1,0,0,0,0.861159," ","integrate((a+I*a*cot(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(-\frac{2 \, a}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}\right)^{n}, x\right)"," ",0,"integral((-2*a/(e^(2*I*d*x + 2*I*c) - 1))^n, x)","F",0
2,1,377,0,0.901831," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(a e^{2} \cos\left(2 \, d x + 2 \, c\right) - a e^{2}\right)} \sqrt{e} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 4 \, {\left(18 \, a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 5 \, a e^{2} \sin\left(2 \, d x + 2 \, c\right) - 12 \, a e^{2}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{30 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)}}, \frac{15 \, \sqrt{2} {\left(a e^{2} \cos\left(2 \, d x + 2 \, c\right) - a e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 2 \, {\left(18 \, a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 5 \, a e^{2} \sin\left(2 \, d x + 2 \, c\right) - 12 \, a e^{2}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{15 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)}}\right]"," ",0,"[1/30*(15*sqrt(2)*(a*e^2*cos(2*d*x + 2*c) - a*e^2)*sqrt(e)*log(sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1) + 2*e*sin(2*d*x + 2*c) + e) + 4*(18*a*e^2*cos(2*d*x + 2*c) + 5*a*e^2*sin(2*d*x + 2*c) - 12*a*e^2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*cos(2*d*x + 2*c) - d), 1/15*(15*sqrt(2)*(a*e^2*cos(2*d*x + 2*c) - a*e^2)*sqrt(-e)*arctan(1/2*sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + 2*(18*a*e^2*cos(2*d*x + 2*c) + 5*a*e^2*sin(2*d*x + 2*c) - 12*a*e^2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*cos(2*d*x + 2*c) - d)]","A",0
3,1,334,0,0.749768," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} a \sqrt{-e} e \log\left(\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(a e \cos\left(2 \, d x + 2 \, c\right) + 3 \, a e \sin\left(2 \, d x + 2 \, c\right) + a e\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{6 \, d \sin\left(2 \, d x + 2 \, c\right)}, -\frac{3 \, \sqrt{2} a e^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a e \cos\left(2 \, d x + 2 \, c\right) + 3 \, a e \sin\left(2 \, d x + 2 \, c\right) + a e\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{3 \, d \sin\left(2 \, d x + 2 \, c\right)}\right]"," ",0,"[1/6*(3*sqrt(2)*a*sqrt(-e)*e*log(sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*e*sin(2*d*x + 2*c) + e)*sin(2*d*x + 2*c) - 4*(a*e*cos(2*d*x + 2*c) + 3*a*e*sin(2*d*x + 2*c) + a*e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*sin(2*d*x + 2*c)), -1/3*(3*sqrt(2)*a*e^(3/2)*arctan(-1/2*sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e))*sin(2*d*x + 2*c) + 2*(a*e*cos(2*d*x + 2*c) + 3*a*e*sin(2*d*x + 2*c) + a*e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*sin(2*d*x + 2*c))]","B",0
4,1,236,0,0.649953," ","integrate((e*cot(d*x+c))^(1/2)*(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{e} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) - 4 \, a \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, d}, -\frac{\sqrt{2} a \sqrt{-e} \arctan\left(\frac{\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 2 \, a \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{d}\right]"," ",0,"[1/2*(sqrt(2)*a*sqrt(e)*log(-sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1) + 2*e*sin(2*d*x + 2*c) + e) - 4*a*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/d, -(sqrt(2)*a*sqrt(-e)*arctan(1/2*sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + 2*a*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/d]","A",0
5,1,172,0,0.600929," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{1}{e}} \log\left(-\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right)}{2 \, d}, \frac{\sqrt{2} a \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right)}{d \sqrt{e}}\right]"," ",0,"[1/2*sqrt(2)*a*sqrt(-1/e)*log(-sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*sin(2*d*x + 2*c) + 1)/d, sqrt(2)*a*arctan(-1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(sqrt(e)*(cos(2*d*x + 2*c) + 1)))/(d*sqrt(e))]","B",0
6,1,321,0,0.532521," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, a \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + \frac{\sqrt{2} {\left(a e \cos\left(2 \, d x + 2 \, c\right) + a e\right)} \log\left(\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)}}{\sqrt{e}} + 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right)}{\sqrt{e}}}{2 \, {\left(d e^{2} \cos\left(2 \, d x + 2 \, c\right) + d e^{2}\right)}}, \frac{\sqrt{2} {\left(a e \cos\left(2 \, d x + 2 \, c\right) + a e\right)} \sqrt{-\frac{1}{e}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right) + 2 \, a \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right)}{d e^{2} \cos\left(2 \, d x + 2 \, c\right) + d e^{2}}\right]"," ",0,"[1/2*(4*a*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + sqrt(2)*(a*e*cos(2*d*x + 2*c) + a*e)*log(sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1)/sqrt(e) + 2*sin(2*d*x + 2*c) + 1)/sqrt(e))/(d*e^2*cos(2*d*x + 2*c) + d*e^2), (sqrt(2)*(a*e*cos(2*d*x + 2*c) + a*e)*sqrt(-1/e)*arctan(1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(cos(2*d*x + 2*c) + 1)) + 2*a*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c))/(d*e^2*cos(2*d*x + 2*c) + d*e^2)]","B",0
7,1,358,0,0.815188," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a e \cos\left(2 \, d x + 2 \, c\right) + a e\right)} \sqrt{-\frac{1}{e}} \log\left(\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right) - 4 \, {\left(a \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \sin\left(2 \, d x + 2 \, c\right) - a\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{6 \, {\left(d e^{3} \cos\left(2 \, d x + 2 \, c\right) + d e^{3}\right)}}, -\frac{\frac{3 \, \sqrt{2} {\left(a e \cos\left(2 \, d x + 2 \, c\right) + a e\right)} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right)}{\sqrt{e}} + 2 \, {\left(a \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \sin\left(2 \, d x + 2 \, c\right) - a\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{3 \, {\left(d e^{3} \cos\left(2 \, d x + 2 \, c\right) + d e^{3}\right)}}\right]"," ",0,"[1/6*(3*sqrt(2)*(a*e*cos(2*d*x + 2*c) + a*e)*sqrt(-1/e)*log(sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*sin(2*d*x + 2*c) + 1) - 4*(a*cos(2*d*x + 2*c) - 3*a*sin(2*d*x + 2*c) - a)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^3*cos(2*d*x + 2*c) + d*e^3), -1/3*(3*sqrt(2)*(a*e*cos(2*d*x + 2*c) + a*e)*arctan(-1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(sqrt(e)*(cos(2*d*x + 2*c) + 1)))/sqrt(e) + 2*(a*cos(2*d*x + 2*c) - 3*a*sin(2*d*x + 2*c) - a)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^3*cos(2*d*x + 2*c) + d*e^3)]","B",0
8,-2,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
9,-2,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
10,-2,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)*(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
11,-2,0,0,0.000000," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
12,-2,0,0,0.000000," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
13,-2,0,0,0.000000," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
14,-2,0,0,0.000000," ","integrate((a+a*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
15,1,535,0,0.950662," ","integrate((e*cot(d*x+c))^(5/2)*(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{2} {\left(a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{3} e^{2}\right)} \sqrt{-e} \log\left(-\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 2 \, {\left(721 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 1330 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right) + 469 \, a^{3} e^{2} - 15 \, {\left(23 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right) - 5 \, a^{3} e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{315 \, {\left(d \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x + 2 \, c\right) + d\right)}}, \frac{2 \, {\left(315 \, \sqrt{2} {\left(a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{3} e^{2}\right)} \sqrt{e} \arctan\left(-\frac{\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + {\left(721 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 1330 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right) + 469 \, a^{3} e^{2} - 15 \, {\left(23 \, a^{3} e^{2} \cos\left(2 \, d x + 2 \, c\right) - 5 \, a^{3} e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{315 \, {\left(d \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, d \cos\left(2 \, d x + 2 \, c\right) + d\right)}}\right]"," ",0,"[1/315*(315*sqrt(2)*(a^3*e^2*cos(2*d*x + 2*c)^2 - 2*a^3*e^2*cos(2*d*x + 2*c) + a^3*e^2)*sqrt(-e)*log(-sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*e*sin(2*d*x + 2*c) + e) + 2*(721*a^3*e^2*cos(2*d*x + 2*c)^2 - 1330*a^3*e^2*cos(2*d*x + 2*c) + 469*a^3*e^2 - 15*(23*a^3*e^2*cos(2*d*x + 2*c) - 5*a^3*e^2)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*cos(2*d*x + 2*c)^2 - 2*d*cos(2*d*x + 2*c) + d), 2/315*(315*sqrt(2)*(a^3*e^2*cos(2*d*x + 2*c)^2 - 2*a^3*e^2*cos(2*d*x + 2*c) + a^3*e^2)*sqrt(e)*arctan(-1/2*sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + (721*a^3*e^2*cos(2*d*x + 2*c)^2 - 1330*a^3*e^2*cos(2*d*x + 2*c) + 469*a^3*e^2 - 15*(23*a^3*e^2*cos(2*d*x + 2*c) - 5*a^3*e^2)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*cos(2*d*x + 2*c)^2 - 2*d*cos(2*d*x + 2*c) + d)]","A",0
16,1,487,0,0.723162," ","integrate((e*cot(d*x+c))^(3/2)*(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right) - a^{3} e\right)} \sqrt{e} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(55 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right)^{2} - 30 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) - 85 \, a^{3} e - 21 \, {\left(13 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) - 7 \, a^{3} e\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{105 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)} \sin\left(2 \, d x + 2 \, c\right)}, \frac{2 \, {\left(105 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right) - a^{3} e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(55 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right)^{2} - 30 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) - 85 \, a^{3} e - 21 \, {\left(13 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) - 7 \, a^{3} e\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{105 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)} \sin\left(2 \, d x + 2 \, c\right)}\right]"," ",0,"[1/105*(105*sqrt(2)*(a^3*e*cos(2*d*x + 2*c) - a^3*e)*sqrt(e)*log(sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1) + 2*e*sin(2*d*x + 2*c) + e)*sin(2*d*x + 2*c) - 2*(55*a^3*e*cos(2*d*x + 2*c)^2 - 30*a^3*e*cos(2*d*x + 2*c) - 85*a^3*e - 21*(13*a^3*e*cos(2*d*x + 2*c) - 7*a^3*e)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/((d*cos(2*d*x + 2*c) - d)*sin(2*d*x + 2*c)), 2/105*(105*sqrt(2)*(a^3*e*cos(2*d*x + 2*c) - a^3*e)*sqrt(-e)*arctan(1/2*sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e))*sin(2*d*x + 2*c) - (55*a^3*e*cos(2*d*x + 2*c)^2 - 30*a^3*e*cos(2*d*x + 2*c) - 85*a^3*e - 21*(13*a^3*e*cos(2*d*x + 2*c) - 7*a^3*e)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/((d*cos(2*d*x + 2*c) - d)*sin(2*d*x + 2*c))]","A",0
17,1,366,0,0.717800," ","integrate((e*cot(d*x+c))^(1/2)*(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) - a^{3}\right)} \sqrt{-e} \log\left(\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) - 2 \, {\left(9 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) - 5 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) - 11 \, a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{5 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)}}, -\frac{2 \, {\left(5 \, \sqrt{2} {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) - a^{3}\right)} \sqrt{e} \arctan\left(-\frac{\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + {\left(9 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) - 5 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) - 11 \, a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{5 \, {\left(d \cos\left(2 \, d x + 2 \, c\right) - d\right)}}\right]"," ",0,"[1/5*(5*sqrt(2)*(a^3*cos(2*d*x + 2*c) - a^3)*sqrt(-e)*log(sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*e*sin(2*d*x + 2*c) + e) - 2*(9*a^3*cos(2*d*x + 2*c) - 5*a^3*sin(2*d*x + 2*c) - 11*a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*cos(2*d*x + 2*c) - d), -2/5*(5*sqrt(2)*(a^3*cos(2*d*x + 2*c) - a^3)*sqrt(e)*arctan(-1/2*sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + (9*a^3*cos(2*d*x + 2*c) - 5*a^3*sin(2*d*x + 2*c) - 11*a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*cos(2*d*x + 2*c) - d)]","A",0
18,1,349,0,0.840650," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} a^{3} \sqrt{e} \log\left(-\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)}}{\sqrt{e}} + 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right) \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) + 9 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) + a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{3 \, d e \sin\left(2 \, d x + 2 \, c\right)}, -\frac{2 \, {\left(3 \, \sqrt{2} a^{3} e \sqrt{-\frac{1}{e}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) + 9 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) + a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{3 \, d e \sin\left(2 \, d x + 2 \, c\right)}\right]"," ",0,"[1/3*(3*sqrt(2)*a^3*sqrt(e)*log(-sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1)/sqrt(e) + 2*sin(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) - 2*(a^3*cos(2*d*x + 2*c) + 9*a^3*sin(2*d*x + 2*c) + a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e*sin(2*d*x + 2*c)), -2/3*(3*sqrt(2)*a^3*e*sqrt(-1/e)*arctan(1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(cos(2*d*x + 2*c) + 1))*sin(2*d*x + 2*c) + (a^3*cos(2*d*x + 2*c) + 9*a^3*sin(2*d*x + 2*c) + a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e*sin(2*d*x + 2*c))]","A",0
19,1,372,0,0.665413," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \sqrt{-\frac{1}{e}} \log\left(-\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right) - 2 \, {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) - a^{3} \sin\left(2 \, d x + 2 \, c\right) + a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{d e^{2} \cos\left(2 \, d x + 2 \, c\right) + d e^{2}}, \frac{2 \, {\left(\frac{\sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right)}{\sqrt{e}} - {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) - a^{3} \sin\left(2 \, d x + 2 \, c\right) + a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{d e^{2} \cos\left(2 \, d x + 2 \, c\right) + d e^{2}}\right]"," ",0,"[(sqrt(2)*(a^3*e*cos(2*d*x + 2*c) + a^3*e)*sqrt(-1/e)*log(-sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*sin(2*d*x + 2*c) + 1) - 2*(a^3*cos(2*d*x + 2*c) - a^3*sin(2*d*x + 2*c) + a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^2*cos(2*d*x + 2*c) + d*e^2), 2*(sqrt(2)*(a^3*e*cos(2*d*x + 2*c) + a^3*e)*arctan(-1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(sqrt(e)*(cos(2*d*x + 2*c) + 1)))/sqrt(e) - (a^3*cos(2*d*x + 2*c) - a^3*sin(2*d*x + 2*c) + a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^2*cos(2*d*x + 2*c) + d*e^2)]","A",0
20,1,378,0,1.540107," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{\frac{3 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \log\left(\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)}}{\sqrt{e}} + 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right)}{\sqrt{e}} - 2 \, {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) - 9 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) - a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{3 \, {\left(d e^{3} \cos\left(2 \, d x + 2 \, c\right) + d e^{3}\right)}}, \frac{2 \, {\left(3 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \sqrt{-\frac{1}{e}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right) - {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right) - 9 \, a^{3} \sin\left(2 \, d x + 2 \, c\right) - a^{3}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{3 \, {\left(d e^{3} \cos\left(2 \, d x + 2 \, c\right) + d e^{3}\right)}}\right]"," ",0,"[1/3*(3*sqrt(2)*(a^3*e*cos(2*d*x + 2*c) + a^3*e)*log(sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1)/sqrt(e) + 2*sin(2*d*x + 2*c) + 1)/sqrt(e) - 2*(a^3*cos(2*d*x + 2*c) - 9*a^3*sin(2*d*x + 2*c) - a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^3*cos(2*d*x + 2*c) + d*e^3), 2/3*(3*sqrt(2)*(a^3*e*cos(2*d*x + 2*c) + a^3*e)*sqrt(-1/e)*arctan(1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(cos(2*d*x + 2*c) + 1)) - (a^3*cos(2*d*x + 2*c) - 9*a^3*sin(2*d*x + 2*c) - a^3)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^3*cos(2*d*x + 2*c) + d*e^3)]","A",0
21,1,485,0,0.453817," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x, algorithm=""fricas"")","\left[\frac{5 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \sqrt{-\frac{1}{e}} \log\left(\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right) - 2 \, {\left(5 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} - 5 \, a^{3} - {\left(9 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) + 11 \, a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{5 \, {\left(d e^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, d e^{4} \cos\left(2 \, d x + 2 \, c\right) + d e^{4}\right)}}, -\frac{2 \, {\left(\frac{5 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right)}{\sqrt{e}} + {\left(5 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} - 5 \, a^{3} - {\left(9 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) + 11 \, a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{5 \, {\left(d e^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, d e^{4} \cos\left(2 \, d x + 2 \, c\right) + d e^{4}\right)}}\right]"," ",0,"[1/5*(5*sqrt(2)*(a^3*e*cos(2*d*x + 2*c)^2 + 2*a^3*e*cos(2*d*x + 2*c) + a^3*e)*sqrt(-1/e)*log(sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*sin(2*d*x + 2*c) + 1) - 2*(5*a^3*cos(2*d*x + 2*c)^2 - 5*a^3 - (9*a^3*cos(2*d*x + 2*c) + 11*a^3)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^4*cos(2*d*x + 2*c)^2 + 2*d*e^4*cos(2*d*x + 2*c) + d*e^4), -2/5*(5*sqrt(2)*(a^3*e*cos(2*d*x + 2*c)^2 + 2*a^3*e*cos(2*d*x + 2*c) + a^3*e)*arctan(-1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(sqrt(e)*(cos(2*d*x + 2*c) + 1)))/sqrt(e) + (5*a^3*cos(2*d*x + 2*c)^2 - 5*a^3 - (9*a^3*cos(2*d*x + 2*c) + 11*a^3)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^4*cos(2*d*x + 2*c)^2 + 2*d*e^4*cos(2*d*x + 2*c) + d*e^4)]","A",0
22,1,514,0,0.865164," ","integrate((a+a*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x, algorithm=""fricas"")","\left[\frac{\frac{105 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \log\left(-\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)}}{\sqrt{e}} + 2 \, \sin\left(2 \, d x + 2 \, c\right) + 1\right)}{\sqrt{e}} - 2 \, {\left(55 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + 30 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) - 85 \, a^{3} + 21 \, {\left(13 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) + 7 \, a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{105 \, {\left(d e^{5} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, d e^{5} \cos\left(2 \, d x + 2 \, c\right) + d e^{5}\right)}}, -\frac{2 \, {\left(105 \, \sqrt{2} {\left(a^{3} e \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{3} e \cos\left(2 \, d x + 2 \, c\right) + a^{3} e\right)} \sqrt{-\frac{1}{e}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sqrt{-\frac{1}{e}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)}}\right) + {\left(55 \, a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + 30 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) - 85 \, a^{3} + 21 \, {\left(13 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) + 7 \, a^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}\right)}}{105 \, {\left(d e^{5} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, d e^{5} \cos\left(2 \, d x + 2 \, c\right) + d e^{5}\right)}}\right]"," ",0,"[1/105*(105*sqrt(2)*(a^3*e*cos(2*d*x + 2*c)^2 + 2*a^3*e*cos(2*d*x + 2*c) + a^3*e)*log(-sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1)/sqrt(e) + 2*sin(2*d*x + 2*c) + 1)/sqrt(e) - 2*(55*a^3*cos(2*d*x + 2*c)^2 + 30*a^3*cos(2*d*x + 2*c) - 85*a^3 + 21*(13*a^3*cos(2*d*x + 2*c) + 7*a^3)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^5*cos(2*d*x + 2*c)^2 + 2*d*e^5*cos(2*d*x + 2*c) + d*e^5), -2/105*(105*sqrt(2)*(a^3*e*cos(2*d*x + 2*c)^2 + 2*a^3*e*cos(2*d*x + 2*c) + a^3*e)*sqrt(-1/e)*arctan(1/2*sqrt(2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sqrt(-1/e)*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(cos(2*d*x + 2*c) + 1)) + (55*a^3*cos(2*d*x + 2*c)^2 + 30*a^3*cos(2*d*x + 2*c) - 85*a^3 + 21*(13*a^3*cos(2*d*x + 2*c) + 7*a^3)*sin(2*d*x + 2*c))*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(d*e^5*cos(2*d*x + 2*c)^2 + 2*d*e^5*cos(2*d*x + 2*c) + d*e^5)]","A",0
23,1,400,0,0.899427," ","integrate((e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-e} e^{2} \log\left({\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - \sqrt{2}\right)} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 2 \, \sqrt{-e} e^{2} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) - 8 \, e^{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{4 \, a d}, -\frac{\sqrt{2} e^{\frac{5}{2}} \arctan\left(-\frac{{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) - 2 \, e^{\frac{5}{2}} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) + 4 \, e^{2} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, a d}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(-e)*e^2*log((sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)*sin(2*d*x + 2*c) - sqrt(2))*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)) - 2*e*sin(2*d*x + 2*c) + e) + 2*sqrt(-e)*e^2*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) - 8*e^2*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a*d), -1/2*(sqrt(2)*e^(5/2)*arctan(-1/2*(sqrt(2)*cos(2*d*x + 2*c) - sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/(e*cos(2*d*x + 2*c) + e)) - 2*e^(5/2)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) + 4*e^2*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a*d)]","A",0
24,1,333,0,0.791768," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-e} e \arctan\left(\frac{{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) - \sqrt{-e} e \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right)}{2 \, a d}, \frac{\sqrt{2} e^{\frac{3}{2}} \log\left(-{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - \sqrt{2}\right)} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) - 4 \, e^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right)}{4 \, a d}\right]"," ",0,"[-1/2*(sqrt(2)*sqrt(-e)*e*arctan(1/2*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/(e*cos(2*d*x + 2*c) + e)) - sqrt(-e)*e*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) - 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)))/(a*d), 1/4*(sqrt(2)*e^(3/2)*log(-(sqrt(2)*cos(2*d*x + 2*c) - sqrt(2)*sin(2*d*x + 2*c) - sqrt(2))*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)) + 2*e*sin(2*d*x + 2*c) + e) - 4*e^(3/2)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)))/(a*d)]","A",0
25,1,331,0,0.841275," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-e} \log\left(-{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - \sqrt{2}\right)} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 2 \, \sqrt{-e} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right)}{4 \, a d}, \frac{\sqrt{2} \sqrt{e} \arctan\left(-\frac{{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 2 \, \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right)}{2 \, a d}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(-e)*log(-(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)*sin(2*d*x + 2*c) - sqrt(2))*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)) - 2*e*sin(2*d*x + 2*c) + e) + 2*sqrt(-e)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)))/(a*d), 1/2*(sqrt(2)*sqrt(e)*arctan(-1/2*(sqrt(2)*cos(2*d*x + 2*c) - sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/(e*cos(2*d*x + 2*c) + e)) + 2*sqrt(e)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)))/(a*d)]","A",0
26,1,321,0,0.623621," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-e} \arctan\left(\frac{\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) - \sqrt{-e} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right)}{2 \, a d e}, \frac{\sqrt{2} \sqrt{e} \log\left(\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) - 4 \, \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right)}{4 \, a d e}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(-e)*arctan(1/2*sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) - sqrt(-e)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)))/(a*d*e), 1/4*(sqrt(2)*sqrt(e)*log(sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1) + 2*e*sin(2*d*x + 2*c) + e) - 4*sqrt(e)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)))/(a*d*e)]","A",0
27,1,472,0,1.134223," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(-\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 2 \, \sqrt{-e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) - 8 \, \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right)}{4 \, {\left(a d e^{2} \cos\left(2 \, d x + 2 \, c\right) + a d e^{2}\right)}}, -\frac{\sqrt{2} \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(-\frac{\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) - 2 \, \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) - 4 \, \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right)}{2 \, {\left(a d e^{2} \cos\left(2 \, d x + 2 \, c\right) + a d e^{2}\right)}}\right]"," ",0,"[-1/4*(sqrt(2)*sqrt(-e)*(cos(2*d*x + 2*c) + 1)*log(-sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*e*sin(2*d*x + 2*c) + e) + 2*sqrt(-e)*(cos(2*d*x + 2*c) + 1)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) - 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) - 8*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c))/(a*d*e^2*cos(2*d*x + 2*c) + a*d*e^2), -1/2*(sqrt(2)*sqrt(e)*(cos(2*d*x + 2*c) + 1)*arctan(-1/2*sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) - 2*sqrt(e)*(cos(2*d*x + 2*c) + 1)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) - 4*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c))/(a*d*e^2*cos(2*d*x + 2*c) + a*d*e^2)]","B",0
28,1,500,0,0.935429," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} \sqrt{-e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 3 \, \sqrt{-e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) + 4 \, \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + 3 \, \sin\left(2 \, d x + 2 \, c\right) - 1\right)}}{6 \, {\left(a d e^{3} \cos\left(2 \, d x + 2 \, c\right) + a d e^{3}\right)}}, \frac{3 \, \sqrt{2} \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) - 12 \, \sqrt{e} {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) - 8 \, \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + 3 \, \sin\left(2 \, d x + 2 \, c\right) - 1\right)}}{12 \, {\left(a d e^{3} \cos\left(2 \, d x + 2 \, c\right) + a d e^{3}\right)}}\right]"," ",0,"[-1/6*(3*sqrt(2)*sqrt(-e)*(cos(2*d*x + 2*c) + 1)*arctan(1/2*sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + 3*sqrt(-e)*(cos(2*d*x + 2*c) + 1)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) + 4*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + 3*sin(2*d*x + 2*c) - 1))/(a*d*e^3*cos(2*d*x + 2*c) + a*d*e^3), 1/12*(3*sqrt(2)*sqrt(e)*(cos(2*d*x + 2*c) + 1)*log(-sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1) + 2*e*sin(2*d*x + 2*c) + e) - 12*sqrt(e)*(cos(2*d*x + 2*c) + 1)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) - 8*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + 3*sin(2*d*x + 2*c) - 1))/(a*d*e^3*cos(2*d*x + 2*c) + a*d*e^3)]","A",0
29,-2,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
30,-2,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
31,-2,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
32,-2,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
33,-2,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
34,-2,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
35,1,567,0,0.465283," ","integrate((e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(\sqrt{2} e^{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} e^{2}\right)} \sqrt{-e} \arctan\left(\frac{{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) - {\left(e^{2} \sin\left(2 \, d x + 2 \, c\right) + e^{2}\right)} \sqrt{-e} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) - {\left(3 \, e^{2} \cos\left(2 \, d x + 2 \, c\right) - 5 \, e^{2} \sin\left(2 \, d x + 2 \, c\right) - 3 \, e^{2}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{16 \, {\left(a^{3} d \sin\left(2 \, d x + 2 \, c\right) + a^{3} d\right)}}, -\frac{2 \, {\left(e^{2} \sin\left(2 \, d x + 2 \, c\right) + e^{2}\right)} \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) - 2 \, {\left(\sqrt{2} e^{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} e^{2}\right)} \sqrt{e} \log\left(-{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - \sqrt{2}\right)} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) - {\left(3 \, e^{2} \cos\left(2 \, d x + 2 \, c\right) - 5 \, e^{2} \sin\left(2 \, d x + 2 \, c\right) - 3 \, e^{2}\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{16 \, {\left(a^{3} d \sin\left(2 \, d x + 2 \, c\right) + a^{3} d\right)}}\right]"," ",0,"[-1/16*(4*(sqrt(2)*e^2*sin(2*d*x + 2*c) + sqrt(2)*e^2)*sqrt(-e)*arctan(1/2*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/(e*cos(2*d*x + 2*c) + e)) - (e^2*sin(2*d*x + 2*c) + e^2)*sqrt(-e)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) - 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) - (3*e^2*cos(2*d*x + 2*c) - 5*e^2*sin(2*d*x + 2*c) - 3*e^2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*sin(2*d*x + 2*c) + a^3*d), -1/16*(2*(e^2*sin(2*d*x + 2*c) + e^2)*sqrt(e)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) - 2*(sqrt(2)*e^2*sin(2*d*x + 2*c) + sqrt(2)*e^2)*sqrt(e)*log(-(sqrt(2)*cos(2*d*x + 2*c) - sqrt(2)*sin(2*d*x + 2*c) - sqrt(2))*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)) + 2*e*sin(2*d*x + 2*c) + e) - (3*e^2*cos(2*d*x + 2*c) - 5*e^2*sin(2*d*x + 2*c) - 3*e^2)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*sin(2*d*x + 2*c) + a^3*d)]","A",0
36,1,533,0,0.543253," ","integrate((e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(\sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} e\right)} \sqrt{-e} \log\left(-{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - \sqrt{2}\right)} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 5 \, {\left(e \sin\left(2 \, d x + 2 \, c\right) + e\right)} \sqrt{-e} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) + {\left(e \cos\left(2 \, d x + 2 \, c\right) + e \sin\left(2 \, d x + 2 \, c\right) - e\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{16 \, {\left(a^{3} d \sin\left(2 \, d x + 2 \, c\right) + a^{3} d\right)}}, \frac{4 \, {\left(\sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} e\right)} \sqrt{e} \arctan\left(-\frac{{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 10 \, {\left(e \sin\left(2 \, d x + 2 \, c\right) + e\right)} \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) + {\left(e \cos\left(2 \, d x + 2 \, c\right) + e \sin\left(2 \, d x + 2 \, c\right) - e\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{16 \, {\left(a^{3} d \sin\left(2 \, d x + 2 \, c\right) + a^{3} d\right)}}\right]"," ",0,"[1/16*(2*(sqrt(2)*e*sin(2*d*x + 2*c) + sqrt(2)*e)*sqrt(-e)*log(-(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)*sin(2*d*x + 2*c) - sqrt(2))*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)) - 2*e*sin(2*d*x + 2*c) + e) + 5*(e*sin(2*d*x + 2*c) + e)*sqrt(-e)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) + (e*cos(2*d*x + 2*c) + e*sin(2*d*x + 2*c) - e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*sin(2*d*x + 2*c) + a^3*d), 1/16*(4*(sqrt(2)*e*sin(2*d*x + 2*c) + sqrt(2)*e)*sqrt(e)*arctan(-1/2*(sqrt(2)*cos(2*d*x + 2*c) - sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/(e*cos(2*d*x + 2*c) + e)) + 10*(e*sin(2*d*x + 2*c) + e)*sqrt(e)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) + (e*cos(2*d*x + 2*c) + e*sin(2*d*x + 2*c) - e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*sin(2*d*x + 2*c) + a^3*d)]","A",0
37,1,518,0,0.533803," ","integrate((e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(\sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{-e} \arctan\left(\frac{{\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + \sqrt{-e} {\left(\sin\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) - \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) - 3 \, \sin\left(2 \, d x + 2 \, c\right) - 5\right)}}{16 \, {\left(a^{3} d \sin\left(2 \, d x + 2 \, c\right) + a^{3} d\right)}}, -\frac{2 \, \sqrt{e} {\left(\sin\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) - 2 \, {\left(\sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sqrt{e} \log\left({\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - \sqrt{2}\right)} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(5 \, \cos\left(2 \, d x + 2 \, c\right) - 3 \, \sin\left(2 \, d x + 2 \, c\right) - 5\right)}}{16 \, {\left(a^{3} d \sin\left(2 \, d x + 2 \, c\right) + a^{3} d\right)}}\right]"," ",0,"[1/16*(4*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(-e)*arctan(1/2*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/(e*cos(2*d*x + 2*c) + e)) + sqrt(-e)*(sin(2*d*x + 2*c) + 1)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) - 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) - sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(5*cos(2*d*x + 2*c) - 3*sin(2*d*x + 2*c) - 5))/(a^3*d*sin(2*d*x + 2*c) + a^3*d), -1/16*(2*sqrt(e)*(sin(2*d*x + 2*c) + 1)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) - 2*(sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*sqrt(e)*log((sqrt(2)*cos(2*d*x + 2*c) - sqrt(2)*sin(2*d*x + 2*c) - sqrt(2))*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)) + 2*e*sin(2*d*x + 2*c) + e) + sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(5*cos(2*d*x + 2*c) - 3*sin(2*d*x + 2*c) - 5))/(a^3*d*sin(2*d*x + 2*c) + a^3*d)]","A",0
38,1,504,0,0.450907," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{2} \sqrt{-e} {\left(\sin\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(-\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 11 \, \sqrt{-e} {\left(\sin\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) - \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(9 \, \cos\left(2 \, d x + 2 \, c\right) - 7 \, \sin\left(2 \, d x + 2 \, c\right) - 9\right)}}{16 \, {\left(a^{3} d e \sin\left(2 \, d x + 2 \, c\right) + a^{3} d e\right)}}, -\frac{4 \, \sqrt{2} \sqrt{e} {\left(\sin\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(-\frac{\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 22 \, \sqrt{e} {\left(\sin\left(2 \, d x + 2 \, c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) - \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(9 \, \cos\left(2 \, d x + 2 \, c\right) - 7 \, \sin\left(2 \, d x + 2 \, c\right) - 9\right)}}{16 \, {\left(a^{3} d e \sin\left(2 \, d x + 2 \, c\right) + a^{3} d e\right)}}\right]"," ",0,"[-1/16*(2*sqrt(2)*sqrt(-e)*(sin(2*d*x + 2*c) + 1)*log(-sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*e*sin(2*d*x + 2*c) + e) + 11*sqrt(-e)*(sin(2*d*x + 2*c) + 1)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) - sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(9*cos(2*d*x + 2*c) - 7*sin(2*d*x + 2*c) - 9))/(a^3*d*e*sin(2*d*x + 2*c) + a^3*d*e), -1/16*(4*sqrt(2)*sqrt(e)*(sin(2*d*x + 2*c) + 1)*arctan(-1/2*sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + 22*sqrt(e)*(sin(2*d*x + 2*c) + 1)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) - sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(9*cos(2*d*x + 2*c) - 7*sin(2*d*x + 2*c) - 9))/(a^3*d*e*sin(2*d*x + 2*c) + a^3*d*e)]","A",0
39,1,697,0,0.661694," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{2} {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) + 31 \, {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{-e} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) + {\left(45 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(11 \, \cos\left(2 \, d x + 2 \, c\right) + 43\right)} \sin\left(2 \, d x + 2 \, c\right) - 45\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{16 \, {\left(a^{3} d e^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{2} + {\left(a^{3} d e^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}, \frac{2 \, \sqrt{2} {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{e} \log\left(-\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) - 1\right)} + 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 62 \, {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) - {\left(45 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(11 \, \cos\left(2 \, d x + 2 \, c\right) + 43\right)} \sin\left(2 \, d x + 2 \, c\right) - 45\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{16 \, {\left(a^{3} d e^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{2} + {\left(a^{3} d e^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}\right]"," ",0,"[-1/16*(4*sqrt(2)*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(-e)*arctan(1/2*sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) + 31*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(-e)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) - 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) + (45*cos(2*d*x + 2*c)^2 - (11*cos(2*d*x + 2*c) + 43)*sin(2*d*x + 2*c) - 45)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*e^2*cos(2*d*x + 2*c) + a^3*d*e^2 + (a^3*d*e^2*cos(2*d*x + 2*c) + a^3*d*e^2)*sin(2*d*x + 2*c)), 1/16*(2*sqrt(2)*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(e)*log(-sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) - 1) + 2*e*sin(2*d*x + 2*c) + e) + 62*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(e)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) - (45*cos(2*d*x + 2*c)^2 - (11*cos(2*d*x + 2*c) + 43)*sin(2*d*x + 2*c) - 45)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*e^2*cos(2*d*x + 2*c) + a^3*d*e^2 + (a^3*d*e^2*cos(2*d*x + 2*c) + a^3*d*e^2)*sin(2*d*x + 2*c))]","B",0
40,1,718,0,0.480396," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+a*cot(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{2} {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{-e} \log\left(\sqrt{2} \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) - 1\right)} - 2 \, e \sin\left(2 \, d x + 2 \, c\right) + e\right) + 177 \, {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{-e} \log\left(\frac{e \cos\left(2 \, d x + 2 \, c\right) - e \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{-e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} \sin\left(2 \, d x + 2 \, c\right) + e}{\cos\left(2 \, d x + 2 \, c\right) + \sin\left(2 \, d x + 2 \, c\right) + 1}\right) - {\left(339 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 7 \, {\left(11 \, \cos\left(2 \, d x + 2 \, c\right) + 43\right)} \sin\left(2 \, d x + 2 \, c\right) - 32 \, \cos\left(2 \, d x + 2 \, c\right) - 307\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{48 \, {\left(a^{3} d e^{3} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{3} + {\left(a^{3} d e^{3} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}, \frac{12 \, \sqrt{2} {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{e} \arctan\left(-\frac{\sqrt{2} \sqrt{e} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}} {\left(\cos\left(2 \, d x + 2 \, c\right) - \sin\left(2 \, d x + 2 \, c\right) + 1\right)}}{2 \, {\left(e \cos\left(2 \, d x + 2 \, c\right) + e\right)}}\right) - 354 \, {\left({\left(\cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) + \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{e} \arctan\left(\frac{\sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{\sqrt{e}}\right) + {\left(339 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 7 \, {\left(11 \, \cos\left(2 \, d x + 2 \, c\right) + 43\right)} \sin\left(2 \, d x + 2 \, c\right) - 32 \, \cos\left(2 \, d x + 2 \, c\right) - 307\right)} \sqrt{\frac{e \cos\left(2 \, d x + 2 \, c\right) + e}{\sin\left(2 \, d x + 2 \, c\right)}}}{48 \, {\left(a^{3} d e^{3} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{3} + {\left(a^{3} d e^{3} \cos\left(2 \, d x + 2 \, c\right) + a^{3} d e^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}\right]"," ",0,"[-1/48*(6*sqrt(2)*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(-e)*log(sqrt(2)*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) - 1) - 2*e*sin(2*d*x + 2*c) + e) + 177*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(-e)*log((e*cos(2*d*x + 2*c) - e*sin(2*d*x + 2*c) + 2*sqrt(-e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*sin(2*d*x + 2*c) + e)/(cos(2*d*x + 2*c) + sin(2*d*x + 2*c) + 1)) - (339*cos(2*d*x + 2*c)^2 - 7*(11*cos(2*d*x + 2*c) + 43)*sin(2*d*x + 2*c) - 32*cos(2*d*x + 2*c) - 307)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*e^3*cos(2*d*x + 2*c) + a^3*d*e^3 + (a^3*d*e^3*cos(2*d*x + 2*c) + a^3*d*e^3)*sin(2*d*x + 2*c)), 1/48*(12*sqrt(2)*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(e)*arctan(-1/2*sqrt(2)*sqrt(e)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))*(cos(2*d*x + 2*c) - sin(2*d*x + 2*c) + 1)/(e*cos(2*d*x + 2*c) + e)) - 354*((cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) + cos(2*d*x + 2*c) + 1)*sqrt(e)*arctan(sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c))/sqrt(e)) + (339*cos(2*d*x + 2*c)^2 - 7*(11*cos(2*d*x + 2*c) + 43)*sin(2*d*x + 2*c) - 32*cos(2*d*x + 2*c) - 307)*sqrt((e*cos(2*d*x + 2*c) + e)/sin(2*d*x + 2*c)))/(a^3*d*e^3*cos(2*d*x + 2*c) + a^3*d*e^3 + (a^3*d*e^3*cos(2*d*x + 2*c) + a^3*d*e^3)*sin(2*d*x + 2*c))]","A",0
41,-1,0,0,0.000000," ","integrate(cot(x)^2*(1+cot(x))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(cot(x)*(1+cot(x))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate(cot(x)^2*(1+cot(x))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,-1,0,0,0.000000," ","integrate(cot(x)*(1+cot(x))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,-1,0,0,0.000000," ","integrate(cot(x)^2/(1+cot(x))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate(cot(x)^2/(1+cot(x))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate(cot(x)^2/(1+cot(x))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^2/(e*cot(d*x+c))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)*(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)*(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^3/(e*cot(d*x+c))^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(9/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(7/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(5/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(1/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))^(3/2)/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,0,0,0,0.999706," ","integrate((a+b*cot(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cot\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((b*cot(d*x + c) + a)^n, x)","F",0
89,0,0,0,1.217840," ","integrate((a+b*cot(f*x+e))^m*(d*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cot\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*cot(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
90,1,159,0,0.709931," ","integrate((1+I*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} \log\left(\frac{1}{2} \, {\left(i \, a + b\right)} d \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} + \sqrt{\frac{{\left(a + i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} \log\left(\frac{1}{2} \, {\left(-i \, a - b\right)} d \sqrt{-\frac{4 i}{{\left(i \, a + b\right)} d^{2}}} + \sqrt{\frac{{\left(a + i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)"," ",0,"-1/2*sqrt(-4*I/((I*a + b)*d^2))*log(1/2*(I*a + b)*d*sqrt(-4*I/((I*a + b)*d^2)) + sqrt(((a + I*b)*e^(2*I*d*x + 2*I*c) - a + I*b)/(e^(2*I*d*x + 2*I*c) - 1))) + 1/2*sqrt(-4*I/((I*a + b)*d^2))*log(1/2*(-I*a - b)*d*sqrt(-4*I/((I*a + b)*d^2)) + sqrt(((a + I*b)*e^(2*I*d*x + 2*I*c) - a + I*b)/(e^(2*I*d*x + 2*I*c) - 1)))","B",0
91,1,159,0,0.590492," ","integrate((1-I*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} \log\left(\frac{1}{2} \, {\left(i \, a - b\right)} d \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} + \sqrt{\frac{{\left(a + i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right) - \frac{1}{2} \, \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} \log\left(\frac{1}{2} \, {\left(-i \, a + b\right)} d \sqrt{\frac{4 i}{{\left(-i \, a + b\right)} d^{2}}} + \sqrt{\frac{{\left(a + i \, b\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - a + i \, b}{e^{\left(2 i \, d x + 2 i \, c\right)} - 1}}\right)"," ",0,"1/2*sqrt(4*I/((-I*a + b)*d^2))*log(1/2*(I*a - b)*d*sqrt(4*I/((-I*a + b)*d^2)) + sqrt(((a + I*b)*e^(2*I*d*x + 2*I*c) - a + I*b)/(e^(2*I*d*x + 2*I*c) - 1))) - 1/2*sqrt(4*I/((-I*a + b)*d^2))*log(1/2*(-I*a + b)*d*sqrt(4*I/((-I*a + b)*d^2)) + sqrt(((a + I*b)*e^(2*I*d*x + 2*I*c) - a + I*b)/(e^(2*I*d*x + 2*I*c) - 1)))","B",0
92,1,79,0,0.545675," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A a + B b\right)} d x + {\left(B a - A b\right)} \log\left(a b \sin\left(2 \, d x + 2 \, c\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)}{2 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"1/2*(2*(A*a + B*b)*d*x + (B*a - A*b)*log(a*b*sin(2*d*x + 2*c) + 1/2*a^2 + 1/2*b^2 - 1/2*(a^2 - b^2)*cos(2*d*x + 2*c)))/((a^2 + b^2)*d)","A",0
93,1,340,0,0.558615," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B a^{2} b - 2 \, A a b^{2} + 2 \, {\left(A a^{2} b + 2 \, B a b^{2} - A b^{3}\right)} d x + 2 \, {\left(B a^{2} b - A a b^{2} + {\left(A a^{2} b + 2 \, B a b^{2} - A b^{3}\right)} d x\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(B a^{2} b - 2 \, A a b^{2} - B b^{3} + {\left(B a^{2} b - 2 \, A a b^{2} - B b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(B a^{3} - 2 \, A a^{2} b - B a b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \log\left(a b \sin\left(2 \, d x + 2 \, c\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right) - 2 \, {\left(B a b^{2} - A b^{3} - {\left(A a^{3} + 2 \, B a^{2} b - A a b^{2}\right)} d x\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sin\left(2 \, d x + 2 \, c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d\right)}}"," ",0,"1/2*(2*B*a^2*b - 2*A*a*b^2 + 2*(A*a^2*b + 2*B*a*b^2 - A*b^3)*d*x + 2*(B*a^2*b - A*a*b^2 + (A*a^2*b + 2*B*a*b^2 - A*b^3)*d*x)*cos(2*d*x + 2*c) + (B*a^2*b - 2*A*a*b^2 - B*b^3 + (B*a^2*b - 2*A*a*b^2 - B*b^3)*cos(2*d*x + 2*c) + (B*a^3 - 2*A*a^2*b - B*a*b^2)*sin(2*d*x + 2*c))*log(a*b*sin(2*d*x + 2*c) + 1/2*a^2 + 1/2*b^2 - 1/2*(a^2 - b^2)*cos(2*d*x + 2*c)) - 2*(B*a*b^2 - A*b^3 - (A*a^3 + 2*B*a^2*b - A*a*b^2)*d*x)*sin(2*d*x + 2*c))/((a^4*b + 2*a^2*b^3 + b^5)*d*cos(2*d*x + 2*c) + (a^5 + 2*a^3*b^2 + a*b^4)*d*sin(2*d*x + 2*c) + (a^4*b + 2*a^2*b^3 + b^5)*d)","B",0
94,1,549,0,0.707682," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} + 2 \, B a b^{4} - 2 \, A b^{5} - 2 \, {\left(A a^{5} + 3 \, B a^{4} b - 2 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} - 3 \, A a b^{4} - B b^{5}\right)} d x - 2 \, {\left(4 \, B a^{3} b^{2} - 6 \, A a^{2} b^{3} - 2 \, B a b^{4} - {\left(A a^{5} + 3 \, B a^{4} b - 4 \, A a^{3} b^{2} - 4 \, B a^{2} b^{3} + 3 \, A a b^{4} + B b^{5}\right)} d x\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(B a^{5} - 3 \, A a^{4} b - 2 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5} - {\left(B a^{5} - 3 \, A a^{4} b - 4 \, B a^{3} b^{2} + 4 \, A a^{2} b^{3} + 3 \, B a b^{4} - A b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + A a b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \log\left(a b \sin\left(2 \, d x + 2 \, c\right) + \frac{1}{2} \, a^{2} + \frac{1}{2} \, b^{2} - \frac{1}{2} \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right) - 2 \, {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 3 \, A a b^{4} + B b^{5} + 2 \, {\left(A a^{4} b + 3 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - B a b^{4}\right)} d x\right)} \sin\left(2 \, d x + 2 \, c\right)}{2 \, {\left({\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \sin\left(2 \, d x + 2 \, c\right) - {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} d\right)}}"," ",0,"1/2*(2*B*a^3*b^2 - 2*A*a^2*b^3 + 2*B*a*b^4 - 2*A*b^5 - 2*(A*a^5 + 3*B*a^4*b - 2*A*a^3*b^2 + 2*B*a^2*b^3 - 3*A*a*b^4 - B*b^5)*d*x - 2*(4*B*a^3*b^2 - 6*A*a^2*b^3 - 2*B*a*b^4 - (A*a^5 + 3*B*a^4*b - 4*A*a^3*b^2 - 4*B*a^2*b^3 + 3*A*a*b^4 + B*b^5)*d*x)*cos(2*d*x + 2*c) - (B*a^5 - 3*A*a^4*b - 2*B*a^3*b^2 - 2*A*a^2*b^3 - 3*B*a*b^4 + A*b^5 - (B*a^5 - 3*A*a^4*b - 4*B*a^3*b^2 + 4*A*a^2*b^3 + 3*B*a*b^4 - A*b^5)*cos(2*d*x + 2*c) + 2*(B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + A*a*b^4)*sin(2*d*x + 2*c))*log(a*b*sin(2*d*x + 2*c) + 1/2*a^2 + 1/2*b^2 - 1/2*(a^2 - b^2)*cos(2*d*x + 2*c)) - 2*(2*B*a^4*b - 3*A*a^3*b^2 - 3*B*a^2*b^3 + 3*A*a*b^4 + B*b^5 + 2*(A*a^4*b + 3*B*a^3*b^2 - 3*A*a^2*b^3 - B*a*b^4)*d*x)*sin(2*d*x + 2*c))/((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d*cos(2*d*x + 2*c) - 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*sin(2*d*x + 2*c) - (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*d)","B",0
95,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^(5/2)*(A+B*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^(3/2)*(A+B*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((a+b*cot(d*x+c))^(1/2)*(A+B*cot(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
