)} {\rm Li}_{6}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 6720 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{5}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 6720 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{5}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 4 \, {\left(420 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 1680 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 2520 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 1680 i \, {\left(d \sqrt{x} + c\right)} b c^{3} + 420 i \, b c^{4}\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 4 \, {\left(-420 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 1680 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 2520 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 1680 i \, {\left(d \sqrt{x} + c\right)} b c^{3} - 420 i \, b c^{4}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 336 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4} - b c^{5}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 336 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4} - b c^{5}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)})}{4 \, d^{8}}"," ",0,"1/4*((d*sqrt(x) + c)^8*a - 8*(d*sqrt(x) + c)^7*a*c + 28*(d*sqrt(x) + c)^6*a*c^2 - 56*(d*sqrt(x) + c)^5*a*c^3 + 70*(d*sqrt(x) + c)^4*a*c^4 - 56*(d*sqrt(x) + c)^3*a*c^5 + 28*(d*sqrt(x) + c)^2*a*c^6 - 8*(d*sqrt(x) + c)*a*c^7 - 8*b*c^7*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 4*(-2*I*(d*sqrt(x) + c)^7*b + 14*I*(d*sqrt(x) + c)^6*b*c - 42*I*(d*sqrt(x) + c)^5*b*c^2 + 70*I*(d*sqrt(x) + c)^4*b*c^3 - 70*I*(d*sqrt(x) + c)^3*b*c^4 + 42*I*(d*sqrt(x) + c)^2*b*c^5 - 14*I*(d*sqrt(x) + c)*b*c^6)*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + 4*(-2*I*(d*sqrt(x) + c)^7*b + 14*I*(d*sqrt(x) + c)^6*b*c - 42*I*(d*sqrt(x) + c)^5*b*c^2 + 70*I*(d*sqrt(x) + c)^4*b*c^3 - 70*I*(d*sqrt(x) + c)^3*b*c^4 + 42*I*(d*sqrt(x) + c)^2*b*c^5 - 14*I*(d*sqrt(x) + c)*b*c^6)*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + 4*(-14*I*(d*sqrt(x) + c)^6*b + 84*I*(d*sqrt(x) + c)^5*b*c - 210*I*(d*sqrt(x) + c)^4*b*c^2 + 280*I*(d*sqrt(x) + c)^3*b*c^3 - 210*I*(d*sqrt(x) + c)^2*b*c^4 + 84*I*(d*sqrt(x) + c)*b*c^5 - 14*I*b*c^6)*dilog(I*e^(I*d*sqrt(x) + I*c)) + 4*(14*I*(d*sqrt(x) + c)^6*b - 84*I*(d*sqrt(x) + c)^5*b*c + 210*I*(d*sqrt(x) + c)^4*b*c^2 - 280*I*(d*sqrt(x) + c)^3*b*c^3 + 210*I*(d*sqrt(x) + c)^2*b*c^4 - 84*I*(d*sqrt(x) + c)*b*c^5 + 14*I*b*c^6)*dilog(-I*e^(I*d*sqrt(x) + I*c)) + 4*((d*sqrt(x) + c)^7*b - 7*(d*sqrt(x) + c)^6*b*c + 21*(d*sqrt(x) + c)^5*b*c^2 - 35*(d*sqrt(x) + c)^4*b*c^3 + 35*(d*sqrt(x) + c)^3*b*c^4 - 21*(d*sqrt(x) + c)^2*b*c^5 + 7*(d*sqrt(x) + c)*b*c^6)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - 4*((d*sqrt(x) + c)^7*b - 7*(d*sqrt(x) + c)^6*b*c + 21*(d*sqrt(x) + c)^5*b*c^2 - 35*(d*sqrt(x) + c)^4*b*c^3 + 35*(d*sqrt(x) + c)^3*b*c^4 - 21*(d*sqrt(x) + c)^2*b*c^5 + 7*(d*sqrt(x) + c)*b*c^6)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) + 40320*I*b*polylog(8, I*e^(I*d*sqrt(x) + I*c)) - 40320*I*b*polylog(8, -I*e^(I*d*sqrt(x) + I*c)) + 40320*((d*sqrt(x) + c)*b - b*c)*polylog(7, I*e^(I*d*sqrt(x) + I*c)) - 40320*((d*sqrt(x) + c)*b - b*c)*polylog(7, -I*e^(I*d*sqrt(x) + I*c)) + 4*(-5040*I*(d*sqrt(x) + c)^2*b + 10080*I*(d*sqrt(x) + c)*b*c - 5040*I*b*c^2)*polylog(6, I*e^(I*d*sqrt(x) + I*c)) + 4*(5040*I*(d*sqrt(x) + c)^2*b - 10080*I*(d*sqrt(x) + c)*b*c + 5040*I*b*c^2)*polylog(6, -I*e^(I*d*sqrt(x) + I*c)) - 6720*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(5, I*e^(I*d*sqrt(x) + I*c)) + 6720*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(5, -I*e^(I*d*sqrt(x) + I*c)) + 4*(420*I*(d*sqrt(x) + c)^4*b - 1680*I*(d*sqrt(x) + c)^3*b*c + 2520*I*(d*sqrt(x) + c)^2*b*c^2 - 1680*I*(d*sqrt(x) + c)*b*c^3 + 420*I*b*c^4)*polylog(4, I*e^(I*d*sqrt(x) + I*c)) + 4*(-420*I*(d*sqrt(x) + c)^4*b + 1680*I*(d*sqrt(x) + c)^3*b*c - 2520*I*(d*sqrt(x) + c)^2*b*c^2 + 1680*I*(d*sqrt(x) + c)*b*c^3 - 420*I*b*c^4)*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) + 336*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4 - b*c^5)*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - 336*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4 - b*c^5)*polylog(3, -I*e^(I*d*sqrt(x) + I*c)))/d^8","B",0
32,1,966,0,1.005687," ","integrate(x^2*(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{6} a - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a c^{5} - 6 \, b c^{5} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + 3 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{5} b + 10 i \, {\left(d \sqrt{x} + c\right)}^{4} b c - 20 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} + 20 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} - 10 i \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + 3 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{5} b + 10 i \, {\left(d \sqrt{x} + c\right)}^{4} b c - 20 i \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} + 20 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} - 10 i \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + 3 \, {\left(-10 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 40 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 60 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 40 i \, {\left(d \sqrt{x} + c\right)} b c^{3} - 10 i \, b c^{4}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 3 \, {\left(10 i \, {\left(d \sqrt{x} + c\right)}^{4} b - 40 i \, {\left(d \sqrt{x} + c\right)}^{3} b c + 60 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 40 i \, {\left(d \sqrt{x} + c\right)} b c^{3} + 10 i \, b c^{4}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 3 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 3 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b c^{4}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 720 i \, b {\rm Li}_{6}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 720 i \, b {\rm Li}_{6}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 720 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{5}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 720 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{5}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 3 \, {\left(120 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 240 i \, {\left(d \sqrt{x} + c\right)} b c + 120 i \, b c^{2}\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 3 \, {\left(-120 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 240 i \, {\left(d \sqrt{x} + c\right)} b c - 120 i \, b c^{2}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 120 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 120 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2} - b c^{3}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)})}{3 \, d^{6}}"," ",0,"1/3*((d*sqrt(x) + c)^6*a - 6*(d*sqrt(x) + c)^5*a*c + 15*(d*sqrt(x) + c)^4*a*c^2 - 20*(d*sqrt(x) + c)^3*a*c^3 + 15*(d*sqrt(x) + c)^2*a*c^4 - 6*(d*sqrt(x) + c)*a*c^5 - 6*b*c^5*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 3*(-2*I*(d*sqrt(x) + c)^5*b + 10*I*(d*sqrt(x) + c)^4*b*c - 20*I*(d*sqrt(x) + c)^3*b*c^2 + 20*I*(d*sqrt(x) + c)^2*b*c^3 - 10*I*(d*sqrt(x) + c)*b*c^4)*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + 3*(-2*I*(d*sqrt(x) + c)^5*b + 10*I*(d*sqrt(x) + c)^4*b*c - 20*I*(d*sqrt(x) + c)^3*b*c^2 + 20*I*(d*sqrt(x) + c)^2*b*c^3 - 10*I*(d*sqrt(x) + c)*b*c^4)*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + 3*(-10*I*(d*sqrt(x) + c)^4*b + 40*I*(d*sqrt(x) + c)^3*b*c - 60*I*(d*sqrt(x) + c)^2*b*c^2 + 40*I*(d*sqrt(x) + c)*b*c^3 - 10*I*b*c^4)*dilog(I*e^(I*d*sqrt(x) + I*c)) + 3*(10*I*(d*sqrt(x) + c)^4*b - 40*I*(d*sqrt(x) + c)^3*b*c + 60*I*(d*sqrt(x) + c)^2*b*c^2 - 40*I*(d*sqrt(x) + c)*b*c^3 + 10*I*b*c^4)*dilog(-I*e^(I*d*sqrt(x) + I*c)) + 3*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - 3*((d*sqrt(x) + c)^5*b - 5*(d*sqrt(x) + c)^4*b*c + 10*(d*sqrt(x) + c)^3*b*c^2 - 10*(d*sqrt(x) + c)^2*b*c^3 + 5*(d*sqrt(x) + c)*b*c^4)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) - 720*I*b*polylog(6, I*e^(I*d*sqrt(x) + I*c)) + 720*I*b*polylog(6, -I*e^(I*d*sqrt(x) + I*c)) - 720*((d*sqrt(x) + c)*b - b*c)*polylog(5, I*e^(I*d*sqrt(x) + I*c)) + 720*((d*sqrt(x) + c)*b - b*c)*polylog(5, -I*e^(I*d*sqrt(x) + I*c)) + 3*(120*I*(d*sqrt(x) + c)^2*b - 240*I*(d*sqrt(x) + c)*b*c + 120*I*b*c^2)*polylog(4, I*e^(I*d*sqrt(x) + I*c)) + 3*(-120*I*(d*sqrt(x) + c)^2*b + 240*I*(d*sqrt(x) + c)*b*c - 120*I*b*c^2)*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) + 120*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - 120*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2 - b*c^3)*polylog(3, -I*e^(I*d*sqrt(x) + I*c)))/d^6","B",0
33,1,540,0,0.894782," ","integrate(x*(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{4} a - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a c^{3} - 4 \, b c^{3} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + 2 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{3} b + 6 i \, {\left(d \sqrt{x} + c\right)}^{2} b c - 6 i \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + 2 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{3} b + 6 i \, {\left(d \sqrt{x} + c\right)}^{2} b c - 6 i \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + 2 \, {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 12 i \, {\left(d \sqrt{x} + c\right)} b c - 6 i \, b c^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 2 \, {\left(6 i \, {\left(d \sqrt{x} + c\right)}^{2} b - 12 i \, {\left(d \sqrt{x} + c\right)} b c + 6 i \, b c^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b c + 3 \, {\left(d \sqrt{x} + c\right)} b c^{2}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + 24 i \, b {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 24 i \, b {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 24 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 24 \, {\left({\left(d \sqrt{x} + c\right)} b - b c\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)})}{2 \, d^{4}}"," ",0,"1/2*((d*sqrt(x) + c)^4*a - 4*(d*sqrt(x) + c)^3*a*c + 6*(d*sqrt(x) + c)^2*a*c^2 - 4*(d*sqrt(x) + c)*a*c^3 - 4*b*c^3*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 2*(-2*I*(d*sqrt(x) + c)^3*b + 6*I*(d*sqrt(x) + c)^2*b*c - 6*I*(d*sqrt(x) + c)*b*c^2)*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + 2*(-2*I*(d*sqrt(x) + c)^3*b + 6*I*(d*sqrt(x) + c)^2*b*c - 6*I*(d*sqrt(x) + c)*b*c^2)*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + 2*(-6*I*(d*sqrt(x) + c)^2*b + 12*I*(d*sqrt(x) + c)*b*c - 6*I*b*c^2)*dilog(I*e^(I*d*sqrt(x) + I*c)) + 2*(6*I*(d*sqrt(x) + c)^2*b - 12*I*(d*sqrt(x) + c)*b*c + 6*I*b*c^2)*dilog(-I*e^(I*d*sqrt(x) + I*c)) + 2*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - 2*((d*sqrt(x) + c)^3*b - 3*(d*sqrt(x) + c)^2*b*c + 3*(d*sqrt(x) + c)*b*c^2)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) + 24*I*b*polylog(4, I*e^(I*d*sqrt(x) + I*c)) - 24*I*b*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) + 24*((d*sqrt(x) + c)*b - b*c)*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - 24*((d*sqrt(x) + c)*b - b*c)*polylog(3, -I*e^(I*d*sqrt(x) + I*c)))/d^4","B",0
34,0,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))/x,x, algorithm=""maxima"")","2 \, b \int \frac{\cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + \cos\left(d \sqrt{x} + c\right)}{{\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right)} x}\,{d x} + a \log\left(x\right)"," ",0,"2*b*integrate((cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + cos(d*sqrt(x) + c))/((cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1)*x), x) + a*log(x)","F",0
35,-1,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,1,6373,0,1.623227," ","integrate(x^3*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{8} a^{2} - 8 \, {\left(d \sqrt{x} + c\right)}^{7} a^{2} c + 28 \, {\left(d \sqrt{x} + c\right)}^{6} a^{2} c^{2} - 56 \, {\left(d \sqrt{x} + c\right)}^{5} a^{2} c^{3} + 70 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c^{4} - 56 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{5} + 28 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{6} - 8 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{7} - 16 \, a b c^{7} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) - \frac{8 \, {\left(60 \, b^{2} c^{7} + {\left(60 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 420 \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 1260 \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 2100 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 2100 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 1260 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 420 \, {\left(d \sqrt{x} + c\right)} a b c^{6} + 60 \, {\left({\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-60 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + 420 i \, {\left(d \sqrt{x} + c\right)}^{6} a b c - 1260 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} + 2100 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} - 2100 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} + 1260 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} - 420 i \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(60 \, {\left(d \sqrt{x} + c\right)}^{7} a b - 420 \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 1260 \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 2100 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 2100 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 1260 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 420 \, {\left(d \sqrt{x} + c\right)} a b c^{6} + 60 \, {\left({\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-60 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + 420 i \, {\left(d \sqrt{x} + c\right)}^{6} a b c - 1260 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} + 2100 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} - 2100 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} + 1260 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} - 420 i \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(1120 \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} - 4032 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c + 6300 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{2} - 5600 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{3} + 3150 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{4} - 1260 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} + 210 \, b^{2} c^{6} + 14 \, {\left(80 \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} - 288 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c + 450 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{2} - 400 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{3} + 225 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{4} - 90 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} + 15 \, b^{2} c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(1120 i \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} - 4032 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c + 6300 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{2} - 5600 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{3} + 3150 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{4} - 1260 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} + 210 i \, b^{2} c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + 60 \, {\left({\left(d \sqrt{x} + c\right)}^{7} b^{2} - 7 \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(3360 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} - 10080 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c + 12600 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} - 8400 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} + 3150 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4} - 630 \, b^{2} c^{5} + 210 \, {\left(16 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} - 48 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c + 60 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} - 40 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} + 15 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4} - 3 \, b^{2} c^{5}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-3360 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} + 10080 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c - 12600 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} + 8400 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} - 3150 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4} + 630 i \, b^{2} c^{5}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) + {\left(420 \, {\left(d \sqrt{x} + c\right)}^{6} a b - 2520 \, {\left(d \sqrt{x} + c\right)}^{5} a b c + 6300 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{2} - 8400 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{3} + 6300 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{4} - 2520 \, {\left(d \sqrt{x} + c\right)} a b c^{5} + 420 \, a b c^{6} + 420 \, {\left({\left(d \sqrt{x} + c\right)}^{6} a b - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a b c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a b c^{5} + a b c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-420 i \, {\left(d \sqrt{x} + c\right)}^{6} a b + 2520 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c - 6300 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{2} + 8400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{3} - 6300 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{4} + 2520 i \, {\left(d \sqrt{x} + c\right)} a b c^{5} - 420 i \, a b c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(420 \, {\left(d \sqrt{x} + c\right)}^{6} a b - 2520 \, {\left(d \sqrt{x} + c\right)}^{5} a b c + 6300 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{2} - 8400 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{3} + 6300 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{4} - 2520 \, {\left(d \sqrt{x} + c\right)} a b c^{5} + 420 \, a b c^{6} + 420 \, {\left({\left(d \sqrt{x} + c\right)}^{6} a b - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a b c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a b c^{5} + a b c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(420 i \, {\left(d \sqrt{x} + c\right)}^{6} a b - 2520 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c + 6300 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{2} - 8400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{3} + 6300 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{4} - 2520 i \, {\left(d \sqrt{x} + c\right)} a b c^{5} + 420 i \, a b c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(-560 i \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} + 2016 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c - 3150 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{2} + 2800 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{3} - 1575 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{4} + 630 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} - 105 i \, b^{2} c^{6} + {\left(-560 i \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} + 2016 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c - 3150 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{2} + 2800 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{3} - 1575 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{4} + 630 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} - 105 i \, b^{2} c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 7 \, {\left(80 \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} - 288 \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c + 450 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{2} - 400 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{3} + 225 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{4} - 90 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{5} + 15 \, b^{2} c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - {\left(-30 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + 210 i \, {\left(d \sqrt{x} + c\right)}^{6} a b c - 630 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} + 1050 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} - 1050 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} + 630 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} - 210 i \, {\left(d \sqrt{x} + c\right)} a b c^{6} + {\left(-30 i \, {\left(d \sqrt{x} + c\right)}^{7} a b + 210 i \, {\left(d \sqrt{x} + c\right)}^{6} a b c - 630 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} + 1050 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} - 1050 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} + 630 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} - 210 i \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 30 \, {\left({\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(30 i \, {\left(d \sqrt{x} + c\right)}^{7} a b - 210 i \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 630 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 1050 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 1050 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 630 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 210 i \, {\left(d \sqrt{x} + c\right)} a b c^{6} + {\left(30 i \, {\left(d \sqrt{x} + c\right)}^{7} a b - 210 i \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 630 i \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 1050 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 1050 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 630 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 210 i \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 30 \, {\left({\left(d \sqrt{x} + c\right)}^{7} a b - 7 \, {\left(d \sqrt{x} + c\right)}^{6} a b c + 21 \, {\left(d \sqrt{x} + c\right)}^{5} a b c^{2} - 35 \, {\left(d \sqrt{x} + c\right)}^{4} a b c^{3} + 35 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{4} - 21 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{5} + 7 \, {\left(d \sqrt{x} + c\right)} a b c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 302400 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{8}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 302400 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{8}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-12600 i \, b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 12600 \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 12600 i \, b^{2}\right)} {\rm Li}_{7}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(-302400 i \, {\left(d \sqrt{x} + c\right)} a b + 302400 i \, a b c + {\left(-302400 i \, {\left(d \sqrt{x} + c\right)} a b + 302400 i \, a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 302400 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{7}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(302400 i \, {\left(d \sqrt{x} + c\right)} a b - 302400 i \, a b c + {\left(302400 i \, {\left(d \sqrt{x} + c\right)} a b - 302400 i \, a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 302400 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{7}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(25200 \, {\left(d \sqrt{x} + c\right)} b^{2} - 15120 \, b^{2} c + 5040 \, {\left(5 \, {\left(d \sqrt{x} + c\right)} b^{2} - 3 \, b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-25200 i \, {\left(d \sqrt{x} + c\right)} b^{2} + 15120 i \, b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{6}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(151200 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 302400 \, {\left(d \sqrt{x} + c\right)} a b c + 151200 \, a b c^{2} + 151200 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-151200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 302400 i \, {\left(d \sqrt{x} + c\right)} a b c - 151200 i \, a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{6}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(151200 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 302400 \, {\left(d \sqrt{x} + c\right)} a b c + 151200 \, a b c^{2} + 151200 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(151200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 302400 i \, {\left(d \sqrt{x} + c\right)} a b c + 151200 i \, a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{6}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(25200 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 30240 i \, {\left(d \sqrt{x} + c\right)} b^{2} c + 9450 i \, b^{2} c^{2} + {\left(25200 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 30240 i \, {\left(d \sqrt{x} + c\right)} b^{2} c + 9450 i \, b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 630 \, {\left(40 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 48 \, {\left(d \sqrt{x} + c\right)} b^{2} c + 15 \, b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(50400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 151200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 151200 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 50400 i \, a b c^{3} + {\left(50400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 151200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 151200 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 50400 i \, a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 50400 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-50400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 151200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 151200 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 50400 i \, a b c^{3} + {\left(-50400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 151200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 151200 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 50400 i \, a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 50400 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(16800 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 30240 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 18900 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 4200 \, b^{2} c^{3} + 420 \, {\left(40 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 72 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 45 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 10 \, b^{2} c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(16800 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 30240 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 18900 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 4200 i \, b^{2} c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(12600 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 50400 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 75600 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 50400 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 12600 \, a b c^{4} + 12600 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(12600 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 50400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 75600 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 50400 i \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 12600 i \, a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(12600 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 50400 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 75600 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 50400 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 12600 \, a b c^{4} + 12600 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-12600 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 50400 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c - 75600 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} + 50400 i \, {\left(d \sqrt{x} + c\right)} a b c^{3} - 12600 i \, a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-8400 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} + 20160 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c - 18900 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} + 8400 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} - 1575 i \, b^{2} c^{4} + {\left(-8400 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} + 20160 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c - 18900 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} + 8400 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} - 1575 i \, b^{2} c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 105 \, {\left(80 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} - 192 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 180 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 80 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} + 15 \, b^{2} c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(-2520 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 12600 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c - 25200 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} + 25200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} - 12600 i \, {\left(d \sqrt{x} + c\right)} a b c^{4} + 2520 i \, a b c^{5} + {\left(-2520 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 12600 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c - 25200 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} + 25200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} - 12600 i \, {\left(d \sqrt{x} + c\right)} a b c^{4} + 2520 i \, a b c^{5}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2520 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a b c^{4} - a b c^{5}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(2520 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 12600 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 25200 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 25200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 12600 i \, {\left(d \sqrt{x} + c\right)} a b c^{4} - 2520 i \, a b c^{5} + {\left(2520 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 12600 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 25200 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 25200 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 12600 i \, {\left(d \sqrt{x} + c\right)} a b c^{4} - 2520 i \, a b c^{5}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2520 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a b c^{4} - a b c^{5}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-60 i \, {\left(d \sqrt{x} + c\right)}^{7} b^{2} + 420 i \, {\left(d \sqrt{x} + c\right)}^{6} b^{2} c - 1260 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} c^{2} + 2100 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c^{3} - 2100 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{4} + 1260 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{5} - 420 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{6}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-30 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 30 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 30 i}}{4 \, d^{8}}"," ",0,"1/4*((d*sqrt(x) + c)^8*a^2 - 8*(d*sqrt(x) + c)^7*a^2*c + 28*(d*sqrt(x) + c)^6*a^2*c^2 - 56*(d*sqrt(x) + c)^5*a^2*c^3 + 70*(d*sqrt(x) + c)^4*a^2*c^4 - 56*(d*sqrt(x) + c)^3*a^2*c^5 + 28*(d*sqrt(x) + c)^2*a^2*c^6 - 8*(d*sqrt(x) + c)*a^2*c^7 - 16*a*b*c^7*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) - 8*(60*b^2*c^7 + (60*(d*sqrt(x) + c)^7*a*b - 420*(d*sqrt(x) + c)^6*a*b*c + 1260*(d*sqrt(x) + c)^5*a*b*c^2 - 2100*(d*sqrt(x) + c)^4*a*b*c^3 + 2100*(d*sqrt(x) + c)^3*a*b*c^4 - 1260*(d*sqrt(x) + c)^2*a*b*c^5 + 420*(d*sqrt(x) + c)*a*b*c^6 + 60*((d*sqrt(x) + c)^7*a*b - 7*(d*sqrt(x) + c)^6*a*b*c + 21*(d*sqrt(x) + c)^5*a*b*c^2 - 35*(d*sqrt(x) + c)^4*a*b*c^3 + 35*(d*sqrt(x) + c)^3*a*b*c^4 - 21*(d*sqrt(x) + c)^2*a*b*c^5 + 7*(d*sqrt(x) + c)*a*b*c^6)*cos(2*d*sqrt(x) + 2*c) - (-60*I*(d*sqrt(x) + c)^7*a*b + 420*I*(d*sqrt(x) + c)^6*a*b*c - 1260*I*(d*sqrt(x) + c)^5*a*b*c^2 + 2100*I*(d*sqrt(x) + c)^4*a*b*c^3 - 2100*I*(d*sqrt(x) + c)^3*a*b*c^4 + 1260*I*(d*sqrt(x) + c)^2*a*b*c^5 - 420*I*(d*sqrt(x) + c)*a*b*c^6)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + (60*(d*sqrt(x) + c)^7*a*b - 420*(d*sqrt(x) + c)^6*a*b*c + 1260*(d*sqrt(x) + c)^5*a*b*c^2 - 2100*(d*sqrt(x) + c)^4*a*b*c^3 + 2100*(d*sqrt(x) + c)^3*a*b*c^4 - 1260*(d*sqrt(x) + c)^2*a*b*c^5 + 420*(d*sqrt(x) + c)*a*b*c^6 + 60*((d*sqrt(x) + c)^7*a*b - 7*(d*sqrt(x) + c)^6*a*b*c + 21*(d*sqrt(x) + c)^5*a*b*c^2 - 35*(d*sqrt(x) + c)^4*a*b*c^3 + 35*(d*sqrt(x) + c)^3*a*b*c^4 - 21*(d*sqrt(x) + c)^2*a*b*c^5 + 7*(d*sqrt(x) + c)*a*b*c^6)*cos(2*d*sqrt(x) + 2*c) - (-60*I*(d*sqrt(x) + c)^7*a*b + 420*I*(d*sqrt(x) + c)^6*a*b*c - 1260*I*(d*sqrt(x) + c)^5*a*b*c^2 + 2100*I*(d*sqrt(x) + c)^4*a*b*c^3 - 2100*I*(d*sqrt(x) + c)^3*a*b*c^4 + 1260*I*(d*sqrt(x) + c)^2*a*b*c^5 - 420*I*(d*sqrt(x) + c)*a*b*c^6)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) - (1120*(d*sqrt(x) + c)^6*b^2 - 4032*(d*sqrt(x) + c)^5*b^2*c + 6300*(d*sqrt(x) + c)^4*b^2*c^2 - 5600*(d*sqrt(x) + c)^3*b^2*c^3 + 3150*(d*sqrt(x) + c)^2*b^2*c^4 - 1260*(d*sqrt(x) + c)*b^2*c^5 + 210*b^2*c^6 + 14*(80*(d*sqrt(x) + c)^6*b^2 - 288*(d*sqrt(x) + c)^5*b^2*c + 450*(d*sqrt(x) + c)^4*b^2*c^2 - 400*(d*sqrt(x) + c)^3*b^2*c^3 + 225*(d*sqrt(x) + c)^2*b^2*c^4 - 90*(d*sqrt(x) + c)*b^2*c^5 + 15*b^2*c^6)*cos(2*d*sqrt(x) + 2*c) + (1120*I*(d*sqrt(x) + c)^6*b^2 - 4032*I*(d*sqrt(x) + c)^5*b^2*c + 6300*I*(d*sqrt(x) + c)^4*b^2*c^2 - 5600*I*(d*sqrt(x) + c)^3*b^2*c^3 + 3150*I*(d*sqrt(x) + c)^2*b^2*c^4 - 1260*I*(d*sqrt(x) + c)*b^2*c^5 + 210*I*b^2*c^6)*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) + 60*((d*sqrt(x) + c)^7*b^2 - 7*(d*sqrt(x) + c)^6*b^2*c + 21*(d*sqrt(x) + c)^5*b^2*c^2 - 35*(d*sqrt(x) + c)^4*b^2*c^3 + 35*(d*sqrt(x) + c)^3*b^2*c^4 - 21*(d*sqrt(x) + c)^2*b^2*c^5 + 7*(d*sqrt(x) + c)*b^2*c^6)*cos(2*d*sqrt(x) + 2*c) + (3360*(d*sqrt(x) + c)^5*b^2 - 10080*(d*sqrt(x) + c)^4*b^2*c + 12600*(d*sqrt(x) + c)^3*b^2*c^2 - 8400*(d*sqrt(x) + c)^2*b^2*c^3 + 3150*(d*sqrt(x) + c)*b^2*c^4 - 630*b^2*c^5 + 210*(16*(d*sqrt(x) + c)^5*b^2 - 48*(d*sqrt(x) + c)^4*b^2*c + 60*(d*sqrt(x) + c)^3*b^2*c^2 - 40*(d*sqrt(x) + c)^2*b^2*c^3 + 15*(d*sqrt(x) + c)*b^2*c^4 - 3*b^2*c^5)*cos(2*d*sqrt(x) + 2*c) - (-3360*I*(d*sqrt(x) + c)^5*b^2 + 10080*I*(d*sqrt(x) + c)^4*b^2*c - 12600*I*(d*sqrt(x) + c)^3*b^2*c^2 + 8400*I*(d*sqrt(x) + c)^2*b^2*c^3 - 3150*I*(d*sqrt(x) + c)*b^2*c^4 + 630*I*b^2*c^5)*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) + (420*(d*sqrt(x) + c)^6*a*b - 2520*(d*sqrt(x) + c)^5*a*b*c + 6300*(d*sqrt(x) + c)^4*a*b*c^2 - 8400*(d*sqrt(x) + c)^3*a*b*c^3 + 6300*(d*sqrt(x) + c)^2*a*b*c^4 - 2520*(d*sqrt(x) + c)*a*b*c^5 + 420*a*b*c^6 + 420*((d*sqrt(x) + c)^6*a*b - 6*(d*sqrt(x) + c)^5*a*b*c + 15*(d*sqrt(x) + c)^4*a*b*c^2 - 20*(d*sqrt(x) + c)^3*a*b*c^3 + 15*(d*sqrt(x) + c)^2*a*b*c^4 - 6*(d*sqrt(x) + c)*a*b*c^5 + a*b*c^6)*cos(2*d*sqrt(x) + 2*c) - (-420*I*(d*sqrt(x) + c)^6*a*b + 2520*I*(d*sqrt(x) + c)^5*a*b*c - 6300*I*(d*sqrt(x) + c)^4*a*b*c^2 + 8400*I*(d*sqrt(x) + c)^3*a*b*c^3 - 6300*I*(d*sqrt(x) + c)^2*a*b*c^4 + 2520*I*(d*sqrt(x) + c)*a*b*c^5 - 420*I*a*b*c^6)*sin(2*d*sqrt(x) + 2*c))*dilog(I*e^(I*d*sqrt(x) + I*c)) - (420*(d*sqrt(x) + c)^6*a*b - 2520*(d*sqrt(x) + c)^5*a*b*c + 6300*(d*sqrt(x) + c)^4*a*b*c^2 - 8400*(d*sqrt(x) + c)^3*a*b*c^3 + 6300*(d*sqrt(x) + c)^2*a*b*c^4 - 2520*(d*sqrt(x) + c)*a*b*c^5 + 420*a*b*c^6 + 420*((d*sqrt(x) + c)^6*a*b - 6*(d*sqrt(x) + c)^5*a*b*c + 15*(d*sqrt(x) + c)^4*a*b*c^2 - 20*(d*sqrt(x) + c)^3*a*b*c^3 + 15*(d*sqrt(x) + c)^2*a*b*c^4 - 6*(d*sqrt(x) + c)*a*b*c^5 + a*b*c^6)*cos(2*d*sqrt(x) + 2*c) + (420*I*(d*sqrt(x) + c)^6*a*b - 2520*I*(d*sqrt(x) + c)^5*a*b*c + 6300*I*(d*sqrt(x) + c)^4*a*b*c^2 - 8400*I*(d*sqrt(x) + c)^3*a*b*c^3 + 6300*I*(d*sqrt(x) + c)^2*a*b*c^4 - 2520*I*(d*sqrt(x) + c)*a*b*c^5 + 420*I*a*b*c^6)*sin(2*d*sqrt(x) + 2*c))*dilog(-I*e^(I*d*sqrt(x) + I*c)) - (-560*I*(d*sqrt(x) + c)^6*b^2 + 2016*I*(d*sqrt(x) + c)^5*b^2*c - 3150*I*(d*sqrt(x) + c)^4*b^2*c^2 + 2800*I*(d*sqrt(x) + c)^3*b^2*c^3 - 1575*I*(d*sqrt(x) + c)^2*b^2*c^4 + 630*I*(d*sqrt(x) + c)*b^2*c^5 - 105*I*b^2*c^6 + (-560*I*(d*sqrt(x) + c)^6*b^2 + 2016*I*(d*sqrt(x) + c)^5*b^2*c - 3150*I*(d*sqrt(x) + c)^4*b^2*c^2 + 2800*I*(d*sqrt(x) + c)^3*b^2*c^3 - 1575*I*(d*sqrt(x) + c)^2*b^2*c^4 + 630*I*(d*sqrt(x) + c)*b^2*c^5 - 105*I*b^2*c^6)*cos(2*d*sqrt(x) + 2*c) + 7*(80*(d*sqrt(x) + c)^6*b^2 - 288*(d*sqrt(x) + c)^5*b^2*c + 450*(d*sqrt(x) + c)^4*b^2*c^2 - 400*(d*sqrt(x) + c)^3*b^2*c^3 + 225*(d*sqrt(x) + c)^2*b^2*c^4 - 90*(d*sqrt(x) + c)*b^2*c^5 + 15*b^2*c^6)*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) - (-30*I*(d*sqrt(x) + c)^7*a*b + 210*I*(d*sqrt(x) + c)^6*a*b*c - 630*I*(d*sqrt(x) + c)^5*a*b*c^2 + 1050*I*(d*sqrt(x) + c)^4*a*b*c^3 - 1050*I*(d*sqrt(x) + c)^3*a*b*c^4 + 630*I*(d*sqrt(x) + c)^2*a*b*c^5 - 210*I*(d*sqrt(x) + c)*a*b*c^6 + (-30*I*(d*sqrt(x) + c)^7*a*b + 210*I*(d*sqrt(x) + c)^6*a*b*c - 630*I*(d*sqrt(x) + c)^5*a*b*c^2 + 1050*I*(d*sqrt(x) + c)^4*a*b*c^3 - 1050*I*(d*sqrt(x) + c)^3*a*b*c^4 + 630*I*(d*sqrt(x) + c)^2*a*b*c^5 - 210*I*(d*sqrt(x) + c)*a*b*c^6)*cos(2*d*sqrt(x) + 2*c) + 30*((d*sqrt(x) + c)^7*a*b - 7*(d*sqrt(x) + c)^6*a*b*c + 21*(d*sqrt(x) + c)^5*a*b*c^2 - 35*(d*sqrt(x) + c)^4*a*b*c^3 + 35*(d*sqrt(x) + c)^3*a*b*c^4 - 21*(d*sqrt(x) + c)^2*a*b*c^5 + 7*(d*sqrt(x) + c)*a*b*c^6)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - (30*I*(d*sqrt(x) + c)^7*a*b - 210*I*(d*sqrt(x) + c)^6*a*b*c + 630*I*(d*sqrt(x) + c)^5*a*b*c^2 - 1050*I*(d*sqrt(x) + c)^4*a*b*c^3 + 1050*I*(d*sqrt(x) + c)^3*a*b*c^4 - 630*I*(d*sqrt(x) + c)^2*a*b*c^5 + 210*I*(d*sqrt(x) + c)*a*b*c^6 + (30*I*(d*sqrt(x) + c)^7*a*b - 210*I*(d*sqrt(x) + c)^6*a*b*c + 630*I*(d*sqrt(x) + c)^5*a*b*c^2 - 1050*I*(d*sqrt(x) + c)^4*a*b*c^3 + 1050*I*(d*sqrt(x) + c)^3*a*b*c^4 - 630*I*(d*sqrt(x) + c)^2*a*b*c^5 + 210*I*(d*sqrt(x) + c)*a*b*c^6)*cos(2*d*sqrt(x) + 2*c) - 30*((d*sqrt(x) + c)^7*a*b - 7*(d*sqrt(x) + c)^6*a*b*c + 21*(d*sqrt(x) + c)^5*a*b*c^2 - 35*(d*sqrt(x) + c)^4*a*b*c^3 + 35*(d*sqrt(x) + c)^3*a*b*c^4 - 21*(d*sqrt(x) + c)^2*a*b*c^5 + 7*(d*sqrt(x) + c)*a*b*c^6)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) - 302400*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(8, I*e^(I*d*sqrt(x) + I*c)) + 302400*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(8, -I*e^(I*d*sqrt(x) + I*c)) - (-12600*I*b^2*cos(2*d*sqrt(x) + 2*c) + 12600*b^2*sin(2*d*sqrt(x) + 2*c) - 12600*I*b^2)*polylog(7, -e^(2*I*d*sqrt(x) + 2*I*c)) - (-302400*I*(d*sqrt(x) + c)*a*b + 302400*I*a*b*c + (-302400*I*(d*sqrt(x) + c)*a*b + 302400*I*a*b*c)*cos(2*d*sqrt(x) + 2*c) + 302400*((d*sqrt(x) + c)*a*b - a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(7, I*e^(I*d*sqrt(x) + I*c)) - (302400*I*(d*sqrt(x) + c)*a*b - 302400*I*a*b*c + (302400*I*(d*sqrt(x) + c)*a*b - 302400*I*a*b*c)*cos(2*d*sqrt(x) + 2*c) - 302400*((d*sqrt(x) + c)*a*b - a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(7, -I*e^(I*d*sqrt(x) + I*c)) + (25200*(d*sqrt(x) + c)*b^2 - 15120*b^2*c + 5040*(5*(d*sqrt(x) + c)*b^2 - 3*b^2*c)*cos(2*d*sqrt(x) + 2*c) - (-25200*I*(d*sqrt(x) + c)*b^2 + 15120*I*b^2*c)*sin(2*d*sqrt(x) + 2*c))*polylog(6, -e^(2*I*d*sqrt(x) + 2*I*c)) + (151200*(d*sqrt(x) + c)^2*a*b - 302400*(d*sqrt(x) + c)*a*b*c + 151200*a*b*c^2 + 151200*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - (-151200*I*(d*sqrt(x) + c)^2*a*b + 302400*I*(d*sqrt(x) + c)*a*b*c - 151200*I*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(6, I*e^(I*d*sqrt(x) + I*c)) - (151200*(d*sqrt(x) + c)^2*a*b - 302400*(d*sqrt(x) + c)*a*b*c + 151200*a*b*c^2 + 151200*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*cos(2*d*sqrt(x) + 2*c) + (151200*I*(d*sqrt(x) + c)^2*a*b - 302400*I*(d*sqrt(x) + c)*a*b*c + 151200*I*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(6, -I*e^(I*d*sqrt(x) + I*c)) - (25200*I*(d*sqrt(x) + c)^2*b^2 - 30240*I*(d*sqrt(x) + c)*b^2*c + 9450*I*b^2*c^2 + (25200*I*(d*sqrt(x) + c)^2*b^2 - 30240*I*(d*sqrt(x) + c)*b^2*c + 9450*I*b^2*c^2)*cos(2*d*sqrt(x) + 2*c) - 630*(40*(d*sqrt(x) + c)^2*b^2 - 48*(d*sqrt(x) + c)*b^2*c + 15*b^2*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(5, -e^(2*I*d*sqrt(x) + 2*I*c)) - (50400*I*(d*sqrt(x) + c)^3*a*b - 151200*I*(d*sqrt(x) + c)^2*a*b*c + 151200*I*(d*sqrt(x) + c)*a*b*c^2 - 50400*I*a*b*c^3 + (50400*I*(d*sqrt(x) + c)^3*a*b - 151200*I*(d*sqrt(x) + c)^2*a*b*c + 151200*I*(d*sqrt(x) + c)*a*b*c^2 - 50400*I*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) - 50400*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2 - a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*polylog(5, I*e^(I*d*sqrt(x) + I*c)) - (-50400*I*(d*sqrt(x) + c)^3*a*b + 151200*I*(d*sqrt(x) + c)^2*a*b*c - 151200*I*(d*sqrt(x) + c)*a*b*c^2 + 50400*I*a*b*c^3 + (-50400*I*(d*sqrt(x) + c)^3*a*b + 151200*I*(d*sqrt(x) + c)^2*a*b*c - 151200*I*(d*sqrt(x) + c)*a*b*c^2 + 50400*I*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) + 50400*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2 - a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*polylog(5, -I*e^(I*d*sqrt(x) + I*c)) - (16800*(d*sqrt(x) + c)^3*b^2 - 30240*(d*sqrt(x) + c)^2*b^2*c + 18900*(d*sqrt(x) + c)*b^2*c^2 - 4200*b^2*c^3 + 420*(40*(d*sqrt(x) + c)^3*b^2 - 72*(d*sqrt(x) + c)^2*b^2*c + 45*(d*sqrt(x) + c)*b^2*c^2 - 10*b^2*c^3)*cos(2*d*sqrt(x) + 2*c) + (16800*I*(d*sqrt(x) + c)^3*b^2 - 30240*I*(d*sqrt(x) + c)^2*b^2*c + 18900*I*(d*sqrt(x) + c)*b^2*c^2 - 4200*I*b^2*c^3)*sin(2*d*sqrt(x) + 2*c))*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) - (12600*(d*sqrt(x) + c)^4*a*b - 50400*(d*sqrt(x) + c)^3*a*b*c + 75600*(d*sqrt(x) + c)^2*a*b*c^2 - 50400*(d*sqrt(x) + c)*a*b*c^3 + 12600*a*b*c^4 + 12600*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3 + a*b*c^4)*cos(2*d*sqrt(x) + 2*c) + (12600*I*(d*sqrt(x) + c)^4*a*b - 50400*I*(d*sqrt(x) + c)^3*a*b*c + 75600*I*(d*sqrt(x) + c)^2*a*b*c^2 - 50400*I*(d*sqrt(x) + c)*a*b*c^3 + 12600*I*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*polylog(4, I*e^(I*d*sqrt(x) + I*c)) + (12600*(d*sqrt(x) + c)^4*a*b - 50400*(d*sqrt(x) + c)^3*a*b*c + 75600*(d*sqrt(x) + c)^2*a*b*c^2 - 50400*(d*sqrt(x) + c)*a*b*c^3 + 12600*a*b*c^4 + 12600*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3 + a*b*c^4)*cos(2*d*sqrt(x) + 2*c) - (-12600*I*(d*sqrt(x) + c)^4*a*b + 50400*I*(d*sqrt(x) + c)^3*a*b*c - 75600*I*(d*sqrt(x) + c)^2*a*b*c^2 + 50400*I*(d*sqrt(x) + c)*a*b*c^3 - 12600*I*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) - (-8400*I*(d*sqrt(x) + c)^4*b^2 + 20160*I*(d*sqrt(x) + c)^3*b^2*c - 18900*I*(d*sqrt(x) + c)^2*b^2*c^2 + 8400*I*(d*sqrt(x) + c)*b^2*c^3 - 1575*I*b^2*c^4 + (-8400*I*(d*sqrt(x) + c)^4*b^2 + 20160*I*(d*sqrt(x) + c)^3*b^2*c - 18900*I*(d*sqrt(x) + c)^2*b^2*c^2 + 8400*I*(d*sqrt(x) + c)*b^2*c^3 - 1575*I*b^2*c^4)*cos(2*d*sqrt(x) + 2*c) + 105*(80*(d*sqrt(x) + c)^4*b^2 - 192*(d*sqrt(x) + c)^3*b^2*c + 180*(d*sqrt(x) + c)^2*b^2*c^2 - 80*(d*sqrt(x) + c)*b^2*c^3 + 15*b^2*c^4)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)) - (-2520*I*(d*sqrt(x) + c)^5*a*b + 12600*I*(d*sqrt(x) + c)^4*a*b*c - 25200*I*(d*sqrt(x) + c)^3*a*b*c^2 + 25200*I*(d*sqrt(x) + c)^2*a*b*c^3 - 12600*I*(d*sqrt(x) + c)*a*b*c^4 + 2520*I*a*b*c^5 + (-2520*I*(d*sqrt(x) + c)^5*a*b + 12600*I*(d*sqrt(x) + c)^4*a*b*c - 25200*I*(d*sqrt(x) + c)^3*a*b*c^2 + 25200*I*(d*sqrt(x) + c)^2*a*b*c^3 - 12600*I*(d*sqrt(x) + c)*a*b*c^4 + 2520*I*a*b*c^5)*cos(2*d*sqrt(x) + 2*c) + 2520*((d*sqrt(x) + c)^5*a*b - 5*(d*sqrt(x) + c)^4*a*b*c + 10*(d*sqrt(x) + c)^3*a*b*c^2 - 10*(d*sqrt(x) + c)^2*a*b*c^3 + 5*(d*sqrt(x) + c)*a*b*c^4 - a*b*c^5)*sin(2*d*sqrt(x) + 2*c))*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - (2520*I*(d*sqrt(x) + c)^5*a*b - 12600*I*(d*sqrt(x) + c)^4*a*b*c + 25200*I*(d*sqrt(x) + c)^3*a*b*c^2 - 25200*I*(d*sqrt(x) + c)^2*a*b*c^3 + 12600*I*(d*sqrt(x) + c)*a*b*c^4 - 2520*I*a*b*c^5 + (2520*I*(d*sqrt(x) + c)^5*a*b - 12600*I*(d*sqrt(x) + c)^4*a*b*c + 25200*I*(d*sqrt(x) + c)^3*a*b*c^2 - 25200*I*(d*sqrt(x) + c)^2*a*b*c^3 + 12600*I*(d*sqrt(x) + c)*a*b*c^4 - 2520*I*a*b*c^5)*cos(2*d*sqrt(x) + 2*c) - 2520*((d*sqrt(x) + c)^5*a*b - 5*(d*sqrt(x) + c)^4*a*b*c + 10*(d*sqrt(x) + c)^3*a*b*c^2 - 10*(d*sqrt(x) + c)^2*a*b*c^3 + 5*(d*sqrt(x) + c)*a*b*c^4 - a*b*c^5)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -I*e^(I*d*sqrt(x) + I*c)) - (-60*I*(d*sqrt(x) + c)^7*b^2 + 420*I*(d*sqrt(x) + c)^6*b^2*c - 1260*I*(d*sqrt(x) + c)^5*b^2*c^2 + 2100*I*(d*sqrt(x) + c)^4*b^2*c^3 - 2100*I*(d*sqrt(x) + c)^3*b^2*c^4 + 1260*I*(d*sqrt(x) + c)^2*b^2*c^5 - 420*I*(d*sqrt(x) + c)*b^2*c^6)*sin(2*d*sqrt(x) + 2*c))/(-30*I*cos(2*d*sqrt(x) + 2*c) + 30*sin(2*d*sqrt(x) + 2*c) - 30*I))/d^8","B",0
37,1,3898,0,1.426580," ","integrate(x^2*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{6} a^{2} - 6 \, {\left(d \sqrt{x} + c\right)}^{5} a^{2} c + 15 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{3} + 15 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{4} - 6 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{5} - 12 \, a b c^{5} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) - \frac{6 \, {\left(12 \, b^{2} c^{5} + {\left(12 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 60 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 120 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 120 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 60 \, {\left(d \sqrt{x} + c\right)} a b c^{4} + 12 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-12 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 60 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c - 120 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} + 120 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} - 60 i \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(12 \, {\left(d \sqrt{x} + c\right)}^{5} a b - 60 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 120 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 120 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 60 \, {\left(d \sqrt{x} + c\right)} a b c^{4} + 12 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-12 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 60 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c - 120 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} + 120 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} - 60 i \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(60 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} - 160 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 180 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 120 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} + 30 \, b^{2} c^{4} + 10 \, {\left(6 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} - 16 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 18 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 12 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} + 3 \, b^{2} c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(60 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} - 160 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 180 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 120 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} + 30 i \, b^{2} c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + 12 \, {\left({\left(d \sqrt{x} + c\right)}^{5} b^{2} - 5 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(120 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 240 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 180 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 60 \, b^{2} c^{3} + 60 \, {\left(2 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 4 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 3 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - b^{2} c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-120 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} + 240 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c - 180 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} + 60 i \, b^{2} c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) + {\left(60 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 240 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 360 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 240 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 60 \, a b c^{4} + 60 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-60 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 240 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c - 360 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} + 240 i \, {\left(d \sqrt{x} + c\right)} a b c^{3} - 60 i \, a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(60 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 240 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 360 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 240 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 60 \, a b c^{4} + 60 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(60 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 240 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 360 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 240 i \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 60 i \, a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(-30 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} + 80 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c - 90 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} + 60 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} - 15 i \, b^{2} c^{4} + {\left(-30 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} + 80 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c - 90 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} + 60 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} - 15 i \, b^{2} c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 5 \, {\left(6 \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} - 16 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 18 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 12 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3} + 3 \, b^{2} c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 30 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c - 60 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} + 60 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} - 30 i \, {\left(d \sqrt{x} + c\right)} a b c^{4} + {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{5} a b + 30 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c - 60 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} + 60 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} - 30 i \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 6 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(6 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 30 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 60 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 60 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 30 i \, {\left(d \sqrt{x} + c\right)} a b c^{4} + {\left(6 i \, {\left(d \sqrt{x} + c\right)}^{5} a b - 30 i \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 60 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 60 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 30 i \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 6 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a b - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a b c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a b c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a b c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + 1440 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{6}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 1440 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{6}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(90 i \, b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 90 \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 90 i \, b^{2}\right)} {\rm Li}_{5}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(1440 i \, {\left(d \sqrt{x} + c\right)} a b - 1440 i \, a b c + {\left(1440 i \, {\left(d \sqrt{x} + c\right)} a b - 1440 i \, a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 1440 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-1440 i \, {\left(d \sqrt{x} + c\right)} a b + 1440 i \, a b c + {\left(-1440 i \, {\left(d \sqrt{x} + c\right)} a b + 1440 i \, a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1440 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{5}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(180 \, {\left(d \sqrt{x} + c\right)} b^{2} - 120 \, b^{2} c + 60 \, {\left(3 \, {\left(d \sqrt{x} + c\right)} b^{2} - 2 \, b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(180 i \, {\left(d \sqrt{x} + c\right)} b^{2} - 120 i \, b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(720 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 1440 \, {\left(d \sqrt{x} + c\right)} a b c + 720 \, a b c^{2} + 720 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(720 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 1440 i \, {\left(d \sqrt{x} + c\right)} a b c + 720 i \, a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(720 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 1440 \, {\left(d \sqrt{x} + c\right)} a b c + 720 \, a b c^{2} + 720 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-720 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 1440 i \, {\left(d \sqrt{x} + c\right)} a b c - 720 i \, a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-180 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} + 240 i \, {\left(d \sqrt{x} + c\right)} b^{2} c - 90 i \, b^{2} c^{2} + {\left(-180 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} + 240 i \, {\left(d \sqrt{x} + c\right)} b^{2} c - 90 i \, b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 30 \, {\left(6 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 8 \, {\left(d \sqrt{x} + c\right)} b^{2} c + 3 \, b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(-240 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 720 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 720 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 240 i \, a b c^{3} + {\left(-240 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 720 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 720 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 240 i \, a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 240 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(240 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 720 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 720 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 240 i \, a b c^{3} + {\left(240 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 720 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 720 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 240 i \, a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 240 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-12 i \, {\left(d \sqrt{x} + c\right)}^{5} b^{2} + 60 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} c - 120 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c^{2} + 120 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{3} - 60 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{4}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-6 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 6 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 6 i}}{3 \, d^{6}}"," ",0,"1/3*((d*sqrt(x) + c)^6*a^2 - 6*(d*sqrt(x) + c)^5*a^2*c + 15*(d*sqrt(x) + c)^4*a^2*c^2 - 20*(d*sqrt(x) + c)^3*a^2*c^3 + 15*(d*sqrt(x) + c)^2*a^2*c^4 - 6*(d*sqrt(x) + c)*a^2*c^5 - 12*a*b*c^5*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) - 6*(12*b^2*c^5 + (12*(d*sqrt(x) + c)^5*a*b - 60*(d*sqrt(x) + c)^4*a*b*c + 120*(d*sqrt(x) + c)^3*a*b*c^2 - 120*(d*sqrt(x) + c)^2*a*b*c^3 + 60*(d*sqrt(x) + c)*a*b*c^4 + 12*((d*sqrt(x) + c)^5*a*b - 5*(d*sqrt(x) + c)^4*a*b*c + 10*(d*sqrt(x) + c)^3*a*b*c^2 - 10*(d*sqrt(x) + c)^2*a*b*c^3 + 5*(d*sqrt(x) + c)*a*b*c^4)*cos(2*d*sqrt(x) + 2*c) - (-12*I*(d*sqrt(x) + c)^5*a*b + 60*I*(d*sqrt(x) + c)^4*a*b*c - 120*I*(d*sqrt(x) + c)^3*a*b*c^2 + 120*I*(d*sqrt(x) + c)^2*a*b*c^3 - 60*I*(d*sqrt(x) + c)*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + (12*(d*sqrt(x) + c)^5*a*b - 60*(d*sqrt(x) + c)^4*a*b*c + 120*(d*sqrt(x) + c)^3*a*b*c^2 - 120*(d*sqrt(x) + c)^2*a*b*c^3 + 60*(d*sqrt(x) + c)*a*b*c^4 + 12*((d*sqrt(x) + c)^5*a*b - 5*(d*sqrt(x) + c)^4*a*b*c + 10*(d*sqrt(x) + c)^3*a*b*c^2 - 10*(d*sqrt(x) + c)^2*a*b*c^3 + 5*(d*sqrt(x) + c)*a*b*c^4)*cos(2*d*sqrt(x) + 2*c) - (-12*I*(d*sqrt(x) + c)^5*a*b + 60*I*(d*sqrt(x) + c)^4*a*b*c - 120*I*(d*sqrt(x) + c)^3*a*b*c^2 + 120*I*(d*sqrt(x) + c)^2*a*b*c^3 - 60*I*(d*sqrt(x) + c)*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) - (60*(d*sqrt(x) + c)^4*b^2 - 160*(d*sqrt(x) + c)^3*b^2*c + 180*(d*sqrt(x) + c)^2*b^2*c^2 - 120*(d*sqrt(x) + c)*b^2*c^3 + 30*b^2*c^4 + 10*(6*(d*sqrt(x) + c)^4*b^2 - 16*(d*sqrt(x) + c)^3*b^2*c + 18*(d*sqrt(x) + c)^2*b^2*c^2 - 12*(d*sqrt(x) + c)*b^2*c^3 + 3*b^2*c^4)*cos(2*d*sqrt(x) + 2*c) + (60*I*(d*sqrt(x) + c)^4*b^2 - 160*I*(d*sqrt(x) + c)^3*b^2*c + 180*I*(d*sqrt(x) + c)^2*b^2*c^2 - 120*I*(d*sqrt(x) + c)*b^2*c^3 + 30*I*b^2*c^4)*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) + 12*((d*sqrt(x) + c)^5*b^2 - 5*(d*sqrt(x) + c)^4*b^2*c + 10*(d*sqrt(x) + c)^3*b^2*c^2 - 10*(d*sqrt(x) + c)^2*b^2*c^3 + 5*(d*sqrt(x) + c)*b^2*c^4)*cos(2*d*sqrt(x) + 2*c) + (120*(d*sqrt(x) + c)^3*b^2 - 240*(d*sqrt(x) + c)^2*b^2*c + 180*(d*sqrt(x) + c)*b^2*c^2 - 60*b^2*c^3 + 60*(2*(d*sqrt(x) + c)^3*b^2 - 4*(d*sqrt(x) + c)^2*b^2*c + 3*(d*sqrt(x) + c)*b^2*c^2 - b^2*c^3)*cos(2*d*sqrt(x) + 2*c) - (-120*I*(d*sqrt(x) + c)^3*b^2 + 240*I*(d*sqrt(x) + c)^2*b^2*c - 180*I*(d*sqrt(x) + c)*b^2*c^2 + 60*I*b^2*c^3)*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) + (60*(d*sqrt(x) + c)^4*a*b - 240*(d*sqrt(x) + c)^3*a*b*c + 360*(d*sqrt(x) + c)^2*a*b*c^2 - 240*(d*sqrt(x) + c)*a*b*c^3 + 60*a*b*c^4 + 60*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3 + a*b*c^4)*cos(2*d*sqrt(x) + 2*c) - (-60*I*(d*sqrt(x) + c)^4*a*b + 240*I*(d*sqrt(x) + c)^3*a*b*c - 360*I*(d*sqrt(x) + c)^2*a*b*c^2 + 240*I*(d*sqrt(x) + c)*a*b*c^3 - 60*I*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*dilog(I*e^(I*d*sqrt(x) + I*c)) - (60*(d*sqrt(x) + c)^4*a*b - 240*(d*sqrt(x) + c)^3*a*b*c + 360*(d*sqrt(x) + c)^2*a*b*c^2 - 240*(d*sqrt(x) + c)*a*b*c^3 + 60*a*b*c^4 + 60*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3 + a*b*c^4)*cos(2*d*sqrt(x) + 2*c) + (60*I*(d*sqrt(x) + c)^4*a*b - 240*I*(d*sqrt(x) + c)^3*a*b*c + 360*I*(d*sqrt(x) + c)^2*a*b*c^2 - 240*I*(d*sqrt(x) + c)*a*b*c^3 + 60*I*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*dilog(-I*e^(I*d*sqrt(x) + I*c)) - (-30*I*(d*sqrt(x) + c)^4*b^2 + 80*I*(d*sqrt(x) + c)^3*b^2*c - 90*I*(d*sqrt(x) + c)^2*b^2*c^2 + 60*I*(d*sqrt(x) + c)*b^2*c^3 - 15*I*b^2*c^4 + (-30*I*(d*sqrt(x) + c)^4*b^2 + 80*I*(d*sqrt(x) + c)^3*b^2*c - 90*I*(d*sqrt(x) + c)^2*b^2*c^2 + 60*I*(d*sqrt(x) + c)*b^2*c^3 - 15*I*b^2*c^4)*cos(2*d*sqrt(x) + 2*c) + 5*(6*(d*sqrt(x) + c)^4*b^2 - 16*(d*sqrt(x) + c)^3*b^2*c + 18*(d*sqrt(x) + c)^2*b^2*c^2 - 12*(d*sqrt(x) + c)*b^2*c^3 + 3*b^2*c^4)*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) - (-6*I*(d*sqrt(x) + c)^5*a*b + 30*I*(d*sqrt(x) + c)^4*a*b*c - 60*I*(d*sqrt(x) + c)^3*a*b*c^2 + 60*I*(d*sqrt(x) + c)^2*a*b*c^3 - 30*I*(d*sqrt(x) + c)*a*b*c^4 + (-6*I*(d*sqrt(x) + c)^5*a*b + 30*I*(d*sqrt(x) + c)^4*a*b*c - 60*I*(d*sqrt(x) + c)^3*a*b*c^2 + 60*I*(d*sqrt(x) + c)^2*a*b*c^3 - 30*I*(d*sqrt(x) + c)*a*b*c^4)*cos(2*d*sqrt(x) + 2*c) + 6*((d*sqrt(x) + c)^5*a*b - 5*(d*sqrt(x) + c)^4*a*b*c + 10*(d*sqrt(x) + c)^3*a*b*c^2 - 10*(d*sqrt(x) + c)^2*a*b*c^3 + 5*(d*sqrt(x) + c)*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - (6*I*(d*sqrt(x) + c)^5*a*b - 30*I*(d*sqrt(x) + c)^4*a*b*c + 60*I*(d*sqrt(x) + c)^3*a*b*c^2 - 60*I*(d*sqrt(x) + c)^2*a*b*c^3 + 30*I*(d*sqrt(x) + c)*a*b*c^4 + (6*I*(d*sqrt(x) + c)^5*a*b - 30*I*(d*sqrt(x) + c)^4*a*b*c + 60*I*(d*sqrt(x) + c)^3*a*b*c^2 - 60*I*(d*sqrt(x) + c)^2*a*b*c^3 + 30*I*(d*sqrt(x) + c)*a*b*c^4)*cos(2*d*sqrt(x) + 2*c) - 6*((d*sqrt(x) + c)^5*a*b - 5*(d*sqrt(x) + c)^4*a*b*c + 10*(d*sqrt(x) + c)^3*a*b*c^2 - 10*(d*sqrt(x) + c)^2*a*b*c^3 + 5*(d*sqrt(x) + c)*a*b*c^4)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) + 1440*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(6, I*e^(I*d*sqrt(x) + I*c)) - 1440*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(6, -I*e^(I*d*sqrt(x) + I*c)) - (90*I*b^2*cos(2*d*sqrt(x) + 2*c) - 90*b^2*sin(2*d*sqrt(x) + 2*c) + 90*I*b^2)*polylog(5, -e^(2*I*d*sqrt(x) + 2*I*c)) - (1440*I*(d*sqrt(x) + c)*a*b - 1440*I*a*b*c + (1440*I*(d*sqrt(x) + c)*a*b - 1440*I*a*b*c)*cos(2*d*sqrt(x) + 2*c) - 1440*((d*sqrt(x) + c)*a*b - a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(5, I*e^(I*d*sqrt(x) + I*c)) - (-1440*I*(d*sqrt(x) + c)*a*b + 1440*I*a*b*c + (-1440*I*(d*sqrt(x) + c)*a*b + 1440*I*a*b*c)*cos(2*d*sqrt(x) + 2*c) + 1440*((d*sqrt(x) + c)*a*b - a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(5, -I*e^(I*d*sqrt(x) + I*c)) - (180*(d*sqrt(x) + c)*b^2 - 120*b^2*c + 60*(3*(d*sqrt(x) + c)*b^2 - 2*b^2*c)*cos(2*d*sqrt(x) + 2*c) + (180*I*(d*sqrt(x) + c)*b^2 - 120*I*b^2*c)*sin(2*d*sqrt(x) + 2*c))*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) - (720*(d*sqrt(x) + c)^2*a*b - 1440*(d*sqrt(x) + c)*a*b*c + 720*a*b*c^2 + 720*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*cos(2*d*sqrt(x) + 2*c) + (720*I*(d*sqrt(x) + c)^2*a*b - 1440*I*(d*sqrt(x) + c)*a*b*c + 720*I*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(4, I*e^(I*d*sqrt(x) + I*c)) + (720*(d*sqrt(x) + c)^2*a*b - 1440*(d*sqrt(x) + c)*a*b*c + 720*a*b*c^2 + 720*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - (-720*I*(d*sqrt(x) + c)^2*a*b + 1440*I*(d*sqrt(x) + c)*a*b*c - 720*I*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) - (-180*I*(d*sqrt(x) + c)^2*b^2 + 240*I*(d*sqrt(x) + c)*b^2*c - 90*I*b^2*c^2 + (-180*I*(d*sqrt(x) + c)^2*b^2 + 240*I*(d*sqrt(x) + c)*b^2*c - 90*I*b^2*c^2)*cos(2*d*sqrt(x) + 2*c) + 30*(6*(d*sqrt(x) + c)^2*b^2 - 8*(d*sqrt(x) + c)*b^2*c + 3*b^2*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)) - (-240*I*(d*sqrt(x) + c)^3*a*b + 720*I*(d*sqrt(x) + c)^2*a*b*c - 720*I*(d*sqrt(x) + c)*a*b*c^2 + 240*I*a*b*c^3 + (-240*I*(d*sqrt(x) + c)^3*a*b + 720*I*(d*sqrt(x) + c)^2*a*b*c - 720*I*(d*sqrt(x) + c)*a*b*c^2 + 240*I*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) + 240*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2 - a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - (240*I*(d*sqrt(x) + c)^3*a*b - 720*I*(d*sqrt(x) + c)^2*a*b*c + 720*I*(d*sqrt(x) + c)*a*b*c^2 - 240*I*a*b*c^3 + (240*I*(d*sqrt(x) + c)^3*a*b - 720*I*(d*sqrt(x) + c)^2*a*b*c + 720*I*(d*sqrt(x) + c)*a*b*c^2 - 240*I*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) - 240*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2 - a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -I*e^(I*d*sqrt(x) + I*c)) - (-12*I*(d*sqrt(x) + c)^5*b^2 + 60*I*(d*sqrt(x) + c)^4*b^2*c - 120*I*(d*sqrt(x) + c)^3*b^2*c^2 + 120*I*(d*sqrt(x) + c)^2*b^2*c^3 - 60*I*(d*sqrt(x) + c)*b^2*c^4)*sin(2*d*sqrt(x) + 2*c))/(-6*I*cos(2*d*sqrt(x) + 2*c) + 6*sin(2*d*sqrt(x) + 2*c) - 6*I))/d^6","B",0
38,1,2006,0,0.919724," ","integrate(x*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{{\left(d \sqrt{x} + c\right)}^{4} a^{2} - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{3} - 8 \, a b c^{3} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) - \frac{4 \, {\left(4 \, b^{2} c^{3} + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 12 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 12 \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 4 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-4 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 12 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 12 i \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 12 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 12 \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 4 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-4 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 12 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 12 i \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(6 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 12 \, {\left(d \sqrt{x} + c\right)} b^{2} c + 6 \, b^{2} c^{2} + 6 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b^{2} - 2 \, {\left(d \sqrt{x} + c\right)} b^{2} c + b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(6 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 12 i \, {\left(d \sqrt{x} + c\right)} b^{2} c + 6 i \, b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + 4 \, {\left({\left(d \sqrt{x} + c\right)}^{3} b^{2} - 3 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 3 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(6 \, {\left(d \sqrt{x} + c\right)} b^{2} - 6 \, b^{2} c + 6 \, {\left({\left(d \sqrt{x} + c\right)} b^{2} - b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-6 i \, {\left(d \sqrt{x} + c\right)} b^{2} + 6 i \, b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) + {\left(12 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 24 \, {\left(d \sqrt{x} + c\right)} a b c + 12 \, a b c^{2} + 12 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-12 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 24 i \, {\left(d \sqrt{x} + c\right)} a b c - 12 i \, a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(12 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 24 \, {\left(d \sqrt{x} + c\right)} a b c + 12 \, a b c^{2} + 12 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(12 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 24 i \, {\left(d \sqrt{x} + c\right)} a b c + 12 i \, a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) - {\left(-3 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} + 6 i \, {\left(d \sqrt{x} + c\right)} b^{2} c - 3 i \, b^{2} c^{2} + {\left(-3 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} + 6 i \, {\left(d \sqrt{x} + c\right)} b^{2} c - 3 i \, b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 3 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b^{2} - 2 \, {\left(d \sqrt{x} + c\right)} b^{2} c + b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 6 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 6 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 6 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 6 i \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 6 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 6 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + {\left(2 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 6 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 6 i \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 24 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 24 \, {\left(a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + a b\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-3 i \, b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 3 \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 3 i \, b^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) - {\left(-24 i \, {\left(d \sqrt{x} + c\right)} a b + 24 i \, a b c + {\left(-24 i \, {\left(d \sqrt{x} + c\right)} a b + 24 i \, a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 24 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(24 i \, {\left(d \sqrt{x} + c\right)} a b - 24 i \, a b c + {\left(24 i \, {\left(d \sqrt{x} + c\right)} a b - 24 i \, a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 24 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(-4 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} + 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c - 12 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-2 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 2 i}}{2 \, d^{4}}"," ",0,"1/2*((d*sqrt(x) + c)^4*a^2 - 4*(d*sqrt(x) + c)^3*a^2*c + 6*(d*sqrt(x) + c)^2*a^2*c^2 - 4*(d*sqrt(x) + c)*a^2*c^3 - 8*a*b*c^3*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) - 4*(4*b^2*c^3 + (4*(d*sqrt(x) + c)^3*a*b - 12*(d*sqrt(x) + c)^2*a*b*c + 12*(d*sqrt(x) + c)*a*b*c^2 + 4*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - (-4*I*(d*sqrt(x) + c)^3*a*b + 12*I*(d*sqrt(x) + c)^2*a*b*c - 12*I*(d*sqrt(x) + c)*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + (4*(d*sqrt(x) + c)^3*a*b - 12*(d*sqrt(x) + c)^2*a*b*c + 12*(d*sqrt(x) + c)*a*b*c^2 + 4*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - (-4*I*(d*sqrt(x) + c)^3*a*b + 12*I*(d*sqrt(x) + c)^2*a*b*c - 12*I*(d*sqrt(x) + c)*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) - (6*(d*sqrt(x) + c)^2*b^2 - 12*(d*sqrt(x) + c)*b^2*c + 6*b^2*c^2 + 6*((d*sqrt(x) + c)^2*b^2 - 2*(d*sqrt(x) + c)*b^2*c + b^2*c^2)*cos(2*d*sqrt(x) + 2*c) + (6*I*(d*sqrt(x) + c)^2*b^2 - 12*I*(d*sqrt(x) + c)*b^2*c + 6*I*b^2*c^2)*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) + 4*((d*sqrt(x) + c)^3*b^2 - 3*(d*sqrt(x) + c)^2*b^2*c + 3*(d*sqrt(x) + c)*b^2*c^2)*cos(2*d*sqrt(x) + 2*c) + (6*(d*sqrt(x) + c)*b^2 - 6*b^2*c + 6*((d*sqrt(x) + c)*b^2 - b^2*c)*cos(2*d*sqrt(x) + 2*c) - (-6*I*(d*sqrt(x) + c)*b^2 + 6*I*b^2*c)*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) + (12*(d*sqrt(x) + c)^2*a*b - 24*(d*sqrt(x) + c)*a*b*c + 12*a*b*c^2 + 12*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - (-12*I*(d*sqrt(x) + c)^2*a*b + 24*I*(d*sqrt(x) + c)*a*b*c - 12*I*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*dilog(I*e^(I*d*sqrt(x) + I*c)) - (12*(d*sqrt(x) + c)^2*a*b - 24*(d*sqrt(x) + c)*a*b*c + 12*a*b*c^2 + 12*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*cos(2*d*sqrt(x) + 2*c) + (12*I*(d*sqrt(x) + c)^2*a*b - 24*I*(d*sqrt(x) + c)*a*b*c + 12*I*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*dilog(-I*e^(I*d*sqrt(x) + I*c)) - (-3*I*(d*sqrt(x) + c)^2*b^2 + 6*I*(d*sqrt(x) + c)*b^2*c - 3*I*b^2*c^2 + (-3*I*(d*sqrt(x) + c)^2*b^2 + 6*I*(d*sqrt(x) + c)*b^2*c - 3*I*b^2*c^2)*cos(2*d*sqrt(x) + 2*c) + 3*((d*sqrt(x) + c)^2*b^2 - 2*(d*sqrt(x) + c)*b^2*c + b^2*c^2)*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) - (-2*I*(d*sqrt(x) + c)^3*a*b + 6*I*(d*sqrt(x) + c)^2*a*b*c - 6*I*(d*sqrt(x) + c)*a*b*c^2 + (-2*I*(d*sqrt(x) + c)^3*a*b + 6*I*(d*sqrt(x) + c)^2*a*b*c - 6*I*(d*sqrt(x) + c)*a*b*c^2)*cos(2*d*sqrt(x) + 2*c) + 2*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - (2*I*(d*sqrt(x) + c)^3*a*b - 6*I*(d*sqrt(x) + c)^2*a*b*c + 6*I*(d*sqrt(x) + c)*a*b*c^2 + (2*I*(d*sqrt(x) + c)^3*a*b - 6*I*(d*sqrt(x) + c)^2*a*b*c + 6*I*(d*sqrt(x) + c)*a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - 2*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) - 24*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(4, I*e^(I*d*sqrt(x) + I*c)) + 24*(a*b*cos(2*d*sqrt(x) + 2*c) + I*a*b*sin(2*d*sqrt(x) + 2*c) + a*b)*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) - (-3*I*b^2*cos(2*d*sqrt(x) + 2*c) + 3*b^2*sin(2*d*sqrt(x) + 2*c) - 3*I*b^2)*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)) - (-24*I*(d*sqrt(x) + c)*a*b + 24*I*a*b*c + (-24*I*(d*sqrt(x) + c)*a*b + 24*I*a*b*c)*cos(2*d*sqrt(x) + 2*c) + 24*((d*sqrt(x) + c)*a*b - a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - (24*I*(d*sqrt(x) + c)*a*b - 24*I*a*b*c + (24*I*(d*sqrt(x) + c)*a*b - 24*I*a*b*c)*cos(2*d*sqrt(x) + 2*c) - 24*((d*sqrt(x) + c)*a*b - a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -I*e^(I*d*sqrt(x) + I*c)) - (-4*I*(d*sqrt(x) + c)^3*b^2 + 12*I*(d*sqrt(x) + c)^2*b^2*c - 12*I*(d*sqrt(x) + c)*b^2*c^2)*sin(2*d*sqrt(x) + 2*c))/(-2*I*cos(2*d*sqrt(x) + 2*c) + 2*sin(2*d*sqrt(x) + 2*c) - 2*I))/d^4","B",0
39,0,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x,x, algorithm=""maxima"")","\frac{4 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x \int \frac{b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(a b d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + a b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + a b d \cos\left(d \sqrt{x} + c\right)\right)} x}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}\,{d x} + {\left(a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} d\right)} x \log\left(x\right)}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x}"," ",0,"(4*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) + (d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x*integrate(2*(b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) + 2*(a*b*d*cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + a*b*d*sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + a*b*d*cos(d*sqrt(x) + c))*x)/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2), x) + (a^2*d*cos(2*d*sqrt(x) + 2*c)^2 + a^2*d*sin(2*d*sqrt(x) + 2*c)^2 + 2*a^2*d*cos(2*d*sqrt(x) + 2*c) + a^2*d)*x*log(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x)","F",0
40,0,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2} \int \frac{3 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(a b d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + a b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + a b d \cos\left(d \sqrt{x} + c\right)\right)} x}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{3}}\,{d x} + 4 \, b^{2} \sqrt{x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} d\right)} x}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}"," ",0,"((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2*integrate(2*(3*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) + 2*(a*b*d*cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + a*b*d*sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + a*b*d*cos(d*sqrt(x) + c))*x)/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^3), x) + 4*b^2*sqrt(x)*sin(2*d*sqrt(x) + 2*c) - (a^2*d*cos(2*d*sqrt(x) + 2*c)^2 + a^2*d*sin(2*d*sqrt(x) + 2*c)^2 + 2*a^2*d*cos(2*d*sqrt(x) + 2*c) + a^2*d)*x)/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2)","F",0
41,-2,0,0,0.000000," ","integrate(x^3/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
42,-2,0,0,0.000000," ","integrate(x^2/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
43,-2,0,0,0.000000," ","integrate(x/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
44,-1,0,0,0.000000," ","integrate(1/x/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-2,0,0,0.000000," ","integrate(x^3/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
47,-2,0,0,0.000000," ","integrate(x^2/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
48,-2,0,0,0.000000," ","integrate(x/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
49,-1,0,0,0.000000," ","integrate(1/x/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(1/x^2/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,1,738,0,0.972321," ","integrate(x^(3/2)*(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\frac{2 \, {\left(d \sqrt{x} + c\right)}^{5} a - 10 \, {\left(d \sqrt{x} + c\right)}^{4} a c + 20 \, {\left(d \sqrt{x} + c\right)}^{3} a c^{2} - 20 \, {\left(d \sqrt{x} + c\right)}^{2} a c^{3} + 10 \, {\left(d \sqrt{x} + c\right)} a c^{4} + 10 \, b c^{4} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + 5 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 8 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 8 i \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + 5 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{4} b + 8 i \, {\left(d \sqrt{x} + c\right)}^{3} b c - 12 i \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} + 8 i \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + 5 \, {\left(-8 i \, {\left(d \sqrt{x} + c\right)}^{3} b + 24 i \, {\left(d \sqrt{x} + c\right)}^{2} b c - 24 i \, {\left(d \sqrt{x} + c\right)} b c^{2} + 8 i \, b c^{3}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 5 \, {\left(8 i \, {\left(d \sqrt{x} + c\right)}^{3} b - 24 i \, {\left(d \sqrt{x} + c\right)}^{2} b c + 24 i \, {\left(d \sqrt{x} + c\right)} b c^{2} - 8 i \, b c^{3}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 5 \, {\left({\left(d \sqrt{x} + c\right)}^{4} b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 5 \, {\left({\left(d \sqrt{x} + c\right)}^{4} b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} b c^{3}\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 240 \, b {\rm Li}_{5}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 240 \, b {\rm Li}_{5}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 5 \, {\left(48 i \, {\left(d \sqrt{x} + c\right)} b - 48 i \, b c\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 5 \, {\left(-48 i \, {\left(d \sqrt{x} + c\right)} b + 48 i \, b c\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 120 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c + b c^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 120 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c + b c^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)})}{5 \, d^{5}}"," ",0,"1/5*(2*(d*sqrt(x) + c)^5*a - 10*(d*sqrt(x) + c)^4*a*c + 20*(d*sqrt(x) + c)^3*a*c^2 - 20*(d*sqrt(x) + c)^2*a*c^3 + 10*(d*sqrt(x) + c)*a*c^4 + 10*b*c^4*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 5*(-2*I*(d*sqrt(x) + c)^4*b + 8*I*(d*sqrt(x) + c)^3*b*c - 12*I*(d*sqrt(x) + c)^2*b*c^2 + 8*I*(d*sqrt(x) + c)*b*c^3)*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + 5*(-2*I*(d*sqrt(x) + c)^4*b + 8*I*(d*sqrt(x) + c)^3*b*c - 12*I*(d*sqrt(x) + c)^2*b*c^2 + 8*I*(d*sqrt(x) + c)*b*c^3)*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + 5*(-8*I*(d*sqrt(x) + c)^3*b + 24*I*(d*sqrt(x) + c)^2*b*c - 24*I*(d*sqrt(x) + c)*b*c^2 + 8*I*b*c^3)*dilog(I*e^(I*d*sqrt(x) + I*c)) + 5*(8*I*(d*sqrt(x) + c)^3*b - 24*I*(d*sqrt(x) + c)^2*b*c + 24*I*(d*sqrt(x) + c)*b*c^2 - 8*I*b*c^3)*dilog(-I*e^(I*d*sqrt(x) + I*c)) + 5*((d*sqrt(x) + c)^4*b - 4*(d*sqrt(x) + c)^3*b*c + 6*(d*sqrt(x) + c)^2*b*c^2 - 4*(d*sqrt(x) + c)*b*c^3)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - 5*((d*sqrt(x) + c)^4*b - 4*(d*sqrt(x) + c)^3*b*c + 6*(d*sqrt(x) + c)^2*b*c^2 - 4*(d*sqrt(x) + c)*b*c^3)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) - 240*b*polylog(5, I*e^(I*d*sqrt(x) + I*c)) + 240*b*polylog(5, -I*e^(I*d*sqrt(x) + I*c)) + 5*(48*I*(d*sqrt(x) + c)*b - 48*I*b*c)*polylog(4, I*e^(I*d*sqrt(x) + I*c)) + 5*(-48*I*(d*sqrt(x) + c)*b + 48*I*b*c)*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) + 120*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c + b*c^2)*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - 120*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c + b*c^2)*polylog(3, -I*e^(I*d*sqrt(x) + I*c)))/d^5","B",0
52,1,374,0,0.980614," ","integrate((a+b*sec(c+d*x^(1/2)))*x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(d \sqrt{x} + c\right)}^{3} a - 6 \, {\left(d \sqrt{x} + c\right)}^{2} a c + 6 \, {\left(d \sqrt{x} + c\right)} a c^{2} + 6 \, b c^{2} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + 3 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 4 i \, {\left(d \sqrt{x} + c\right)} b c\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) + 3 \, {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{2} b + 4 i \, {\left(d \sqrt{x} + c\right)} b c\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + 3 \, {\left(-4 i \, {\left(d \sqrt{x} + c\right)} b + 4 i \, b c\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 3 \, {\left(4 i \, {\left(d \sqrt{x} + c\right)} b - 4 i \, b c\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + 3 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) - 3 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b - 2 \, {\left(d \sqrt{x} + c\right)} b c\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + 12 \, b {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - 12 \, b {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)})}{3 \, d^{3}}"," ",0,"1/3*(2*(d*sqrt(x) + c)^3*a - 6*(d*sqrt(x) + c)^2*a*c + 6*(d*sqrt(x) + c)*a*c^2 + 6*b*c^2*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 3*(-2*I*(d*sqrt(x) + c)^2*b + 4*I*(d*sqrt(x) + c)*b*c)*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) + 3*(-2*I*(d*sqrt(x) + c)^2*b + 4*I*(d*sqrt(x) + c)*b*c)*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + 3*(-4*I*(d*sqrt(x) + c)*b + 4*I*b*c)*dilog(I*e^(I*d*sqrt(x) + I*c)) + 3*(4*I*(d*sqrt(x) + c)*b - 4*I*b*c)*dilog(-I*e^(I*d*sqrt(x) + I*c)) + 3*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) - 3*((d*sqrt(x) + c)^2*b - 2*(d*sqrt(x) + c)*b*c)*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) + 12*b*polylog(3, I*e^(I*d*sqrt(x) + I*c)) - 12*b*polylog(3, -I*e^(I*d*sqrt(x) + I*c)))/d^3","B",0
53,1,31,0,0.372011," ","integrate((a+b*sec(c+d*x^(1/2)))/x^(1/2),x, algorithm=""maxima"")","2 \, a \sqrt{x} + \frac{2 \, b \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right)}{d}"," ",0,"2*a*sqrt(x) + 2*b*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c))/d","A",0
54,-1,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))/x^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))/x^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,1,2876,0,0.866272," ","integrate(x^(3/2)*(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{2 \, {\left({\left(d \sqrt{x} + c\right)}^{5} a^{2} - 5 \, {\left(d \sqrt{x} + c\right)}^{4} a^{2} c + 10 \, {\left(d \sqrt{x} + c\right)}^{3} a^{2} c^{2} - 10 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c^{3} + 5 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{4} + 10 \, a b c^{4} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + \frac{5 \, {\left(6 \, b^{2} c^{4} - {\left(6 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 24 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 36 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 24 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 6 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 24 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c - 36 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} + 24 i \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(6 \, {\left(d \sqrt{x} + c\right)}^{4} a b - 24 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 36 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 24 \, {\left(d \sqrt{x} + c\right)} a b c^{3} + 6 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 24 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c - 36 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} + 24 i \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(16 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 36 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 36 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 12 \, b^{2} c^{3} + 4 \, {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 9 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 9 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 3 \, b^{2} c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(16 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 36 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 36 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 12 i \, b^{2} c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 6 \, {\left({\left(d \sqrt{x} + c\right)}^{4} b^{2} - 4 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(24 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 36 \, {\left(d \sqrt{x} + c\right)} b^{2} c + 18 \, b^{2} c^{2} + 6 \, {\left(4 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} - 6 \, {\left(d \sqrt{x} + c\right)} b^{2} c + 3 \, b^{2} c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-24 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} + 36 i \, {\left(d \sqrt{x} + c\right)} b^{2} c - 18 i \, b^{2} c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) - {\left(24 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 72 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 72 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 24 \, a b c^{3} + 24 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-24 i \, {\left(d \sqrt{x} + c\right)}^{3} a b + 72 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c - 72 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} + 24 i \, a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(24 \, {\left(d \sqrt{x} + c\right)}^{3} a b - 72 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 72 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 24 \, a b c^{3} + 24 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a b - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 3 \, {\left(d \sqrt{x} + c\right)} a b c^{2} - a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(24 i \, {\left(d \sqrt{x} + c\right)}^{3} a b - 72 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c + 72 i \, {\left(d \sqrt{x} + c\right)} a b c^{2} - 24 i \, a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(-8 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} + 18 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c - 18 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} + 6 i \, b^{2} c^{3} + {\left(-8 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} + 18 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c - 18 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} + 6 i \, b^{2} c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 2 \, {\left(4 \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} - 9 \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c + 9 \, {\left(d \sqrt{x} + c\right)} b^{2} c^{2} - 3 \, b^{2} c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + {\left(-3 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 12 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c - 18 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} + 12 i \, {\left(d \sqrt{x} + c\right)} a b c^{3} + {\left(-3 i \, {\left(d \sqrt{x} + c\right)}^{4} a b + 12 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c - 18 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} + 12 i \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 3 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(3 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 12 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 18 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 12 i \, {\left(d \sqrt{x} + c\right)} a b c^{3} + {\left(3 i \, {\left(d \sqrt{x} + c\right)}^{4} a b - 12 i \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 18 i \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 12 i \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 3 \, {\left({\left(d \sqrt{x} + c\right)}^{4} a b - 4 \, {\left(d \sqrt{x} + c\right)}^{3} a b c + 6 \, {\left(d \sqrt{x} + c\right)}^{2} a b c^{2} - 4 \, {\left(d \sqrt{x} + c\right)} a b c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(144 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 144 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 144 i \, a b\right)} {\rm Li}_{5}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(-144 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 144 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 144 i \, a b\right)} {\rm Li}_{5}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + 12 \, {\left(b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + b^{2}\right)} {\rm Li}_{4}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(144 \, {\left(d \sqrt{x} + c\right)} a b - 144 \, a b c + 144 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(144 i \, {\left(d \sqrt{x} + c\right)} a b - 144 i \, a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) - {\left(144 \, {\left(d \sqrt{x} + c\right)} a b - 144 \, a b c + 144 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-144 i \, {\left(d \sqrt{x} + c\right)} a b + 144 i \, a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(-24 i \, {\left(d \sqrt{x} + c\right)} b^{2} + 18 i \, b^{2} c + {\left(-24 i \, {\left(d \sqrt{x} + c\right)} b^{2} + 18 i \, b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 6 \, {\left(4 \, {\left(d \sqrt{x} + c\right)} b^{2} - 3 \, b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}) + {\left(-72 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 144 i \, {\left(d \sqrt{x} + c\right)} a b c - 72 i \, a b c^{2} + {\left(-72 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 144 i \, {\left(d \sqrt{x} + c\right)} a b c - 72 i \, a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 72 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(72 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 144 i \, {\left(d \sqrt{x} + c\right)} a b c + 72 i \, a b c^{2} + {\left(72 i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 144 i \, {\left(d \sqrt{x} + c\right)} a b c + 72 i \, a b c^{2}\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 72 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c + a b c^{2}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(-6 i \, {\left(d \sqrt{x} + c\right)}^{4} b^{2} + 24 i \, {\left(d \sqrt{x} + c\right)}^{3} b^{2} c - 36 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} c^{2} + 24 i \, {\left(d \sqrt{x} + c\right)} b^{2} c^{3}\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-3 i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 3 \, \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 3 i}\right)}}{5 \, d^{5}}"," ",0,"2/5*((d*sqrt(x) + c)^5*a^2 - 5*(d*sqrt(x) + c)^4*a^2*c + 10*(d*sqrt(x) + c)^3*a^2*c^2 - 10*(d*sqrt(x) + c)^2*a^2*c^3 + 5*(d*sqrt(x) + c)*a^2*c^4 + 10*a*b*c^4*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 5*(6*b^2*c^4 - (6*(d*sqrt(x) + c)^4*a*b - 24*(d*sqrt(x) + c)^3*a*b*c + 36*(d*sqrt(x) + c)^2*a*b*c^2 - 24*(d*sqrt(x) + c)*a*b*c^3 + 6*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) - (-6*I*(d*sqrt(x) + c)^4*a*b + 24*I*(d*sqrt(x) + c)^3*a*b*c - 36*I*(d*sqrt(x) + c)^2*a*b*c^2 + 24*I*(d*sqrt(x) + c)*a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) - (6*(d*sqrt(x) + c)^4*a*b - 24*(d*sqrt(x) + c)^3*a*b*c + 36*(d*sqrt(x) + c)^2*a*b*c^2 - 24*(d*sqrt(x) + c)*a*b*c^3 + 6*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) - (-6*I*(d*sqrt(x) + c)^4*a*b + 24*I*(d*sqrt(x) + c)^3*a*b*c - 36*I*(d*sqrt(x) + c)^2*a*b*c^2 + 24*I*(d*sqrt(x) + c)*a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + (16*(d*sqrt(x) + c)^3*b^2 - 36*(d*sqrt(x) + c)^2*b^2*c + 36*(d*sqrt(x) + c)*b^2*c^2 - 12*b^2*c^3 + 4*(4*(d*sqrt(x) + c)^3*b^2 - 9*(d*sqrt(x) + c)^2*b^2*c + 9*(d*sqrt(x) + c)*b^2*c^2 - 3*b^2*c^3)*cos(2*d*sqrt(x) + 2*c) + (16*I*(d*sqrt(x) + c)^3*b^2 - 36*I*(d*sqrt(x) + c)^2*b^2*c + 36*I*(d*sqrt(x) + c)*b^2*c^2 - 12*I*b^2*c^3)*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - 6*((d*sqrt(x) + c)^4*b^2 - 4*(d*sqrt(x) + c)^3*b^2*c + 6*(d*sqrt(x) + c)^2*b^2*c^2 - 4*(d*sqrt(x) + c)*b^2*c^3)*cos(2*d*sqrt(x) + 2*c) - (24*(d*sqrt(x) + c)^2*b^2 - 36*(d*sqrt(x) + c)*b^2*c + 18*b^2*c^2 + 6*(4*(d*sqrt(x) + c)^2*b^2 - 6*(d*sqrt(x) + c)*b^2*c + 3*b^2*c^2)*cos(2*d*sqrt(x) + 2*c) - (-24*I*(d*sqrt(x) + c)^2*b^2 + 36*I*(d*sqrt(x) + c)*b^2*c - 18*I*b^2*c^2)*sin(2*d*sqrt(x) + 2*c))*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) - (24*(d*sqrt(x) + c)^3*a*b - 72*(d*sqrt(x) + c)^2*a*b*c + 72*(d*sqrt(x) + c)*a*b*c^2 - 24*a*b*c^3 + 24*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2 - a*b*c^3)*cos(2*d*sqrt(x) + 2*c) - (-24*I*(d*sqrt(x) + c)^3*a*b + 72*I*(d*sqrt(x) + c)^2*a*b*c - 72*I*(d*sqrt(x) + c)*a*b*c^2 + 24*I*a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*dilog(I*e^(I*d*sqrt(x) + I*c)) + (24*(d*sqrt(x) + c)^3*a*b - 72*(d*sqrt(x) + c)^2*a*b*c + 72*(d*sqrt(x) + c)*a*b*c^2 - 24*a*b*c^3 + 24*((d*sqrt(x) + c)^3*a*b - 3*(d*sqrt(x) + c)^2*a*b*c + 3*(d*sqrt(x) + c)*a*b*c^2 - a*b*c^3)*cos(2*d*sqrt(x) + 2*c) + (24*I*(d*sqrt(x) + c)^3*a*b - 72*I*(d*sqrt(x) + c)^2*a*b*c + 72*I*(d*sqrt(x) + c)*a*b*c^2 - 24*I*a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*dilog(-I*e^(I*d*sqrt(x) + I*c)) + (-8*I*(d*sqrt(x) + c)^3*b^2 + 18*I*(d*sqrt(x) + c)^2*b^2*c - 18*I*(d*sqrt(x) + c)*b^2*c^2 + 6*I*b^2*c^3 + (-8*I*(d*sqrt(x) + c)^3*b^2 + 18*I*(d*sqrt(x) + c)^2*b^2*c - 18*I*(d*sqrt(x) + c)*b^2*c^2 + 6*I*b^2*c^3)*cos(2*d*sqrt(x) + 2*c) + 2*(4*(d*sqrt(x) + c)^3*b^2 - 9*(d*sqrt(x) + c)^2*b^2*c + 9*(d*sqrt(x) + c)*b^2*c^2 - 3*b^2*c^3)*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) + (-3*I*(d*sqrt(x) + c)^4*a*b + 12*I*(d*sqrt(x) + c)^3*a*b*c - 18*I*(d*sqrt(x) + c)^2*a*b*c^2 + 12*I*(d*sqrt(x) + c)*a*b*c^3 + (-3*I*(d*sqrt(x) + c)^4*a*b + 12*I*(d*sqrt(x) + c)^3*a*b*c - 18*I*(d*sqrt(x) + c)^2*a*b*c^2 + 12*I*(d*sqrt(x) + c)*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) + 3*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) + (3*I*(d*sqrt(x) + c)^4*a*b - 12*I*(d*sqrt(x) + c)^3*a*b*c + 18*I*(d*sqrt(x) + c)^2*a*b*c^2 - 12*I*(d*sqrt(x) + c)*a*b*c^3 + (3*I*(d*sqrt(x) + c)^4*a*b - 12*I*(d*sqrt(x) + c)^3*a*b*c + 18*I*(d*sqrt(x) + c)^2*a*b*c^2 - 12*I*(d*sqrt(x) + c)*a*b*c^3)*cos(2*d*sqrt(x) + 2*c) - 3*((d*sqrt(x) + c)^4*a*b - 4*(d*sqrt(x) + c)^3*a*b*c + 6*(d*sqrt(x) + c)^2*a*b*c^2 - 4*(d*sqrt(x) + c)*a*b*c^3)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) + (144*I*a*b*cos(2*d*sqrt(x) + 2*c) - 144*a*b*sin(2*d*sqrt(x) + 2*c) + 144*I*a*b)*polylog(5, I*e^(I*d*sqrt(x) + I*c)) + (-144*I*a*b*cos(2*d*sqrt(x) + 2*c) + 144*a*b*sin(2*d*sqrt(x) + 2*c) - 144*I*a*b)*polylog(5, -I*e^(I*d*sqrt(x) + I*c)) + 12*(b^2*cos(2*d*sqrt(x) + 2*c) + I*b^2*sin(2*d*sqrt(x) + 2*c) + b^2)*polylog(4, -e^(2*I*d*sqrt(x) + 2*I*c)) + (144*(d*sqrt(x) + c)*a*b - 144*a*b*c + 144*((d*sqrt(x) + c)*a*b - a*b*c)*cos(2*d*sqrt(x) + 2*c) + (144*I*(d*sqrt(x) + c)*a*b - 144*I*a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(4, I*e^(I*d*sqrt(x) + I*c)) - (144*(d*sqrt(x) + c)*a*b - 144*a*b*c + 144*((d*sqrt(x) + c)*a*b - a*b*c)*cos(2*d*sqrt(x) + 2*c) - (-144*I*(d*sqrt(x) + c)*a*b + 144*I*a*b*c)*sin(2*d*sqrt(x) + 2*c))*polylog(4, -I*e^(I*d*sqrt(x) + I*c)) + (-24*I*(d*sqrt(x) + c)*b^2 + 18*I*b^2*c + (-24*I*(d*sqrt(x) + c)*b^2 + 18*I*b^2*c)*cos(2*d*sqrt(x) + 2*c) + 6*(4*(d*sqrt(x) + c)*b^2 - 3*b^2*c)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -e^(2*I*d*sqrt(x) + 2*I*c)) + (-72*I*(d*sqrt(x) + c)^2*a*b + 144*I*(d*sqrt(x) + c)*a*b*c - 72*I*a*b*c^2 + (-72*I*(d*sqrt(x) + c)^2*a*b + 144*I*(d*sqrt(x) + c)*a*b*c - 72*I*a*b*c^2)*cos(2*d*sqrt(x) + 2*c) + 72*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(3, I*e^(I*d*sqrt(x) + I*c)) + (72*I*(d*sqrt(x) + c)^2*a*b - 144*I*(d*sqrt(x) + c)*a*b*c + 72*I*a*b*c^2 + (72*I*(d*sqrt(x) + c)^2*a*b - 144*I*(d*sqrt(x) + c)*a*b*c + 72*I*a*b*c^2)*cos(2*d*sqrt(x) + 2*c) - 72*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c + a*b*c^2)*sin(2*d*sqrt(x) + 2*c))*polylog(3, -I*e^(I*d*sqrt(x) + I*c)) + (-6*I*(d*sqrt(x) + c)^4*b^2 + 24*I*(d*sqrt(x) + c)^3*b^2*c - 36*I*(d*sqrt(x) + c)^2*b^2*c^2 + 24*I*(d*sqrt(x) + c)*b^2*c^3)*sin(2*d*sqrt(x) + 2*c))/(-3*I*cos(2*d*sqrt(x) + 2*c) + 3*sin(2*d*sqrt(x) + 2*c) - 3*I))/d^5","B",0
57,1,1279,0,0.997644," ","integrate((a+b*sec(c+d*x^(1/2)))^2*x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(d \sqrt{x} + c\right)}^{3} a^{2} - 3 \, {\left(d \sqrt{x} + c\right)}^{2} a^{2} c + 3 \, {\left(d \sqrt{x} + c\right)} a^{2} c^{2} + 6 \, a b c^{2} \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right) + \frac{3 \, {\left(2 \, b^{2} c^{2} - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 4 \, {\left(d \sqrt{x} + c\right)} a b c + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 4 i \, {\left(d \sqrt{x} + c\right)} a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), \sin\left(d \sqrt{x} + c\right) + 1\right) - {\left(2 \, {\left(d \sqrt{x} + c\right)}^{2} a b - 4 \, {\left(d \sqrt{x} + c\right)} a b c + 2 \, {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 4 i \, {\left(d \sqrt{x} + c\right)} a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\cos\left(d \sqrt{x} + c\right), -\sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(2 \, {\left(d \sqrt{x} + c\right)} b^{2} - 2 \, b^{2} c + 2 \, {\left({\left(d \sqrt{x} + c\right)} b^{2} - b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(2 i \, {\left(d \sqrt{x} + c\right)} b^{2} - 2 i \, b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \arctan\left(\sin\left(2 \, d \sqrt{x} + 2 \, c\right), \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) - 2 \, {\left({\left(d \sqrt{x} + c\right)}^{2} b^{2} - 2 \, {\left(d \sqrt{x} + c\right)} b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(b^{2} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + i \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + b^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, d \sqrt{x} + 2 i \, c\right)}\right) - {\left(4 \, {\left(d \sqrt{x} + c\right)} a b - 4 \, a b c + 4 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left(-4 i \, {\left(d \sqrt{x} + c\right)} a b + 4 i \, a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(4 \, {\left(d \sqrt{x} + c\right)} a b - 4 \, a b c + 4 \, {\left({\left(d \sqrt{x} + c\right)} a b - a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(4 i \, {\left(d \sqrt{x} + c\right)} a b - 4 i \, a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}\right) + {\left(-i \, {\left(d \sqrt{x} + c\right)} b^{2} + i \, b^{2} c + {\left(-i \, {\left(d \sqrt{x} + c\right)} b^{2} + i \, b^{2} c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(d \sqrt{x} + c\right)} b^{2} - b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 1\right) + {\left(-i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 2 i \, {\left(d \sqrt{x} + c\right)} a b c + {\left(-i \, {\left(d \sqrt{x} + c\right)}^{2} a b + 2 i \, {\left(d \sqrt{x} + c\right)} a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} + 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 2 i \, {\left(d \sqrt{x} + c\right)} a b c + {\left(i \, {\left(d \sqrt{x} + c\right)}^{2} a b - 2 i \, {\left(d \sqrt{x} + c\right)} a b c\right)} \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - {\left({\left(d \sqrt{x} + c\right)}^{2} a b - 2 \, {\left(d \sqrt{x} + c\right)} a b c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)} \log\left(\cos\left(d \sqrt{x} + c\right)^{2} + \sin\left(d \sqrt{x} + c\right)^{2} - 2 \, \sin\left(d \sqrt{x} + c\right) + 1\right) + {\left(-4 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - 4 i \, a b\right)} {\rm Li}_{3}(i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(4 i \, a b \cos\left(2 \, d \sqrt{x} + 2 \, c\right) - 4 \, a b \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 i \, a b\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d \sqrt{x} + i \, c\right)}) + {\left(-2 i \, {\left(d \sqrt{x} + c\right)}^{2} b^{2} + 4 i \, {\left(d \sqrt{x} + c\right)} b^{2} c\right)} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)\right)}}{-i \, \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + \sin\left(2 \, d \sqrt{x} + 2 \, c\right) - i}\right)}}{3 \, d^{3}}"," ",0,"2/3*((d*sqrt(x) + c)^3*a^2 - 3*(d*sqrt(x) + c)^2*a^2*c + 3*(d*sqrt(x) + c)*a^2*c^2 + 6*a*b*c^2*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c)) + 3*(2*b^2*c^2 - (2*(d*sqrt(x) + c)^2*a*b - 4*(d*sqrt(x) + c)*a*b*c + 2*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c)*cos(2*d*sqrt(x) + 2*c) - (-2*I*(d*sqrt(x) + c)^2*a*b + 4*I*(d*sqrt(x) + c)*a*b*c)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), sin(d*sqrt(x) + c) + 1) - (2*(d*sqrt(x) + c)^2*a*b - 4*(d*sqrt(x) + c)*a*b*c + 2*((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c)*cos(2*d*sqrt(x) + 2*c) - (-2*I*(d*sqrt(x) + c)^2*a*b + 4*I*(d*sqrt(x) + c)*a*b*c)*sin(2*d*sqrt(x) + 2*c))*arctan2(cos(d*sqrt(x) + c), -sin(d*sqrt(x) + c) + 1) + (2*(d*sqrt(x) + c)*b^2 - 2*b^2*c + 2*((d*sqrt(x) + c)*b^2 - b^2*c)*cos(2*d*sqrt(x) + 2*c) + (2*I*(d*sqrt(x) + c)*b^2 - 2*I*b^2*c)*sin(2*d*sqrt(x) + 2*c))*arctan2(sin(2*d*sqrt(x) + 2*c), cos(2*d*sqrt(x) + 2*c) + 1) - 2*((d*sqrt(x) + c)^2*b^2 - 2*(d*sqrt(x) + c)*b^2*c)*cos(2*d*sqrt(x) + 2*c) - (b^2*cos(2*d*sqrt(x) + 2*c) + I*b^2*sin(2*d*sqrt(x) + 2*c) + b^2)*dilog(-e^(2*I*d*sqrt(x) + 2*I*c)) - (4*(d*sqrt(x) + c)*a*b - 4*a*b*c + 4*((d*sqrt(x) + c)*a*b - a*b*c)*cos(2*d*sqrt(x) + 2*c) - (-4*I*(d*sqrt(x) + c)*a*b + 4*I*a*b*c)*sin(2*d*sqrt(x) + 2*c))*dilog(I*e^(I*d*sqrt(x) + I*c)) + (4*(d*sqrt(x) + c)*a*b - 4*a*b*c + 4*((d*sqrt(x) + c)*a*b - a*b*c)*cos(2*d*sqrt(x) + 2*c) + (4*I*(d*sqrt(x) + c)*a*b - 4*I*a*b*c)*sin(2*d*sqrt(x) + 2*c))*dilog(-I*e^(I*d*sqrt(x) + I*c)) + (-I*(d*sqrt(x) + c)*b^2 + I*b^2*c + (-I*(d*sqrt(x) + c)*b^2 + I*b^2*c)*cos(2*d*sqrt(x) + 2*c) + ((d*sqrt(x) + c)*b^2 - b^2*c)*sin(2*d*sqrt(x) + 2*c))*log(cos(2*d*sqrt(x) + 2*c)^2 + sin(2*d*sqrt(x) + 2*c)^2 + 2*cos(2*d*sqrt(x) + 2*c) + 1) + (-I*(d*sqrt(x) + c)^2*a*b + 2*I*(d*sqrt(x) + c)*a*b*c + (-I*(d*sqrt(x) + c)^2*a*b + 2*I*(d*sqrt(x) + c)*a*b*c)*cos(2*d*sqrt(x) + 2*c) + ((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 + 2*sin(d*sqrt(x) + c) + 1) + (I*(d*sqrt(x) + c)^2*a*b - 2*I*(d*sqrt(x) + c)*a*b*c + (I*(d*sqrt(x) + c)^2*a*b - 2*I*(d*sqrt(x) + c)*a*b*c)*cos(2*d*sqrt(x) + 2*c) - ((d*sqrt(x) + c)^2*a*b - 2*(d*sqrt(x) + c)*a*b*c)*sin(2*d*sqrt(x) + 2*c))*log(cos(d*sqrt(x) + c)^2 + sin(d*sqrt(x) + c)^2 - 2*sin(d*sqrt(x) + c) + 1) + (-4*I*a*b*cos(2*d*sqrt(x) + 2*c) + 4*a*b*sin(2*d*sqrt(x) + 2*c) - 4*I*a*b)*polylog(3, I*e^(I*d*sqrt(x) + I*c)) + (4*I*a*b*cos(2*d*sqrt(x) + 2*c) - 4*a*b*sin(2*d*sqrt(x) + 2*c) + 4*I*a*b)*polylog(3, -I*e^(I*d*sqrt(x) + I*c)) + (-2*I*(d*sqrt(x) + c)^2*b^2 + 4*I*(d*sqrt(x) + c)*b^2*c)*sin(2*d*sqrt(x) + 2*c))/(-I*cos(2*d*sqrt(x) + 2*c) + sin(2*d*sqrt(x) + 2*c) - I))/d^3","B",0
58,1,50,0,0.529134," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""maxima"")","2 \, a^{2} \sqrt{x} + \frac{4 \, a b \log\left(\sec\left(d \sqrt{x} + c\right) + \tan\left(d \sqrt{x} + c\right)\right)}{d} + \frac{2 \, b^{2} \tan\left(d \sqrt{x} + c\right)}{d}"," ",0,"2*a^2*sqrt(x) + 4*a*b*log(sec(d*sqrt(x) + c) + tan(d*sqrt(x) + c))/d + 2*b^2*tan(d*sqrt(x) + c)/d","A",0
59,0,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^(3/2),x, algorithm=""maxima"")","\frac{4 \, b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + 4 \, {\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} \int \frac{b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a b d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + a b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + a b d \cos\left(d \sqrt{x} + c\right)\right)} \sqrt{x}}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}\,{d x} + d \int \frac{b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a b d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + a b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + a b d \cos\left(d \sqrt{x} + c\right)\right)} \sqrt{x}}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}\,{d x} \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \int \frac{b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a b d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + a b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + a b d \cos\left(d \sqrt{x} + c\right)\right)} \sqrt{x}}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}\,{d x} + d \int \frac{b^{2} \sin\left(2 \, d \sqrt{x} + 2 \, c\right) + {\left(a b d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) \cos\left(d \sqrt{x} + c\right) + a b d \sin\left(2 \, d \sqrt{x} + 2 \, c\right) \sin\left(d \sqrt{x} + c\right) + a b d \cos\left(d \sqrt{x} + c\right)\right)} \sqrt{x}}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x^{2}}\,{d x}\right)} x - 2 \, {\left(a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + a^{2} d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, a^{2} d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + a^{2} d\right)} \sqrt{x}}{{\left(d \cos\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + d \sin\left(2 \, d \sqrt{x} + 2 \, c\right)^{2} + 2 \, d \cos\left(2 \, d \sqrt{x} + 2 \, c\right) + d\right)} x}"," ",0,"(4*b^2*sin(2*d*sqrt(x) + 2*c) + (d*cos(2*d*sqrt(x) + 2*c)^2*integrate(4*(b^2*sin(2*d*sqrt(x) + 2*c) + (a*b*d*cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + a*b*d*sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + a*b*d*cos(d*sqrt(x) + c))*sqrt(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2), x) + d*integrate(4*(b^2*sin(2*d*sqrt(x) + 2*c) + (a*b*d*cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + a*b*d*sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + a*b*d*cos(d*sqrt(x) + c))*sqrt(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2), x)*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c)*integrate(4*(b^2*sin(2*d*sqrt(x) + 2*c) + (a*b*d*cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + a*b*d*sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + a*b*d*cos(d*sqrt(x) + c))*sqrt(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2), x) + d*integrate(4*(b^2*sin(2*d*sqrt(x) + 2*c) + (a*b*d*cos(2*d*sqrt(x) + 2*c)*cos(d*sqrt(x) + c) + a*b*d*sin(2*d*sqrt(x) + 2*c)*sin(d*sqrt(x) + c) + a*b*d*cos(d*sqrt(x) + c))*sqrt(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x^2), x))*x - 2*(a^2*d*cos(2*d*sqrt(x) + 2*c)^2 + a^2*d*sin(2*d*sqrt(x) + 2*c)^2 + 2*a^2*d*cos(2*d*sqrt(x) + 2*c) + a^2*d)*sqrt(x))/((d*cos(2*d*sqrt(x) + 2*c)^2 + d*sin(2*d*sqrt(x) + 2*c)^2 + 2*d*cos(2*d*sqrt(x) + 2*c) + d)*x)","F",0
60,-1,0,0,0.000000," ","integrate((a+b*sec(c+d*x^(1/2)))^2/x^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-2,0,0,0.000000," ","integrate(x^(3/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
62,-2,0,0,0.000000," ","integrate(x^(1/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
63,-2,0,0,0.000000," ","integrate(1/(a+b*sec(c+d*x^(1/2)))/x^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
64,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(a+b*sec(c+d*x^(1/2))),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-2,0,0,0.000000," ","integrate(x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
67,-2,0,0,0.000000," ","integrate(x^(1/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
68,-2,0,0,0.000000," ","integrate(1/(a+b*sec(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
69,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(a+b*sec(c+d*x^(1/2)))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,0,0,0,0.000000," ","integrate((e*x)^m*(a+b*sec(c+d*x^n))^p,x, algorithm=""maxima"")","\int \left(e x\right)^{m} {\left(b \sec\left(d x^{n} + c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x)^m*(b*sec(d*x^n + c) + a)^p, x)","F",0
72,0,0,0,0.000000," ","integrate((e*x)^(-1+n)*(a+b*sec(c+d*x^n)),x, algorithm=""maxima"")","2 \, b e^{n} \int \frac{x^{n} \cos\left(2 \, d x^{n} + 2 \, c\right) \cos\left(d x^{n} + c\right) + x^{n} \sin\left(2 \, d x^{n} + 2 \, c\right) \sin\left(d x^{n} + c\right) + x^{n} \cos\left(d x^{n} + c\right)}{e x \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + e x \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, e x \cos\left(2 \, d x^{n} + 2 \, c\right) + e x}\,{d x} + \frac{\left(e x\right)^{n} a}{e n}"," ",0,"2*b*e^n*integrate((x^n*cos(2*d*x^n + 2*c)*cos(d*x^n + c) + x^n*sin(2*d*x^n + 2*c)*sin(d*x^n + c) + x^n*cos(d*x^n + c))/(e*x*cos(2*d*x^n + 2*c)^2 + e*x*sin(2*d*x^n + 2*c)^2 + 2*e*x*cos(2*d*x^n + 2*c) + e*x), x) + (e*x)^n*a/(e*n)","F",0
73,0,0,0,0.000000," ","integrate((e*x)^(-1+2*n)*(a+b*sec(c+d*x^n)),x, algorithm=""maxima"")","2 \, b e^{2 \, n} \int \frac{x^{2 \, n} \cos\left(2 \, d x^{n} + 2 \, c\right) \cos\left(d x^{n} + c\right) + x^{2 \, n} \sin\left(2 \, d x^{n} + 2 \, c\right) \sin\left(d x^{n} + c\right) + x^{2 \, n} \cos\left(d x^{n} + c\right)}{e x \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + e x \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, e x \cos\left(2 \, d x^{n} + 2 \, c\right) + e x}\,{d x} + \frac{\left(e x\right)^{2 \, n} a}{2 \, e n}"," ",0,"2*b*e^(2*n)*integrate((x^(2*n)*cos(2*d*x^n + 2*c)*cos(d*x^n + c) + x^(2*n)*sin(2*d*x^n + 2*c)*sin(d*x^n + c) + x^(2*n)*cos(d*x^n + c))/(e*x*cos(2*d*x^n + 2*c)^2 + e*x*sin(2*d*x^n + 2*c)^2 + 2*e*x*cos(2*d*x^n + 2*c) + e*x), x) + 1/2*(e*x)^(2*n)*a/(e*n)","F",0
74,0,0,0,0.000000," ","integrate((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n)),x, algorithm=""maxima"")","2 \, b e^{3 \, n} \int \frac{x^{3 \, n} \cos\left(2 \, d x^{n} + 2 \, c\right) \cos\left(d x^{n} + c\right) + x^{3 \, n} \sin\left(2 \, d x^{n} + 2 \, c\right) \sin\left(d x^{n} + c\right) + x^{3 \, n} \cos\left(d x^{n} + c\right)}{e x \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + e x \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, e x \cos\left(2 \, d x^{n} + 2 \, c\right) + e x}\,{d x} + \frac{\left(e x\right)^{3 \, n} a}{3 \, e n}"," ",0,"2*b*e^(3*n)*integrate((x^(3*n)*cos(2*d*x^n + 2*c)*cos(d*x^n + c) + x^(3*n)*sin(2*d*x^n + 2*c)*sin(d*x^n + c) + x^(3*n)*cos(d*x^n + c))/(e*x*cos(2*d*x^n + 2*c)^2 + e*x*sin(2*d*x^n + 2*c)^2 + 2*e*x*cos(2*d*x^n + 2*c) + e*x), x) + 1/3*(e*x)^(3*n)*a/(e*n)","F",0
75,-1,0,0,0.000000," ","integrate((e*x)^(-1+n)*(a+b*sec(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,0,0,0,0.000000," ","integrate((e*x)^(-1+2*n)*(a+b*sec(c+d*x^n))^2,x, algorithm=""maxima"")","\frac{\left(e x\right)^{2 \, n} a^{2}}{2 \, e n} + \frac{2 \, b^{2} e^{2 \, n} x^{n} \sin\left(2 \, d x^{n} + 2 \, c\right) + 2 \, {\left(d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n\right)} \int \frac{2 \, a b d e^{2 \, n} x^{2 \, n} \cos\left(2 \, d x^{n} + 2 \, c\right) \cos\left(d x^{n} + c\right) + 2 \, a b d e^{2 \, n} x^{2 \, n} \cos\left(d x^{n} + c\right) + {\left(2 \, a b d e^{2 \, n} x^{2 \, n} \sin\left(d x^{n} + c\right) - b^{2} e^{2 \, n} x^{n}\right)} \sin\left(2 \, d x^{n} + 2 \, c\right)}{d e x \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e x \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, d e x \cos\left(2 \, d x^{n} + 2 \, c\right) + d e x}\,{d x}}{d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n}"," ",0,"1/2*(e*x)^(2*n)*a^2/(e*n) + (2*b^2*e^(2*n)*x^n*sin(2*d*x^n + 2*c) + (d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 + 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)*integrate(2*(2*a*b*d*e^(2*n)*x^(2*n)*cos(2*d*x^n + 2*c)*cos(d*x^n + c) + 2*a*b*d*e^(2*n)*x^(2*n)*cos(d*x^n + c) + (2*a*b*d*e^(2*n)*x^(2*n)*sin(d*x^n + c) - b^2*e^(2*n)*x^n)*sin(2*d*x^n + 2*c))/(d*e*x*cos(2*d*x^n + 2*c)^2 + d*e*x*sin(2*d*x^n + 2*c)^2 + 2*d*e*x*cos(2*d*x^n + 2*c) + d*e*x), x))/(d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 + 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)","F",0
77,0,0,0,0.000000," ","integrate((e*x)^(-1+3*n)*(a+b*sec(c+d*x^n))^2,x, algorithm=""maxima"")","\frac{\left(e x\right)^{3 \, n} a^{2}}{3 \, e n} + \frac{2 \, b^{2} e^{3 \, n} x^{2 \, n} \sin\left(2 \, d x^{n} + 2 \, c\right) + 4 \, {\left(d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n\right)} \int \frac{a b d e^{3 \, n} x^{3 \, n} \cos\left(2 \, d x^{n} + 2 \, c\right) \cos\left(d x^{n} + c\right) + a b d e^{3 \, n} x^{3 \, n} \cos\left(d x^{n} + c\right) + {\left(a b d e^{3 \, n} x^{3 \, n} \sin\left(d x^{n} + c\right) - b^{2} e^{3 \, n} x^{2 \, n}\right)} \sin\left(2 \, d x^{n} + 2 \, c\right)}{d e x \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e x \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, d e x \cos\left(2 \, d x^{n} + 2 \, c\right) + d e x}\,{d x}}{d e n \cos\left(2 \, d x^{n} + 2 \, c\right)^{2} + d e n \sin\left(2 \, d x^{n} + 2 \, c\right)^{2} + 2 \, d e n \cos\left(2 \, d x^{n} + 2 \, c\right) + d e n}"," ",0,"1/3*(e*x)^(3*n)*a^2/(e*n) + (2*b^2*e^(3*n)*x^(2*n)*sin(2*d*x^n + 2*c) + (d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 + 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)*integrate(4*(a*b*d*e^(3*n)*x^(3*n)*cos(2*d*x^n + 2*c)*cos(d*x^n + c) + a*b*d*e^(3*n)*x^(3*n)*cos(d*x^n + c) + (a*b*d*e^(3*n)*x^(3*n)*sin(d*x^n + c) - b^2*e^(3*n)*x^(2*n))*sin(2*d*x^n + 2*c))/(d*e*x*cos(2*d*x^n + 2*c)^2 + d*e*x*sin(2*d*x^n + 2*c)^2 + 2*d*e*x*cos(2*d*x^n + 2*c) + d*e*x), x))/(d*e*n*cos(2*d*x^n + 2*c)^2 + d*e*n*sin(2*d*x^n + 2*c)^2 + 2*d*e*n*cos(2*d*x^n + 2*c) + d*e*n)","F",0
78,-1,0,0,0.000000," ","integrate((e*x)^(-1+n)/(a+b*sec(c+d*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((e*x)^(-1+2*n)/(a+b*sec(c+d*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((e*x)^(-1+n)/(a+b*sec(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*x)^(-1+2*n)/(a+b*sec(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((e*x)^(-1+3*n)/(a+b*sec(c+d*x^n))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
