1,1,47,0,0.611240," ","integrate((b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\frac{b^{\frac{5}{2}} \tan\left(f x + e\right)^{4} - 2 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{2} + 2 \, b^{\frac{5}{2}} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{4 \, f}"," ",0,"1/4*(b^(5/2)*tan(f*x + e)^4 - 2*b^(5/2)*tan(f*x + e)^2 + 2*b^(5/2)*log(tan(f*x + e)^2 + 1))/f","A",0
2,1,34,0,0.825181," ","integrate((b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{b^{\frac{3}{2}} \tan\left(f x + e\right)^{2} - b^{\frac{3}{2}} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{2 \, f}"," ",0,"1/2*(b^(3/2)*tan(f*x + e)^2 - b^(3/2)*log(tan(f*x + e)^2 + 1))/f","A",0
3,1,19,0,0.688254," ","integrate((b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{2 \, f}"," ",0,"1/2*sqrt(b)*log(tan(f*x + e)^2 + 1)/f","A",0
4,1,33,0,0.647082," ","integrate(1/(b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\tan\left(f x + e\right)^{2} + 1\right)}{\sqrt{b}} - \frac{2 \, \log\left(\tan\left(f x + e\right)\right)}{\sqrt{b}}}{2 \, f}"," ",0,"-1/2*(log(tan(f*x + e)^2 + 1)/sqrt(b) - 2*log(tan(f*x + e))/sqrt(b))/f","A",0
5,1,46,0,0.990816," ","integrate(1/(b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{\frac{\log\left(\tan\left(f x + e\right)^{2} + 1\right)}{b^{\frac{3}{2}}} - \frac{2 \, \log\left(\tan\left(f x + e\right)\right)}{b^{\frac{3}{2}}} - \frac{1}{b^{\frac{3}{2}} \tan\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*(log(tan(f*x + e)^2 + 1)/b^(3/2) - 2*log(tan(f*x + e))/b^(3/2) - 1/(b^(3/2)*tan(f*x + e)^2))/f","A",0
6,1,66,0,1.214582," ","integrate(1/(b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{b^{\frac{5}{2}}} - \frac{4 \, \log\left(\tan\left(f x + e\right)\right)}{b^{\frac{5}{2}}} - \frac{2 \, \sqrt{b} \tan\left(f x + e\right)^{2} - \sqrt{b}}{b^{3} \tan\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"-1/4*(2*log(tan(f*x + e)^2 + 1)/b^(5/2) - 4*log(tan(f*x + e))/b^(5/2) - (2*sqrt(b)*tan(f*x + e)^2 - sqrt(b))/(b^3*tan(f*x + e)^4))/f","A",0
7,1,178,0,1.266287," ","integrate((b*tan(f*x+e)^3)^(5/2),x, algorithm=""maxima"")","\frac{360 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{\frac{13}{2}} - 520 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{\frac{9}{2}} + 936 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{\frac{5}{2}} + 585 \, {\left(2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + 2 \, \sqrt{2} \sqrt{b} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + \sqrt{2} \sqrt{b} \log\left(\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) - \sqrt{2} \sqrt{b} \log\left(-\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right)\right)} b^{2} - 4680 \, b^{\frac{5}{2}} \sqrt{\tan\left(f x + e\right)}}{2340 \, f}"," ",0,"1/2340*(360*b^(5/2)*tan(f*x + e)^(13/2) - 520*b^(5/2)*tan(f*x + e)^(9/2) + 936*b^(5/2)*tan(f*x + e)^(5/2) + 585*(2*sqrt(2)*sqrt(b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(f*x + e)))) + 2*sqrt(2)*sqrt(b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(f*x + e)))) + sqrt(2)*sqrt(b)*log(sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) - sqrt(2)*sqrt(b)*log(-sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1))*b^2 - 4680*b^(5/2)*sqrt(tan(f*x + e)))/f","A",0
8,1,140,0,0.807290," ","integrate((b*tan(f*x+e)^3)^(3/2),x, algorithm=""maxima"")","\frac{24 \, b^{\frac{3}{2}} \tan\left(f x + e\right)^{\frac{7}{2}} - 56 \, b^{\frac{3}{2}} \tan\left(f x + e\right)^{\frac{3}{2}} + 21 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right)\right)} b^{\frac{3}{2}}}{84 \, f}"," ",0,"1/84*(24*b^(3/2)*tan(f*x + e)^(7/2) - 56*b^(3/2)*tan(f*x + e)^(3/2) + 21*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(f*x + e)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(f*x + e)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1))*b^(3/2))/f","A",0
9,1,133,0,2.157535," ","integrate((b*tan(f*x+e)^3)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + 2 \, \sqrt{2} \sqrt{b} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + \sqrt{2} \sqrt{b} \log\left(\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) - \sqrt{2} \sqrt{b} \log\left(-\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) - 8 \, \sqrt{b} \sqrt{\tan\left(f x + e\right)}}{4 \, f}"," ",0,"-1/4*(2*sqrt(2)*sqrt(b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(f*x + e)))) + 2*sqrt(2)*sqrt(b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(f*x + e)))) + sqrt(2)*sqrt(b)*log(sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) - sqrt(2)*sqrt(b)*log(-sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) - 8*sqrt(b)*sqrt(tan(f*x + e)))/f","A",0
10,1,126,0,1.333182," ","integrate(1/(b*tan(f*x+e)^3)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right)}{\sqrt{b}} + \frac{8}{\sqrt{b} \sqrt{\tan\left(f x + e\right)}}}{4 \, f}"," ",0,"-1/4*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(f*x + e)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(f*x + e)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1))/sqrt(b) + 8/(sqrt(b)*sqrt(tan(f*x + e))))/f","A",0
11,1,163,0,3.344318," ","integrate(1/(b*tan(f*x+e)^3)^(3/2),x, algorithm=""maxima"")","\frac{\frac{21 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right)\right)}}{b^{\frac{3}{2}}} + \frac{8 \, {\left(21 \, \sqrt{\tan\left(f x + e\right)} + \frac{7}{\tan\left(f x + e\right)^{\frac{3}{2}}} - \frac{3}{\tan\left(f x + e\right)^{\frac{7}{2}}}\right)}}{b^{\frac{3}{2}}} - \frac{168 \, \sqrt{\tan\left(f x + e\right)}}{b^{\frac{3}{2}}}}{84 \, f}"," ",0,"1/84*(21*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(f*x + e)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(f*x + e)))) + sqrt(2)*log(sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) - sqrt(2)*log(-sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1))/b^(3/2) + 8*(21*sqrt(tan(f*x + e)) + 7/tan(f*x + e)^(3/2) - 3/tan(f*x + e)^(7/2))/b^(3/2) - 168*sqrt(tan(f*x + e))/b^(3/2))/f","A",0
12,1,172,0,1.916125," ","integrate(1/(b*tan(f*x+e)^3)^(5/2),x, algorithm=""maxima"")","\frac{\frac{585 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(f x + e\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(f x + e\right)} + \tan\left(f x + e\right) + 1\right)\right)}}{b^{\frac{5}{2}}} + \frac{8 \, {\left(\frac{585 \, \sqrt{b}}{\sqrt{\tan\left(f x + e\right)}} - \frac{117 \, \sqrt{b}}{\tan\left(f x + e\right)^{\frac{5}{2}}} + \frac{65 \, \sqrt{b}}{\tan\left(f x + e\right)^{\frac{9}{2}}} - \frac{45 \, \sqrt{b}}{\tan\left(f x + e\right)^{\frac{13}{2}}}\right)}}{b^{3}}}{2340 \, f}"," ",0,"1/2340*(585*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(f*x + e)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(f*x + e)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(f*x + e)) + tan(f*x + e) + 1))/b^(5/2) + 8*(585*sqrt(b)/sqrt(tan(f*x + e)) - 117*sqrt(b)/tan(f*x + e)^(5/2) + 65*sqrt(b)/tan(f*x + e)^(9/2) - 45*sqrt(b)/tan(f*x + e)^(13/2))/b^3)/f","A",0
13,1,79,0,0.948219," ","integrate((b*tan(f*x+e)^4)^(5/2),x, algorithm=""maxima"")","\frac{35 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{9} - 45 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{7} + 63 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{5} - 105 \, b^{\frac{5}{2}} \tan\left(f x + e\right)^{3} - 315 \, {\left(f x + e\right)} b^{\frac{5}{2}} + 315 \, b^{\frac{5}{2}} \tan\left(f x + e\right)}{315 \, f}"," ",0,"1/315*(35*b^(5/2)*tan(f*x + e)^9 - 45*b^(5/2)*tan(f*x + e)^7 + 63*b^(5/2)*tan(f*x + e)^5 - 105*b^(5/2)*tan(f*x + e)^3 - 315*(f*x + e)*b^(5/2) + 315*b^(5/2)*tan(f*x + e))/f","A",0
14,1,53,0,0.850294," ","integrate((b*tan(f*x+e)^4)^(3/2),x, algorithm=""maxima"")","\frac{3 \, b^{\frac{3}{2}} \tan\left(f x + e\right)^{5} - 5 \, b^{\frac{3}{2}} \tan\left(f x + e\right)^{3} - 15 \, {\left(f x + e\right)} b^{\frac{3}{2}} + 15 \, b^{\frac{3}{2}} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*b^(3/2)*tan(f*x + e)^5 - 5*b^(3/2)*tan(f*x + e)^3 - 15*(f*x + e)*b^(3/2) + 15*b^(3/2)*tan(f*x + e))/f","A",0
15,1,26,0,1.012009," ","integrate((b*tan(f*x+e)^4)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(f x + e\right)} \sqrt{b} - \sqrt{b} \tan\left(f x + e\right)}{f}"," ",0,"-((f*x + e)*sqrt(b) - sqrt(b)*tan(f*x + e))/f","A",0
16,1,27,0,1.192402," ","integrate(1/(b*tan(f*x+e)^4)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{f x + e}{\sqrt{b}} + \frac{1}{\sqrt{b} \tan\left(f x + e\right)}}{f}"," ",0,"-((f*x + e)/sqrt(b) + 1/(sqrt(b)*tan(f*x + e)))/f","A",0
17,1,50,0,0.877786," ","integrate(1/(b*tan(f*x+e)^4)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(f x + e\right)}}{b^{\frac{3}{2}}} + \frac{15 \, \tan\left(f x + e\right)^{4} - 5 \, \tan\left(f x + e\right)^{2} + 3}{b^{\frac{3}{2}} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*(f*x + e)/b^(3/2) + (15*tan(f*x + e)^4 - 5*tan(f*x + e)^2 + 3)/(b^(3/2)*tan(f*x + e)^5))/f","A",0
18,1,70,0,0.684122," ","integrate(1/(b*tan(f*x+e)^4)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{315 \, {\left(f x + e\right)}}{b^{\frac{5}{2}}} + \frac{315 \, \tan\left(f x + e\right)^{8} - 105 \, \tan\left(f x + e\right)^{6} + 63 \, \tan\left(f x + e\right)^{4} - 45 \, \tan\left(f x + e\right)^{2} + 35}{b^{\frac{5}{2}} \tan\left(f x + e\right)^{9}}}{315 \, f}"," ",0,"-1/315*(315*(f*x + e)/b^(5/2) + (315*tan(f*x + e)^8 - 105*tan(f*x + e)^6 + 63*tan(f*x + e)^4 - 45*tan(f*x + e)^2 + 35)/(b^(5/2)*tan(f*x + e)^9))/f","A",0
19,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^n)^(5/2),x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{n}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n)^(5/2), x)","F",0
20,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^n)^(3/2),x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{n}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n)^(3/2), x)","F",0
21,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^n)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{n}}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^n), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)^n)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(f x + e\right)^{n}}}\,{d x}"," ",0,"integrate(1/sqrt(b*tan(f*x + e)^n), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)^n)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \tan\left(f x + e\right)^{n}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n)^(-3/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)^n)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(b \tan\left(f x + e\right)^{n}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n)^(-5/2), x)","F",0
25,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^n)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{n}\right)^{p}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n)^p, x)","F",0
26,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p, x)","F",0
27,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^3)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{3}\right)^{p}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^3)^p, x)","F",0
28,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^4)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{4}\right)^{p}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^4)^p, x)","F",0
29,0,0,0,0.000000," ","integrate((b*tan(f*x+e)^n)^(1/n),x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{n}\right)^{\left(\frac{1}{n}\right)}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n)^(1/n), x)","F",0
30,1,62,0,0.723738," ","integrate(sin(f*x+e)^5*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{3 \, {\left(a - b\right)} \cos\left(f x + e\right)^{5} - 5 \, {\left(2 \, a - 3 \, b\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a - 3 \, b\right)} \cos\left(f x + e\right) - \frac{15 \, b}{\cos\left(f x + e\right)}}{15 \, f}"," ",0,"-1/15*(3*(a - b)*cos(f*x + e)^5 - 5*(2*a - 3*b)*cos(f*x + e)^3 + 15*(a - 3*b)*cos(f*x + e) - 15*b/cos(f*x + e))/f","A",0
31,1,44,0,0.307139," ","integrate(sin(f*x+e)^3*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(a - b\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(a - 2 \, b\right)} \cos\left(f x + e\right) + \frac{3 \, b}{\cos\left(f x + e\right)}}{3 \, f}"," ",0,"1/3*((a - b)*cos(f*x + e)^3 - 3*(a - 2*b)*cos(f*x + e) + 3*b/cos(f*x + e))/f","A",0
32,1,31,0,0.750813," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{b {\left(\frac{1}{\cos\left(f x + e\right)} + \cos\left(f x + e\right)\right)} - a \cos\left(f x + e\right)}{f}"," ",0,"(b*(1/cos(f*x + e) + cos(f*x + e)) - a*cos(f*x + e))/f","A",0
33,1,40,0,0.672051," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{a \log\left(\cos\left(f x + e\right) + 1\right) - a \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, b}{\cos\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(a*log(cos(f*x + e) + 1) - a*log(cos(f*x + e) - 1) - 2*b/cos(f*x + e))/f","A",0
34,1,76,0,0.461333," ","integrate(csc(f*x+e)^3*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(a + 2 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right) - {\left(a + 2 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left({\left(a + 2 \, b\right)} \cos\left(f x + e\right)^{2} - 2 \, b\right)}}{\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)}}{4 \, f}"," ",0,"-1/4*((a + 2*b)*log(cos(f*x + e) + 1) - (a + 2*b)*log(cos(f*x + e) - 1) - 2*((a + 2*b)*cos(f*x + e)^2 - 2*b)/(cos(f*x + e)^3 - cos(f*x + e)))/f","A",0
35,1,101,0,0.580407," ","integrate(csc(f*x+e)^5*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{3 \, {\left(a + 4 \, b\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(a + 4 \, b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(a + 4 \, b\right)} \cos\left(f x + e\right)^{4} - 5 \, {\left(a + 4 \, b\right)} \cos\left(f x + e\right)^{2} + 8 \, b\right)}}{\cos\left(f x + e\right)^{5} - 2 \, \cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)}}{16 \, f}"," ",0,"-1/16*(3*(a + 4*b)*log(cos(f*x + e) + 1) - 3*(a + 4*b)*log(cos(f*x + e) - 1) - 2*(3*(a + 4*b)*cos(f*x + e)^4 - 5*(a + 4*b)*cos(f*x + e)^2 + 8*b)/(cos(f*x + e)^5 - 2*cos(f*x + e)^3 + cos(f*x + e)))/f","A",0
36,1,111,0,0.643814," ","integrate(sin(f*x+e)^6*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, {\left(f x + e\right)} {\left(a - 7 \, b\right)} + 48 \, b \tan\left(f x + e\right) - \frac{3 \, {\left(11 \, a - 29 \, b\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a - 17 \, b\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(5 \, a - 19 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{6} + 3 \, \tan\left(f x + e\right)^{4} + 3 \, \tan\left(f x + e\right)^{2} + 1}}{48 \, f}"," ",0,"1/48*(15*(f*x + e)*(a - 7*b) + 48*b*tan(f*x + e) - (3*(11*a - 29*b)*tan(f*x + e)^5 + 8*(5*a - 17*b)*tan(f*x + e)^3 + 3*(5*a - 19*b)*tan(f*x + e))/(tan(f*x + e)^6 + 3*tan(f*x + e)^4 + 3*tan(f*x + e)^2 + 1))/f","A",0
37,1,82,0,0.808562," ","integrate(sin(f*x+e)^4*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} {\left(a - 5 \, b\right)} + 8 \, b \tan\left(f x + e\right) - \frac{{\left(5 \, a - 9 \, b\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a - 7 \, b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{8 \, f}"," ",0,"1/8*(3*(f*x + e)*(a - 5*b) + 8*b*tan(f*x + e) - ((5*a - 9*b)*tan(f*x + e)^3 + (3*a - 7*b)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
38,1,51,0,1.003688," ","integrate(sin(f*x+e)^2*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{{\left(f x + e\right)} {\left(a - 3 \, b\right)} + 2 \, b \tan\left(f x + e\right) - \frac{{\left(a - b\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}}{2 \, f}"," ",0,"1/2*((f*x + e)*(a - 3*b) + 2*b*tan(f*x + e) - (a - b)*tan(f*x + e)/(tan(f*x + e)^2 + 1))/f","A",0
39,1,23,0,0.749051," ","integrate(a+b*tan(f*x+e)^2,x, algorithm=""maxima"")","a x - \frac{{\left(f x + e - \tan\left(f x + e\right)\right)} b}{f}"," ",0,"a*x - (f*x + e - tan(f*x + e))*b/f","A",0
40,1,24,0,0.572166," ","integrate(csc(f*x+e)^2*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{b \tan\left(f x + e\right) - \frac{a}{\tan\left(f x + e\right)}}{f}"," ",0,"(b*tan(f*x + e) - a/tan(f*x + e))/f","A",0
41,1,40,0,0.480334," ","integrate(csc(f*x+e)^4*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(f x + e\right) - \frac{3 \, {\left(a + b\right)} \tan\left(f x + e\right)^{2} + a}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*b*tan(f*x + e) - (3*(a + b)*tan(f*x + e)^2 + a)/tan(f*x + e)^3)/f","A",0
42,1,59,0,0.629805," ","integrate(csc(f*x+e)^6*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, b \tan\left(f x + e\right) - \frac{15 \, {\left(a + 2 \, b\right)} \tan\left(f x + e\right)^{4} + 5 \, {\left(2 \, a + b\right)} \tan\left(f x + e\right)^{2} + 3 \, a}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*b*tan(f*x + e) - (15*(a + 2*b)*tan(f*x + e)^4 + 5*(2*a + b)*tan(f*x + e)^2 + 3*a)/tan(f*x + e)^5)/f","A",0
43,1,104,0,0.438302," ","integrate(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(f x + e\right)^{5} - 10 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \cos\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 6 \, a b + 6 \, b^{2}\right)} \cos\left(f x + e\right) - \frac{5 \, {\left(6 \, {\left(a b - 2 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + b^{2}\right)}}{\cos\left(f x + e\right)^{3}}}{15 \, f}"," ",0,"-1/15*(3*(a^2 - 2*a*b + b^2)*cos(f*x + e)^5 - 10*(a^2 - 3*a*b + 2*b^2)*cos(f*x + e)^3 + 15*(a^2 - 6*a*b + 6*b^2)*cos(f*x + e) - 5*(6*(a*b - 2*b^2)*cos(f*x + e)^2 + b^2)/cos(f*x + e)^3)/f","A",0
44,1,80,0,0.525854," ","integrate(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cos\left(f x + e\right) + \frac{3 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cos\left(f x + e\right)^{2} + b^{2}}{\cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*((a^2 - 2*a*b + b^2)*cos(f*x + e)^3 - 3*(a^2 - 4*a*b + 3*b^2)*cos(f*x + e) + (3*(2*a*b - 3*b^2)*cos(f*x + e)^2 + b^2)/cos(f*x + e)^3)/f","A",0
45,1,71,0,0.723618," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{6 \, a b {\left(\frac{1}{\cos\left(f x + e\right)} + \cos\left(f x + e\right)\right)} - b^{2} {\left(\frac{6 \, \cos\left(f x + e\right)^{2} - 1}{\cos\left(f x + e\right)^{3}} + 3 \, \cos\left(f x + e\right)\right)} - 3 \, a^{2} \cos\left(f x + e\right)}{3 \, f}"," ",0,"1/3*(6*a*b*(1/cos(f*x + e) + cos(f*x + e)) - b^2*((6*cos(f*x + e)^2 - 1)/cos(f*x + e)^3 + 3*cos(f*x + e)) - 3*a^2*cos(f*x + e))/f","A",0
46,1,68,0,0.309968," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, a^{2} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(2 \, a b - b^{2}\right)} \cos\left(f x + e\right)^{2} + b^{2}\right)}}{\cos\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"-1/6*(3*a^2*log(cos(f*x + e) + 1) - 3*a^2*log(cos(f*x + e) - 1) - 2*(3*(2*a*b - b^2)*cos(f*x + e)^2 + b^2)/cos(f*x + e)^3)/f","A",0
47,1,111,0,0.616958," ","integrate(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} + 4 \, a b\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(a^{2} + 4 \, a b\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(a^{2} + 4 \, a b\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(6 \, a b - b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, b^{2}\right)}}{\cos\left(f x + e\right)^{5} - \cos\left(f x + e\right)^{3}}}{12 \, f}"," ",0,"-1/12*(3*(a^2 + 4*a*b)*log(cos(f*x + e) + 1) - 3*(a^2 + 4*a*b)*log(cos(f*x + e) - 1) - 2*(3*(a^2 + 4*a*b)*cos(f*x + e)^4 - 2*(6*a*b - b^2)*cos(f*x + e)^2 - 2*b^2)/(cos(f*x + e)^5 - cos(f*x + e)^3))/f","A",0
48,1,163,0,0.686172," ","integrate(csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, a^{2} + 24 \, a b + 8 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) + 1\right) - 3 \, {\left(3 \, a^{2} + 24 \, a b + 8 \, b^{2}\right)} \log\left(\cos\left(f x + e\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(3 \, a^{2} + 24 \, a b + 8 \, b^{2}\right)} \cos\left(f x + e\right)^{6} - 5 \, {\left(3 \, a^{2} + 24 \, a b + 8 \, b^{2}\right)} \cos\left(f x + e\right)^{4} + 8 \, {\left(6 \, a b + b^{2}\right)} \cos\left(f x + e\right)^{2} + 8 \, b^{2}\right)}}{\cos\left(f x + e\right)^{7} - 2 \, \cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{3}}}{48 \, f}"," ",0,"-1/48*(3*(3*a^2 + 24*a*b + 8*b^2)*log(cos(f*x + e) + 1) - 3*(3*a^2 + 24*a*b + 8*b^2)*log(cos(f*x + e) - 1) - 2*(3*(3*a^2 + 24*a*b + 8*b^2)*cos(f*x + e)^6 - 5*(3*a^2 + 24*a*b + 8*b^2)*cos(f*x + e)^4 + 8*(6*a*b + b^2)*cos(f*x + e)^2 + 8*b^2)/(cos(f*x + e)^7 - 2*cos(f*x + e)^5 + cos(f*x + e)^3))/f","A",0
49,1,130,0,0.591496," ","integrate(sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{8 \, b^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 30 \, a b + 35 \, b^{2}\right)} {\left(f x + e\right)} + 24 \, {\left(2 \, a b - 3 \, b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left({\left(5 \, a^{2} - 18 \, a b + 13 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a^{2} - 14 \, a b + 11 \, b^{2}\right)} \tan\left(f x + e\right)\right)}}{\tan\left(f x + e\right)^{4} + 2 \, \tan\left(f x + e\right)^{2} + 1}}{24 \, f}"," ",0,"1/24*(8*b^2*tan(f*x + e)^3 + 3*(3*a^2 - 30*a*b + 35*b^2)*(f*x + e) + 24*(2*a*b - 3*b^2)*tan(f*x + e) - 3*((5*a^2 - 18*a*b + 13*b^2)*tan(f*x + e)^3 + (3*a^2 - 14*a*b + 11*b^2)*tan(f*x + e))/(tan(f*x + e)^4 + 2*tan(f*x + e)^2 + 1))/f","A",0
50,1,87,0,0.837593," ","integrate(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 6 \, a b + 5 \, b^{2}\right)} {\left(f x + e\right)} + 12 \, {\left(a b - b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{\tan\left(f x + e\right)^{2} + 1}}{6 \, f}"," ",0,"1/6*(2*b^2*tan(f*x + e)^3 + 3*(a^2 - 6*a*b + 5*b^2)*(f*x + e) + 12*(a*b - b^2)*tan(f*x + e) - 3*(a^2 - 2*a*b + b^2)*tan(f*x + e)/(tan(f*x + e)^2 + 1))/f","A",0
51,1,58,0,0.755441," ","integrate((a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","a^{2} x - \frac{2 \, {\left(f x + e - \tan\left(f x + e\right)\right)} a b}{f} + \frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, f x + 3 \, e - 3 \, \tan\left(f x + e\right)\right)} b^{2}}{3 \, f}"," ",0,"a^2*x - 2*(f*x + e - tan(f*x + e))*a*b/f + 1/3*(tan(f*x + e)^3 + 3*f*x + 3*e - 3*tan(f*x + e))*b^2/f","A",0
52,1,41,0,0.548906," ","integrate(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(f x + e\right)^{3} + 6 \, a b \tan\left(f x + e\right) - \frac{3 \, a^{2}}{\tan\left(f x + e\right)}}{3 \, f}"," ",0,"1/3*(b^2*tan(f*x + e)^3 + 6*a*b*tan(f*x + e) - 3*a^2/tan(f*x + e))/f","A",0
53,1,66,0,0.667622," ","integrate(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(2 \, a b + b^{2}\right)} \tan\left(f x + e\right) - \frac{3 \, {\left(a^{2} + 2 \, a b\right)} \tan\left(f x + e\right)^{2} + a^{2}}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(b^2*tan(f*x + e)^3 + 3*(2*a*b + b^2)*tan(f*x + e) - (3*(a^2 + 2*a*b)*tan(f*x + e)^2 + a^2)/tan(f*x + e)^3)/f","A",0
54,1,88,0,0.333461," ","integrate(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{5 \, b^{2} \tan\left(f x + e\right)^{3} + 30 \, {\left(a b + b^{2}\right)} \tan\left(f x + e\right) - \frac{15 \, {\left(a^{2} + 4 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{4} + 10 \, {\left(a^{2} + a b\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2}}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(5*b^2*tan(f*x + e)^3 + 30*(a*b + b^2)*tan(f*x + e) - (15*(a^2 + 4*a*b + b^2)*tan(f*x + e)^4 + 10*(a^2 + a*b)*tan(f*x + e)^2 + 3*a^2)/tan(f*x + e)^5)/f","A",0
55,-2,0,0,0.000000," ","integrate(sin(f*x+e)^5/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
56,-2,0,0,0.000000," ","integrate(sin(f*x+e)^3/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
57,-2,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
58,-2,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
59,-2,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
60,-2,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
61,1,305,0,0.806683," ","integrate(sin(f*x+e)^6/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{48 \, a^{3} b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} \sqrt{a b}} - \frac{3 \, {\left(5 \, a^{3} + 15 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} {\left(f x + e\right)}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{3 \, {\left(11 \, a^{2} - 4 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + 8 \, {\left(5 \, a^{2} + 2 \, a b - b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{2} + 4 \, a b - b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \tan\left(f x + e\right)^{6} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \tan\left(f x + e\right)^{4} + a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \tan\left(f x + e\right)^{2}}}{48 \, f}"," ",0,"-1/48*(48*a^3*b*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*sqrt(a*b)) - 3*(5*a^3 + 15*a^2*b - 5*a*b^2 + b^3)*(f*x + e)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + (3*(11*a^2 - 4*a*b + b^2)*tan(f*x + e)^5 + 8*(5*a^2 + 2*a*b - b^2)*tan(f*x + e)^3 + 3*(5*a^2 + 4*a*b - b^2)*tan(f*x + e))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*tan(f*x + e)^6 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*tan(f*x + e)^4 + a^3 - 3*a^2*b + 3*a*b^2 - b^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*tan(f*x + e)^2))/f","A",0
62,1,183,0,0.847064," ","integrate(sin(f*x+e)^4/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, a^{2} b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sqrt{a b}} - \frac{{\left(3 \, a^{2} + 6 \, a b - b^{2}\right)} {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(5 \, a - b\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a + b\right)} \tan\left(f x + e\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} - 2 \, a b + b^{2}}}{8 \, f}"," ",0,"-1/8*(8*a^2*b*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sqrt(a*b)) - (3*a^2 + 6*a*b - b^2)*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + ((5*a - b)*tan(f*x + e)^3 + (3*a + b)*tan(f*x + e))/((a^2 - 2*a*b + b^2)*tan(f*x + e)^4 + 2*(a^2 - 2*a*b + b^2)*tan(f*x + e)^2 + a^2 - 2*a*b + b^2))/f","A",0
63,1,93,0,0.959715," ","integrate(sin(f*x+e)^2/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{2 \, a b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{{\left(f x + e\right)} {\left(a + b\right)}}{a^{2} - 2 \, a b + b^{2}} + \frac{\tan\left(f x + e\right)}{{\left(a - b\right)} \tan\left(f x + e\right)^{2} + a - b}}{2 \, f}"," ",0,"-1/2*(2*a*b*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^2 - 2*a*b + b^2)*sqrt(a*b)) - (f*x + e)*(a + b)/(a^2 - 2*a*b + b^2) + tan(f*x + e)/((a - b)*tan(f*x + e)^2 + a - b))/f","A",0
64,1,48,0,0.855972," ","integrate(1/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} - \frac{f x + e}{a - b}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*(a - b)) - (f*x + e)/(a - b))/f","A",0
65,1,42,0,0.955897," ","integrate(csc(f*x+e)^2/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{1}{a \tan\left(f x + e\right)}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a) + 1/(a*tan(f*x + e)))/f","A",0
66,1,68,0,0.877915," ","integrate(csc(f*x+e)^4/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a b - b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{3 \, {\left(a - b\right)} \tan\left(f x + e\right)^{2} + a}{a^{2} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*(a*b - b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^2) + (3*(a - b)*tan(f*x + e)^2 + a)/(a^2*tan(f*x + e)^3))/f","A",0
67,1,104,0,0.802166," ","integrate(csc(f*x+e)^6/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} + \frac{15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{4} + 5 \, {\left(2 \, a^{2} - a b\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2}}{a^{3} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*(a^2*b - 2*a*b^2 + b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^3) + (15*(a^2 - 2*a*b + b^2)*tan(f*x + e)^4 + 5*(2*a^2 - a*b)*tan(f*x + e)^2 + 3*a^2)/(a^3*tan(f*x + e)^5))/f","A",0
68,-2,0,0,0.000000," ","integrate(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
69,-2,0,0,0.000000," ","integrate(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
70,-2,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
71,-2,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
72,-2,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
73,-2,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
74,1,312,0,1.022756," ","integrate(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{2} + 6 \, a b + b^{2}\right)} {\left(f x + e\right)}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{12 \, {\left(a^{2} b + a b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} \sqrt{a b}} - \frac{3 \, {\left(3 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} + {\left(5 \, a^{2} + 14 \, a b + 5 \, b^{2}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(a^{2} + 3 \, a b\right)} \tan\left(f x + e\right)}{{\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \tan\left(f x + e\right)^{6} + {\left(a^{4} - a^{3} b - 3 \, a^{2} b^{2} + 5 \, a b^{3} - 2 \, b^{4}\right)} \tan\left(f x + e\right)^{4} + a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3} + {\left(2 \, a^{4} - 5 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - b^{4}\right)} \tan\left(f x + e\right)^{2}}}{8 \, f}"," ",0,"1/8*(3*(a^2 + 6*a*b + b^2)*(f*x + e)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - 12*(a^2*b + a*b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*sqrt(a*b)) - (3*(3*a*b + b^2)*tan(f*x + e)^5 + (5*a^2 + 14*a*b + 5*b^2)*tan(f*x + e)^3 + 3*(a^2 + 3*a*b)*tan(f*x + e))/((a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*tan(f*x + e)^6 + (a^4 - a^3*b - 3*a^2*b^2 + 5*a*b^3 - 2*b^4)*tan(f*x + e)^4 + a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3 + (2*a^4 - 5*a^3*b + 3*a^2*b^2 + a*b^3 - b^4)*tan(f*x + e)^2))/f","A",0
75,1,185,0,0.726774," ","integrate(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(f x + e\right)} {\left(a + 3 \, b\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(3 \, a b + b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sqrt{a b}} - \frac{2 \, b \tan\left(f x + e\right)^{3} + {\left(a + b\right)} \tan\left(f x + e\right)}{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{4} + a^{3} - 2 \, a^{2} b + a b^{2} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"1/2*((f*x + e)*(a + 3*b)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (3*a*b + b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sqrt(a*b)) - (2*b*tan(f*x + e)^3 + (a + b)*tan(f*x + e))/((a^2*b - 2*a*b^2 + b^3)*tan(f*x + e)^4 + a^3 - 2*a^2*b + a*b^2 + (a^3 - a^2*b - a*b^2 + b^3)*tan(f*x + e)^2))/f","A",0
76,1,114,0,0.582320," ","integrate(1/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \tan\left(f x + e\right)}{a^{3} - a^{2} b + {\left(a^{2} b - a b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{{\left(3 \, a b - b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}}}{2 \, f}"," ",0,"-1/2*(b*tan(f*x + e)/(a^3 - a^2*b + (a^2*b - a*b^2)*tan(f*x + e)^2) + (3*a*b - b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3 - 2*a^2*b + a*b^2)*sqrt(a*b)) - 2*(f*x + e)/(a^2 - 2*a*b + b^2))/f","A",0
77,1,73,0,0.932141," ","integrate(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, b \tan\left(f x + e\right)^{2} + 2 \, a}{a^{2} b \tan\left(f x + e\right)^{3} + a^{3} \tan\left(f x + e\right)} + \frac{3 \, b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}}}{2 \, f}"," ",0,"-1/2*((3*b*tan(f*x + e)^2 + 2*a)/(a^2*b*tan(f*x + e)^3 + a^3*tan(f*x + e)) + 3*b*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^2))/f","A",0
78,1,115,0,0.620323," ","integrate(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(3 \, a b - 5 \, b^{2}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(3 \, a^{2} - 5 \, a b\right)} \tan\left(f x + e\right)^{2} + 2 \, a^{2}}{a^{3} b \tan\left(f x + e\right)^{5} + a^{4} \tan\left(f x + e\right)^{3}} + \frac{3 \, {\left(3 \, a b - 5 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}}}{6 \, f}"," ",0,"-1/6*((3*(3*a*b - 5*b^2)*tan(f*x + e)^4 + 2*(3*a^2 - 5*a*b)*tan(f*x + e)^2 + 2*a^2)/(a^3*b*tan(f*x + e)^5 + a^4*tan(f*x + e)^3) + 3*(3*a*b - 5*b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^3))/f","A",0
79,1,161,0,0.789663," ","integrate(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(3 \, a^{2} b - 10 \, a b^{2} + 7 \, b^{3}\right)} \tan\left(f x + e\right)^{6} + 10 \, {\left(3 \, a^{3} - 10 \, a^{2} b + 7 \, a b^{2}\right)} \tan\left(f x + e\right)^{4} + 6 \, a^{3} + 2 \, {\left(10 \, a^{3} - 7 \, a^{2} b\right)} \tan\left(f x + e\right)^{2}}{a^{4} b \tan\left(f x + e\right)^{7} + a^{5} \tan\left(f x + e\right)^{5}} + \frac{15 \, {\left(3 \, a^{2} b - 10 \, a b^{2} + 7 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}}}{30 \, f}"," ",0,"-1/30*((15*(3*a^2*b - 10*a*b^2 + 7*b^3)*tan(f*x + e)^6 + 10*(3*a^3 - 10*a^2*b + 7*a*b^2)*tan(f*x + e)^4 + 6*a^3 + 2*(10*a^3 - 7*a^2*b)*tan(f*x + e)^2)/(a^4*b*tan(f*x + e)^7 + a^5*tan(f*x + e)^5) + 15*(3*a^2*b - 10*a*b^2 + 7*b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^4))/f","A",0
80,-2,0,0,0.000000," ","integrate(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
81,-2,0,0,0.000000," ","integrate(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
82,-2,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
83,-2,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
84,-2,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
85,-2,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
86,1,460,0,0.704912," ","integrate(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{2} + 10 \, a b + 5 \, b^{2}\right)} {\left(f x + e\right)}}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} - \frac{3 \, {\left(5 \, a^{2} b + 10 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} \sqrt{a b}} - \frac{12 \, {\left(a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{7} + {\left(19 \, a^{2} b + 34 \, a b^{2} + 19 \, b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(5 \, a^{3} + 31 \, a^{2} b + 31 \, a b^{2} + 5 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + 6 \, a^{2} b + a b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{8} + 2 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 2 \, a^{2} b^{4} - 3 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{6} + a^{6} - 4 \, a^{5} b + 6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} - 9 \, a^{4} b^{2} + 16 \, a^{3} b^{3} - 9 \, a^{2} b^{4} + b^{6}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{6} - 3 \, a^{5} b + 2 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + a b^{5}\right)} \tan\left(f x + e\right)^{2}}}{8 \, f}"," ",0,"1/8*(3*(a^2 + 10*a*b + 5*b^2)*(f*x + e)/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) - 3*(5*a^2*b + 10*a*b^2 + b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*sqrt(a*b)) - (12*(a*b^2 + b^3)*tan(f*x + e)^7 + (19*a^2*b + 34*a*b^2 + 19*b^3)*tan(f*x + e)^5 + (5*a^3 + 31*a^2*b + 31*a*b^2 + 5*b^3)*tan(f*x + e)^3 + 3*(a^3 + 6*a^2*b + a*b^2)*tan(f*x + e))/((a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*tan(f*x + e)^8 + 2*(a^5*b - 3*a^4*b^2 + 2*a^3*b^3 + 2*a^2*b^4 - 3*a*b^5 + b^6)*tan(f*x + e)^6 + a^6 - 4*a^5*b + 6*a^4*b^2 - 4*a^3*b^3 + a^2*b^4 + (a^6 - 9*a^4*b^2 + 16*a^3*b^3 - 9*a^2*b^4 + b^6)*tan(f*x + e)^4 + 2*(a^6 - 3*a^5*b + 2*a^4*b^2 + 2*a^3*b^3 - 3*a^2*b^4 + a*b^5)*tan(f*x + e)^2))/f","A",0
87,1,346,0,0.641944," ","integrate(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(f x + e\right)} {\left(a + 5 \, b\right)}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(15 \, a^{2} b + 10 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a b}} - \frac{{\left(11 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(17 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b - a b^{2}\right)} \tan\left(f x + e\right)}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} \tan\left(f x + e\right)^{6} + a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3} + {\left(2 \, a^{5} b - 5 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4} - a b^{5}\right)} \tan\left(f x + e\right)^{4} + {\left(a^{6} - a^{5} b - 3 \, a^{4} b^{2} + 5 \, a^{3} b^{3} - 2 \, a^{2} b^{4}\right)} \tan\left(f x + e\right)^{2}}}{8 \, f}"," ",0,"1/8*(4*(f*x + e)*(a + 5*b)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (15*a^2*b + 10*a*b^2 - b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*sqrt(a*b)) - ((11*a*b^2 + b^3)*tan(f*x + e)^5 + (17*a^2*b + 6*a*b^2 + b^3)*tan(f*x + e)^3 + (4*a^3 + 9*a^2*b - a*b^2)*tan(f*x + e))/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*tan(f*x + e)^6 + a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3 + (2*a^5*b - 5*a^4*b^2 + 3*a^3*b^3 + a^2*b^4 - a*b^5)*tan(f*x + e)^4 + (a^6 - a^5*b - 3*a^4*b^2 + 5*a^3*b^3 - 2*a^2*b^4)*tan(f*x + e)^2))/f","A",0
88,1,227,0,0.543631," ","integrate(1/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{a b}} + \frac{{\left(7 \, a b^{2} - 3 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 5 \, a b^{2}\right)} \tan\left(f x + e\right)}{a^{6} - 2 \, a^{5} b + a^{4} b^{2} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, f}"," ",0,"-1/8*((15*a^2*b - 10*a*b^2 + 3*b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*sqrt(a*b)) + ((7*a*b^2 - 3*b^3)*tan(f*x + e)^3 + (9*a^2*b - 5*a*b^2)*tan(f*x + e))/(a^6 - 2*a^5*b + a^4*b^2 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*tan(f*x + e)^4 + 2*(a^5*b - 2*a^4*b^2 + a^3*b^3)*tan(f*x + e)^2) - 8*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
89,1,105,0,0.582559," ","integrate(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, b^{2} \tan\left(f x + e\right)^{4} + 25 \, a b \tan\left(f x + e\right)^{2} + 8 \, a^{2}}{a^{3} b^{2} \tan\left(f x + e\right)^{5} + 2 \, a^{4} b \tan\left(f x + e\right)^{3} + a^{5} \tan\left(f x + e\right)} + \frac{15 \, b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}}}{8 \, f}"," ",0,"-1/8*((15*b^2*tan(f*x + e)^4 + 25*a*b*tan(f*x + e)^2 + 8*a^2)/(a^3*b^2*tan(f*x + e)^5 + 2*a^4*b*tan(f*x + e)^3 + a^5*tan(f*x + e)) + 15*b*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^3))/f","A",0
90,1,158,0,0.697537," ","integrate(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(3 \, a b^{2} - 7 \, b^{3}\right)} \tan\left(f x + e\right)^{6} + 25 \, {\left(3 \, a^{2} b - 7 \, a b^{2}\right)} \tan\left(f x + e\right)^{4} + 8 \, a^{3} + 8 \, {\left(3 \, a^{3} - 7 \, a^{2} b\right)} \tan\left(f x + e\right)^{2}}{a^{4} b^{2} \tan\left(f x + e\right)^{7} + 2 \, a^{5} b \tan\left(f x + e\right)^{5} + a^{6} \tan\left(f x + e\right)^{3}} + \frac{15 \, {\left(3 \, a b - 7 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}}}{24 \, f}"," ",0,"-1/24*((15*(3*a*b^2 - 7*b^3)*tan(f*x + e)^6 + 25*(3*a^2*b - 7*a*b^2)*tan(f*x + e)^4 + 8*a^3 + 8*(3*a^3 - 7*a^2*b)*tan(f*x + e)^2)/(a^4*b^2*tan(f*x + e)^7 + 2*a^5*b*tan(f*x + e)^5 + a^6*tan(f*x + e)^3) + 15*(3*a*b - 7*b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^4))/f","A",0
91,1,212,0,0.726634," ","integrate(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(15 \, a^{2} b^{2} - 70 \, a b^{3} + 63 \, b^{4}\right)} \tan\left(f x + e\right)^{8} + 25 \, {\left(15 \, a^{3} b - 70 \, a^{2} b^{2} + 63 \, a b^{3}\right)} \tan\left(f x + e\right)^{6} + 8 \, {\left(15 \, a^{4} - 70 \, a^{3} b + 63 \, a^{2} b^{2}\right)} \tan\left(f x + e\right)^{4} + 24 \, a^{4} + 8 \, {\left(10 \, a^{4} - 9 \, a^{3} b\right)} \tan\left(f x + e\right)^{2}}{a^{5} b^{2} \tan\left(f x + e\right)^{9} + 2 \, a^{6} b \tan\left(f x + e\right)^{7} + a^{7} \tan\left(f x + e\right)^{5}} + \frac{15 \, {\left(15 \, a^{2} b - 70 \, a b^{2} + 63 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a^{5}}}{120 \, f}"," ",0,"-1/120*((15*(15*a^2*b^2 - 70*a*b^3 + 63*b^4)*tan(f*x + e)^8 + 25*(15*a^3*b - 70*a^2*b^2 + 63*a*b^3)*tan(f*x + e)^6 + 8*(15*a^4 - 70*a^3*b + 63*a^2*b^2)*tan(f*x + e)^4 + 24*a^4 + 8*(10*a^4 - 9*a^3*b)*tan(f*x + e)^2)/(a^5*b^2*tan(f*x + e)^9 + 2*a^6*b*tan(f*x + e)^7 + a^7*tan(f*x + e)^5) + 15*(15*a^2*b - 70*a*b^2 + 63*b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*a^5))/f","A",0
92,1,203,0,0.805173," ","integrate(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{20 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}{a - b} - 30 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - 15 \, \sqrt{b} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right) - \frac{2 \, {\left(3 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 5 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3}\right)}}{a^{2} - 2 \, a b + b^{2}}}{30 \, f}"," ",0,"1/30*(20*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3/(a - b) - 30*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - 15*sqrt(b)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))) - 2*(3*(a - b + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 5*(a - b + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3)/(a^2 - 2*a*b + b^2))/f","A",0
93,1,132,0,0.859047," ","integrate(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}{a - b} - 6 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - 3 \, \sqrt{b} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{6 \, f}"," ",0,"1/6*(2*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3/(a - b) - 6*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - 3*sqrt(b)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
94,1,97,0,0.445108," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{2 \, f}"," ",0,"-1/2*(2*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))))/f","A",0
95,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*csc(f*x + e), x)","F",0
96,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*csc(f*x + e)^3, x)","F",0
97,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*csc(f*x + e)^5, x)","F",0
98,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*sin(f*x + e)^4, x)","F",0
99,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*sin(f*x + e)^2, x)","F",0
100,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a zero or nonzero?","F(-2)",0
101,1,47,0,0.627341," ","integrate(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) - \frac{\sqrt{b \tan\left(f x + e\right)^{2} + a}}{\tan\left(f x + e\right)}}{f}"," ",0,"(sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) - sqrt(b*tan(f*x + e)^2 + a)/tan(f*x + e))/f","A",0
102,1,76,0,0.499307," ","integrate(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) - \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a}}{\tan\left(f x + e\right)} - \frac{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) - 3*sqrt(b*tan(f*x + e)^2 + a)/tan(f*x + e) - (b*tan(f*x + e)^2 + a)^(3/2)/(a*tan(f*x + e)^3))/f","A",0
103,1,131,0,0.492012," ","integrate(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\frac{15 \, \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) - \frac{15 \, \sqrt{b \tan\left(f x + e\right)^{2} + a}}{\tan\left(f x + e\right)} - \frac{10 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \tan\left(f x + e\right)^{3}} + \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b}{a^{2} \tan\left(f x + e\right)^{3}} - \frac{3 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{a \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) - 15*sqrt(b*tan(f*x + e)^2 + a)/tan(f*x + e) - 10*(b*tan(f*x + e)^2 + a)^(3/2)/(a*tan(f*x + e)^3) + 2*(b*tan(f*x + e)^2 + a)^(3/2)*b/(a^2*tan(f*x + e)^3) - 3*(b*tan(f*x + e)^2 + a)^(3/2)/(a*tan(f*x + e)^5))/f","A",0
104,1,330,0,0.810049," ","integrate(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5}}{a - b} - 40 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} + 60 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} {\left(a - b\right)} \cos\left(f x + e\right) - 120 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right) - 60 \, b^{\frac{3}{2}} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right) - \frac{30 \, {\left(a b - b^{2}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{{\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} \cos\left(f x + e\right)^{2} - b} + \frac{45 \, {\left(a b - b^{2}\right)} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{\sqrt{b}}}{60 \, f}"," ",0,"-1/60*(12*(a - b + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5/(a - b) - 40*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 + 60*sqrt(a - b + b/cos(f*x + e)^2)*(a - b)*cos(f*x + e) - 120*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e) - 60*b^(3/2)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))) - 30*(a*b - b^2)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/((a - b + b/cos(f*x + e)^2)*cos(f*x + e)^2 - b) + 45*(a*b - b^2)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b)))/sqrt(b))/f","A",0
105,1,296,0,0.980405," ","integrate(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 12 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} {\left(a - b\right)} \cos\left(f x + e\right) + 12 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right) + 6 \, b^{\frac{3}{2}} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right) + \frac{6 \, {\left(a b - b^{2}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{{\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} \cos\left(f x + e\right)^{2} - b} - \frac{9 \, {\left(a b - b^{2}\right)} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{\sqrt{b}}}{12 \, f}"," ",0,"1/12*(4*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 12*sqrt(a - b + b/cos(f*x + e)^2)*(a - b)*cos(f*x + e) + 12*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e) + 6*b^(3/2)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b))) + 6*(a*b - b^2)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/((a - b + b/cos(f*x + e)^2)*cos(f*x + e)^2 - b) - 9*(a*b - b^2)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b)))/sqrt(b))/f","A",0
106,1,176,0,0.846056," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{4 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} {\left(a - b\right)} \cos\left(f x + e\right) - \frac{2 \, {\left(a b - b^{2}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{{\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} \cos\left(f x + e\right)^{2} - b} + \frac{3 \, {\left(a b - b^{2}\right)} \log\left(\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) - \sqrt{b}}{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right) + \sqrt{b}}\right)}{\sqrt{b}}}{4 \, f}"," ",0,"-1/4*(4*sqrt(a - b + b/cos(f*x + e)^2)*(a - b)*cos(f*x + e) - 2*(a*b - b^2)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/((a - b + b/cos(f*x + e)^2)*cos(f*x + e)^2 - b) + 3*(a*b - b^2)*log((sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) - sqrt(b))/(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e) + sqrt(b)))/sqrt(b))/f","A",0
107,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*csc(f*x + e), x)","F",0
108,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^3, x)","F",0
109,0,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \csc\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*csc(f*x + e)^5, x)","F",0
110,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^4, x)","F",0
111,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*sin(f*x + e)^2, x)","F",0
112,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
113,1,73,0,0.666496," ","integrate(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{3 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) + 3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b \tan\left(f x + e\right) - \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{\tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(3*a*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) + 3*sqrt(b*tan(f*x + e)^2 + a)*b*tan(f*x + e) - 2*(b*tan(f*x + e)^2 + a)^(3/2)/tan(f*x + e))/f","A",0
114,1,175,0,0.514624," ","integrate(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{9 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) + 6 \, b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) + 9 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b \tan\left(f x + e\right) + \frac{6 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b^{2} \tan\left(f x + e\right)}{a} - \frac{6 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{\tan\left(f x + e\right)} - \frac{4 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b}{a \tan\left(f x + e\right)} - \frac{2 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}{a \tan\left(f x + e\right)^{3}}}{6 \, f}"," ",0,"1/6*(9*a*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) + 6*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) + 9*sqrt(b*tan(f*x + e)^2 + a)*b*tan(f*x + e) + 6*sqrt(b*tan(f*x + e)^2 + a)*b^2*tan(f*x + e)/a - 6*(b*tan(f*x + e)^2 + a)^(3/2)/tan(f*x + e) - 4*(b*tan(f*x + e)^2 + a)^(3/2)*b/(a*tan(f*x + e)) - 2*(b*tan(f*x + e)^2 + a)^(5/2)/(a*tan(f*x + e)^3))/f","A",0
115,1,202,0,0.685552," ","integrate(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\frac{45 \, a \sqrt{b} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) + 60 \, b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right) + 45 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b \tan\left(f x + e\right) + \frac{60 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b^{2} \tan\left(f x + e\right)}{a} - \frac{30 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}{\tan\left(f x + e\right)} - \frac{40 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} b}{a \tan\left(f x + e\right)} - \frac{20 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}{a \tan\left(f x + e\right)^{3}} - \frac{6 \, {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}{a \tan\left(f x + e\right)^{5}}}{30 \, f}"," ",0,"1/30*(45*a*sqrt(b)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) + 60*b^(3/2)*arcsinh(b*tan(f*x + e)/sqrt(a*b)) + 45*sqrt(b*tan(f*x + e)^2 + a)*b*tan(f*x + e) + 60*sqrt(b*tan(f*x + e)^2 + a)*b^2*tan(f*x + e)/a - 30*(b*tan(f*x + e)^2 + a)^(3/2)/tan(f*x + e) - 40*(b*tan(f*x + e)^2 + a)^(3/2)*b/(a*tan(f*x + e)) - 20*(b*tan(f*x + e)^2 + a)^(5/2)/(a*tan(f*x + e)^3) - 6*(b*tan(f*x + e)^2 + a)^(5/2)/(a*tan(f*x + e)^5))/f","A",0
116,1,214,0,0.492473," ","integrate(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a - b} + \frac{3 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 10 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3} + 15 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b^{2} \cos\left(f x + e\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{10 \, {\left({\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 3 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)\right)}}{a^{2} - 2 \, a b + b^{2}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a - b) + (3*(a - b + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 10*(a - b + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3 + 15*sqrt(a - b + b/cos(f*x + e)^2)*b^2*cos(f*x + e))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - 10*((a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 3*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e))/(a^2 - 2*a*b + b^2))/f","A",0
117,1,106,0,0.352678," ","integrate(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a - b} - \frac{{\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 3 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)}{a^{2} - 2 \, a b + b^{2}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a - b) - ((a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 3*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e))/(a^2 - 2*a*b + b^2))/f","A",0
118,1,35,0,0.622291," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{{\left(a - b\right)} f}"," ",0,"-sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/((a - b)*f)","A",0
119,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
120,0,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{3}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^3/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
121,-1,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
124,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
125,1,30,0,0.372730," ","integrate(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{b \tan\left(f x + e\right)^{2} + a}}{a f \tan\left(f x + e\right)}"," ",0,"-sqrt(b*tan(f*x + e)^2 + a)/(a*f*tan(f*x + e))","A",0
126,1,87,0,0.779476," ","integrate(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a}}{a \tan\left(f x + e\right)} - \frac{2 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b}{a^{2} \tan\left(f x + e\right)} + \frac{\sqrt{b \tan\left(f x + e\right)^{2} + a}}{a \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(b*tan(f*x + e)^2 + a)/(a*tan(f*x + e)) - 2*sqrt(b*tan(f*x + e)^2 + a)*b/(a^2*tan(f*x + e)) + sqrt(b*tan(f*x + e)^2 + a)/(a*tan(f*x + e)^3))/f","A",0
127,1,173,0,0.781488," ","integrate(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{b \tan\left(f x + e\right)^{2} + a}}{a \tan\left(f x + e\right)} - \frac{20 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b}{a^{2} \tan\left(f x + e\right)} + \frac{8 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b^{2}}{a^{3} \tan\left(f x + e\right)} + \frac{10 \, \sqrt{b \tan\left(f x + e\right)^{2} + a}}{a \tan\left(f x + e\right)^{3}} - \frac{4 \, \sqrt{b \tan\left(f x + e\right)^{2} + a} b}{a^{2} \tan\left(f x + e\right)^{3}} + \frac{3 \, \sqrt{b \tan\left(f x + e\right)^{2} + a}}{a \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(b*tan(f*x + e)^2 + a)/(a*tan(f*x + e)) - 20*sqrt(b*tan(f*x + e)^2 + a)*b/(a^2*tan(f*x + e)) + 8*sqrt(b*tan(f*x + e)^2 + a)*b^2/(a^3*tan(f*x + e)) + 10*sqrt(b*tan(f*x + e)^2 + a)/(a*tan(f*x + e)^3) - 4*sqrt(b*tan(f*x + e)^2 + a)*b/(a^2*tan(f*x + e)^3) + 3*sqrt(b*tan(f*x + e)^2 + a)/(a*tan(f*x + e)^5))/f","A",0
128,1,389,0,0.511359," ","integrate(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, b^{3}}{{\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)} + \frac{15 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{3 \, {\left({\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 5 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3} + 15 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b^{2} \cos\left(f x + e\right)\right)}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{10 \, {\left({\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 6 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{30 \, b^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)} + \frac{15 \, b}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}}{15 \, f}"," ",0,"-1/15*(15*b^3/((a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)) + 15*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a^2 - 2*a*b + b^2) + 3*((a - b + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 5*(a - b + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3 + 15*sqrt(a - b + b/cos(f*x + e)^2)*b^2*cos(f*x + e))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - 10*((a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 6*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + 30*b^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)) + 15*b/((a^2 - 2*a*b + b^2)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)))/f","B",0
129,1,216,0,0.762982," ","integrate(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 6 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{3 \, b^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)} + \frac{3 \, b}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a^2 - 2*a*b + b^2) - ((a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 6*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + 3*b^2/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)) + 3*b/((a^2 - 2*a*b + b^2)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)))/f","A",0
130,1,83,0,0.628617," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{b}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}}{f}"," ",0,"-(sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a^2 - 2*a*b + b^2) + b/((a^2 - 2*a*b + b^2)*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)))/f","A",0
131,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)/(b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
132,-1,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
135,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
136,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
137,1,58,0,0.535225," ","integrate(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{2}} + \frac{1}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a \tan\left(f x + e\right)}}{f}"," ",0,"-(2*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^2) + 1/(sqrt(b*tan(f*x + e)^2 + a)*a*tan(f*x + e)))/f","A",0
138,1,141,0,0.697567," ","integrate(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{6 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{2}} - \frac{8 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{3}} + \frac{3}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a \tan\left(f x + e\right)} - \frac{4 \, b}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{2} \tan\left(f x + e\right)} + \frac{1}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(6*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^2) - 8*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^3) + 3/(sqrt(b*tan(f*x + e)^2 + a)*a*tan(f*x + e)) - 4*b/(sqrt(b*tan(f*x + e)^2 + a)*a^2*tan(f*x + e)) + 1/(sqrt(b*tan(f*x + e)^2 + a)*a*tan(f*x + e)^3))/f","A",0
139,1,255,0,0.747679," ","integrate(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{30 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{2}} - \frac{80 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{3}} + \frac{48 \, b^{3} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{4}} + \frac{15}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a \tan\left(f x + e\right)} - \frac{40 \, b}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{2} \tan\left(f x + e\right)} + \frac{24 \, b^{2}}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{3} \tan\left(f x + e\right)} + \frac{10}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a \tan\left(f x + e\right)^{3}} - \frac{6 \, b}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{2} \tan\left(f x + e\right)^{3}} + \frac{3}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(30*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^2) - 80*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^3) + 48*b^3*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^4) + 15/(sqrt(b*tan(f*x + e)^2 + a)*a*tan(f*x + e)) - 40*b/(sqrt(b*tan(f*x + e)^2 + a)*a^2*tan(f*x + e)) + 24*b^2/(sqrt(b*tan(f*x + e)^2 + a)*a^3*tan(f*x + e)) + 10/(sqrt(b*tan(f*x + e)^2 + a)*a*tan(f*x + e)^3) - 6*b/(sqrt(b*tan(f*x + e)^2 + a)*a^2*tan(f*x + e)^3) + 3/(sqrt(b*tan(f*x + e)^2 + a)*a*tan(f*x + e)^5))/f","A",0
140,1,534,0,0.716707," ","integrate(sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{3 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{5} - 20 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} b \cos\left(f x + e\right)^{3} + 90 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b^{2} \cos\left(f x + e\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} - \frac{10 \, {\left({\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 9 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)\right)}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{5 \, {\left(12 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b^{3} \cos\left(f x + e\right)^{2} - b^{4}\right)}}{{\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}} + \frac{10 \, {\left(9 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b^{2} \cos\left(f x + e\right)^{2} - b^{3}\right)}}{{\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}} + \frac{5 \, {\left(6 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b \cos\left(f x + e\right)^{2} - b^{2}\right)}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}}{15 \, f}"," ",0,"-1/15*(15*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*(a - b + b/cos(f*x + e)^2)^(5/2)*cos(f*x + e)^5 - 20*(a - b + b/cos(f*x + e)^2)^(3/2)*b*cos(f*x + e)^3 + 90*sqrt(a - b + b/cos(f*x + e)^2)*b^2*cos(f*x + e))/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) - 10*((a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 9*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + 5*(12*(a - b + b/cos(f*x + e)^2)*b^3*cos(f*x + e)^2 - b^4)/((a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3) + 10*(9*(a - b + b/cos(f*x + e)^2)*b^2*cos(f*x + e)^2 - b^3)/((a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3) + 5*(6*(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e)^2 - b^2)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3))/f","B",0
141,1,308,0,1.048179," ","integrate(sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3} - 9 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} b \cos\left(f x + e\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{9 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b^{2} \cos\left(f x + e\right)^{2} - b^{3}}{{\left(a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}} + \frac{6 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b \cos\left(f x + e\right)^{2} - b^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - ((a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3 - 9*sqrt(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e))/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + (9*(a - b + b/cos(f*x + e)^2)*b^2*cos(f*x + e)^2 - b^3)/((a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4)*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3) + (6*(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e)^2 - b^2)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3))/f","A",0
142,1,135,0,0.474223," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{a - b + \frac{b}{\cos\left(f x + e\right)^{2}}} \cos\left(f x + e\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{6 \, {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)} b \cos\left(f x + e\right)^{2} - b^{2}}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(a - b + \frac{b}{\cos\left(f x + e\right)^{2}}\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*sqrt(a - b + b/cos(f*x + e)^2)*cos(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (6*(a - b + b/cos(f*x + e)^2)*b*cos(f*x + e)^2 - b^2)/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(a - b + b/cos(f*x + e)^2)^(3/2)*cos(f*x + e)^3))/f","A",0
143,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(f*x + e)/(b*tan(f*x + e)^2 + a)^(5/2), x)","F",0
144,-1,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(b*tan(f*x + e)^2 + a)^(5/2), x)","F",0
147,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(b*tan(f*x + e)^2 + a)^(5/2), x)","F",0
148,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
149,1,85,0,0.792938," ","integrate(csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{3}} + \frac{4 \, b \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{3}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \tan\left(f x + e\right)}}{3 \, f}"," ",0,"-1/3*(8*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^3) + 4*b*tan(f*x + e)/((b*tan(f*x + e)^2 + a)^(3/2)*a^2) + 3/((b*tan(f*x + e)^2 + a)^(3/2)*a*tan(f*x + e)))/f","A",0
150,1,195,0,0.780780," ","integrate(csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{3}} + \frac{4 \, b \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{16 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{4}} - \frac{8 \, b^{2} \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{3}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \tan\left(f x + e\right)} - \frac{6 \, b}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} \tan\left(f x + e\right)} + \frac{1}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(8*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^3) + 4*b*tan(f*x + e)/((b*tan(f*x + e)^2 + a)^(3/2)*a^2) - 16*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^4) - 8*b^2*tan(f*x + e)/((b*tan(f*x + e)^2 + a)^(3/2)*a^3) + 3/((b*tan(f*x + e)^2 + a)^(3/2)*a*tan(f*x + e)) - 6*b/((b*tan(f*x + e)^2 + a)^(3/2)*a^2*tan(f*x + e)) + 1/((b*tan(f*x + e)^2 + a)^(3/2)*a*tan(f*x + e)^3))/f","A",0
151,1,337,0,0.729908," ","integrate(csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","-\frac{\frac{40 \, b \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{3}} + \frac{20 \, b \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{160 \, b^{2} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{4}} - \frac{80 \, b^{2} \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{3}} + \frac{128 \, b^{3} \tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a} a^{5}} + \frac{64 \, b^{3} \tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{4}} + \frac{15}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \tan\left(f x + e\right)} - \frac{60 \, b}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} \tan\left(f x + e\right)} + \frac{48 \, b^{2}}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{3} \tan\left(f x + e\right)} + \frac{10}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \tan\left(f x + e\right)^{3}} - \frac{8 \, b}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a^{2} \tan\left(f x + e\right)^{3}} + \frac{3}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} a \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(40*b*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^3) + 20*b*tan(f*x + e)/((b*tan(f*x + e)^2 + a)^(3/2)*a^2) - 160*b^2*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^4) - 80*b^2*tan(f*x + e)/((b*tan(f*x + e)^2 + a)^(3/2)*a^3) + 128*b^3*tan(f*x + e)/(sqrt(b*tan(f*x + e)^2 + a)*a^5) + 64*b^3*tan(f*x + e)/((b*tan(f*x + e)^2 + a)^(3/2)*a^4) + 15/((b*tan(f*x + e)^2 + a)^(3/2)*a*tan(f*x + e)) - 60*b/((b*tan(f*x + e)^2 + a)^(3/2)*a^2*tan(f*x + e)) + 48*b^2/((b*tan(f*x + e)^2 + a)^(3/2)*a^3*tan(f*x + e)) + 10/((b*tan(f*x + e)^2 + a)^(3/2)*a*tan(f*x + e)^3) - 8*b/((b*tan(f*x + e)^2 + a)^(3/2)*a^2*tan(f*x + e)^3) + 3/((b*tan(f*x + e)^2 + a)^(3/2)*a*tan(f*x + e)^5))/f","A",0
152,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p*(d*sin(f*x + e))^m, x)","F",0
153,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*(d*sin(f*x + e))^m, x)","F",0
154,0,0,0,0.000000," ","integrate(sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*sin(f*x + e)^5, x)","F",0
155,0,0,0,0.000000," ","integrate(sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*sin(f*x + e)^3, x)","F",0
156,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*sin(f*x + e), x)","F",0
157,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*csc(f*x + e), x)","F",0
158,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*csc(f*x + e)^3, x)","F",0
159,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*sin(f*x + e)^2, x)","F",0
160,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p, x)","F",0
161,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*csc(f*x + e)^2, x)","F",0
162,0,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*csc(f*x + e)^4, x)","F",0
163,0,0,0,0.000000," ","integrate(csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \csc\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*csc(f*x + e)^6, x)","F",0
164,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*(d*sin(f*x + e))^m, x)","F",0
165,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*sin(f*x + e)^2, x)","F",0
166,0,0,0,0.000000," ","integrate((b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p, x)","F",0
167,1,37,0,0.770589," ","integrate(csc(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p}}{{\left(n p - 1\right)} f \tan\left(f x + e\right)}"," ",0,"b^p*c^(n*p)*(tan(f*x + e)^n)^p/((n*p - 1)*f*tan(f*x + e))","A",0
168,1,73,0,0.371945," ","integrate(csc(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\frac{\frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p}}{{\left(n p - 1\right)} \tan\left(f x + e\right)} + \frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p}}{{\left(n p - 3\right)} \tan\left(f x + e\right)^{3}}}{f}"," ",0,"(b^p*c^(n*p)*(tan(f*x + e)^n)^p/((n*p - 1)*tan(f*x + e)) + b^p*c^(n*p)*(tan(f*x + e)^n)^p/((n*p - 3)*tan(f*x + e)^3))/f","A",0
169,1,108,0,0.515298," ","integrate(csc(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\frac{\frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p}}{{\left(n p - 1\right)} \tan\left(f x + e\right)} + \frac{2 \, b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p}}{{\left(n p - 3\right)} \tan\left(f x + e\right)^{3}} + \frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p}}{{\left(n p - 5\right)} \tan\left(f x + e\right)^{5}}}{f}"," ",0,"(b^p*c^(n*p)*(tan(f*x + e)^n)^p/((n*p - 1)*tan(f*x + e)) + 2*b^p*c^(n*p)*(tan(f*x + e)^n)^p/((n*p - 3)*tan(f*x + e)^3) + b^p*c^(n*p)*(tan(f*x + e)^n)^p/((n*p - 5)*tan(f*x + e)^5))/f","A",0
170,0,0,0,0.000000," ","integrate(sin(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \sin\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*sin(f*x + e)^3, x)","F",0
171,0,0,0,0.000000," ","integrate(sin(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*sin(f*x + e), x)","F",0
172,0,0,0,0.000000," ","integrate(csc(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*csc(f*x + e), x)","F",0
173,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*csc(f*x + e)^3, x)","F",0
174,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^n)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{n} + a\right)}^{p} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^n + a)^p*(d*sin(f*x + e))^m, x)","F",0
175,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p*(d*cos(f*x + e))^m, x)","F",0
176,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*(d*cos(f*x + e))^m, x)","F",0
177,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*(d*cos(f*x + e))^m, x)","F",0
178,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*(d*cos(f*x + e))^m, x)","F",0
179,1,157,0,0.466287," ","integrate((a+a*tan(d*x+c)^2)^4,x, algorithm=""maxima"")","a^{4} x + \frac{{\left(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 \, c - 105 \, \tan\left(d x + c\right)\right)} a^{4}}{105 \, d} + \frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{4}}{15 \, d} + \frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{4}}{d} - \frac{4 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{4}}{d}"," ",0,"a^4*x + 1/105*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*a^4/d + 4/15*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^4/d + 2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^4/d - 4*(d*x + c - tan(d*x + c))*a^4/d","B",0
180,1,102,0,0.462462," ","integrate((a+a*tan(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x + \frac{{\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{3}}{15 \, d} + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3}}{d} - \frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3}}{d}"," ",0,"a^3*x + 1/15*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^3/d + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3/d - 3*(d*x + c - tan(d*x + c))*a^3/d","B",0
181,1,59,0,0.530026," ","integrate((a+a*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2}}{3 \, d} - \frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2}}{d}"," ",0,"a^2*x + 1/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2/d - 2*(d*x + c - tan(d*x + c))*a^2/d","A",0
182,1,36,0,0.475872," ","integrate(1/(a+a*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{d x + c}{a} + \frac{\tan\left(d x + c\right)}{a \tan\left(d x + c\right)^{2} + a}}{2 \, d}"," ",0,"1/2*((d*x + c)/a + tan(d*x + c)/(a*tan(d*x + c)^2 + a))/d","A",0
183,1,67,0,0.783178," ","integrate(1/(a+a*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, \tan\left(d x + c\right)^{3} + 5 \, \tan\left(d x + c\right)}{a^{2} \tan\left(d x + c\right)^{4} + 2 \, a^{2} \tan\left(d x + c\right)^{2} + a^{2}} + \frac{3 \, {\left(d x + c\right)}}{a^{2}}}{8 \, d}"," ",0,"1/8*((3*tan(d*x + c)^3 + 5*tan(d*x + c))/(a^2*tan(d*x + c)^4 + 2*a^2*tan(d*x + c)^2 + a^2) + 3*(d*x + c)/a^2)/d","A",0
184,1,90,0,0.942727," ","integrate(1/(a+a*tan(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{\frac{15 \, \tan\left(d x + c\right)^{5} + 40 \, \tan\left(d x + c\right)^{3} + 33 \, \tan\left(d x + c\right)}{a^{3} \tan\left(d x + c\right)^{6} + 3 \, a^{3} \tan\left(d x + c\right)^{4} + 3 \, a^{3} \tan\left(d x + c\right)^{2} + a^{3}} + \frac{15 \, {\left(d x + c\right)}}{a^{3}}}{48 \, d}"," ",0,"1/48*((15*tan(d*x + c)^5 + 40*tan(d*x + c)^3 + 33*tan(d*x + c))/(a^3*tan(d*x + c)^6 + 3*a^3*tan(d*x + c)^4 + 3*a^3*tan(d*x + c)^2 + a^3) + 15*(d*x + c)/a^3)/d","A",0
185,1,99,0,0.442598," ","integrate(tan(f*x+e)^5*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{6 \, {\left(a - b\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{6 \, {\left(2 \, a - 3 \, b\right)} \sin\left(f x + e\right)^{4} - 3 \, {\left(7 \, a - 9 \, b\right)} \sin\left(f x + e\right)^{2} + 9 \, a - 11 \, b}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1}}{12 \, f}"," ",0,"-1/12*(6*(a - b)*log(sin(f*x + e)^2 - 1) - (6*(2*a - 3*b)*sin(f*x + e)^4 - 3*(7*a - 9*b)*sin(f*x + e)^2 + 9*a - 11*b)/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1))/f","A",0
186,1,70,0,0.543705," ","integrate(tan(f*x+e)^3*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(a - b\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{2 \, {\left(a - 2 \, b\right)} \sin\left(f x + e\right)^{2} - 2 \, a + 3 \, b}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1}}{4 \, f}"," ",0,"1/4*(2*(a - b)*log(sin(f*x + e)^2 - 1) - (2*(a - 2*b)*sin(f*x + e)^2 - 2*a + 3*b)/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1))/f","A",0
187,1,37,0,0.594190," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) + \frac{b}{\sin\left(f x + e\right)^{2} - 1}}{2 \, f}"," ",0,"-1/2*((a - b)*log(sin(f*x + e)^2 - 1) + b/(sin(f*x + e)^2 - 1))/f","A",0
188,1,31,0,0.632480," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{b \log\left(\sin\left(f x + e\right)^{2} - 1\right) - a \log\left(\sin\left(f x + e\right)^{2}\right)}{2 \, f}"," ",0,"-1/2*(b*log(sin(f*x + e)^2 - 1) - a*log(sin(f*x + e)^2))/f","A",0
189,1,31,0,0.314510," ","integrate(cot(f*x+e)^3*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{a}{\sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*((a - b)*log(sin(f*x + e)^2) + a/sin(f*x + e)^2)/f","A",0
190,1,52,0,0.503860," ","integrate(cot(f*x+e)^5*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(a - b\right)} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{2 \, {\left(2 \, a - b\right)} \sin\left(f x + e\right)^{2} - a}{\sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*(a - b)*log(sin(f*x + e)^2) + (2*(2*a - b)*sin(f*x + e)^2 - a)/sin(f*x + e)^4)/f","A",0
191,1,72,0,0.920120," ","integrate(tan(f*x+e)^6*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{15 \, b \tan\left(f x + e\right)^{7} + 21 \, {\left(a - b\right)} \tan\left(f x + e\right)^{5} - 35 \, {\left(a - b\right)} \tan\left(f x + e\right)^{3} - 105 \, {\left(f x + e\right)} {\left(a - b\right)} + 105 \, {\left(a - b\right)} \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*b*tan(f*x + e)^7 + 21*(a - b)*tan(f*x + e)^5 - 35*(a - b)*tan(f*x + e)^3 - 105*(f*x + e)*(a - b) + 105*(a - b)*tan(f*x + e))/f","A",0
192,1,57,0,1.755893," ","integrate(tan(f*x+e)^4*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(f x + e\right)^{5} + 5 \, {\left(a - b\right)} \tan\left(f x + e\right)^{3} + 15 \, {\left(f x + e\right)} {\left(a - b\right)} - 15 \, {\left(a - b\right)} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*b*tan(f*x + e)^5 + 5*(a - b)*tan(f*x + e)^3 + 15*(f*x + e)*(a - b) - 15*(a - b)*tan(f*x + e))/f","A",0
193,1,41,0,0.775223," ","integrate(tan(f*x+e)^2*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{b \tan\left(f x + e\right)^{3} - 3 \, {\left(f x + e\right)} {\left(a - b\right)} + 3 \, {\left(a - b\right)} \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*(b*tan(f*x + e)^3 - 3*(f*x + e)*(a - b) + 3*(a - b)*tan(f*x + e))/f","A",0
194,1,23,0,0.793032," ","integrate(a+b*tan(f*x+e)^2,x, algorithm=""maxima"")","a x - \frac{{\left(f x + e - \tan\left(f x + e\right)\right)} b}{f}"," ",0,"a*x - (f*x + e - tan(f*x + e))*b/f","A",0
195,1,27,0,0.665284," ","integrate(cot(f*x+e)^2*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{{\left(f x + e\right)} {\left(a - b\right)} + \frac{a}{\tan\left(f x + e\right)}}{f}"," ",0,"-((f*x + e)*(a - b) + a/tan(f*x + e))/f","A",0
196,1,46,0,0.766912," ","integrate(cot(f*x+e)^4*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} {\left(a - b\right)} + \frac{3 \, {\left(a - b\right)} \tan\left(f x + e\right)^{2} - a}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*(a - b) + (3*(a - b)*tan(f*x + e)^2 - a)/tan(f*x + e)^3)/f","A",0
197,1,61,0,0.793709," ","integrate(cot(f*x+e)^6*(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{15 \, {\left(f x + e\right)} {\left(a - b\right)} + \frac{15 \, {\left(a - b\right)} \tan\left(f x + e\right)^{4} - 5 \, {\left(a - b\right)} \tan\left(f x + e\right)^{2} + 3 \, a}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*(f*x + e)*(a - b) + (15*(a - b)*tan(f*x + e)^4 - 5*(a - b)*tan(f*x + e)^2 + 3*a)/tan(f*x + e)^5)/f","A",0
198,1,162,0,0.559541," ","integrate(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{12 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{24 \, {\left(a^{2} - 3 \, a b + 2 \, b^{2}\right)} \sin\left(f x + e\right)^{6} - 6 \, {\left(11 \, a^{2} - 30 \, a b + 18 \, b^{2}\right)} \sin\left(f x + e\right)^{4} + 4 \, {\left(15 \, a^{2} - 38 \, a b + 22 \, b^{2}\right)} \sin\left(f x + e\right)^{2} - 18 \, a^{2} + 44 \, a b - 25 \, b^{2}}{\sin\left(f x + e\right)^{8} - 4 \, \sin\left(f x + e\right)^{6} + 6 \, \sin\left(f x + e\right)^{4} - 4 \, \sin\left(f x + e\right)^{2} + 1}}{24 \, f}"," ",0,"-1/24*(12*(a^2 - 2*a*b + b^2)*log(sin(f*x + e)^2 - 1) - (24*(a^2 - 3*a*b + 2*b^2)*sin(f*x + e)^6 - 6*(11*a^2 - 30*a*b + 18*b^2)*sin(f*x + e)^4 + 4*(15*a^2 - 38*a*b + 22*b^2)*sin(f*x + e)^2 - 18*a^2 + 44*a*b - 25*b^2)/(sin(f*x + e)^8 - 4*sin(f*x + e)^6 + 6*sin(f*x + e)^4 - 4*sin(f*x + e)^2 + 1))/f","A",0
199,1,127,0,0.780844," ","integrate(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{6 \, {\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} \sin\left(f x + e\right)^{4} - 3 \, {\left(4 \, a^{2} - 14 \, a b + 9 \, b^{2}\right)} \sin\left(f x + e\right)^{2} + 6 \, a^{2} - 18 \, a b + 11 \, b^{2}}{\sin\left(f x + e\right)^{6} - 3 \, \sin\left(f x + e\right)^{4} + 3 \, \sin\left(f x + e\right)^{2} - 1}}{12 \, f}"," ",0,"1/12*(6*(a^2 - 2*a*b + b^2)*log(sin(f*x + e)^2 - 1) - (6*(a^2 - 4*a*b + 3*b^2)*sin(f*x + e)^4 - 3*(4*a^2 - 14*a*b + 9*b^2)*sin(f*x + e)^2 + 6*a^2 - 18*a*b + 11*b^2)/(sin(f*x + e)^6 - 3*sin(f*x + e)^4 + 3*sin(f*x + e)^2 - 1))/f","A",0
200,1,82,0,0.556127," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) + \frac{4 \, {\left(a b - b^{2}\right)} \sin\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}}{\sin\left(f x + e\right)^{4} - 2 \, \sin\left(f x + e\right)^{2} + 1}}{4 \, f}"," ",0,"-1/4*(2*(a^2 - 2*a*b + b^2)*log(sin(f*x + e)^2 - 1) + (4*(a*b - b^2)*sin(f*x + e)^2 - 4*a*b + 3*b^2)/(sin(f*x + e)^4 - 2*sin(f*x + e)^2 + 1))/f","A",0
201,1,59,0,0.604757," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{a^{2} \log\left(\sin\left(f x + e\right)^{2}\right) - {\left(2 \, a b - b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right) - \frac{b^{2}}{\sin\left(f x + e\right)^{2} - 1}}{2 \, f}"," ",0,"1/2*(a^2*log(sin(f*x + e)^2) - (2*a*b - b^2)*log(sin(f*x + e)^2 - 1) - b^2/(sin(f*x + e)^2 - 1))/f","A",0
202,1,51,0,0.688488," ","integrate(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(\sin\left(f x + e\right)^{2} - 1\right) + {\left(a^{2} - 2 \, a b\right)} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{a^{2}}{\sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*(b^2*log(sin(f*x + e)^2 - 1) + (a^2 - 2*a*b)*log(sin(f*x + e)^2) + a^2/sin(f*x + e)^2)/f","A",0
203,1,61,0,0.315638," ","integrate(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right) + \frac{4 \, {\left(a^{2} - a b\right)} \sin\left(f x + e\right)^{2} - a^{2}}{\sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*(a^2 - 2*a*b + b^2)*log(sin(f*x + e)^2) + (4*(a^2 - a*b)*sin(f*x + e)^2 - a^2)/sin(f*x + e)^4)/f","A",0
204,1,118,0,0.979899," ","integrate(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{35 \, b^{2} \tan\left(f x + e\right)^{9} + 45 \, {\left(2 \, a b - b^{2}\right)} \tan\left(f x + e\right)^{7} + 63 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{5} - 105 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3} - 315 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(f x + e\right)} + 315 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{315 \, f}"," ",0,"1/315*(35*b^2*tan(f*x + e)^9 + 45*(2*a*b - b^2)*tan(f*x + e)^7 + 63*(a^2 - 2*a*b + b^2)*tan(f*x + e)^5 - 105*(a^2 - 2*a*b + b^2)*tan(f*x + e)^3 - 315*(a^2 - 2*a*b + b^2)*(f*x + e) + 315*(a^2 - 2*a*b + b^2)*tan(f*x + e))/f","A",0
205,1,97,0,0.648000," ","integrate(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{15 \, b^{2} \tan\left(f x + e\right)^{7} + 21 \, {\left(2 \, a b - b^{2}\right)} \tan\left(f x + e\right)^{5} + 35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3} + 105 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(f x + e\right)} - 105 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{105 \, f}"," ",0,"1/105*(15*b^2*tan(f*x + e)^7 + 21*(2*a*b - b^2)*tan(f*x + e)^5 + 35*(a^2 - 2*a*b + b^2)*tan(f*x + e)^3 + 105*(a^2 - 2*a*b + b^2)*(f*x + e) - 105*(a^2 - 2*a*b + b^2)*tan(f*x + e))/f","A",0
206,1,76,0,1.040378," ","integrate(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} \tan\left(f x + e\right)^{5} + 5 \, {\left(2 \, a b - b^{2}\right)} \tan\left(f x + e\right)^{3} - 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(f x + e\right)} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*b^2*tan(f*x + e)^5 + 5*(2*a*b - b^2)*tan(f*x + e)^3 - 15*(a^2 - 2*a*b + b^2)*(f*x + e) + 15*(a^2 - 2*a*b + b^2)*tan(f*x + e))/f","A",0
207,1,58,0,0.853194," ","integrate((a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","a^{2} x - \frac{2 \, {\left(f x + e - \tan\left(f x + e\right)\right)} a b}{f} + \frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, f x + 3 \, e - 3 \, \tan\left(f x + e\right)\right)} b^{2}}{3 \, f}"," ",0,"a^2*x - 2*(f*x + e - tan(f*x + e))*a*b/f + 1/3*(tan(f*x + e)^3 + 3*f*x + 3*e - 3*tan(f*x + e))*b^2/f","A",0
208,1,46,0,0.558592," ","integrate(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(f x + e\right) - {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(f x + e\right)} - \frac{a^{2}}{\tan\left(f x + e\right)}}{f}"," ",0,"(b^2*tan(f*x + e) - (a^2 - 2*a*b + b^2)*(f*x + e) - a^2/tan(f*x + e))/f","A",0
209,1,57,0,0.784290," ","integrate(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(f x + e\right)} + \frac{3 \, {\left(a^{2} - 2 \, a b\right)} \tan\left(f x + e\right)^{2} - a^{2}}{\tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*(3*(a^2 - 2*a*b + b^2)*(f*x + e) + (3*(a^2 - 2*a*b)*tan(f*x + e)^2 - a^2)/tan(f*x + e)^3)/f","A",0
210,1,78,0,0.795271," ","integrate(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(f x + e\right)} + \frac{15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{4} - 5 \, {\left(a^{2} - 2 \, a b\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2}}{\tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"-1/15*(15*(a^2 - 2*a*b + b^2)*(f*x + e) + (15*(a^2 - 2*a*b + b^2)*tan(f*x + e)^4 - 5*(a^2 - 2*a*b)*tan(f*x + e)^2 + 3*a^2)/tan(f*x + e)^5)/f","A",0
211,1,76,0,0.761329," ","integrate(tan(f*x+e)^5/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{a^{2} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a b^{2} - b^{3}} - \frac{{\left(a + b\right)} \log\left(\sin\left(f x + e\right)^{2} - 1\right)}{b^{2}} + \frac{1}{b \sin\left(f x + e\right)^{2} - b}}{2 \, f}"," ",0,"-1/2*(a^2*log(-(a - b)*sin(f*x + e)^2 + a)/(a*b^2 - b^3) - (a + b)*log(sin(f*x + e)^2 - 1)/b^2 + 1/(b*sin(f*x + e)^2 - b))/f","A",0
212,1,53,0,0.307479," ","integrate(tan(f*x+e)^3/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{a \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a b - b^{2}} - \frac{\log\left(\sin\left(f x + e\right)^{2} - 1\right)}{b}}{2 \, f}"," ",0,"1/2*(a*log(-(a - b)*sin(f*x + e)^2 + a)/(a*b - b^2) - log(sin(f*x + e)^2 - 1)/b)/f","A",0
213,1,30,0,0.306765," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{2 \, {\left(a - b\right)} f}"," ",0,"-1/2*log(-(a - b)*sin(f*x + e)^2 + a)/((a - b)*f)","A",0
214,1,49,0,0.830315," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{b \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{2} - a b} + \frac{\log\left(\sin\left(f x + e\right)^{2}\right)}{a}}{2 \, f}"," ",0,"1/2*(b*log(-(a - b)*sin(f*x + e)^2 + a)/(a^2 - a*b) + log(sin(f*x + e)^2)/a)/f","A",0
215,1,68,0,0.540675," ","integrate(cot(f*x+e)^3/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b^{2} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{3} - a^{2} b} + \frac{{\left(a + b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{2}} + \frac{1}{a \sin\left(f x + e\right)^{2}}}{2 \, f}"," ",0,"-1/2*(b^2*log(-(a - b)*sin(f*x + e)^2 + a)/(a^3 - a^2*b) + (a + b)*log(sin(f*x + e)^2)/a^2 + 1/(a*sin(f*x + e)^2))/f","A",0
216,1,96,0,0.458618," ","integrate(cot(f*x+e)^5/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{3} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{4} - a^{3} b} + \frac{2 \, {\left(a^{2} + a b + b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{3}} + \frac{2 \, {\left(2 \, a + b\right)} \sin\left(f x + e\right)^{2} - a}{a^{2} \sin\left(f x + e\right)^{4}}}{4 \, f}"," ",0,"1/4*(2*b^3*log(-(a - b)*sin(f*x + e)^2 + a)/(a^4 - a^3*b) + 2*(a^2 + a*b + b^2)*log(sin(f*x + e)^2)/a^3 + (2*(2*a + b)*sin(f*x + e)^2 - a)/(a^2*sin(f*x + e)^4))/f","A",0
217,1,83,0,0.898487," ","integrate(tan(f*x+e)^6/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{3} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a b^{2} - b^{3}\right)} \sqrt{a b}} - \frac{3 \, {\left(f x + e\right)}}{a - b} + \frac{b \tan\left(f x + e\right)^{3} - 3 \, {\left(a + b\right)} \tan\left(f x + e\right)}{b^{2}}}{3 \, f}"," ",0,"1/3*(3*a^3*arctan(b*tan(f*x + e)/sqrt(a*b))/((a*b^2 - b^3)*sqrt(a*b)) - 3*(f*x + e)/(a - b) + (b*tan(f*x + e)^3 - 3*(a + b)*tan(f*x + e))/b^2)/f","A",0
218,1,65,0,1.007645," ","integrate(tan(f*x+e)^4/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{a^{2} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a b - b^{2}\right)} \sqrt{a b}} - \frac{f x + e}{a - b} - \frac{\tan\left(f x + e\right)}{b}}{f}"," ",0,"-(a^2*arctan(b*tan(f*x + e)/sqrt(a*b))/((a*b - b^2)*sqrt(a*b)) - (f*x + e)/(a - b) - tan(f*x + e)/b)/f","A",0
219,1,47,0,0.736508," ","integrate(tan(f*x+e)^2/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{a \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} - \frac{f x + e}{a - b}}{f}"," ",0,"(a*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*(a - b)) - (f*x + e)/(a - b))/f","A",0
220,1,48,0,0.764312," ","integrate(1/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} - \frac{f x + e}{a - b}}{f}"," ",0,"-(b*arctan(b*tan(f*x + e)/sqrt(a*b))/(sqrt(a*b)*(a - b)) - (f*x + e)/(a - b))/f","A",0
221,1,65,0,1.074568," ","integrate(cot(f*x+e)^2/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{b^{2} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{2} - a b\right)} \sqrt{a b}} - \frac{f x + e}{a - b} - \frac{1}{a \tan\left(f x + e\right)}}{f}"," ",0,"(b^2*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^2 - a*b)*sqrt(a*b)) - (f*x + e)/(a - b) - 1/(a*tan(f*x + e)))/f","A",0
222,1,86,0,0.964540," ","integrate(cot(f*x+e)^4/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","-\frac{\frac{3 \, b^{3} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - a^{2} b\right)} \sqrt{a b}} - \frac{3 \, {\left(f x + e\right)}}{a - b} - \frac{3 \, {\left(a + b\right)} \tan\left(f x + e\right)^{2} - a}{a^{2} \tan\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"-1/3*(3*b^3*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3 - a^2*b)*sqrt(a*b)) - 3*(f*x + e)/(a - b) - (3*(a + b)*tan(f*x + e)^2 - a)/(a^2*tan(f*x + e)^3))/f","A",0
223,1,112,0,0.708499," ","integrate(cot(f*x+e)^6/(a+b*tan(f*x+e)^2),x, algorithm=""maxima"")","\frac{\frac{15 \, b^{4} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{4} - a^{3} b\right)} \sqrt{a b}} - \frac{15 \, {\left(f x + e\right)}}{a - b} - \frac{15 \, {\left(a^{2} + a b + b^{2}\right)} \tan\left(f x + e\right)^{4} - 5 \, {\left(a^{2} + a b\right)} \tan\left(f x + e\right)^{2} + 3 \, a^{2}}{a^{3} \tan\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*(15*b^4*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^4 - a^3*b)*sqrt(a*b)) - 15*(f*x + e)/(a - b) - (15*(a^2 + a*b + b^2)*tan(f*x + e)^4 - 5*(a^2 + a*b)*tan(f*x + e)^2 + 3*a^2)/(a^3*tan(f*x + e)^5))/f","A",0
224,1,128,0,0.334749," ","integrate(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{a^{2}}{a^{3} b - 2 \, a^{2} b^{2} + a b^{3} - {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sin\left(f x + e\right)^{2}} - \frac{{\left(a^{2} - 2 \, a b\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{2} b^{2} - 2 \, a b^{3} + b^{4}} + \frac{\log\left(\sin\left(f x + e\right)^{2} - 1\right)}{b^{2}}}{2 \, f}"," ",0,"-1/2*(a^2/(a^3*b - 2*a^2*b^2 + a*b^3 - (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sin(f*x + e)^2) - (a^2 - 2*a*b)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^2*b^2 - 2*a*b^3 + b^4) + log(sin(f*x + e)^2 - 1)/b^2)/f","A",0
225,1,88,0,0.344675," ","integrate(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{a}{a^{3} - 2 \, a^{2} b + a b^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{\log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{2} - 2 \, a b + b^{2}}}{2 \, f}"," ",0,"1/2*(a/(a^3 - 2*a^2*b + a*b^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sin(f*x + e)^2) + log(-(a - b)*sin(f*x + e)^2 + a)/(a^2 - 2*a*b + b^2))/f","A",0
226,1,88,0,0.643986," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b}{a^{3} - 2 \, a^{2} b + a b^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{\log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{2} - 2 \, a b + b^{2}}}{2 \, f}"," ",0,"-1/2*(b/(a^3 - 2*a^2*b + a*b^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sin(f*x + e)^2) + log(-(a - b)*sin(f*x + e)^2 + a)/(a^2 - 2*a*b + b^2))/f","A",0
227,1,124,0,0.541516," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{b^{2}}{a^{4} - 2 \, a^{3} b + a^{2} b^{2} - {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{{\left(2 \, a b - b^{2}\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{4} - 2 \, a^{3} b + a^{2} b^{2}} + \frac{\log\left(\sin\left(f x + e\right)^{2}\right)}{a^{2}}}{2 \, f}"," ",0,"1/2*(b^2/(a^4 - 2*a^3*b + a^2*b^2 - (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*sin(f*x + e)^2) + (2*a*b - b^2)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^4 - 2*a^3*b + a^2*b^2) + log(sin(f*x + e)^2)/a^2)/f","A",0
228,1,187,0,1.387173," ","integrate(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, a b^{2} - 2 \, b^{3}\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{5} - 2 \, a^{4} b + a^{3} b^{2}} - \frac{a^{3} - 2 \, a^{2} b + a b^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - 2 \, b^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(f x + e\right)^{4} - {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} \sin\left(f x + e\right)^{2}} + \frac{{\left(a + 2 \, b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{3}}}{2 \, f}"," ",0,"-1/2*((3*a*b^2 - 2*b^3)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^5 - 2*a^4*b + a^3*b^2) - (a^3 - 2*a^2*b + a*b^2 - (a^3 - 3*a^2*b + 3*a*b^2 - 2*b^3)*sin(f*x + e)^2)/((a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*sin(f*x + e)^4 - (a^5 - 2*a^4*b + a^3*b^2)*sin(f*x + e)^2) + (a + 2*b)*log(sin(f*x + e)^2)/a^3)/f","A",0
229,1,236,0,1.190428," ","integrate(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{6} - 2 \, a^{5} b + a^{4} b^{2}} + \frac{2 \, {\left(2 \, a^{4} - 4 \, a^{3} b + 4 \, a b^{3} - 3 \, b^{4}\right)} \sin\left(f x + e\right)^{4} + a^{4} - 2 \, a^{3} b + a^{2} b^{2} - {\left(5 \, a^{4} - 7 \, a^{3} b - a^{2} b^{2} + 3 \, a b^{3}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} \sin\left(f x + e\right)^{6} - {\left(a^{6} - 2 \, a^{5} b + a^{4} b^{2}\right)} \sin\left(f x + e\right)^{4}} + \frac{2 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{4}}}{4 \, f}"," ",0,"1/4*(2*(4*a*b^3 - 3*b^4)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^6 - 2*a^5*b + a^4*b^2) + (2*(2*a^4 - 4*a^3*b + 4*a*b^3 - 3*b^4)*sin(f*x + e)^4 + a^4 - 2*a^3*b + a^2*b^2 - (5*a^4 - 7*a^3*b - a^2*b^2 + 3*a*b^3)*sin(f*x + e)^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*sin(f*x + e)^6 - (a^6 - 2*a^5*b + a^4*b^2)*sin(f*x + e)^4) + 2*(a^2 + 2*a*b + 3*b^2)*log(sin(f*x + e)^2)/a^4)/f","A",0
230,1,135,0,1.642071," ","integrate(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{a^{2} \tan\left(f x + e\right)}{a^{2} b^{2} - a b^{3} + {\left(a b^{3} - b^{4}\right)} \tan\left(f x + e\right)^{2}} - \frac{{\left(3 \, a^{3} - 5 \, a^{2} b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sqrt{a b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}} + \frac{2 \, \tan\left(f x + e\right)}{b^{2}}}{2 \, f}"," ",0,"1/2*(a^2*tan(f*x + e)/(a^2*b^2 - a*b^3 + (a*b^3 - b^4)*tan(f*x + e)^2) - (3*a^3 - 5*a^2*b)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^2*b^2 - 2*a*b^3 + b^4)*sqrt(a*b)) - 2*(f*x + e)/(a^2 - 2*a*b + b^2) + 2*tan(f*x + e)/b^2)/f","A",0
231,1,114,0,0.752083," ","integrate(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{a \tan\left(f x + e\right)}{a^{2} b - a b^{2} + {\left(a b^{2} - b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{{\left(a^{2} - 3 \, a b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sqrt{a b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}}}{2 \, f}"," ",0,"-1/2*(a*tan(f*x + e)/(a^2*b - a*b^2 + (a*b^2 - b^3)*tan(f*x + e)^2) - (a^2 - 3*a*b)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^2*b - 2*a*b^2 + b^3)*sqrt(a*b)) - 2*(f*x + e)/(a^2 - 2*a*b + b^2))/f","A",0
232,1,97,0,0.765834," ","integrate(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(a + b\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}} + \frac{\tan\left(f x + e\right)}{{\left(a b - b^{2}\right)} \tan\left(f x + e\right)^{2} + a^{2} - a b}}{2 \, f}"," ",0,"1/2*((a + b)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^2 - 2*a*b + b^2)*sqrt(a*b)) - 2*(f*x + e)/(a^2 - 2*a*b + b^2) + tan(f*x + e)/((a*b - b^2)*tan(f*x + e)^2 + a^2 - a*b))/f","A",0
233,1,114,0,0.757979," ","integrate(1/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \tan\left(f x + e\right)}{a^{3} - a^{2} b + {\left(a^{2} b - a b^{2}\right)} \tan\left(f x + e\right)^{2}} + \frac{{\left(3 \, a b - b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} - \frac{2 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}}}{2 \, f}"," ",0,"-1/2*(b*tan(f*x + e)/(a^3 - a^2*b + (a^2*b - a*b^2)*tan(f*x + e)^2) + (3*a*b - b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3 - 2*a^2*b + a*b^2)*sqrt(a*b)) - 2*(f*x + e)/(a^2 - 2*a*b + b^2))/f","A",0
234,1,151,0,0.714614," ","integrate(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(5 \, a b^{2} - 3 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{a b}} - \frac{{\left(2 \, a b - 3 \, b^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, a^{2} - 2 \, a b}{{\left(a^{3} b - a^{2} b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{4} - a^{3} b\right)} \tan\left(f x + e\right)} - \frac{2 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}}}{2 \, f}"," ",0,"1/2*((5*a*b^2 - 3*b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^4 - 2*a^3*b + a^2*b^2)*sqrt(a*b)) - ((2*a*b - 3*b^2)*tan(f*x + e)^2 + 2*a^2 - 2*a*b)/((a^3*b - a^2*b^2)*tan(f*x + e)^3 + (a^4 - a^3*b)*tan(f*x + e)) - 2*(f*x + e)/(a^2 - 2*a*b + b^2))/f","A",0
235,1,193,0,0.769021," ","integrate(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(7 \, a b^{3} - 5 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{a b}} - \frac{3 \, {\left(2 \, a^{2} b + 2 \, a b^{2} - 5 \, b^{3}\right)} \tan\left(f x + e\right)^{4} - 2 \, a^{3} + 2 \, a^{2} b + 2 \, {\left(3 \, a^{3} + 2 \, a^{2} b - 5 \, a b^{2}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{4} b - a^{3} b^{2}\right)} \tan\left(f x + e\right)^{5} + {\left(a^{5} - a^{4} b\right)} \tan\left(f x + e\right)^{3}} - \frac{6 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}}}{6 \, f}"," ",0,"-1/6*(3*(7*a*b^3 - 5*b^4)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^5 - 2*a^4*b + a^3*b^2)*sqrt(a*b)) - (3*(2*a^2*b + 2*a*b^2 - 5*b^3)*tan(f*x + e)^4 - 2*a^3 + 2*a^2*b + 2*(3*a^3 + 2*a^2*b - 5*a*b^2)*tan(f*x + e)^2)/((a^4*b - a^3*b^2)*tan(f*x + e)^5 + (a^5 - a^4*b)*tan(f*x + e)^3) - 6*(f*x + e)/(a^2 - 2*a*b + b^2))/f","A",0
236,1,239,0,0.754242," ","integrate(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(9 \, a b^{4} - 7 \, b^{5}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{6} - 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{a b}} - \frac{15 \, {\left(2 \, a^{3} b + 2 \, a^{2} b^{2} + 2 \, a b^{3} - 7 \, b^{4}\right)} \tan\left(f x + e\right)^{6} + 10 \, {\left(3 \, a^{4} + 2 \, a^{3} b + 2 \, a^{2} b^{2} - 7 \, a b^{3}\right)} \tan\left(f x + e\right)^{4} + 6 \, a^{4} - 6 \, a^{3} b - 2 \, {\left(5 \, a^{4} + 2 \, a^{3} b - 7 \, a^{2} b^{2}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{5} b - a^{4} b^{2}\right)} \tan\left(f x + e\right)^{7} + {\left(a^{6} - a^{5} b\right)} \tan\left(f x + e\right)^{5}} - \frac{30 \, {\left(f x + e\right)}}{a^{2} - 2 \, a b + b^{2}}}{30 \, f}"," ",0,"1/30*(15*(9*a*b^4 - 7*b^5)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^6 - 2*a^5*b + a^4*b^2)*sqrt(a*b)) - (15*(2*a^3*b + 2*a^2*b^2 + 2*a*b^3 - 7*b^4)*tan(f*x + e)^6 + 10*(3*a^4 + 2*a^3*b + 2*a^2*b^2 - 7*a*b^3)*tan(f*x + e)^4 + 6*a^4 - 6*a^3*b - 2*(5*a^4 + 2*a^3*b - 7*a^2*b^2)*tan(f*x + e)^2)/((a^5*b - a^4*b^2)*tan(f*x + e)^7 + (a^6 - a^5*b)*tan(f*x + e)^5) - 30*(f*x + e)/(a^2 - 2*a*b + b^2))/f","A",0
237,1,189,0,0.543321," ","integrate(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(a^{2} - a b\right)} \sin\left(f x + e\right)^{2} - 3 \, a^{2}}{a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(f x + e\right)^{2}} - \frac{2 \, \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{4 \, f}"," ",0,"1/4*((4*(a^2 - a*b)*sin(f*x + e)^2 - 3*a^2)/(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*sin(f*x + e)^4 - 2*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*sin(f*x + e)^2) - 2*log(-(a - b)*sin(f*x + e)^2 + a)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
238,1,194,0,0.434944," ","integrate(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} - b^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, a^{2} - a b}{a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(f x + e\right)^{2}} - \frac{2 \, \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{4 \, f}"," ",0,"-1/4*((2*(a^2 - b^2)*sin(f*x + e)^2 - 2*a^2 - a*b)/(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*sin(f*x + e)^4 - 2*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*sin(f*x + e)^2) - 2*log(-(a - b)*sin(f*x + e)^2 + a)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","B",0
239,1,192,0,0.526957," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(a b - b^{2}\right)} \sin\left(f x + e\right)^{2} - 4 \, a b + b^{2}}{a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(f x + e\right)^{2}} - \frac{2 \, \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{4 \, f}"," ",0,"1/4*((4*(a*b - b^2)*sin(f*x + e)^2 - 4*a*b + b^2)/(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3 + (a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*sin(f*x + e)^4 - 2*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*sin(f*x + e)^2) - 2*log(-(a - b)*sin(f*x + e)^2 + a)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","B",0
240,1,250,0,0.410621," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}} + \frac{6 \, a^{2} b^{2} - 3 \, a b^{3} - 2 \, {\left(3 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}\right)} \sin\left(f x + e\right)^{2}}{a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3} + {\left(a^{7} - 5 \, a^{6} b + 10 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} - a^{2} b^{5}\right)} \sin\left(f x + e\right)^{4} - 2 \, {\left(a^{7} - 4 \, a^{6} b + 6 \, a^{5} b^{2} - 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sin\left(f x + e\right)^{2}} + \frac{2 \, \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{3}}}{4 \, f}"," ",0,"1/4*(2*(3*a^2*b - 3*a*b^2 + b^3)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3) + (6*a^2*b^2 - 3*a*b^3 - 2*(3*a^2*b^2 - 4*a*b^3 + b^4)*sin(f*x + e)^2)/(a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3 + (a^7 - 5*a^6*b + 10*a^5*b^2 - 10*a^4*b^3 + 5*a^3*b^4 - a^2*b^5)*sin(f*x + e)^4 - 2*(a^7 - 4*a^6*b + 6*a^5*b^2 - 4*a^4*b^3 + a^3*b^4)*sin(f*x + e)^2) + 2*log(sin(f*x + e)^2)/a^3)/f","A",0
241,1,345,0,0.968051," ","integrate(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(6 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}} + \frac{2 \, a^{5} - 6 \, a^{4} b + 6 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 2 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 11 \, a b^{4} - 3 \, b^{5}\right)} \sin\left(f x + e\right)^{4} - {\left(4 \, a^{5} - 16 \, a^{4} b + 24 \, a^{3} b^{2} - 24 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{8} - 5 \, a^{7} b + 10 \, a^{6} b^{2} - 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} - a^{3} b^{5}\right)} \sin\left(f x + e\right)^{6} - 2 \, {\left(a^{8} - 4 \, a^{7} b + 6 \, a^{6} b^{2} - 4 \, a^{5} b^{3} + a^{4} b^{4}\right)} \sin\left(f x + e\right)^{4} + {\left(a^{8} - 3 \, a^{7} b + 3 \, a^{6} b^{2} - a^{5} b^{3}\right)} \sin\left(f x + e\right)^{2}} + \frac{2 \, {\left(a + 3 \, b\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{4}}}{4 \, f}"," ",0,"-1/4*(2*(6*a^2*b^2 - 8*a*b^3 + 3*b^4)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3) + (2*a^5 - 6*a^4*b + 6*a^3*b^2 - 2*a^2*b^3 + 2*(a^5 - 5*a^4*b + 10*a^3*b^2 - 14*a^2*b^3 + 11*a*b^4 - 3*b^5)*sin(f*x + e)^4 - (4*a^5 - 16*a^4*b + 24*a^3*b^2 - 24*a^2*b^3 + 9*a*b^4)*sin(f*x + e)^2)/((a^8 - 5*a^7*b + 10*a^6*b^2 - 10*a^5*b^3 + 5*a^4*b^4 - a^3*b^5)*sin(f*x + e)^6 - 2*(a^8 - 4*a^7*b + 6*a^6*b^2 - 4*a^5*b^3 + a^4*b^4)*sin(f*x + e)^4 + (a^8 - 3*a^7*b + 3*a^6*b^2 - a^5*b^3)*sin(f*x + e)^2) + 2*(a + 3*b)*log(sin(f*x + e)^2)/a^4)/f","A",0
242,1,416,0,0.383180," ","integrate(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(10 \, a^{2} b^{3} - 15 \, a b^{4} + 6 \, b^{5}\right)} \log\left(-{\left(a - b\right)} \sin\left(f x + e\right)^{2} + a\right)}{a^{8} - 3 \, a^{7} b + 3 \, a^{6} b^{2} - a^{5} b^{3}} + \frac{2 \, {\left(2 \, a^{6} - 7 \, a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} - 25 \, a^{2} b^{4} + 21 \, a b^{5} - 6 \, b^{6}\right)} \sin\left(f x + e\right)^{6} - a^{6} + 3 \, a^{5} b - 3 \, a^{4} b^{2} + a^{3} b^{3} - {\left(9 \, a^{6} - 25 \, a^{5} b + 10 \, a^{4} b^{2} + 30 \, a^{3} b^{3} - 45 \, a^{2} b^{4} + 18 \, a b^{5}\right)} \sin\left(f x + e\right)^{4} + 2 \, {\left(3 \, a^{6} - 7 \, a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - 2 \, a^{2} b^{4}\right)} \sin\left(f x + e\right)^{2}}{{\left(a^{9} - 5 \, a^{8} b + 10 \, a^{7} b^{2} - 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} - a^{4} b^{5}\right)} \sin\left(f x + e\right)^{8} - 2 \, {\left(a^{9} - 4 \, a^{8} b + 6 \, a^{7} b^{2} - 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} \sin\left(f x + e\right)^{6} + {\left(a^{9} - 3 \, a^{8} b + 3 \, a^{7} b^{2} - a^{6} b^{3}\right)} \sin\left(f x + e\right)^{4}} + \frac{2 \, {\left(a^{2} + 3 \, a b + 6 \, b^{2}\right)} \log\left(\sin\left(f x + e\right)^{2}\right)}{a^{5}}}{4 \, f}"," ",0,"1/4*(2*(10*a^2*b^3 - 15*a*b^4 + 6*b^5)*log(-(a - b)*sin(f*x + e)^2 + a)/(a^8 - 3*a^7*b + 3*a^6*b^2 - a^5*b^3) + (2*(2*a^6 - 7*a^5*b + 5*a^4*b^2 + 10*a^3*b^3 - 25*a^2*b^4 + 21*a*b^5 - 6*b^6)*sin(f*x + e)^6 - a^6 + 3*a^5*b - 3*a^4*b^2 + a^3*b^3 - (9*a^6 - 25*a^5*b + 10*a^4*b^2 + 30*a^3*b^3 - 45*a^2*b^4 + 18*a*b^5)*sin(f*x + e)^4 + 2*(3*a^6 - 7*a^5*b + 3*a^4*b^2 + 3*a^3*b^3 - 2*a^2*b^4)*sin(f*x + e)^2)/((a^9 - 5*a^8*b + 10*a^7*b^2 - 10*a^6*b^3 + 5*a^5*b^4 - a^4*b^5)*sin(f*x + e)^8 - 2*(a^9 - 4*a^8*b + 6*a^7*b^2 - 4*a^6*b^3 + a^5*b^4)*sin(f*x + e)^6 + (a^9 - 3*a^8*b + 3*a^7*b^2 - a^6*b^3)*sin(f*x + e)^4) + 2*(a^2 + 3*a*b + 6*b^2)*log(sin(f*x + e)^2)/a^5)/f","B",0
243,1,229,0,0.838213," ","integrate(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{3} - 10 \, a^{2} b + 15 \, a b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \sqrt{a b}} - \frac{{\left(5 \, a^{2} b - 9 \, a b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(3 \, a^{3} - 7 \, a^{2} b\right)} \tan\left(f x + e\right)}{a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{2} b^{4} - 2 \, a b^{5} + b^{6}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{3} b^{3} - 2 \, a^{2} b^{4} + a b^{5}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, f}"," ",0,"1/8*((3*a^3 - 10*a^2*b + 15*a*b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*sqrt(a*b)) - ((5*a^2*b - 9*a*b^2)*tan(f*x + e)^3 + (3*a^3 - 7*a^2*b)*tan(f*x + e))/(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 + (a^2*b^4 - 2*a*b^5 + b^6)*tan(f*x + e)^4 + 2*(a^3*b^3 - 2*a^2*b^4 + a*b^5)*tan(f*x + e)^2) - 8*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
244,1,212,0,0.878009," ","integrate(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{2} - 6 \, a b - 3 \, b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} \sqrt{a b}} + \frac{{\left(a b - 5 \, b^{2}\right)} \tan\left(f x + e\right)^{3} - {\left(a^{2} + 3 \, a b\right)} \tan\left(f x + e\right)}{a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \tan\left(f x + e\right)^{2}} + \frac{8 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, f}"," ",0,"1/8*((a^2 - 6*a*b - 3*b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*sqrt(a*b)) + ((a*b - 5*b^2)*tan(f*x + e)^3 - (a^2 + 3*a*b)*tan(f*x + e))/(a^4*b - 2*a^3*b^2 + a^2*b^3 + (a^2*b^3 - 2*a*b^4 + b^5)*tan(f*x + e)^4 + 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*tan(f*x + e)^2) + 8*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
245,1,213,0,0.881127," ","integrate(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{2} + 6 \, a b - b^{2}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} \sqrt{a b}} + \frac{{\left(3 \, a b + b^{2}\right)} \tan\left(f x + e\right)^{3} + {\left(5 \, a^{2} - a b\right)} \tan\left(f x + e\right)}{a^{5} - 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, f}"," ",0,"1/8*((3*a^2 + 6*a*b - b^2)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*sqrt(a*b)) + ((3*a*b + b^2)*tan(f*x + e)^3 + (5*a^2 - a*b)*tan(f*x + e))/(a^5 - 2*a^4*b + a^3*b^2 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*tan(f*x + e)^4 + 2*(a^4*b - 2*a^3*b^2 + a^2*b^3)*tan(f*x + e)^2) - 8*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
246,1,227,0,1.050294," ","integrate(1/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{a b}} + \frac{{\left(7 \, a b^{2} - 3 \, b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 5 \, a b^{2}\right)} \tan\left(f x + e\right)}{a^{6} - 2 \, a^{5} b + a^{4} b^{2} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} + 2 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(f x + e\right)^{2}} - \frac{8 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, f}"," ",0,"-1/8*((15*a^2*b - 10*a*b^2 + 3*b^3)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*sqrt(a*b)) + ((7*a*b^2 - 3*b^3)*tan(f*x + e)^3 + (9*a^2*b - 5*a*b^2)*tan(f*x + e))/(a^6 - 2*a^5*b + a^4*b^2 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*tan(f*x + e)^4 + 2*(a^5*b - 2*a^4*b^2 + a^3*b^3)*tan(f*x + e)^2) - 8*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
247,1,275,0,0.821304," ","integrate(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(35 \, a^{2} b^{2} - 42 \, a b^{3} + 15 \, b^{4}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} \sqrt{a b}} - \frac{{\left(8 \, a^{2} b^{2} - 27 \, a b^{3} + 15 \, b^{4}\right)} \tan\left(f x + e\right)^{4} + 8 \, a^{4} - 16 \, a^{3} b + 8 \, a^{2} b^{2} + {\left(16 \, a^{3} b - 45 \, a^{2} b^{2} + 25 \, a b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} \tan\left(f x + e\right)^{5} + 2 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} \tan\left(f x + e\right)} - \frac{8 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, f}"," ",0,"1/8*((35*a^2*b^2 - 42*a*b^3 + 15*b^4)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*sqrt(a*b)) - ((8*a^2*b^2 - 27*a*b^3 + 15*b^4)*tan(f*x + e)^4 + 8*a^4 - 16*a^3*b + 8*a^2*b^2 + (16*a^3*b - 45*a^2*b^2 + 25*a*b^3)*tan(f*x + e)^2)/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*tan(f*x + e)^5 + 2*(a^6*b - 2*a^5*b^2 + a^4*b^3)*tan(f*x + e)^3 + (a^7 - 2*a^6*b + a^5*b^2)*tan(f*x + e)) - 8*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
248,1,332,0,0.579995," ","integrate(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(63 \, a^{2} b^{3} - 90 \, a b^{4} + 35 \, b^{5}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} \sqrt{a b}} - \frac{3 \, {\left(8 \, a^{3} b^{2} + 8 \, a^{2} b^{3} - 55 \, a b^{4} + 35 \, b^{5}\right)} \tan\left(f x + e\right)^{6} - 8 \, a^{5} + 16 \, a^{4} b - 8 \, a^{3} b^{2} + {\left(48 \, a^{4} b + 40 \, a^{3} b^{2} - 275 \, a^{2} b^{3} + 175 \, a b^{4}\right)} \tan\left(f x + e\right)^{4} + 8 \, {\left(3 \, a^{5} + a^{4} b - 11 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{6} b^{2} - 2 \, a^{5} b^{3} + a^{4} b^{4}\right)} \tan\left(f x + e\right)^{7} + 2 \, {\left(a^{7} b - 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} \tan\left(f x + e\right)^{5} + {\left(a^{8} - 2 \, a^{7} b + a^{6} b^{2}\right)} \tan\left(f x + e\right)^{3}} - \frac{24 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{24 \, f}"," ",0,"-1/24*(3*(63*a^2*b^3 - 90*a*b^4 + 35*b^5)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*sqrt(a*b)) - (3*(8*a^3*b^2 + 8*a^2*b^3 - 55*a*b^4 + 35*b^5)*tan(f*x + e)^6 - 8*a^5 + 16*a^4*b - 8*a^3*b^2 + (48*a^4*b + 40*a^3*b^2 - 275*a^2*b^3 + 175*a*b^4)*tan(f*x + e)^4 + 8*(3*a^5 + a^4*b - 11*a^3*b^2 + 7*a^2*b^3)*tan(f*x + e)^2)/((a^6*b^2 - 2*a^5*b^3 + a^4*b^4)*tan(f*x + e)^7 + 2*(a^7*b - 2*a^6*b^2 + a^5*b^3)*tan(f*x + e)^5 + (a^8 - 2*a^7*b + a^6*b^2)*tan(f*x + e)^3) - 24*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
249,1,396,0,1.386474," ","integrate(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(99 \, a^{2} b^{4} - 154 \, a b^{5} + 63 \, b^{6}\right)} \arctan\left(\frac{b \tan\left(f x + e\right)}{\sqrt{a b}}\right)}{{\left(a^{8} - 3 \, a^{7} b + 3 \, a^{6} b^{2} - a^{5} b^{3}\right)} \sqrt{a b}} - \frac{15 \, {\left(8 \, a^{4} b^{2} + 8 \, a^{3} b^{3} + 8 \, a^{2} b^{4} - 91 \, a b^{5} + 63 \, b^{6}\right)} \tan\left(f x + e\right)^{8} + 5 \, {\left(48 \, a^{5} b + 40 \, a^{4} b^{2} + 40 \, a^{3} b^{3} - 455 \, a^{2} b^{4} + 315 \, a b^{5}\right)} \tan\left(f x + e\right)^{6} + 24 \, a^{6} - 48 \, a^{5} b + 24 \, a^{4} b^{2} + 8 \, {\left(15 \, a^{6} + 5 \, a^{5} b + 8 \, a^{4} b^{2} - 91 \, a^{3} b^{3} + 63 \, a^{2} b^{4}\right)} \tan\left(f x + e\right)^{4} - 8 \, {\left(5 \, a^{6} - a^{5} b - 13 \, a^{4} b^{2} + 9 \, a^{3} b^{3}\right)} \tan\left(f x + e\right)^{2}}{{\left(a^{7} b^{2} - 2 \, a^{6} b^{3} + a^{5} b^{4}\right)} \tan\left(f x + e\right)^{9} + 2 \, {\left(a^{8} b - 2 \, a^{7} b^{2} + a^{6} b^{3}\right)} \tan\left(f x + e\right)^{7} + {\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} \tan\left(f x + e\right)^{5}} - \frac{120 \, {\left(f x + e\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{120 \, f}"," ",0,"1/120*(15*(99*a^2*b^4 - 154*a*b^5 + 63*b^6)*arctan(b*tan(f*x + e)/sqrt(a*b))/((a^8 - 3*a^7*b + 3*a^6*b^2 - a^5*b^3)*sqrt(a*b)) - (15*(8*a^4*b^2 + 8*a^3*b^3 + 8*a^2*b^4 - 91*a*b^5 + 63*b^6)*tan(f*x + e)^8 + 5*(48*a^5*b + 40*a^4*b^2 + 40*a^3*b^3 - 455*a^2*b^4 + 315*a*b^5)*tan(f*x + e)^6 + 24*a^6 - 48*a^5*b + 24*a^4*b^2 + 8*(15*a^6 + 5*a^5*b + 8*a^4*b^2 - 91*a^3*b^3 + 63*a^2*b^4)*tan(f*x + e)^4 - 8*(5*a^6 - a^5*b - 13*a^4*b^2 + 9*a^3*b^3)*tan(f*x + e)^2)/((a^7*b^2 - 2*a^6*b^3 + a^5*b^4)*tan(f*x + e)^9 + 2*(a^8*b - 2*a^7*b^2 + a^6*b^3)*tan(f*x + e)^7 + (a^9 - 2*a^8*b + a^7*b^2)*tan(f*x + e)^5) - 120*(f*x + e)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/f","A",0
250,1,162,0,0.416802," ","integrate((a+b*tan(d*x+c)^2)^4,x, algorithm=""maxima"")","a^{4} x - \frac{4 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} b}{d} + \frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} b^{2}}{d} + \frac{4 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a b^{3}}{15 \, d} + \frac{{\left(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 \, c - 105 \, \tan\left(d x + c\right)\right)} b^{4}}{105 \, d}"," ",0,"a^4*x - 4*(d*x + c - tan(d*x + c))*a^3*b/d + 2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2*b^2/d + 4/15*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a*b^3/d + 1/105*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*b^4/d","A",0
251,1,104,0,0.910430," ","integrate((a+b*tan(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x - \frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} b}{d} + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a b^{2}}{d} + \frac{{\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} b^{3}}{15 \, d}"," ",0,"a^3*x - 3*(d*x + c - tan(d*x + c))*a^2*b/d + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a*b^2/d + 1/15*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*b^3/d","A",0
252,1,58,0,1.128332," ","integrate((a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} x - \frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b}{d} + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} b^{2}}{3 \, d}"," ",0,"a^2*x - 2*(d*x + c - tan(d*x + c))*a*b/d + 1/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*b^2/d","A",0
253,1,23,0,0.821749," ","integrate(a+b*tan(d*x+c)^2,x, algorithm=""maxima"")","a x - \frac{{\left(d x + c - \tan\left(d x + c\right)\right)} b}{d}"," ",0,"a*x - (d*x + c - tan(d*x + c))*b/d","A",0
254,1,48,0,0.780650," ","integrate(1/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} - \frac{d x + c}{a - b}}{d}"," ",0,"-(b*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*(a - b)) - (d*x + c)/(a - b))/d","A",0
255,1,114,0,0.859310," ","integrate(1/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{b \tan\left(d x + c\right)}{a^{3} - a^{2} b + {\left(a^{2} b - a b^{2}\right)} \tan\left(d x + c\right)^{2}} + \frac{{\left(3 \, a b - b^{2}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} - \frac{2 \, {\left(d x + c\right)}}{a^{2} - 2 \, a b + b^{2}}}{2 \, d}"," ",0,"-1/2*(b*tan(d*x + c)/(a^3 - a^2*b + (a^2*b - a*b^2)*tan(d*x + c)^2) + (3*a*b - b^2)*arctan(b*tan(d*x + c)/sqrt(a*b))/((a^3 - 2*a^2*b + a*b^2)*sqrt(a*b)) - 2*(d*x + c)/(a^2 - 2*a*b + b^2))/d","A",0
256,1,227,0,1.008199," ","integrate(1/(a+b*tan(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{a b}} + \frac{{\left(7 \, a b^{2} - 3 \, b^{3}\right)} \tan\left(d x + c\right)^{3} + {\left(9 \, a^{2} b - 5 \, a b^{2}\right)} \tan\left(d x + c\right)}{a^{6} - 2 \, a^{5} b + a^{4} b^{2} + {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(d x + c\right)^{2}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, d}"," ",0,"-1/8*((15*a^2*b - 10*a*b^2 + 3*b^3)*arctan(b*tan(d*x + c)/sqrt(a*b))/((a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*sqrt(a*b)) + ((7*a*b^2 - 3*b^3)*tan(d*x + c)^3 + (9*a^2*b - 5*a*b^2)*tan(d*x + c))/(a^6 - 2*a^5*b + a^4*b^2 + (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*tan(d*x + c)^4 + 2*(a^5*b - 2*a^4*b^2 + a^3*b^3)*tan(d*x + c)^2) - 8*(d*x + c)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/d","A",0
257,1,860,0,1.550346," ","integrate((a+a*tan(x)^2)^(1/2)*tan(x)^4,x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(5 \, \sin\left(7 \, x\right) - 3 \, \sin\left(5 \, x\right) + 3 \, \sin\left(3 \, x\right) - 5 \, \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 40 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 16 \, {\left(3 \, \sin\left(5 \, x\right) - 3 \, \sin\left(3 \, x\right) + 5 \, \sin\left(x\right)\right)} \cos\left(6 \, x\right) + 24 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) + 24 \, {\left(3 \, \sin\left(3 \, x\right) - 5 \, \sin\left(x\right)\right)} \cos\left(4 \, x\right) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(5 \, \cos\left(7 \, x\right) - 3 \, \cos\left(5 \, x\right) + 3 \, \cos\left(3 \, x\right) - 5 \, \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 20 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(7 \, x\right) + 16 \, {\left(3 \, \cos\left(5 \, x\right) - 3 \, \cos\left(3 \, x\right) + 5 \, \cos\left(x\right)\right)} \sin\left(6 \, x\right) - 12 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(5 \, x\right) - 24 \, {\left(3 \, \cos\left(3 \, x\right) - 5 \, \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) - 48 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 80 \, \cos\left(x\right) \sin\left(2 \, x\right) - 80 \, \cos\left(2 \, x\right) \sin\left(x\right) - 20 \, \sin\left(x\right)\right)} \sqrt{a}}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-1/16*(4*(5*sin(7*x) - 3*sin(5*x) + 3*sin(3*x) - 5*sin(x))*cos(8*x) - 40*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*cos(7*x) - 16*(3*sin(5*x) - 3*sin(3*x) + 5*sin(x))*cos(6*x) + 24*(3*sin(4*x) + 2*sin(2*x))*cos(5*x) + 24*(3*sin(3*x) - 5*sin(x))*cos(4*x) - 3*(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 3*(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(5*cos(7*x) - 3*cos(5*x) + 3*cos(3*x) - 5*cos(x))*sin(8*x) + 20*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*sin(7*x) + 16*(3*cos(5*x) - 3*cos(3*x) + 5*cos(x))*sin(6*x) - 12*(6*cos(4*x) + 4*cos(2*x) + 1)*sin(5*x) - 24*(3*cos(3*x) - 5*cos(x))*sin(4*x) + 12*(4*cos(2*x) + 1)*sin(3*x) - 48*cos(3*x)*sin(2*x) + 80*cos(x)*sin(2*x) - 80*cos(2*x)*sin(x) - 20*sin(x))*sqrt(a)/(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)","B",0
258,1,276,0,0.788389," ","integrate((a+a*tan(x)^2)^(1/2)*tan(x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(3 \, \cos\left(5 \, x\right) + 2 \, \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \cos\left(6 \, x\right) + 3 \, {\left(3 \, \cos\left(4 \, x\right) + 3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(5 \, x\right) + 3 \, {\left(2 \, \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \cos\left(4 \, x\right) + 2 \, {\left(3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(3 \, x\right) + 9 \, \cos\left(2 \, x\right) \cos\left(x\right) + {\left(3 \, \sin\left(5 \, x\right) + 2 \, \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \sin\left(6 \, x\right) + 9 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(5 \, x\right) + 3 \, {\left(2 \, \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 6 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) + 9 \, \sin\left(2 \, x\right) \sin\left(x\right) + 3 \, \cos\left(x\right)\right)} \sqrt{a}}{3 \, {\left(2 \, {\left(3 \, \cos\left(4 \, x\right) + 3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + \cos\left(6 \, x\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 9 \, \cos\left(4 \, x\right)^{2} + 9 \, \cos\left(2 \, x\right)^{2} + 6 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + \sin\left(6 \, x\right)^{2} + 9 \, \sin\left(4 \, x\right)^{2} + 18 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 9 \, \sin\left(2 \, x\right)^{2} + 6 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-2/3*((3*cos(5*x) + 2*cos(3*x) + 3*cos(x))*cos(6*x) + 3*(3*cos(4*x) + 3*cos(2*x) + 1)*cos(5*x) + 3*(2*cos(3*x) + 3*cos(x))*cos(4*x) + 2*(3*cos(2*x) + 1)*cos(3*x) + 9*cos(2*x)*cos(x) + (3*sin(5*x) + 2*sin(3*x) + 3*sin(x))*sin(6*x) + 9*(sin(4*x) + sin(2*x))*sin(5*x) + 3*(2*sin(3*x) + 3*sin(x))*sin(4*x) + 6*sin(3*x)*sin(2*x) + 9*sin(2*x)*sin(x) + 3*cos(x))*sqrt(a)/(2*(3*cos(4*x) + 3*cos(2*x) + 1)*cos(6*x) + cos(6*x)^2 + 6*(3*cos(2*x) + 1)*cos(4*x) + 9*cos(4*x)^2 + 9*cos(2*x)^2 + 6*(sin(4*x) + sin(2*x))*sin(6*x) + sin(6*x)^2 + 9*sin(4*x)^2 + 18*sin(4*x)*sin(2*x) + 9*sin(2*x)^2 + 6*cos(2*x) + 1)","B",0
259,1,295,0,0.884429," ","integrate((a+a*tan(x)^2)^(1/2)*tan(x)^2,x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 4 \, {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 4 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) - 8 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 8 \, \cos\left(x\right) \sin\left(2 \, x\right) - 8 \, \cos\left(2 \, x\right) \sin\left(x\right) - 4 \, \sin\left(x\right)\right)} \sqrt{a}}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/4*(4*(sin(3*x) - sin(x))*cos(4*x) - (2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + (2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 4*(cos(3*x) - cos(x))*sin(4*x) + 4*(2*cos(2*x) + 1)*sin(3*x) - 8*cos(3*x)*sin(2*x) + 8*cos(x)*sin(2*x) - 8*cos(2*x)*sin(x) - 4*sin(x))*sqrt(a)/(2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)","B",0
260,0,0,0,0.000000," ","integrate((a+a*tan(x)^2)^(1/2)*tan(x),x, algorithm=""maxima"")","\int \sqrt{a \tan\left(x\right)^{2} + a} \tan\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*tan(x)^2 + a)*tan(x), x)","F",0
261,1,38,0,1.043728," ","integrate(cot(x)*(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{a} {\left(\log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)\right)}"," ",0,"-1/2*sqrt(a)*(log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1))","B",0
262,1,17,0,0.847869," ","integrate(cot(x)^2*(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{\tan\left(x\right)^{2} + 1} \sqrt{a}}{\tan\left(x\right)}"," ",0,"-sqrt(tan(x)^2 + 1)*sqrt(a)/tan(x)","A",0
263,1,303,0,0.862279," ","integrate(cot(x)^3*(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) \cos\left(x\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + 4 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 8 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 8 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \cos\left(x\right)\right)} \sqrt{a}}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"-1/4*(4*(cos(3*x) + cos(x))*cos(4*x) - 4*(2*cos(2*x) - 1)*cos(3*x) - 8*cos(2*x)*cos(x) - (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*(sin(3*x) + sin(x))*sin(4*x) - 8*sin(3*x)*sin(2*x) - 8*sin(2*x)*sin(x) + 4*cos(x))*sqrt(a)/(2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)","B",0
264,1,29,0,0.974792," ","integrate(cot(x)^4*(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{a} \tan\left(x\right)^{2} - \sqrt{a}\right)} \sqrt{\tan\left(x\right)^{2} + 1}}{3 \, \tan\left(x\right)^{3}}"," ",0,"1/3*(2*sqrt(a)*tan(x)^2 - sqrt(a))*sqrt(tan(x)^2 + 1)/tan(x)^3","A",0
265,1,65,0,1.143328," ","integrate((a+a*tan(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{2 \, d}"," ",0,"1/2*sqrt(a)*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","B",0
266,1,559,0,1.634282," ","integrate(tan(x)^3*(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(50 \, a \cos\left(4 \, x\right) \cos\left(3 \, x\right) + 50 \, a \sin\left(4 \, x\right) \sin\left(3 \, x\right) + 25 \, a \sin\left(3 \, x\right) \sin\left(2 \, x\right) + {\left(5 \, a \cos\left(7 \, x\right) - 2 \, a \cos\left(5 \, x\right) + 5 \, a \cos\left(3 \, x\right)\right)} \cos\left(10 \, x\right) + 5 \, {\left(5 \, a \cos\left(7 \, x\right) - 2 \, a \cos\left(5 \, x\right) + 5 \, a \cos\left(3 \, x\right)\right)} \cos\left(8 \, x\right) + 5 \, {\left(10 \, a \cos\left(6 \, x\right) + 10 \, a \cos\left(4 \, x\right) + 5 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(7 \, x\right) - 10 \, {\left(2 \, a \cos\left(5 \, x\right) - 5 \, a \cos\left(3 \, x\right)\right)} \cos\left(6 \, x\right) - 2 \, {\left(10 \, a \cos\left(4 \, x\right) + 5 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(5 \, x\right) + 5 \, {\left(5 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(3 \, x\right) + {\left(5 \, a \sin\left(7 \, x\right) - 2 \, a \sin\left(5 \, x\right) + 5 \, a \sin\left(3 \, x\right)\right)} \sin\left(10 \, x\right) + 5 \, {\left(5 \, a \sin\left(7 \, x\right) - 2 \, a \sin\left(5 \, x\right) + 5 \, a \sin\left(3 \, x\right)\right)} \sin\left(8 \, x\right) + 25 \, {\left(2 \, a \sin\left(6 \, x\right) + 2 \, a \sin\left(4 \, x\right) + a \sin\left(2 \, x\right)\right)} \sin\left(7 \, x\right) - 10 \, {\left(2 \, a \sin\left(5 \, x\right) - 5 \, a \sin\left(3 \, x\right)\right)} \sin\left(6 \, x\right) - 10 \, {\left(2 \, a \sin\left(4 \, x\right) + a \sin\left(2 \, x\right)\right)} \sin\left(5 \, x\right)\right)} \sqrt{a}}{15 \, {\left(2 \, {\left(5 \, \cos\left(8 \, x\right) + 10 \, \cos\left(6 \, x\right) + 10 \, \cos\left(4 \, x\right) + 5 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(10 \, x\right) + \cos\left(10 \, x\right)^{2} + 10 \, {\left(10 \, \cos\left(6 \, x\right) + 10 \, \cos\left(4 \, x\right) + 5 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + 25 \, \cos\left(8 \, x\right)^{2} + 20 \, {\left(10 \, \cos\left(4 \, x\right) + 5 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 100 \, \cos\left(6 \, x\right)^{2} + 20 \, {\left(5 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 100 \, \cos\left(4 \, x\right)^{2} + 25 \, \cos\left(2 \, x\right)^{2} + 10 \, {\left(\sin\left(8 \, x\right) + 2 \, \sin\left(6 \, x\right) + 2 \, \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) + \sin\left(10 \, x\right)^{2} + 50 \, {\left(2 \, \sin\left(6 \, x\right) + 2 \, \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 25 \, \sin\left(8 \, x\right)^{2} + 100 \, {\left(2 \, \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 100 \, \sin\left(6 \, x\right)^{2} + 100 \, \sin\left(4 \, x\right)^{2} + 100 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 25 \, \sin\left(2 \, x\right)^{2} + 10 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-8/15*(50*a*cos(4*x)*cos(3*x) + 50*a*sin(4*x)*sin(3*x) + 25*a*sin(3*x)*sin(2*x) + (5*a*cos(7*x) - 2*a*cos(5*x) + 5*a*cos(3*x))*cos(10*x) + 5*(5*a*cos(7*x) - 2*a*cos(5*x) + 5*a*cos(3*x))*cos(8*x) + 5*(10*a*cos(6*x) + 10*a*cos(4*x) + 5*a*cos(2*x) + a)*cos(7*x) - 10*(2*a*cos(5*x) - 5*a*cos(3*x))*cos(6*x) - 2*(10*a*cos(4*x) + 5*a*cos(2*x) + a)*cos(5*x) + 5*(5*a*cos(2*x) + a)*cos(3*x) + (5*a*sin(7*x) - 2*a*sin(5*x) + 5*a*sin(3*x))*sin(10*x) + 5*(5*a*sin(7*x) - 2*a*sin(5*x) + 5*a*sin(3*x))*sin(8*x) + 25*(2*a*sin(6*x) + 2*a*sin(4*x) + a*sin(2*x))*sin(7*x) - 10*(2*a*sin(5*x) - 5*a*sin(3*x))*sin(6*x) - 10*(2*a*sin(4*x) + a*sin(2*x))*sin(5*x))*sqrt(a)/(2*(5*cos(8*x) + 10*cos(6*x) + 10*cos(4*x) + 5*cos(2*x) + 1)*cos(10*x) + cos(10*x)^2 + 10*(10*cos(6*x) + 10*cos(4*x) + 5*cos(2*x) + 1)*cos(8*x) + 25*cos(8*x)^2 + 20*(10*cos(4*x) + 5*cos(2*x) + 1)*cos(6*x) + 100*cos(6*x)^2 + 20*(5*cos(2*x) + 1)*cos(4*x) + 100*cos(4*x)^2 + 25*cos(2*x)^2 + 10*(sin(8*x) + 2*sin(6*x) + 2*sin(4*x) + sin(2*x))*sin(10*x) + sin(10*x)^2 + 50*(2*sin(6*x) + 2*sin(4*x) + sin(2*x))*sin(8*x) + 25*sin(8*x)^2 + 100*(2*sin(4*x) + sin(2*x))*sin(6*x) + 100*sin(6*x)^2 + 100*sin(4*x)^2 + 100*sin(4*x)*sin(2*x) + 25*sin(2*x)^2 + 10*cos(2*x) + 1)","B",0
267,1,934,0,1.590013," ","integrate(tan(x)^2*(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(112 \, a \cos\left(3 \, x\right) \sin\left(2 \, x\right) - 16 \, a \cos\left(x\right) \sin\left(2 \, x\right) + 16 \, a \cos\left(2 \, x\right) \sin\left(x\right) - 4 \, {\left(a \sin\left(7 \, x\right) - 7 \, a \sin\left(5 \, x\right) + 7 \, a \sin\left(3 \, x\right) - a \sin\left(x\right)\right)} \cos\left(8 \, x\right) + 8 \, {\left(2 \, a \sin\left(6 \, x\right) + 3 \, a \sin\left(4 \, x\right) + 2 \, a \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) + 16 \, {\left(7 \, a \sin\left(5 \, x\right) - 7 \, a \sin\left(3 \, x\right) + a \sin\left(x\right)\right)} \cos\left(6 \, x\right) - 56 \, {\left(3 \, a \sin\left(4 \, x\right) + 2 \, a \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - 24 \, {\left(7 \, a \sin\left(3 \, x\right) - a \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(a \cos\left(8 \, x\right)^{2} + 16 \, a \cos\left(6 \, x\right)^{2} + 36 \, a \cos\left(4 \, x\right)^{2} + 16 \, a \cos\left(2 \, x\right)^{2} + a \sin\left(8 \, x\right)^{2} + 16 \, a \sin\left(6 \, x\right)^{2} + 36 \, a \sin\left(4 \, x\right)^{2} + 48 \, a \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, x\right) + 6 \, a \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(8 \, x\right) + 8 \, {\left(6 \, a \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(6 \, x\right) + 12 \, {\left(4 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(4 \, x\right) + 8 \, a \cos\left(2 \, x\right) + 4 \, {\left(2 \, a \sin\left(6 \, x\right) + 3 \, a \sin\left(4 \, x\right) + 2 \, a \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 16 \, {\left(3 \, a \sin\left(4 \, x\right) + 2 \, a \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + a\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left(a \cos\left(8 \, x\right)^{2} + 16 \, a \cos\left(6 \, x\right)^{2} + 36 \, a \cos\left(4 \, x\right)^{2} + 16 \, a \cos\left(2 \, x\right)^{2} + a \sin\left(8 \, x\right)^{2} + 16 \, a \sin\left(6 \, x\right)^{2} + 36 \, a \sin\left(4 \, x\right)^{2} + 48 \, a \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a \sin\left(2 \, x\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, x\right) + 6 \, a \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(8 \, x\right) + 8 \, {\left(6 \, a \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(6 \, x\right) + 12 \, {\left(4 \, a \cos\left(2 \, x\right) + a\right)} \cos\left(4 \, x\right) + 8 \, a \cos\left(2 \, x\right) + 4 \, {\left(2 \, a \sin\left(6 \, x\right) + 3 \, a \sin\left(4 \, x\right) + 2 \, a \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + 16 \, {\left(3 \, a \sin\left(4 \, x\right) + 2 \, a \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + a\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, {\left(a \cos\left(7 \, x\right) - 7 \, a \cos\left(5 \, x\right) + 7 \, a \cos\left(3 \, x\right) - a \cos\left(x\right)\right)} \sin\left(8 \, x\right) - 4 \, {\left(4 \, a \cos\left(6 \, x\right) + 6 \, a \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \sin\left(7 \, x\right) - 16 \, {\left(7 \, a \cos\left(5 \, x\right) - 7 \, a \cos\left(3 \, x\right) + a \cos\left(x\right)\right)} \sin\left(6 \, x\right) + 28 \, {\left(6 \, a \cos\left(4 \, x\right) + 4 \, a \cos\left(2 \, x\right) + a\right)} \sin\left(5 \, x\right) + 24 \, {\left(7 \, a \cos\left(3 \, x\right) - a \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 28 \, {\left(4 \, a \cos\left(2 \, x\right) + a\right)} \sin\left(3 \, x\right) + 4 \, a \sin\left(x\right)\right)} \sqrt{a}}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) + 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) + 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + 36 \, \cos\left(4 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) + 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) + \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) + 16 \, \sin\left(6 \, x\right)^{2} + 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/16*(112*a*cos(3*x)*sin(2*x) - 16*a*cos(x)*sin(2*x) + 16*a*cos(2*x)*sin(x) - 4*(a*sin(7*x) - 7*a*sin(5*x) + 7*a*sin(3*x) - a*sin(x))*cos(8*x) + 8*(2*a*sin(6*x) + 3*a*sin(4*x) + 2*a*sin(2*x))*cos(7*x) + 16*(7*a*sin(5*x) - 7*a*sin(3*x) + a*sin(x))*cos(6*x) - 56*(3*a*sin(4*x) + 2*a*sin(2*x))*cos(5*x) - 24*(7*a*sin(3*x) - a*sin(x))*cos(4*x) - (a*cos(8*x)^2 + 16*a*cos(6*x)^2 + 36*a*cos(4*x)^2 + 16*a*cos(2*x)^2 + a*sin(8*x)^2 + 16*a*sin(6*x)^2 + 36*a*sin(4*x)^2 + 48*a*sin(4*x)*sin(2*x) + 16*a*sin(2*x)^2 + 2*(4*a*cos(6*x) + 6*a*cos(4*x) + 4*a*cos(2*x) + a)*cos(8*x) + 8*(6*a*cos(4*x) + 4*a*cos(2*x) + a)*cos(6*x) + 12*(4*a*cos(2*x) + a)*cos(4*x) + 8*a*cos(2*x) + 4*(2*a*sin(6*x) + 3*a*sin(4*x) + 2*a*sin(2*x))*sin(8*x) + 16*(3*a*sin(4*x) + 2*a*sin(2*x))*sin(6*x) + a)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + (a*cos(8*x)^2 + 16*a*cos(6*x)^2 + 36*a*cos(4*x)^2 + 16*a*cos(2*x)^2 + a*sin(8*x)^2 + 16*a*sin(6*x)^2 + 36*a*sin(4*x)^2 + 48*a*sin(4*x)*sin(2*x) + 16*a*sin(2*x)^2 + 2*(4*a*cos(6*x) + 6*a*cos(4*x) + 4*a*cos(2*x) + a)*cos(8*x) + 8*(6*a*cos(4*x) + 4*a*cos(2*x) + a)*cos(6*x) + 12*(4*a*cos(2*x) + a)*cos(4*x) + 8*a*cos(2*x) + 4*(2*a*sin(6*x) + 3*a*sin(4*x) + 2*a*sin(2*x))*sin(8*x) + 16*(3*a*sin(4*x) + 2*a*sin(2*x))*sin(6*x) + a)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*(a*cos(7*x) - 7*a*cos(5*x) + 7*a*cos(3*x) - a*cos(x))*sin(8*x) - 4*(4*a*cos(6*x) + 6*a*cos(4*x) + 4*a*cos(2*x) + a)*sin(7*x) - 16*(7*a*cos(5*x) - 7*a*cos(3*x) + a*cos(x))*sin(6*x) + 28*(6*a*cos(4*x) + 4*a*cos(2*x) + a)*sin(5*x) + 24*(7*a*cos(3*x) - a*cos(x))*sin(4*x) - 28*(4*a*cos(2*x) + a)*sin(3*x) + 4*a*sin(x))*sqrt(a)/(2*(4*cos(6*x) + 6*cos(4*x) + 4*cos(2*x) + 1)*cos(8*x) + cos(8*x)^2 + 8*(6*cos(4*x) + 4*cos(2*x) + 1)*cos(6*x) + 16*cos(6*x)^2 + 12*(4*cos(2*x) + 1)*cos(4*x) + 36*cos(4*x)^2 + 16*cos(2*x)^2 + 4*(2*sin(6*x) + 3*sin(4*x) + 2*sin(2*x))*sin(8*x) + sin(8*x)^2 + 16*(3*sin(4*x) + 2*sin(2*x))*sin(6*x) + 16*sin(6*x)^2 + 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) + 16*sin(2*x)^2 + 8*cos(2*x) + 1)","B",0
268,0,0,0,0.000000," ","integrate(tan(x)*(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(a \tan\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(x\right)\,{d x}"," ",0,"integrate((a*tan(x)^2 + a)^(3/2)*tan(x), x)","F",0
269,1,134,0,0.957352," ","integrate(cot(x)*(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(4 \, a \cos\left(2 \, x\right) \cos\left(x\right) + 4 \, a \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, a \cos\left(x\right) - {\left(a \cos\left(2 \, x\right)^{2} + a \sin\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(a \cos\left(2 \, x\right)^{2} + a \sin\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)\right)} \sqrt{a}}{2 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/2*(4*a*cos(2*x)*cos(x) + 4*a*sin(2*x)*sin(x) + 4*a*cos(x) - (a*cos(2*x)^2 + a*sin(2*x)^2 + 2*a*cos(2*x) + a)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (a*cos(2*x)^2 + a*sin(2*x)^2 + 2*a*cos(2*x) + a)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1))*sqrt(a)/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
270,1,134,0,1.007552," ","integrate(cot(x)^2*(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, a \cos\left(x\right) \sin\left(2 \, x\right) - 4 \, a \cos\left(2 \, x\right) \sin\left(x\right) - {\left(a \cos\left(2 \, x\right)^{2} + a \sin\left(2 \, x\right)^{2} - 2 \, a \cos\left(2 \, x\right) + a\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left(a \cos\left(2 \, x\right)^{2} + a \sin\left(2 \, x\right)^{2} - 2 \, a \cos\left(2 \, x\right) + a\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, a \sin\left(x\right)\right)} \sqrt{a}}{2 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"-1/2*(4*a*cos(x)*sin(2*x) - 4*a*cos(2*x)*sin(x) - (a*cos(2*x)^2 + a*sin(2*x)^2 - 2*a*cos(2*x) + a)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + (a*cos(2*x)^2 + a*sin(2*x)^2 - 2*a*cos(2*x) + a)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*a*sin(x))*sqrt(a)/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)","B",0
271,1,556,0,1.009993," ","integrate((a+a*tan(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(8 \, a \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 8 \, a \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - 4 \, {\left(a \sin\left(3 \, d x + 3 \, c\right) - a \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(a \cos\left(3 \, d x + 3 \, c\right) - a \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, a \sin\left(d x + c\right)\right)} \sqrt{a}}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(8*a*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) - 8*a*cos(d*x + c)*sin(2*d*x + 2*c) + 8*a*cos(2*d*x + 2*c)*sin(d*x + c) - 4*(a*sin(3*d*x + 3*c) - a*sin(d*x + c))*cos(4*d*x + 4*c) - (a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 4*(a*cos(3*d*x + 3*c) - a*cos(d*x + c))*sin(4*d*x + 4*c) - 4*(2*a*cos(2*d*x + 2*c) + a)*sin(3*d*x + 3*c) + 4*a*sin(d*x + c))*sqrt(a)/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*d)","B",0
272,1,1769,0,1.643402," ","integrate((a+a*tan(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\frac{{\left(176 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 48 \, a^{2} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) - 48 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) - 12 \, a^{2} \sin\left(d x + c\right) + 4 \, {\left(3 \, a^{2} \sin\left(7 \, d x + 7 \, c\right) + 11 \, a^{2} \sin\left(5 \, d x + 5 \, c\right) - 11 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - 3 \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) - 24 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(7 \, d x + 7 \, c\right) + 16 \, {\left(11 \, a^{2} \sin\left(5 \, d x + 5 \, c\right) - 11 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - 3 \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) - 88 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(5 \, d x + 5 \, c\right) - 24 \, {\left(11 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + 3 \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 3 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2} + 2 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(3 \, a^{2} \cos\left(7 \, d x + 7 \, c\right) + 11 \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - 11 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 12 \, {\left(4 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(7 \, d x + 7 \, c\right) - 16 \, {\left(11 \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - 11 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 44 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + 24 \, {\left(11 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 44 \, {\left(4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sqrt{a}}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, d x + 6 \, c\right) + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + \cos\left(8 \, d x + 8 \, c\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, d x + 4 \, c\right) + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 16 \, \cos\left(6 \, d x + 6 \, c\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 16 \, \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/16*(176*a^2*cos(3*d*x + 3*c)*sin(2*d*x + 2*c) + 48*a^2*cos(d*x + c)*sin(2*d*x + 2*c) - 48*a^2*cos(2*d*x + 2*c)*sin(d*x + c) - 12*a^2*sin(d*x + c) + 4*(3*a^2*sin(7*d*x + 7*c) + 11*a^2*sin(5*d*x + 5*c) - 11*a^2*sin(3*d*x + 3*c) - 3*a^2*sin(d*x + c))*cos(8*d*x + 8*c) - 24*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*cos(7*d*x + 7*c) + 16*(11*a^2*sin(5*d*x + 5*c) - 11*a^2*sin(3*d*x + 3*c) - 3*a^2*sin(d*x + c))*cos(6*d*x + 6*c) - 88*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*cos(5*d*x + 5*c) - 24*(11*a^2*sin(3*d*x + 3*c) + 3*a^2*sin(d*x + c))*cos(4*d*x + 4*c) + 3*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - 3*(a^2*cos(8*d*x + 8*c)^2 + 16*a^2*cos(6*d*x + 6*c)^2 + 36*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*cos(2*d*x + 2*c)^2 + a^2*sin(8*d*x + 8*c)^2 + 16*a^2*sin(6*d*x + 6*c)^2 + 36*a^2*sin(4*d*x + 4*c)^2 + 48*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a^2*sin(2*d*x + 2*c)^2 + 8*a^2*cos(2*d*x + 2*c) + a^2 + 2*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(8*d*x + 8*c) + 8*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*cos(6*d*x + 6*c) + 12*(4*a^2*cos(2*d*x + 2*c) + a^2)*cos(4*d*x + 4*c) + 4*(2*a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a^2*sin(4*d*x + 4*c) + 2*a^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - 4*(3*a^2*cos(7*d*x + 7*c) + 11*a^2*cos(5*d*x + 5*c) - 11*a^2*cos(3*d*x + 3*c) - 3*a^2*cos(d*x + c))*sin(8*d*x + 8*c) + 12*(4*a^2*cos(6*d*x + 6*c) + 6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*sin(7*d*x + 7*c) - 16*(11*a^2*cos(5*d*x + 5*c) - 11*a^2*cos(3*d*x + 3*c) - 3*a^2*cos(d*x + c))*sin(6*d*x + 6*c) + 44*(6*a^2*cos(4*d*x + 4*c) + 4*a^2*cos(2*d*x + 2*c) + a^2)*sin(5*d*x + 5*c) + 24*(11*a^2*cos(3*d*x + 3*c) + 3*a^2*cos(d*x + c))*sin(4*d*x + 4*c) - 44*(4*a^2*cos(2*d*x + 2*c) + a^2)*sin(3*d*x + 3*c))*sqrt(a)/((2*(4*cos(6*d*x + 6*c) + 6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + cos(8*d*x + 8*c)^2 + 8*(6*cos(4*d*x + 4*c) + 4*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 16*cos(6*d*x + 6*c)^2 + 12*(4*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 36*cos(4*d*x + 4*c)^2 + 16*cos(2*d*x + 2*c)^2 + 4*(2*sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + sin(8*d*x + 8*c)^2 + 16*(3*sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 16*sin(6*d*x + 6*c)^2 + 36*sin(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sin(2*d*x + 2*c)^2 + 8*cos(2*d*x + 2*c) + 1)*d)","B",0
273,1,37,0,0.694369," ","integrate(tan(x)^3/(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(\sin\left(x\right)^{2} - 2\right)} \sqrt{\sin\left(x\right) + 1} \sqrt{-\sin\left(x\right) + 1}}{\sqrt{a} \sin\left(x\right)^{2} - \sqrt{a}}"," ",0,"(sin(x)^2 - 2)*sqrt(sin(x) + 1)*sqrt(-sin(x) + 1)/(sqrt(a)*sin(x)^2 - sqrt(a))","A",0
274,1,42,0,1.881689," ","integrate(tan(x)^2/(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - 2 \, \sin\left(x\right)}{2 \, \sqrt{a}}"," ",0,"1/2*(log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - 2*sin(x))/sqrt(a)","A",0
275,0,0,0,0.000000," ","integrate(tan(x)/(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{\sqrt{a \tan\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(x)/sqrt(a*tan(x)^2 + a), x)","F",0
276,1,42,0,0.895996," ","integrate(cot(x)/(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \cos\left(x\right) - \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}{2 \, \sqrt{a}}"," ",0,"1/2*(2*cos(x) - log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1))/sqrt(a)","A",0
277,1,128,0,1.482478," ","integrate(cot(x)^2/(a+a*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) - {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + 6 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) - 6 \, \cos\left(x\right) \sin\left(2 \, x\right) + 6 \, \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)\right)} \sqrt{a}}{2 \, {\left(a \cos\left(3 \, x\right)^{2} - 2 \, a \cos\left(3 \, x\right) \cos\left(x\right) + a \cos\left(x\right)^{2} + a \sin\left(3 \, x\right)^{2} - 2 \, a \sin\left(3 \, x\right) \sin\left(x\right) + a \sin\left(x\right)^{2}\right)}}"," ",0,"1/2*((sin(3*x) - sin(x))*cos(4*x) - (cos(3*x) - cos(x))*sin(4*x) - (6*cos(2*x) - 1)*sin(3*x) + 6*cos(3*x)*sin(2*x) - 6*cos(x)*sin(2*x) + 6*cos(2*x)*sin(x) - sin(x))*sqrt(a)/(a*cos(3*x)^2 - 2*a*cos(3*x)*cos(x) + a*cos(x)^2 + a*sin(3*x)^2 - 2*a*sin(3*x)*sin(x) + a*sin(x)^2)","B",0
278,1,38,0,0.536407," ","integrate(tan(x)^3/(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(\sin\left(x\right)^{2} + 2\right)} {\left(\sin\left(x\right) + 1\right)}^{\frac{3}{2}} {\left(-\sin\left(x\right) + 1\right)}^{\frac{3}{2}}}{3 \, {\left(a^{\frac{3}{2}} \sin\left(x\right)^{2} - a^{\frac{3}{2}}\right)}}"," ",0,"1/3*(sin(x)^2 + 2)*(sin(x) + 1)^(3/2)*(-sin(x) + 1)^(3/2)/(a^(3/2)*sin(x)^2 - a^(3/2))","A",0
279,1,14,0,0.948615," ","integrate(tan(x)^2/(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{\sin\left(3 \, x\right) - 3 \, \sin\left(x\right)}{12 \, a^{\frac{3}{2}}}"," ",0,"-1/12*(sin(3*x) - 3*sin(x))/a^(3/2)","A",0
280,0,0,0,0.000000," ","integrate(tan(x)/(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(a \tan\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(x)/(a*tan(x)^2 + a)^(3/2), x)","F",0
281,1,48,0,0.883074," ","integrate(cot(x)/(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{\cos\left(3 \, x\right) + 15 \, \cos\left(x\right) - 6 \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + 6 \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}{12 \, a^{\frac{3}{2}}}"," ",0,"1/12*(cos(3*x) + 15*cos(x) - 6*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 6*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1))/a^(3/2)","A",0
282,1,225,0,1.344137," ","integrate(cot(x)^2/(a+a*tan(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left({\left(\sin\left(5 \, x\right) - \sin\left(3 \, x\right)\right)} \cos\left(8 \, x\right) + 20 \, {\left(\sin\left(5 \, x\right) - \sin\left(3 \, x\right)\right)} \cos\left(6 \, x\right) + 10 \, {\left(9 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) - {\left(\cos\left(5 \, x\right) - \cos\left(3 \, x\right)\right)} \sin\left(8 \, x\right) - 20 \, {\left(\cos\left(5 \, x\right) - \cos\left(3 \, x\right)\right)} \sin\left(6 \, x\right) - {\left(90 \, \cos\left(4 \, x\right) - 20 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(5 \, x\right) - 90 \, \cos\left(3 \, x\right) \sin\left(4 \, x\right) - {\left(20 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right) + 90 \, \cos\left(4 \, x\right) \sin\left(3 \, x\right) + 20 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right)\right)} \sqrt{a}}{24 \, {\left(a^{2} \cos\left(5 \, x\right)^{2} - 2 \, a^{2} \cos\left(5 \, x\right) \cos\left(3 \, x\right) + a^{2} \cos\left(3 \, x\right)^{2} + a^{2} \sin\left(5 \, x\right)^{2} - 2 \, a^{2} \sin\left(5 \, x\right) \sin\left(3 \, x\right) + a^{2} \sin\left(3 \, x\right)^{2}\right)}}"," ",0,"1/24*((sin(5*x) - sin(3*x))*cos(8*x) + 20*(sin(5*x) - sin(3*x))*cos(6*x) + 10*(9*sin(4*x) - 2*sin(2*x))*cos(5*x) - (cos(5*x) - cos(3*x))*sin(8*x) - 20*(cos(5*x) - cos(3*x))*sin(6*x) - (90*cos(4*x) - 20*cos(2*x) - 1)*sin(5*x) - 90*cos(3*x)*sin(4*x) - (20*cos(2*x) + 1)*sin(3*x) + 90*cos(4*x)*sin(3*x) + 20*cos(3*x)*sin(2*x))*sqrt(a)/(a^2*cos(5*x)^2 - 2*a^2*cos(5*x)*cos(3*x) + a^2*cos(3*x)^2 + a^2*sin(5*x)^2 - 2*a^2*sin(5*x)*sin(3*x) + a^2*sin(3*x)^2)","B",0
283,1,13,0,1.440658," ","integrate(1/(a+a*tan(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)}{\sqrt{a} d}"," ",0,"sin(d*x + c)/(sqrt(a)*d)","A",0
284,1,26,0,0.705659," ","integrate(1/(a+a*tan(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","\frac{\sin\left(3 \, d x + 3 \, c\right) + 9 \, \sin\left(d x + c\right)}{12 \, a^{\frac{3}{2}} d}"," ",0,"1/12*(sin(3*d*x + 3*c) + 9*sin(d*x + c))/(a^(3/2)*d)","A",0
285,1,39,0,0.611836," ","integrate(1/(a+a*tan(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\frac{3 \, \sin\left(5 \, d x + 5 \, c\right) + 25 \, \sin\left(3 \, d x + 3 \, c\right) + 150 \, \sin\left(d x + c\right)}{240 \, a^{\frac{5}{2}} d}"," ",0,"1/240*(3*sin(5*d*x + 5*c) + 25*sin(3*d*x + 3*c) + 150*sin(d*x + c))/(a^(5/2)*d)","A",0
286,1,50,0,0.595460," ","integrate(1/(a+a*tan(d*x+c)^2)^(7/2),x, algorithm=""maxima"")","\frac{5 \, \sin\left(7 \, d x + 7 \, c\right) + 49 \, \sin\left(5 \, d x + 5 \, c\right) + 245 \, \sin\left(3 \, d x + 3 \, c\right) + 1225 \, \sin\left(d x + c\right)}{2240 \, a^{\frac{7}{2}} d}"," ",0,"1/2240*(5*sin(7*d*x + 7*c) + 49*sin(5*d*x + 5*c) + 245*sin(3*d*x + 3*c) + 1225*sin(d*x + c))/(a^(7/2)*d)","A",0
287,1,18,0,0.546632," ","integrate((1+tan(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{\tan\left(x\right)^{2} + 1} \tan\left(x\right) + \frac{1}{2} \, \operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"1/2*sqrt(tan(x)^2 + 1)*tan(x) + 1/2*arcsinh(tan(x))","A",0
288,1,3,0,0.754283," ","integrate((1+tan(x)^2)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"arcsinh(tan(x))","A",0
289,1,11,0,0.380916," ","integrate(1/(1+tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{\sqrt{\tan\left(x\right)^{2} + 1}}"," ",0,"tan(x)/sqrt(tan(x)^2 + 1)","A",0
290,1,20,0,0.575898," ","integrate((-1-tan(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{-\tan\left(x\right)^{2} - 1} \tan\left(x\right) - \frac{1}{2} i \, \operatorname{arsinh}\left(\tan\left(x\right)\right)"," ",0,"-1/2*sqrt(-tan(x)^2 - 1)*tan(x) - 1/2*I*arcsinh(tan(x))","C",0
291,1,17,0,0.855191," ","integrate((-1-tan(x)^2)^(1/2),x, algorithm=""maxima"")","\arctan\left(\cos\left(x\right), \sin\left(x\right) + 1\right) + \arctan\left(\cos\left(x\right), -\sin\left(x\right) + 1\right)"," ",0,"arctan2(cos(x), sin(x) + 1) + arctan2(cos(x), -sin(x) + 1)","A",0
292,0,0,0,0.000000," ","integrate(1/(-1-tan(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\tan\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-tan(x)^2 - 1), x)","F",0
293,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*tan(f*x + e)^5, x)","F",0
294,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*tan(f*x + e)^3, x)","F",0
295,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*tan(f*x + e), x)","F",0
296,-2,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
297,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*cot(f*x + e)^3, x)","F",0
298,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*cot(f*x + e)^5, x)","F",0
299,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^6,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*tan(f*x + e)^6, x)","F",0
300,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*tan(f*x + e)^4, x)","F",0
301,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*tan(f*x + e)^2, x)","F",0
302,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a zero or nonzero?","F(-2)",0
303,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*cot(f*x + e)^2, x)","F",0
304,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*cot(f*x + e)^4, x)","F",0
305,0,0,0,0.000000," ","integrate(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right)^{2} + a} \cot\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e)^2 + a)*cot(f*x + e)^6, x)","F",0
306,0,0,0,0.000000," ","integrate(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^5, x)","F",0
307,0,0,0,0.000000," ","integrate(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^3, x)","F",0
308,0,0,0,0.000000," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*tan(f*x + e), x)","F",0
309,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*cot(f*x + e), x)","F",0
310,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^3, x)","F",0
311,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^5, x)","F",0
312,0,0,0,0.000000," ","integrate(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^6, x)","F",0
313,0,0,0,0.000000," ","integrate(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^4, x)","F",0
314,0,0,0,0.000000," ","integrate(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*tan(f*x + e)^2, x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
316,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^2, x)","F",0
317,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^4, x)","F",0
318,0,0,0,0.000000," ","integrate(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^(3/2)*cot(f*x + e)^6, x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right)^{2} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c)^2 + a)^(5/2), x)","F",0
320,-1,0,0,0.000000," ","integrate(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,0,0,0,0.000000," ","integrate(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{3}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^3/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
322,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
323,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
324,0,0,0,0.000000," ","integrate(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{3}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^3/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
325,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
328,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
329,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
330,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{\sqrt{b \tan\left(f x + e\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/sqrt(b*tan(f*x + e)^2 + a), x)","F",0
331,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-2,0,0,0.000000," ","integrate(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
335,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)/(b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
336,-1,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/(b*tan(f*x + e)^2 + a)^(3/2), x)","F",0
341,-2,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
342,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
343,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
346,-2,0,0,0.000000," ","integrate(tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
347,-2,0,0,0.000000," ","integrate(tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
348,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{{\left(b \tan\left(f x + e\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(f*x + e)/(b*tan(f*x + e)^2 + a)^(5/2), x)","F",0
349,-1,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate(cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-2,0,0,0.000000," ","integrate(tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
354,-2,0,0,0.000000," ","integrate(tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
355,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
356,-1,0,0,0.000000," ","integrate(cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^m*(b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p*(d*tan(f*x + e))^m, x)","F",0
360,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*(d*tan(f*x + e))^m, x)","F",0
361,0,0,0,0.000000," ","integrate(tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*tan(f*x + e)^5, x)","F",0
362,0,0,0,0.000000," ","integrate(tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*tan(f*x + e)^3, x)","F",0
363,0,0,0,0.000000," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*tan(f*x + e), x)","F",0
364,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*cot(f*x + e), x)","F",0
365,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*cot(f*x + e)^3, x)","F",0
366,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*cot(f*x + e)^5, x)","F",0
367,-1,0,0,0.000000," ","integrate(tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,0,0,0,0.000000," ","integrate(tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*tan(f*x + e)^4, x)","F",0
369,0,0,0,0.000000," ","integrate(tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*tan(f*x + e)^2, x)","F",0
370,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p, x)","F",0
371,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*cot(f*x + e)^2, x)","F",0
372,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*cot(f*x + e)^4, x)","F",0
373,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,1,260,0,0.991342," ","integrate((a+b*tan(d*x+c)^3)^4,x, algorithm=""maxima"")","a^{4} x + \frac{2 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{2} b^{2}}{5 \, d} + \frac{{\left(315 \, \tan\left(d x + c\right)^{11} - 385 \, \tan\left(d x + c\right)^{9} + 495 \, \tan\left(d x + c\right)^{7} - 693 \, \tan\left(d x + c\right)^{5} + 1155 \, \tan\left(d x + c\right)^{3} + 3465 \, d x + 3465 \, c - 3465 \, \tan\left(d x + c\right)\right)} b^{4}}{3465 \, d} + \frac{a b^{3} {\left(\frac{48 \, \sin\left(d x + c\right)^{6} - 108 \, \sin\left(d x + c\right)^{4} + 88 \, \sin\left(d x + c\right)^{2} - 25}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 12 \, \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{6 \, d} - \frac{2 \, a^{3} b {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{d}"," ",0,"a^4*x + 2/5*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^2*b^2/d + 1/3465*(315*tan(d*x + c)^11 - 385*tan(d*x + c)^9 + 495*tan(d*x + c)^7 - 693*tan(d*x + c)^5 + 1155*tan(d*x + c)^3 + 3465*d*x + 3465*c - 3465*tan(d*x + c))*b^4/d + 1/6*a*b^3*((48*sin(d*x + c)^6 - 108*sin(d*x + c)^4 + 88*sin(d*x + c)^2 - 25)/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 12*log(sin(d*x + c)^2 - 1))/d - 2*a^3*b*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d","A",0
375,1,183,0,0.655236," ","integrate((a+b*tan(d*x+c)^3)^3,x, algorithm=""maxima"")","a^{3} x + \frac{{\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a b^{2}}{5 \, d} + \frac{b^{3} {\left(\frac{48 \, \sin\left(d x + c\right)^{6} - 108 \, \sin\left(d x + c\right)^{4} + 88 \, \sin\left(d x + c\right)^{2} - 25}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{2} + 1} - 12 \, \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{24 \, d} - \frac{3 \, a^{2} b {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{2 \, d}"," ",0,"a^3*x + 1/5*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a*b^2/d + 1/24*b^3*((48*sin(d*x + c)^6 - 108*sin(d*x + c)^4 + 88*sin(d*x + c)^2 - 25)/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 12*log(sin(d*x + c)^2 - 1))/d - 3/2*a^2*b*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d","A",0
376,1,83,0,0.924307," ","integrate((a+b*tan(d*x+c)^3)^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} b^{2}}{15 \, d} - \frac{a b {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{d}"," ",0,"a^2*x + 1/15*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*b^2/d - a*b*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d","A",0
377,1,36,0,0.302801," ","integrate(a+b*tan(d*x+c)^3,x, algorithm=""maxima"")","a x - \frac{b {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{2 \, d}"," ",0,"a*x - 1/2*b*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d","A",0
378,1,291,0,1.131161," ","integrate(1/(a+b*tan(d*x+c)^3),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{3} {\left(a {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2\right)} - b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{2 \, a}{b}\right)}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \tan\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{18 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} + \frac{3 \, {\left(b {\left(2 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 1\right)} + a \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\tan\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \tan\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{9 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{6 \, {\left(b {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} - a \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \tan\left(d x + c\right)\right)}{a^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}}{18 \, d}"," ",0,"-1/18*(2*sqrt(3)*(a*(3*(a/b)^(2/3) - 2) - b*(3*(a/b)^(1/3) - 2*a/b))*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*tan(d*x + c))/(a/b)^(1/3))/((a^2*(a/b)^(2/3) + b^2*(a/b)^(2/3))*(a/b)^(1/3)) - 18*(d*x + c)*a/(a^2 + b^2) + 3*(b*(2*(a/b)^(2/3) + 1) + a*(a/b)^(1/3))*log(tan(d*x + c)^2 - (a/b)^(1/3)*tan(d*x + c) + (a/b)^(2/3))/(a^2*(a/b)^(2/3) + b^2*(a/b)^(2/3)) - 9*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 6*(b*((a/b)^(2/3) - 1) - a*(a/b)^(1/3))*log((a/b)^(1/3) + tan(d*x + c))/(a^2*(a/b)^(2/3) + b^2*(a/b)^(2/3)))/d","A",0
379,1,502,0,1.233300," ","integrate(1/(a+b*tan(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{\frac{9 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, \sqrt{3} {\left(2 \, a^{3} {\left(\left(\frac{a}{b}\right)^{\frac{2}{3}} - 1\right)} - 2 \, a^{2} b {\left(2 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} - \frac{a}{b}\right)} - a b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \arctan\left(-\frac{\sqrt{3} {\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, \tan\left(d x + c\right)\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{9 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a^{2} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2\right)} + 2 \, a^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} - a b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} + b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} - \left(\frac{a}{b}\right)^{\frac{1}{3}} \tan\left(d x + c\right) + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(a^{2} b {\left(3 \, \left(\frac{a}{b}\right)^{\frac{2}{3}} - 4\right)} - 2 \, a^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} + a b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - b^{3}\right)} \log\left(\left(\frac{a}{b}\right)^{\frac{1}{3}} + \tan\left(d x + c\right)\right)}{a^{5} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a^{3} b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{3 \, {\left(a b \tan\left(d x + c\right)^{2} - b^{2} \tan\left(d x + c\right) - a b\right)}}{a^{4} + a^{2} b^{2} + {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)^{3}}}{9 \, d}"," ",0,"1/9*(9*a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*sqrt(3)*(2*a^3*((a/b)^(2/3) - 1) - 2*a^2*b*(2*(a/b)^(1/3) - a/b) - a*b^2*(a/b)^(2/3) - b^3*(a/b)^(1/3))*arctan(-1/3*sqrt(3)*((a/b)^(1/3) - 2*tan(d*x + c))/(a/b)^(1/3))/((a^5*(a/b)^(2/3) + 2*a^3*b^2*(a/b)^(2/3) + a*b^4*(a/b)^(2/3))*(a/b)^(1/3)) + 9*(a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (2*a^2*b*(3*(a/b)^(2/3) + 2) + 2*a^3*(a/b)^(1/3) - a*b^2*(a/b)^(1/3) + b^3)*log(tan(d*x + c)^2 - (a/b)^(1/3)*tan(d*x + c) + (a/b)^(2/3))/(a^5*(a/b)^(2/3) + 2*a^3*b^2*(a/b)^(2/3) + a*b^4*(a/b)^(2/3)) - 2*(a^2*b*(3*(a/b)^(2/3) - 4) - 2*a^3*(a/b)^(1/3) + a*b^2*(a/b)^(1/3) - b^3)*log((a/b)^(1/3) + tan(d*x + c))/(a^5*(a/b)^(2/3) + 2*a^3*b^2*(a/b)^(2/3) + a*b^4*(a/b)^(2/3)) - 3*(a*b*tan(d*x + c)^2 - b^2*tan(d*x + c) - a*b)/(a^4 + a^2*b^2 + (a^3*b + a*b^3)*tan(d*x + c)^3))/d","A",0
380,1,33,0,0.752340," ","integrate(1/(1+tan(x)^3),x, algorithm=""maxima"")","\frac{1}{2} \, x - \frac{1}{3} \, \log\left(\tan\left(x\right)^{2} - \tan\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \frac{1}{6} \, \log\left(\tan\left(x\right) + 1\right)"," ",0,"1/2*x - 1/3*log(tan(x)^2 - tan(x) + 1) + 1/4*log(tan(x)^2 + 1) + 1/6*log(tan(x) + 1)","A",0
381,1,265,0,0.789548," ","integrate((a+tan(d*x+c)^4*b)^4,x, algorithm=""maxima"")","a^{4} x + \frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} b}{3 \, d} + \frac{2 \, {\left(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 \, c - 105 \, \tan\left(d x + c\right)\right)} a^{2} b^{2}}{35 \, d} + \frac{4 \, {\left(315 \, \tan\left(d x + c\right)^{11} - 385 \, \tan\left(d x + c\right)^{9} + 495 \, \tan\left(d x + c\right)^{7} - 693 \, \tan\left(d x + c\right)^{5} + 1155 \, \tan\left(d x + c\right)^{3} + 3465 \, d x + 3465 \, c - 3465 \, \tan\left(d x + c\right)\right)} a b^{3}}{3465 \, d} + \frac{{\left(3003 \, \tan\left(d x + c\right)^{15} - 3465 \, \tan\left(d x + c\right)^{13} + 4095 \, \tan\left(d x + c\right)^{11} - 5005 \, \tan\left(d x + c\right)^{9} + 6435 \, \tan\left(d x + c\right)^{7} - 9009 \, \tan\left(d x + c\right)^{5} + 15015 \, \tan\left(d x + c\right)^{3} + 45045 \, d x + 45045 \, c - 45045 \, \tan\left(d x + c\right)\right)} b^{4}}{45045 \, d}"," ",0,"a^4*x + 4/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3*b/d + 2/35*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*a^2*b^2/d + 4/3465*(315*tan(d*x + c)^11 - 385*tan(d*x + c)^9 + 495*tan(d*x + c)^7 - 693*tan(d*x + c)^5 + 1155*tan(d*x + c)^3 + 3465*d*x + 3465*c - 3465*tan(d*x + c))*a*b^3/d + 1/45045*(3003*tan(d*x + c)^15 - 3465*tan(d*x + c)^13 + 4095*tan(d*x + c)^11 - 5005*tan(d*x + c)^9 + 6435*tan(d*x + c)^7 - 9009*tan(d*x + c)^5 + 15015*tan(d*x + c)^3 + 45045*d*x + 45045*c - 45045*tan(d*x + c))*b^4/d","A",0
382,1,167,0,0.768146," ","integrate((a+tan(d*x+c)^4*b)^3,x, algorithm=""maxima"")","a^{3} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} b}{d} + \frac{{\left(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 \, c - 105 \, \tan\left(d x + c\right)\right)} a b^{2}}{35 \, d} + \frac{{\left(315 \, \tan\left(d x + c\right)^{11} - 385 \, \tan\left(d x + c\right)^{9} + 495 \, \tan\left(d x + c\right)^{7} - 693 \, \tan\left(d x + c\right)^{5} + 1155 \, \tan\left(d x + c\right)^{3} + 3465 \, d x + 3465 \, c - 3465 \, \tan\left(d x + c\right)\right)} b^{3}}{3465 \, d}"," ",0,"a^3*x + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2*b/d + 1/35*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*a*b^2/d + 1/3465*(315*tan(d*x + c)^11 - 385*tan(d*x + c)^9 + 495*tan(d*x + c)^7 - 693*tan(d*x + c)^5 + 1155*tan(d*x + c)^3 + 3465*d*x + 3465*c - 3465*tan(d*x + c))*b^3/d","A",0
383,1,91,0,0.587293," ","integrate((a+tan(d*x+c)^4*b)^2,x, algorithm=""maxima"")","a^{2} x + \frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a b}{3 \, d} + \frac{{\left(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 \, c - 105 \, \tan\left(d x + c\right)\right)} b^{2}}{105 \, d}"," ",0,"a^2*x + 2/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a*b/d + 1/105*(15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*b^2/d","A",0
384,1,34,0,0.459555," ","integrate(a+tan(d*x+c)^4*b,x, algorithm=""maxima"")","a x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} b}{3 \, d}"," ",0,"a*x + 1/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*b/d","A",0
385,1,261,0,0.860854," ","integrate(1/(a+tan(d*x+c)^4*b),x, algorithm=""maxima"")","-\frac{\frac{b {\left(\frac{2 \, \sqrt{2} {\left(\sqrt{a} - \sqrt{b}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} \tan\left(d x + c\right) + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} {\left(\sqrt{a} - \sqrt{b}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} \tan\left(d x + c\right) - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} {\left(\sqrt{a} + \sqrt{b}\right)} \log\left(\sqrt{b} \tan\left(d x + c\right)^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \tan\left(d x + c\right) + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(\sqrt{a} + \sqrt{b}\right)} \log\left(\sqrt{b} \tan\left(d x + c\right)^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \tan\left(d x + c\right) + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}}\right)}}{a + b} - \frac{8 \, {\left(d x + c\right)}}{a + b}}{8 \, d}"," ",0,"-1/8*(b*(2*sqrt(2)*(sqrt(a) - sqrt(b))*arctan(1/2*sqrt(2)*(2*sqrt(b)*tan(d*x + c) + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*(sqrt(a) - sqrt(b))*arctan(1/2*sqrt(2)*(2*sqrt(b)*tan(d*x + c) - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*(sqrt(a) + sqrt(b))*log(sqrt(b)*tan(d*x + c)^2 + sqrt(2)*a^(1/4)*b^(1/4)*tan(d*x + c) + sqrt(a))/(a^(3/4)*b^(3/4)) + sqrt(2)*(sqrt(a) + sqrt(b))*log(sqrt(b)*tan(d*x + c)^2 - sqrt(2)*a^(1/4)*b^(1/4)*tan(d*x + c) + sqrt(a))/(a^(3/4)*b^(3/4)))/(a + b) - 8*(d*x + c)/(a + b))/d","A",0
386,1,394,0,0.804471," ","integrate(1/(a+tan(d*x+c)^4*b)^2,x, algorithm=""maxima"")","-\frac{\frac{b {\left(\frac{2 \, \sqrt{2} {\left(b {\left(\sqrt{a} - 3 \, \sqrt{b}\right)} + 5 \, a^{\frac{3}{2}} - 7 \, a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} \tan\left(d x + c\right) + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} {\left(b {\left(\sqrt{a} - 3 \, \sqrt{b}\right)} + 5 \, a^{\frac{3}{2}} - 7 \, a \sqrt{b}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{b} \tan\left(d x + c\right) - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} {\left(b {\left(\sqrt{a} + 3 \, \sqrt{b}\right)} + 5 \, a^{\frac{3}{2}} + 7 \, a \sqrt{b}\right)} \log\left(\sqrt{b} \tan\left(d x + c\right)^{2} + \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \tan\left(d x + c\right) + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} {\left(b {\left(\sqrt{a} + 3 \, \sqrt{b}\right)} + 5 \, a^{\frac{3}{2}} + 7 \, a \sqrt{b}\right)} \log\left(\sqrt{b} \tan\left(d x + c\right)^{2} - \sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \tan\left(d x + c\right) + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{3}{4}}}\right)}}{a^{3} + 2 \, a^{2} b + a b^{2}} + \frac{8 \, {\left(b \tan\left(d x + c\right)^{3} - b \tan\left(d x + c\right)\right)}}{{\left(a^{2} b + a b^{2}\right)} \tan\left(d x + c\right)^{4} + a^{3} + a^{2} b} - \frac{32 \, {\left(d x + c\right)}}{a^{2} + 2 \, a b + b^{2}}}{32 \, d}"," ",0,"-1/32*(b*(2*sqrt(2)*(b*(sqrt(a) - 3*sqrt(b)) + 5*a^(3/2) - 7*a*sqrt(b))*arctan(1/2*sqrt(2)*(2*sqrt(b)*tan(d*x + c) + sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*(b*(sqrt(a) - 3*sqrt(b)) + 5*a^(3/2) - 7*a*sqrt(b))*arctan(1/2*sqrt(2)*(2*sqrt(b)*tan(d*x + c) - sqrt(2)*a^(1/4)*b^(1/4))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*(b*(sqrt(a) + 3*sqrt(b)) + 5*a^(3/2) + 7*a*sqrt(b))*log(sqrt(b)*tan(d*x + c)^2 + sqrt(2)*a^(1/4)*b^(1/4)*tan(d*x + c) + sqrt(a))/(a^(3/4)*b^(3/4)) + sqrt(2)*(b*(sqrt(a) + 3*sqrt(b)) + 5*a^(3/2) + 7*a*sqrt(b))*log(sqrt(b)*tan(d*x + c)^2 - sqrt(2)*a^(1/4)*b^(1/4)*tan(d*x + c) + sqrt(a))/(a^(3/4)*b^(3/4)))/(a^3 + 2*a^2*b + a*b^2) + 8*(b*tan(d*x + c)^3 - b*tan(d*x + c))/((a^2*b + a*b^2)*tan(d*x + c)^4 + a^3 + a^2*b) - 32*(d*x + c)/(a^2 + 2*a*b + b^2))/d","A",0
387,0,0,0,0.000000," ","integrate((a+tan(d*x+c)^4*b)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right)^{4} + a}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c)^4 + a), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(a+tan(d*x+c)^4*b)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right)^{4} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*tan(d*x + c)^4 + a), x)","F",0
389,0,0,0,0.000000," ","integrate((a+b*tan(x)^4)^(1/2)*tan(x)^3,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(x\right)^{4} + a} \tan\left(x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tan(x)^4 + a)*tan(x)^3, x)","F",0
390,0,0,0,0.000000," ","integrate((a+b*tan(x)^4)^(1/2)*tan(x),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(x\right)^{4} + a} \tan\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*tan(x)^4 + a)*tan(x), x)","F",0
391,0,0,0,0.000000," ","integrate(cot(x)*(a+b*tan(x)^4)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(x\right)^{4} + a} \cot\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*tan(x)^4 + a)*cot(x), x)","F",0
392,0,0,0,0.000000," ","integrate((a+b*tan(x)^4)^(1/2)*tan(x)^2,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(x\right)^{4} + a} \tan\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tan(x)^4 + a)*tan(x)^2, x)","F",0
393,0,0,0,0.000000," ","integrate(tan(x)^3*(a+b*tan(x)^4)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{3}{2}} \tan\left(x\right)^{3}\,{d x}"," ",0,"integrate((b*tan(x)^4 + a)^(3/2)*tan(x)^3, x)","F",0
394,0,0,0,0.000000," ","integrate(tan(x)*(a+b*tan(x)^4)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{3}{2}} \tan\left(x\right)\,{d x}"," ",0,"integrate((b*tan(x)^4 + a)^(3/2)*tan(x), x)","F",0
395,0,0,0,0.000000," ","integrate(cot(x)*(a+b*tan(x)^4)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{3}{2}} \cot\left(x\right)\,{d x}"," ",0,"integrate((b*tan(x)^4 + a)^(3/2)*cot(x), x)","F",0
396,0,0,0,0.000000," ","integrate(tan(x)^3/(a+b*tan(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)^{3}}{\sqrt{b \tan\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(x)^3/sqrt(b*tan(x)^4 + a), x)","F",0
397,0,0,0,0.000000," ","integrate(tan(x)/(a+b*tan(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{\sqrt{b \tan\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(x)/sqrt(b*tan(x)^4 + a), x)","F",0
398,0,0,0,0.000000," ","integrate(cot(x)/(a+b*tan(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{\sqrt{b \tan\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(cot(x)/sqrt(b*tan(x)^4 + a), x)","F",0
399,0,0,0,0.000000," ","integrate(tan(x)^2/(a+b*tan(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)^{2}}{\sqrt{b \tan\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(tan(x)^2/sqrt(b*tan(x)^4 + a), x)","F",0
400,0,0,0,0.000000," ","integrate(tan(x)^3/(a+b*tan(x)^4)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)^{3}}{{\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(x)^3/(b*tan(x)^4 + a)^(3/2), x)","F",0
401,0,0,0,0.000000," ","integrate(tan(x)/(a+b*tan(x)^4)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(x)/(b*tan(x)^4 + a)^(3/2), x)","F",0
402,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*tan(x)^4)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
403,0,0,0,0.000000," ","integrate(tan(x)^3/(a+b*tan(x)^4)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)^{3}}{{\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(x)^3/(b*tan(x)^4 + a)^(5/2), x)","F",0
404,0,0,0,0.000000," ","integrate(tan(x)/(a+b*tan(x)^4)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(b \tan\left(x\right)^{4} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(x)/(b*tan(x)^4 + a)^(5/2), x)","F",0
405,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*tan(x)^4)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
406,0,0,0,0.000000," ","integrate((a+b*(c*tan(f*x+e))^(1/2))^2*(d*tan(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sqrt{c \tan\left(f x + e\right)} b + a\right)}^{2} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((sqrt(c*tan(f*x + e))*b + a)^2*(d*tan(f*x + e))^m, x)","F",0
407,0,0,0,0.000000," ","integrate((a+b*(c*tan(f*x+e))^(1/2))*(d*tan(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(\sqrt{c \tan\left(f x + e\right)} b + a\right)} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((sqrt(c*tan(f*x + e))*b + a)*(d*tan(f*x + e))^m, x)","F",0
408,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^m/(a+b*(c*tan(f*x+e))^(1/2)),x, algorithm=""maxima"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{m}}{\sqrt{c \tan\left(f x + e\right)} b + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^m/(sqrt(c*tan(f*x + e))*b + a), x)","F",0
409,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^m/(a+b*(c*tan(f*x+e))^(1/2))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
410,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*(d*tan(f*x + e))^m, x)","F",0
411,0,0,0,0.000000," ","integrate(tan(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*tan(f*x + e)^2, x)","F",0
412,0,0,0,0.000000," ","integrate((b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p, x)","F",0
413,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*cot(f*x + e)^2, x)","F",0
414,-1,0,0,0.000000," ","integrate(cot(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate(cot(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,0,0,0,0.000000," ","integrate(tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*tan(f*x + e)^3, x)","F",0
417,0,0,0,0.000000," ","integrate(tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*tan(f*x + e), x)","F",0
418,0,0,0,0.000000," ","integrate(cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*cot(f*x + e), x)","F",0
419,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*cot(f*x + e)^3, x)","F",0
420,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \left(d \tan\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*(d*tan(f*x + e))^m, x)","F",0
421,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^m*(b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p} \left(d \cot\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p*(d*cot(f*x + e))^m, x)","F",0
422,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \left(d \cot\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*(d*cot(f*x + e))^m, x)","F",0
423,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \left(d \cot\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*(d*cot(f*x + e))^m, x)","F",0
424,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \left(d \cot\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*(d*cot(f*x + e))^m, x)","F",0
425,1,95,0,0.517567," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(4 \, a - b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(4 \, a - b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(4 \, a - b\right)} \sin\left(d x + c\right)^{3} - {\left(4 \, a + b\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((4*a - b)*log(sin(d*x + c) + 1) - (4*a - b)*log(sin(d*x + c) - 1) - 2*((4*a - b)*sin(d*x + c)^3 - (4*a + b)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
426,1,62,0,1.103709," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(2 \, a - b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, a - b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, b \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((2*a - b)*log(sin(d*x + c) + 1) - (2*a - b)*log(sin(d*x + c) - 1) - 2*b*sin(d*x + c)/(sin(d*x + c)^2 - 1))/d","A",0
427,1,46,0,0.318949," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 2 \, a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 2*a*sin(d*x + c))/d","A",0
428,1,29,0,0.311404," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \sin\left(d x + c\right)^{3} - 3 \, a \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*((a - b)*sin(d*x + c)^3 - 3*a*sin(d*x + c))/d","A",0
429,1,47,0,0.712498," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(a - b\right)} \sin\left(d x + c\right)^{5} - 5 \, {\left(2 \, a - b\right)} \sin\left(d x + c\right)^{3} + 15 \, a \sin\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*(a - b)*sin(d*x + c)^5 - 5*(2*a - b)*sin(d*x + c)^3 + 15*a*sin(d*x + c))/d","A",0
430,1,64,0,0.437876," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","-\frac{15 \, {\left(a - b\right)} \sin\left(d x + c\right)^{7} - 21 \, {\left(3 \, a - 2 \, b\right)} \sin\left(d x + c\right)^{5} + 35 \, {\left(3 \, a - b\right)} \sin\left(d x + c\right)^{3} - 105 \, a \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(15*(a - b)*sin(d*x + c)^7 - 21*(3*a - 2*b)*sin(d*x + c)^5 + 35*(3*a - b)*sin(d*x + c)^3 - 105*a*sin(d*x + c))/d","A",0
431,1,56,0,0.340477," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{15 \, b \tan\left(d x + c\right)^{7} + 21 \, {\left(a + 2 \, b\right)} \tan\left(d x + c\right)^{5} + 35 \, {\left(2 \, a + b\right)} \tan\left(d x + c\right)^{3} + 105 \, a \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b*tan(d*x + c)^7 + 21*(a + 2*b)*tan(d*x + c)^5 + 35*(2*a + b)*tan(d*x + c)^3 + 105*a*tan(d*x + c))/d","A",0
432,1,39,0,0.307560," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(d x + c\right)^{5} + 5 \, {\left(a + b\right)} \tan\left(d x + c\right)^{3} + 15 \, a \tan\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*b*tan(d*x + c)^5 + 5*(a + b)*tan(d*x + c)^3 + 15*a*tan(d*x + c))/d","A",0
433,1,25,0,0.501611," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \tan\left(d x + c\right)^{3} + 3 \, a \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(b*tan(d*x + c)^3 + 3*a*tan(d*x + c))/d","A",0
434,1,39,0,0.555342," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} {\left(a + b\right)} + \frac{{\left(a - b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*((d*x + c)*(a + b) + (a - b)*tan(d*x + c)/(tan(d*x + c)^2 + 1))/d","A",0
435,1,69,0,1.688040," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} {\left(3 \, a + b\right)} + \frac{{\left(3 \, a + b\right)} \tan\left(d x + c\right)^{3} + {\left(5 \, a - b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*((d*x + c)*(3*a + b) + ((3*a + b)*tan(d*x + c)^3 + (5*a - b)*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
436,1,97,0,1.038059," ","integrate(cos(d*x+c)^6*(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} {\left(5 \, a + b\right)} + \frac{3 \, {\left(5 \, a + b\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(5 \, a + b\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(11 \, a - b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"1/48*(3*(d*x + c)*(5*a + b) + (3*(5*a + b)*tan(d*x + c)^5 + 8*(5*a + b)*tan(d*x + c)^3 + 3*(11*a - b)*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
437,1,156,0,0.569207," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(8 \, a^{2} - 4 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, a^{2} - 4 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(8 \, a^{2} - 4 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{5} - 8 \, {\left(6 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1}}{96 \, d}"," ",0,"1/96*(3*(8*a^2 - 4*a*b + b^2)*log(sin(d*x + c) + 1) - 3*(8*a^2 - 4*a*b + b^2)*log(sin(d*x + c) - 1) - 2*(3*(8*a^2 - 4*a*b + b^2)*sin(d*x + c)^5 - 8*(6*a^2 - b^2)*sin(d*x + c)^3 + 3*(8*a^2 + 4*a*b - b^2)*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1))/d","A",0
438,1,119,0,0.437105," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(8 \, a b - 5 \, b^{2}\right)} \sin\left(d x + c\right)^{3} - {\left(8 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((8*a^2 - 8*a*b + 3*b^2)*log(sin(d*x + c) + 1) - (8*a^2 - 8*a*b + 3*b^2)*log(sin(d*x + c) - 1) - 2*((8*a*b - 5*b^2)*sin(d*x + c)^3 - (8*a*b - 3*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
439,1,105,0,0.469929," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right) - 4 \, \sin\left(d x + c\right)\right)} - 4 \, a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - 4 \, a^{2} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) - 4*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - 4*a^2*sin(d*x + c))/d","A",0
440,1,72,0,0.649892," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{3} - 3 \, b^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, b^{2} \log\left(\sin\left(d x + c\right) - 1\right) - 6 \, {\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(a^2 - 2*a*b + b^2)*sin(d*x + c)^3 - 3*b^2*log(sin(d*x + c) + 1) + 3*b^2*log(sin(d*x + c) - 1) - 6*(a^2 - b^2)*sin(d*x + c))/d","A",0
441,1,56,0,0.380608," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{5} - 10 \, {\left(a^{2} - a b\right)} \sin\left(d x + c\right)^{3} + 15 \, a^{2} \sin\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*(a^2 - 2*a*b + b^2)*sin(d*x + c)^5 - 10*(a^2 - a*b)*sin(d*x + c)^3 + 15*a^2*sin(d*x + c))/d","A",0
442,1,81,0,0.314054," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{7} - 21 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{5} + 35 \, {\left(3 \, a^{2} - 2 \, a b\right)} \sin\left(d x + c\right)^{3} - 105 \, a^{2} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(15*(a^2 - 2*a*b + b^2)*sin(d*x + c)^7 - 21*(3*a^2 - 4*a*b + b^2)*sin(d*x + c)^5 + 35*(3*a^2 - 2*a*b)*sin(d*x + c)^3 - 105*a^2*sin(d*x + c))/d","A",0
443,1,104,0,0.491753," ","integrate(cos(d*x+c)^9*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{9} - 90 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{7} + 63 \, {\left(6 \, a^{2} - 6 \, a b + b^{2}\right)} \sin\left(d x + c\right)^{5} - 210 \, {\left(2 \, a^{2} - a b\right)} \sin\left(d x + c\right)^{3} + 315 \, a^{2} \sin\left(d x + c\right)}{315 \, d}"," ",0,"1/315*(35*(a^2 - 2*a*b + b^2)*sin(d*x + c)^9 - 90*(2*a^2 - 3*a*b + b^2)*sin(d*x + c)^7 + 63*(6*a^2 - 6*a*b + b^2)*sin(d*x + c)^5 - 210*(2*a^2 - a*b)*sin(d*x + c)^3 + 315*a^2*sin(d*x + c))/d","A",0
444,1,85,0,0.490273," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{35 \, b^{2} \tan\left(d x + c\right)^{9} + 90 \, {\left(a b + b^{2}\right)} \tan\left(d x + c\right)^{7} + 63 \, {\left(a^{2} + 4 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{5} + 210 \, {\left(a^{2} + a b\right)} \tan\left(d x + c\right)^{3} + 315 \, a^{2} \tan\left(d x + c\right)}{315 \, d}"," ",0,"1/315*(35*b^2*tan(d*x + c)^9 + 90*(a*b + b^2)*tan(d*x + c)^7 + 63*(a^2 + 4*a*b + b^2)*tan(d*x + c)^5 + 210*(a^2 + a*b)*tan(d*x + c)^3 + 315*a^2*tan(d*x + c))/d","A",0
445,1,66,0,0.620818," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{15 \, b^{2} \tan\left(d x + c\right)^{7} + 21 \, {\left(2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{5} + 35 \, {\left(a^{2} + 2 \, a b\right)} \tan\left(d x + c\right)^{3} + 105 \, a^{2} \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b^2*tan(d*x + c)^7 + 21*(2*a*b + b^2)*tan(d*x + c)^5 + 35*(a^2 + 2*a*b)*tan(d*x + c)^3 + 105*a^2*tan(d*x + c))/d","A",0
446,1,42,0,0.501941," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} \tan\left(d x + c\right)^{5} + 10 \, a b \tan\left(d x + c\right)^{3} + 15 \, a^{2} \tan\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*b^2*tan(d*x + c)^5 + 10*a*b*tan(d*x + c)^3 + 15*a^2*tan(d*x + c))/d","A",0
447,1,66,0,0.759619," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} \tan\left(d x + c\right) + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(2*b^2*tan(d*x + c) + (a^2 + 2*a*b - 3*b^2)*(d*x + c) + (a^2 - 2*a*b + b^2)*tan(d*x + c)/(tan(d*x + c)^2 + 1))/d","A",0
448,1,97,0,0.756788," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} {\left(d x + c\right)} + \frac{{\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(5 \, a^{2} - 2 \, a b - 3 \, b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*((3*a^2 + 2*a*b + 3*b^2)*(d*x + c) + ((3*a^2 + 2*a*b - 5*b^2)*tan(d*x + c)^3 + (5*a^2 - 2*a*b - 3*b^2)*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
449,1,131,0,0.497946," ","integrate(cos(d*x+c)^6*(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} {\left(d x + c\right)} + \frac{3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{5} + 8 \, {\left(5 \, a^{2} + 2 \, a b - b^{2}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(11 \, a^{2} - 2 \, a b - b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"1/48*(3*(5*a^2 + 2*a*b + b^2)*(d*x + c) + (3*(5*a^2 + 2*a*b + b^2)*tan(d*x + c)^5 + 8*(5*a^2 + 2*a*b - b^2)*tan(d*x + c)^3 + 3*(11*a^2 - 2*a*b - b^2)*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
450,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
451,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
452,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
453,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
454,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
455,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
456,1,110,0,0.508432," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} - \frac{3 \, b^{2} \tan\left(d x + c\right)^{5} - 5 \, {\left(a b - 3 \, b^{2}\right)} \tan\left(d x + c\right)^{3} + 15 \, {\left(a^{2} - 3 \, a b + 3 \, b^{2}\right)} \tan\left(d x + c\right)}{b^{3}}}{15 \, d}"," ",0,"-1/15*(15*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*b^3) - (3*b^2*tan(d*x + c)^5 - 5*(a*b - 3*b^2)*tan(d*x + c)^3 + 15*(a^2 - 3*a*b + 3*b^2)*tan(d*x + c))/b^3)/d","A",0
457,1,69,0,0.664637," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b \tan\left(d x + c\right)^{3} - 3 \, {\left(a - 2 \, b\right)} \tan\left(d x + c\right)}{b^{2}}}{3 \, d}"," ",0,"1/3*(3*(a^2 - 2*a*b + b^2)*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*b^2) + (b*tan(d*x + c)^3 - 3*(a - 2*b)*tan(d*x + c))/b^2)/d","A",0
458,1,45,0,0.742155," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{{\left(a - b\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{\tan\left(d x + c\right)}{b}}{d}"," ",0,"-((a - b)*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*b) - tan(d*x + c)/b)/d","A",0
459,1,23,0,0.468513," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} d}"," ",0,"arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*d)","A",0
460,1,95,0,0.438146," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a b}} + \frac{{\left(d x + c\right)} {\left(a - 3 \, b\right)}}{a^{2} - 2 \, a b + b^{2}} + \frac{\tan\left(d x + c\right)}{{\left(a - b\right)} \tan\left(d x + c\right)^{2} + a - b}}{2 \, d}"," ",0,"1/2*(2*b^2*arctan(b*tan(d*x + c)/sqrt(a*b))/((a^2 - 2*a*b + b^2)*sqrt(a*b)) + (d*x + c)*(a - 3*b)/(a^2 - 2*a*b + b^2) + tan(d*x + c)/((a - b)*tan(d*x + c)^2 + a - b))/d","A",0
461,1,185,0,0.645063," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{8 \, b^{3} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sqrt{a b}} - \frac{{\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} {\left(d x + c\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(3 \, a - 7 \, b\right)} \tan\left(d x + c\right)^{3} + {\left(5 \, a - 9 \, b\right)} \tan\left(d x + c\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}}}{8 \, d}"," ",0,"-1/8*(8*b^3*arctan(b*tan(d*x + c)/sqrt(a*b))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sqrt(a*b)) - (3*a^2 - 10*a*b + 15*b^2)*(d*x + c)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - ((3*a - 7*b)*tan(d*x + c)^3 + (5*a - 9*b)*tan(d*x + c))/((a^2 - 2*a*b + b^2)*tan(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*tan(d*x + c)^2 + a^2 - 2*a*b + b^2))/d","A",0
462,-2,0,0,0.000000," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
463,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
464,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
465,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
466,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
467,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
468,1,137,0,0.808885," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \tan\left(d x + c\right)}{a b^{4} \tan\left(d x + c\right)^{2} + a^{2} b^{3}} - \frac{2 \, {\left(b \tan\left(d x + c\right)^{3} - 3 \, {\left(2 \, a - 3 \, b\right)} \tan\left(d x + c\right)\right)}}{b^{3}} - \frac{3 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*tan(d*x + c)/(a*b^4*tan(d*x + c)^2 + a^2*b^3) - 2*(b*tan(d*x + c)^3 - 3*(2*a - 3*b)*tan(d*x + c))/b^3 - 3*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*a*b^3))/d","A",0
469,1,100,0,0.937266," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} \tan\left(d x + c\right)}{a b^{3} \tan\left(d x + c\right)^{2} + a^{2} b^{2}} + \frac{2 \, \tan\left(d x + c\right)}{b^{2}} - \frac{{\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a b^{2}}}{2 \, d}"," ",0,"1/2*((a^2 - 2*a*b + b^2)*tan(d*x + c)/(a*b^3*tan(d*x + c)^2 + a^2*b^2) + 2*tan(d*x + c)/b^2 - (3*a^2 - 2*a*b - b^2)*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*a*b^2))/d","A",0
470,1,69,0,0.570606," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(a - b\right)} \tan\left(d x + c\right)}{a b^{2} \tan\left(d x + c\right)^{2} + a^{2} b} - \frac{{\left(a + b\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a b}}{2 \, d}"," ",0,"-1/2*((a - b)*tan(d*x + c)/(a*b^2*tan(d*x + c)^2 + a^2*b) - (a + b)*arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*a*b))/d","A",0
471,1,53,0,0.477274," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{\tan\left(d x + c\right)}{a b \tan\left(d x + c\right)^{2} + a^{2}} + \frac{\arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} a}}{2 \, d}"," ",0,"1/2*(tan(d*x + c)/(a*b*tan(d*x + c)^2 + a^2) + arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*a))/d","A",0
472,1,209,0,1.046549," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(d x + c\right)} {\left(a - 5 \, b\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(5 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} \sqrt{a b}} + \frac{{\left(a b + b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} \tan\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} - a^{3} b - a^{2} b^{2} + a b^{3}\right)} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*((d*x + c)*(a - 5*b)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (5*a*b^2 - b^3)*arctan(b*tan(d*x + c)/sqrt(a*b))/((a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*sqrt(a*b)) + ((a*b + b^2)*tan(d*x + c)^3 + (a^2 + b^2)*tan(d*x + c))/((a^3*b - 2*a^2*b^2 + a*b^3)*tan(d*x + c)^4 + a^4 - 2*a^3*b + a^2*b^2 + (a^4 - a^3*b - a^2*b^2 + a*b^3)*tan(d*x + c)^2))/d","A",0
473,1,355,0,0.766410," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{2} - 14 \, a b + 35 \, b^{2}\right)} {\left(d x + c\right)}}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{4 \, {\left(7 \, a b^{3} - b^{4}\right)} \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a b}} + \frac{{\left(3 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} \tan\left(d x + c\right)^{5} + {\left(3 \, a^{3} - 6 \, a^{2} b - 13 \, a b^{2} - 8 \, b^{3}\right)} \tan\left(d x + c\right)^{3} + {\left(5 \, a^{3} - 13 \, a^{2} b - 4 \, b^{3}\right)} \tan\left(d x + c\right)}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} \tan\left(d x + c\right)^{6} + a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} - a^{4} b - 3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 2 \, a b^{4}\right)} \tan\left(d x + c\right)^{4} + {\left(2 \, a^{5} - 5 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} - a b^{4}\right)} \tan\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"1/8*((3*a^2 - 14*a*b + 35*b^2)*(d*x + c)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - 4*(7*a*b^3 - b^4)*arctan(b*tan(d*x + c)/sqrt(a*b))/((a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*sqrt(a*b)) + ((3*a^2*b - 11*a*b^2 - 4*b^3)*tan(d*x + c)^5 + (3*a^3 - 6*a^2*b - 13*a*b^2 - 8*b^3)*tan(d*x + c)^3 + (5*a^3 - 13*a^2*b - 4*b^3)*tan(d*x + c))/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*tan(d*x + c)^6 + a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3 + (a^5 - a^4*b - 3*a^3*b^2 + 5*a^2*b^3 - 2*a*b^4)*tan(d*x + c)^4 + (2*a^5 - 5*a^4*b + 3*a^3*b^2 + a^2*b^3 - a*b^4)*tan(d*x + c)^2))/d","A",0
474,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p*(d*sec(f*x + e))^m, x)","F",0
475,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*(d*sec(f*x + e))^m, x)","F",0
476,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*(d*sec(f*x + e))^m, x)","F",0
477,1,106,0,0.739515," ","integrate(sec(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\frac{\frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p} \tan\left(f x + e\right)^{5}}{n p + 5} + \frac{2 \, b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p} \tan\left(f x + e\right)^{3}}{n p + 3} + \frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p} \tan\left(f x + e\right)}{n p + 1}}{f}"," ",0,"(b^p*c^(n*p)*(tan(f*x + e)^n)^p*tan(f*x + e)^5/(n*p + 5) + 2*b^p*c^(n*p)*(tan(f*x + e)^n)^p*tan(f*x + e)^3/(n*p + 3) + b^p*c^(n*p)*(tan(f*x + e)^n)^p*tan(f*x + e)/(n*p + 1))/f","A",0
478,1,71,0,0.758166," ","integrate(sec(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\frac{\frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p} \tan\left(f x + e\right)^{3}}{n p + 3} + \frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p} \tan\left(f x + e\right)}{n p + 1}}{f}"," ",0,"(b^p*c^(n*p)*(tan(f*x + e)^n)^p*tan(f*x + e)^3/(n*p + 3) + b^p*c^(n*p)*(tan(f*x + e)^n)^p*tan(f*x + e)/(n*p + 1))/f","A",0
479,1,35,0,0.889714," ","integrate(sec(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\frac{b^{p} c^{n p} {\left(\tan\left(f x + e\right)^{n}\right)}^{p} \tan\left(f x + e\right)}{{\left(n p + 1\right)} f}"," ",0,"b^p*c^(n*p)*(tan(f*x + e)^n)^p*tan(f*x + e)/((n*p + 1)*f)","A",0
480,0,0,0,0.000000," ","integrate((b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p, x)","F",0
481,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*cos(f*x + e)^2, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*sec(f*x + e)^3, x)","F",0
483,0,0,0,0.000000," ","integrate(sec(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*sec(f*x + e), x)","F",0
484,0,0,0,0.000000," ","integrate(cos(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*cos(f*x + e), x)","F",0
485,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*cos(f*x + e)^3, x)","F",0
486,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*(d*sec(f*x + e))^m, x)","F",0
487,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*sec(f*x + e)^3, x)","F",0
488,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*sec(f*x + e), x)","F",0
489,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \cos\left(f x + e\right)\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*cos(f*x + e), x)","F",0
490,0,0,0,0.000000," ","integrate(cos(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \cos\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*cos(f*x + e)^3, x)","F",0
491,0,0,0,0.000000," ","integrate(sec(f*x+e)^6*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \sec\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*sec(f*x + e)^6, x)","F",0
492,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*sec(f*x + e)^4, x)","F",0
493,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*sec(f*x + e)^2, x)","F",0
494,0,0,0,0.000000," ","integrate((a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p, x)","F",0
495,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*cos(f*x + e)^2, x)","F",0
496,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^m*(b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int \left(b \tan\left(f x + e\right)^{2}\right)^{p} \left(d \csc\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2)^p*(d*csc(f*x + e))^m, x)","F",0
497,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right)^{2} + a\right)}^{p} \left(d \csc\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e)^2 + a)^p*(d*csc(f*x + e))^m, x)","F",0
498,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int \left(\left(c \tan\left(f x + e\right)\right)^{n} b\right)^{p} \left(d \csc\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b)^p*(d*csc(f*x + e))^m, x)","F",0
499,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x, algorithm=""maxima"")","\int {\left(\left(c \tan\left(f x + e\right)\right)^{n} b + a\right)}^{p} \left(d \csc\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate(((c*tan(f*x + e))^n*b + a)^p*(d*csc(f*x + e))^m, x)","F",0
