1,1,24,0,1.399526," ","integrate(tan(d*x + c),x, algorithm="fricas")","-\frac{\log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"-1/2*log(1/(tan(d*x + c)^2 + 1))/d","A"
2,1,23,0,1.139701," ","integrate(tan(d*x + c)^2,x, algorithm="fricas")","-\frac{d x - \tan\left(d x + c\right)}{d}"," ",0,"-(d*x - tan(d*x + c))/d","A"
3,1,36,0,1.154782," ","integrate(tan(d*x + c)^3,x, algorithm="fricas")","\frac{\tan\left(d x + c\right)^{2} + \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"1/2*(tan(d*x + c)^2 + log(1/(tan(d*x + c)^2 + 1)))/d","A"
4,1,35,0,1.158927," ","integrate(tan(d*x + c)^4,x, algorithm="fricas")","\frac{\tan\left(d x + c\right)^{3} + 3 \, d x - 3 \, \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(tan(d*x + c)^3 + 3*d*x - 3*tan(d*x + c))/d","A"
5,1,53,0,1.166215," ","integrate(tan(d*x + c)^5,x, algorithm="fricas")","\frac{\tan\left(d x + c\right)^{4} - 2 \, \tan\left(d x + c\right)^{2} - 2 \, \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{4 \, d}"," ",0,"1/4*(tan(d*x + c)^4 - 2*tan(d*x + c)^2 - 2*log(1/(tan(d*x + c)^2 + 1)))/d","A"
6,1,51,0,1.163514," ","integrate(tan(d*x + c)^6,x, algorithm="fricas")","\frac{3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x + 15 \, \tan\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x + 15*tan(d*x + c))/d","A"
7,1,69,0,1.195874," ","integrate(tan(d*x + c)^7,x, algorithm="fricas")","\frac{2 \, \tan\left(d x + c\right)^{6} - 3 \, \tan\left(d x + c\right)^{4} + 6 \, \tan\left(d x + c\right)^{2} + 6 \, \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{12 \, d}"," ",0,"1/12*(2*tan(d*x + c)^6 - 3*tan(d*x + c)^4 + 6*tan(d*x + c)^2 + 6*log(1/(tan(d*x + c)^2 + 1)))/d","A"
8,1,65,0,1.177114," ","integrate(tan(d*x + c)^8,x, algorithm="fricas")","\frac{15 \, \tan\left(d x + c\right)^{7} - 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 105 \, d x - 105 \, \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x - 105*tan(d*x + c))/d","A"
9,1,810,0,1.275188," ","integrate((b*tan(d*x + c))^(7/2),x, algorithm="fricas")","-\frac{20 \, \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} d \arctan\left(-\frac{b^{14} + \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{3}{4}} b^{3} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{3}{4}} d^{3} \sqrt{\frac{b^{7} \sin\left(d x + c\right) + \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + \sqrt{\frac{b^{14}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}}}{b^{14}}\right) \cos\left(d x + c\right)^{2} + 20 \, \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} d \arctan\left(\frac{b^{14} - \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{3}{4}} b^{3} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{3}{4}} d^{3} \sqrt{\frac{b^{7} \sin\left(d x + c\right) - \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + \sqrt{\frac{b^{14}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}}}{b^{14}}\right) \cos\left(d x + c\right)^{2} - 5 \, \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} d \cos\left(d x + c\right)^{2} \log\left(\frac{b^{7} \sin\left(d x + c\right) + \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + \sqrt{\frac{b^{14}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 5 \, \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} d \cos\left(d x + c\right)^{2} \log\left(\frac{b^{7} \sin\left(d x + c\right) - \sqrt{2} \left(\frac{b^{14}}{d^{4}}\right)^{\frac{1}{4}} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + \sqrt{\frac{b^{14}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, {\left(6 \, b^{3} \cos\left(d x + c\right)^{2} - b^{3}\right)} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{20 \, d \cos\left(d x + c\right)^{2}}"," ",0,"-1/20*(20*sqrt(2)*(b^14/d^4)^(1/4)*d*arctan(-(b^14 + sqrt(2)*(b^14/d^4)^(3/4)*b^3*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c)) - sqrt(2)*(b^14/d^4)^(3/4)*d^3*sqrt((b^7*sin(d*x + c) + sqrt(2)*(b^14/d^4)^(1/4)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + sqrt(b^14/d^4)*d^2*cos(d*x + c))/cos(d*x + c)))/b^14)*cos(d*x + c)^2 + 20*sqrt(2)*(b^14/d^4)^(1/4)*d*arctan((b^14 - sqrt(2)*(b^14/d^4)^(3/4)*b^3*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c)) + sqrt(2)*(b^14/d^4)^(3/4)*d^3*sqrt((b^7*sin(d*x + c) - sqrt(2)*(b^14/d^4)^(1/4)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + sqrt(b^14/d^4)*d^2*cos(d*x + c))/cos(d*x + c)))/b^14)*cos(d*x + c)^2 - 5*sqrt(2)*(b^14/d^4)^(1/4)*d*cos(d*x + c)^2*log((b^7*sin(d*x + c) + sqrt(2)*(b^14/d^4)^(1/4)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + sqrt(b^14/d^4)*d^2*cos(d*x + c))/cos(d*x + c)) + 5*sqrt(2)*(b^14/d^4)^(1/4)*d*cos(d*x + c)^2*log((b^7*sin(d*x + c) - sqrt(2)*(b^14/d^4)^(1/4)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + sqrt(b^14/d^4)*d^2*cos(d*x + c))/cos(d*x + c)) + 8*(6*b^3*cos(d*x + c)^2 - b^3)*sqrt(b*sin(d*x + c)/cos(d*x + c)))/(d*cos(d*x + c)^2)","A"
10,1,802,0,1.245490," ","integrate((b*tan(d*x + c))^(5/2),x, algorithm="fricas")","\frac{12 \, \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} d \arctan\left(-\frac{b^{10} + \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} b^{7} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} d \sqrt{\frac{b^{15} \sin\left(d x + c\right) + \sqrt{\frac{b^{10}}{d^{4}}} b^{10} d^{2} \cos\left(d x + c\right) + \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{3}{4}} b^{7} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}}}{b^{10}}\right) \cos\left(d x + c\right) + 12 \, \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} d \arctan\left(\frac{b^{10} - \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} b^{7} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} d \sqrt{\frac{b^{15} \sin\left(d x + c\right) + \sqrt{\frac{b^{10}}{d^{4}}} b^{10} d^{2} \cos\left(d x + c\right) - \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{3}{4}} b^{7} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}}}{b^{10}}\right) \cos\left(d x + c\right) + 3 \, \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} d \cos\left(d x + c\right) \log\left(\frac{b^{15} \sin\left(d x + c\right) + \sqrt{\frac{b^{10}}{d^{4}}} b^{10} d^{2} \cos\left(d x + c\right) + \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{3}{4}} b^{7} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 3 \, \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{1}{4}} d \cos\left(d x + c\right) \log\left(\frac{b^{15} \sin\left(d x + c\right) + \sqrt{\frac{b^{10}}{d^{4}}} b^{10} d^{2} \cos\left(d x + c\right) - \sqrt{2} \left(\frac{b^{10}}{d^{4}}\right)^{\frac{3}{4}} b^{7} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, b^{2} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)}"," ",0,"1/12*(12*sqrt(2)*(b^10/d^4)^(1/4)*d*arctan(-(b^10 + sqrt(2)*(b^10/d^4)^(1/4)*b^7*d*sqrt(b*sin(d*x + c)/cos(d*x + c)) - sqrt(2)*(b^10/d^4)^(1/4)*d*sqrt((b^15*sin(d*x + c) + sqrt(b^10/d^4)*b^10*d^2*cos(d*x + c) + sqrt(2)*(b^10/d^4)^(3/4)*b^7*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c))/cos(d*x + c)))/b^10)*cos(d*x + c) + 12*sqrt(2)*(b^10/d^4)^(1/4)*d*arctan((b^10 - sqrt(2)*(b^10/d^4)^(1/4)*b^7*d*sqrt(b*sin(d*x + c)/cos(d*x + c)) + sqrt(2)*(b^10/d^4)^(1/4)*d*sqrt((b^15*sin(d*x + c) + sqrt(b^10/d^4)*b^10*d^2*cos(d*x + c) - sqrt(2)*(b^10/d^4)^(3/4)*b^7*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c))/cos(d*x + c)))/b^10)*cos(d*x + c) + 3*sqrt(2)*(b^10/d^4)^(1/4)*d*cos(d*x + c)*log((b^15*sin(d*x + c) + sqrt(b^10/d^4)*b^10*d^2*cos(d*x + c) + sqrt(2)*(b^10/d^4)^(3/4)*b^7*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c))/cos(d*x + c)) - 3*sqrt(2)*(b^10/d^4)^(1/4)*d*cos(d*x + c)*log((b^15*sin(d*x + c) + sqrt(b^10/d^4)*b^10*d^2*cos(d*x + c) - sqrt(2)*(b^10/d^4)^(3/4)*b^7*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c))/cos(d*x + c)) + 8*b^2*sqrt(b*sin(d*x + c)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))","A"
11,1,720,0,1.231865," ","integrate((b*tan(d*x + c))^(3/2),x, algorithm="fricas")","\frac{4 \, \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} d \arctan\left(-\frac{b^{6} + \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{3}{4}} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} - \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{3}{4}} d^{3} \sqrt{\frac{\sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right) + \sqrt{\frac{b^{6}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}}}{b^{6}}\right) + 4 \, \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} d \arctan\left(\frac{b^{6} - \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{3}{4}} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} + \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{3}{4}} d^{3} \sqrt{-\frac{\sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right) - \sqrt{\frac{b^{6}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}}}{b^{6}}\right) - \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} d \log\left(\frac{\sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right) + \sqrt{\frac{b^{6}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} d \log\left(-\frac{\sqrt{2} \left(\frac{b^{6}}{d^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right) - \sqrt{\frac{b^{6}}{d^{4}}} d^{2} \cos\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 8 \, b \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(4*sqrt(2)*(b^6/d^4)^(1/4)*d*arctan(-(b^6 + sqrt(2)*(b^6/d^4)^(3/4)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c)) - sqrt(2)*(b^6/d^4)^(3/4)*d^3*sqrt((sqrt(2)*(b^6/d^4)^(1/4)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + b^3*sin(d*x + c) + sqrt(b^6/d^4)*d^2*cos(d*x + c))/cos(d*x + c)))/b^6) + 4*sqrt(2)*(b^6/d^4)^(1/4)*d*arctan((b^6 - sqrt(2)*(b^6/d^4)^(3/4)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c)) + sqrt(2)*(b^6/d^4)^(3/4)*d^3*sqrt(-(sqrt(2)*(b^6/d^4)^(1/4)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - b^3*sin(d*x + c) - sqrt(b^6/d^4)*d^2*cos(d*x + c))/cos(d*x + c)))/b^6) - sqrt(2)*(b^6/d^4)^(1/4)*d*log((sqrt(2)*(b^6/d^4)^(1/4)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) + b^3*sin(d*x + c) + sqrt(b^6/d^4)*d^2*cos(d*x + c))/cos(d*x + c)) + sqrt(2)*(b^6/d^4)^(1/4)*d*log(-(sqrt(2)*(b^6/d^4)^(1/4)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c) - b^3*sin(d*x + c) - sqrt(b^6/d^4)*d^2*cos(d*x + c))/cos(d*x + c)) + 8*b*sqrt(b*sin(d*x + c)/cos(d*x + c)))/d","A"
12,1,701,0,1.245893," ","integrate(sqrt(b*tan(d*x + c)),x, algorithm="fricas")","-\sqrt{2} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} - \sqrt{2} d \sqrt{\frac{\sqrt{2} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + b^{2} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} + b^{2}}{b^{2}}\right) - \sqrt{2} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} - \sqrt{2} d \sqrt{-\frac{\sqrt{2} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - b^{2} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} - b^{2}}{b^{2}}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + b^{2} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} \cos\left(d x + c\right) + b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{b^{2}}{d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - b^{2} d^{2} \sqrt{\frac{b^{2}}{d^{4}}} \cos\left(d x + c\right) - b^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)"," ",0,"-sqrt(2)*(b^2/d^4)^(1/4)*arctan(-(sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(b^2/d^4)^(1/4) - sqrt(2)*d*sqrt((sqrt(2)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(b^2/d^4)^(3/4)*cos(d*x + c) + b^2*d^2*sqrt(b^2/d^4)*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c))*(b^2/d^4)^(1/4) + b^2)/b^2) - sqrt(2)*(b^2/d^4)^(1/4)*arctan(-(sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(b^2/d^4)^(1/4) - sqrt(2)*d*sqrt(-(sqrt(2)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(b^2/d^4)^(3/4)*cos(d*x + c) - b^2*d^2*sqrt(b^2/d^4)*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))*(b^2/d^4)^(1/4) - b^2)/b^2) - 1/4*sqrt(2)*(b^2/d^4)^(1/4)*log((sqrt(2)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(b^2/d^4)^(3/4)*cos(d*x + c) + b^2*d^2*sqrt(b^2/d^4)*cos(d*x + c) + b^3*sin(d*x + c))/cos(d*x + c)) + 1/4*sqrt(2)*(b^2/d^4)^(1/4)*log(-(sqrt(2)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(b^2/d^4)^(3/4)*cos(d*x + c) - b^2*d^2*sqrt(b^2/d^4)*cos(d*x + c) - b^3*sin(d*x + c))/cos(d*x + c))","A"
13,1,666,0,1.215679," ","integrate(1/sqrt(b*tan(d*x + c)),x, algorithm="fricas")","-\sqrt{2} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} b d^{3} \sqrt{\frac{b^{2} d^{2} \sqrt{\frac{1}{b^{2} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{3}{4}} - 1\right) - \sqrt{2} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} b d^{3} \sqrt{\frac{b^{2} d^{2} \sqrt{\frac{1}{b^{2} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{3}{4}} + 1\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{b^{2} d^{2} \sqrt{\frac{1}{b^{2} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{b^{2} d^{2} \sqrt{\frac{1}{b^{2} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{2} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)"," ",0,"-sqrt(2)*(1/(b^2*d^4))^(1/4)*arctan(-sqrt(2)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^2*d^4))^(3/4) + sqrt(2)*b*d^3*sqrt((b^2*d^2*sqrt(1/(b^2*d^4))*cos(d*x + c) + sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^2*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/(b^2*d^4))^(3/4) - 1) - sqrt(2)*(1/(b^2*d^4))^(1/4)*arctan(-sqrt(2)*b*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^2*d^4))^(3/4) + sqrt(2)*b*d^3*sqrt((b^2*d^2*sqrt(1/(b^2*d^4))*cos(d*x + c) - sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^2*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/(b^2*d^4))^(3/4) + 1) + 1/4*sqrt(2)*(1/(b^2*d^4))^(1/4)*log((b^2*d^2*sqrt(1/(b^2*d^4))*cos(d*x + c) + sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^2*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - 1/4*sqrt(2)*(1/(b^2*d^4))^(1/4)*log((b^2*d^2*sqrt(1/(b^2*d^4))*cos(d*x + c) - sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^2*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))","A"
14,1,880,0,1.245885," ","integrate((b*tan(d*x + c))^(-3/2),x, algorithm="fricas")","\frac{8 \, \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, {\left(\sqrt{2} b^{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{2} d\right)} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} + \sqrt{2} b d \sqrt{\frac{\sqrt{2} b^{5} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + b^{4} d^{2} \sqrt{\frac{1}{b^{6} d^{4}}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} - 1\right) + 4 \, {\left(\sqrt{2} b^{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{2} d\right)} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} + \sqrt{2} b d \sqrt{-\frac{\sqrt{2} b^{5} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - b^{4} d^{2} \sqrt{\frac{1}{b^{6} d^{4}}} \cos\left(d x + c\right) - b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} + 1\right) + {\left(\sqrt{2} b^{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{2} d\right)} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{5} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + b^{4} d^{2} \sqrt{\frac{1}{b^{6} d^{4}}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - {\left(\sqrt{2} b^{2} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{2} d\right)} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{5} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{6} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - b^{4} d^{2} \sqrt{\frac{1}{b^{6} d^{4}}} \cos\left(d x + c\right) - b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{4 \, {\left(b^{2} d \cos\left(d x + c\right)^{2} - b^{2} d\right)}}"," ",0,"1/4*(8*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 4*(sqrt(2)*b^2*d*cos(d*x + c)^2 - sqrt(2)*b^2*d)*(1/(b^6*d^4))^(1/4)*arctan(-sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^6*d^4))^(1/4) + sqrt(2)*b*d*sqrt((sqrt(2)*b^5*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^6*d^4))^(3/4)*cos(d*x + c) + b^4*d^2*sqrt(1/(b^6*d^4))*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/(b^6*d^4))^(1/4) - 1) + 4*(sqrt(2)*b^2*d*cos(d*x + c)^2 - sqrt(2)*b^2*d)*(1/(b^6*d^4))^(1/4)*arctan(-sqrt(2)*b*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^6*d^4))^(1/4) + sqrt(2)*b*d*sqrt(-(sqrt(2)*b^5*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^6*d^4))^(3/4)*cos(d*x + c) - b^4*d^2*sqrt(1/(b^6*d^4))*cos(d*x + c) - b*sin(d*x + c))/cos(d*x + c))*(1/(b^6*d^4))^(1/4) + 1) + (sqrt(2)*b^2*d*cos(d*x + c)^2 - sqrt(2)*b^2*d)*(1/(b^6*d^4))^(1/4)*log((sqrt(2)*b^5*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^6*d^4))^(3/4)*cos(d*x + c) + b^4*d^2*sqrt(1/(b^6*d^4))*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - (sqrt(2)*b^2*d*cos(d*x + c)^2 - sqrt(2)*b^2*d)*(1/(b^6*d^4))^(1/4)*log(-(sqrt(2)*b^5*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^6*d^4))^(3/4)*cos(d*x + c) - b^4*d^2*sqrt(1/(b^6*d^4))*cos(d*x + c) - b*sin(d*x + c))/cos(d*x + c)))/(b^2*d*cos(d*x + c)^2 - b^2*d)","A"
15,1,882,0,1.256242," ","integrate((b*tan(d*x + c))^(-5/2),x, algorithm="fricas")","\frac{8 \, \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)^{2} + 12 \, {\left(\sqrt{2} b^{3} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{3} d\right)} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b^{7} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} b^{7} d^{3} \sqrt{\frac{b^{6} d^{2} \sqrt{\frac{1}{b^{10} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{3}{4}} - 1\right) + 12 \, {\left(\sqrt{2} b^{3} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{3} d\right)} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b^{7} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{3}{4}} + \sqrt{2} b^{7} d^{3} \sqrt{\frac{b^{6} d^{2} \sqrt{\frac{1}{b^{10} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{3}{4}} + 1\right) - 3 \, {\left(\sqrt{2} b^{3} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{3} d\right)} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{b^{6} d^{2} \sqrt{\frac{1}{b^{10} d^{4}}} \cos\left(d x + c\right) + \sqrt{2} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) + 3 \, {\left(\sqrt{2} b^{3} d \cos\left(d x + c\right)^{2} - \sqrt{2} b^{3} d\right)} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{b^{6} d^{2} \sqrt{\frac{1}{b^{10} d^{4}}} \cos\left(d x + c\right) - \sqrt{2} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{10} d^{4}}\right)^{\frac{1}{4}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{12 \, {\left(b^{3} d \cos\left(d x + c\right)^{2} - b^{3} d\right)}}"," ",0,"1/12*(8*sqrt(b*sin(d*x + c)/cos(d*x + c))*cos(d*x + c)^2 + 12*(sqrt(2)*b^3*d*cos(d*x + c)^2 - sqrt(2)*b^3*d)*(1/(b^10*d^4))^(1/4)*arctan(-sqrt(2)*b^7*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^10*d^4))^(3/4) + sqrt(2)*b^7*d^3*sqrt((b^6*d^2*sqrt(1/(b^10*d^4))*cos(d*x + c) + sqrt(2)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^10*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/(b^10*d^4))^(3/4) - 1) + 12*(sqrt(2)*b^3*d*cos(d*x + c)^2 - sqrt(2)*b^3*d)*(1/(b^10*d^4))^(1/4)*arctan(-sqrt(2)*b^7*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^10*d^4))^(3/4) + sqrt(2)*b^7*d^3*sqrt((b^6*d^2*sqrt(1/(b^10*d^4))*cos(d*x + c) - sqrt(2)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^10*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/(b^10*d^4))^(3/4) + 1) - 3*(sqrt(2)*b^3*d*cos(d*x + c)^2 - sqrt(2)*b^3*d)*(1/(b^10*d^4))^(1/4)*log((b^6*d^2*sqrt(1/(b^10*d^4))*cos(d*x + c) + sqrt(2)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^10*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) + 3*(sqrt(2)*b^3*d*cos(d*x + c)^2 - sqrt(2)*b^3*d)*(1/(b^10*d^4))^(1/4)*log((b^6*d^2*sqrt(1/(b^10*d^4))*cos(d*x + c) - sqrt(2)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^10*d^4))^(1/4)*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)))/(b^3*d*cos(d*x + c)^2 - b^3*d)","A"
16,1,1014,0,1.280425," ","integrate((b*tan(d*x + c))^(-7/2),x, algorithm="fricas")","-\frac{8 \, {\left(6 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + 20 \, {\left(\sqrt{2} b^{4} d \cos\left(d x + c\right)^{4} - 2 \, \sqrt{2} b^{4} d \cos\left(d x + c\right)^{2} + \sqrt{2} b^{4} d\right)} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} + \sqrt{2} b^{3} d \sqrt{\frac{\sqrt{2} b^{11} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + b^{8} d^{2} \sqrt{\frac{1}{b^{14} d^{4}}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} - 1\right) + 20 \, {\left(\sqrt{2} b^{4} d \cos\left(d x + c\right)^{4} - 2 \, \sqrt{2} b^{4} d \cos\left(d x + c\right)^{2} + \sqrt{2} b^{4} d\right)} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b^{3} d \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} + \sqrt{2} b^{3} d \sqrt{-\frac{\sqrt{2} b^{11} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - b^{8} d^{2} \sqrt{\frac{1}{b^{14} d^{4}}} \cos\left(d x + c\right) - b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} + 1\right) + 5 \, {\left(\sqrt{2} b^{4} d \cos\left(d x + c\right)^{4} - 2 \, \sqrt{2} b^{4} d \cos\left(d x + c\right)^{2} + \sqrt{2} b^{4} d\right)} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{11} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) + b^{8} d^{2} \sqrt{\frac{1}{b^{14} d^{4}}} \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right) - 5 \, {\left(\sqrt{2} b^{4} d \cos\left(d x + c\right)^{4} - 2 \, \sqrt{2} b^{4} d \cos\left(d x + c\right)^{2} + \sqrt{2} b^{4} d\right)} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{11} d^{3} \sqrt{\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}} \left(\frac{1}{b^{14} d^{4}}\right)^{\frac{3}{4}} \cos\left(d x + c\right) - b^{8} d^{2} \sqrt{\frac{1}{b^{14} d^{4}}} \cos\left(d x + c\right) - b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)}{20 \, {\left(b^{4} d \cos\left(d x + c\right)^{4} - 2 \, b^{4} d \cos\left(d x + c\right)^{2} + b^{4} d\right)}}"," ",0,"-1/20*(8*(6*cos(d*x + c)^3 - 5*cos(d*x + c))*sqrt(b*sin(d*x + c)/cos(d*x + c))*sin(d*x + c) + 20*(sqrt(2)*b^4*d*cos(d*x + c)^4 - 2*sqrt(2)*b^4*d*cos(d*x + c)^2 + sqrt(2)*b^4*d)*(1/(b^14*d^4))^(1/4)*arctan(-sqrt(2)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^14*d^4))^(1/4) + sqrt(2)*b^3*d*sqrt((sqrt(2)*b^11*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^14*d^4))^(3/4)*cos(d*x + c) + b^8*d^2*sqrt(1/(b^14*d^4))*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))*(1/(b^14*d^4))^(1/4) - 1) + 20*(sqrt(2)*b^4*d*cos(d*x + c)^4 - 2*sqrt(2)*b^4*d*cos(d*x + c)^2 + sqrt(2)*b^4*d)*(1/(b^14*d^4))^(1/4)*arctan(-sqrt(2)*b^3*d*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^14*d^4))^(1/4) + sqrt(2)*b^3*d*sqrt(-(sqrt(2)*b^11*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^14*d^4))^(3/4)*cos(d*x + c) - b^8*d^2*sqrt(1/(b^14*d^4))*cos(d*x + c) - b*sin(d*x + c))/cos(d*x + c))*(1/(b^14*d^4))^(1/4) + 1) + 5*(sqrt(2)*b^4*d*cos(d*x + c)^4 - 2*sqrt(2)*b^4*d*cos(d*x + c)^2 + sqrt(2)*b^4*d)*(1/(b^14*d^4))^(1/4)*log((sqrt(2)*b^11*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^14*d^4))^(3/4)*cos(d*x + c) + b^8*d^2*sqrt(1/(b^14*d^4))*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c)) - 5*(sqrt(2)*b^4*d*cos(d*x + c)^4 - 2*sqrt(2)*b^4*d*cos(d*x + c)^2 + sqrt(2)*b^4*d)*(1/(b^14*d^4))^(1/4)*log(-(sqrt(2)*b^11*d^3*sqrt(b*sin(d*x + c)/cos(d*x + c))*(1/(b^14*d^4))^(3/4)*cos(d*x + c) - b^8*d^2*sqrt(1/(b^14*d^4))*cos(d*x + c) - b*sin(d*x + c))/cos(d*x + c)))/(b^4*d*cos(d*x + c)^4 - 2*b^4*d*cos(d*x + c)^2 + b^4*d)","A"
17,1,794,0,1.247475," ","integrate((b*tan(d*x + c))^(4/3),x, algorithm="fricas")","-\frac{\sqrt{3} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} d \log\left(\sqrt{3} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} + b^{2} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}} + \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{3}} d^{2}\right) - \sqrt{3} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} d \log\left(-\sqrt{3} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} + b^{2} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}} + \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{3}} d^{2}\right) - 4 \, \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} d \arctan\left(-\frac{\sqrt{3} b^{8} + 2 \, \left(\frac{b^{8}}{d^{6}}\right)^{\frac{5}{6}} b d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} - 2 \, \sqrt{\sqrt{3} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} + b^{2} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}} + \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{3}} d^{2}} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{5}{6}} d^{5}}{b^{8}}\right) - 4 \, \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} d \arctan\left(\frac{\sqrt{3} b^{8} - 2 \, \left(\frac{b^{8}}{d^{6}}\right)^{\frac{5}{6}} b d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} + 2 \, \sqrt{-\sqrt{3} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} + b^{2} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}} + \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{3}} d^{2}} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{5}{6}} d^{5}}{b^{8}}\right) - 8 \, \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{6}} d \arctan\left(-\frac{\left(\frac{b^{8}}{d^{6}}\right)^{\frac{5}{6}} b d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} - \sqrt{b^{2} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}} + \left(\frac{b^{8}}{d^{6}}\right)^{\frac{1}{3}} d^{2}} \left(\frac{b^{8}}{d^{6}}\right)^{\frac{5}{6}} d^{5}}{b^{8}}\right) - 12 \, b \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}}}{4 \, d}"," ",0,"-1/4*(sqrt(3)*(b^8/d^6)^(1/6)*d*log(sqrt(3)*(b^8/d^6)^(1/6)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3) + b^2*(b*sin(d*x + c)/cos(d*x + c))^(2/3) + (b^8/d^6)^(1/3)*d^2) - sqrt(3)*(b^8/d^6)^(1/6)*d*log(-sqrt(3)*(b^8/d^6)^(1/6)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3) + b^2*(b*sin(d*x + c)/cos(d*x + c))^(2/3) + (b^8/d^6)^(1/3)*d^2) - 4*(b^8/d^6)^(1/6)*d*arctan(-(sqrt(3)*b^8 + 2*(b^8/d^6)^(5/6)*b*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3) - 2*sqrt(sqrt(3)*(b^8/d^6)^(1/6)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3) + b^2*(b*sin(d*x + c)/cos(d*x + c))^(2/3) + (b^8/d^6)^(1/3)*d^2)*(b^8/d^6)^(5/6)*d^5)/b^8) - 4*(b^8/d^6)^(1/6)*d*arctan((sqrt(3)*b^8 - 2*(b^8/d^6)^(5/6)*b*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3) + 2*sqrt(-sqrt(3)*(b^8/d^6)^(1/6)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3) + b^2*(b*sin(d*x + c)/cos(d*x + c))^(2/3) + (b^8/d^6)^(1/3)*d^2)*(b^8/d^6)^(5/6)*d^5)/b^8) - 8*(b^8/d^6)^(1/6)*d*arctan(-((b^8/d^6)^(5/6)*b*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3) - sqrt(b^2*(b*sin(d*x + c)/cos(d*x + c))^(2/3) + (b^8/d^6)^(1/3)*d^2)*(b^8/d^6)^(5/6)*d^5)/b^8) - 12*b*(b*sin(d*x + c)/cos(d*x + c))^(1/3))/d","A"
18,1,787,0,1.248709," ","integrate((b*tan(d*x + c))^(2/3),x, algorithm="fricas")","-\frac{1}{4} \, \sqrt{3} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} \log\left(\sqrt{3} b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{5}{6}} + b^{4} d^{4} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{2}{3}} + b^{6} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) + \frac{1}{4} \, \sqrt{3} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} \log\left(-\sqrt{3} b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{5}{6}} + b^{4} d^{4} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{2}{3}} + b^{6} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} \arctan\left(-\frac{\sqrt{3} b^{4} + 2 \, b^{3} d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} - 2 \, \sqrt{\sqrt{3} b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{5}{6}} + b^{4} d^{4} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{2}{3}} + b^{6} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} d \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}}}{b^{4}}\right) - \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} \arctan\left(\frac{\sqrt{3} b^{4} - 2 \, b^{3} d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} + 2 \, \sqrt{-\sqrt{3} b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{5}{6}} + b^{4} d^{4} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{2}{3}} + b^{6} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} d \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}}}{b^{4}}\right) - 2 \, \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} \arctan\left(-\frac{b^{3} d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}} - \sqrt{b^{4} d^{4} \left(\frac{b^{4}}{d^{6}}\right)^{\frac{2}{3}} + b^{6} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} d \left(\frac{b^{4}}{d^{6}}\right)^{\frac{1}{6}}}{b^{4}}\right)"," ",0,"-1/4*sqrt(3)*(b^4/d^6)^(1/6)*log(sqrt(3)*b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(5/6) + b^4*d^4*(b^4/d^6)^(2/3) + b^6*(b*sin(d*x + c)/cos(d*x + c))^(2/3)) + 1/4*sqrt(3)*(b^4/d^6)^(1/6)*log(-sqrt(3)*b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(5/6) + b^4*d^4*(b^4/d^6)^(2/3) + b^6*(b*sin(d*x + c)/cos(d*x + c))^(2/3)) - (b^4/d^6)^(1/6)*arctan(-(sqrt(3)*b^4 + 2*b^3*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(1/6) - 2*sqrt(sqrt(3)*b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(5/6) + b^4*d^4*(b^4/d^6)^(2/3) + b^6*(b*sin(d*x + c)/cos(d*x + c))^(2/3))*d*(b^4/d^6)^(1/6))/b^4) - (b^4/d^6)^(1/6)*arctan((sqrt(3)*b^4 - 2*b^3*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(1/6) + 2*sqrt(-sqrt(3)*b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(5/6) + b^4*d^4*(b^4/d^6)^(2/3) + b^6*(b*sin(d*x + c)/cos(d*x + c))^(2/3))*d*(b^4/d^6)^(1/6))/b^4) - 2*(b^4/d^6)^(1/6)*arctan(-(b^3*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(b^4/d^6)^(1/6) - sqrt(b^4*d^4*(b^4/d^6)^(2/3) + b^6*(b*sin(d*x + c)/cos(d*x + c))^(2/3))*d*(b^4/d^6)^(1/6))/b^4)","A"
19,1,167,0,1.169917," ","integrate((b*tan(d*x + c))^(1/3),x, algorithm="fricas")","\frac{2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} \left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} \left(-b\right)^{\frac{1}{3}} + \sqrt{3} b}{3 \, b}\right) - \left(-b\right)^{\frac{1}{3}} \log\left(\left(b \tan\left(d x + c\right)\right)^{\frac{1}{3}} b \tan\left(d x + c\right) - \left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} - \left(-b\right)^{\frac{1}{3}} b\right) + 2 \, \left(-b\right)^{\frac{1}{3}} \log\left(\left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} + \left(-b\right)^{\frac{2}{3}}\right)}{4 \, d}"," ",0,"1/4*(2*sqrt(3)*(-b)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*tan(d*x + c))^(2/3)*(-b)^(1/3) + sqrt(3)*b)/b) - (-b)^(1/3)*log((b*tan(d*x + c))^(1/3)*b*tan(d*x + c) - (b*tan(d*x + c))^(2/3)*(-b)^(2/3) - (-b)^(1/3)*b) + 2*(-b)^(1/3)*log((b*tan(d*x + c))^(2/3) + (-b)^(2/3)))/d","A"
20,1,1,0,1.211566," ","integrate((b*tan(d*x + c))^(-1/3),x, algorithm="fricas")","\left[\frac{\sqrt{3} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(\frac{2 \, \sqrt{3} \left(b \tan\left(d x + c\right)\right)^{\frac{1}{3}} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \tan\left(d x + c\right) + 2 \, b \tan\left(d x + c\right)^{2} - \sqrt{3} b^{\frac{4}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + \left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} {\left(\sqrt{3} b^{\frac{2}{3}} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 3 \, b^{\frac{1}{3}}\right)} - b}{\tan\left(d x + c\right)^{2} + 1}\right) - b^{\frac{2}{3}} \log\left(\left(b \tan\left(d x + c\right)\right)^{\frac{1}{3}} b \tan\left(d x + c\right) - \left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} b^{\frac{2}{3}} + b^{\frac{4}{3}}\right) + 2 \, b^{\frac{2}{3}} \log\left(\left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} + b^{\frac{2}{3}}\right)}{4 \, b d}, \frac{2 \, \sqrt{3} b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, \left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} b^{\frac{2}{3}} - b^{\frac{4}{3}}\right)}}{3 \, b^{\frac{4}{3}}}\right) - b^{\frac{2}{3}} \log\left(\left(b \tan\left(d x + c\right)\right)^{\frac{1}{3}} b \tan\left(d x + c\right) - \left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} b^{\frac{2}{3}} + b^{\frac{4}{3}}\right) + 2 \, b^{\frac{2}{3}} \log\left(\left(b \tan\left(d x + c\right)\right)^{\frac{2}{3}} + b^{\frac{2}{3}}\right)}{4 \, b d}\right]"," ",0,"[1/4*(sqrt(3)*b*sqrt(-1/b^(2/3))*log((2*sqrt(3)*(b*tan(d*x + c))^(1/3)*b*sqrt(-1/b^(2/3))*tan(d*x + c) + 2*b*tan(d*x + c)^2 - sqrt(3)*b^(4/3)*sqrt(-1/b^(2/3)) + (b*tan(d*x + c))^(2/3)*(sqrt(3)*b^(2/3)*sqrt(-1/b^(2/3)) - 3*b^(1/3)) - b)/(tan(d*x + c)^2 + 1)) - b^(2/3)*log((b*tan(d*x + c))^(1/3)*b*tan(d*x + c) - (b*tan(d*x + c))^(2/3)*b^(2/3) + b^(4/3)) + 2*b^(2/3)*log((b*tan(d*x + c))^(2/3) + b^(2/3)))/(b*d), 1/4*(2*sqrt(3)*b^(2/3)*arctan(1/3*sqrt(3)*(2*(b*tan(d*x + c))^(2/3)*b^(2/3) - b^(4/3))/b^(4/3)) - b^(2/3)*log((b*tan(d*x + c))^(1/3)*b*tan(d*x + c) - (b*tan(d*x + c))^(2/3)*b^(2/3) + b^(4/3)) + 2*b^(2/3)*log((b*tan(d*x + c))^(2/3) + b^(2/3)))/(b*d)]","A"
21,1,740,0,1.221119," ","integrate((b*tan(d*x + c))^(-2/3),x, algorithm="fricas")","\frac{1}{4} \, \sqrt{3} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} \log\left(b^{2} d^{2} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{3}} + \sqrt{3} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - \frac{1}{4} \, \sqrt{3} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} \log\left(b^{2} d^{2} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{3}} - \sqrt{3} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} \arctan\left(2 \, \sqrt{b^{2} d^{2} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{3}} + \sqrt{3} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} b^{3} d^{5} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{5}{6}} - 2 \, b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{5}{6}} - \sqrt{3}\right) - \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} \arctan\left(2 \, \sqrt{b^{2} d^{2} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{3}} - \sqrt{3} b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} b^{3} d^{5} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{5}{6}} - 2 \, b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{5}{6}} + \sqrt{3}\right) - 2 \, \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{6}} \arctan\left(\sqrt{b^{2} d^{2} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{3}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} b^{3} d^{5} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{5}{6}} - b^{3} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{5}{6}}\right)"," ",0,"1/4*sqrt(3)*(1/(b^4*d^6))^(1/6)*log(b^2*d^2*(1/(b^4*d^6))^(1/3) + sqrt(3)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(1/6) + (b*sin(d*x + c)/cos(d*x + c))^(2/3)) - 1/4*sqrt(3)*(1/(b^4*d^6))^(1/6)*log(b^2*d^2*(1/(b^4*d^6))^(1/3) - sqrt(3)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(1/6) + (b*sin(d*x + c)/cos(d*x + c))^(2/3)) - (1/(b^4*d^6))^(1/6)*arctan(2*sqrt(b^2*d^2*(1/(b^4*d^6))^(1/3) + sqrt(3)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(1/6) + (b*sin(d*x + c)/cos(d*x + c))^(2/3))*b^3*d^5*(1/(b^4*d^6))^(5/6) - 2*b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(5/6) - sqrt(3)) - (1/(b^4*d^6))^(1/6)*arctan(2*sqrt(b^2*d^2*(1/(b^4*d^6))^(1/3) - sqrt(3)*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(1/6) + (b*sin(d*x + c)/cos(d*x + c))^(2/3))*b^3*d^5*(1/(b^4*d^6))^(5/6) - 2*b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(5/6) + sqrt(3)) - 2*(1/(b^4*d^6))^(1/6)*arctan(sqrt(b^2*d^2*(1/(b^4*d^6))^(1/3) + (b*sin(d*x + c)/cos(d*x + c))^(2/3))*b^3*d^5*(1/(b^4*d^6))^(5/6) - b^3*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^4*d^6))^(5/6))","A"
22,1,946,0,1.272775," ","integrate((b*tan(d*x + c))^(-4/3),x, algorithm="fricas")","\frac{12 \, \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, {\left(b^{2} d \cos\left(d x + c\right)^{2} - b^{2} d\right)} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} \arctan\left(2 \, \sqrt{\sqrt{3} b^{7} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{5}{6}} + b^{6} d^{4} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{2}{3}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} b d \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} - 2 \, b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} - \sqrt{3}\right) + 4 \, {\left(b^{2} d \cos\left(d x + c\right)^{2} - b^{2} d\right)} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} \arctan\left(2 \, \sqrt{-\sqrt{3} b^{7} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{5}{6}} + b^{6} d^{4} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{2}{3}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} b d \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} - 2 \, b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} + \sqrt{3}\right) + 8 \, {\left(b^{2} d \cos\left(d x + c\right)^{2} - b^{2} d\right)} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} \arctan\left(\sqrt{b^{6} d^{4} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{2}{3}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}} b d \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} - b d \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}}\right) + {\left(\sqrt{3} b^{2} d \cos\left(d x + c\right)^{2} - \sqrt{3} b^{2} d\right)} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} \log\left(\sqrt{3} b^{7} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{5}{6}} + b^{6} d^{4} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{2}{3}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right) - {\left(\sqrt{3} b^{2} d \cos\left(d x + c\right)^{2} - \sqrt{3} b^{2} d\right)} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{1}{6}} \log\left(-\sqrt{3} b^{7} d^{5} \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{1}{3}} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{5}{6}} + b^{6} d^{4} \left(\frac{1}{b^{8} d^{6}}\right)^{\frac{2}{3}} + \left(\frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{\frac{2}{3}}\right)}{4 \, {\left(b^{2} d \cos\left(d x + c\right)^{2} - b^{2} d\right)}}"," ",0,"1/4*(12*(b*sin(d*x + c)/cos(d*x + c))^(2/3)*cos(d*x + c)*sin(d*x + c) + 4*(b^2*d*cos(d*x + c)^2 - b^2*d)*(1/(b^8*d^6))^(1/6)*arctan(2*sqrt(sqrt(3)*b^7*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(5/6) + b^6*d^4*(1/(b^8*d^6))^(2/3) + (b*sin(d*x + c)/cos(d*x + c))^(2/3))*b*d*(1/(b^8*d^6))^(1/6) - 2*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(1/6) - sqrt(3)) + 4*(b^2*d*cos(d*x + c)^2 - b^2*d)*(1/(b^8*d^6))^(1/6)*arctan(2*sqrt(-sqrt(3)*b^7*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(5/6) + b^6*d^4*(1/(b^8*d^6))^(2/3) + (b*sin(d*x + c)/cos(d*x + c))^(2/3))*b*d*(1/(b^8*d^6))^(1/6) - 2*b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(1/6) + sqrt(3)) + 8*(b^2*d*cos(d*x + c)^2 - b^2*d)*(1/(b^8*d^6))^(1/6)*arctan(sqrt(b^6*d^4*(1/(b^8*d^6))^(2/3) + (b*sin(d*x + c)/cos(d*x + c))^(2/3))*b*d*(1/(b^8*d^6))^(1/6) - b*d*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(1/6)) + (sqrt(3)*b^2*d*cos(d*x + c)^2 - sqrt(3)*b^2*d)*(1/(b^8*d^6))^(1/6)*log(sqrt(3)*b^7*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(5/6) + b^6*d^4*(1/(b^8*d^6))^(2/3) + (b*sin(d*x + c)/cos(d*x + c))^(2/3)) - (sqrt(3)*b^2*d*cos(d*x + c)^2 - sqrt(3)*b^2*d)*(1/(b^8*d^6))^(1/6)*log(-sqrt(3)*b^7*d^5*(b*sin(d*x + c)/cos(d*x + c))^(1/3)*(1/(b^8*d^6))^(5/6) + b^6*d^4*(1/(b^8*d^6))^(2/3) + (b*sin(d*x + c)/cos(d*x + c))^(2/3)))/(b^2*d*cos(d*x + c)^2 - b^2*d)","A"
23,0,0,0,0.000000," ","integrate((b*tan(d*x + c))^n,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((b*tan(d*x + c))^n, x)","F"
24,1,100,0,1.192721," ","integrate((b*tan(d*x + c)^2)^(5/2),x, algorithm="fricas")","\frac{{\left(b^{2} \tan\left(d x + c\right)^{4} - 2 \, b^{2} \tan\left(d x + c\right)^{2} - 2 \, b^{2} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) - 3 \, b^{2}\right)} \sqrt{b \tan\left(d x + c\right)^{2}}}{4 \, d \tan\left(d x + c\right)}"," ",0,"1/4*(b^2*tan(d*x + c)^4 - 2*b^2*tan(d*x + c)^2 - 2*b^2*log(1/(tan(d*x + c)^2 + 1)) - 3*b^2)*sqrt(b*tan(d*x + c)^2)/(d*tan(d*x + c))","A"
25,1,70,0,1.203440," ","integrate((b*tan(d*x + c)^2)^(3/2),x, algorithm="fricas")","\frac{{\left(b \tan\left(d x + c\right)^{2} + b \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right) + b\right)} \sqrt{b \tan\left(d x + c\right)^{2}}}{2 \, d \tan\left(d x + c\right)}"," ",0,"1/2*(b*tan(d*x + c)^2 + b*log(1/(tan(d*x + c)^2 + 1)) + b)*sqrt(b*tan(d*x + c)^2)/(d*tan(d*x + c))","A"
26,1,51,0,1.171100," ","integrate(sqrt(b*tan(d*x + c)^2),x, algorithm="fricas")","-\frac{\sqrt{b \tan\left(d x + c\right)^{2}} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d \tan\left(d x + c\right)}"," ",0,"-1/2*sqrt(b*tan(d*x + c)^2)*log(1/(tan(d*x + c)^2 + 1))/(d*tan(d*x + c))","A"
27,1,68,0,1.188071," ","integrate(1/sqrt(b*tan(d*x + c)^2),x, algorithm="fricas")","\frac{\sqrt{b \tan\left(d x + c\right)^{2}} \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, b d \tan\left(d x + c\right)}"," ",0,"1/2*sqrt(b*tan(d*x + c)^2)*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))/(b*d*tan(d*x + c))","A"
28,1,93,0,1.184959," ","integrate((b*tan(d*x + c)^2)^(-3/2),x, algorithm="fricas")","-\frac{\sqrt{b \tan\left(d x + c\right)^{2}} {\left(\log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{2} + \tan\left(d x + c\right)^{2} + 1\right)}}{2 \, b^{2} d \tan\left(d x + c\right)^{3}}"," ",0,"-1/2*sqrt(b*tan(d*x + c)^2)*(log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^2 + tan(d*x + c)^2 + 1)/(b^2*d*tan(d*x + c)^3)","A"
29,1,111,0,1.176196," ","integrate((b*tan(d*x + c)^2)^(-5/2),x, algorithm="fricas")","\frac{{\left(2 \, \log\left(\frac{\tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{2} + 1}\right) \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} - 1\right)} \sqrt{b \tan\left(d x + c\right)^{2}}}{4 \, b^{3} d \tan\left(d x + c\right)^{5}}"," ",0,"1/4*(2*log(tan(d*x + c)^2/(tan(d*x + c)^2 + 1))*tan(d*x + c)^4 + 3*tan(d*x + c)^4 + 2*tan(d*x + c)^2 - 1)*sqrt(b*tan(d*x + c)^2)/(b^3*d*tan(d*x + c)^5)","A"
30,-1,0,0,0.000000," ","integrate((b*tan(d*x + c)^3)^(5/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
31,-1,0,0,0.000000," ","integrate((b*tan(d*x + c)^3)^(3/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
32,-1,0,0,0.000000," ","integrate(sqrt(b*tan(d*x + c)^3),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
33,-1,0,0,0.000000," ","integrate(1/sqrt(b*tan(d*x + c)^3),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
34,-1,0,0,0.000000," ","integrate((b*tan(d*x + c)^3)^(-3/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
35,-1,0,0,0.000000," ","integrate((b*tan(d*x + c)^3)^(-5/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
36,1,130,0,1.192138," ","integrate((b*tan(d*x + c)^4)^(5/2),x, algorithm="fricas")","\frac{{\left(35 \, b^{2} \tan\left(d x + c\right)^{9} - 45 \, b^{2} \tan\left(d x + c\right)^{7} + 63 \, b^{2} \tan\left(d x + c\right)^{5} - 105 \, b^{2} \tan\left(d x + c\right)^{3} - 315 \, b^{2} d x + 315 \, b^{2} \tan\left(d x + c\right)\right)} \sqrt{b \tan\left(d x + c\right)^{4}}}{315 \, d \tan\left(d x + c\right)^{2}}"," ",0,"1/315*(35*b^2*tan(d*x + c)^9 - 45*b^2*tan(d*x + c)^7 + 63*b^2*tan(d*x + c)^5 - 105*b^2*tan(d*x + c)^3 - 315*b^2*d*x + 315*b^2*tan(d*x + c))*sqrt(b*tan(d*x + c)^4)/(d*tan(d*x + c)^2)","A"
37,1,84,0,1.150923," ","integrate((b*tan(d*x + c)^4)^(3/2),x, algorithm="fricas")","\frac{{\left(3 \, b \tan\left(d x + c\right)^{5} - 5 \, b \tan\left(d x + c\right)^{3} - 15 \, b d x + 15 \, b \tan\left(d x + c\right)\right)} \sqrt{b \tan\left(d x + c\right)^{4}}}{15 \, d \tan\left(d x + c\right)^{2}}"," ",0,"1/15*(3*b*tan(d*x + c)^5 - 5*b*tan(d*x + c)^3 - 15*b*d*x + 15*b*tan(d*x + c))*sqrt(b*tan(d*x + c)^4)/(d*tan(d*x + c)^2)","A"
38,1,50,0,1.160439," ","integrate(sqrt(b*tan(d*x + c)^4),x, algorithm="fricas")","-\frac{\sqrt{b \tan\left(d x + c\right)^{4}} {\left(d x - \tan\left(d x + c\right)\right)}}{d \tan\left(d x + c\right)^{2}}"," ",0,"-sqrt(b*tan(d*x + c)^4)*(d*x - tan(d*x + c))/(d*tan(d*x + c)^2)","A"
39,1,53,0,1.145930," ","integrate(1/sqrt(b*tan(d*x + c)^4),x, algorithm="fricas")","-\frac{\sqrt{b \tan\left(d x + c\right)^{4}} {\left(d x \tan\left(d x + c\right) + 1\right)}}{b d \tan\left(d x + c\right)^{3}}"," ",0,"-sqrt(b*tan(d*x + c)^4)*(d*x*tan(d*x + c) + 1)/(b*d*tan(d*x + c)^3)","A"
40,1,84,0,1.162448," ","integrate((b*tan(d*x + c)^4)^(-3/2),x, algorithm="fricas")","-\frac{{\left(15 \, d x \tan\left(d x + c\right)^{5} + 15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3\right)} \sqrt{b \tan\left(d x + c\right)^{4}}}{15 \, b^{2} d \tan\left(d x + c\right)^{7}}"," ",0,"-1/15*(15*d*x*tan(d*x + c)^5 + 15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)*sqrt(b*tan(d*x + c)^4)/(b^2*d*tan(d*x + c)^7)","A"
41,1,111,0,1.180720," ","integrate((b*tan(d*x + c)^4)^(-5/2),x, algorithm="fricas")","-\frac{{\left(315 \, d x \tan\left(d x + c\right)^{9} + 315 \, \tan\left(d x + c\right)^{8} - 105 \, \tan\left(d x + c\right)^{6} + 63 \, \tan\left(d x + c\right)^{4} - 45 \, \tan\left(d x + c\right)^{2} + 35\right)} \sqrt{b \tan\left(d x + c\right)^{4}}}{315 \, b^{3} d \tan\left(d x + c\right)^{11}}"," ",0,"-1/315*(315*d*x*tan(d*x + c)^9 + 315*tan(d*x + c)^8 - 105*tan(d*x + c)^6 + 63*tan(d*x + c)^4 - 45*tan(d*x + c)^2 + 35)*sqrt(b*tan(d*x + c)^4)/(b^3*d*tan(d*x + c)^11)","A"
42,0,0,0,0.000000," ","integrate((b*tan(d*x + c)^p)^n,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(d x + c\right)^{p}\right)^{n}, x\right)"," ",0,"integral((b*tan(d*x + c)^p)^n, x)","F"
43,0,0,0,0.000000," ","integrate((b*tan(d*x + c)^2)^n,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(d x + c\right)^{2}\right)^{n}, x\right)"," ",0,"integral((b*tan(d*x + c)^2)^n, x)","F"
44,0,0,0,0.000000," ","integrate((b*tan(d*x + c)^3)^n,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(d x + c\right)^{3}\right)^{n}, x\right)"," ",0,"integral((b*tan(d*x + c)^3)^n, x)","F"
45,0,0,0,0.000000," ","integrate((b*tan(d*x + c)^4)^n,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(d x + c\right)^{4}\right)^{n}, x\right)"," ",0,"integral((b*tan(d*x + c)^4)^n, x)","F"
46,-2,0,0,0.000000," ","integrate((b*tan(d*x + c)^p)^(5/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
47,-2,0,0,0.000000," ","integrate((b*tan(d*x + c)^p)^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
48,-2,0,0,0.000000," ","integrate(sqrt(b*tan(d*x + c)^p),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
49,-2,0,0,0.000000," ","integrate(1/sqrt(b*tan(d*x + c)^p),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
50,-2,0,0,0.000000," ","integrate((b*tan(d*x + c)^p)^(-3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
51,-2,0,0,0.000000," ","integrate((b*tan(d*x + c)^p)^(-5/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
52,1,31,0,1.162621," ","integrate((b*tan(d*x + c)^p)^(1/p),x, algorithm="fricas")","-\frac{b^{\left(\frac{1}{p}\right)} \log\left(\frac{1}{\tan\left(d x + c\right)^{2} + 1}\right)}{2 \, d}"," ",0,"-1/2*b^(1/p)*log(1/(tan(d*x + c)^2 + 1))/d","A"
53,0,0,0,0.000000," ","integrate(((b*tan(d*x + c))^p*a)^n,x, algorithm="fricas")","{\rm integral}\left(\left(\left(b \tan\left(d x + c\right)\right)^{p} a\right)^{n}, x\right)"," ",0,"integral(((b*tan(d*x + c))^p*a)^n, x)","F"
54,-1,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*sin(b*x + a)^4,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
55,-1,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*sin(b*x + a)^2,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
56,1,50,0,1.153668," ","integrate(sqrt(d*tan(b*x + a))*csc(b*x + a)^2,x, algorithm="fricas")","-\frac{2 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)}{b \sin\left(b x + a\right)}"," ",0,"-2*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)/(b*sin(b*x + a))","A"
57,1,85,0,1.191020," ","integrate(sqrt(d*tan(b*x + a))*csc(b*x + a)^4,x, algorithm="fricas")","-\frac{2 \, {\left(4 \, \cos\left(b x + a\right)^{3} - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{5 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-2/5*(4*cos(b*x + a)^3 - 5*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A"
58,1,111,0,1.219023," ","integrate(sqrt(d*tan(b*x + a))*csc(b*x + a)^6,x, algorithm="fricas")","-\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{5} - 72 \, \cos\left(b x + a\right)^{3} + 45 \, \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{45 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)} \sin\left(b x + a\right)}"," ",0,"-2/45*(32*cos(b*x + a)^5 - 72*cos(b*x + a)^3 + 45*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))/((b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)*sin(b*x + a))","A"
59,0,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*sin(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right), x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(d*tan(b*x + a))*sin(b*x + a), x)","F"
60,0,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*sin(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sin(b*x + a), x)","F"
61,0,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*csc(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a), x)","F"
62,0,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*csc(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)^{3}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)^3, x)","F"
63,0,0,0,0.000000," ","integrate(sqrt(d*tan(b*x + a))*csc(b*x + a)^5,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)^{5}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)^5, x)","F"
64,1,2133,0,142.785954," ","integrate((d*tan(b*x + a))^(3/2)*sin(b*x + a)^4,x, algorithm="fricas")","\frac{90 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{2 \, d^{10} \sin\left(b x + a\right) + \sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{7} \cos\left(b x + a\right)^{3} - b^{2} d^{7} \cos\left(b x + a\right)\right)} \sqrt{\frac{d^{6}}{b^{4}}} + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, {\left(2 \, d^{10} \cos\left(b x + a\right)^{2} - d^{10}\right)} \sin\left(b x + a\right)}\right) + 90 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{2 \, d^{10} \sin\left(b x + a\right) - \sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{7} \cos\left(b x + a\right)^{3} - b^{2} d^{7} \cos\left(b x + a\right)\right)} \sqrt{\frac{d^{6}}{b^{4}}} - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, {\left(2 \, d^{10} \cos\left(b x + a\right)^{2} - d^{10}\right)} \sin\left(b x + a\right)}\right) - 90 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(2 \, d^{5} \sin\left(b x + a\right) + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)} - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, d^{10} \sin\left(b x + a\right)}\right) - 90 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(2 \, d^{5} \sin\left(b x + a\right) - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)} + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, d^{10} \sin\left(b x + a\right)}\right) - 45 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(33215062500 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + 8303765625 \, d^{10} + 16607531250 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right) + 45 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(33215062500 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + 8303765625 \, d^{10} - 16607531250 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right) - 16 \, {\left(4 \, d \cos\left(b x + a\right)^{4} - 17 \, d \cos\left(b x + a\right)^{2} - 32 \, d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{256 \, b}"," ",0,"1/256*(90*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(1/2*(2*d^10*sin(b*x + a) + sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^7*cos(b*x + a)^3 - b^2*d^7*cos(b*x + a))*sqrt(d^6/b^4) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/((2*d^10*cos(b*x + a)^2 - d^10)*sin(b*x + a))) + 90*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-1/2*(2*d^10*sin(b*x + a) - sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^7*cos(b*x + a)^3 - b^2*d^7*cos(b*x + a))*sqrt(d^6/b^4) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/((2*d^10*cos(b*x + a)^2 - d^10)*sin(b*x + a))) - 90*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(1/2*(sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(2*d^5*sin(b*x + a) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(d^10*sin(b*x + a))) - 90*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-1/2*(sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(2*d^5*sin(b*x + a) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(d^10*sin(b*x + a))) - 45*sqrt(2)*(d^6/b^4)^(1/4)*b*log(33215062500*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + 8303765625*d^10 + 16607531250*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))) + 45*sqrt(2)*(d^6/b^4)^(1/4)*b*log(33215062500*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + 8303765625*d^10 - 16607531250*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))) - 16*(4*d*cos(b*x + a)^4 - 17*d*cos(b*x + a)^2 - 32*d)*sqrt(d*sin(b*x + a)/cos(b*x + a)))/b","A"
65,1,2117,0,142.891439," ","integrate((d*tan(b*x + a))^(3/2)*sin(b*x + a)^2,x, algorithm="fricas")","\frac{10 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{2 \, d^{10} \sin\left(b x + a\right) + \sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{7} \cos\left(b x + a\right)^{3} - b^{2} d^{7} \cos\left(b x + a\right)\right)} \sqrt{\frac{d^{6}}{b^{4}}} + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, {\left(2 \, d^{10} \cos\left(b x + a\right)^{2} - d^{10}\right)} \sin\left(b x + a\right)}\right) + 10 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{2 \, d^{10} \sin\left(b x + a\right) - \sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{7} \cos\left(b x + a\right)^{3} - b^{2} d^{7} \cos\left(b x + a\right)\right)} \sqrt{\frac{d^{6}}{b^{4}}} - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, {\left(2 \, d^{10} \cos\left(b x + a\right)^{2} - d^{10}\right)} \sin\left(b x + a\right)}\right) - 10 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(2 \, d^{5} \sin\left(b x + a\right) + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)} - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, d^{10} \sin\left(b x + a\right)}\right) - 10 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(2 \, d^{5} \sin\left(b x + a\right) - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)} + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, d^{10} \sin\left(b x + a\right)}\right) - 5 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(62500 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + 15625 \, d^{10} + 31250 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right) + 5 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(62500 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + 15625 \, d^{10} - 31250 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right) + 16 \, {\left(d \cos\left(b x + a\right)^{2} + 4 \, d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{32 \, b}"," ",0,"1/32*(10*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(1/2*(2*d^10*sin(b*x + a) + sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^7*cos(b*x + a)^3 - b^2*d^7*cos(b*x + a))*sqrt(d^6/b^4) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/((2*d^10*cos(b*x + a)^2 - d^10)*sin(b*x + a))) + 10*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-1/2*(2*d^10*sin(b*x + a) - sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^7*cos(b*x + a)^3 - b^2*d^7*cos(b*x + a))*sqrt(d^6/b^4) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/((2*d^10*cos(b*x + a)^2 - d^10)*sin(b*x + a))) - 10*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(1/2*(sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(2*d^5*sin(b*x + a) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(d^10*sin(b*x + a))) - 10*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-1/2*(sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(2*d^5*sin(b*x + a) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(d^10*sin(b*x + a))) - 5*sqrt(2)*(d^6/b^4)^(1/4)*b*log(62500*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + 15625*d^10 + 31250*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))) + 5*sqrt(2)*(d^6/b^4)^(1/4)*b*log(62500*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + 15625*d^10 - 31250*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))) + 16*(d*cos(b*x + a)^2 + 4*d)*sqrt(d*sin(b*x + a)/cos(b*x + a)))/b","A"
66,1,32,0,1.165492," ","integrate((d*tan(b*x + a))^(3/2)*csc(b*x + a)^2,x, algorithm="fricas")","\frac{2 \, d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{b}"," ",0,"2*d*sqrt(d*sin(b*x + a)/cos(b*x + a))/b","A"
67,1,69,0,1.172180," ","integrate((d*tan(b*x + a))^(3/2)*csc(b*x + a)^4,x, algorithm="fricas")","\frac{2 \, {\left(4 \, d \cos\left(b x + a\right)^{2} - 3 \, d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"2/3*(4*d*cos(b*x + a)^2 - 3*d)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*cos(b*x + a)^2 - b)","A"
68,1,96,0,1.211275," ","integrate((d*tan(b*x + a))^(3/2)*csc(b*x + a)^6,x, algorithm="fricas")","\frac{2 \, {\left(32 \, d \cos\left(b x + a\right)^{4} - 56 \, d \cos\left(b x + a\right)^{2} + 21 \, d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{21 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"2/21*(32*d*cos(b*x + a)^4 - 56*d*cos(b*x + a)^2 + 21*d)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","A"
69,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*sin(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(-{\left(d \cos\left(b x + a\right)^{2} - d\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right) \tan\left(b x + a\right), x\right)"," ",0,"integral(-(d*cos(b*x + a)^2 - d)*sqrt(d*tan(b*x + a))*sin(b*x + a)*tan(b*x + a), x)","F"
70,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*sin(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \sin\left(b x + a\right) \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*sin(b*x + a)*tan(b*x + a), x)","F"
71,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*csc(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \csc\left(b x + a\right) \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*csc(b*x + a)*tan(b*x + a), x)","F"
72,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*csc(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \csc\left(b x + a\right)^{3} \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*csc(b*x + a)^3*tan(b*x + a), x)","F"
73,-1,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*sin(b*x + a)^4,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
74,-1,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*sin(b*x + a)^2,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
75,1,54,0,1.452241," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a)^2,x, algorithm="fricas")","\frac{2 \, d^{2} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \sin\left(b x + a\right)}{3 \, b \cos\left(b x + a\right)}"," ",0,"2/3*d^2*sqrt(d*sin(b*x + a)/cos(b*x + a))*sin(b*x + a)/(b*cos(b*x + a))","A"
76,1,78,0,1.202128," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a)^4,x, algorithm="fricas")","-\frac{2 \, {\left(4 \, d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{3 \, b \cos\left(b x + a\right) \sin\left(b x + a\right)}"," ",0,"-2/3*(4*d^2*cos(b*x + a)^2 - d^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*cos(b*x + a)*sin(b*x + a))","A"
77,1,111,0,1.192934," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a)^6,x, algorithm="fricas")","-\frac{2 \, {\left(32 \, d^{2} \cos\left(b x + a\right)^{4} - 40 \, d^{2} \cos\left(b x + a\right)^{2} + 5 \, d^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{15 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}"," ",0,"-2/15*(32*d^2*cos(b*x + a)^4 - 40*d^2*cos(b*x + a)^2 + 5*d^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))/((b*cos(b*x + a)^3 - b*cos(b*x + a))*sin(b*x + a))","A"
78,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*sin(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(-{\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right) \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral(-(d^2*cos(b*x + a)^2 - d^2)*sqrt(d*tan(b*x + a))*sin(b*x + a)*tan(b*x + a)^2, x)","F"
79,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*sin(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d^{2} \sin\left(b x + a\right) \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d^2*sin(b*x + a)*tan(b*x + a)^2, x)","F"
80,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d^{2} \csc\left(b x + a\right) \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d^2*csc(b*x + a)*tan(b*x + a)^2, x)","F"
81,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d^{2} \csc\left(b x + a\right)^{3} \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d^2*csc(b*x + a)^3*tan(b*x + a)^2, x)","F"
82,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a)^5,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d^{2} \csc\left(b x + a\right)^{5} \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d^2*csc(b*x + a)^5*tan(b*x + a)^2, x)","F"
83,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(5/2)*csc(b*x + a)^7,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d^{2} \csc\left(b x + a\right)^{7} \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d^2*csc(b*x + a)^7*tan(b*x + a)^2, x)","F"
84,1,1966,0,130.277708," ","integrate(sin(b*x + a)^4/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","-\frac{10 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 10 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 10 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d \cos\left(b x + a\right)^{3} - b^{2} d \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{2}}} + 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) + 10 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 4 \, {\left(b^{2} d \cos\left(b x + a\right)^{3} - b^{2} d \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{2}}} - 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) - 5 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) + 5 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) - 16 \, {\left(4 \, \cos\left(b x + a\right)^{4} - 9 \, \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{256 \, b d}"," ",0,"-1/256*(10*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*(sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 2*sin(b*x + a)) - (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) - sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 10*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*(sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 2*sin(b*x + a)) - (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) - sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 10*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d*cos(b*x + a)^3 - b^2*d*cos(b*x + a))*sqrt(1/(b^4*d^2)) + 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) + 10*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 4*(b^2*d*cos(b*x + a)^3 - b^2*d*cos(b*x + a))*sqrt(1/(b^4*d^2)) - 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) - 5*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*log(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) + 5*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*log(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) - 16*(4*cos(b*x + a)^4 - 9*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(b*d)","A"
85,1,1947,0,127.488807," ","integrate(sin(b*x + a)^2/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","-\frac{2 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d \cos\left(b x + a\right)^{3} - b^{2} d \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{2}}} + 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 4 \, {\left(b^{2} d \cos\left(b x + a\right)^{3} - b^{2} d \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{2}}} - 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) - \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) + \sqrt{2} b d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d \sqrt{\frac{1}{b^{4} d^{2}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b \left(\frac{1}{b^{4} d^{2}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) + 16 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)^{2}}{32 \, b d}"," ",0,"-1/32*(2*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*(sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 2*sin(b*x + a)) - (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) - sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 2*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*(sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 2*sin(b*x + a)) - (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) - sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 2*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d*cos(b*x + a)^3 - b^2*d*cos(b*x + a))*sqrt(1/(b^4*d^2)) + 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) + 2*sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*sin(b*x + a) + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 4*(b^2*d*cos(b*x + a)^3 - b^2*d*cos(b*x + a))*sqrt(1/(b^4*d^2)) - 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) - sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*log(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) + sqrt(2)*b*d*(1/(b^4*d^2))^(1/4)*log(4*b^2*d*sqrt(1/(b^4*d^2))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d*(1/(b^4*d^2))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*(1/(b^4*d^2))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) + 16*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)^2)/(b*d)","A"
86,1,62,0,1.143968," ","integrate(csc(b*x + a)^2/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","\frac{2 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)^{2}}{3 \, {\left(b d \cos\left(b x + a\right)^{2} - b d\right)}}"," ",0,"2/3*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)^2/(b*d*cos(b*x + a)^2 - b*d)","A"
87,1,95,0,1.186191," ","integrate(csc(b*x + a)^4/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","\frac{2 \, {\left(4 \, \cos\left(b x + a\right)^{4} - 7 \, \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{21 \, {\left(b d \cos\left(b x + a\right)^{4} - 2 \, b d \cos\left(b x + a\right)^{2} + b d\right)}}"," ",0,"2/21*(4*cos(b*x + a)^4 - 7*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*d*cos(b*x + a)^4 - 2*b*d*cos(b*x + a)^2 + b*d)","A"
88,1,126,0,1.250653," ","integrate(csc(b*x + a)^6/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{6} - 88 \, \cos\left(b x + a\right)^{4} + 77 \, \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{231 \, {\left(b d \cos\left(b x + a\right)^{6} - 3 \, b d \cos\left(b x + a\right)^{4} + 3 \, b d \cos\left(b x + a\right)^{2} - b d\right)}}"," ",0,"2/231*(32*cos(b*x + a)^6 - 88*cos(b*x + a)^4 + 77*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*d*cos(b*x + a)^6 - 3*b*d*cos(b*x + a)^4 + 3*b*d*cos(b*x + a)^2 - b*d)","A"
89,0,0,0,0.000000," ","integrate(sin(b*x + a)^5/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d \tan\left(b x + a\right)}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*tan(b*x + a))*sin(b*x + a)/(d*tan(b*x + a)), x)","F"
90,0,0,0,0.000000," ","integrate(sin(b*x + a)^3/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d \tan\left(b x + a\right)}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(d*tan(b*x + a))*sin(b*x + a)/(d*tan(b*x + a)), x)","F"
91,0,0,0,0.000000," ","integrate(sin(b*x + a)/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d \tan\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sin(b*x + a)/(d*tan(b*x + a)), x)","F"
92,0,0,0,0.000000," ","integrate(csc(b*x + a)/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)}{d \tan\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)/(d*tan(b*x + a)), x)","F"
93,0,0,0,0.000000," ","integrate(csc(b*x + a)^3/sqrt(d*tan(b*x + a)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)^{3}}{d \tan\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)^3/(d*tan(b*x + a)), x)","F"
94,-1,0,0,0.000000," ","integrate(sin(b*x + a)^4/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
95,-1,0,0,0.000000," ","integrate(sin(b*x + a)^2/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
96,1,78,0,1.168884," ","integrate(csc(b*x + a)^2/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\frac{2 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)^{3}}{5 \, {\left(b d^{2} \cos\left(b x + a\right)^{2} - b d^{2}\right)} \sin\left(b x + a\right)}"," ",0,"2/5*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)^3/((b*d^2*cos(b*x + a)^2 - b*d^2)*sin(b*x + a))","A"
97,1,113,0,1.242419," ","integrate(csc(b*x + a)^4/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\frac{2 \, {\left(4 \, \cos\left(b x + a\right)^{5} - 9 \, \cos\left(b x + a\right)^{3}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{45 \, {\left(b d^{2} \cos\left(b x + a\right)^{4} - 2 \, b d^{2} \cos\left(b x + a\right)^{2} + b d^{2}\right)} \sin\left(b x + a\right)}"," ",0,"2/45*(4*cos(b*x + a)^5 - 9*cos(b*x + a)^3)*sqrt(d*sin(b*x + a)/cos(b*x + a))/((b*d^2*cos(b*x + a)^4 - 2*b*d^2*cos(b*x + a)^2 + b*d^2)*sin(b*x + a))","A"
98,1,147,0,1.322328," ","integrate(csc(b*x + a)^6/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{7} - 104 \, \cos\left(b x + a\right)^{5} + 117 \, \cos\left(b x + a\right)^{3}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{585 \, {\left(b d^{2} \cos\left(b x + a\right)^{6} - 3 \, b d^{2} \cos\left(b x + a\right)^{4} + 3 \, b d^{2} \cos\left(b x + a\right)^{2} - b d^{2}\right)} \sin\left(b x + a\right)}"," ",0,"2/585*(32*cos(b*x + a)^7 - 104*cos(b*x + a)^5 + 117*cos(b*x + a)^3)*sqrt(d*sin(b*x + a)/cos(b*x + a))/((b*d^2*cos(b*x + a)^6 - 3*b*d^2*cos(b*x + a)^4 + 3*b*d^2*cos(b*x + a)^2 - b*d^2)*sin(b*x + a))","A"
99,0,0,0,0.000000," ","integrate(sin(b*x + a)^3/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(d*tan(b*x + a))*sin(b*x + a)/(d^2*tan(b*x + a)^2), x)","F"
100,0,0,0,0.000000," ","integrate(sin(b*x + a)/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sin(b*x + a)/(d^2*tan(b*x + a)^2), x)","F"
101,0,0,0,0.000000," ","integrate(csc(b*x + a)/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)/(d^2*tan(b*x + a)^2), x)","F"
102,0,0,0,0.000000," ","integrate(csc(b*x + a)^3/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)^{3}}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)^3/(d^2*tan(b*x + a)^2), x)","F"
103,1,2103,0,131.947243," ","integrate(sin(b*x + a)^4/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","-\frac{6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{5} \cos\left(b x + a\right)^{3} - b^{2} d^{5} \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{10}}} + 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) + 6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 4 \, {\left(b^{2} d^{5} \cos\left(b x + a\right)^{3} - b^{2} d^{5} \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{10}}} - 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) - 3 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) + 3 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) + 16 \, {\left(4 \, \cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{256 \, b d^{3}}"," ",0,"-1/256*(6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*(sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 2*sin(b*x + a)) - (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) - sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*(sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 2*sin(b*x + a)) - (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) - sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^5*cos(b*x + a)^3 - b^2*d^5*cos(b*x + a))*sqrt(1/(b^4*d^10)) + 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) + 6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 4*(b^2*d^5*cos(b*x + a)^3 - b^2*d^5*cos(b*x + a))*sqrt(1/(b^4*d^10)) - 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) - 3*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*log(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) + 3*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*log(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) + 16*(4*cos(b*x + a)^4 - cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(b*d^3)","A"
104,1,2086,0,132.847963," ","integrate(sin(b*x + a)^2/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","-\frac{6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} {\left({\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 2 \, \sin\left(b x + a\right)\right)} - {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) - \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, \sin\left(b x + a\right)}\right) + 6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{5} \cos\left(b x + a\right)^{3} - b^{2} d^{5} \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{10}}} + 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) + 6 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \sin\left(b x + a\right) + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 4 \, {\left(b^{2} d^{5} \cos\left(b x + a\right)^{3} - b^{2} d^{5} \cos\left(b x + a\right)\right)} \sqrt{\frac{1}{b^{4} d^{10}}} - 2 \, \sin\left(b x + a\right)}{2 \, {\left(2 \, \cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}\right) - 3 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) + 3 \, \sqrt{2} b d^{3} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \log\left(4 \, b^{2} d^{5} \sqrt{\frac{1}{b^{4} d^{10}}} \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, {\left(\sqrt{2} b^{3} d^{7} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{3}{4}} \cos\left(b x + a\right)^{2} + \sqrt{2} b d^{2} \left(\frac{1}{b^{4} d^{10}}\right)^{\frac{1}{4}} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + 1\right) - 16 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)^{2}}{32 \, b d^{3}}"," ",0,"-1/32*(6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*(sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 2*sin(b*x + a)) - (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) - sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*(sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 2*sin(b*x + a)) - (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) - sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/sin(b*x + a)) + 6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^5*cos(b*x + a)^3 - b^2*d^5*cos(b*x + a))*sqrt(1/(b^4*d^10)) + 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) + 6*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*arctan(1/2*((sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1)*sqrt(d*sin(b*x + a)/cos(b*x + a)) + (sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*sin(b*x + a) + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 4*(b^2*d^5*cos(b*x + a)^3 - b^2*d^5*cos(b*x + a))*sqrt(1/(b^4*d^10)) - 2*sin(b*x + a))/((2*cos(b*x + a)^2 - 1)*sin(b*x + a))) - 3*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*log(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) + 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) + 3*sqrt(2)*b*d^3*(1/(b^4*d^10))^(1/4)*log(4*b^2*d^5*sqrt(1/(b^4*d^10))*cos(b*x + a)*sin(b*x + a) - 2*(sqrt(2)*b^3*d^7*(1/(b^4*d^10))^(3/4)*cos(b*x + a)^2 + sqrt(2)*b*d^2*(1/(b^4*d^10))^(1/4)*cos(b*x + a)*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) + 1) - 16*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)^2)/(b*d^3)","A"
105,1,85,0,1.189277," ","integrate(csc(b*x + a)^2/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","-\frac{2 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)^{4}}{7 \, {\left(b d^{3} \cos\left(b x + a\right)^{4} - 2 \, b d^{3} \cos\left(b x + a\right)^{2} + b d^{3}\right)}}"," ",0,"-2/7*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)^4/(b*d^3*cos(b*x + a)^4 - 2*b*d^3*cos(b*x + a)^2 + b*d^3)","A"
106,1,123,0,1.286224," ","integrate(csc(b*x + a)^4/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","-\frac{2 \, {\left(4 \, \cos\left(b x + a\right)^{6} - 11 \, \cos\left(b x + a\right)^{4}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{77 \, {\left(b d^{3} \cos\left(b x + a\right)^{6} - 3 \, b d^{3} \cos\left(b x + a\right)^{4} + 3 \, b d^{3} \cos\left(b x + a\right)^{2} - b d^{3}\right)}}"," ",0,"-2/77*(4*cos(b*x + a)^6 - 11*cos(b*x + a)^4)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*d^3*cos(b*x + a)^6 - 3*b*d^3*cos(b*x + a)^4 + 3*b*d^3*cos(b*x + a)^2 - b*d^3)","A"
107,1,154,0,1.397092," ","integrate(csc(b*x + a)^6/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","-\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{8} - 120 \, \cos\left(b x + a\right)^{6} + 165 \, \cos\left(b x + a\right)^{4}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{1155 \, {\left(b d^{3} \cos\left(b x + a\right)^{8} - 4 \, b d^{3} \cos\left(b x + a\right)^{6} + 6 \, b d^{3} \cos\left(b x + a\right)^{4} - 4 \, b d^{3} \cos\left(b x + a\right)^{2} + b d^{3}\right)}}"," ",0,"-2/1155*(32*cos(b*x + a)^8 - 120*cos(b*x + a)^6 + 165*cos(b*x + a)^4)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*d^3*cos(b*x + a)^8 - 4*b*d^3*cos(b*x + a)^6 + 6*b*d^3*cos(b*x + a)^4 - 4*b*d^3*cos(b*x + a)^2 + b*d^3)","A"
108,0,0,0,0.000000," ","integrate(sin(b*x + a)^7/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(-(cos(b*x + a)^6 - 3*cos(b*x + a)^4 + 3*cos(b*x + a)^2 - 1)*sqrt(d*tan(b*x + a))*sin(b*x + a)/(d^3*tan(b*x + a)^3), x)","F"
109,0,0,0,0.000000," ","integrate(sin(b*x + a)^5/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral((cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sqrt(d*tan(b*x + a))*sin(b*x + a)/(d^3*tan(b*x + a)^3), x)","F"
110,0,0,0,0.000000," ","integrate(sin(b*x + a)^3/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(d*tan(b*x + a))*sin(b*x + a)/(d^3*tan(b*x + a)^3), x)","F"
111,0,0,0,0.000000," ","integrate(sin(b*x + a)/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sin\left(b x + a\right)}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sin(b*x + a)/(d^3*tan(b*x + a)^3), x)","F"
112,0,0,0,0.000000," ","integrate(csc(b*x + a)/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)/(d^3*tan(b*x + a)^3), x)","F"
113,0,0,0,0.000000," ","integrate(csc(b*x + a)^3/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \csc\left(b x + a\right)^{3}}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*csc(b*x + a)^3/(d^3*tan(b*x + a)^3), x)","F"
114,1,88,0,1.145489," ","integrate((a*sin(f*x + e))^(5/2)*sqrt(b*tan(f*x + e)),x, algorithm="fricas")","\frac{2 \, {\left(a^{2} \cos\left(f x + e\right)^{3} - 5 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{5 \, f \sin\left(f x + e\right)}"," ",0,"2/5*(a^2*cos(f*x + e)^3 - 5*a^2*cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))/(f*sin(f*x + e))","A"
115,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(3/2)*sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} a \sin\left(f x + e\right), x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*a*sin(f*x + e), x)","F"
116,1,63,0,1.130842," ","integrate(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e)),x, algorithm="fricas")","-\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{f \sin\left(f x + e\right)}"," ",0,"-2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/(f*sin(f*x + e))","A"
117,0,0,0,0.000000," ","integrate(sqrt(b*tan(f*x + e))/sqrt(a*sin(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{a \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/(a*sin(f*x + e)), x)","F"
118,1,1,0,1.897675," ","integrate(sqrt(b*tan(f*x + e))/(a*sin(f*x + e))^(3/2),x, algorithm="fricas")","\left[\frac{2 \, \sqrt{-\frac{b}{a}} \arctan\left(\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{a}} \cos\left(f x + e\right)}{{\left(b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right)}\right) + \sqrt{-\frac{b}{a}} \log\left(-\frac{b \cos\left(f x + e\right)^{3} + 4 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 5 \, b \cos\left(f x + e\right)^{2} - 5 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1}\right)}{4 \, a f}, \frac{2 \, \sqrt{\frac{b}{a}} \arctan\left(\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{a}} \cos\left(f x + e\right)}{{\left(b \cos\left(f x + e\right) - b\right)} \sin\left(f x + e\right)}\right) + \sqrt{\frac{b}{a}} \log\left(\frac{4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{a}} - {\left(b \cos\left(f x + e\right)^{2} + 6 \, b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}\right)}{4 \, a f}\right]"," ",0,"[1/4*(2*sqrt(-b/a)*arctan(2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/a)*cos(f*x + e)/((b*cos(f*x + e) + b)*sin(f*x + e))) + sqrt(-b/a)*log(-(b*cos(f*x + e)^3 + 4*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/a)*cos(f*x + e)*sin(f*x + e) - 5*b*cos(f*x + e)^2 - 5*b*cos(f*x + e) + b)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 3*cos(f*x + e) + 1)))/(a*f), 1/4*(2*sqrt(b/a)*arctan(2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/a)*cos(f*x + e)/((b*cos(f*x + e) - b)*sin(f*x + e))) + sqrt(b/a)*log((4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/a) - (b*cos(f*x + e)^2 + 6*b*cos(f*x + e) + b)*sin(f*x + e))/((cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sin(f*x + e))))/(a*f)]","A"
119,0,0,0,0.000000," ","integrate(sqrt(b*tan(f*x + e))/(a*sin(f*x + e))^(5/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{{\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/((a^3*cos(f*x + e)^2 - a^3)*sin(f*x + e)), x)","F"
120,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(5/2)*(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(-{\left(a^{2} b \cos\left(f x + e\right)^{2} - a^{2} b\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} \tan\left(f x + e\right), x\right)"," ",0,"integral(-(a^2*b*cos(f*x + e)^2 - a^2*b)*sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*tan(f*x + e), x)","F"
121,1,77,0,1.143579," ","integrate((a*sin(f*x + e))^(3/2)*(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","\frac{2 \, {\left(a b \cos\left(f x + e\right)^{2} + 3 \, a b\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{3 \, f \sin\left(f x + e\right)}"," ",0,"2/3*(a*b*cos(f*x + e)^2 + 3*a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))/(f*sin(f*x + e))","A"
122,0,0,0,0.000000," ","integrate(sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*b*tan(f*x + e), x)","F"
123,1,61,0,1.139757," ","integrate((b*tan(f*x + e))^(3/2)/sqrt(a*sin(f*x + e)),x, algorithm="fricas")","\frac{2 \, \sqrt{a \sin\left(f x + e\right)} b \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{a f \sin\left(f x + e\right)}"," ",0,"2*sqrt(a*sin(f*x + e))*b*sqrt(b*sin(f*x + e)/cos(f*x + e))/(a*f*sin(f*x + e))","A"
124,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(3/2)/(a*sin(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b \tan\left(f x + e\right)}{a^{2} \cos\left(f x + e\right)^{2} - a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*b*tan(f*x + e)/(a^2*cos(f*x + e)^2 - a^2), x)","F"
125,1,1,0,1.979701," ","integrate((b*tan(f*x + e))^(3/2)/(a*sin(f*x + e))^(5/2),x, algorithm="fricas")","\left[\frac{2 \, a b \sqrt{-\frac{b}{a}} \arctan\left(\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{a}} \cos\left(f x + e\right)}{{\left(b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + a b \sqrt{-\frac{b}{a}} \log\left(-\frac{b \cos\left(f x + e\right)^{3} - 4 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 5 \, b \cos\left(f x + e\right)^{2} - 5 \, b \cos\left(f x + e\right) + b}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 8 \, \sqrt{a \sin\left(f x + e\right)} b \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{4 \, a^{3} f \sin\left(f x + e\right)}, -\frac{2 \, a b \sqrt{\frac{b}{a}} \arctan\left(\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{a}} \cos\left(f x + e\right)}{{\left(b \cos\left(f x + e\right) - b\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - a b \sqrt{\frac{b}{a}} \log\left(\frac{4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{a}} - {\left(b \cos\left(f x + e\right)^{2} + 6 \, b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 8 \, \sqrt{a \sin\left(f x + e\right)} b \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{4 \, a^{3} f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(2*a*b*sqrt(-b/a)*arctan(2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/a)*cos(f*x + e)/((b*cos(f*x + e) + b)*sin(f*x + e)))*sin(f*x + e) + a*b*sqrt(-b/a)*log(-(b*cos(f*x + e)^3 - 4*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/a)*cos(f*x + e)*sin(f*x + e) - 5*b*cos(f*x + e)^2 - 5*b*cos(f*x + e) + b)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 3*cos(f*x + e) + 1))*sin(f*x + e) + 8*sqrt(a*sin(f*x + e))*b*sqrt(b*sin(f*x + e)/cos(f*x + e)))/(a^3*f*sin(f*x + e)), -1/4*(2*a*b*sqrt(b/a)*arctan(2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/a)*cos(f*x + e)/((b*cos(f*x + e) - b)*sin(f*x + e)))*sin(f*x + e) - a*b*sqrt(b/a)*log((4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/a) - (b*cos(f*x + e)^2 + 6*b*cos(f*x + e) + b)*sin(f*x + e))/((cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sin(f*x + e)))*sin(f*x + e) - 8*sqrt(a*sin(f*x + e))*b*sqrt(b*sin(f*x + e)/cos(f*x + e)))/(a^3*f*sin(f*x + e))]","A"
126,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(9/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(f x + e\right)^{4} - 2 \, a^{4} \cos\left(f x + e\right)^{2} + a^{4}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b \tan\left(f x + e\right)}, x\right)"," ",0,"integral((a^4*cos(f*x + e)^4 - 2*a^4*cos(f*x + e)^2 + a^4)*sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/(b*tan(f*x + e)), x)","F"
127,1,96,0,1.158380," ","integrate((a*sin(f*x + e))^(7/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","\frac{2 \, {\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 7 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{21 \, b f \sin\left(f x + e\right)}"," ",0,"2/21*(3*a^3*cos(f*x + e)^4 - 7*a^3*cos(f*x + e)^2)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))/(b*f*sin(f*x + e))","A"
128,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(5/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(f x + e\right)^{2} - a^{2}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b \tan\left(f x + e\right)}, x\right)"," ",0,"integral(-(a^2*cos(f*x + e)^2 - a^2)*sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/(b*tan(f*x + e)), x)","F"
129,1,72,0,1.134807," ","integrate((a*sin(f*x + e))^(3/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","-\frac{2 \, \sqrt{a \sin\left(f x + e\right)} a \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{3 \, b f \sin\left(f x + e\right)}"," ",0,"-2/3*sqrt(a*sin(f*x + e))*a*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)^2/(b*f*sin(f*x + e))","A"
130,0,0,0,0.000000," ","integrate(sqrt(a*sin(f*x + e))/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/(b*tan(f*x + e)), x)","F"
131,1,1,0,1.812703," ","integrate(1/(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))),x, algorithm="fricas")","\left[\frac{2 \, \sqrt{-a b} \arctan\left(\frac{2 \, \sqrt{-a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a b \cos\left(f x + e\right) + a b\right)} \sin\left(f x + e\right)}\right) - \sqrt{-a b} \log\left(-\frac{a b \cos\left(f x + e\right)^{3} - 5 \, a b \cos\left(f x + e\right)^{2} + 4 \, \sqrt{-a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 5 \, a b \cos\left(f x + e\right) + a b}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1}\right)}{4 \, a b f}, -\frac{2 \, \sqrt{a b} \arctan\left(\frac{2 \, \sqrt{a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a b \cos\left(f x + e\right) - a b\right)} \sin\left(f x + e\right)}\right) - \sqrt{a b} \log\left(\frac{4 \, \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - {\left(a b \cos\left(f x + e\right)^{2} + 6 \, a b \cos\left(f x + e\right) + a b\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}\right)}{4 \, a b f}\right]"," ",0,"[1/4*(2*sqrt(-a*b)*arctan(2*sqrt(-a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/((a*b*cos(f*x + e) + a*b)*sin(f*x + e))) - sqrt(-a*b)*log(-(a*b*cos(f*x + e)^3 - 5*a*b*cos(f*x + e)^2 + 4*sqrt(-a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 5*a*b*cos(f*x + e) + a*b)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 3*cos(f*x + e) + 1)))/(a*b*f), -1/4*(2*sqrt(a*b)*arctan(2*sqrt(a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/((a*b*cos(f*x + e) - a*b)*sin(f*x + e))) - sqrt(a*b)*log((4*sqrt(a*b)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e)) - (a*b*cos(f*x + e)^2 + 6*a*b*cos(f*x + e) + a*b)*sin(f*x + e))/((cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sin(f*x + e))))/(a*b*f)]","A"
132,0,0,0,0.000000," ","integrate(1/((a*sin(f*x + e))^(3/2)*sqrt(b*tan(f*x + e))),x, algorithm="fricas")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{{\left(a^{2} b \cos\left(f x + e\right)^{2} - a^{2} b\right)} \tan\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/((a^2*b*cos(f*x + e)^2 - a^2*b)*tan(f*x + e)), x)","F"
133,1,1,0,2.068644," ","integrate(1/((a*sin(f*x + e))^(5/2)*sqrt(b*tan(f*x + e))),x, algorithm="fricas")","\left[\frac{2 \, \sqrt{-a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \arctan\left(\frac{2 \, \sqrt{-a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a b \cos\left(f x + e\right) + a b\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - \sqrt{-a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(-\frac{a b \cos\left(f x + e\right)^{3} - 5 \, a b \cos\left(f x + e\right)^{2} + 4 \, \sqrt{-a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 5 \, a b \cos\left(f x + e\right) + a b}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 8 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{16 \, {\left(a^{3} b f \cos\left(f x + e\right)^{2} - a^{3} b f\right)} \sin\left(f x + e\right)}, -\frac{2 \, \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \arctan\left(\frac{2 \, \sqrt{a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a b \cos\left(f x + e\right) - a b\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(\frac{4 \, \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - {\left(a b \cos\left(f x + e\right)^{2} + 6 \, a b \cos\left(f x + e\right) + a b\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 8 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2}}{16 \, {\left(a^{3} b f \cos\left(f x + e\right)^{2} - a^{3} b f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/16*(2*sqrt(-a*b)*(cos(f*x + e)^2 - 1)*arctan(2*sqrt(-a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/((a*b*cos(f*x + e) + a*b)*sin(f*x + e)))*sin(f*x + e) - sqrt(-a*b)*(cos(f*x + e)^2 - 1)*log(-(a*b*cos(f*x + e)^3 - 5*a*b*cos(f*x + e)^2 + 4*sqrt(-a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 5*a*b*cos(f*x + e) + a*b)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 3*cos(f*x + e) + 1))*sin(f*x + e) + 8*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)^2)/((a^3*b*f*cos(f*x + e)^2 - a^3*b*f)*sin(f*x + e)), -1/16*(2*sqrt(a*b)*(cos(f*x + e)^2 - 1)*arctan(2*sqrt(a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/((a*b*cos(f*x + e) - a*b)*sin(f*x + e)))*sin(f*x + e) - sqrt(a*b)*(cos(f*x + e)^2 - 1)*log((4*sqrt(a*b)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e)) - (a*b*cos(f*x + e)^2 + 6*a*b*cos(f*x + e) + a*b)*sin(f*x + e))/((cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sin(f*x + e)))*sin(f*x + e) - 8*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)^2)/((a^3*b*f*cos(f*x + e)^2 - a^3*b*f)*sin(f*x + e))]","A"
134,1,113,0,1.189691," ","integrate((a*sin(f*x + e))^(13/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","-\frac{2 \, {\left(45 \, a^{6} \cos\left(f x + e\right)^{7} - 130 \, a^{6} \cos\left(f x + e\right)^{5} + 117 \, a^{6} \cos\left(f x + e\right)^{3}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{585 \, b^{2} f \sin\left(f x + e\right)}"," ",0,"-2/585*(45*a^6*cos(f*x + e)^7 - 130*a^6*cos(f*x + e)^5 + 117*a^6*cos(f*x + e)^3)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))/(b^2*f*sin(f*x + e))","A"
135,1,96,0,1.170845," ","integrate((a*sin(f*x + e))^(9/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","\frac{2 \, {\left(5 \, a^{4} \cos\left(f x + e\right)^{5} - 9 \, a^{4} \cos\left(f x + e\right)^{3}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}}}{45 \, b^{2} f \sin\left(f x + e\right)}"," ",0,"2/45*(5*a^4*cos(f*x + e)^5 - 9*a^4*cos(f*x + e)^3)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))/(b^2*f*sin(f*x + e))","A"
136,1,74,0,1.158128," ","integrate((a*sin(f*x + e))^(5/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","-\frac{2 \, \sqrt{a \sin\left(f x + e\right)} a^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{3}}{5 \, b^{2} f \sin\left(f x + e\right)}"," ",0,"-2/5*sqrt(a*sin(f*x + e))*a^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)^3/(b^2*f*sin(f*x + e))","A"
137,1,1,0,1.901611," ","integrate(sqrt(a*sin(f*x + e))/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","\left[\frac{2 \, b \sqrt{-\frac{a}{b}} \arctan\left(\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{a}{b}} \cos\left(f x + e\right)}{{\left(a \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + b \sqrt{-\frac{a}{b}} \log\left(-\frac{a \cos\left(f x + e\right)^{3} + 4 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{a}{b}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 5 \, a \cos\left(f x + e\right)^{2} - 5 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 8 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, b^{2} f \sin\left(f x + e\right)}, \frac{2 \, b \sqrt{\frac{a}{b}} \arctan\left(\frac{2 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{a}{b}} \cos\left(f x + e\right)}{{\left(a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + b \sqrt{\frac{a}{b}} \log\left(\frac{4 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{a}{b}} - {\left(a \cos\left(f x + e\right)^{2} + 6 \, a \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 8 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, b^{2} f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(2*b*sqrt(-a/b)*arctan(2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-a/b)*cos(f*x + e)/((a*cos(f*x + e) + a)*sin(f*x + e)))*sin(f*x + e) + b*sqrt(-a/b)*log(-(a*cos(f*x + e)^3 + 4*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-a/b)*cos(f*x + e)*sin(f*x + e) - 5*a*cos(f*x + e)^2 - 5*a*cos(f*x + e) + a)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 3*cos(f*x + e) + 1))*sin(f*x + e) + 8*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/(b^2*f*sin(f*x + e)), 1/4*(2*b*sqrt(a/b)*arctan(2*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(a/b)*cos(f*x + e)/((a*cos(f*x + e) - a)*sin(f*x + e)))*sin(f*x + e) + b*sqrt(a/b)*log((4*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(a/b) - (a*cos(f*x + e)^2 + 6*a*cos(f*x + e) + a)*sin(f*x + e))/((cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sin(f*x + e)))*sin(f*x + e) + 8*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/(b^2*f*sin(f*x + e))]","A"
138,1,1,0,2.090860," ","integrate(1/((a*sin(f*x + e))^(3/2)*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","\left[-\frac{2 \, \sqrt{-a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \arctan\left(\frac{2 \, \sqrt{-a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a b \cos\left(f x + e\right) + a b\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + \sqrt{-a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(-\frac{a b \cos\left(f x + e\right)^{3} - 5 \, a b \cos\left(f x + e\right)^{2} + 4 \, \sqrt{-a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 5 \, a b \cos\left(f x + e\right) + a b}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 8 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{16 \, {\left(a^{2} b^{2} f \cos\left(f x + e\right)^{2} - a^{2} b^{2} f\right)} \sin\left(f x + e\right)}, -\frac{2 \, \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \arctan\left(\frac{2 \, \sqrt{a b} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(a b \cos\left(f x + e\right) - a b\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(-\frac{4 \, \sqrt{a b} {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + {\left(a b \cos\left(f x + e\right)^{2} + 6 \, a b \cos\left(f x + e\right) + a b\right)} \sin\left(f x + e\right)}{{\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) - 8 \, \sqrt{a \sin\left(f x + e\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{16 \, {\left(a^{2} b^{2} f \cos\left(f x + e\right)^{2} - a^{2} b^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(2*sqrt(-a*b)*(cos(f*x + e)^2 - 1)*arctan(2*sqrt(-a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/((a*b*cos(f*x + e) + a*b)*sin(f*x + e)))*sin(f*x + e) + sqrt(-a*b)*(cos(f*x + e)^2 - 1)*log(-(a*b*cos(f*x + e)^3 - 5*a*b*cos(f*x + e)^2 + 4*sqrt(-a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 5*a*b*cos(f*x + e) + a*b)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 3*cos(f*x + e) + 1))*sin(f*x + e) - 8*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/((a^2*b^2*f*cos(f*x + e)^2 - a^2*b^2*f)*sin(f*x + e)), -1/16*(2*sqrt(a*b)*(cos(f*x + e)^2 - 1)*arctan(2*sqrt(a*b)*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e)/((a*b*cos(f*x + e) - a*b)*sin(f*x + e)))*sin(f*x + e) - sqrt(a*b)*(cos(f*x + e)^2 - 1)*log(-(4*sqrt(a*b)*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e)) + (a*b*cos(f*x + e)^2 + 6*a*b*cos(f*x + e) + a*b)*sin(f*x + e))/((cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sin(f*x + e)))*sin(f*x + e) - 8*sqrt(a*sin(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/((a^2*b^2*f*cos(f*x + e)^2 - a^2*b^2*f)*sin(f*x + e))]","A"
139,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(11/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{{\left(a^{5} \cos\left(f x + e\right)^{4} - 2 \, a^{5} \cos\left(f x + e\right)^{2} + a^{5}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} \sin\left(f x + e\right)}{b^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((a^5*cos(f*x + e)^4 - 2*a^5*cos(f*x + e)^2 + a^5)*sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*sin(f*x + e)/(b^2*tan(f*x + e)^2), x)","F"
140,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(7/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{{\left(a^{3} \cos\left(f x + e\right)^{2} - a^{3}\right)} \sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} \sin\left(f x + e\right)}{b^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(-(a^3*cos(f*x + e)^2 - a^3)*sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*sin(f*x + e)/(b^2*tan(f*x + e)^2), x)","F"
141,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(3/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} a \sin\left(f x + e\right)}{b^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))*a*sin(f*x + e)/(b^2*tan(f*x + e)^2), x)","F"
142,0,0,0,0.000000," ","integrate(1/(sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{a b^{2} \sin\left(f x + e\right) \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/(a*b^2*sin(f*x + e)*tan(f*x + e)^2), x)","F"
143,0,0,0,0.000000," ","integrate(1/((a*sin(f*x + e))^(5/2)*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{{\left(a^{3} b^{2} \cos\left(f x + e\right)^{2} - a^{3} b^{2}\right)} \sin\left(f x + e\right) \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/((a^3*b^2*cos(f*x + e)^2 - a^3*b^2)*sin(f*x + e)*tan(f*x + e)^2), x)","F"
144,0,0,0,0.000000," ","integrate(1/((a*sin(f*x + e))^(9/2)*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{{\left(a^{5} b^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{5} b^{2} \cos\left(f x + e\right)^{2} + a^{5} b^{2}\right)} \sin\left(f x + e\right) \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*sqrt(b*tan(f*x + e))/((a^5*b^2*cos(f*x + e)^4 - 2*a^5*b^2*cos(f*x + e)^2 + a^5*b^2)*sin(f*x + e)*tan(f*x + e)^2), x)","F"
145,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(4/3)*sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)} b \sin\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*sqrt(d*tan(f*x + e))*b*sin(f*x + e), x)","F"
146,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(1/3)*sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*sqrt(d*tan(f*x + e)), x)","F"
147,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))/(b*sin(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)}}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))/(b*sin(f*x + e)), x)","F"
148,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))/(b*sin(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)}}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))/(b^2*cos(f*x + e)^2 - b^2), x)","F"
149,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(4/3)*(d*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)} b d \sin\left(f x + e\right) \tan\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*sqrt(d*tan(f*x + e))*b*d*sin(f*x + e)*tan(f*x + e), x)","F"
150,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(1/3)*(d*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\left(b \sin\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right), x\right)"," ",0,"integral((b*sin(f*x + e))^(1/3)*sqrt(d*tan(f*x + e))*d*tan(f*x + e), x)","F"
151,0,0,0,0.000000," ","integrate((d*tan(f*x + e))^(3/2)/(b*sin(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right)}{b \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sin(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))*d*tan(f*x + e)/(b*sin(f*x + e)), x)","F"
152,0,0,0,0.000000," ","integrate((d*tan(f*x + e))^(3/2)/(b*sin(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(-\frac{\left(b \sin\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right)}{b^{2} \cos\left(f x + e\right)^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))*d*tan(f*x + e)/(b^2*cos(f*x + e)^2 - b^2), x)","F"
153,0,0,0,0.000000," ","integrate(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}} d \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(1/3)*d*tan(f*x + e), x)","F"
154,0,0,0,0.000000," ","integrate(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(1/3), x)","F"
155,0,0,0,0.000000," ","integrate(sqrt(b*sin(f*x + e))/(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}}}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(2/3)/(d*tan(f*x + e)), x)","F"
156,0,0,0,0.000000," ","integrate(sqrt(b*sin(f*x + e))/(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}}}{d^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(2/3)/(d^2*tan(f*x + e)^2), x)","F"
157,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(3/2)*(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}} b d \sin\left(f x + e\right) \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(1/3)*b*d*sin(f*x + e)*tan(f*x + e), x)","F"
158,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(3/2)*(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}} b \sin\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(1/3)*b*sin(f*x + e), x)","F"
159,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(3/2)/(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}} b \sin\left(f x + e\right)}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(2/3)*b*sin(f*x + e)/(d*tan(f*x + e)), x)","F"
160,0,0,0,0.000000," ","integrate((b*sin(f*x + e))^(3/2)/(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}} b \sin\left(f x + e\right)}{d^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e))*(d*tan(f*x + e))^(2/3)*b*sin(f*x + e)/(d^2*tan(f*x + e)^2), x)","F"
161,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*tan(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{3}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*tan(f*x + e)^3, x)","F"
162,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*tan(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \tan\left(f x + e\right), x\right)"," ",0,"integral((a*sin(f*x + e))^m*tan(f*x + e), x)","F"
163,1,23,0,1.142368," ","integrate((a*sin(f*x + e))^m*cot(f*x + e),x, algorithm="fricas")","\frac{\left(a \sin\left(f x + e\right)\right)^{m}}{f m}"," ",0,"(a*sin(f*x + e))^m/(f*m)","A"
164,1,77,0,1.145367," ","integrate((a*sin(f*x + e))^m*cot(f*x + e)^3,x, algorithm="fricas")","\frac{{\left({\left(m - 2\right)} \cos\left(f x + e\right)^{2} + 2\right)} \left(a \sin\left(f x + e\right)\right)^{m}}{f m^{2} - {\left(f m^{2} - 2 \, f m\right)} \cos\left(f x + e\right)^{2} - 2 \, f m}"," ",0,"((m - 2)*cos(f*x + e)^2 + 2)*(a*sin(f*x + e))^m/(f*m^2 - (f*m^2 - 2*f*m)*cos(f*x + e)^2 - 2*f*m)","A"
165,1,151,0,1.154273," ","integrate((a*sin(f*x + e))^m*cot(f*x + e)^5,x, algorithm="fricas")","\frac{{\left({\left(m^{2} - 6 \, m + 8\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(m - 4\right)} \cos\left(f x + e\right)^{2} + 8\right)} \left(a \sin\left(f x + e\right)\right)^{m}}{{\left(f m^{3} - 6 \, f m^{2} + 8 \, f m\right)} \cos\left(f x + e\right)^{4} + f m^{3} - 6 \, f m^{2} - 2 \, {\left(f m^{3} - 6 \, f m^{2} + 8 \, f m\right)} \cos\left(f x + e\right)^{2} + 8 \, f m}"," ",0,"((m^2 - 6*m + 8)*cos(f*x + e)^4 + 4*(m - 4)*cos(f*x + e)^2 + 8)*(a*sin(f*x + e))^m/((f*m^3 - 6*f*m^2 + 8*f*m)*cos(f*x + e)^4 + f*m^3 - 6*f*m^2 - 2*(f*m^3 - 6*f*m^2 + 8*f*m)*cos(f*x + e)^2 + 8*f*m)","A"
166,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*tan(f*x + e)^4, x)","F"
167,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*tan(f*x + e)^2, x)","F"
168,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*cot(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*cot(f*x + e)^2, x)","F"
169,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*cot(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{4}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*cot(f*x + e)^4, x)","F"
170,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(3/2)*(a*sin(f*x + e))^m,x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \tan\left(f x + e\right)} \left(a \sin\left(f x + e\right)\right)^{m} b \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*tan(f*x + e))*(a*sin(f*x + e))^m*b*tan(f*x + e), x)","F"
171,0,0,0,0.000000," ","integrate(sqrt(b*tan(f*x + e))*(a*sin(f*x + e))^m,x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \tan\left(f x + e\right)} \left(a \sin\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral(sqrt(b*tan(f*x + e))*(a*sin(f*x + e))^m, x)","F"
172,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \tan\left(f x + e\right)} \left(a \sin\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*tan(f*x + e))*(a*sin(f*x + e))^m/(b*tan(f*x + e)), x)","F"
173,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \tan\left(f x + e\right)} \left(a \sin\left(f x + e\right)\right)^{m}}{b^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*tan(f*x + e))*(a*sin(f*x + e))^m/(b^2*tan(f*x + e)^2), x)","F"
174,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^m*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \sin\left(f x + e\right)\right)^{m} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sin(f*x + e))^m*(b*tan(f*x + e))^n, x)","F"
175,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*sin(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left({\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*(b*tan(f*x + e))^n, x)","F"
176,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*sin(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*(b*tan(f*x + e))^n, x)","F"
177,1,57,0,1.130821," ","integrate((b*tan(f*x + e))^n*csc(f*x + e)^2,x, algorithm="fricas")","\frac{\left(\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{n} \cos\left(f x + e\right)}{{\left(f n - f\right)} \sin\left(f x + e\right)}"," ",0,"(b*sin(f*x + e)/cos(f*x + e))^n*cos(f*x + e)/((f*n - f)*sin(f*x + e))","A"
178,1,116,0,1.144606," ","integrate((b*tan(f*x + e))^n*csc(f*x + e)^4,x, algorithm="fricas")","\frac{{\left(2 \, \cos\left(f x + e\right)^{3} + {\left(n - 3\right)} \cos\left(f x + e\right)\right)} \left(\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{n}}{{\left(f n^{2} - {\left(f n^{2} - 4 \, f n + 3 \, f\right)} \cos\left(f x + e\right)^{2} - 4 \, f n + 3 \, f\right)} \sin\left(f x + e\right)}"," ",0,"(2*cos(f*x + e)^3 + (n - 3)*cos(f*x + e))*(b*sin(f*x + e)/cos(f*x + e))^n/((f*n^2 - (f*n^2 - 4*f*n + 3*f)*cos(f*x + e)^2 - 4*f*n + 3*f)*sin(f*x + e))","A"
179,1,194,0,1.152468," ","integrate((b*tan(f*x + e))^n*csc(f*x + e)^6,x, algorithm="fricas")","\frac{{\left(8 \, \cos\left(f x + e\right)^{5} + 4 \, {\left(n - 5\right)} \cos\left(f x + e\right)^{3} + {\left(n^{2} - 8 \, n + 15\right)} \cos\left(f x + e\right)\right)} \left(\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)^{n}}{{\left({\left(f n^{3} - 9 \, f n^{2} + 23 \, f n - 15 \, f\right)} \cos\left(f x + e\right)^{4} + f n^{3} - 9 \, f n^{2} - 2 \, {\left(f n^{3} - 9 \, f n^{2} + 23 \, f n - 15 \, f\right)} \cos\left(f x + e\right)^{2} + 23 \, f n - 15 \, f\right)} \sin\left(f x + e\right)}"," ",0,"(8*cos(f*x + e)^5 + 4*(n - 5)*cos(f*x + e)^3 + (n^2 - 8*n + 15)*cos(f*x + e))*(b*sin(f*x + e)/cos(f*x + e))^n/(((f*n^3 - 9*f*n^2 + 23*f*n - 15*f)*cos(f*x + e)^4 + f*n^3 - 9*f*n^2 - 2*(f*n^3 - 9*f*n^2 + 23*f*n - 15*f)*cos(f*x + e)^2 + 23*f*n - 15*f)*sin(f*x + e))","A"
180,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*sin(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \left(b \tan\left(f x + e\right)\right)^{n} \sin\left(f x + e\right), x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*(b*tan(f*x + e))^n*sin(f*x + e), x)","F"
181,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*sin(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(f x + e\right)\right)^{n} \sin\left(f x + e\right), x\right)"," ",0,"integral((b*tan(f*x + e))^n*sin(f*x + e), x)","F"
182,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*csc(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(f x + e\right)\right)^{n} \csc\left(f x + e\right), x\right)"," ",0,"integral((b*tan(f*x + e))^n*csc(f*x + e), x)","F"
183,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*csc(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*tan(f*x + e))^n*csc(f*x + e)^3, x)","F"
184,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*csc(f*x + e)^5,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{5}, x\right)"," ",0,"integral((b*tan(f*x + e))^n*csc(f*x + e)^5, x)","F"
185,0,0,0,0.000000," ","integrate((a*sin(f*x + e))^(3/2)*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\sqrt{a \sin\left(f x + e\right)} \left(b \tan\left(f x + e\right)\right)^{n} a \sin\left(f x + e\right), x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^n*a*sin(f*x + e), x)","F"
186,0,0,0,0.000000," ","integrate(sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\sqrt{a \sin\left(f x + e\right)} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^n, x)","F"
187,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n/sqrt(a*sin(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right)} \left(b \tan\left(f x + e\right)\right)^{n}}{a \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^n/(a*sin(f*x + e)), x)","F"
188,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n/(a*sin(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right)} \left(b \tan\left(f x + e\right)\right)^{n}}{a^{2} \cos\left(f x + e\right)^{2} - a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e))*(b*tan(f*x + e))^n/(a^2*cos(f*x + e)^2 - a^2), x)","F"
189,0,0,0,0.000000," ","integrate((a*cos(f*x + e))^m*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \cos\left(f x + e\right)\right)^{m} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*cos(f*x + e))^m*(b*tan(f*x + e))^n, x)","F"
190,0,0,0,0.000000," ","integrate((a*tan(f*x + e))^m*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \tan\left(f x + e\right)\right)^{m} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*tan(f*x + e))^m*(b*tan(f*x + e))^n, x)","F"
191,1,818,0,1.192607," ","integrate(sqrt(d*cot(f*x + e))*tan(f*x + e)^4,x, algorithm="fricas")","\frac{20 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - \sqrt{2} f \sqrt{\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} + d^{2}}{d^{2}}\right) \cos\left(f x + e\right)^{3} + 20 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - \sqrt{2} f \sqrt{-\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - d^{2}}{d^{2}}\right) \cos\left(f x + e\right)^{3} + 5 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{3} \log\left(\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 5 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{3} \log\left(-\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, {\left(6 \, \cos\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{20 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/20*(20*sqrt(2)*f*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4) - sqrt(2)*f*sqrt((sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) + d^3*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(1/4) + d^2)/d^2)*cos(f*x + e)^3 + 20*sqrt(2)*f*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4) - sqrt(2)*f*sqrt(-(sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) - d^3*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(1/4) - d^2)/d^2)*cos(f*x + e)^3 + 5*sqrt(2)*f*(d^2/f^4)^(1/4)*cos(f*x + e)^3*log((sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) + d^3*cos(f*x + e))/sin(f*x + e)) - 5*sqrt(2)*f*(d^2/f^4)^(1/4)*cos(f*x + e)^3*log(-(sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) - d^3*cos(f*x + e))/sin(f*x + e)) - 8*(6*cos(f*x + e)^2 - 1)*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)","A"
192,1,767,0,1.185649," ","integrate(sqrt(d*cot(f*x + e))*tan(f*x + e)^3,x, algorithm="fricas")","-\frac{12 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} f^{3} \sqrt{\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} + d^{2}}{d^{2}}\right) \cos\left(f x + e\right)^{2} + 12 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} f^{3} \sqrt{\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} - d^{2}}{d^{2}}\right) \cos\left(f x + e\right)^{2} - 3 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{2} \log\left(\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 3 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{2} \log\left(\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 8 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}}}{12 \, f \cos\left(f x + e\right)^{2}}"," ",0,"-1/12*(12*sqrt(2)*f*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4) - sqrt(2)*f^3*sqrt((f^2*sqrt(d^2/f^4)*sin(f*x + e) + sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(3/4) + d^2)/d^2)*cos(f*x + e)^2 + 12*sqrt(2)*f*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4) - sqrt(2)*f^3*sqrt((f^2*sqrt(d^2/f^4)*sin(f*x + e) - sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(3/4) - d^2)/d^2)*cos(f*x + e)^2 - 3*sqrt(2)*f*(d^2/f^4)^(1/4)*cos(f*x + e)^2*log((f^2*sqrt(d^2/f^4)*sin(f*x + e) + sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 3*sqrt(2)*f*(d^2/f^4)^(1/4)*cos(f*x + e)^2*log((f^2*sqrt(d^2/f^4)*sin(f*x + e) - sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 8*(cos(f*x + e)^2 - 1)*sqrt(d*cos(f*x + e)/sin(f*x + e)))/(f*cos(f*x + e)^2)","A"
193,1,790,0,1.180999," ","integrate(sqrt(d*cot(f*x + e))*tan(f*x + e)^2,x, algorithm="fricas")","-\frac{4 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - \sqrt{2} f \sqrt{\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} + d^{2}}{d^{2}}\right) \cos\left(f x + e\right) + 4 \, \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - \sqrt{2} f \sqrt{-\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - d^{2}}{d^{2}}\right) \cos\left(f x + e\right) + \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) \log\left(\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - \sqrt{2} f \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) \log\left(-\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)}"," ",0,"-1/4*(4*sqrt(2)*f*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4) - sqrt(2)*f*sqrt((sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) + d^3*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(1/4) + d^2)/d^2)*cos(f*x + e) + 4*sqrt(2)*f*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4) - sqrt(2)*f*sqrt(-(sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) - d^3*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(1/4) - d^2)/d^2)*cos(f*x + e) + sqrt(2)*f*(d^2/f^4)^(1/4)*cos(f*x + e)*log((sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) + d^3*cos(f*x + e))/sin(f*x + e)) - sqrt(2)*f*(d^2/f^4)^(1/4)*cos(f*x + e)*log(-(sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(d^2/f^4)*sin(f*x + e) - d^3*cos(f*x + e))/sin(f*x + e)) - 8*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(f*cos(f*x + e))","A"
194,1,657,0,1.159951," ","integrate(sqrt(d*cot(f*x + e))*tan(f*x + e),x, algorithm="fricas")","\sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} f^{3} \sqrt{\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} + d^{2}}{d^{2}}\right) + \sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} - \sqrt{2} f^{3} \sqrt{\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} - d^{2}}{d^{2}}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) + \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \sin\left(f x + e\right) - \sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right)"," ",0,"sqrt(2)*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4) - sqrt(2)*f^3*sqrt((f^2*sqrt(d^2/f^4)*sin(f*x + e) + sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(3/4) + d^2)/d^2) + sqrt(2)*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(3/4) - sqrt(2)*f^3*sqrt((f^2*sqrt(d^2/f^4)*sin(f*x + e) - sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(d^2/f^4)^(3/4) - d^2)/d^2) - 1/4*sqrt(2)*(d^2/f^4)^(1/4)*log((f^2*sqrt(d^2/f^4)*sin(f*x + e) + sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 1/4*sqrt(2)*(d^2/f^4)^(1/4)*log((f^2*sqrt(d^2/f^4)*sin(f*x + e) - sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(d^2/f^4)^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))","A"
195,-2,0,0,0.000000," ","integrate(sqrt(d*cot(f*x + e)),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
196,-2,0,0,0.000000," ","integrate(sqrt(d*cot(f*x + e))*cot(f*x + e),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
197,-2,0,0,0.000000," ","integrate(sqrt(d*cot(f*x + e))*cot(f*x + e)^2,x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
198,-2,0,0,0.000000," ","integrate(sqrt(d*cot(f*x + e))*cot(f*x + e)^3,x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
199,1,833,0,1.219697," ","integrate((d*cot(f*x + e))^(3/2)*tan(f*x + e)^5,x, algorithm="fricas")","\frac{20 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d^{4} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} + d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{9} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) \cos\left(f x + e\right)^{3} + 20 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d^{4} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} - d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{9} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) \cos\left(f x + e\right)^{3} + 5 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{3} \log\left(\frac{d^{9} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 5 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{3} \log\left(\frac{d^{9} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, {\left(6 \, d \cos\left(f x + e\right)^{2} - d\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{20 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/20*(20*sqrt(2)*(d^6/f^4)^(1/4)*f*arctan(-(sqrt(2)*(d^6/f^4)^(1/4)*d^4*f*sqrt(d*cos(f*x + e)/sin(f*x + e)) + d^6 - sqrt(2)*(d^6/f^4)^(1/4)*f*sqrt((d^9*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)))/d^6)*cos(f*x + e)^3 + 20*sqrt(2)*(d^6/f^4)^(1/4)*f*arctan(-(sqrt(2)*(d^6/f^4)^(1/4)*d^4*f*sqrt(d*cos(f*x + e)/sin(f*x + e)) - d^6 - sqrt(2)*(d^6/f^4)^(1/4)*f*sqrt((d^9*cos(f*x + e) - sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)))/d^6)*cos(f*x + e)^3 + 5*sqrt(2)*(d^6/f^4)^(1/4)*f*cos(f*x + e)^3*log((d^9*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)) - 5*sqrt(2)*(d^6/f^4)^(1/4)*f*cos(f*x + e)^3*log((d^9*cos(f*x + e) - sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)) - 8*(6*d*cos(f*x + e)^2 - d)*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)","A"
200,1,792,0,1.198122," ","integrate((d*cot(f*x + e))^(3/2)*tan(f*x + e)^4,x, algorithm="fricas")","-\frac{12 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{d^{6} + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) \cos\left(f x + e\right)^{2} + 12 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(\frac{d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right) - \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) \cos\left(f x + e\right)^{2} - 3 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{2} \log\left(\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 3 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right)^{2} \log\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right) - \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 8 \, {\left(d \cos\left(f x + e\right)^{2} - d\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}}}{12 \, f \cos\left(f x + e\right)^{2}}"," ",0,"-1/12*(12*sqrt(2)*(d^6/f^4)^(1/4)*f*arctan(-(d^6 + sqrt(2)*(d^6/f^4)^(3/4)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e)) - sqrt(2)*(d^6/f^4)^(3/4)*f^3*sqrt((sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + d^3*cos(f*x + e) + sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)))/d^6)*cos(f*x + e)^2 + 12*sqrt(2)*(d^6/f^4)^(1/4)*f*arctan((d^6 - sqrt(2)*(d^6/f^4)^(3/4)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e)) + sqrt(2)*(d^6/f^4)^(3/4)*f^3*sqrt(-(sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) - d^3*cos(f*x + e) - sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)))/d^6)*cos(f*x + e)^2 - 3*sqrt(2)*(d^6/f^4)^(1/4)*f*cos(f*x + e)^2*log((sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + d^3*cos(f*x + e) + sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)) + 3*sqrt(2)*(d^6/f^4)^(1/4)*f*cos(f*x + e)^2*log(-(sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) - d^3*cos(f*x + e) - sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)) + 8*(d*cos(f*x + e)^2 - d)*sqrt(d*cos(f*x + e)/sin(f*x + e)))/(f*cos(f*x + e)^2)","A"
201,1,802,0,1.207679," ","integrate((d*cot(f*x + e))^(3/2)*tan(f*x + e)^3,x, algorithm="fricas")","-\frac{4 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d^{4} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} + d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{9} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) \cos\left(f x + e\right) + 4 \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d^{4} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} - d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{9} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right) \log\left(\frac{d^{9} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right) \log\left(\frac{d^{9} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, d \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)}"," ",0,"-1/4*(4*sqrt(2)*(d^6/f^4)^(1/4)*f*arctan(-(sqrt(2)*(d^6/f^4)^(1/4)*d^4*f*sqrt(d*cos(f*x + e)/sin(f*x + e)) + d^6 - sqrt(2)*(d^6/f^4)^(1/4)*f*sqrt((d^9*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)))/d^6)*cos(f*x + e) + 4*sqrt(2)*(d^6/f^4)^(1/4)*f*arctan(-(sqrt(2)*(d^6/f^4)^(1/4)*d^4*f*sqrt(d*cos(f*x + e)/sin(f*x + e)) - d^6 - sqrt(2)*(d^6/f^4)^(1/4)*f*sqrt((d^9*cos(f*x + e) - sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)))/d^6)*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(1/4)*f*cos(f*x + e)*log((d^9*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)) - sqrt(2)*(d^6/f^4)^(1/4)*f*cos(f*x + e)*log((d^9*cos(f*x + e) - sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)) - 8*d*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(f*cos(f*x + e))","A"
202,1,678,0,1.175158," ","integrate((d*cot(f*x + e))^(3/2)*tan(f*x + e)^2,x, algorithm="fricas")","\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{d^{6} + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} f^{3} \sqrt{-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right) - \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + d^{3} \cos\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) - d^{3} \cos\left(f x + e\right) - \sqrt{\frac{d^{6}}{f^{4}}} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right)"," ",0,"sqrt(2)*(d^6/f^4)^(1/4)*arctan(-(d^6 + sqrt(2)*(d^6/f^4)^(3/4)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e)) - sqrt(2)*(d^6/f^4)^(3/4)*f^3*sqrt((sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + d^3*cos(f*x + e) + sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)))/d^6) + sqrt(2)*(d^6/f^4)^(1/4)*arctan((d^6 - sqrt(2)*(d^6/f^4)^(3/4)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e)) + sqrt(2)*(d^6/f^4)^(3/4)*f^3*sqrt(-(sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) - d^3*cos(f*x + e) - sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)))/d^6) - 1/4*sqrt(2)*(d^6/f^4)^(1/4)*log((sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + d^3*cos(f*x + e) + sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e)) + 1/4*sqrt(2)*(d^6/f^4)^(1/4)*log(-(sqrt(2)*(d^6/f^4)^(1/4)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) - d^3*cos(f*x + e) - sqrt(d^6/f^4)*f^2*sin(f*x + e))/sin(f*x + e))","A"
203,1,709,0,1.176097," ","integrate((d*cot(f*x + e))^(3/2)*tan(f*x + e),x, algorithm="fricas")","\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d^{4} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} + d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{9} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} d^{4} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} - d^{6} - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{9} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}}}{d^{6}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{d^{9} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{d^{9} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{6}}{f^{4}}\right)^{\frac{3}{4}} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{\frac{d^{6}}{f^{4}}} d^{6} f^{2} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right)"," ",0,"sqrt(2)*(d^6/f^4)^(1/4)*arctan(-(sqrt(2)*(d^6/f^4)^(1/4)*d^4*f*sqrt(d*cos(f*x + e)/sin(f*x + e)) + d^6 - sqrt(2)*(d^6/f^4)^(1/4)*f*sqrt((d^9*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)))/d^6) + sqrt(2)*(d^6/f^4)^(1/4)*arctan(-(sqrt(2)*(d^6/f^4)^(1/4)*d^4*f*sqrt(d*cos(f*x + e)/sin(f*x + e)) - d^6 - sqrt(2)*(d^6/f^4)^(1/4)*f*sqrt((d^9*cos(f*x + e) - sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)))/d^6) + 1/4*sqrt(2)*(d^6/f^4)^(1/4)*log((d^9*cos(f*x + e) + sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e)) - 1/4*sqrt(2)*(d^6/f^4)^(1/4)*log((d^9*cos(f*x + e) - sqrt(2)*(d^6/f^4)^(3/4)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e) + sqrt(d^6/f^4)*d^6*f^2*sin(f*x + e))/sin(f*x + e))","A"
204,-2,0,0,0.000000," ","integrate((d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
205,-2,0,0,0.000000," ","integrate((d*cot(f*x + e))^(3/2)*cot(f*x + e),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
206,-2,0,0,0.000000," ","integrate((d*cot(f*x + e))^(3/2)*cot(f*x + e)^2,x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
207,1,803,0,1.211333," ","integrate(tan(f*x + e)^3/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","\frac{20 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} f \sqrt{\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} - 1\right) \cos\left(f x + e\right)^{3} + 20 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} f \sqrt{-\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) - d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} + 1\right) \cos\left(f x + e\right)^{3} + 5 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{3} \log\left(\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 5 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{3} \log\left(-\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) - d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, {\left(6 \, \cos\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{20 \, d f \cos\left(f x + e\right)^{3}}"," ",0,"1/20*(20*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*arctan(-sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4) + sqrt(2)*f*sqrt((sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^2*f^4))^(1/4) - 1)*cos(f*x + e)^3 + 20*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*arctan(-sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4) + sqrt(2)*f*sqrt(-(sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) - d*cos(f*x + e))/sin(f*x + e))*(1/(d^2*f^4))^(1/4) + 1)*cos(f*x + e)^3 + 5*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*cos(f*x + e)^3*log((sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) - 5*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*cos(f*x + e)^3*log(-(sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) - d*cos(f*x + e))/sin(f*x + e)) - 8*(6*cos(f*x + e)^2 - 1)*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(d*f*cos(f*x + e)^3)","A"
208,1,782,0,1.198756," ","integrate(tan(f*x + e)^2/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","-\frac{12 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} d f^{3} \sqrt{\frac{d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) + \sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} - 1\right) \cos\left(f x + e\right)^{2} + 12 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} d f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} d f^{3} \sqrt{\frac{d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) - \sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} + 1\right) \cos\left(f x + e\right)^{2} - 3 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{2} \log\left(\frac{d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) + \sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 3 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{2} \log\left(\frac{d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) - \sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 8 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}}}{12 \, d f \cos\left(f x + e\right)^{2}}"," ",0,"-1/12*(12*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*arctan(-sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4) + sqrt(2)*d*f^3*sqrt((d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) + sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^2*f^4))^(3/4) - 1)*cos(f*x + e)^2 + 12*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*arctan(-sqrt(2)*d*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4) + sqrt(2)*d*f^3*sqrt((d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) - sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^2*f^4))^(3/4) + 1)*cos(f*x + e)^2 - 3*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*cos(f*x + e)^2*log((d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) + sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 3*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*cos(f*x + e)^2*log((d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) - sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 8*(cos(f*x + e)^2 - 1)*sqrt(d*cos(f*x + e)/sin(f*x + e)))/(d*f*cos(f*x + e)^2)","A"
209,1,775,0,1.183888," ","integrate(tan(f*x + e)/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","-\frac{4 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} f \sqrt{\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} - 1\right) \cos\left(f x + e\right) + 4 \, \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} f \sqrt{-\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) - d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} + 1\right) \cos\left(f x + e\right) + \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) \log\left(\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - \sqrt{2} d f \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right) \log\left(-\frac{\sqrt{2} d^{2} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{2} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{1}{d^{2} f^{4}}} \sin\left(f x + e\right) - d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, d f \cos\left(f x + e\right)}"," ",0,"-1/4*(4*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*arctan(-sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4) + sqrt(2)*f*sqrt((sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^2*f^4))^(1/4) - 1)*cos(f*x + e) + 4*sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*arctan(-sqrt(2)*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(1/4) + sqrt(2)*f*sqrt(-(sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) - d*cos(f*x + e))/sin(f*x + e))*(1/(d^2*f^4))^(1/4) + 1)*cos(f*x + e) + sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*cos(f*x + e)*log((sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) + d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) - sqrt(2)*d*f*(1/(d^2*f^4))^(1/4)*cos(f*x + e)*log(-(sqrt(2)*d^2*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^2*f^4))^(3/4)*sin(f*x + e) - d^2*f^2*sqrt(1/(d^2*f^4))*sin(f*x + e) - d*cos(f*x + e))/sin(f*x + e)) - 8*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(d*f*cos(f*x + e))","A"
210,-2,0,0,0.000000," ","integrate(1/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
211,-2,0,0,0.000000," ","integrate(cot(f*x + e)/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
212,-2,0,0,0.000000," ","integrate(cot(f*x + e)^2/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
213,-2,0,0,0.000000," ","integrate(cot(f*x + e)^3/sqrt(d*cot(f*x + e)),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
214,1,819,0,1.237254," ","integrate(tan(f*x + e)^2/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\frac{20 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} d f \sqrt{\frac{\sqrt{2} d^{5} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} - 1\right) \cos\left(f x + e\right)^{3} + 20 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} d f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} + \sqrt{2} d f \sqrt{-\frac{\sqrt{2} d^{5} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) - d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} + 1\right) \cos\left(f x + e\right)^{3} + 5 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{3} \log\left(\frac{\sqrt{2} d^{5} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) + d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 5 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{3} \log\left(-\frac{\sqrt{2} d^{5} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} \sin\left(f x + e\right) - d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) - d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) - 8 \, {\left(6 \, \cos\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \sin\left(f x + e\right)}{20 \, d^{2} f \cos\left(f x + e\right)^{3}}"," ",0,"1/20*(20*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*arctan(-sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(1/4) + sqrt(2)*d*f*sqrt((sqrt(2)*d^5*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(3/4)*sin(f*x + e) + d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^6*f^4))^(1/4) - 1)*cos(f*x + e)^3 + 20*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*arctan(-sqrt(2)*d*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(1/4) + sqrt(2)*d*f*sqrt(-(sqrt(2)*d^5*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(3/4)*sin(f*x + e) - d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) - d*cos(f*x + e))/sin(f*x + e))*(1/(d^6*f^4))^(1/4) + 1)*cos(f*x + e)^3 + 5*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*cos(f*x + e)^3*log((sqrt(2)*d^5*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(3/4)*sin(f*x + e) + d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) - 5*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*cos(f*x + e)^3*log(-(sqrt(2)*d^5*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(3/4)*sin(f*x + e) - d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) - d*cos(f*x + e))/sin(f*x + e)) - 8*(6*cos(f*x + e)^2 - 1)*sqrt(d*cos(f*x + e)/sin(f*x + e))*sin(f*x + e))/(d^2*f*cos(f*x + e)^3)","A"
215,1,814,0,1.236546," ","integrate(tan(f*x + e)/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","-\frac{12 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} d^{4} f^{3} \sqrt{\frac{d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) + \sqrt{2} d^{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} - 1\right) \cos\left(f x + e\right)^{2} + 12 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} d^{4} f^{3} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} + \sqrt{2} d^{4} f^{3} \sqrt{\frac{d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) - \sqrt{2} d^{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{3}{4}} + 1\right) \cos\left(f x + e\right)^{2} - 3 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{2} \log\left(\frac{d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) + \sqrt{2} d^{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 3 \, \sqrt{2} d^{2} f \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \cos\left(f x + e\right)^{2} \log\left(\frac{d^{4} f^{2} \sqrt{\frac{1}{d^{6} f^{4}}} \sin\left(f x + e\right) - \sqrt{2} d^{2} f \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}} \left(\frac{1}{d^{6} f^{4}}\right)^{\frac{1}{4}} \sin\left(f x + e\right) + d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right) + 8 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}}}{12 \, d^{2} f \cos\left(f x + e\right)^{2}}"," ",0,"-1/12*(12*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*arctan(-sqrt(2)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(3/4) + sqrt(2)*d^4*f^3*sqrt((d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) + sqrt(2)*d^2*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^6*f^4))^(3/4) - 1)*cos(f*x + e)^2 + 12*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*arctan(-sqrt(2)*d^4*f^3*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(3/4) + sqrt(2)*d^4*f^3*sqrt((d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) - sqrt(2)*d^2*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e))*(1/(d^6*f^4))^(3/4) + 1)*cos(f*x + e)^2 - 3*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*cos(f*x + e)^2*log((d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) + sqrt(2)*d^2*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 3*sqrt(2)*d^2*f*(1/(d^6*f^4))^(1/4)*cos(f*x + e)^2*log((d^4*f^2*sqrt(1/(d^6*f^4))*sin(f*x + e) - sqrt(2)*d^2*f*sqrt(d*cos(f*x + e)/sin(f*x + e))*(1/(d^6*f^4))^(1/4)*sin(f*x + e) + d*cos(f*x + e))/sin(f*x + e)) + 8*(cos(f*x + e)^2 - 1)*sqrt(d*cos(f*x + e)/sin(f*x + e)))/(d^2*f*cos(f*x + e)^2)","A"
216,-2,0,0,0.000000," ","integrate((d*cot(f*x + e))^(-3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
217,-2,0,0,0.000000," ","integrate(cot(f*x + e)/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
218,-2,0,0,0.000000," ","integrate(cot(f*x + e)^2/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
219,-2,0,0,0.000000," ","integrate(cot(f*x + e)^3/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
220,-2,0,0,0.000000," ","integrate(cot(f*x + e)^4/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
221,-2,0,0,0.000000," ","integrate(cot(f*x + e)^5/(d*cot(f*x + e))^(3/2),x, algorithm="fricas")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)"
222,0,0,0,0.000000," ","integrate(cot(f*x + e)^m*tan(f*x + e)^n,x, algorithm="fricas")","{\rm integral}\left(\cot\left(f x + e\right)^{m} \tan\left(f x + e\right)^{n}, x\right)"," ",0,"integral(cot(f*x + e)^m*tan(f*x + e)^n, x)","F"
223,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^n*cot(f*x + e)^m,x, algorithm="fricas")","{\rm integral}\left(\left(b \tan\left(f x + e\right)\right)^{n} \cot\left(f x + e\right)^{m}, x\right)"," ",0,"integral((b*tan(f*x + e))^n*cot(f*x + e)^m, x)","F"
224,0,0,0,0.000000," ","integrate((a*cot(f*x + e))^m*tan(f*x + e)^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \cot\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a*cot(f*x + e))^m*tan(f*x + e)^n, x)","F"
225,0,0,0,0.000000," ","integrate((a*cot(f*x + e))^m*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \cot\left(f x + e\right)\right)^{m} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*cot(f*x + e))^m*(b*tan(f*x + e))^n, x)","F"
226,1,80,0,1.236508," ","integrate(sqrt(d*tan(f*x + e))*sec(f*x + e)^6,x, algorithm="fricas")","\frac{2 \, {\left(32 \, \cos\left(f x + e\right)^{4} + 24 \, \cos\left(f x + e\right)^{2} + 21\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{231 \, f \cos\left(f x + e\right)^{5}}"," ",0,"2/231*(32*cos(f*x + e)^4 + 24*cos(f*x + e)^2 + 21)*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e)/(f*cos(f*x + e)^5)","A"
227,1,66,0,1.181169," ","integrate(sqrt(d*tan(f*x + e))*sec(f*x + e)^4,x, algorithm="fricas")","\frac{2 \, {\left(4 \, \cos\left(f x + e\right)^{2} + 3\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{21 \, f \cos\left(f x + e\right)^{3}}"," ",0,"2/21*(4*cos(f*x + e)^2 + 3)*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e)/(f*cos(f*x + e)^3)","A"
228,1,50,0,1.139043," ","integrate(sqrt(d*tan(f*x + e))*sec(f*x + e)^2,x, algorithm="fricas")","\frac{2 \, \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, f \cos\left(f x + e\right)}"," ",0,"2/3*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e)/(f*cos(f*x + e))","A"
229,1,701,0,1.155089," ","integrate(sqrt(d*tan(f*x + e)),x, algorithm="fricas")","-\sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} d f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - \sqrt{2} f \sqrt{\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \cos\left(f x + e\right) + d^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} + d^{2}}{d^{2}}\right) - \sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} d f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - \sqrt{2} f \sqrt{-\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \cos\left(f x + e\right) - d^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} - d^{2}}{d^{2}}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) + d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \cos\left(f x + e\right) + d^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} d f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \left(\frac{d^{2}}{f^{4}}\right)^{\frac{3}{4}} \cos\left(f x + e\right) - d^{2} f^{2} \sqrt{\frac{d^{2}}{f^{4}}} \cos\left(f x + e\right) - d^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right)}\right)"," ",0,"-sqrt(2)*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*d*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/f^4)^(1/4) - sqrt(2)*f*sqrt((sqrt(2)*d*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/f^4)^(3/4)*cos(f*x + e) + d^2*f^2*sqrt(d^2/f^4)*cos(f*x + e) + d^3*sin(f*x + e))/cos(f*x + e))*(d^2/f^4)^(1/4) + d^2)/d^2) - sqrt(2)*(d^2/f^4)^(1/4)*arctan(-(sqrt(2)*d*f*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/f^4)^(1/4) - sqrt(2)*f*sqrt(-(sqrt(2)*d*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/f^4)^(3/4)*cos(f*x + e) - d^2*f^2*sqrt(d^2/f^4)*cos(f*x + e) - d^3*sin(f*x + e))/cos(f*x + e))*(d^2/f^4)^(1/4) - d^2)/d^2) - 1/4*sqrt(2)*(d^2/f^4)^(1/4)*log((sqrt(2)*d*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/f^4)^(3/4)*cos(f*x + e) + d^2*f^2*sqrt(d^2/f^4)*cos(f*x + e) + d^3*sin(f*x + e))/cos(f*x + e)) + 1/4*sqrt(2)*(d^2/f^4)^(1/4)*log(-(sqrt(2)*d*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*(d^2/f^4)^(3/4)*cos(f*x + e) - d^2*f^2*sqrt(d^2/f^4)*cos(f*x + e) - d^3*sin(f*x + e))/cos(f*x + e))","A"
230,-1,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*cos(f*x + e)^2,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
231,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*sec(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \sec\left(f x + e\right)^{3}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*sec(f*x + e)^3, x)","F"
232,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*sec(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*sec(f*x + e), x)","F"
233,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*cos(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*cos(f*x + e), x)","F"
234,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*cos(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \cos\left(f x + e\right)^{3}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*cos(f*x + e)^3, x)","F"
235,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*cos(f*x + e)^5,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \cos\left(f x + e\right)^{5}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*cos(f*x + e)^5, x)","F"
236,1,92,0,1.293184," ","integrate((d*tan(b*x + a))^(3/2)*sec(b*x + a)^6,x, algorithm="fricas")","-\frac{2 \, {\left(32 \, d \cos\left(b x + a\right)^{6} + 8 \, d \cos\left(b x + a\right)^{4} + 5 \, d \cos\left(b x + a\right)^{2} - 45 \, d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{585 \, b \cos\left(b x + a\right)^{6}}"," ",0,"-2/585*(32*d*cos(b*x + a)^6 + 8*d*cos(b*x + a)^4 + 5*d*cos(b*x + a)^2 - 45*d)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*cos(b*x + a)^6)","A"
237,1,76,0,1.217160," ","integrate((d*tan(b*x + a))^(3/2)*sec(b*x + a)^4,x, algorithm="fricas")","-\frac{2 \, {\left(4 \, d \cos\left(b x + a\right)^{4} + d \cos\left(b x + a\right)^{2} - 5 \, d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{45 \, b \cos\left(b x + a\right)^{4}}"," ",0,"-2/45*(4*d*cos(b*x + a)^4 + d*cos(b*x + a)^2 - 5*d)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*cos(b*x + a)^4)","A"
238,1,61,0,1.156085," ","integrate((d*tan(b*x + a))^(3/2)*sec(b*x + a)^2,x, algorithm="fricas")","-\frac{2 \, {\left(d \cos\left(b x + a\right)^{2} - d\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{5 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-2/5*(d*cos(b*x + a)^2 - d)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*cos(b*x + a)^2)","A"
239,1,720,0,1.175269," ","integrate((d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\frac{4 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{d^{6} + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sqrt{\frac{\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right) + d^{3} \sin\left(b x + a\right) + \sqrt{\frac{d^{6}}{b^{4}}} b^{2} \cos\left(b x + a\right)}{\cos\left(b x + a\right)}}}{d^{6}}\right) + 4 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{d^{6} - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sqrt{-\frac{\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right) - d^{3} \sin\left(b x + a\right) - \sqrt{\frac{d^{6}}{b^{4}}} b^{2} \cos\left(b x + a\right)}{\cos\left(b x + a\right)}}}{d^{6}}\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(\frac{\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right) + d^{3} \sin\left(b x + a\right) + \sqrt{\frac{d^{6}}{b^{4}}} b^{2} \cos\left(b x + a\right)}{\cos\left(b x + a\right)}\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(-\frac{\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right) - d^{3} \sin\left(b x + a\right) - \sqrt{\frac{d^{6}}{b^{4}}} b^{2} \cos\left(b x + a\right)}{\cos\left(b x + a\right)}\right) + 8 \, d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{4 \, b}"," ",0,"1/4*(4*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-(d^6 + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d*sqrt(d*sin(b*x + a)/cos(b*x + a)) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*sqrt((sqrt(2)*(d^6/b^4)^(1/4)*b*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a) + d^3*sin(b*x + a) + sqrt(d^6/b^4)*b^2*cos(b*x + a))/cos(b*x + a)))/d^6) + 4*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan((d^6 - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d*sqrt(d*sin(b*x + a)/cos(b*x + a)) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sqrt(-(sqrt(2)*(d^6/b^4)^(1/4)*b*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a) - d^3*sin(b*x + a) - sqrt(d^6/b^4)*b^2*cos(b*x + a))/cos(b*x + a)))/d^6) - sqrt(2)*(d^6/b^4)^(1/4)*b*log((sqrt(2)*(d^6/b^4)^(1/4)*b*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a) + d^3*sin(b*x + a) + sqrt(d^6/b^4)*b^2*cos(b*x + a))/cos(b*x + a)) + sqrt(2)*(d^6/b^4)^(1/4)*b*log(-(sqrt(2)*(d^6/b^4)^(1/4)*b*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a) - d^3*sin(b*x + a) - sqrt(d^6/b^4)*b^2*cos(b*x + a))/cos(b*x + a)) + 8*d*sqrt(d*sin(b*x + a)/cos(b*x + a)))/b","A"
240,1,2103,0,140.326275," ","integrate((d*tan(b*x + a))^(3/2)*cos(b*x + a)^2,x, algorithm="fricas")","-\frac{16 \, d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)^{2} + 2 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{2 \, d^{10} \sin\left(b x + a\right) + \sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{7} \cos\left(b x + a\right)^{3} - b^{2} d^{7} \cos\left(b x + a\right)\right)} \sqrt{\frac{d^{6}}{b^{4}}} + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, {\left(2 \, d^{10} \cos\left(b x + a\right)^{2} - d^{10}\right)} \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{2 \, d^{10} \sin\left(b x + a\right) - \sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} - 4 \, {\left(b^{2} d^{7} \cos\left(b x + a\right)^{3} - b^{2} d^{7} \cos\left(b x + a\right)\right)} \sqrt{\frac{d^{6}}{b^{4}}} - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, {\left(2 \, d^{10} \cos\left(b x + a\right)^{2} - d^{10}\right)} \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(2 \, d^{5} \sin\left(b x + a\right) + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)} + {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, d^{10} \sin\left(b x + a\right)}\right) + 2 \, \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}} {\left(2 \, d^{5} \sin\left(b x + a\right) - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{3} \cos\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)} - {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \sin\left(b x + a\right)\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{2 \, d^{10} \sin\left(b x + a\right)}\right) - \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} + 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b \log\left(4 \, \sqrt{\frac{d^{6}}{b^{4}}} b^{2} d^{7} \cos\left(b x + a\right) \sin\left(b x + a\right) + d^{10} - 2 \, {\left(\sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{1}{4}} b d^{8} \cos\left(b x + a\right) \sin\left(b x + a\right) + \sqrt{2} \left(\frac{d^{6}}{b^{4}}\right)^{\frac{3}{4}} b^{3} d^{5} \cos\left(b x + a\right)^{2}\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}\right)}{32 \, b}"," ",0,"-1/32*(16*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)^2 + 2*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(1/2*(2*d^10*sin(b*x + a) + sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^7*cos(b*x + a)^3 - b^2*d^7*cos(b*x + a))*sqrt(d^6/b^4) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/((2*d^10*cos(b*x + a)^2 - d^10)*sin(b*x + a))) + 2*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-1/2*(2*d^10*sin(b*x + a) - sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)) - 4*(b^2*d^7*cos(b*x + a)^3 - b^2*d^7*cos(b*x + a))*sqrt(d^6/b^4) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/((2*d^10*cos(b*x + a)^2 - d^10)*sin(b*x + a))) + 2*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(1/2*(sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(2*d^5*sin(b*x + a) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))) + (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(d^10*sin(b*x + a))) + 2*sqrt(2)*(d^6/b^4)^(1/4)*b*arctan(-1/2*(sqrt(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a)))*(2*d^5*sin(b*x + a) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^3*cos(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a))) - (sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a) - sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*sin(b*x + a))*sqrt(d*sin(b*x + a)/cos(b*x + a)))/(d^10*sin(b*x + a))) - sqrt(2)*(d^6/b^4)^(1/4)*b*log(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 + 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))) + sqrt(2)*(d^6/b^4)^(1/4)*b*log(4*sqrt(d^6/b^4)*b^2*d^7*cos(b*x + a)*sin(b*x + a) + d^10 - 2*(sqrt(2)*(d^6/b^4)^(1/4)*b*d^8*cos(b*x + a)*sin(b*x + a) + sqrt(2)*(d^6/b^4)^(3/4)*b^3*d^5*cos(b*x + a)^2)*sqrt(d*sin(b*x + a)/cos(b*x + a))))/b","A"
241,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*sec(b*x + a)^5,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \sec\left(b x + a\right)^{5} \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*sec(b*x + a)^5*tan(b*x + a), x)","F"
242,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*sec(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \sec\left(b x + a\right)^{3} \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*sec(b*x + a)^3*tan(b*x + a), x)","F"
243,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*sec(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \sec\left(b x + a\right) \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*sec(b*x + a)*tan(b*x + a), x)","F"
244,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*cos(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \cos\left(b x + a\right) \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*cos(b*x + a)*tan(b*x + a), x)","F"
245,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*cos(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \cos\left(b x + a\right)^{3} \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*cos(b*x + a)^3*tan(b*x + a), x)","F"
246,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^(3/2)*cos(b*x + a)^5,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(b x + a\right)} d \cos\left(b x + a\right)^{5} \tan\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*d*cos(b*x + a)^5*tan(b*x + a), x)","F"
247,1,111,0,1.371533," ","integrate((d*tan(f*x + e))^(5/2)*sec(f*x + e)^6,x, algorithm="fricas")","-\frac{2 \, {\left(32 \, d^{2} \cos\left(f x + e\right)^{6} + 24 \, d^{2} \cos\left(f x + e\right)^{4} + 21 \, d^{2} \cos\left(f x + e\right)^{2} - 77 \, d^{2}\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{1155 \, f \cos\left(f x + e\right)^{7}}"," ",0,"-2/1155*(32*d^2*cos(f*x + e)^6 + 24*d^2*cos(f*x + e)^4 + 21*d^2*cos(f*x + e)^2 - 77*d^2)*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e)/(f*cos(f*x + e)^7)","A"
248,1,93,0,1.273887," ","integrate((d*tan(f*x + e))^(5/2)*sec(f*x + e)^4,x, algorithm="fricas")","-\frac{2 \, {\left(4 \, d^{2} \cos\left(f x + e\right)^{4} + 3 \, d^{2} \cos\left(f x + e\right)^{2} - 7 \, d^{2}\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{77 \, f \cos\left(f x + e\right)^{5}}"," ",0,"-2/77*(4*d^2*cos(f*x + e)^4 + 3*d^2*cos(f*x + e)^2 - 7*d^2)*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e)/(f*cos(f*x + e)^5)","A"
249,1,74,0,1.193292," ","integrate((d*tan(f*x + e))^(5/2)*sec(f*x + e)^2,x, algorithm="fricas")","-\frac{2 \, {\left(d^{2} \cos\left(f x + e\right)^{2} - d^{2}\right)} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{7 \, f \cos\left(f x + e\right)^{3}}"," ",0,"-2/7*(d^2*cos(f*x + e)^2 - d^2)*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e)/(f*cos(f*x + e)^3)","A"
250,1,802,0,1.198552," ","integrate((d*tan(f*x + e))^(5/2),x, algorithm="fricas")","\frac{12 \, \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(-\frac{d^{10} + \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} d^{7} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} - \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{15} \sin\left(f x + e\right) + \sqrt{\frac{d^{10}}{f^{4}}} d^{10} f^{2} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{3}{4}} d^{7} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{d^{10}}\right) \cos\left(f x + e\right) + 12 \, \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \arctan\left(\frac{d^{10} - \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} d^{7} f \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} + \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \sqrt{\frac{d^{15} \sin\left(f x + e\right) + \sqrt{\frac{d^{10}}{f^{4}}} d^{10} f^{2} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{3}{4}} d^{7} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}}}{d^{10}}\right) \cos\left(f x + e\right) + 3 \, \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right) \log\left(\frac{d^{15} \sin\left(f x + e\right) + \sqrt{\frac{d^{10}}{f^{4}}} d^{10} f^{2} \cos\left(f x + e\right) + \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{3}{4}} d^{7} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) - 3 \, \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{1}{4}} f \cos\left(f x + e\right) \log\left(\frac{d^{15} \sin\left(f x + e\right) + \sqrt{\frac{d^{10}}{f^{4}}} d^{10} f^{2} \cos\left(f x + e\right) - \sqrt{2} \left(\frac{d^{10}}{f^{4}}\right)^{\frac{3}{4}} d^{7} f^{3} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\cos\left(f x + e\right)}\right) + 8 \, d^{2} \sqrt{\frac{d \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{12 \, f \cos\left(f x + e\right)}"," ",0,"1/12*(12*sqrt(2)*(d^10/f^4)^(1/4)*f*arctan(-(d^10 + sqrt(2)*(d^10/f^4)^(1/4)*d^7*f*sqrt(d*sin(f*x + e)/cos(f*x + e)) - sqrt(2)*(d^10/f^4)^(1/4)*f*sqrt((d^15*sin(f*x + e) + sqrt(d^10/f^4)*d^10*f^2*cos(f*x + e) + sqrt(2)*(d^10/f^4)^(3/4)*d^7*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)))/d^10)*cos(f*x + e) + 12*sqrt(2)*(d^10/f^4)^(1/4)*f*arctan((d^10 - sqrt(2)*(d^10/f^4)^(1/4)*d^7*f*sqrt(d*sin(f*x + e)/cos(f*x + e)) + sqrt(2)*(d^10/f^4)^(1/4)*f*sqrt((d^15*sin(f*x + e) + sqrt(d^10/f^4)*d^10*f^2*cos(f*x + e) - sqrt(2)*(d^10/f^4)^(3/4)*d^7*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)))/d^10)*cos(f*x + e) + 3*sqrt(2)*(d^10/f^4)^(1/4)*f*cos(f*x + e)*log((d^15*sin(f*x + e) + sqrt(d^10/f^4)*d^10*f^2*cos(f*x + e) + sqrt(2)*(d^10/f^4)^(3/4)*d^7*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)) - 3*sqrt(2)*(d^10/f^4)^(1/4)*f*cos(f*x + e)*log((d^15*sin(f*x + e) + sqrt(d^10/f^4)*d^10*f^2*cos(f*x + e) - sqrt(2)*(d^10/f^4)^(3/4)*d^7*f^3*sqrt(d*sin(f*x + e)/cos(f*x + e))*cos(f*x + e))/cos(f*x + e)) + 8*d^2*sqrt(d*sin(f*x + e)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e))","A"
251,-1,0,0,0.000000," ","integrate((d*tan(f*x + e))^(5/2)*cos(f*x + e)^2,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
252,-1,0,0,0.000000," ","integrate((d*tan(f*x + e))^(5/2)*cos(f*x + e)^4,x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
253,0,0,0,0.000000," ","integrate(sec(f*x + e)^5/sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \sec\left(f x + e\right)^{5}}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*sec(f*x + e)^5/(d*tan(f*x + e)), x)","F"
254,0,0,0,0.000000," ","integrate(sec(f*x + e)^3/sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \sec\left(f x + e\right)^{3}}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*sec(f*x + e)^3/(d*tan(f*x + e)), x)","F"
255,0,0,0,0.000000," ","integrate(sec(f*x + e)/sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \sec\left(f x + e\right)}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*sec(f*x + e)/(d*tan(f*x + e)), x)","F"
256,0,0,0,0.000000," ","integrate(cos(f*x + e)/sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \cos\left(f x + e\right)}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*cos(f*x + e)/(d*tan(f*x + e)), x)","F"
257,0,0,0,0.000000," ","integrate(cos(f*x + e)^3/sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \cos\left(f x + e\right)^{3}}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*cos(f*x + e)^3/(d*tan(f*x + e)), x)","F"
258,1,86,0,1.197929," ","integrate(sec(b*x + a)^6/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","-\frac{2 \, {\left(32 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} - 3\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{21 \, b d^{2} \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)}"," ",0,"-2/21*(32*cos(b*x + a)^4 - 8*cos(b*x + a)^2 - 3)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*d^2*cos(b*x + a)^3*sin(b*x + a))","A"
259,1,73,0,1.156713," ","integrate(sec(b*x + a)^4/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","-\frac{2 \, {\left(4 \, \cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}}}{3 \, b d^{2} \cos\left(b x + a\right) \sin\left(b x + a\right)}"," ",0,"-2/3*(4*cos(b*x + a)^2 - 1)*sqrt(d*sin(b*x + a)/cos(b*x + a))/(b*d^2*cos(b*x + a)*sin(b*x + a))","A"
260,1,54,0,1.145350," ","integrate(sec(b*x + a)^2/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","-\frac{2 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right)}{b d^{2} \sin\left(b x + a\right)}"," ",0,"-2*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)/(b*d^2*sin(b*x + a))","A"
261,1,880,0,1.191498," ","integrate((d*tan(b*x + a))^(-3/2),x, algorithm="fricas")","\frac{8 \, \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(\sqrt{2} b d^{2} \cos\left(b x + a\right)^{2} - \sqrt{2} b d^{2}\right)} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} + \sqrt{2} b d \sqrt{\frac{\sqrt{2} b^{3} d^{5} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + b^{2} d^{4} \sqrt{\frac{1}{b^{4} d^{6}}} \cos\left(b x + a\right) + d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} - 1\right) + 4 \, {\left(\sqrt{2} b d^{2} \cos\left(b x + a\right)^{2} - \sqrt{2} b d^{2}\right)} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b d \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} + \sqrt{2} b d \sqrt{-\frac{\sqrt{2} b^{3} d^{5} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) - b^{2} d^{4} \sqrt{\frac{1}{b^{4} d^{6}}} \cos\left(b x + a\right) - d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} + 1\right) + {\left(\sqrt{2} b d^{2} \cos\left(b x + a\right)^{2} - \sqrt{2} b d^{2}\right)} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} \log\left(\frac{\sqrt{2} b^{3} d^{5} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) + b^{2} d^{4} \sqrt{\frac{1}{b^{4} d^{6}}} \cos\left(b x + a\right) + d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}\right) - {\left(\sqrt{2} b d^{2} \cos\left(b x + a\right)^{2} - \sqrt{2} b d^{2}\right)} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} b^{3} d^{5} \sqrt{\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}} \left(\frac{1}{b^{4} d^{6}}\right)^{\frac{3}{4}} \cos\left(b x + a\right) - b^{2} d^{4} \sqrt{\frac{1}{b^{4} d^{6}}} \cos\left(b x + a\right) - d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}\right)}{4 \, {\left(b d^{2} \cos\left(b x + a\right)^{2} - b d^{2}\right)}}"," ",0,"1/4*(8*sqrt(d*sin(b*x + a)/cos(b*x + a))*cos(b*x + a)*sin(b*x + a) + 4*(sqrt(2)*b*d^2*cos(b*x + a)^2 - sqrt(2)*b*d^2)*(1/(b^4*d^6))^(1/4)*arctan(-sqrt(2)*b*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*(1/(b^4*d^6))^(1/4) + sqrt(2)*b*d*sqrt((sqrt(2)*b^3*d^5*sqrt(d*sin(b*x + a)/cos(b*x + a))*(1/(b^4*d^6))^(3/4)*cos(b*x + a) + b^2*d^4*sqrt(1/(b^4*d^6))*cos(b*x + a) + d*sin(b*x + a))/cos(b*x + a))*(1/(b^4*d^6))^(1/4) - 1) + 4*(sqrt(2)*b*d^2*cos(b*x + a)^2 - sqrt(2)*b*d^2)*(1/(b^4*d^6))^(1/4)*arctan(-sqrt(2)*b*d*sqrt(d*sin(b*x + a)/cos(b*x + a))*(1/(b^4*d^6))^(1/4) + sqrt(2)*b*d*sqrt(-(sqrt(2)*b^3*d^5*sqrt(d*sin(b*x + a)/cos(b*x + a))*(1/(b^4*d^6))^(3/4)*cos(b*x + a) - b^2*d^4*sqrt(1/(b^4*d^6))*cos(b*x + a) - d*sin(b*x + a))/cos(b*x + a))*(1/(b^4*d^6))^(1/4) + 1) + (sqrt(2)*b*d^2*cos(b*x + a)^2 - sqrt(2)*b*d^2)*(1/(b^4*d^6))^(1/4)*log((sqrt(2)*b^3*d^5*sqrt(d*sin(b*x + a)/cos(b*x + a))*(1/(b^4*d^6))^(3/4)*cos(b*x + a) + b^2*d^4*sqrt(1/(b^4*d^6))*cos(b*x + a) + d*sin(b*x + a))/cos(b*x + a)) - (sqrt(2)*b*d^2*cos(b*x + a)^2 - sqrt(2)*b*d^2)*(1/(b^4*d^6))^(1/4)*log(-(sqrt(2)*b^3*d^5*sqrt(d*sin(b*x + a)/cos(b*x + a))*(1/(b^4*d^6))^(3/4)*cos(b*x + a) - b^2*d^4*sqrt(1/(b^4*d^6))*cos(b*x + a) - d*sin(b*x + a))/cos(b*x + a)))/(b*d^2*cos(b*x + a)^2 - b*d^2)","A"
262,-1,0,0,0.000000," ","integrate(cos(b*x + a)^2/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","\text{Timed out}"," ",0,"Timed out","F(-1)"
263,0,0,0,0.000000," ","integrate(sec(b*x + a)^5/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sec\left(b x + a\right)^{5}}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sec(b*x + a)^5/(d^2*tan(b*x + a)^2), x)","F"
264,0,0,0,0.000000," ","integrate(sec(b*x + a)^3/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sec\left(b x + a\right)^{3}}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sec(b*x + a)^3/(d^2*tan(b*x + a)^2), x)","F"
265,0,0,0,0.000000," ","integrate(sec(b*x + a)/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sec\left(b x + a\right)}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sec(b*x + a)/(d^2*tan(b*x + a)^2), x)","F"
266,0,0,0,0.000000," ","integrate(cos(b*x + a)/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \cos\left(b x + a\right)}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*cos(b*x + a)/(d^2*tan(b*x + a)^2), x)","F"
267,0,0,0,0.000000," ","integrate(cos(b*x + a)^3/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \cos\left(b x + a\right)^{3}}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*cos(b*x + a)^3/(d^2*tan(b*x + a)^2), x)","F"
268,0,0,0,0.000000," ","integrate(cos(b*x + a)^5/(d*tan(b*x + a))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \cos\left(b x + a\right)^{5}}{d^{2} \tan\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*cos(b*x + a)^5/(d^2*tan(b*x + a)^2), x)","F"
269,0,0,0,0.000000," ","integrate(sec(b*x + a)/(d*tan(b*x + a))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sec\left(b x + a\right)}{d^{3} \tan\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sec(b*x + a)/(d^3*tan(b*x + a)^3), x)","F"
270,0,0,0,0.000000," ","integrate(sec(b*x + a)^3/(d*tan(b*x + a))^(7/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(b x + a\right)} \sec\left(b x + a\right)^{3}}{d^{4} \tan\left(b x + a\right)^{4}}, x\right)"," ",0,"integral(sqrt(d*tan(b*x + a))*sec(b*x + a)^3/(d^4*tan(b*x + a)^4), x)","F"
271,0,0,0,0.000000," ","integrate(sec(f*x + e)^(4/3)*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\sec\left(f x + e\right)^{\frac{4}{3}} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sec(f*x + e)^(4/3)*tan(f*x + e)^2, x)","F"
272,0,0,0,0.000000," ","integrate(sec(f*x + e)^(2/3)*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\sec\left(f x + e\right)^{\frac{2}{3}} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sec(f*x + e)^(2/3)*tan(f*x + e)^2, x)","F"
273,0,0,0,0.000000," ","integrate(sec(f*x + e)^(1/3)*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\sec\left(f x + e\right)^{\frac{1}{3}} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sec(f*x + e)^(1/3)*tan(f*x + e)^2, x)","F"
274,0,0,0,0.000000," ","integrate(tan(f*x + e)^2/sec(f*x + e)^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\tan\left(f x + e\right)^{2}}{\sec\left(f x + e\right)^{\frac{1}{3}}}, x\right)"," ",0,"integral(tan(f*x + e)^2/sec(f*x + e)^(1/3), x)","F"
275,0,0,0,0.000000," ","integrate(tan(f*x + e)^2/sec(f*x + e)^(2/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\tan\left(f x + e\right)^{2}}{\sec\left(f x + e\right)^{\frac{2}{3}}}, x\right)"," ",0,"integral(tan(f*x + e)^2/sec(f*x + e)^(2/3), x)","F"
276,0,0,0,0.000000," ","integrate(sec(f*x + e)^(4/3)*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\sec\left(f x + e\right)^{\frac{4}{3}} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sec(f*x + e)^(4/3)*tan(f*x + e)^4, x)","F"
277,0,0,0,0.000000," ","integrate(sec(f*x + e)^(2/3)*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\sec\left(f x + e\right)^{\frac{2}{3}} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sec(f*x + e)^(2/3)*tan(f*x + e)^4, x)","F"
278,0,0,0,0.000000," ","integrate(sec(f*x + e)^(1/3)*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\sec\left(f x + e\right)^{\frac{1}{3}} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sec(f*x + e)^(1/3)*tan(f*x + e)^4, x)","F"
279,0,0,0,0.000000," ","integrate(tan(f*x + e)^4/sec(f*x + e)^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\tan\left(f x + e\right)^{4}}{\sec\left(f x + e\right)^{\frac{1}{3}}}, x\right)"," ",0,"integral(tan(f*x + e)^4/sec(f*x + e)^(1/3), x)","F"
280,0,0,0,0.000000," ","integrate(tan(f*x + e)^4/sec(f*x + e)^(2/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\tan\left(f x + e\right)^{4}}{\sec\left(f x + e\right)^{\frac{2}{3}}}, x\right)"," ",0,"integral(tan(f*x + e)^4/sec(f*x + e)^(2/3), x)","F"
281,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(4/3)*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*d*sec(f*x + e)*tan(f*x + e)^2, x)","F"
282,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(2/3)*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral((d*sec(f*x + e))^(2/3)*tan(f*x + e)^2, x)","F"
283,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(1/3)*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*tan(f*x + e)^2, x)","F"
284,0,0,0,0.000000," ","integrate(tan(f*x + e)^2/(d*sec(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} \tan\left(f x + e\right)^{2}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((d*sec(f*x + e))^(2/3)*tan(f*x + e)^2/(d*sec(f*x + e)), x)","F"
285,0,0,0,0.000000," ","integrate(tan(f*x + e)^2/(d*sec(f*x + e))^(2/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} \tan\left(f x + e\right)^{2}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*tan(f*x + e)^2/(d*sec(f*x + e)), x)","F"
286,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(4/3)*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*d*sec(f*x + e)*tan(f*x + e)^4, x)","F"
287,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(2/3)*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral((d*sec(f*x + e))^(2/3)*tan(f*x + e)^4, x)","F"
288,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(1/3)*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*tan(f*x + e)^4, x)","F"
289,0,0,0,0.000000," ","integrate(tan(f*x + e)^4/(d*sec(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} \tan\left(f x + e\right)^{4}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((d*sec(f*x + e))^(2/3)*tan(f*x + e)^4/(d*sec(f*x + e)), x)","F"
290,0,0,0,0.000000," ","integrate(tan(f*x + e)^4/(d*sec(f*x + e))^(2/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} \tan\left(f x + e\right)^{4}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*tan(f*x + e)^4/(d*sec(f*x + e)), x)","F"
291,1,1,0,1.578124," ","integrate((d*sec(f*x + e))^(5/2)*sqrt(b*tan(f*x + e)),x, algorithm="fricas")","\left[-\frac{2 \, \sqrt{-b d} d^{2} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d - {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) - \sqrt{-b d} d^{2} \cos\left(f x + e\right) \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d + 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, d^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, f \cos\left(f x + e\right)}, -\frac{2 \, \sqrt{b d} d^{2} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d + {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) - \sqrt{b d} d^{2} \cos\left(f x + e\right) \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d - 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, d^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, f \cos\left(f x + e\right)}\right]"," ",0,"[-1/32*(2*sqrt(-b*d)*d^2*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d - (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e) - sqrt(-b*d)*d^2*cos(f*x + e)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d + 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*d^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)), -1/32*(2*sqrt(b*d)*d^2*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d + (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e) - sqrt(b*d)*d^2*cos(f*x + e)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d - 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*d^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e))]","A"
292,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(3/2)*sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} d \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*d*sec(f*x + e), x)","F"
293,1,1,0,1.554265," ","integrate(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e)),x, algorithm="fricas")","\left[-\frac{2 \, \sqrt{-b d} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d - {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) - \sqrt{-b d} \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d + 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{8 \, f}, -\frac{2 \, \sqrt{b d} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d + {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) - \sqrt{b d} \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d - 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{8 \, f}\right]"," ",0,"[-1/8*(2*sqrt(-b*d)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d - (b*d*cos(f*x + e) + b*d)*sin(f*x + e))) - sqrt(-b*d)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d + 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/f, -1/8*(2*sqrt(b*d)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d + (b*d*cos(f*x + e) + b*d)*sin(f*x + e))) - sqrt(b*d)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d - 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/f]","A"
294,0,0,0,0.000000," ","integrate(sqrt(b*tan(f*x + e))/sqrt(d*sec(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(d*sec(f*x + e)), x)","F"
295,1,68,0,1.160371," ","integrate(sqrt(b*tan(f*x + e))/(d*sec(f*x + e))^(3/2),x, algorithm="fricas")","\frac{2 \, \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{3 \, d^{2} f}"," ",0,"2/3*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(d^2*f)","A"
296,0,0,0,0.000000," ","integrate(sqrt(b*tan(f*x + e))/(d*sec(f*x + e))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{d^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(d^3*sec(f*x + e)^3), x)","F"
297,1,85,0,1.186173," ","integrate(sqrt(b*tan(f*x + e))/(d*sec(f*x + e))^(7/2),x, algorithm="fricas")","\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} + 4 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{21 \, d^{4} f}"," ",0,"2/21*(3*cos(f*x + e)^3 + 4*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e)/(d^4*f)","A"
298,0,0,0,0.000000," ","integrate(sqrt(b*tan(f*x + e))/(d*sec(f*x + e))^(9/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{d^{5} \sec\left(f x + e\right)^{5}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(d^5*sec(f*x + e)^5), x)","F"
299,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b*d^2*sec(f*x + e)^2*tan(f*x + e), x)","F"
300,1,1,0,1.579385," ","integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","\left[\frac{2 \, \sqrt{-b d} b d \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d - {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) + \sqrt{-b d} b d \cos\left(f x + e\right) \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d + 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) + 16 \, b d \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{32 \, f \cos\left(f x + e\right)}, -\frac{2 \, \sqrt{b d} b d \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d + {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) - \sqrt{b d} b d \cos\left(f x + e\right) \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d - 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, b d \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{32 \, f \cos\left(f x + e\right)}\right]"," ",0,"[1/32*(2*sqrt(-b*d)*b*d*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d - (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e) + sqrt(-b*d)*b*d*cos(f*x + e)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d + 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) + 16*b*d*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)))/(f*cos(f*x + e)), -1/32*(2*sqrt(b*d)*b*d*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d + (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e) - sqrt(b*d)*b*d*cos(f*x + e)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d - 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*b*d*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)))/(f*cos(f*x + e))]","A"
301,0,0,0,0.000000," ","integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b*tan(f*x + e), x)","F"
302,1,1,0,2.259713," ","integrate((b*tan(f*x + e))^(3/2)/sqrt(d*sec(f*x + e)),x, algorithm="fricas")","\left[-\frac{2 \, b d \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b \cos\left(f x + e\right)^{2} - {\left(b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right) - b\right)}}\right) - b d \sqrt{-\frac{b}{d}} \log\left(\frac{b \cos\left(f x + e\right)^{4} - 72 \, b \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 28 \, {\left(b \cos\left(f x + e\right)^{2} - 2 \, b\right)} \sin\left(f x + e\right) + 72 \, b}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) + 16 \, b \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{8 \, d f}, \frac{2 \, b d \sqrt{\frac{b}{d}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b \cos\left(f x + e\right)^{2} + {\left(b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right) - b\right)}}\right) + b d \sqrt{\frac{b}{d}} \log\left(\frac{b \cos\left(f x + e\right)^{4} - 72 \, b \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} - 28 \, {\left(b \cos\left(f x + e\right)^{2} - 2 \, b\right)} \sin\left(f x + e\right) + 72 \, b}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, b \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{8 \, d f}\right]"," ",0,"[-1/8*(2*b*d*sqrt(-b/d)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/d)*sqrt(d/cos(f*x + e))/(b*cos(f*x + e)^2 - (b*cos(f*x + e) + b)*sin(f*x + e) - b)) - b*d*sqrt(-b/d)*log((b*cos(f*x + e)^4 - 72*b*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/d)*sqrt(d/cos(f*x + e)) + 28*(b*cos(f*x + e)^2 - 2*b)*sin(f*x + e) + 72*b)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) + 16*b*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e))/(d*f), 1/8*(2*b*d*sqrt(b/d)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/d)*sqrt(d/cos(f*x + e))/(b*cos(f*x + e)^2 + (b*cos(f*x + e) + b)*sin(f*x + e) - b)) + b*d*sqrt(b/d)*log((b*cos(f*x + e)^4 - 72*b*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/d)*sqrt(d/cos(f*x + e)) - 28*(b*cos(f*x + e)^2 - 2*b)*sin(f*x + e) + 72*b)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*b*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e))/(d*f)]","A"
303,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(3/2)/(d*sec(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b \tan\left(f x + e\right)}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b*tan(f*x + e)/(d^2*sec(f*x + e)^2), x)","F"
304,1,78,0,1.166922," ","integrate((b*tan(f*x + e))^(3/2)/(d*sec(f*x + e))^(5/2),x, algorithm="fricas")","-\frac{2 \, {\left(b \cos\left(f x + e\right)^{3} - b \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{5 \, d^{3} f}"," ",0,"-2/5*(b*cos(f*x + e)^3 - b*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(d^3*f)","A"
305,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(3/2)/(d*sec(f*x + e))^(7/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b \tan\left(f x + e\right)}{d^{4} \sec\left(f x + e\right)^{4}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b*tan(f*x + e)/(d^4*sec(f*x + e)^4), x)","F"
306,1,95,0,1.350286," ","integrate((b*tan(f*x + e))^(3/2)/(d*sec(f*x + e))^(9/2),x, algorithm="fricas")","-\frac{2 \, {\left(5 \, b \cos\left(f x + e\right)^{5} - b \cos\left(f x + e\right)^{3} - 4 \, b \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{45 \, d^{5} f}"," ",0,"-2/45*(5*b*cos(f*x + e)^5 - b*cos(f*x + e)^3 - 4*b*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(d^5*f)","A"
307,1,1,0,1.958353," ","integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","\left[\frac{6 \, \sqrt{-b d} b^{2} d^{2} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d - {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right)^{3} + 3 \, \sqrt{-b d} b^{2} d^{2} \cos\left(f x + e\right)^{3} \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d + 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, {\left(3 \, b^{2} d^{2} \cos\left(f x + e\right)^{2} - 4 \, b^{2} d^{2}\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{256 \, f \cos\left(f x + e\right)^{3}}, \frac{6 \, \sqrt{b d} b^{2} d^{2} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d + {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right)^{3} + 3 \, \sqrt{b d} b^{2} d^{2} \cos\left(f x + e\right)^{3} \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d - 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, {\left(3 \, b^{2} d^{2} \cos\left(f x + e\right)^{2} - 4 \, b^{2} d^{2}\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{256 \, f \cos\left(f x + e\right)^{3}}\right]"," ",0,"[1/256*(6*sqrt(-b*d)*b^2*d^2*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d - (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e)^3 + 3*sqrt(-b*d)*b^2*d^2*cos(f*x + e)^3*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d + 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*(3*b^2*d^2*cos(f*x + e)^2 - 4*b^2*d^2)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3), 1/256*(6*sqrt(b*d)*b^2*d^2*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d + (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e)^3 + 3*sqrt(b*d)*b^2*d^2*cos(f*x + e)^3*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d - 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*(3*b^2*d^2*cos(f*x + e)^2 - 4*b^2*d^2)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)]","A"
308,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b^{2} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b^2*d*sec(f*x + e)*tan(f*x + e)^2, x)","F"
309,1,1,0,1.582443," ","integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","\left[\frac{6 \, \sqrt{-b d} b^{2} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d - {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) + 3 \, \sqrt{-b d} b^{2} \cos\left(f x + e\right) \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{-b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d + 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) + 16 \, b^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, f \cos\left(f x + e\right)}, \frac{6 \, \sqrt{b d} b^{2} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b d \cos\left(f x + e\right)^{2} - b d + {\left(b d \cos\left(f x + e\right) + b d\right)} \sin\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) + 3 \, \sqrt{b d} b^{2} \cos\left(f x + e\right) \log\left(\frac{b d \cos\left(f x + e\right)^{4} - 72 \, b d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{b d} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 72 \, b d - 28 \, {\left(b d \cos\left(f x + e\right)^{2} - 2 \, b d\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) + 16 \, b^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, f \cos\left(f x + e\right)}\right]"," ",0,"[1/32*(6*sqrt(-b*d)*b^2*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d - (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e) + 3*sqrt(-b*d)*b^2*cos(f*x + e)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(-b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d + 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) + 16*b^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)), 1/32*(6*sqrt(b*d)*b^2*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d*cos(f*x + e)^2 - b*d + (b*d*cos(f*x + e) + b*d)*sin(f*x + e)))*cos(f*x + e) + 3*sqrt(b*d)*b^2*cos(f*x + e)*log((b*d*cos(f*x + e)^4 - 72*b*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*d)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)) + 72*b*d - 28*(b*d*cos(f*x + e)^2 - 2*b*d)*sin(f*x + e))/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) + 16*b^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e))]","A"
310,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(5/2)/sqrt(d*sec(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b^{2} \tan\left(f x + e\right)^{2}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b^2*tan(f*x + e)^2/(d*sec(f*x + e)), x)","F"
311,1,1,0,2.401076," ","integrate((b*tan(f*x + e))^(5/2)/(d*sec(f*x + e))^(3/2),x, algorithm="fricas")","\left[-\frac{16 \, b^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 6 \, b^{2} d \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b \cos\left(f x + e\right)^{2} - {\left(b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right) - b\right)}}\right) - 3 \, b^{2} d \sqrt{-\frac{b}{d}} \log\left(\frac{b \cos\left(f x + e\right)^{4} - 72 \, b \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 28 \, {\left(b \cos\left(f x + e\right)^{2} - 2 \, b\right)} \sin\left(f x + e\right) + 72 \, b}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{24 \, d^{2} f}, -\frac{16 \, b^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 6 \, b^{2} d \sqrt{\frac{b}{d}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(b \cos\left(f x + e\right)^{2} + {\left(b \cos\left(f x + e\right) + b\right)} \sin\left(f x + e\right) - b\right)}}\right) - 3 \, b^{2} d \sqrt{\frac{b}{d}} \log\left(\frac{b \cos\left(f x + e\right)^{4} - 72 \, b \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{b}{d}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} - 28 \, {\left(b \cos\left(f x + e\right)^{2} - 2 \, b\right)} \sin\left(f x + e\right) + 72 \, b}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{24 \, d^{2} f}\right]"," ",0,"[-1/24*(16*b^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 6*b^2*d*sqrt(-b/d)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/d)*sqrt(d/cos(f*x + e))/(b*cos(f*x + e)^2 - (b*cos(f*x + e) + b)*sin(f*x + e) - b)) - 3*b^2*d*sqrt(-b/d)*log((b*cos(f*x + e)^4 - 72*b*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-b/d)*sqrt(d/cos(f*x + e)) + 28*(b*cos(f*x + e)^2 - 2*b)*sin(f*x + e) + 72*b)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/(d^2*f), -1/24*(16*b^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 6*b^2*d*sqrt(b/d)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/d)*sqrt(d/cos(f*x + e))/(b*cos(f*x + e)^2 + (b*cos(f*x + e) + b)*sin(f*x + e) - b)) - 3*b^2*d*sqrt(b/d)*log((b*cos(f*x + e)^4 - 72*b*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(b/d)*sqrt(d/cos(f*x + e)) - 28*(b*cos(f*x + e)^2 - 2*b)*sin(f*x + e) + 72*b)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/(d^2*f)]","A"
312,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(5/2)/(d*sec(f*x + e))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b^{2} \tan\left(f x + e\right)^{2}}{d^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b^2*tan(f*x + e)^2/(d^3*sec(f*x + e)^3), x)","F"
313,1,92,0,1.178049," ","integrate((b*tan(f*x + e))^(5/2)/(d*sec(f*x + e))^(7/2),x, algorithm="fricas")","-\frac{2 \, {\left(b^{2} \cos\left(f x + e\right)^{3} - b^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{7 \, d^{4} f}"," ",0,"-2/7*(b^2*cos(f*x + e)^3 - b^2*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*sin(f*x + e)/(d^4*f)","A"
314,0,0,0,0.000000," ","integrate((b*tan(f*x + e))^(5/2)/(d*sec(f*x + e))^(9/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} b^{2} \tan\left(f x + e\right)^{2}}{d^{5} \sec\left(f x + e\right)^{5}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*b^2*tan(f*x + e)^2/(d^5*sec(f*x + e)^5), x)","F"
315,1,1,0,1.693658," ","integrate((d*sec(f*x + e))^(7/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","\left[-\frac{6 \, b d^{3} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} - {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) \cos\left(f x + e\right) - 3 \, b d^{3} \sqrt{-\frac{d}{b}} \cos\left(f x + e\right) \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) - 16 \, d^{3} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{32 \, b f \cos\left(f x + e\right)}, \frac{6 \, b d^{3} \sqrt{\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} + {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) \cos\left(f x + e\right) + 3 \, b d^{3} \sqrt{\frac{d}{b}} \cos\left(f x + e\right) \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} - 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) + 16 \, d^{3} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{32 \, b f \cos\left(f x + e\right)}\right]"," ",0,"[-1/32*(6*b*d^3*sqrt(-d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 - (d*cos(f*x + e) + d)*sin(f*x + e) - d))*cos(f*x + e) - 3*b*d^3*sqrt(-d/b)*cos(f*x + e)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e)) + 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) - 16*d^3*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)))/(b*f*cos(f*x + e)), 1/32*(6*b*d^3*sqrt(d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 + (d*cos(f*x + e) + d)*sin(f*x + e) - d))*cos(f*x + e) + 3*b*d^3*sqrt(d/b)*cos(f*x + e)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e)) - 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)) + 16*d^3*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e)))/(b*f*cos(f*x + e))]","A"
316,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(5/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} d^{2} \sec\left(f x + e\right)^{2}}{b \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*d^2*sec(f*x + e)^2/(b*tan(f*x + e)), x)","F"
317,1,1,0,1.582391," ","integrate((d*sec(f*x + e))^(3/2)/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","\left[-\frac{2 \, d \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} - {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) - d \sqrt{-\frac{d}{b}} \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{8 \, f}, \frac{2 \, d \sqrt{\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} + {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) + d \sqrt{\frac{d}{b}} \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} - 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{8 \, f}\right]"," ",0,"[-1/8*(2*d*sqrt(-d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 - (d*cos(f*x + e) + d)*sin(f*x + e) - d)) - d*sqrt(-d/b)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e)) + 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/f, 1/8*(2*d*sqrt(d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 + (d*cos(f*x + e) + d)*sin(f*x + e) - d)) + d*sqrt(d/b)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e)) - 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/f]","A"
318,0,0,0,0.000000," ","integrate(sqrt(d*sec(f*x + e))/sqrt(b*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(b*tan(f*x + e)), x)","F"
319,1,63,0,1.150822," ","integrate(1/(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))),x, algorithm="fricas")","\frac{2 \, \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{b d f}"," ",0,"2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e)/(b*d*f)","A"
320,0,0,0,0.000000," ","integrate(1/((d*sec(f*x + e))^(3/2)*sqrt(b*tan(f*x + e))),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(b*d^2*sec(f*x + e)^2*tan(f*x + e)), x)","F"
321,1,78,0,1.167545," ","integrate(1/((d*sec(f*x + e))^(5/2)*sqrt(b*tan(f*x + e))),x, algorithm="fricas")","\frac{2 \, {\left(\cos\left(f x + e\right)^{3} + 4 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{5 \, b d^{3} f}"," ",0,"2/5*(cos(f*x + e)^3 + 4*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b*d^3*f)","A"
322,1,1,0,1.672405," ","integrate((d*sec(f*x + e))^(5/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","\left[-\frac{2 \, b d^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} - {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) \sin\left(f x + e\right) - b d^{2} \sqrt{-\frac{d}{b}} \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) \sin\left(f x + e\right) + 16 \, d^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{8 \, b^{2} f \sin\left(f x + e\right)}, -\frac{2 \, b d^{2} \sqrt{\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} + {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) \sin\left(f x + e\right) - b d^{2} \sqrt{\frac{d}{b}} \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} - 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right) \sin\left(f x + e\right) + 16 \, d^{2} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{8 \, b^{2} f \sin\left(f x + e\right)}\right]"," ",0,"[-1/8*(2*b*d^2*sqrt(-d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 - (d*cos(f*x + e) + d)*sin(f*x + e) - d))*sin(f*x + e) - b*d^2*sqrt(-d/b)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e)) + 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8))*sin(f*x + e) + 16*d^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e))/(b^2*f*sin(f*x + e)), -1/8*(2*b*d^2*sqrt(d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 + (d*cos(f*x + e) + d)*sin(f*x + e) - d))*sin(f*x + e) - b*d^2*sqrt(d/b)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e)) - 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8))*sin(f*x + e) + 16*d^2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e))/(b^2*f*sin(f*x + e))]","A"
323,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(3/2)/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} d \sec\left(f x + e\right)}{b^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*d*sec(f*x + e)/(b^2*tan(f*x + e)^2), x)","F"
324,1,70,0,1.132363," ","integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e))^(3/2),x, algorithm="fricas")","-\frac{2 \, \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{b^{2} f \sin\left(f x + e\right)}"," ",0,"-2*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e)/(b^2*f*sin(f*x + e))","A"
325,0,0,0,0.000000," ","integrate(1/(sqrt(d*sec(f*x + e))*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b^{2} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(b^2*d*sec(f*x + e)*tan(f*x + e)^2), x)","F"
326,1,89,0,1.159223," ","integrate(1/((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","\frac{2 \, {\left(\cos\left(f x + e\right)^{3} - 4 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{3 \, b^{2} d^{2} f \sin\left(f x + e\right)}"," ",0,"2/3*(cos(f*x + e)^3 - 4*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b^2*d^2*f*sin(f*x + e))","A"
327,0,0,0,0.000000," ","integrate(1/((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e))^(3/2)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b^{2} d^{3} \sec\left(f x + e\right)^{3} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(b^2*d^3*sec(f*x + e)^3*tan(f*x + e)^2), x)","F"
328,1,1,0,1.917193," ","integrate((d*sec(f*x + e))^(7/2)/(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","\left[\frac{16 \, d^{3} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) - 6 \, {\left(b d^{3} \cos\left(f x + e\right)^{2} - b d^{3}\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} - {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) + 3 \, {\left(b d^{3} \cos\left(f x + e\right)^{2} - b d^{3}\right)} \sqrt{-\frac{d}{b}} \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} - {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{-\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} + 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{24 \, {\left(b^{3} f \cos\left(f x + e\right)^{2} - b^{3} f\right)}}, \frac{16 \, d^{3} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) + 6 \, {\left(b d^{3} \cos\left(f x + e\right)^{2} - b d^{3}\right)} \sqrt{\frac{d}{b}} \arctan\left(\frac{{\left(\cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) + 4\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{4 \, {\left(d \cos\left(f x + e\right)^{2} + {\left(d \cos\left(f x + e\right) + d\right)} \sin\left(f x + e\right) - d\right)}}\right) + 3 \, {\left(b d^{3} \cos\left(f x + e\right)^{2} - b d^{3}\right)} \sqrt{\frac{d}{b}} \log\left(\frac{d \cos\left(f x + e\right)^{4} - 72 \, d \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, \cos\left(f x + e\right)^{3} + {\left(\cos\left(f x + e\right)^{3} - 8 \, \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) - 8 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{b}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} - 28 \, {\left(d \cos\left(f x + e\right)^{2} - 2 \, d\right)} \sin\left(f x + e\right) + 72 \, d}{\cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{2} + 4 \, {\left(\cos\left(f x + e\right)^{2} - 2\right)} \sin\left(f x + e\right) + 8}\right)}{24 \, {\left(b^{3} f \cos\left(f x + e\right)^{2} - b^{3} f\right)}}\right]"," ",0,"[1/24*(16*d^3*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e) - 6*(b*d^3*cos(f*x + e)^2 - b*d^3)*sqrt(-d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 - (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 - (d*cos(f*x + e) + d)*sin(f*x + e) - d)) + 3*(b*d^3*cos(f*x + e)^2 - b*d^3)*sqrt(-d/b)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 + 8*(7*cos(f*x + e)^3 - (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(-d/b)*sqrt(d/cos(f*x + e)) + 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/(b^3*f*cos(f*x + e)^2 - b^3*f), 1/24*(16*d^3*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e) + 6*(b*d^3*cos(f*x + e)^2 - b*d^3)*sqrt(d/b)*arctan(1/4*(cos(f*x + e)^3 - 5*cos(f*x + e)^2 + (cos(f*x + e)^2 + 6*cos(f*x + e) + 4)*sin(f*x + e) - 2*cos(f*x + e) + 4)*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e))/(d*cos(f*x + e)^2 + (d*cos(f*x + e) + d)*sin(f*x + e) - d)) + 3*(b*d^3*cos(f*x + e)^2 - b*d^3)*sqrt(d/b)*log((d*cos(f*x + e)^4 - 72*d*cos(f*x + e)^2 - 8*(7*cos(f*x + e)^3 + (cos(f*x + e)^3 - 8*cos(f*x + e))*sin(f*x + e) - 8*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/b)*sqrt(d/cos(f*x + e)) - 28*(d*cos(f*x + e)^2 - 2*d)*sin(f*x + e) + 72*d)/(cos(f*x + e)^4 - 8*cos(f*x + e)^2 + 4*(cos(f*x + e)^2 - 2)*sin(f*x + e) + 8)))/(b^3*f*cos(f*x + e)^2 - b^3*f)]","A"
329,0,0,0,0.000000," ","integrate((d*sec(f*x + e))^(5/2)/(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)} d^{2} \sec\left(f x + e\right)^{2}}{b^{3} \tan\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))*d^2*sec(f*x + e)^2/(b^3*tan(f*x + e)^3), x)","F"
330,1,82,0,1.134735," ","integrate((d*sec(f*x + e))^(3/2)/(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","\frac{2 \, d \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{3 \, {\left(b^{3} f \cos\left(f x + e\right)^{2} - b^{3} f\right)}}"," ",0,"2/3*d*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))*cos(f*x + e)/(b^3*f*cos(f*x + e)^2 - b^3*f)","A"
331,0,0,0,0.000000," ","integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e))^(5/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b^{3} \tan\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(b^3*tan(f*x + e)^3), x)","F"
332,1,101,0,1.162142," ","integrate(1/(sqrt(d*sec(f*x + e))*(b*tan(f*x + e))^(5/2)),x, algorithm="fricas")","-\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} - 4 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{3 \, {\left(b^{3} d f \cos\left(f x + e\right)^{2} - b^{3} d f\right)}}"," ",0,"-2/3*(3*cos(f*x + e)^3 - 4*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b^3*d*f*cos(f*x + e)^2 - b^3*d*f)","A"
333,0,0,0,0.000000," ","integrate(1/((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e))^(5/2)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} \sqrt{b \tan\left(f x + e\right)}}{b^{3} d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*sqrt(b*tan(f*x + e))/(b^3*d^2*sec(f*x + e)^2*tan(f*x + e)^3), x)","F"
334,1,120,0,1.208332," ","integrate(1/((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e))^(5/2)),x, algorithm="fricas")","-\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{5} + 24 \, \cos\left(f x + e\right)^{3} - 32 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{b \sin\left(f x + e\right)}{\cos\left(f x + e\right)}} \sqrt{\frac{d}{\cos\left(f x + e\right)}}}{15 \, {\left(b^{3} d^{3} f \cos\left(f x + e\right)^{2} - b^{3} d^{3} f\right)}}"," ",0,"-2/15*(3*cos(f*x + e)^5 + 24*cos(f*x + e)^3 - 32*cos(f*x + e))*sqrt(b*sin(f*x + e)/cos(f*x + e))*sqrt(d/cos(f*x + e))/(b^3*d^3*f*cos(f*x + e)^2 - b^3*d^3*f)","A"
335,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(4/3)*sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)} b \sec\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e))^(1/3)*sqrt(d*tan(f*x + e))*b*sec(f*x + e), x)","F"
336,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(1/3)*sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral((b*sec(f*x + e))^(1/3)*sqrt(d*tan(f*x + e)), x)","F"
337,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))/(b*sec(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(b \sec\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)}}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b*sec(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))/(b*sec(f*x + e)), x)","F"
338,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))/(b*sec(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(b \sec\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)}}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((b*sec(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))/(b^2*sec(f*x + e)^2), x)","F"
339,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(4/3)*(d*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)} b d \sec\left(f x + e\right) \tan\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e))^(1/3)*sqrt(d*tan(f*x + e))*b*d*sec(f*x + e)*tan(f*x + e), x)","F"
340,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(1/3)*(d*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{\frac{1}{3}} \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e))^(1/3)*sqrt(d*tan(f*x + e))*d*tan(f*x + e), x)","F"
341,0,0,0,0.000000," ","integrate((d*tan(f*x + e))^(3/2)/(b*sec(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(b \sec\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right)}{b \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b*sec(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))*d*tan(f*x + e)/(b*sec(f*x + e)), x)","F"
342,0,0,0,0.000000," ","integrate((d*tan(f*x + e))^(3/2)/(b*sec(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\left(b \sec\left(f x + e\right)\right)^{\frac{2}{3}} \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right)}{b^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((b*sec(f*x + e))^(2/3)*sqrt(d*tan(f*x + e))*d*tan(f*x + e)/(b^2*sec(f*x + e)^2), x)","F"
343,0,0,0,0.000000," ","integrate(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}} d \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(1/3)*d*tan(f*x + e), x)","F"
344,0,0,0,0.000000," ","integrate(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(1/3), x)","F"
345,0,0,0,0.000000," ","integrate(sqrt(b*sec(f*x + e))/(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}}}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(2/3)/(d*tan(f*x + e)), x)","F"
346,0,0,0,0.000000," ","integrate(sqrt(b*sec(f*x + e))/(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}}}{d^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(2/3)/(d^2*tan(f*x + e)^2), x)","F"
347,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(3/2)*(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}} b d \sec\left(f x + e\right) \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(1/3)*b*d*sec(f*x + e)*tan(f*x + e), x)","F"
348,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(3/2)*(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{1}{3}} b \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(1/3)*b*sec(f*x + e), x)","F"
349,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(3/2)/(d*tan(f*x + e))^(1/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}} b \sec\left(f x + e\right)}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(2/3)*b*sec(f*x + e)/(d*tan(f*x + e)), x)","F"
350,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^(3/2)/(d*tan(f*x + e))^(4/3),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right)} \left(d \tan\left(f x + e\right)\right)^{\frac{2}{3}} b \sec\left(f x + e\right)}{d^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e))*(d*tan(f*x + e))^(2/3)*b*sec(f*x + e)/(d^2*tan(f*x + e)^2), x)","F"
351,1,108,0,1.168352," ","integrate((b*sec(f*x + e))^m*tan(f*x + e)^5,x, algorithm="fricas")","\frac{{\left({\left(m^{2} + 6 \, m + 8\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(m^{2} + 4 \, m\right)} \cos\left(f x + e\right)^{2} + m^{2} + 2 \, m\right)} \left(\frac{b}{\cos\left(f x + e\right)}\right)^{m}}{{\left(f m^{3} + 6 \, f m^{2} + 8 \, f m\right)} \cos\left(f x + e\right)^{4}}"," ",0,"((m^2 + 6*m + 8)*cos(f*x + e)^4 - 2*(m^2 + 4*m)*cos(f*x + e)^2 + m^2 + 2*m)*(b/cos(f*x + e))^m/((f*m^3 + 6*f*m^2 + 8*f*m)*cos(f*x + e)^4)","A"
352,1,68,0,1.146702," ","integrate((b*sec(f*x + e))^m*tan(f*x + e)^3,x, algorithm="fricas")","-\frac{{\left({\left(m + 2\right)} \cos\left(f x + e\right)^{2} - m\right)} \left(\frac{b}{\cos\left(f x + e\right)}\right)^{m}}{{\left(f m^{2} + 2 \, f m\right)} \cos\left(f x + e\right)^{2}}"," ",0,"-((m + 2)*cos(f*x + e)^2 - m)*(b/cos(f*x + e))^m/((f*m^2 + 2*f*m)*cos(f*x + e)^2)","A"
353,1,26,0,1.131526," ","integrate((b*sec(f*x + e))^m*tan(f*x + e),x, algorithm="fricas")","\frac{\left(\frac{b}{\cos\left(f x + e\right)}\right)^{m}}{f m}"," ",0,"(b/cos(f*x + e))^m/(f*m)","A"
354,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*cot(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \cot\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e))^m*cot(f*x + e), x)","F"
355,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*cot(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*cot(f*x + e)^3, x)","F"
356,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*cot(f*x + e)^5,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{5}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*cot(f*x + e)^5, x)","F"
357,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*tan(f*x + e)^4, x)","F"
358,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*tan(f*x + e)^2, x)","F"
359,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*cot(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*cot(f*x + e)^2, x)","F"
360,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*cot(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*cot(f*x + e)^4, x)","F"
361,0,0,0,0.000000," ","integrate((b*sec(f*x + e))^m*cot(f*x + e)^6,x, algorithm="fricas")","{\rm integral}\left(\left(b \sec\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{6}, x\right)"," ",0,"integral((b*sec(f*x + e))^m*cot(f*x + e)^6, x)","F"
362,0,0,0,0.000000," ","integrate((a*sec(f*x + e))^m*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \sec\left(f x + e\right)\right)^{m} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e))^m*(b*tan(f*x + e))^n, x)","F"
363,1,115,0,1.171607," ","integrate((d*tan(b*x + a))^n*sec(b*x + a)^6,x, algorithm="fricas")","\frac{{\left(8 \, \cos\left(b x + a\right)^{4} + 4 \, {\left(n + 1\right)} \cos\left(b x + a\right)^{2} + n^{2} + 4 \, n + 3\right)} \left(\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}\right)^{n} \sin\left(b x + a\right)}{{\left(b n^{3} + 9 \, b n^{2} + 23 \, b n + 15 \, b\right)} \cos\left(b x + a\right)^{5}}"," ",0,"(8*cos(b*x + a)^4 + 4*(n + 1)*cos(b*x + a)^2 + n^2 + 4*n + 3)*(d*sin(b*x + a)/cos(b*x + a))^n*sin(b*x + a)/((b*n^3 + 9*b*n^2 + 23*b*n + 15*b)*cos(b*x + a)^5)","A"
364,1,82,0,1.148701," ","integrate((d*tan(b*x + a))^n*sec(b*x + a)^4,x, algorithm="fricas")","\frac{{\left(2 \, \cos\left(b x + a\right)^{2} + n + 1\right)} \left(\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}\right)^{n} \sin\left(b x + a\right)}{{\left(b n^{2} + 4 \, b n + 3 \, b\right)} \cos\left(b x + a\right)^{3}}"," ",0,"(2*cos(b*x + a)^2 + n + 1)*(d*sin(b*x + a)/cos(b*x + a))^n*sin(b*x + a)/((b*n^2 + 4*b*n + 3*b)*cos(b*x + a)^3)","A"
365,1,54,0,1.138283," ","integrate((d*tan(b*x + a))^n*sec(b*x + a)^2,x, algorithm="fricas")","\frac{\left(\frac{d \sin\left(b x + a\right)}{\cos\left(b x + a\right)}\right)^{n} \sin\left(b x + a\right)}{{\left(b n + b\right)} \cos\left(b x + a\right)}"," ",0,"(d*sin(b*x + a)/cos(b*x + a))^n*sin(b*x + a)/((b*n + b)*cos(b*x + a))","A"
366,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n,x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral((d*tan(b*x + a))^n, x)","F"
367,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*cos(b*x + a)^2,x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \cos\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*tan(b*x + a))^n*cos(b*x + a)^2, x)","F"
368,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*cos(b*x + a)^4,x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \cos\left(b x + a\right)^{4}, x\right)"," ",0,"integral((d*tan(b*x + a))^n*cos(b*x + a)^4, x)","F"
369,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*sec(b*x + a)^5,x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \sec\left(b x + a\right)^{5}, x\right)"," ",0,"integral((d*tan(b*x + a))^n*sec(b*x + a)^5, x)","F"
370,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*sec(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \sec\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*tan(b*x + a))^n*sec(b*x + a)^3, x)","F"
371,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*sec(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \sec\left(b x + a\right), x\right)"," ",0,"integral((d*tan(b*x + a))^n*sec(b*x + a), x)","F"
372,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*cos(b*x + a),x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \cos\left(b x + a\right), x\right)"," ",0,"integral((d*tan(b*x + a))^n*cos(b*x + a), x)","F"
373,0,0,0,0.000000," ","integrate((d*tan(b*x + a))^n*cos(b*x + a)^3,x, algorithm="fricas")","{\rm integral}\left(\left(d \tan\left(b x + a\right)\right)^{n} \cos\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*tan(b*x + a))^n*cos(b*x + a)^3, x)","F"
374,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m*tan(f*x + e)^3,x, algorithm="fricas")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*csc(f*x + e))^m*tan(f*x + e)^3, x)","F"
375,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m*tan(f*x + e),x, algorithm="fricas")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{m} \tan\left(f x + e\right), x\right)"," ",0,"integral((b*csc(f*x + e))^m*tan(f*x + e), x)","F"
376,1,27,0,1.145656," ","integrate((b*csc(f*x + e))^m*cot(f*x + e),x, algorithm="fricas")","-\frac{\left(\frac{b}{\sin\left(f x + e\right)}\right)^{m}}{f m}"," ",0,"-(b/sin(f*x + e))^m/(f*m)","A"
377,1,81,0,1.139227," ","integrate((b*csc(f*x + e))^m*cot(f*x + e)^3,x, algorithm="fricas")","-\frac{{\left({\left(m + 2\right)} \cos\left(f x + e\right)^{2} - 2\right)} \left(\frac{b}{\sin\left(f x + e\right)}\right)^{m}}{f m^{2} - {\left(f m^{2} + 2 \, f m\right)} \cos\left(f x + e\right)^{2} + 2 \, f m}"," ",0,"-((m + 2)*cos(f*x + e)^2 - 2)*(b/sin(f*x + e))^m/(f*m^2 - (f*m^2 + 2*f*m)*cos(f*x + e)^2 + 2*f*m)","A"
378,1,155,0,1.152121," ","integrate((b*csc(f*x + e))^m*cot(f*x + e)^5,x, algorithm="fricas")","-\frac{{\left({\left(m^{2} + 6 \, m + 8\right)} \cos\left(f x + e\right)^{4} - 4 \, {\left(m + 4\right)} \cos\left(f x + e\right)^{2} + 8\right)} \left(\frac{b}{\sin\left(f x + e\right)}\right)^{m}}{{\left(f m^{3} + 6 \, f m^{2} + 8 \, f m\right)} \cos\left(f x + e\right)^{4} + f m^{3} + 6 \, f m^{2} - 2 \, {\left(f m^{3} + 6 \, f m^{2} + 8 \, f m\right)} \cos\left(f x + e\right)^{2} + 8 \, f m}"," ",0,"-((m^2 + 6*m + 8)*cos(f*x + e)^4 - 4*(m + 4)*cos(f*x + e)^2 + 8)*(b/sin(f*x + e))^m/((f*m^3 + 6*f*m^2 + 8*f*m)*cos(f*x + e)^4 + f*m^3 + 6*f*m^2 - 2*(f*m^3 + 6*f*m^2 + 8*f*m)*cos(f*x + e)^2 + 8*f*m)","A"
379,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m*tan(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*csc(f*x + e))^m*tan(f*x + e)^4, x)","F"
380,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m*tan(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{m} \tan\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*csc(f*x + e))^m*tan(f*x + e)^2, x)","F"
381,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m*cot(f*x + e)^2,x, algorithm="fricas")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*csc(f*x + e))^m*cot(f*x + e)^2, x)","F"
382,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m*cot(f*x + e)^4,x, algorithm="fricas")","{\rm integral}\left(\left(b \csc\left(f x + e\right)\right)^{m} \cot\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*csc(f*x + e))^m*cot(f*x + e)^4, x)","F"
383,0,0,0,0.000000," ","integrate((d*tan(f*x + e))^(3/2)*(b*csc(f*x + e))^m,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \left(b \csc\left(f x + e\right)\right)^{m} d \tan\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*(b*csc(f*x + e))^m*d*tan(f*x + e), x)","F"
384,0,0,0,0.000000," ","integrate(sqrt(d*tan(f*x + e))*(b*csc(f*x + e))^m,x, algorithm="fricas")","{\rm integral}\left(\sqrt{d \tan\left(f x + e\right)} \left(b \csc\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*(b*csc(f*x + e))^m, x)","F"
385,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m/sqrt(d*tan(f*x + e)),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \left(b \csc\left(f x + e\right)\right)^{m}}{d \tan\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*(b*csc(f*x + e))^m/(d*tan(f*x + e)), x)","F"
386,0,0,0,0.000000," ","integrate((b*csc(f*x + e))^m/(d*tan(f*x + e))^(3/2),x, algorithm="fricas")","{\rm integral}\left(\frac{\sqrt{d \tan\left(f x + e\right)} \left(b \csc\left(f x + e\right)\right)^{m}}{d^{2} \tan\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*tan(f*x + e))*(b*csc(f*x + e))^m/(d^2*tan(f*x + e)^2), x)","F"
387,0,0,0,0.000000," ","integrate((a*csc(f*x + e))^m*(b*tan(f*x + e))^n,x, algorithm="fricas")","{\rm integral}\left(\left(a \csc\left(f x + e\right)\right)^{m} \left(b \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*csc(f*x + e))^m*(b*tan(f*x + e))^n, x)","F"
