1,1,94,0,0.716806," ","integrate(sin(f*x+e)^3*(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{4} \, a^{2} x - \frac{a^{2} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{3 \, a^{2} \cos\left(3 \, f x + 3 \, e\right)}{16 \, f} - \frac{11 \, a^{2} \cos\left(f x + e\right)}{8 \, f} + \frac{a^{2} \sin\left(4 \, f x + 4 \, e\right)}{16 \, f} - \frac{a^{2} \sin\left(2 \, f x + 2 \, e\right)}{2 \, f}"," ",0,"3/4*a^2*x - 1/80*a^2*cos(5*f*x + 5*e)/f + 3/16*a^2*cos(3*f*x + 3*e)/f - 11/8*a^2*cos(f*x + e)/f + 1/16*a^2*sin(4*f*x + 4*e)/f - 1/2*a^2*sin(2*f*x + 2*e)/f","A",0
2,1,112,0,1.929365," ","integrate(sin(f*x+e)^3*(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{23}{16} \, a^{3} x - \frac{3 \, a^{3} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{19 \, a^{3} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{21 \, a^{3} \cos\left(f x + e\right)}{8 \, f} - \frac{a^{3} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{9 \, a^{3} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} - \frac{63 \, a^{3} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"23/16*a^3*x - 3/80*a^3*cos(5*f*x + 5*e)/f + 19/48*a^3*cos(3*f*x + 3*e)/f - 21/8*a^3*cos(f*x + e)/f - 1/192*a^3*sin(6*f*x + 6*e)/f + 9/64*a^3*sin(4*f*x + 4*e)/f - 63/64*a^3*sin(2*f*x + 2*e)/f","A",0
3,1,67,0,0.912409," ","integrate(sin(x)^4/(a+a*sin(x)),x, algorithm=""giac"")","-\frac{3 \, x}{2 \, a} - \frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}} - \frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{5} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 24 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, x\right) + 10}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3} a}"," ",0,"-3/2*x/a - 2/(a*(tan(1/2*x) + 1)) - 1/3*(3*tan(1/2*x)^5 + 6*tan(1/2*x)^4 + 24*tan(1/2*x)^2 - 3*tan(1/2*x) + 10)/((tan(1/2*x)^2 + 1)^3*a)","A",0
4,1,56,0,1.951094," ","integrate(sin(x)^3/(a+a*sin(x)),x, algorithm=""giac"")","\frac{3 \, x}{2 \, a} + \frac{\tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{1}{2} \, x\right) + 2}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{2} a} + \frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}}"," ",0,"3/2*x/a + (tan(1/2*x)^3 + 2*tan(1/2*x)^2 - tan(1/2*x) + 2)/((tan(1/2*x)^2 + 1)^2*a) + 2/(a*(tan(1/2*x) + 1))","A",0
5,1,44,0,0.288112," ","integrate(sin(x)^2/(a+a*sin(x)),x, algorithm=""giac"")","-\frac{x}{a} - \frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right) + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right) + 1\right)} a}"," ",0,"-x/a - 2*(tan(1/2*x)^2 + tan(1/2*x) + 2)/((tan(1/2*x)^3 + tan(1/2*x)^2 + tan(1/2*x) + 1)*a)","A",0
6,1,19,0,0.924170," ","integrate(sin(x)/(a+a*sin(x)),x, algorithm=""giac"")","\frac{x}{a} + \frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}}"," ",0,"x/a + 2/(a*(tan(1/2*x) + 1))","A",0
7,1,13,0,0.320484," ","integrate(1/(a+a*sin(x)),x, algorithm=""giac"")","-\frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}}"," ",0,"-2/(a*(tan(1/2*x) + 1))","A",0
8,1,24,0,0.240033," ","integrate(csc(x)/(a+a*sin(x)),x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a} + \frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}}"," ",0,"log(abs(tan(1/2*x)))/a + 2/(a*(tan(1/2*x) + 1))","A",0
9,1,53,0,0.687557," ","integrate(csc(x)^2/(a+a*sin(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a} + \frac{\tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, \tan\left(\frac{1}{2} \, x\right) - 1}{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)\right)} a}"," ",0,"-log(abs(tan(1/2*x)))/a + 1/2*tan(1/2*x)/a + 1/2*(tan(1/2*x)^2 - 4*tan(1/2*x) - 1)/((tan(1/2*x)^2 + tan(1/2*x))*a)","B",0
10,1,73,0,0.311938," ","integrate(csc(x)^3/(a+a*sin(x)),x, algorithm=""giac"")","\frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a} + \frac{a \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{2}} + \frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}} - \frac{18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, \tan\left(\frac{1}{2} \, x\right) + 1}{8 \, a \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"3/2*log(abs(tan(1/2*x)))/a + 1/8*(a*tan(1/2*x)^2 - 4*a*tan(1/2*x))/a^2 + 2/(a*(tan(1/2*x) + 1)) - 1/8*(18*tan(1/2*x)^2 - 4*tan(1/2*x) + 1)/(a*tan(1/2*x)^2)","A",0
11,1,96,0,0.307535," ","integrate(csc(x)^4/(a+a*sin(x)),x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a} + \frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 21 \, a^{2} \tan\left(\frac{1}{2} \, x\right)}{24 \, a^{3}} - \frac{2}{a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}} + \frac{66 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 21 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, x\right) - 1}{24 \, a \tan\left(\frac{1}{2} \, x\right)^{3}}"," ",0,"-3/2*log(abs(tan(1/2*x)))/a + 1/24*(a^2*tan(1/2*x)^3 - 3*a^2*tan(1/2*x)^2 + 21*a^2*tan(1/2*x))/a^3 - 2/(a*(tan(1/2*x) + 1)) + 1/24*(66*tan(1/2*x)^3 - 21*tan(1/2*x)^2 + 3*tan(1/2*x) - 1)/(a*tan(1/2*x)^3)","A",0
12,1,72,0,0.334516," ","integrate(sin(x)^4/(a+a*sin(x))^2,x, algorithm=""giac"")","\frac{7 \, x}{2 \, a^{2}} + \frac{\tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{1}{2} \, x\right) + 4}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{2} a^{2}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 21 \, \tan\left(\frac{1}{2} \, x\right) + 10\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"7/2*x/a^2 + (tan(1/2*x)^3 + 4*tan(1/2*x)^2 - tan(1/2*x) + 4)/((tan(1/2*x)^2 + 1)^2*a^2) + 2/3*(9*tan(1/2*x)^2 + 21*tan(1/2*x) + 10)/(a^2*(tan(1/2*x) + 1)^3)","A",0
13,1,51,0,0.384311," ","integrate(sin(x)^3/(a+a*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, x}{a^{2}} - \frac{2}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} a^{2}} - \frac{2 \, {\left(6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, x\right) + 7\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"-2*x/a^2 - 2/((tan(1/2*x)^2 + 1)*a^2) - 2/3*(6*tan(1/2*x)^2 + 15*tan(1/2*x) + 7)/(a^2*(tan(1/2*x) + 1)^3)","A",0
14,1,35,0,0.825429," ","integrate(sin(x)^2/(a+a*sin(x))^2,x, algorithm=""giac"")","\frac{x}{a^{2}} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, x\right) + 4\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"x/a^2 + 2/3*(3*tan(1/2*x)^2 + 9*tan(1/2*x) + 4)/(a^2*(tan(1/2*x) + 1)^3)","A",0
15,1,21,0,1.950449," ","integrate(sin(x)/(a+a*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"-2/3*(3*tan(1/2*x) + 1)/(a^2*(tan(1/2*x) + 1)^3)","A",0
16,1,29,0,1.789313," ","integrate(1/(a+a*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, x\right) + 2\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"-2/3*(3*tan(1/2*x)^2 + 3*tan(1/2*x) + 2)/(a^2*(tan(1/2*x) + 1)^3)","A",0
17,1,40,0,1.703021," ","integrate(csc(x)/(a+a*sin(x))^2,x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}} + \frac{2 \, {\left(6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, x\right) + 5\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"log(abs(tan(1/2*x)))/a^2 + 2/3*(6*tan(1/2*x)^2 + 9*tan(1/2*x) + 5)/(a^2*(tan(1/2*x) + 1)^3)","A",0
18,1,69,0,0.302658," ","integrate(csc(x)^2/(a+a*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a^{2}} + \frac{4 \, \tan\left(\frac{1}{2} \, x\right) - 1}{2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)} - \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, x\right) + 8\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"-2*log(abs(tan(1/2*x)))/a^2 + 1/2*tan(1/2*x)/a^2 + 1/2*(4*tan(1/2*x) - 1)/(a^2*tan(1/2*x)) - 2/3*(9*tan(1/2*x)^2 + 15*tan(1/2*x) + 8)/(a^2*(tan(1/2*x) + 1)^3)","A",0
19,1,93,0,0.968410," ","integrate(csc(x)^3/(a+a*sin(x))^2,x, algorithm=""giac"")","\frac{7 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{2}} + \frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, a^{2} \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{4}} - \frac{42 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, x\right) + 1}{8 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2}} + \frac{2 \, {\left(12 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 21 \, \tan\left(\frac{1}{2} \, x\right) + 11\right)}}{3 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"7/2*log(abs(tan(1/2*x)))/a^2 + 1/8*(a^2*tan(1/2*x)^2 - 8*a^2*tan(1/2*x))/a^4 - 1/8*(42*tan(1/2*x)^2 - 8*tan(1/2*x) + 1)/(a^2*tan(1/2*x)^2) + 2/3*(12*tan(1/2*x)^2 + 21*tan(1/2*x) + 11)/(a^2*(tan(1/2*x) + 1)^3)","A",0
20,1,114,0,0.284091," ","integrate(csc(x)^4/(a+a*sin(x))^2,x, algorithm=""giac"")","-\frac{5 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}} + \frac{110 \, \tan\left(\frac{1}{2} \, x\right)^{6} + 45 \, \tan\left(\frac{1}{2} \, x\right)^{5} - 231 \, \tan\left(\frac{1}{2} \, x\right)^{4} - 232 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 30 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, x\right) - 1}{24 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)\right)}^{3} a^{2}} + \frac{a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 45 \, a^{4} \tan\left(\frac{1}{2} \, x\right)}{24 \, a^{6}}"," ",0,"-5*log(abs(tan(1/2*x)))/a^2 + 1/24*(110*tan(1/2*x)^6 + 45*tan(1/2*x)^5 - 231*tan(1/2*x)^4 - 232*tan(1/2*x)^3 - 30*tan(1/2*x)^2 + 3*tan(1/2*x) - 1)/((tan(1/2*x)^2 + tan(1/2*x))^3*a^2) + 1/24*(a^4*tan(1/2*x)^3 - 6*a^4*tan(1/2*x)^2 + 45*a^4*tan(1/2*x))/a^6","A",0
21,1,99,0,0.966364," ","integrate(sin(x)^6/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{23 \, x}{2 \, a^{3}} - \frac{9 \, \tan\left(\frac{1}{2} \, x\right)^{5} + 36 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 84 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, x\right) + 40}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3} a^{3}} - \frac{4 \, {\left(75 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 330 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 530 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 355 \, \tan\left(\frac{1}{2} \, x\right) + 86\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"-23/2*x/a^3 - 1/3*(9*tan(1/2*x)^5 + 36*tan(1/2*x)^4 + 84*tan(1/2*x)^2 - 9*tan(1/2*x) + 40)/((tan(1/2*x)^2 + 1)^3*a^3) - 4/15*(75*tan(1/2*x)^4 + 330*tan(1/2*x)^3 + 530*tan(1/2*x)^2 + 355*tan(1/2*x) + 86)/(a^3*(tan(1/2*x) + 1)^5)","A",0
22,1,88,0,0.377846," ","integrate(sin(x)^5/(a+a*sin(x))^3,x, algorithm=""giac"")","\frac{13 \, x}{2 \, a^{3}} + \frac{\tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{1}{2} \, x\right) + 6}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{2} a^{3}} + \frac{2 \, {\left(90 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 405 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 665 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 445 \, \tan\left(\frac{1}{2} \, x\right) + 107\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"13/2*x/a^3 + (tan(1/2*x)^3 + 6*tan(1/2*x)^2 - tan(1/2*x) + 6)/((tan(1/2*x)^2 + 1)^2*a^3) + 2/15*(90*tan(1/2*x)^4 + 405*tan(1/2*x)^3 + 665*tan(1/2*x)^2 + 445*tan(1/2*x) + 107)/(a^3*(tan(1/2*x) + 1)^5)","A",0
23,1,67,0,0.883746," ","integrate(sin(x)^4/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{3 \, x}{a^{3}} - \frac{2}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} a^{3}} - \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 70 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 120 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 80 \, \tan\left(\frac{1}{2} \, x\right) + 19\right)}}{5 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"-3*x/a^3 - 2/((tan(1/2*x)^2 + 1)*a^3) - 2/5*(15*tan(1/2*x)^4 + 70*tan(1/2*x)^3 + 120*tan(1/2*x)^2 + 80*tan(1/2*x) + 19)/(a^3*(tan(1/2*x) + 1)^5)","A",0
24,1,51,0,0.327386," ","integrate(sin(x)^3/(a+a*sin(x))^3,x, algorithm=""giac"")","\frac{x}{a^{3}} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 75 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 145 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 95 \, \tan\left(\frac{1}{2} \, x\right) + 22\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"x/a^3 + 2/15*(15*tan(1/2*x)^4 + 75*tan(1/2*x)^3 + 145*tan(1/2*x)^2 + 95*tan(1/2*x) + 22)/(a^3*(tan(1/2*x) + 1)^5)","A",0
25,1,29,0,0.267790," ","integrate(sin(x)^2/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{4 \, {\left(10 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"-4/15*(10*tan(1/2*x)^2 + 5*tan(1/2*x) + 1)/(a^3*(tan(1/2*x) + 1)^5)","A",0
26,1,37,0,0.318935," ","integrate(sin(x)/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{5 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"-2/5*(5*tan(1/2*x)^3 + 5*tan(1/2*x)^2 + 5*tan(1/2*x) + 1)/(a^3*(tan(1/2*x) + 1)^5)","A",0
27,1,45,0,0.495229," ","integrate(1/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 40 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 20 \, \tan\left(\frac{1}{2} \, x\right) + 7\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"-2/15*(15*tan(1/2*x)^4 + 30*tan(1/2*x)^3 + 40*tan(1/2*x)^2 + 20*tan(1/2*x) + 7)/(a^3*(tan(1/2*x) + 1)^5)","A",0
28,1,56,0,0.759248," ","integrate(csc(x)/(a+a*sin(x))^3,x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{3}} + \frac{2 \, {\left(45 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 135 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 185 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 115 \, \tan\left(\frac{1}{2} \, x\right) + 32\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"log(abs(tan(1/2*x)))/a^3 + 2/15*(45*tan(1/2*x)^4 + 135*tan(1/2*x)^3 + 185*tan(1/2*x)^2 + 115*tan(1/2*x) + 32)/(a^3*(tan(1/2*x) + 1)^5)","A",0
29,1,85,0,0.638416," ","integrate(csc(x)^2/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{3}} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a^{3}} + \frac{6 \, \tan\left(\frac{1}{2} \, x\right) - 1}{2 \, a^{3} \tan\left(\frac{1}{2} \, x\right)} - \frac{4 \, {\left(15 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 50 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 70 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 45 \, \tan\left(\frac{1}{2} \, x\right) + 12\right)}}{5 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"-3*log(abs(tan(1/2*x)))/a^3 + 1/2*tan(1/2*x)/a^3 + 1/2*(6*tan(1/2*x) - 1)/(a^3*tan(1/2*x)) - 4/5*(15*tan(1/2*x)^4 + 50*tan(1/2*x)^3 + 70*tan(1/2*x)^2 + 45*tan(1/2*x) + 12)/(a^3*(tan(1/2*x) + 1)^5)","A",0
30,1,109,0,0.249473," ","integrate(csc(x)^3/(a+a*sin(x))^3,x, algorithm=""giac"")","\frac{13 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{3}} - \frac{78 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, x\right) + 1}{8 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{2}} + \frac{a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{6}} + \frac{2 \, {\left(150 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 525 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 745 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 485 \, \tan\left(\frac{1}{2} \, x\right) + 127\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"13/2*log(abs(tan(1/2*x)))/a^3 - 1/8*(78*tan(1/2*x)^2 - 12*tan(1/2*x) + 1)/(a^3*tan(1/2*x)^2) + 1/8*(a^3*tan(1/2*x)^2 - 12*a^3*tan(1/2*x))/a^6 + 2/15*(150*tan(1/2*x)^4 + 525*tan(1/2*x)^3 + 745*tan(1/2*x)^2 + 485*tan(1/2*x) + 127)/(a^3*(tan(1/2*x) + 1)^5)","A",0
31,1,128,0,0.280527," ","integrate(csc(x)^4/(a+a*sin(x))^3,x, algorithm=""giac"")","-\frac{23 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{3}} + \frac{506 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 81 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, x\right) - 1}{24 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{3}} - \frac{2 \, {\left(225 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 810 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 1160 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 760 \, \tan\left(\frac{1}{2} \, x\right) + 197\right)}}{15 \, a^{3} {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}} + \frac{a^{6} \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, a^{6} \tan\left(\frac{1}{2} \, x\right)^{2} + 81 \, a^{6} \tan\left(\frac{1}{2} \, x\right)}{24 \, a^{9}}"," ",0,"-23/2*log(abs(tan(1/2*x)))/a^3 + 1/24*(506*tan(1/2*x)^3 - 81*tan(1/2*x)^2 + 9*tan(1/2*x) - 1)/(a^3*tan(1/2*x)^3) - 2/15*(225*tan(1/2*x)^4 + 810*tan(1/2*x)^3 + 1160*tan(1/2*x)^2 + 760*tan(1/2*x) + 197)/(a^3*(tan(1/2*x) + 1)^5) + 1/24*(a^6*tan(1/2*x)^3 - 9*a^6*tan(1/2*x)^2 + 81*a^6*tan(1/2*x))/a^9","A",0
32,1,159,0,0.582076," ","integrate(sin(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} \sqrt{a} {\left(\frac{45 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{420 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{35 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{252 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{1890 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"1/2520*sqrt(2)*sqrt(a)*(45*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 420*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 35*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 252*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 1890*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
33,1,129,0,0.946126," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{1}{140} \, \sqrt{2} \sqrt{a} {\left(\frac{7 \, \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{105 \, \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{5 \, \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{35 \, \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}\right)}"," ",0,"1/140*sqrt(2)*sqrt(a)*(7*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 105*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 5*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 35*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d)","A",0
34,1,99,0,0.444845," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{30} \, \sqrt{2} \sqrt{a} {\left(\frac{5 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{30 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)}"," ",0,"-1/30*sqrt(2)*sqrt(a)*(5*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 30*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)","A",0
35,1,68,0,1.392273," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{2} \sqrt{a} {\left(\frac{3 \, \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{\cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}\right)}"," ",0,"-1/3*sqrt(2)*sqrt(a)*(3*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d)","A",0
36,1,36,0,0.802557," ","integrate((a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} \sqrt{a} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d","A",0
37,1,67,0,0.459881," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{a} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-sqrt(a)*log(abs(-2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c))/abs(2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c)))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d","B",0
38,1,122,0,0.435670," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + \frac{4 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{2 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}\right)} \sqrt{a}}{4 \, d}"," ",0,"-1/4*sqrt(2)*(sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c))/abs(2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c)))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) + 4*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/(2*sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 - 1))*sqrt(a)/d","B",0
39,1,155,0,1.119144," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + \frac{4 \, {\left(6 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(2 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}\right)} \sqrt{a}}{16 \, d}"," ",0,"-1/16*sqrt(2)*(3*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c))/abs(2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c)))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) + 4*(6*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^3 - 5*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c))/(2*sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 - 1)^2)*sqrt(a)/d","A",0
40,1,184,0,0.714668," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(15 \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + \frac{4 \, {\left(60 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 80 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 33 \, \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(2 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}\right)} \sqrt{a}}{96 \, d}"," ",0,"-1/96*sqrt(2)*(15*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c))/abs(2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c)))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)) + 4*(60*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^5 - 80*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)^3 + 33*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c))/(2*sin(-1/4*pi + 1/2*d*x + 1/2*c)^2 - 1)^3)*sqrt(a)/d","A",0
41,1,104,0,1.425310," ","integrate(csc(d*x+c)*(a-a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a} \log\left(\frac{{\left| -4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - 6 \right|}}{{\left| 4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - 6 \right|}}\right) \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"sqrt(a)*log(abs(-4*sqrt(2) - 2*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) - 6)/abs(4*sqrt(2) - 2*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) - 6))*sgn(sin(-1/4*pi + 1/2*d*x + 1/2*c))/d","B",0
42,1,106,0,1.108281," ","integrate(csc(d*x+c)*(-a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{-a} \log\left(\frac{{\left| -4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - 6 \right|}}{{\left| 4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}}{\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1} - 6 \right|}}\right) \mathrm{sgn}\left(\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"sqrt(-a)*log(abs(-4*sqrt(2) - 2*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) - 6)/abs(4*sqrt(2) - 2*(cos(-1/4*pi + 1/2*d*x + 1/2*c) - 1)/(cos(-1/4*pi + 1/2*d*x + 1/2*c) + 1) - 6))*sgn(sin(-1/4*pi + 1/2*d*x + 1/2*c))/d","B",0
43,1,69,0,0.683456," ","integrate(csc(d*x+c)*(-a-a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-a} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-sqrt(-a)*log(abs(-2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c))/abs(2*sqrt(2) + 4*sin(-1/4*pi + 1/2*d*x + 1/2*c)))*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d","B",0
44,1,288,0,1.176823," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{126 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{1890 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{90 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{630 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{45 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{420 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{35 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{252 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{1890 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(126*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 1890*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 90*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 630*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 45*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 420*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 35*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 252*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 1890*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
45,1,226,0,0.597448," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{21 \, a \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{315 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{15 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{105 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{70 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{42 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{420 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(21*a*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 315*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 15*a*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 105*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 70*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 42*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 420*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
46,1,164,0,1.023689," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{30} \, \sqrt{2} {\left(\frac{30 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{10 \, a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{5 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{30 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/30*sqrt(2)*(30*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 10*a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 5*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 30*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
47,1,101,0,0.753059," ","integrate((a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{2} {\left(\frac{3 \, a \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{a \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/3*sqrt(2)*(3*a*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + a*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
48,1,2251,0,5.434140," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2} \sqrt{a} {\left(\frac{{\left(\sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 2 \right|}}{{\left| -2 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 2 \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} + \frac{{\left(\sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{4} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{5} - 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{4} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{5} + \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right)^{2} - 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{3} + 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{4} - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} + 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 60 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{3} - 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 45 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 20 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 18 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{1}{4} \, c\right) + 15 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 3 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - \sqrt{2} a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \log\left(\frac{{\left| -6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) \right|}}{{\left| -6 \, \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}} + 2 \, \tan\left(\frac{1}{4} \, d x + c\right) - 6 \, \tan\left(\frac{1}{2} \, c\right) \right|}}\right)}{{\left(\tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{\frac{3}{2}}} - \frac{8 \, {\left(a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{6} + 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{5} - a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{6} - 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{5} - 20 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{4} + 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 20 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{3} + 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) \tan\left(\frac{1}{4} \, c\right) - 15 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x + c\right) + 6 \, a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + a \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{{\left(\sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{6} + 3 \, \sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{4} + 3 \, \sqrt{2} \tan\left(\frac{1}{4} \, c\right)^{2} + \sqrt{2}\right)} {\left(\tan\left(\frac{1}{4} \, d x + c\right)^{2} + 1\right)}}\right)}}{2 \, d}"," ",0,"1/2*sqrt(2)*sqrt(a)*((sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 + 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) + sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))*log(abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 - 2*(tan(1/2*c)^2 + 1)^(3/2) + 2)/abs(-2*tan(1/4*d*x + c)*tan(1/2*c)^3 + 6*tan(1/4*d*x + c)*tan(1/2*c) - 6*tan(1/2*c)^2 + 2*(tan(1/2*c)^2 + 1)^(3/2) + 2))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) + (sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^6 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^6 - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^4 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^5 - 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^6 - 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^4 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^5 + sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c)^2 - 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^3 + 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^4 - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 + 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c)^2 + 60*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^3 - 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^3 + 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2*tan(1/4*c) - 45*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c)^2 + 20*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)^2 - 18*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c)*tan(1/4*c) + 15*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 3*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/2*c) - 6*sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) - sqrt(2)*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))*log(abs(-6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 - 2*(tan(1/2*c)^2 + 1)^(3/2) + 2*tan(1/4*d*x + c) - 6*tan(1/2*c))/abs(-6*tan(1/4*d*x + c)*tan(1/2*c)^2 + 2*tan(1/2*c)^3 + 2*(tan(1/2*c)^2 + 1)^(3/2) + 2*tan(1/4*d*x + c) - 6*tan(1/2*c)))/((tan(1/4*c)^6 + 3*tan(1/4*c)^4 + 3*tan(1/4*c)^2 + 1)*(tan(1/2*c)^2 + 1)^(3/2)) - 8*(a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^6 + 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^5 - a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^6 - 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^4 + 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^5 - 20*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^3 + 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^4 + 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c)^2 - 20*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^3 + 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c)*tan(1/4*c) - 15*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c)^2 - a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*d*x + c) + 6*a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*tan(1/4*c) + a*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c)))/((sqrt(2)*tan(1/4*c)^6 + 3*sqrt(2)*tan(1/4*c)^4 + 3*sqrt(2)*tan(1/4*c)^2 + sqrt(2))*(tan(1/4*d*x + c)^2 + 1)))/d","B",0
49,-1,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,372,0,0.979411," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{55440} \, \sqrt{2} {\left(\frac{385 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6237 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{76230 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{315 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{11}{2} \, d x + \frac{11}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{4455 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{25410 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{1980 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{18480 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{1540 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} + \frac{11088 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{83160 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/55440*sqrt(2)*(385*a^2*cos(1/4*pi + 9/2*d*x + 9/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 6237*a^2*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 76230*a^2*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 315*a^2*cos(-1/4*pi + 11/2*d*x + 11/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 4455*a^2*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 25410*a^2*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 1980*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d + 18480*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 1540*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d + 11088*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 83160*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
53,1,306,0,0.790357," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{1}{2520} \, \sqrt{2} {\left(\frac{252 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{3780 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{180 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{1260 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{45 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} - \frac{840 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{35 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{9}{2} \, d x + \frac{9}{2} \, c\right)}{d} - \frac{504 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{4410 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/2520*sqrt(2)*(252*a^2*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 3780*a^2*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 180*a^2*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 1260*a^2*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 45*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 7/2*d*x + 7/2*c)/d - 840*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 35*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 9/2*d*x + 9/2*c)/d - 504*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 4410*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
54,1,240,0,0.731743," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{1}{420} \, \sqrt{2} {\left(\frac{21 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{735 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{15 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{7}{2} \, d x + \frac{7}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{245 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{140 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{84 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{840 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/420*sqrt(2)*(21*a^2*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 735*a^2*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 15*a^2*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 245*a^2*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 140*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d - 84*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d + 840*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
55,1,174,0,0.985435," ","integrate((a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{1}{30} \, \sqrt{2} {\left(\frac{60 \, a^{2} \cos\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{20 \, a^{2} \cos\left(-\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right) \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} + \frac{5 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{4} \, \pi + \frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{3 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} - \frac{90 \, a^{2} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"-1/30*sqrt(2)*(60*a^2*cos(1/4*pi + 1/2*d*x + 1/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 20*a^2*cos(-1/4*pi + 3/2*d*x + 3/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d + 5*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(1/4*pi + 3/2*d*x + 3/2*c)/d + 3*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 5/2*d*x + 5/2*c)/d - 90*a^2*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))*sin(-1/4*pi + 1/2*d*x + 1/2*c)/d)*sqrt(a)","B",0
56,-1,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate(csc(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,1,314,0,0.919522," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(15 \, \sqrt{2} a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 17 \, \sqrt{2} \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a} - \frac{15 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{{\left({\left({\left({\left(\frac{13 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{15 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{40 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{40 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{15 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{13 \, a^{2}}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}}\right)}}{15 \, d}"," ",0,"2/15*((15*sqrt(2)*a*arctan(sqrt(a)/sqrt(-a)) + 17*sqrt(2)*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a) - 15*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + (((((13*a^2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 15*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 40*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 40*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 15*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 13*a^2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2))/d","B",0
62,1,245,0,2.279480," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(3 \, \sqrt{2} a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + 2 \, \sqrt{2} \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a} - \frac{3 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{{\left({\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}}\right)}}{3 \, d}"," ",0,"-2/3*((3*sqrt(2)*a*arctan(sqrt(a)/sqrt(-a)) + 2*sqrt(2)*sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a) - 3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + (((a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 3*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 3*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2))/d","B",0
63,1,182,0,5.687645," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{2} {\left(a \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) + \sqrt{-a} \sqrt{a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{-a} a} + \frac{\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{1}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{d}"," ",0,"2*(sqrt(2)*(a*arctan(sqrt(a)/sqrt(-a)) + sqrt(-a)*sqrt(a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(-a)*a) + (tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 1/sgn(tan(1/2*d*x + 1/2*c) + 1))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
64,1,111,0,0.700162," ","integrate(1/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \sin\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\cos\left(-\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{4 \, d}"," ",0,"1/4*(sqrt(2)*log(abs(1/sin(-1/4*pi + 1/2*d*x + 1/2*c) + sin(-1/4*pi + 1/2*d*x + 1/2*c) + 2))/(sqrt(a)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))) - sqrt(2)*log(abs(1/sin(-1/4*pi + 1/2*d*x + 1/2*c) + sin(-1/4*pi + 1/2*d*x + 1/2*c) - 2))/(sqrt(a)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))))/d","B",0
65,-2,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Error: Bad Argument Type","F(-2)",0
66,1,465,0,0.813126," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 8 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - \sqrt{2} \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 4 \, \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 8 \, \sqrt{a} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 2 \, \sqrt{-a} \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 3 \, \sqrt{2} \sqrt{-a} - 2 \, \sqrt{-a}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{\sqrt{2} \sqrt{-a} \sqrt{a} + 2 \, \sqrt{-a} \sqrt{a}} + \frac{4 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, \sqrt{a}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*((2*sqrt(2)*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 8*sqrt(2)*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - sqrt(2)*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) + 4*sqrt(a)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 8*sqrt(a)*arctan(sqrt(a)/sqrt(-a)) - 2*sqrt(-a)*log(sqrt(2)*sqrt(a) + sqrt(a)) - 3*sqrt(2)*sqrt(-a) - 2*sqrt(-a))*sgn(tan(1/2*d*x + 1/2*c) + 1)/(sqrt(2)*sqrt(-a)*sqrt(a) + 2*sqrt(-a)*sqrt(a)) + 4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*sqrt(a)/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
67,1,615,0,3.049353," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{{\left(42 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 64 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 21 \, \sqrt{2} \sqrt{-a} a \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) + 56 \, a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} \sqrt{a} + \sqrt{a}}{\sqrt{-a}}\right) - 96 \, a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{a}}{\sqrt{-a}}\right) - 28 \, \sqrt{-a} a \log\left(\sqrt{2} \sqrt{a} + \sqrt{a}\right) - 18 \, \sqrt{2} \sqrt{-a} a - 28 \, \sqrt{-a} a\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{3 \, \sqrt{2} \sqrt{-a} a^{\frac{3}{2}} + 4 \, \sqrt{-a} a^{\frac{3}{2}}} - \frac{16 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{14 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{7 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 2 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{8 \, d}"," ",0,"1/8*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2/(a*sgn(tan(1/2*d*x + 1/2*c) + 1))) - (42*sqrt(2)*a^(3/2)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 64*sqrt(2)*a^(3/2)*arctan(sqrt(a)/sqrt(-a)) - 21*sqrt(2)*sqrt(-a)*a*log(sqrt(2)*sqrt(a) + sqrt(a)) + 56*a^(3/2)*arctan((sqrt(2)*sqrt(a) + sqrt(a))/sqrt(-a)) - 96*a^(3/2)*arctan(sqrt(a)/sqrt(-a)) - 28*sqrt(-a)*a*log(sqrt(2)*sqrt(a) + sqrt(a)) - 18*sqrt(2)*sqrt(-a)*a - 28*sqrt(-a)*a)*sgn(tan(1/2*d*x + 1/2*c) + 1)/(3*sqrt(2)*sqrt(-a)*a^(3/2) + 4*sqrt(-a)*a^(3/2)) - 16*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 14*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 7*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 2*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
68,1,469,0,0.837873," ","integrate(sin(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{75 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{4 \, {\left({\left({\left({\left({\left(\frac{11 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{15 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{30 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{30 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{15 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{11 \, a}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}} - \frac{10 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{10 \, d}"," ",0,"-1/10*(75*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 4*(((((11*a*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 15*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 30*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 30*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 15*a/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 11*a/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2) - 10*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
69,1,409,0,0.743310," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{8 \, {\left({\left({\left(\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{3}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} - \frac{33 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{6 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{6 \, d}"," ",0,"-1/6*(8*(((2*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 3/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 2/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 33*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 6*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
70,1,360,0,0.780046," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{4 \, {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{1}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{7 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*(4*(tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 1/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - 7*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
71,1,294,0,1.432168," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*(3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
72,1,293,0,1.963521," ","integrate(1/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*(sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
73,1,412,0,3.094887," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{5 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{4 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"-1/2*(5*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 4*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
74,1,507,0,0.977168," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{\frac{9 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{6 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{3 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} \sqrt{a} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(3 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{2} a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{2 \, d}"," ",0,"1/2*(9*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 6*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*sqrt(a)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(3*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^2*a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
75,-2,0,0,0.000000," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((d*t_nostep+c)/2-pi/4))]Discontinuities at zeroes of cos((d*t_nostep+c)/2-pi/4) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.42Error: Bad Argument Type","F(-2)",0
76,1,626,0,1.523881," ","integrate(sin(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{64 \, {\left({\left({\left({\left({\left(\frac{34 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{45}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{85}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{85}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{45}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{34}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{5}{2}}} - \frac{4245 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{30 \, {\left(91 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 445 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 305 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 429 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 41 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 215 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 173 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 33 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{240 \, d}"," ",0,"1/240*(64*(((((34*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) - 45/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 85/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 85/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) + 45/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1/2*d*x + 1/2*c) - 34/sgn(tan(1/2*d*x + 1/2*c) + 1))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(5/2) - 4245*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 30*(91*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 445*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 305*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 429*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 41*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 215*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 173*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 33*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
77,1,584,0,8.722319," ","integrate(sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{32 \, {\left({\left({\left(\frac{7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{9}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{9}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{7}{a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a\right)}^{\frac{3}{2}}} - \frac{489 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{6 \, {\left(67 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 341 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 233 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 325 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 33 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 159 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 133 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 25 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{48 \, d}"," ",0,"-1/48*(32*(((7*tan(1/2*d*x + 1/2*c)/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 9/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) + 9/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))*tan(1/2*d*x + 1/2*c) - 7/(a*sgn(tan(1/2*d*x + 1/2*c) + 1)))/(a*tan(1/2*d*x + 1/2*c)^2 + a)^(3/2) - 489*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 6*(67*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 341*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 233*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 325*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 33*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 159*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 133*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 25*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
78,1,523,0,0.934847," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{32 \, {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{1}{a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)}}{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}} - \frac{75 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(43 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 237 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 161 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 221 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 25 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 103 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 93 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 17 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"1/16*(32*(tan(1/2*d*x + 1/2*c)/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 1/(a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) - 75*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(43*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 237*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 161*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 221*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 25*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 103*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 93*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 17*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
79,1,457,0,0.832068," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{19 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(19 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 133 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 89 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 117 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 17 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 47 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 53 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 9 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"1/16*(19*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(19*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 133*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 89*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 117*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 17*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 47*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 53*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 9*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
80,1,457,0,0.790543," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{5 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(5 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} - 29 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} - 17 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a + 13 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} - 9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 9 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} + 13 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} - a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"1/16*(5*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(5*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 - 29*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) - 17*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a + 13*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) - 9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 9*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) + 13*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 - a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
81,1,457,0,1.323577," ","integrate(1/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(29 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 75 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 55 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 91 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} - {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 65 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 27 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 7 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"1/16*(3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(29*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 75*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 55*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 91*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) - (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 65*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 27*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 7*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
82,1,575,0,1.266812," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{\frac{43 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{32 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{16 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(53 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 179 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 127 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 195 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 7 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 121 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 67 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 15 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"-1/16*(43*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 32*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 16*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(53*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 179*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 127*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 195*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 7*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 121*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 67*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 15*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
83,1,671,0,3.135009," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\frac{115 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{80 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{40 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{8 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{16}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)} a^{\frac{3}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{2 \, {\left(77 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 283 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 199 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 299 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 15 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 177 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 107 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 23 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"1/16*(115*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 80*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 40*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 8*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 16/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)*a^(3/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 2*(77*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 283*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 199*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 299*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 15*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 177*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 107*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 23*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
84,1,817,0,1.359231," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{10}{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}\right)} - \frac{219 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} + \sqrt{a}\right)}}{2 \, \sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{156 \, \arctan\left(-\frac{\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{78 \, \log\left({\left| -\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \right|}\right)}{a^{\frac{5}{2}} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} + \frac{4 \, {\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} - 10 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} \sqrt{a} + {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a + 10 \, a^{\frac{3}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} - a\right)}^{2} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} - \frac{2 \, {\left(101 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{7} + 387 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{6} \sqrt{a} + 271 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{5} a - 403 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{4} a^{\frac{3}{2}} + 23 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{3} a^{2} + 233 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} a^{\frac{5}{2}} - 147 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} a^{3} + 31 \, a^{\frac{7}{2}}\right)}}{{\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)}^{2} + 2 \, {\left(\sqrt{a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a}\right)} \sqrt{a} - a\right)}^{4} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{16 \, d}"," ",0,"1/16*(2*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(tan(1/2*d*x + 1/2*c)/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 10/(a^3*sgn(tan(1/2*d*x + 1/2*c) + 1))) - 219*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a) + sqrt(a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 156*arctan(-(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 78*log(abs(-sqrt(a)*tan(1/2*d*x + 1/2*c) + sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)))/(a^(5/2)*sgn(tan(1/2*d*x + 1/2*c) + 1)) + 4*((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3 - 10*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*sqrt(a) + (sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a + 10*a^(3/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 - a)^2*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)) - 2*(101*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^7 + 387*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^6*sqrt(a) + 271*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^5*a - 403*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^4*a^(3/2) + 23*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^3*a^2 + 233*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2*a^(5/2) - 147*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*a^3 + 31*a^(7/2))/(((sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))^2 + 2*(sqrt(a)*tan(1/2*d*x + 1/2*c) - sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a))*sqrt(a) - a)^4*a^2*sgn(tan(1/2*d*x + 1/2*c) + 1)))/d","B",0
85,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{\sqrt{\sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/sqrt(sin(f*x + e)), x)","F",0
86,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)/(-sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)-4*sqrt(2*a)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*atan((-sqrt(2)+2*(4*sqrt(2)-2*sqrt(-tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+6*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-1))/(-2*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+6))/sqrt(2))/sqrt(2)/f","F(-2)",0
87,0,0,0,0.000000," ","integrate(1/sin(x)^(1/2)/(1+sin(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\sin\left(x\right) + 1} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(sin(x) + 1)*sqrt(sin(x))), x)","F",0
88,0,0,0,0.000000," ","integrate(1/sin(x)^(1/2)/(a+a*sin(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(x\right) + a} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(x) + a)*sqrt(sin(x))), x)","F",0
89,0,0,0,0.000000," ","integrate(1/(1-sin(x))^(1/2)/sin(x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-\sin\left(x\right) + 1} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-sin(x) + 1)*sqrt(sin(x))), x)","F",0
90,0,0,0,0.000000," ","integrate(1/sin(x)^(1/2)/(a-a*sin(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-a \sin\left(x\right) + a} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-a*sin(x) + a)*sqrt(sin(x))), x)","F",0
91,0,0,0,0.000000," ","integrate(sin(d*x+c)^(1/3)/(a+a*sin(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{\frac{1}{3}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^(1/3)/(a*sin(d*x + c) + a)^2, x)","F",0
92,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*sin(d*x + c)^3, x)","F",0
93,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*sin(d*x + c)^2, x)","F",0
94,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*sin(d*x + c), x)","F",0
95,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3), x)","F",0
96,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*csc(d*x + c), x)","F",0
97,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(2/3)*csc(d*x + c)^2, x)","F",0
98,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*sin(d*x + c)^3, x)","F",0
99,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*sin(d*x + c)^2, x)","F",0
100,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*sin(d*x + c), x)","F",0
101,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3), x)","F",0
102,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*csc(d*x + c), x)","F",0
103,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(4/3)*csc(d*x + c)^2, x)","F",0
104,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/(a*sin(d*x + c) + a)^(1/3), x)","F",0
105,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(a*sin(d*x + c) + a)^(1/3), x)","F",0
106,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(a*sin(d*x + c) + a)^(1/3), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(-1/3), x)","F",0
108,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)/(a*sin(d*x + c) + a)^(1/3), x)","F",0
109,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/(a*sin(d*x + c) + a)^(1/3), x)","F",0
110,0,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^3/(a*sin(d*x + c) + a)^(4/3), x)","F",0
111,0,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)^2/(a*sin(d*x + c) + a)^(4/3), x)","F",0
112,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(a*sin(d*x + c) + a)^(4/3), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(-4/3), x)","F",0
114,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)/(a*sin(d*x + c) + a)^(4/3), x)","F",0
115,0,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(csc(d*x + c)^2/(a*sin(d*x + c) + a)^(4/3), x)","F",0
116,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(1+sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \sin\left(f x + e\right)^{n} {\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n*(sin(f*x + e) + 1)^(3/2), x)","F",0
117,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(1+sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sin\left(f x + e\right)^{n} \sqrt{\sin\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate(sin(f*x + e)^n*sqrt(sin(f*x + e) + 1), x)","F",0
118,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(1+sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{n}}{\sqrt{\sin\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/sqrt(sin(f*x + e) + 1), x)","F",0
119,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(1+sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{n}}{{\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/(sin(f*x + e) + 1)^(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*sin(f*x + e)^n, x)","F",0
121,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sin(f*x + e)^n, x)","F",0
122,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/sqrt(a*sin(f*x + e) + a), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(f*x+e)^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sin(f*x + e)^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(1+sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \left(d \sin\left(f x + e\right)\right)^{n} {\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*(sin(f*x + e) + 1)^(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(1+sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \left(d \sin\left(f x + e\right)\right)^{n} \sqrt{\sin\left(f x + e\right) + 1}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*sqrt(sin(f*x + e) + 1), x)","F",0
126,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(1+sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{\sqrt{\sin\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/sqrt(sin(f*x + e) + 1), x)","F",0
127,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(1+sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{{\left(\sin\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/(sin(f*x + e) + 1)^(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e))^n, x)","F",0
129,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
130,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/sqrt(a*sin(f*x + e) + a), x)","F",0
131,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
132,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*sin(f*x + e)^n, x)","F",0
133,0,0,0,0.000000," ","integrate((1-sin(f*x+e))^m*(-sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(-\sin\left(f x + e\right)\right)^{n} {\left(-\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((-sin(f*x + e))^n*(-sin(f*x + e) + 1)^m, x)","F",0
134,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(d \sin\left(f x + e\right)\right)^{n} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*(sin(f*x + e) + 1)^m, x)","F",0
135,0,0,0,0.000000," ","integrate((1-sin(f*x+e))^m*(d*sin(f*x+e))^n,x, algorithm=""giac"")","\int \left(d \sin\left(f x + e\right)\right)^{n} {\left(-\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^n*(-sin(f*x + e) + 1)^m, x)","F",0
136,0,0,0,0.000000," ","integrate(sin(f*x+e)^n*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sin\left(f x + e\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*sin(f*x + e)^n, x)","F",0
137,0,0,0,0.000000," ","integrate((-sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(-a \sin\left(f x + e\right) + a\right)}^{m} \left(-\sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sin(f*x + e) + a)^m*(-sin(f*x + e))^n, x)","F",0
138,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
139,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(-a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
140,0,0,0,0.000000," ","integrate(sin(d*x+c)^4*(a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c)^4, x)","F",0
141,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
142,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
143,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*sin(d*x + c), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n, x)","F",0
145,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*csc(d*x + c), x)","F",0
146,0,0,0,0.000000," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^n*csc(d*x + c)^2, x)","F",0
147,0,0,0,0.000000," ","integrate((1+sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(\sin\left(d x + c\right) + 1\right)}^{n}\,{d x}"," ",0,"integrate((sin(d*x + c) + 1)^n, x)","F",0
148,0,0,0,0.000000," ","integrate((1-sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-\sin\left(d x + c\right) + 1\right)}^{n}\,{d x}"," ",0,"integrate((-sin(d*x + c) + 1)^n, x)","F",0
149,1,66,0,0.143756," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{3}{8} \, b x + \frac{a \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{3 \, a \cos\left(f x + e\right)}{4 \, f} + \frac{b \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{b \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"3/8*b*x + 1/12*a*cos(3*f*x + 3*e)/f - 3/4*a*cos(f*x + e)/f + 1/32*b*sin(4*f*x + 4*e)/f - 1/4*b*sin(2*f*x + 2*e)/f","A",0
150,1,50,0,0.146481," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{1}{2} \, a x + \frac{b \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{3 \, b \cos\left(f x + e\right)}{4 \, f} - \frac{a \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*a*x + 1/12*b*cos(3*f*x + 3*e)/f - 3/4*b*cos(f*x + e)/f - 1/4*a*sin(2*f*x + 2*e)/f","A",0
151,1,34,0,0.144557," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{1}{2} \, b x - \frac{a \cos\left(f x + e\right)}{f} - \frac{b \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*b*x - a*cos(f*x + e)/f - 1/4*b*sin(2*f*x + 2*e)/f","A",0
152,1,17,0,0.151456," ","integrate(a+b*sin(f*x+e),x, algorithm=""giac"")","a x - \frac{b \cos\left(f x + e\right)}{f}"," ",0,"a*x - b*cos(f*x + e)/f","A",0
153,-2,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(a/2*ln(abs(tan((f*x+exp(1))/2)))+2*b/2*(f*x+exp(1))/2)","F(-2)",0
154,-2,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(tan((f*x+exp(1))/2)*a/4+(-2*tan((f*x+exp(1))/2)*b-a)*1/4/tan((f*x+exp(1))/2)+b/2*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
155,-2,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((4*tan((f*x+exp(1))/2)^2*a+16*tan((f*x+exp(1))/2)*b)/64+(-6*tan((f*x+exp(1))/2)^2*a-4*tan((f*x+exp(1))/2)*b-a)*1/16/tan((f*x+exp(1))/2)^2+a/4*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
156,-2,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((256/3*tan((f*x+exp(1))/2)^3*a+256*tan((f*x+exp(1))/2)^2*b+768*tan((f*x+exp(1))/2)*a)/4096+(-22*tan((f*x+exp(1))/2)^3*b-9*tan((f*x+exp(1))/2)^2*a-3*tan((f*x+exp(1))/2)*b-a)*1/48/tan((f*x+exp(1))/2)^3+b/4*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
157,1,128,0,0.222604," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{4} \, a b x - \frac{b^{2} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{a b \sin\left(4 \, f x + 4 \, e\right)}{16 \, f} - \frac{a b \sin\left(2 \, f x + 2 \, e\right)}{2 \, f} + \frac{{\left(4 \, a^{2} + 5 \, b^{2}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(2 \, a^{2} + 3 \, b^{2}\right)} \cos\left(f x + e\right)}{8 \, f} - \frac{{\left(2 \, a^{2} + b^{2}\right)} \cos\left(f x + e\right)}{4 \, f}"," ",0,"3/4*a*b*x - 1/80*b^2*cos(5*f*x + 5*e)/f + 1/16*a*b*sin(4*f*x + 4*e)/f - 1/2*a*b*sin(2*f*x + 2*e)/f + 1/48*(4*a^2 + 5*b^2)*cos(3*f*x + 3*e)/f - 1/8*(2*a^2 + 3*b^2)*cos(f*x + e)/f - 1/4*(2*a^2 + b^2)*cos(f*x + e)/f","A",0
158,1,86,0,0.882118," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} x + \frac{a b \cos\left(3 \, f x + 3 \, e\right)}{6 \, f} - \frac{3 \, a b \cos\left(f x + e\right)}{2 \, f} + \frac{b^{2} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{{\left(a^{2} + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/8*(4*a^2 + 3*b^2)*x + 1/6*a*b*cos(3*f*x + 3*e)/f - 3/2*a*b*cos(f*x + e)/f + 1/32*b^2*sin(4*f*x + 4*e)/f - 1/4*(a^2 + b^2)*sin(2*f*x + 2*e)/f","A",0
159,1,76,0,0.281248," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","a b x + \frac{b^{2} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{b^{2} \cos\left(f x + e\right)}{4 \, f} - \frac{a b \sin\left(2 \, f x + 2 \, e\right)}{2 \, f} - \frac{{\left(2 \, a^{2} + b^{2}\right)} \cos\left(f x + e\right)}{2 \, f}"," ",0,"a*b*x + 1/12*b^2*cos(3*f*x + 3*e)/f - 1/4*b^2*cos(f*x + e)/f - 1/2*a*b*sin(2*f*x + 2*e)/f - 1/2*(2*a^2 + b^2)*cos(f*x + e)/f","A",0
160,1,45,0,0.160517," ","integrate((a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, a^{2} + b^{2}\right)} x - \frac{2 \, a b \cos\left(f x + e\right)}{f} - \frac{b^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*(2*a^2 + b^2)*x - 2*a*b*cos(f*x + e)/f - 1/4*b^2*sin(2*f*x + 2*e)/f","A",0
161,-2,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(a^2/2*ln(abs(tan((f*x+exp(1))/2)))+4*a*b/2*(f*x+exp(1))/2-b^2/(tan((f*x+exp(1))/2)^2+1))","F(-2)",0
162,-2,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(tan((f*x+exp(1))/2)*a^2/4+(-4*tan((f*x+exp(1))/2)*b*a-a^2)*1/4/tan((f*x+exp(1))/2)+2*b^2/2*(f*x+exp(1))/2+b*a*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
163,-2,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((4*tan((f*x+exp(1))/2)^2*a^2+32*tan((f*x+exp(1))/2)*b*a)/64+(-12*tan((f*x+exp(1))/2)^2*b^2-6*tan((f*x+exp(1))/2)^2*a^2-8*tan((f*x+exp(1))/2)*b*a-a^2)*1/16/tan((f*x+exp(1))/2)^2+(2*b^2+a^2)/4*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
164,-2,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((256/3*tan((f*x+exp(1))/2)^3*a^2+512*tan((f*x+exp(1))/2)^2*b*a+1024*tan((f*x+exp(1))/2)*b^2+768*tan((f*x+exp(1))/2)*a^2)/4096+(-44*tan((f*x+exp(1))/2)^3*b*a-12*tan((f*x+exp(1))/2)^2*b^2-9*tan((f*x+exp(1))/2)^2*a^2-6*tan((f*x+exp(1))/2)*b*a-a^2)*1/48/tan((f*x+exp(1))/2)^3+b*a/2*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
165,-2,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((8192*tan((f*x+exp(1))/2)^4*a^2+131072/3*tan((f*x+exp(1))/2)^3*b*a+65536*tan((f*x+exp(1))/2)^2*b^2+65536*tan((f*x+exp(1))/2)^2*a^2+393216*tan((f*x+exp(1))/2)*b*a)/1048576+(-200*tan((f*x+exp(1))/2)^4*b^2-150*tan((f*x+exp(1))/2)^4*a^2-144*tan((f*x+exp(1))/2)^3*b*a-24*tan((f*x+exp(1))/2)^2*b^2-24*tan((f*x+exp(1))/2)^2*a^2-16*tan((f*x+exp(1))/2)*b*a-3*a^2)*1/384/tan((f*x+exp(1))/2)^4+(4*b^2+3*a^2)/16*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
166,1,180,0,0.198256," ","integrate(sin(f*x+e)^3*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{3 \, a b^{2} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} - \frac{b^{3} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{1}{16} \, {\left(18 \, a^{2} b + 5 \, b^{3}\right)} x + \frac{{\left(4 \, a^{3} + 15 \, a b^{2}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(2 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(f x + e\right)}{8 \, f} - \frac{{\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(f x + e\right)}{4 \, f} + \frac{3 \, {\left(2 \, a^{2} b + b^{3}\right)} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} - \frac{3 \, {\left(16 \, a^{2} b + 5 \, b^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"-3/80*a*b^2*cos(5*f*x + 5*e)/f - 1/192*b^3*sin(6*f*x + 6*e)/f + 1/16*(18*a^2*b + 5*b^3)*x + 1/48*(4*a^3 + 15*a*b^2)*cos(3*f*x + 3*e)/f - 1/8*(2*a^3 + 9*a*b^2)*cos(f*x + e)/f - 1/4*(2*a^3 + 3*a*b^2)*cos(f*x + e)/f + 3/64*(2*a^2*b + b^3)*sin(4*f*x + 4*e)/f - 3/64*(16*a^2*b + 5*b^3)*sin(2*f*x + 2*e)/f","A",0
167,1,129,0,0.175521," ","integrate(sin(f*x+e)^2*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{b^{3} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{3 \, a b^{2} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{8} \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} x + \frac{{\left(12 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(18 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(f x + e\right)}{8 \, f} - \frac{{\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-1/80*b^3*cos(5*f*x + 5*e)/f + 3/32*a*b^2*sin(4*f*x + 4*e)/f + 1/8*(4*a^3 + 9*a*b^2)*x + 1/48*(12*a^2*b + 5*b^3)*cos(3*f*x + 3*e)/f - 1/8*(18*a^2*b + 5*b^3)*cos(f*x + e)/f - 1/4*(a^3 + 3*a*b^2)*sin(2*f*x + 2*e)/f","A",0
168,1,116,0,0.394338," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{a b^{2} \cos\left(3 \, f x + 3 \, e\right)}{4 \, f} - \frac{3 \, a b^{2} \cos\left(f x + e\right)}{4 \, f} + \frac{b^{3} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{3}{8} \, {\left(4 \, a^{2} b + b^{3}\right)} x - \frac{{\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(f x + e\right)}{2 \, f} - \frac{{\left(3 \, a^{2} b + b^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/4*a*b^2*cos(3*f*x + 3*e)/f - 3/4*a*b^2*cos(f*x + e)/f + 1/32*b^3*sin(4*f*x + 4*e)/f + 3/8*(4*a^2*b + b^3)*x - 1/2*(2*a^3 + 3*a*b^2)*cos(f*x + e)/f - 1/4*(3*a^2*b + b^3)*sin(2*f*x + 2*e)/f","A",0
169,1,75,0,0.169370," ","integrate((a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{b^{3} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{3 \, a b^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{2} \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} x - \frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/12*b^3*cos(3*f*x + 3*e)/f - 3/4*a*b^2*sin(2*f*x + 2*e)/f + 1/2*(2*a^3 + 3*a*b^2)*x - 3/4*(4*a^2*b + b^3)*cos(f*x + e)/f","A",0
170,-2,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(a^3/2*ln(abs(tan((f*x+exp(1))/2)))+(6*a^2*b+b^3)/2*(f*x+exp(1))/2+(tan((f*x+exp(1))/2)^3*b^3-6*tan((f*x+exp(1))/2)^2*a*b^2-tan((f*x+exp(1))/2)*b^3-6*a*b^2)*1/2/(tan((f*x+exp(1))/2)^2+1)^2)","F(-2)",0
171,-2,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(tan((f*x+exp(1))/2)*a^3/4+(-2*tan((f*x+exp(1))/2)^3*b*a^2-tan((f*x+exp(1))/2)^2*a^3-4*tan((f*x+exp(1))/2)*b^3-2*tan((f*x+exp(1))/2)*b*a^2-a^3)*1/4/(tan((f*x+exp(1))/2)^3+tan((f*x+exp(1))/2))+3*b*a^2/2*ln(abs(tan((f*x+exp(1))/2)))+6*b^2*a/2*(f*x+exp(1))/2)","F(-2)",0
172,-2,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((4*tan((f*x+exp(1))/2)^2*a^3+48*tan((f*x+exp(1))/2)*b*a^2)/64+(-36*tan((f*x+exp(1))/2)^2*b^2*a-6*tan((f*x+exp(1))/2)^2*a^3-12*tan((f*x+exp(1))/2)*b*a^2-a^3)*1/16/tan((f*x+exp(1))/2)^2+2*b^3/2*(f*x+exp(1))/2+(6*b^2*a+a^3)/4*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
173,-2,0,0,0.000000," ","integrate(csc(f*x+e)^4*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((256/3*tan((f*x+exp(1))/2)^3*a^3+768*tan((f*x+exp(1))/2)^2*b*a^2+3072*tan((f*x+exp(1))/2)*b^2*a+768*tan((f*x+exp(1))/2)*a^3)/4096+(-44*tan((f*x+exp(1))/2)^3*b^3-66*tan((f*x+exp(1))/2)^3*b*a^2-36*tan((f*x+exp(1))/2)^2*b^2*a-9*tan((f*x+exp(1))/2)^2*a^3-9*tan((f*x+exp(1))/2)*b*a^2-a^3)*1/48/tan((f*x+exp(1))/2)^3+(2*b^3+3*b*a^2)/4*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
174,-2,0,0,0.000000," ","integrate(csc(f*x+e)^5*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((8192*tan((f*x+exp(1))/2)^4*a^3+65536*tan((f*x+exp(1))/2)^3*b*a^2+196608*tan((f*x+exp(1))/2)^2*b^2*a+65536*tan((f*x+exp(1))/2)^2*a^3+262144*tan((f*x+exp(1))/2)*b^3+589824*tan((f*x+exp(1))/2)*b*a^2)/1048576+(-200*tan((f*x+exp(1))/2)^4*b^2*a-50*tan((f*x+exp(1))/2)^4*a^3-32*tan((f*x+exp(1))/2)^3*b^3-72*tan((f*x+exp(1))/2)^3*b*a^2-24*tan((f*x+exp(1))/2)^2*b^2*a-8*tan((f*x+exp(1))/2)^2*a^3-8*tan((f*x+exp(1))/2)*b*a^2-a^3)*1/128/tan((f*x+exp(1))/2)^4+(12*b^2*a+3*a^3)/16*ln(abs(tan((f*x+exp(1))/2))))","F(-2)",0
175,1,112,0,0.168395," ","integrate((a+b*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{a b^{3} \cos\left(3 \, f x + 3 \, e\right)}{3 \, f} + \frac{b^{4} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{8} \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} x - \frac{{\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(f x + e\right)}{f} - \frac{{\left(6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/3*a*b^3*cos(3*f*x + 3*e)/f + 1/32*b^4*sin(4*f*x + 4*e)/f + 1/8*(8*a^4 + 24*a^2*b^2 + 3*b^4)*x - (4*a^3*b + 3*a*b^3)*cos(f*x + e)/f - 1/4*(6*a^2*b^2 + b^4)*sin(2*f*x + 2*e)/f","A",0
176,1,149,0,0.197835," ","integrate(sin(x)^4/(a+b*sin(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{4}}{\sqrt{a^{2} - b^{2}} b^{4}} - \frac{{\left(2 \, a^{3} + a b^{2}\right)} x}{2 \, b^{4}} - \frac{3 \, a b \tan\left(\frac{1}{2} \, x\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 12 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, x\right) + 6 \, a^{2} + 4 \, b^{2}}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3} b^{3}}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a^4/(sqrt(a^2 - b^2)*b^4) - 1/2*(2*a^3 + a*b^2)*x/b^4 - 1/3*(3*a*b*tan(1/2*x)^5 + 6*a^2*tan(1/2*x)^4 + 12*a^2*tan(1/2*x)^2 + 12*b^2*tan(1/2*x)^2 - 3*a*b*tan(1/2*x) + 6*a^2 + 4*b^2)/((tan(1/2*x)^2 + 1)^3*b^3)","A",0
177,1,112,0,0.229837," ","integrate(sin(x)^3/(a+b*sin(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{3}}{\sqrt{a^{2} - b^{2}} b^{3}} + \frac{{\left(2 \, a^{2} + b^{2}\right)} x}{2 \, b^{3}} + \frac{b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right) + 2 \, a}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{2} b^{2}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a^3/(sqrt(a^2 - b^2)*b^3) + 1/2*(2*a^2 + b^2)*x/b^3 + (b*tan(1/2*x)^3 + 2*a*tan(1/2*x)^2 - b*tan(1/2*x) + 2*a)/((tan(1/2*x)^2 + 1)^2*b^2)","A",0
178,1,77,0,0.358763," ","integrate(sin(x)^2/(a+b*sin(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{2}}{\sqrt{a^{2} - b^{2}} b^{2}} - \frac{a x}{b^{2}} - \frac{2}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} b}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a^2/(sqrt(a^2 - b^2)*b^2) - a*x/b^2 - 2/((tan(1/2*x)^2 + 1)*b)","A",0
179,1,58,0,0.318959," ","integrate(sin(x)/(a+b*sin(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a}{\sqrt{a^{2} - b^{2}} b} + \frac{x}{b}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a/(sqrt(a^2 - b^2)*b) + x/b","A",0
180,1,48,0,0.169259," ","integrate(1/(a+b*sin(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}}}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/sqrt(a^2 - b^2)","A",0
181,1,63,0,0.182652," ","integrate(csc(x)/(a+b*sin(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b}{\sqrt{a^{2} - b^{2}} a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*b/(sqrt(a^2 - b^2)*a) + log(abs(tan(1/2*x)))/a","A",0
182,1,98,0,0.161624," ","integrate(csc(x)^2/(a+b*sin(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{2}}{\sqrt{a^{2} - b^{2}} a^{2}} - \frac{b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a} + \frac{2 \, b \tan\left(\frac{1}{2} \, x\right) - a}{2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*b^2/(sqrt(a^2 - b^2)*a^2) - b*log(abs(tan(1/2*x)))/a^2 + 1/2*tan(1/2*x)/a + 1/2*(2*b*tan(1/2*x) - a)/(a^2*tan(1/2*x))","A",0
183,1,141,0,0.263031," ","integrate(csc(x)^3/(a+b*sin(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{3}}{\sqrt{a^{2} - b^{2}} a^{3}} + \frac{a \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{2}} + \frac{{\left(a^{2} + 2 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{3}} - \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 12 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}}{8 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*b^3/(sqrt(a^2 - b^2)*a^3) + 1/8*(a*tan(1/2*x)^2 - 4*b*tan(1/2*x))/a^2 + 1/2*(a^2 + 2*b^2)*log(abs(tan(1/2*x)))/a^3 - 1/8*(6*a^2*tan(1/2*x)^2 + 12*b^2*tan(1/2*x)^2 - 4*a*b*tan(1/2*x) + a^2)/(a^3*tan(1/2*x)^2)","A",0
184,1,194,0,0.238973," ","integrate(csc(x)^4/(a+b*sin(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{4}}{\sqrt{a^{2} - b^{2}} a^{4}} + \frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, a b \tan\left(\frac{1}{2} \, x\right)^{2} + 9 \, a^{2} \tan\left(\frac{1}{2} \, x\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, x\right)}{24 \, a^{3}} - \frac{{\left(a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{4}} + \frac{22 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{3} + 44 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right) - a^{3}}{24 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{3}}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*b^4/(sqrt(a^2 - b^2)*a^4) + 1/24*(a^2*tan(1/2*x)^3 - 3*a*b*tan(1/2*x)^2 + 9*a^2*tan(1/2*x) + 12*b^2*tan(1/2*x))/a^3 - 1/2*(a^2*b + 2*b^3)*log(abs(tan(1/2*x)))/a^4 + 1/24*(22*a^2*b*tan(1/2*x)^3 + 44*b^3*tan(1/2*x)^3 - 9*a^3*tan(1/2*x)^2 - 12*a*b^2*tan(1/2*x)^2 + 3*a^2*b*tan(1/2*x) - a^3)/(a^4*tan(1/2*x)^3)","A",0
185,1,184,0,0.170174," ","integrate(sin(x)^4/(a+b*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(a^{3} b \tan\left(\frac{1}{2} \, x\right) + a^{4}\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}} + \frac{{\left(6 \, a^{2} + b^{2}\right)} x}{2 \, b^{4}} + \frac{b \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right) + 4 \, a}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{2} b^{3}}"," ",0,"-2*(3*a^5 - 4*a^3*b^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 2*(a^3*b*tan(1/2*x) + a^4)/((a^2*b^3 - b^5)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)) + 1/2*(6*a^2 + b^2)*x/b^4 + (b*tan(1/2*x)^3 + 4*a*tan(1/2*x)^2 - b*tan(1/2*x) + 4*a)/((tan(1/2*x)^2 + 1)^2*b^3)","A",0
186,1,204,0,0.167047," ","integrate(sin(x)^3/(a+b*sin(x))^2,x, algorithm=""giac"")","\frac{2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - a b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right) - 2 \, b^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, a^{3} - a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)} {\left(a^{2} b^{2} - b^{4}\right)}} - \frac{2 \, a x}{b^{3}}"," ",0,"2*(2*a^4 - 3*a^2*b^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^2*b^3 - b^5)*sqrt(a^2 - b^2)) - 2*(a^2*b*tan(1/2*x)^3 + 2*a^3*tan(1/2*x)^2 - a*b^2*tan(1/2*x)^2 + 3*a^2*b*tan(1/2*x) - 2*b^3*tan(1/2*x) + 2*a^3 - a*b^2)/((a*tan(1/2*x)^4 + 2*b*tan(1/2*x)^3 + 2*a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)*(a^2*b^2 - b^4)) - 2*a*x/b^3","A",0
187,1,124,0,0.162190," ","integrate(sin(x)^2/(a+b*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(a^{3} - 2 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{{\left(a^{2} b - b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}} + \frac{x}{b^{2}}"," ",0,"-2*(a^3 - 2*a*b^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) + 2*(a*b*tan(1/2*x) + a^2)/((a^2*b - b^3)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)) + x/b^2","A",0
188,1,90,0,0.172803," ","integrate(sin(x)/(a+b*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, x\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)} {\left(a^{2} - b^{2}\right)}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*b/(a^2 - b^2)^(3/2) - 2*(b*tan(1/2*x) + a)/((a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)*(a^2 - b^2))","A",0
189,1,95,0,0.171011," ","integrate(1/(a+b*sin(x))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, x\right) + a b\right)}}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a/(a^2 - b^2)^(3/2) + 2*(b^2*tan(1/2*x) + a*b)/((a^3 - a*b^2)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a))","A",0
190,1,134,0,0.252360," ","integrate(csc(x)/(a+b*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, a^{2} b - b^{3}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(b^{3} \tan\left(\frac{1}{2} \, x\right) + a b^{2}\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{2}}"," ",0,"-2*(2*a^2*b - b^3)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^4 - a^2*b^2)*sqrt(a^2 - b^2)) - 2*(b^3*tan(1/2*x) + a*b^2)/((a^4 - a^2*b^2)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)) + log(abs(tan(1/2*x)))/a^2","A",0
191,1,234,0,0.151843," ","integrate(csc(x)^2/(a+b*sin(x))^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, a^{2} b^{2} - 2 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 11 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, a^{3} b \tan\left(\frac{1}{2} \, x\right) + 14 \, a b^{3} \tan\left(\frac{1}{2} \, x\right) - 3 \, a^{4} + 3 \, a^{2} b^{2}}{6 \, {\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + a \tan\left(\frac{1}{2} \, x\right)\right)}} - \frac{2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{3}} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a^{2}}"," ",0,"2*(3*a^2*b^2 - 2*b^4)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^5 - a^3*b^2)*sqrt(a^2 - b^2)) + 1/6*(4*a^3*b*tan(1/2*x)^3 - 4*a*b^3*tan(1/2*x)^3 - 3*a^4*tan(1/2*x)^2 + 11*a^2*b^2*tan(1/2*x)^2 + 4*b^4*tan(1/2*x)^2 - 2*a^3*b*tan(1/2*x) + 14*a*b^3*tan(1/2*x) - 3*a^4 + 3*a^2*b^2)/((a^5 - a^3*b^2)*(a*tan(1/2*x)^3 + 2*b*tan(1/2*x)^2 + a*tan(1/2*x))) - 2*b*log(abs(tan(1/2*x)))/a^3 + 1/2*tan(1/2*x)/a^2","A",0
192,1,215,0,0.183609," ","integrate(csc(x)^3/(a+b*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(4 \, a^{2} b^{3} - 3 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(b^{5} \tan\left(\frac{1}{2} \, x\right) + a b^{4}\right)}}{{\left(a^{6} - a^{4} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}} + \frac{{\left(a^{2} + 6 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{4}} + \frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{4}} - \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 36 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}}{8 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"-2*(4*a^2*b^3 - 3*b^5)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^6 - a^4*b^2)*sqrt(a^2 - b^2)) - 2*(b^5*tan(1/2*x) + a*b^4)/((a^6 - a^4*b^2)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)) + 1/2*(a^2 + 6*b^2)*log(abs(tan(1/2*x)))/a^4 + 1/8*(a^2*tan(1/2*x)^2 - 8*a*b*tan(1/2*x))/a^4 - 1/8*(6*a^2*tan(1/2*x)^2 + 36*b^2*tan(1/2*x)^2 - 8*a*b*tan(1/2*x) + a^2)/(a^4*tan(1/2*x)^2)","A",0
193,1,516,0,0.422609," ","integrate(sin(x)^5/(a+b*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(12 \, a^{7} - 29 \, a^{5} b^{2} + 20 \, a^{3} b^{4}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \sqrt{a^{2} - b^{2}}} + \frac{6 \, a^{6} b \tan\left(\frac{1}{2} \, x\right)^{7} - 10 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right)^{7} + a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right)^{7} + 12 \, a^{7} \tan\left(\frac{1}{2} \, x\right)^{6} - 5 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x\right)^{6} - 20 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right)^{6} + 4 \, a b^{6} \tan\left(\frac{1}{2} \, x\right)^{6} + 54 \, a^{6} b \tan\left(\frac{1}{2} \, x\right)^{5} - 90 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} + 17 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right)^{5} + 4 \, b^{7} \tan\left(\frac{1}{2} \, x\right)^{5} + 36 \, a^{7} \tan\left(\frac{1}{2} \, x\right)^{4} - 15 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 66 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right)^{4} + 24 \, a b^{6} \tan\left(\frac{1}{2} \, x\right)^{4} + 90 \, a^{6} b \tan\left(\frac{1}{2} \, x\right)^{3} - 162 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 55 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, b^{7} \tan\left(\frac{1}{2} \, x\right)^{3} + 36 \, a^{7} \tan\left(\frac{1}{2} \, x\right)^{2} - 31 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 40 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 20 \, a b^{6} \tan\left(\frac{1}{2} \, x\right)^{2} + 42 \, a^{6} b \tan\left(\frac{1}{2} \, x\right) - 74 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right) + 23 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right) + 12 \, a^{7} - 21 \, a^{5} b^{2} + 6 \, a^{3} b^{4}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}} + \frac{{\left(12 \, a^{2} + b^{2}\right)} x}{2 \, b^{5}}"," ",0,"-(12*a^7 - 29*a^5*b^2 + 20*a^3*b^4)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^4*b^5 - 2*a^2*b^7 + b^9)*sqrt(a^2 - b^2)) + (6*a^6*b*tan(1/2*x)^7 - 10*a^4*b^3*tan(1/2*x)^7 + a^2*b^5*tan(1/2*x)^7 + 12*a^7*tan(1/2*x)^6 - 5*a^5*b^2*tan(1/2*x)^6 - 20*a^3*b^4*tan(1/2*x)^6 + 4*a*b^6*tan(1/2*x)^6 + 54*a^6*b*tan(1/2*x)^5 - 90*a^4*b^3*tan(1/2*x)^5 + 17*a^2*b^5*tan(1/2*x)^5 + 4*b^7*tan(1/2*x)^5 + 36*a^7*tan(1/2*x)^4 - 15*a^5*b^2*tan(1/2*x)^4 - 66*a^3*b^4*tan(1/2*x)^4 + 24*a*b^6*tan(1/2*x)^4 + 90*a^6*b*tan(1/2*x)^3 - 162*a^4*b^3*tan(1/2*x)^3 + 55*a^2*b^5*tan(1/2*x)^3 - 4*b^7*tan(1/2*x)^3 + 36*a^7*tan(1/2*x)^2 - 31*a^5*b^2*tan(1/2*x)^2 - 40*a^3*b^4*tan(1/2*x)^2 + 20*a*b^6*tan(1/2*x)^2 + 42*a^6*b*tan(1/2*x) - 74*a^4*b^3*tan(1/2*x) + 23*a^2*b^5*tan(1/2*x) + 12*a^7 - 21*a^5*b^2 + 6*a^3*b^4)/((a^4*b^4 - 2*a^2*b^6 + b^8)*(a*tan(1/2*x)^4 + 2*b*tan(1/2*x)^3 + 2*a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2) + 1/2*(12*a^2 + b^2)*x/b^5","B",0
194,1,256,0,0.262020," ","integrate(sin(x)^4/(a+b*sin(x))^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, a^{5} b \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a^{6} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{4} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 14 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 13 \, a^{5} b \tan\left(\frac{1}{2} \, x\right) - 22 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, x\right) + 4 \, a^{6} - 7 \, a^{4} b^{2}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}} - \frac{3 \, a x}{b^{4}} - \frac{2}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} b^{3}}"," ",0,"3*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) - (3*a^5*b*tan(1/2*x)^3 - 6*a^3*b^3*tan(1/2*x)^3 + 4*a^6*tan(1/2*x)^2 + a^4*b^2*tan(1/2*x)^2 - 14*a^2*b^4*tan(1/2*x)^2 + 13*a^5*b*tan(1/2*x) - 22*a^3*b^3*tan(1/2*x) + 4*a^6 - 7*a^4*b^2)/((a^4*b^3 - 2*a^2*b^5 + b^7)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2) - 3*a*x/b^4 - 2/((tan(1/2*x)^2 + 1)*b^3)","A",0
195,1,234,0,0.221166," ","integrate(sin(x)^3/(a+b*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(2 \, a^{5} - 5 \, a^{3} b^{2} + 6 \, a b^{4}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a^{2} - b^{2}}} + \frac{a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a^{5} \tan\left(\frac{1}{2} \, x\right)^{2} - a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 10 \, a b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 7 \, a^{4} b \tan\left(\frac{1}{2} \, x\right) - 16 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, a^{5} - 5 \, a^{3} b^{2}}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}} + \frac{x}{b^{3}}"," ",0,"-(2*a^5 - 5*a^3*b^2 + 6*a*b^4)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(a^2 - b^2)) + (a^4*b*tan(1/2*x)^3 - 4*a^2*b^3*tan(1/2*x)^3 + 2*a^5*tan(1/2*x)^2 - a^3*b^2*tan(1/2*x)^2 - 10*a*b^4*tan(1/2*x)^2 + 7*a^4*b*tan(1/2*x) - 16*a^2*b^3*tan(1/2*x) + 2*a^5 - 5*a^3*b^2)/((a^4*b^2 - 2*a^2*b^4 + b^6)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2) + x/b^3","A",0
196,1,182,0,0.154719," ","integrate(sin(x)^2/(a+b*sin(x))^3,x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(a^{2} + 2 \, b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} + 6 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, x\right) + 10 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) + 3 \, a^{2} b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}}"," ",0,"(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*(a^2 + 2*b^2)/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (a^3*tan(1/2*x)^3 + 2*a*b^2*tan(1/2*x)^3 + 3*a^2*b*tan(1/2*x)^2 + 6*b^3*tan(1/2*x)^2 - a^3*tan(1/2*x) + 10*a*b^2*tan(1/2*x) + 3*a^2*b)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2)","A",0
197,1,189,0,0.421633," ","integrate(sin(x)/(a+b*sin(x))^3,x, algorithm=""giac"")","-\frac{3 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{3 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 5 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 5 \, a^{3} b \tan\left(\frac{1}{2} \, x\right) + 4 \, a b^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, a^{4} + a^{2} b^{2}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}}"," ",0,"-3*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) - (3*a^3*b*tan(1/2*x)^3 + 2*a^4*tan(1/2*x)^2 + 5*a^2*b^2*tan(1/2*x)^2 + 2*b^4*tan(1/2*x)^2 + 5*a^3*b*tan(1/2*x) + 4*a*b^3*tan(1/2*x) + 2*a^4 + a^2*b^2)/((a^5 - 2*a^3*b^2 + a*b^4)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2)","B",0
198,1,215,0,0.165188," ","integrate(1/(a+b*sin(x))^3,x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(2 \, a^{2} + b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, x\right)^{2} + 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, a b^{4} \tan\left(\frac{1}{2} \, x\right) + 4 \, a^{4} b - a^{2} b^{3}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}}"," ",0,"(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*(2*a^2 + b^2)/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (5*a^3*b^2*tan(1/2*x)^3 - 2*a*b^4*tan(1/2*x)^3 + 4*a^4*b*tan(1/2*x)^2 + 7*a^2*b^3*tan(1/2*x)^2 - 2*b^5*tan(1/2*x)^2 + 11*a^3*b^2*tan(1/2*x) - 2*a*b^4*tan(1/2*x) + 4*a^4*b - a^2*b^3)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2)","B",0
199,1,246,0,0.177058," ","integrate(csc(x)/(a+b*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(6 \, a^{4} b - 5 \, a^{2} b^{3} + 2 \, b^{5}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{7 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, a b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 9 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 6 \, b^{6} \tan\left(\frac{1}{2} \, x\right)^{2} + 17 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, x\right) - 8 \, a b^{5} \tan\left(\frac{1}{2} \, x\right) + 6 \, a^{4} b^{2} - 3 \, a^{2} b^{4}}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{3}}"," ",0,"-(6*a^4*b - 5*a^2*b^3 + 2*b^5)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)) - (7*a^3*b^3*tan(1/2*x)^3 - 4*a*b^5*tan(1/2*x)^3 + 6*a^4*b^2*tan(1/2*x)^2 + 9*a^2*b^4*tan(1/2*x)^2 - 6*b^6*tan(1/2*x)^2 + 17*a^3*b^3*tan(1/2*x) - 8*a*b^5*tan(1/2*x) + 6*a^4*b^2 - 3*a^2*b^4)/((a^7 - 2*a^5*b^2 + a^3*b^4)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2) + log(abs(tan(1/2*x)))/a^3","A",0
200,1,280,0,0.229215," ","integrate(csc(x)^2/(a+b*sin(x))^3,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{9 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a b^{6} \tan\left(\frac{1}{2} \, x\right)^{3} + 8 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 11 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right)^{2} - 10 \, b^{7} \tan\left(\frac{1}{2} \, x\right)^{2} + 23 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right) - 14 \, a b^{6} \tan\left(\frac{1}{2} \, x\right) + 8 \, a^{4} b^{3} - 5 \, a^{2} b^{5}}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{2}} - \frac{3 \, b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a^{4}} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, a^{3}} + \frac{6 \, b \tan\left(\frac{1}{2} \, x\right) - a}{2 \, a^{4} \tan\left(\frac{1}{2} \, x\right)}"," ",0,"3*(4*a^4*b^2 - 5*a^2*b^4 + 2*b^6)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^8 - 2*a^6*b^2 + a^4*b^4)*sqrt(a^2 - b^2)) + (9*a^3*b^4*tan(1/2*x)^3 - 6*a*b^6*tan(1/2*x)^3 + 8*a^4*b^3*tan(1/2*x)^2 + 11*a^2*b^5*tan(1/2*x)^2 - 10*b^7*tan(1/2*x)^2 + 23*a^3*b^4*tan(1/2*x) - 14*a*b^6*tan(1/2*x) + 8*a^4*b^3 - 5*a^2*b^5)/((a^8 - 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^2) - 3*b*log(abs(tan(1/2*x)))/a^4 + 1/2*tan(1/2*x)/a^3 + 1/2*(6*b*tan(1/2*x) - a)/(a^4*tan(1/2*x))","A",0
201,1,514,0,0.457360," ","integrate(csc(x)^3/(a+b*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(20 \, a^{4} b^{3} - 29 \, a^{2} b^{5} + 12 \, b^{7}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, a^{8} \tan\left(\frac{1}{2} \, x\right)^{6} + 20 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x\right)^{6} - 46 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x\right)^{6} + 24 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x\right)^{6} - 4 \, a^{7} b \tan\left(\frac{1}{2} \, x\right)^{5} + 104 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} - 108 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x\right)^{5} + 32 \, a b^{7} \tan\left(\frac{1}{2} \, x\right)^{5} + 5 \, a^{8} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 165 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x\right)^{4} - 80 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x\right)^{4} - 16 \, b^{8} \tan\left(\frac{1}{2} \, x\right)^{4} - 12 \, a^{7} b \tan\left(\frac{1}{2} \, x\right)^{3} + 72 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 124 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 112 \, a b^{7} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a^{8} \tan\left(\frac{1}{2} \, x\right)^{2} - 28 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 124 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 76 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, a^{7} b \tan\left(\frac{1}{2} \, x\right) + 16 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x\right) - 8 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x\right) + a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}}{8 \, {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + a \tan\left(\frac{1}{2} \, x\right)\right)}^{2}} + \frac{{\left(a^{2} + 12 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a^{5}} + \frac{a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{6}}"," ",0,"-(20*a^4*b^3 - 29*a^2*b^5 + 12*b^7)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^9 - 2*a^7*b^2 + a^5*b^4)*sqrt(a^2 - b^2)) - 1/8*(2*a^8*tan(1/2*x)^6 + 20*a^6*b^2*tan(1/2*x)^6 - 46*a^4*b^4*tan(1/2*x)^6 + 24*a^2*b^6*tan(1/2*x)^6 - 4*a^7*b*tan(1/2*x)^5 + 104*a^5*b^3*tan(1/2*x)^5 - 108*a^3*b^5*tan(1/2*x)^5 + 32*a*b^7*tan(1/2*x)^5 + 5*a^8*tan(1/2*x)^4 - 2*a^6*b^2*tan(1/2*x)^4 + 165*a^4*b^4*tan(1/2*x)^4 - 80*a^2*b^6*tan(1/2*x)^4 - 16*b^8*tan(1/2*x)^4 - 12*a^7*b*tan(1/2*x)^3 + 72*a^5*b^3*tan(1/2*x)^3 + 124*a^3*b^5*tan(1/2*x)^3 - 112*a*b^7*tan(1/2*x)^3 + 4*a^8*tan(1/2*x)^2 - 28*a^6*b^2*tan(1/2*x)^2 + 124*a^4*b^4*tan(1/2*x)^2 - 76*a^2*b^6*tan(1/2*x)^2 - 8*a^7*b*tan(1/2*x) + 16*a^5*b^3*tan(1/2*x) - 8*a^3*b^5*tan(1/2*x) + a^8 - 2*a^6*b^2 + a^4*b^4)/((a^9 - 2*a^7*b^2 + a^5*b^4)*(a*tan(1/2*x)^3 + 2*b*tan(1/2*x)^2 + a*tan(1/2*x))^2) + 1/2*(a^2 + 12*b^2)*log(abs(tan(1/2*x)))/a^5 + 1/8*(a^3*tan(1/2*x)^2 - 12*a^2*b*tan(1/2*x))/a^6","B",0
202,1,510,0,0.359509," ","integrate(1/(a+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{d x + c}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{27 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 81 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 108 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 42 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 36 \, a^{7} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 18 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 81 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 18 \, a^{7} b - 5 \, a^{5} b^{3} + 2 \, a^{3} b^{5}}{{\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(2*a^3 + 3*a*b^2)*(pi*floor(1/2*(d*x + c)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*d*x + 1/2*c) + b)/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + (27*a^6*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^4*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*b^6*tan(1/2*d*x + 1/2*c)^5 + 18*a^7*b*tan(1/2*d*x + 1/2*c)^4 + 81*a^5*b^3*tan(1/2*d*x + 1/2*c)^4 - 36*a^3*b^5*tan(1/2*d*x + 1/2*c)^4 + 12*a*b^7*tan(1/2*d*x + 1/2*c)^4 + 108*a^6*b^2*tan(1/2*d*x + 1/2*c)^3 + 42*a^4*b^4*tan(1/2*d*x + 1/2*c)^3 - 8*a^2*b^6*tan(1/2*d*x + 1/2*c)^3 + 8*b^8*tan(1/2*d*x + 1/2*c)^3 + 36*a^7*b*tan(1/2*d*x + 1/2*c)^2 + 120*a^5*b^3*tan(1/2*d*x + 1/2*c)^2 - 18*a^3*b^5*tan(1/2*d*x + 1/2*c)^2 + 12*a*b^7*tan(1/2*d*x + 1/2*c)^2 + 81*a^6*b^2*tan(1/2*d*x + 1/2*c) - 12*a^4*b^4*tan(1/2*d*x + 1/2*c) + 6*a^2*b^6*tan(1/2*d*x + 1/2*c) + 18*a^7*b - 5*a^5*b^3 + 2*a^3*b^5)/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 + 2*b*tan(1/2*d*x + 1/2*c) + a)^3))/d","B",0
203,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sin(f*x + e), x)","F",0
204,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a), x)","F",0
205,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*csc(f*x + e), x)","F",0
206,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*csc(f*x + e)^2, x)","F",0
207,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sin\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sin(f*x + e)/sqrt(b*sin(f*x + e) + a), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(f*x + e) + a), x)","F",0
209,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)/sqrt(b*sin(f*x + e) + a), x)","F",0
210,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/sqrt(b*sin(f*x + e) + a), x)","F",0
211,-2,0,0,0.000000," ","integrate(sin(d*x+c)^(1/2)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)ext_reduce Error: Bad Argument TypeSimplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)ext_reduce Error: Bad Argument TypeDone","F(-2)",0
212,0,0,0,0.000000," ","integrate(1/sin(d*x+c)^(1/2)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sin\left(d x + c\right) + a} \sqrt{\sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(d*x + c) + a)*sqrt(sin(d*x + c))), x)","F",0
213,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*sin(f*x + e))^m, x)","F",0
214,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e))^m, x)","F",0
215,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e))^m, x)","F",0
216,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{m}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^m/(b*sin(f*x + e) + a), x)","F",0
217,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{m}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^m/(b*sin(f*x + e) + a)^2, x)","F",0
218,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{m}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^m/(b*sin(f*x + e) + a)^3, x)","F",0
219,0,0,0,0.000000," ","integrate(sin(d*x+c)^(-1-a^2/(a^2+b^2))*(a+b*sin(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{-\frac{a^{2}}{a^{2} + b^{2}} - 1}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*sin(d*x + c)^(-a^2/(a^2 + b^2) - 1), x)","F",0
220,0,0,0,0.000000," ","integrate((1+2*sin(d*x+c))^2/sin(d*x+c)^(6/5),x, algorithm=""giac"")","\int \frac{{\left(2 \, \sin\left(d x + c\right) + 1\right)}^{2}}{\sin\left(d x + c\right)^{\frac{6}{5}}}\,{d x}"," ",0,"integrate((2*sin(d*x + c) + 1)^2/sin(d*x + c)^(6/5), x)","F",0
221,0,0,0,0.000000," ","integrate(sin(d*x+c)^m*(a+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c)^m, x)","F",0
222,0,0,0,0.000000," ","integrate(sin(d*x+c)^3*(a+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c)^3, x)","F",0
223,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c)^2, x)","F",0
224,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*sin(d*x + c), x)","F",0
225,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n, x)","F",0
226,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{n} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^n*csc(d*x + c), x)","F",0
227,1,100,0,0.432631," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{7}{8} \, a c^{4} x - \frac{a c^{4} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{13 \, a c^{4} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} + \frac{7 \, a c^{4} \cos\left(f x + e\right)}{8 \, f} - \frac{3 \, a c^{4} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a c^{4} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"7/8*a*c^4*x - 1/80*a*c^4*cos(5*f*x + 5*e)/f + 13/48*a*c^4*cos(3*f*x + 3*e)/f + 7/8*a*c^4*cos(f*x + e)/f - 3/32*a*c^4*sin(4*f*x + 4*e)/f + 1/4*a*c^4*sin(2*f*x + 2*e)/f","A",0
228,1,81,0,0.187947," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{5}{8} \, a c^{3} x + \frac{a c^{3} \cos\left(3 \, f x + 3 \, e\right)}{6 \, f} + \frac{a c^{3} \cos\left(f x + e\right)}{2 \, f} - \frac{a c^{3} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a c^{3} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"5/8*a*c^3*x + 1/6*a*c^3*cos(3*f*x + 3*e)/f + 1/2*a*c^3*cos(f*x + e)/f - 1/32*a*c^3*sin(4*f*x + 4*e)/f + 1/4*a*c^3*sin(2*f*x + 2*e)/f","A",0
229,1,62,0,0.192355," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{2} \, a c^{2} x + \frac{a c^{2} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} + \frac{a c^{2} \cos\left(f x + e\right)}{4 \, f} + \frac{a c^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*a*c^2*x + 1/12*a*c^2*cos(3*f*x + 3*e)/f + 1/4*a*c^2*cos(f*x + e)/f + 1/4*a*c^2*sin(2*f*x + 2*e)/f","A",0
230,1,23,0,0.171528," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""giac"")","\frac{1}{2} \, a c x + \frac{a c \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*a*c*x + 1/4*a*c*sin(2*f*x + 2*e)/f","A",0
231,1,37,0,0.158724," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left(f x + e\right)} a}{c} + \frac{4 \, a}{c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}}}{f}"," ",0,"-((f*x + e)*a/c + 4*a/(c*(tan(1/2*f*x + 1/2*e) - 1)))/f","A",0
232,1,39,0,0.196698," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a\right)}}{3 \, c^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{3}}"," ",0,"-2/3*(3*a*tan(1/2*f*x + 1/2*e)^2 + a)/(c^2*f*(tan(1/2*f*x + 1/2*e) - 1)^3)","A",0
233,1,84,0,0.240258," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 15 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 25 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 5 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a\right)}}{15 \, c^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{5}}"," ",0,"-2/15*(15*a*tan(1/2*f*x + 1/2*e)^4 - 15*a*tan(1/2*f*x + 1/2*e)^3 + 25*a*tan(1/2*f*x + 1/2*e)^2 - 5*a*tan(1/2*f*x + 1/2*e) + 4*a)/(c^3*f*(tan(1/2*f*x + 1/2*e) - 1)^5)","A",0
234,1,114,0,0.212263," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 210 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 455 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 350 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 273 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 56 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 23 \, a\right)}}{105 \, c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{7}}"," ",0,"-2/105*(105*a*tan(1/2*f*x + 1/2*e)^6 - 210*a*tan(1/2*f*x + 1/2*e)^5 + 455*a*tan(1/2*f*x + 1/2*e)^4 - 350*a*tan(1/2*f*x + 1/2*e)^3 + 273*a*tan(1/2*f*x + 1/2*e)^2 - 56*a*tan(1/2*f*x + 1/2*e) + 23*a)/(c^4*f*(tan(1/2*f*x + 1/2*e) - 1)^7)","A",0
235,1,144,0,0.600075," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 945 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 2625 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 3465 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 3843 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 2247 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1143 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 207 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 58 \, a\right)}}{315 \, c^{5} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{9}}"," ",0,"-2/315*(315*a*tan(1/2*f*x + 1/2*e)^8 - 945*a*tan(1/2*f*x + 1/2*e)^7 + 2625*a*tan(1/2*f*x + 1/2*e)^6 - 3465*a*tan(1/2*f*x + 1/2*e)^5 + 3843*a*tan(1/2*f*x + 1/2*e)^4 - 2247*a*tan(1/2*f*x + 1/2*e)^3 + 1143*a*tan(1/2*f*x + 1/2*e)^2 - 207*a*tan(1/2*f*x + 1/2*e) + 58*a)/(c^5*f*(tan(1/2*f*x + 1/2*e) - 1)^9)","A",0
236,1,154,0,0.231588," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","\frac{9}{16} \, a^{2} c^{5} x - \frac{a^{2} c^{5} \cos\left(7 \, f x + 7 \, e\right)}{448 \, f} + \frac{11 \, a^{2} c^{5} \cos\left(5 \, f x + 5 \, e\right)}{320 \, f} + \frac{13 \, a^{2} c^{5} \cos\left(3 \, f x + 3 \, e\right)}{64 \, f} + \frac{27 \, a^{2} c^{5} \cos\left(f x + e\right)}{64 \, f} - \frac{a^{2} c^{5} \sin\left(6 \, f x + 6 \, e\right)}{64 \, f} - \frac{a^{2} c^{5} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} + \frac{19 \, a^{2} c^{5} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"9/16*a^2*c^5*x - 1/448*a^2*c^5*cos(7*f*x + 7*e)/f + 11/320*a^2*c^5*cos(5*f*x + 5*e)/f + 13/64*a^2*c^5*cos(3*f*x + 3*e)/f + 27/64*a^2*c^5*cos(f*x + e)/f - 1/64*a^2*c^5*sin(6*f*x + 6*e)/f - 1/64*a^2*c^5*sin(4*f*x + 4*e)/f + 19/64*a^2*c^5*sin(2*f*x + 2*e)/f","A",0
237,1,133,0,0.219721," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{7}{16} \, a^{2} c^{4} x + \frac{a^{2} c^{4} \cos\left(5 \, f x + 5 \, e\right)}{40 \, f} + \frac{a^{2} c^{4} \cos\left(3 \, f x + 3 \, e\right)}{8 \, f} + \frac{a^{2} c^{4} \cos\left(f x + e\right)}{4 \, f} - \frac{a^{2} c^{4} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{a^{2} c^{4} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} + \frac{17 \, a^{2} c^{4} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"7/16*a^2*c^4*x + 1/40*a^2*c^4*cos(5*f*x + 5*e)/f + 1/8*a^2*c^4*cos(3*f*x + 3*e)/f + 1/4*a^2*c^4*cos(f*x + e)/f - 1/192*a^2*c^4*sin(6*f*x + 6*e)/f + 1/64*a^2*c^4*sin(4*f*x + 4*e)/f + 17/64*a^2*c^4*sin(2*f*x + 2*e)/f","A",0
238,1,112,0,0.197622," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{3}{8} \, a^{2} c^{3} x + \frac{a^{2} c^{3} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{a^{2} c^{3} \cos\left(3 \, f x + 3 \, e\right)}{16 \, f} + \frac{a^{2} c^{3} \cos\left(f x + e\right)}{8 \, f} + \frac{a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"3/8*a^2*c^3*x + 1/80*a^2*c^3*cos(5*f*x + 5*e)/f + 1/16*a^2*c^3*cos(3*f*x + 3*e)/f + 1/8*a^2*c^3*cos(f*x + e)/f + 1/32*a^2*c^3*sin(4*f*x + 4*e)/f + 1/4*a^2*c^3*sin(2*f*x + 2*e)/f","A",0
239,1,52,0,1.252224," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{8} \, a^{2} c^{2} x + \frac{a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"3/8*a^2*c^2*x + 1/32*a^2*c^2*sin(4*f*x + 4*e)/f + 1/4*a^2*c^2*sin(2*f*x + 2*e)/f","A",0
240,1,62,0,0.221028," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""giac"")","\frac{1}{2} \, a^{2} c x - \frac{a^{2} c \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{a^{2} c \cos\left(f x + e\right)}{4 \, f} + \frac{a^{2} c \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*a^2*c*x - 1/12*a^2*c*cos(3*f*x + 3*e)/f - 1/4*a^2*c*cos(f*x + e)/f + 1/4*a^2*c*sin(2*f*x + 2*e)/f","A",0
241,1,103,0,0.238197," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(f x + e\right)} a^{2}}{c} + \frac{2 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 5 \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)} c}}{f}"," ",0,"-(3*(f*x + e)*a^2/c + 2*(4*a^2*tan(1/2*f*x + 1/2*e)^2 - a^2*tan(1/2*f*x + 1/2*e) + 5*a^2)/((tan(1/2*f*x + 1/2*e)^3 - tan(1/2*f*x + 1/2*e)^2 + tan(1/2*f*x + 1/2*e) - 1)*c))/f","A",0
242,1,60,0,0.242210," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(f x + e\right)} a^{2}}{c^{2}} - \frac{8 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a^{2}\right)}}{c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a^2/c^2 - 8*(3*a^2*tan(1/2*f*x + 1/2*e) - a^2)/(c^2*(tan(1/2*f*x + 1/2*e) - 1)^3))/f","A",0
243,1,60,0,0.271215," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 10 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{2}\right)}}{5 \, c^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{5}}"," ",0,"-2/5*(5*a^2*tan(1/2*f*x + 1/2*e)^4 + 10*a^2*tan(1/2*f*x + 1/2*e)^2 + a^2)/(c^3*f*(tan(1/2*f*x + 1/2*e) - 1)^5)","A",0
244,1,128,0,0.218579," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 35 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 140 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 70 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 91 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 7 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{2}\right)}}{35 \, c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{7}}"," ",0,"-2/35*(35*a^2*tan(1/2*f*x + 1/2*e)^6 - 35*a^2*tan(1/2*f*x + 1/2*e)^5 + 140*a^2*tan(1/2*f*x + 1/2*e)^4 - 70*a^2*tan(1/2*f*x + 1/2*e)^3 + 91*a^2*tan(1/2*f*x + 1/2*e)^2 - 7*a^2*tan(1/2*f*x + 1/2*e) + 6*a^2)/(c^4*f*(tan(1/2*f*x + 1/2*e) - 1)^7)","A",0
245,1,162,0,0.271696," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(315 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 630 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 2310 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 2520 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 3402 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 1638 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1062 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 108 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 47 \, a^{2}\right)}}{315 \, c^{5} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{9}}"," ",0,"-2/315*(315*a^2*tan(1/2*f*x + 1/2*e)^8 - 630*a^2*tan(1/2*f*x + 1/2*e)^7 + 2310*a^2*tan(1/2*f*x + 1/2*e)^6 - 2520*a^2*tan(1/2*f*x + 1/2*e)^5 + 3402*a^2*tan(1/2*f*x + 1/2*e)^4 - 1638*a^2*tan(1/2*f*x + 1/2*e)^3 + 1062*a^2*tan(1/2*f*x + 1/2*e)^2 - 108*a^2*tan(1/2*f*x + 1/2*e) + 47*a^2)/(c^5*f*(tan(1/2*f*x + 1/2*e) - 1)^9)","A",0
246,1,196,0,0.263954," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^6,x, algorithm=""giac"")","-\frac{2 \, {\left(1155 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{10} - 3465 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} + 13860 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 23100 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 37422 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 32802 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 27060 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 11220 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4895 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 517 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 152 \, a^{2}\right)}}{1155 \, c^{6} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{11}}"," ",0,"-2/1155*(1155*a^2*tan(1/2*f*x + 1/2*e)^10 - 3465*a^2*tan(1/2*f*x + 1/2*e)^9 + 13860*a^2*tan(1/2*f*x + 1/2*e)^8 - 23100*a^2*tan(1/2*f*x + 1/2*e)^7 + 37422*a^2*tan(1/2*f*x + 1/2*e)^6 - 32802*a^2*tan(1/2*f*x + 1/2*e)^5 + 27060*a^2*tan(1/2*f*x + 1/2*e)^4 - 11220*a^2*tan(1/2*f*x + 1/2*e)^3 + 4895*a^2*tan(1/2*f*x + 1/2*e)^2 - 517*a^2*tan(1/2*f*x + 1/2*e) + 152*a^2)/(c^6*f*(tan(1/2*f*x + 1/2*e) - 1)^11)","A",0
247,1,196,0,0.294324," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^6,x, algorithm=""giac"")","\frac{55}{128} \, a^{3} c^{6} x - \frac{a^{3} c^{6} \cos\left(9 \, f x + 9 \, e\right)}{2304 \, f} + \frac{9 \, a^{3} c^{6} \cos\left(7 \, f x + 7 \, e\right)}{1792 \, f} + \frac{3 \, a^{3} c^{6} \cos\left(5 \, f x + 5 \, e\right)}{64 \, f} + \frac{29 \, a^{3} c^{6} \cos\left(3 \, f x + 3 \, e\right)}{192 \, f} + \frac{33 \, a^{3} c^{6} \cos\left(f x + e\right)}{128 \, f} - \frac{3 \, a^{3} c^{6} \sin\left(8 \, f x + 8 \, e\right)}{1024 \, f} - \frac{a^{3} c^{6} \sin\left(6 \, f x + 6 \, e\right)}{96 \, f} + \frac{3 \, a^{3} c^{6} \sin\left(4 \, f x + 4 \, e\right)}{128 \, f} + \frac{9 \, a^{3} c^{6} \sin\left(2 \, f x + 2 \, e\right)}{32 \, f}"," ",0,"55/128*a^3*c^6*x - 1/2304*a^3*c^6*cos(9*f*x + 9*e)/f + 9/1792*a^3*c^6*cos(7*f*x + 7*e)/f + 3/64*a^3*c^6*cos(5*f*x + 5*e)/f + 29/192*a^3*c^6*cos(3*f*x + 3*e)/f + 33/128*a^3*c^6*cos(f*x + e)/f - 3/1024*a^3*c^6*sin(8*f*x + 8*e)/f - 1/96*a^3*c^6*sin(6*f*x + 6*e)/f + 3/128*a^3*c^6*sin(4*f*x + 4*e)/f + 9/32*a^3*c^6*sin(2*f*x + 2*e)/f","A",0
248,1,154,0,0.258655," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","\frac{45}{128} \, a^{3} c^{5} x + \frac{a^{3} c^{5} \cos\left(7 \, f x + 7 \, e\right)}{224 \, f} + \frac{a^{3} c^{5} \cos\left(5 \, f x + 5 \, e\right)}{32 \, f} + \frac{3 \, a^{3} c^{5} \cos\left(3 \, f x + 3 \, e\right)}{32 \, f} + \frac{5 \, a^{3} c^{5} \cos\left(f x + e\right)}{32 \, f} - \frac{a^{3} c^{5} \sin\left(8 \, f x + 8 \, e\right)}{1024 \, f} + \frac{5 \, a^{3} c^{5} \sin\left(4 \, f x + 4 \, e\right)}{128 \, f} + \frac{a^{3} c^{5} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"45/128*a^3*c^5*x + 1/224*a^3*c^5*cos(7*f*x + 7*e)/f + 1/32*a^3*c^5*cos(5*f*x + 5*e)/f + 3/32*a^3*c^5*cos(3*f*x + 3*e)/f + 5/32*a^3*c^5*cos(f*x + e)/f - 1/1024*a^3*c^5*sin(8*f*x + 8*e)/f + 5/128*a^3*c^5*sin(4*f*x + 4*e)/f + 1/4*a^3*c^5*sin(2*f*x + 2*e)/f","A",0
249,1,154,0,0.230933," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{5}{16} \, a^{3} c^{4} x + \frac{a^{3} c^{4} \cos\left(7 \, f x + 7 \, e\right)}{448 \, f} + \frac{a^{3} c^{4} \cos\left(5 \, f x + 5 \, e\right)}{64 \, f} + \frac{3 \, a^{3} c^{4} \cos\left(3 \, f x + 3 \, e\right)}{64 \, f} + \frac{5 \, a^{3} c^{4} \cos\left(f x + e\right)}{64 \, f} + \frac{a^{3} c^{4} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{3 \, a^{3} c^{4} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} + \frac{15 \, a^{3} c^{4} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"5/16*a^3*c^4*x + 1/448*a^3*c^4*cos(7*f*x + 7*e)/f + 1/64*a^3*c^4*cos(5*f*x + 5*e)/f + 3/64*a^3*c^4*cos(3*f*x + 3*e)/f + 5/64*a^3*c^4*cos(f*x + e)/f + 1/192*a^3*c^4*sin(6*f*x + 6*e)/f + 3/64*a^3*c^4*sin(4*f*x + 4*e)/f + 15/64*a^3*c^4*sin(2*f*x + 2*e)/f","A",0
250,1,73,0,0.240985," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{5}{16} \, a^{3} c^{3} x + \frac{a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{3 \, a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} + \frac{15 \, a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"5/16*a^3*c^3*x + 1/192*a^3*c^3*sin(6*f*x + 6*e)/f + 3/64*a^3*c^3*sin(4*f*x + 4*e)/f + 15/64*a^3*c^3*sin(2*f*x + 2*e)/f","A",0
251,1,112,0,0.172199," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{8} \, a^{3} c^{2} x - \frac{a^{3} c^{2} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} - \frac{a^{3} c^{2} \cos\left(3 \, f x + 3 \, e\right)}{16 \, f} - \frac{a^{3} c^{2} \cos\left(f x + e\right)}{8 \, f} + \frac{a^{3} c^{2} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a^{3} c^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"3/8*a^3*c^2*x - 1/80*a^3*c^2*cos(5*f*x + 5*e)/f - 1/16*a^3*c^2*cos(3*f*x + 3*e)/f - 1/8*a^3*c^2*cos(f*x + e)/f + 1/32*a^3*c^2*sin(4*f*x + 4*e)/f + 1/4*a^3*c^2*sin(2*f*x + 2*e)/f","A",0
252,1,81,0,0.423704," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e)),x, algorithm=""giac"")","\frac{5}{8} \, a^{3} c x - \frac{a^{3} c \cos\left(3 \, f x + 3 \, e\right)}{6 \, f} - \frac{a^{3} c \cos\left(f x + e\right)}{2 \, f} - \frac{a^{3} c \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{a^{3} c \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"5/8*a^3*c*x - 1/6*a^3*c*cos(3*f*x + 3*e)/f - 1/2*a^3*c*cos(f*x + e)/f - 1/32*a^3*c*sin(4*f*x + 4*e)/f + 1/4*a^3*c*sin(2*f*x + 2*e)/f","A",0
253,1,117,0,0.288146," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(f x + e\right)} a^{3}}{c} + \frac{32 \, a^{3}}{c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}} + \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 8 \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} c}}{2 \, f}"," ",0,"-1/2*(15*(f*x + e)*a^3/c + 32*a^3/(c*(tan(1/2*f*x + 1/2*e) - 1)) + 2*(a^3*tan(1/2*f*x + 1/2*e)^3 - 8*a^3*tan(1/2*f*x + 1/2*e)^2 - a^3*tan(1/2*f*x + 1/2*e) - 8*a^3)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*c))/f","A",0
254,1,101,0,0.381867," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(f x + e\right)} a^{3}}{c^{2}} - \frac{6 \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} c^{2}} + \frac{8 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 5 \, a^{3}\right)}}{c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(15*(f*x + e)*a^3/c^2 - 6*a^3/((tan(1/2*f*x + 1/2*e)^2 + 1)*c^2) + 8*(3*a^3*tan(1/2*f*x + 1/2*e)^2 - 12*a^3*tan(1/2*f*x + 1/2*e) + 5*a^3)/(c^2*(tan(1/2*f*x + 1/2*e) - 1)^3))/f","A",0
255,1,111,0,0.202903," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(f x + e\right)} a^{3}}{c^{3}} + \frac{4 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 30 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 100 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 50 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 13 \, a^{3}\right)}}{c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{5}}}{15 \, f}"," ",0,"-1/15*(15*(f*x + e)*a^3/c^3 + 4*(15*a^3*tan(1/2*f*x + 1/2*e)^4 - 30*a^3*tan(1/2*f*x + 1/2*e)^3 + 100*a^3*tan(1/2*f*x + 1/2*e)^2 - 50*a^3*tan(1/2*f*x + 1/2*e) + 13*a^3)/(c^3*(tan(1/2*f*x + 1/2*e) - 1)^5))/f","A",0
256,1,77,0,0.224589," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(7 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 35 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 21 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{3}\right)}}{7 \, c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{7}}"," ",0,"-2/7*(7*a^3*tan(1/2*f*x + 1/2*e)^6 + 35*a^3*tan(1/2*f*x + 1/2*e)^4 + 21*a^3*tan(1/2*f*x + 1/2*e)^2 + a^3)/(c^4*f*(tan(1/2*f*x + 1/2*e) - 1)^7)","B",0
257,1,162,0,0.259790," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(63 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 63 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 483 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 315 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 693 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 189 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 225 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8 \, a^{3}\right)}}{63 \, c^{5} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{9}}"," ",0,"-2/63*(63*a^3*tan(1/2*f*x + 1/2*e)^8 - 63*a^3*tan(1/2*f*x + 1/2*e)^7 + 483*a^3*tan(1/2*f*x + 1/2*e)^6 - 315*a^3*tan(1/2*f*x + 1/2*e)^5 + 693*a^3*tan(1/2*f*x + 1/2*e)^4 - 189*a^3*tan(1/2*f*x + 1/2*e)^3 + 225*a^3*tan(1/2*f*x + 1/2*e)^2 - 9*a^3*tan(1/2*f*x + 1/2*e) + 8*a^3)/(c^5*f*(tan(1/2*f*x + 1/2*e) - 1)^9)","B",0
258,1,196,0,0.365788," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x, algorithm=""giac"")","-\frac{2 \, {\left(693 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{10} - 1386 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} + 8085 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 10626 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 21252 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 15246 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 15444 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4950 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2959 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 176 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 79 \, a^{3}\right)}}{693 \, c^{6} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{11}}"," ",0,"-2/693*(693*a^3*tan(1/2*f*x + 1/2*e)^10 - 1386*a^3*tan(1/2*f*x + 1/2*e)^9 + 8085*a^3*tan(1/2*f*x + 1/2*e)^8 - 10626*a^3*tan(1/2*f*x + 1/2*e)^7 + 21252*a^3*tan(1/2*f*x + 1/2*e)^6 - 15246*a^3*tan(1/2*f*x + 1/2*e)^5 + 15444*a^3*tan(1/2*f*x + 1/2*e)^4 - 4950*a^3*tan(1/2*f*x + 1/2*e)^3 + 2959*a^3*tan(1/2*f*x + 1/2*e)^2 - 176*a^3*tan(1/2*f*x + 1/2*e) + 79*a^3)/(c^6*f*(tan(1/2*f*x + 1/2*e) - 1)^11)","A",0
259,1,230,0,0.325974," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^7,x, algorithm=""giac"")","-\frac{2 \, {\left(3003 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{12} - 9009 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{11} + 51051 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{10} - 99099 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} + 216216 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 246246 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 285714 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 182754 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 122551 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 37609 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 15171 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1027 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 310 \, a^{3}\right)}}{3003 \, c^{7} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{13}}"," ",0,"-2/3003*(3003*a^3*tan(1/2*f*x + 1/2*e)^12 - 9009*a^3*tan(1/2*f*x + 1/2*e)^11 + 51051*a^3*tan(1/2*f*x + 1/2*e)^10 - 99099*a^3*tan(1/2*f*x + 1/2*e)^9 + 216216*a^3*tan(1/2*f*x + 1/2*e)^8 - 246246*a^3*tan(1/2*f*x + 1/2*e)^7 + 285714*a^3*tan(1/2*f*x + 1/2*e)^6 - 182754*a^3*tan(1/2*f*x + 1/2*e)^5 + 122551*a^3*tan(1/2*f*x + 1/2*e)^4 - 37609*a^3*tan(1/2*f*x + 1/2*e)^3 + 15171*a^3*tan(1/2*f*x + 1/2*e)^2 - 1027*a^3*tan(1/2*f*x + 1/2*e) + 310*a^3)/(c^7*f*(tan(1/2*f*x + 1/2*e) - 1)^13)","A",0
260,1,264,0,0.331347," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(45045 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{14} - 180180 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{13} + 1066065 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{12} - 2702700 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{11} + 6675669 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{10} - 10210200 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} + 14124825 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 13178880 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 11026015 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 6066060 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 3088995 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 864500 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 265335 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 18600 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4243 \, a^{3}\right)}}{45045 \, c^{8} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{15}}"," ",0,"-2/45045*(45045*a^3*tan(1/2*f*x + 1/2*e)^14 - 180180*a^3*tan(1/2*f*x + 1/2*e)^13 + 1066065*a^3*tan(1/2*f*x + 1/2*e)^12 - 2702700*a^3*tan(1/2*f*x + 1/2*e)^11 + 6675669*a^3*tan(1/2*f*x + 1/2*e)^10 - 10210200*a^3*tan(1/2*f*x + 1/2*e)^9 + 14124825*a^3*tan(1/2*f*x + 1/2*e)^8 - 13178880*a^3*tan(1/2*f*x + 1/2*e)^7 + 11026015*a^3*tan(1/2*f*x + 1/2*e)^6 - 6066060*a^3*tan(1/2*f*x + 1/2*e)^5 + 3088995*a^3*tan(1/2*f*x + 1/2*e)^4 - 864500*a^3*tan(1/2*f*x + 1/2*e)^3 + 265335*a^3*tan(1/2*f*x + 1/2*e)^2 - 18600*a^3*tan(1/2*f*x + 1/2*e) + 4243*a^3)/(c^8*f*(tan(1/2*f*x + 1/2*e) - 1)^15)","A",0
261,1,135,0,0.217718," ","integrate((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(f x + e\right)} c^{4}}{a} + \frac{192 \, c^{4}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{2 \, {\left(15 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 66 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 144 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 15 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 70 \, c^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{3} a}}{6 \, f}"," ",0,"-1/6*(105*(f*x + e)*c^4/a + 192*c^4/(a*(tan(1/2*f*x + 1/2*e) + 1)) + 2*(15*c^4*tan(1/2*f*x + 1/2*e)^5 + 66*c^4*tan(1/2*f*x + 1/2*e)^4 + 144*c^4*tan(1/2*f*x + 1/2*e)^2 - 15*c^4*tan(1/2*f*x + 1/2*e) + 70*c^4)/((tan(1/2*f*x + 1/2*e)^2 + 1)^3*a))/f","A",0
262,1,117,0,0.198157," ","integrate((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(f x + e\right)} c^{3}}{a} + \frac{32 \, c^{3}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{2 \, {\left(c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8 \, c^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} a}}{2 \, f}"," ",0,"-1/2*(15*(f*x + e)*c^3/a + 32*c^3/(a*(tan(1/2*f*x + 1/2*e) + 1)) + 2*(c^3*tan(1/2*f*x + 1/2*e)^3 + 8*c^3*tan(1/2*f*x + 1/2*e)^2 - c^3*tan(1/2*f*x + 1/2*e) + 8*c^3)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*a))/f","A",0
263,1,100,0,0.203794," ","integrate((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(f x + e\right)} c^{2}}{a} + \frac{2 \, {\left(4 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 5 \, c^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)} a}}{f}"," ",0,"-(3*(f*x + e)*c^2/a + 2*(4*c^2*tan(1/2*f*x + 1/2*e)^2 + c^2*tan(1/2*f*x + 1/2*e) + 5*c^2)/((tan(1/2*f*x + 1/2*e)^3 + tan(1/2*f*x + 1/2*e)^2 + tan(1/2*f*x + 1/2*e) + 1)*a))/f","A",0
264,1,37,0,0.225608," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left(f x + e\right)} c}{a} + \frac{4 \, c}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}}{f}"," ",0,"-((f*x + e)*c/a + 4*c/(a*(tan(1/2*f*x + 1/2*e) + 1)))/f","A",0
265,1,17,0,0.163004," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""giac"")","\frac{\tan\left(f x + e\right)}{a c f}"," ",0,"tan(f*x + e)/(a*c*f)","A",0
266,1,77,0,0.189691," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{3}{a c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{9 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7}{a c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{3}}}{6 \, f}"," ",0,"-1/6*(3/(a*c^2*(tan(1/2*f*x + 1/2*e) + 1)) + (9*tan(1/2*f*x + 1/2*e)^2 - 12*tan(1/2*f*x + 1/2*e) + 7)/(a*c^2*(tan(1/2*f*x + 1/2*e) - 1)^3))/f","A",0
267,1,105,0,0.304392," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{5}{a c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{35 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 90 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 120 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 70 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 21}{a c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{5}}}{20 \, f}"," ",0,"-1/20*(5/(a*c^3*(tan(1/2*f*x + 1/2*e) + 1)) + (35*tan(1/2*f*x + 1/2*e)^4 - 90*tan(1/2*f*x + 1/2*e)^3 + 120*tan(1/2*f*x + 1/2*e)^2 - 70*tan(1/2*f*x + 1/2*e) + 21)/(a*c^3*(tan(1/2*f*x + 1/2*e) - 1)^5))/f","A",0
268,1,133,0,0.227447," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{35}{a c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{525 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 1960 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 4025 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4480 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3143 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1176 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 243}{a c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{7}}}{280 \, f}"," ",0,"-1/280*(35/(a*c^4*(tan(1/2*f*x + 1/2*e) + 1)) + (525*tan(1/2*f*x + 1/2*e)^6 - 1960*tan(1/2*f*x + 1/2*e)^5 + 4025*tan(1/2*f*x + 1/2*e)^4 - 4480*tan(1/2*f*x + 1/2*e)^3 + 3143*tan(1/2*f*x + 1/2*e)^2 - 1176*tan(1/2*f*x + 1/2*e) + 243)/(a*c^4*(tan(1/2*f*x + 1/2*e) - 1)^7))/f","A",0
269,1,203,0,0.246915," ","integrate((c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{315 \, {\left(f x + e\right)} c^{5}}{a^{2}} + \frac{2 \, {\left(309 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} + 969 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 1693 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 3027 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 2901 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 3247 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1995 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1173 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 494 \, c^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3} a^{2}}}{6 \, f}"," ",0,"1/6*(315*(f*x + e)*c^5/a^2 + 2*(309*c^5*tan(1/2*f*x + 1/2*e)^8 + 969*c^5*tan(1/2*f*x + 1/2*e)^7 + 1693*c^5*tan(1/2*f*x + 1/2*e)^6 + 3027*c^5*tan(1/2*f*x + 1/2*e)^5 + 2901*c^5*tan(1/2*f*x + 1/2*e)^4 + 3247*c^5*tan(1/2*f*x + 1/2*e)^3 + 1995*c^5*tan(1/2*f*x + 1/2*e)^2 + 1173*c^5*tan(1/2*f*x + 1/2*e) + 494*c^5)/((tan(1/2*f*x + 1/2*e)^3 + tan(1/2*f*x + 1/2*e)^2 + tan(1/2*f*x + 1/2*e) + 1)^3*a^2))/f","A",0
270,1,152,0,0.193240," ","integrate((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{105 \, {\left(f x + e\right)} c^{4}}{a^{2}} + \frac{6 \, {\left(c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 \, c^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} a^{2}} + \frac{64 \, {\left(3 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 9 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, c^{4}\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{6 \, f}"," ",0,"1/6*(105*(f*x + e)*c^4/a^2 + 6*(c^4*tan(1/2*f*x + 1/2*e)^3 + 12*c^4*tan(1/2*f*x + 1/2*e)^2 - c^4*tan(1/2*f*x + 1/2*e) + 12*c^4)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*a^2) + 64*(3*c^4*tan(1/2*f*x + 1/2*e)^2 + 9*c^4*tan(1/2*f*x + 1/2*e) + 4*c^4)/(a^2*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
271,1,101,0,0.197914," ","integrate((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(f x + e\right)} c^{3}}{a^{2}} + \frac{6 \, c^{3}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} a^{2}} + \frac{8 \, {\left(3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 5 \, c^{3}\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(15*(f*x + e)*c^3/a^2 + 6*c^3/((tan(1/2*f*x + 1/2*e)^2 + 1)*a^2) + 8*(3*c^3*tan(1/2*f*x + 1/2*e)^2 + 12*c^3*tan(1/2*f*x + 1/2*e) + 5*c^3)/(a^2*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
272,1,58,0,0.169965," ","integrate((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(f x + e\right)} c^{2}}{a^{2}} + \frac{8 \, {\left(3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c^{2}\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*c^2/a^2 + 8*(3*c^2*tan(1/2*f*x + 1/2*e) + c^2)/(a^2*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
273,1,39,0,0.178864," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + c\right)}}{3 \, a^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}"," ",0,"-2/3*(3*c*tan(1/2*f*x + 1/2*e)^2 + c)/(a^2*f*(tan(1/2*f*x + 1/2*e) + 1)^3)","A",0
274,1,77,0,0.206381," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{3}{a^{2} c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}} + \frac{9 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7}{a^{2} c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{6 \, f}"," ",0,"-1/6*(3/(a^2*c*(tan(1/2*f*x + 1/2*e) - 1)) + (9*tan(1/2*f*x + 1/2*e)^2 + 12*tan(1/2*f*x + 1/2*e) + 7)/(a^2*c*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
275,1,30,0,0.436119," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)}{3 \, a^{2} c^{2} f}"," ",0,"1/3*(tan(f*x + e)^3 + 3*tan(f*x + e))/(a^2*c^2*f)","A",0
276,1,133,0,0.231129," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(15 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 13\right)}}{a^{2} c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}} + \frac{165 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 480 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 650 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 400 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 113}{a^{2} c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{5}}}{120 \, f}"," ",0,"-1/120*(5*(15*tan(1/2*f*x + 1/2*e)^2 + 24*tan(1/2*f*x + 1/2*e) + 13)/(a^2*c^3*(tan(1/2*f*x + 1/2*e) + 1)^3) + (165*tan(1/2*f*x + 1/2*e)^4 - 480*tan(1/2*f*x + 1/2*e)^3 + 650*tan(1/2*f*x + 1/2*e)^2 - 400*tan(1/2*f*x + 1/2*e) + 113)/(a^2*c^3*(tan(1/2*f*x + 1/2*e) - 1)^5))/f","A",0
277,1,161,0,0.323349," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(9 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8\right)}}{a^{2} c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}} + \frac{273 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 1155 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 2450 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 2870 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2037 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 791 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 152}{a^{2} c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{7}}}{168 \, f}"," ",0,"-1/168*(7*(9*tan(1/2*f*x + 1/2*e)^2 + 15*tan(1/2*f*x + 1/2*e) + 8)/(a^2*c^4*(tan(1/2*f*x + 1/2*e) + 1)^3) + (273*tan(1/2*f*x + 1/2*e)^6 - 1155*tan(1/2*f*x + 1/2*e)^5 + 2450*tan(1/2*f*x + 1/2*e)^4 - 2870*tan(1/2*f*x + 1/2*e)^3 + 2037*tan(1/2*f*x + 1/2*e)^2 - 791*tan(1/2*f*x + 1/2*e) + 152)/(a^2*c^4*(tan(1/2*f*x + 1/2*e) - 1)^7))/f","A",0
278,1,189,0,0.242867," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","-\frac{\frac{21 \, {\left(21 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 19\right)}}{a^{2} c^{5} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}} + \frac{3591 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 19656 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 56196 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 95760 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 107730 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 79464 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 38484 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10944 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1615}{a^{2} c^{5} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{9}}}{2016 \, f}"," ",0,"-1/2016*(21*(21*tan(1/2*f*x + 1/2*e)^2 + 36*tan(1/2*f*x + 1/2*e) + 19)/(a^2*c^5*(tan(1/2*f*x + 1/2*e) + 1)^3) + (3591*tan(1/2*f*x + 1/2*e)^8 - 19656*tan(1/2*f*x + 1/2*e)^7 + 56196*tan(1/2*f*x + 1/2*e)^6 - 95760*tan(1/2*f*x + 1/2*e)^5 + 107730*tan(1/2*f*x + 1/2*e)^4 - 79464*tan(1/2*f*x + 1/2*e)^3 + 38484*tan(1/2*f*x + 1/2*e)^2 - 10944*tan(1/2*f*x + 1/2*e) + 1615)/(a^2*c^5*(tan(1/2*f*x + 1/2*e) - 1)^9))/f","A",0
279,1,186,0,0.241084," ","integrate((c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{315 \, {\left(f x + e\right)} c^{5}}{a^{3}} + \frac{10 \, {\left(c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 16 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 16 \, c^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} a^{3}} + \frac{64 \, {\left(10 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 85 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 55 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 13 \, c^{5}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{10 \, f}"," ",0,"-1/10*(315*(f*x + e)*c^5/a^3 + 10*(c^5*tan(1/2*f*x + 1/2*e)^3 + 16*c^5*tan(1/2*f*x + 1/2*e)^2 - c^5*tan(1/2*f*x + 1/2*e) + 16*c^5)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*a^3) + 64*(10*c^5*tan(1/2*f*x + 1/2*e)^4 + 45*c^5*tan(1/2*f*x + 1/2*e)^3 + 85*c^5*tan(1/2*f*x + 1/2*e)^2 + 55*c^5*tan(1/2*f*x + 1/2*e) + 13*c^5)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","A",0
280,1,135,0,0.211199," ","integrate((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{105 \, {\left(f x + e\right)} c^{4}}{a^{3}} + \frac{30 \, c^{4}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} a^{3}} + \frac{16 \, {\left(15 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 60 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 130 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 80 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 19 \, c^{4}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{15 \, f}"," ",0,"-1/15*(105*(f*x + e)*c^4/a^3 + 30*c^4/((tan(1/2*f*x + 1/2*e)^2 + 1)*a^3) + 16*(15*c^4*tan(1/2*f*x + 1/2*e)^4 + 60*c^4*tan(1/2*f*x + 1/2*e)^3 + 130*c^4*tan(1/2*f*x + 1/2*e)^2 + 80*c^4*tan(1/2*f*x + 1/2*e) + 19*c^4)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","A",0
281,1,111,0,0.231659," ","integrate((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(f x + e\right)} c^{3}}{a^{3}} + \frac{4 \, {\left(15 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 100 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 50 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 13 \, c^{3}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{15 \, f}"," ",0,"-1/15*(15*(f*x + e)*c^3/a^3 + 4*(15*c^3*tan(1/2*f*x + 1/2*e)^4 + 30*c^3*tan(1/2*f*x + 1/2*e)^3 + 100*c^3*tan(1/2*f*x + 1/2*e)^2 + 50*c^3*tan(1/2*f*x + 1/2*e) + 13*c^3)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","A",0
282,1,60,0,0.258363," ","integrate((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 10 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + c^{2}\right)}}{5 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}"," ",0,"-2/5*(5*c^2*tan(1/2*f*x + 1/2*e)^4 + 10*c^2*tan(1/2*f*x + 1/2*e)^2 + c^2)/(a^3*f*(tan(1/2*f*x + 1/2*e) + 1)^5)","A",0
283,1,84,0,0.701117," ","integrate((c-c*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 15 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 25 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, c\right)}}{15 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}"," ",0,"-2/15*(15*c*tan(1/2*f*x + 1/2*e)^4 + 15*c*tan(1/2*f*x + 1/2*e)^3 + 25*c*tan(1/2*f*x + 1/2*e)^2 + 5*c*tan(1/2*f*x + 1/2*e) + 4*c)/(a^3*f*(tan(1/2*f*x + 1/2*e) + 1)^5)","A",0
284,1,105,0,0.198189," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{5}{a^{3} c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}} + \frac{35 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 90 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 120 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 70 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 21}{a^{3} c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{20 \, f}"," ",0,"-1/20*(5/(a^3*c*(tan(1/2*f*x + 1/2*e) - 1)) + (35*tan(1/2*f*x + 1/2*e)^4 + 90*tan(1/2*f*x + 1/2*e)^3 + 120*tan(1/2*f*x + 1/2*e)^2 + 70*tan(1/2*f*x + 1/2*e) + 21)/(a^3*c*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","A",0
285,1,133,0,0.293980," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(15 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 24 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 13\right)}}{a^{3} c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{3}} + \frac{165 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 480 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 650 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 400 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 113}{a^{3} c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{120 \, f}"," ",0,"-1/120*(5*(15*tan(1/2*f*x + 1/2*e)^2 - 24*tan(1/2*f*x + 1/2*e) + 13)/(a^3*c^2*(tan(1/2*f*x + 1/2*e) - 1)^3) + (165*tan(1/2*f*x + 1/2*e)^4 + 480*tan(1/2*f*x + 1/2*e)^3 + 650*tan(1/2*f*x + 1/2*e)^2 + 400*tan(1/2*f*x + 1/2*e) + 113)/(a^3*c^2*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","A",0
286,1,43,0,0.219839," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)}{15 \, a^{3} c^{3} f}"," ",0,"1/15*(3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))/(a^3*c^3*f)","A",0
287,1,189,0,1.432804," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(55 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 180 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 250 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 160 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 43\right)}}{a^{3} c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}} + \frac{735 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 3360 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 7315 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 8820 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6321 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2492 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 461}{a^{3} c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{7}}}{560 \, f}"," ",0,"-1/560*(7*(55*tan(1/2*f*x + 1/2*e)^4 + 180*tan(1/2*f*x + 1/2*e)^3 + 250*tan(1/2*f*x + 1/2*e)^2 + 160*tan(1/2*f*x + 1/2*e) + 43)/(a^3*c^4*(tan(1/2*f*x + 1/2*e) + 1)^5) + (735*tan(1/2*f*x + 1/2*e)^6 - 3360*tan(1/2*f*x + 1/2*e)^5 + 7315*tan(1/2*f*x + 1/2*e)^4 - 8820*tan(1/2*f*x + 1/2*e)^3 + 6321*tan(1/2*f*x + 1/2*e)^2 - 2492*tan(1/2*f*x + 1/2*e) + 461)/(a^3*c^4*(tan(1/2*f*x + 1/2*e) - 1)^7))/f","B",0
288,1,217,0,0.252005," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(435 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 1470 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2060 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1330 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 353\right)}}{a^{3} c^{5} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}} + \frac{4455 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 26460 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 78120 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 137340 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 157374 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 118356 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 57744 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 16596 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2339}{a^{3} c^{5} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{9}}}{2880 \, f}"," ",0,"-1/2880*(3*(435*tan(1/2*f*x + 1/2*e)^4 + 1470*tan(1/2*f*x + 1/2*e)^3 + 2060*tan(1/2*f*x + 1/2*e)^2 + 1330*tan(1/2*f*x + 1/2*e) + 353)/(a^3*c^5*(tan(1/2*f*x + 1/2*e) + 1)^5) + (4455*tan(1/2*f*x + 1/2*e)^8 - 26460*tan(1/2*f*x + 1/2*e)^7 + 78120*tan(1/2*f*x + 1/2*e)^6 - 137340*tan(1/2*f*x + 1/2*e)^5 + 157374*tan(1/2*f*x + 1/2*e)^4 - 118356*tan(1/2*f*x + 1/2*e)^3 + 57744*tan(1/2*f*x + 1/2*e)^2 - 16596*tan(1/2*f*x + 1/2*e) + 2339)/(a^3*c^5*(tan(1/2*f*x + 1/2*e) - 1)^9))/f","A",0
289,1,245,0,0.261612," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x, algorithm=""giac"")","-\frac{\frac{33 \, {\left(555 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 1920 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2710 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1760 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 463\right)}}{a^{3} c^{6} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}} + \frac{108405 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{10} - 784080 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} + 2901195 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 6652800 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 10407474 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 11435424 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 8949270 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4899840 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1816265 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 411664 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 47279}{a^{3} c^{6} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}^{11}}}{63360 \, f}"," ",0,"-1/63360*(33*(555*tan(1/2*f*x + 1/2*e)^4 + 1920*tan(1/2*f*x + 1/2*e)^3 + 2710*tan(1/2*f*x + 1/2*e)^2 + 1760*tan(1/2*f*x + 1/2*e) + 463)/(a^3*c^6*(tan(1/2*f*x + 1/2*e) + 1)^5) + (108405*tan(1/2*f*x + 1/2*e)^10 - 784080*tan(1/2*f*x + 1/2*e)^9 + 2901195*tan(1/2*f*x + 1/2*e)^8 - 6652800*tan(1/2*f*x + 1/2*e)^7 + 10407474*tan(1/2*f*x + 1/2*e)^6 - 11435424*tan(1/2*f*x + 1/2*e)^5 + 8949270*tan(1/2*f*x + 1/2*e)^4 - 4899840*tan(1/2*f*x + 1/2*e)^3 + 1816265*tan(1/2*f*x + 1/2*e)^2 - 411664*tan(1/2*f*x + 1/2*e) + 47279)/(a^3*c^6*(tan(1/2*f*x + 1/2*e) - 1)^11))/f","A",0
290,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a*c^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f-8*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(4*f)^2+24*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(12*f)^2-40*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(20*f)^2+56*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(28*f)^2+24*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-224*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2+288*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2+48*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2)","F(-2)",0
291,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a*c^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f-16*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2+48*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2-80*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2+112*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2+24*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+4*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2)","F(-2)",0
292,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+24*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+4*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2)","F(-2)",0
293,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+4*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(2*f)^2-12*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(6*f)^2)","F(-2)",0
294,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(4*a*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1)+2*sqrt(c*tan((f*x+exp(1))/2)^2+c)*(1/2*a/sign(tan((f*x+exp(1))/2)-1)+1/2*a*tan((f*x+exp(1))/2)/sign(tan((f*x+exp(1))/2)-1))/(c*tan((f*x+exp(1))/2)^2+c)+(-4*a*c*atan(sqrt(c)/sqrt(-c))-2*a*sqrt(-c)*sqrt(c))/c/sqrt(-c)/sqrt(2)*sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
295,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/2*(-3*a*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+a*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-a*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-a*sqrt(c)*c)/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^2/c/sign(tan((f*x+exp(1))/2)-1)-1/2*a*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/c/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
296,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/16*(-17*a*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7-23*a*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6-19*a*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5+39*a*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+5*a*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+7*a*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-37*a*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-3*a*sqrt(c)*c^3)/c^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^4/sign(tan((f*x+exp(1))/2)-1)-1/16*a*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^2/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
297,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (8*pi/t_nostep/2)>(-8*pi/t_nostep/2)Discontinuities at zeroes of sin((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep-1)]Evaluation time: 0.69Not invertible Error: Bad Argument Value","F(-2)",0
298,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^2*c^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f-32*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(16*f)^2+96*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(48*f)^2-960*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(160*f)^2+1344*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(224*f)^2-576*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(18*f*x+18*exp(1)+pi))/(288*f)^2+704*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(22*f*x+22*exp(1)-pi))/(352*f)^2+24*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+224*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2-288*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2+80*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2)","F(-2)",0
299,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^2*c^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+24*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+224*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2-288*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2+80*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2)","F(-2)",0
300,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+16*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2-48*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2+80*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2-112*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2+24*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+4*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2)","F(-2)",0
301,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(2*a^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/f-2*a^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f-6*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(3*f)^2-24*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+40*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-4*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2)","F(-2)",0
302,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2/sqrt(c*tan((f*x+exp(1))/2)^2+c)/(c*tan((f*x+exp(1))/2)^2+c)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(3/2*a^2*c/sign(tan((f*x+exp(1))/2)-1)+7/6*a^2*c*tan((f*x+exp(1))/2)/sign(tan((f*x+exp(1))/2)-1))+3/2*a^2*c/sign(tan((f*x+exp(1))/2)-1))+7/6*a^2*c/sign(tan((f*x+exp(1))/2)-1))+8*a^2*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1)+(-24*a^2*c*atan(sqrt(c)/sqrt(-c))-16*a^2*sqrt(-c)*sqrt(c))/3/c/sqrt(-c)/sqrt(2)*sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
303,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2*sqrt(c*tan((f*x+exp(1))/2)^2+c)*(-1/2*a^2/c/sign(tan((f*x+exp(1))/2)-1)-1/2*a^2*tan((f*x+exp(1))/2)/c/sign(tan((f*x+exp(1))/2)-1))/(c*tan((f*x+exp(1))/2)^2+c)+2*(-(3*a^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3-a^2*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+a^2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+a^2*sqrt(c)*c)/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^2/c/sign(tan((f*x+exp(1))/2)-1)-3*a^2*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/c/sign(tan((f*x+exp(1))/2)-1)))","F(-2)",0
304,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/8*(-5*a^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7+29*a^2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6+17*a^2*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-13*a^2*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+9*a^2*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3-13*a^2*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-9*a^2*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+a^2*sqrt(c)*c^3)/c^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^4/sign(tan((f*x+exp(1))/2)-1)+3/8*a^2*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^2/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
305,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (8*pi/t_nostep/2)>(-8*pi/t_nostep/2)Discontinuities at zeroes of sin((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep-1)]Evaluation time: 0.88Not invertible Error: Bad Argument Value","F(-2)",0
306,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/512*(-509*a^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^15-1491*a^2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^14-7411*a^2*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^13-7937*a^2*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^12+711*a^2*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^11+22673*a^2*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^10+8457*a^2*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^9-23829*a^2*sqrt(c)*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^8-8391*a^2*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7+18823*a^2*sqrt(c)*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6-3657*a^2*c^5*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-10627*a^2*sqrt(c)*c^5*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+5693*a^2*c^6*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+115*a^2*c^7*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-2565*a^2*sqrt(c)*c^6*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-39*a^2*sqrt(c)*c^7)/c^4/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^8/sign(tan((f*x+exp(1))/2)-1)+3/512*a^2*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^4/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
307,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^3*c^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+5760*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(192*f)^2-9600*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(320*f)^2+1344*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)+pi))/(224*f)^2-1728*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)-pi))/(288*f)^2+1408*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(22*f*x+22*exp(1)+pi))/(704*f)^2-1664*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(26*f*x+26*exp(1)-pi))/(832*f)^2+352*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(16*f)^2)","F(-2)",0
308,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^3*c^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+32*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(16*f)^2-96*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(48*f)^2+960*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(160*f)^2-1344*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(224*f)^2+576*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(18*f*x+18*exp(1)+pi))/(288*f)^2-704*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(22*f*x+22*exp(1)-pi))/(352*f)^2+24*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+224*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2-288*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2+80*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2)","F(-2)",0
309,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^3*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+8*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(4*f)^2-24*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(12*f)^2+40*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(20*f)^2-56*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(28*f)^2+24*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-224*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2+288*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2+48*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2)","F(-2)",0
310,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)*(-2*a^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/f+240*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2-720*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2-80*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2+112*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2-72*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+120*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-12*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2)","F(-2)",0
311,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2/sqrt(c*tan((f*x+exp(1))/2)^2+c)/(c*tan((f*x+exp(1))/2)^2+c)^2*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(7/2*a^3*c^2/sign(tan((f*x+exp(1))/2)-1)+73/30*a^3*c^2*tan((f*x+exp(1))/2)/sign(tan((f*x+exp(1))/2)-1))+19/3*a^3*c^2/sign(tan((f*x+exp(1))/2)-1))+19/3*a^3*c^2/sign(tan((f*x+exp(1))/2)-1))+7/2*a^3*c^2/sign(tan((f*x+exp(1))/2)-1))+73/30*a^3*c^2/sign(tan((f*x+exp(1))/2)-1))+16*a^3*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1)+(-240*a^3*c*atan(sqrt(c)/sqrt(-c))-184*a^3*sqrt(-c)*sqrt(c))/15/c/sqrt(-c)/sqrt(2)*sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
312,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2/sqrt(c*tan((f*x+exp(1))/2)^2+c)/(c*tan((f*x+exp(1))/2)^2+c)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(-5/2*a^3/sign(tan((f*x+exp(1))/2)-1)-13/6*a^3*tan((f*x+exp(1))/2)/sign(tan((f*x+exp(1))/2)-1))-5/2*a^3/sign(tan((f*x+exp(1))/2)-1))-13/6*a^3/sign(tan((f*x+exp(1))/2)-1))+2*((-6*a^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+2*a^3*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-2*a^3*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*a^3*sqrt(c)*c)/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^2/c/sign(tan((f*x+exp(1))/2)-1)-10*a^3*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/c/sign(tan((f*x+exp(1))/2)-1)))","F(-2)",0
313,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2*sqrt(c*tan((f*x+exp(1))/2)^2+c)*(1/2*a^3/c^2/sign(tan((f*x+exp(1))/2)-1)+1/2*a^3*tan((f*x+exp(1))/2)/c^2/sign(tan((f*x+exp(1))/2)-1))/(c*tan((f*x+exp(1))/2)^2+c)+2*(1/4*(7*a^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7+81*a^3*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6+53*a^3*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-65*a^3*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+13*a^3*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3-33*a^3*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+19*a^3*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+5*a^3*sqrt(c)*c^3)/c^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^4/sign(tan((f*x+exp(1))/2)-1)+15/4*a^3*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^2/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1)))","F(-2)",0
314,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (8*pi/t_nostep/2)>(-8*pi/t_nostep/2)Discontinuities at zeroes of sin((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep-1)]Evaluation time: 0.99Not invertible Error: Bad Argument Value","F(-2)",0
315,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/768*(-783*a^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^15-993*a^3*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^14-14913*a^3*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^13-11259*a^3*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^12+285*a^3*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^11+28715*a^3*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^10+17363*a^3*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^9-37271*a^3*sqrt(c)*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^8-8989*a^3*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7+36189*a^3*sqrt(c)*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6-6547*a^3*c^5*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-17777*a^3*sqrt(c)*c^5*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+5583*a^3*c^6*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+193*a^3*c^7*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-5351*a^3*sqrt(c)*c^6*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-61*a^3*sqrt(c)*c^7)/c^4/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^8/sign(tan((f*x+exp(1))/2)-1)-5/256*a^3*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^4/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
316,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/5120*(-5135*a^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^19-15645*a^3*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^18-150755*a^3*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^17-270725*a^3*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^16-385756*a^3*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^15+333260*a^3*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^14+983140*a^3*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^13+258460*a^3*sqrt(c)*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^12-1312610*a^3*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^11-597862*a^3*sqrt(c)*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^10+1413590*a^3*c^5*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^9+283610*a^3*sqrt(c)*c^5*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^8-1071020*a^3*c^6*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7+237340*a^3*sqrt(c)*c^6*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6+268532*a^3*c^7*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-352180*a^3*sqrt(c)*c^7*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+96505*a^3*c^8*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+1205*a^3*c^9*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-38245*a^3*sqrt(c)*c^8*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-317*a^3*sqrt(c)*c^9)/c^5/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^10/sign(tan((f*x+exp(1))/2)-1)-3/1024*a^3*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^5/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
317,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: 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3933440*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^2-71776119061217280*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^3-41165715343933440*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^4+21532835718365184*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^5+2744381022928896*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^6+21532835718365184*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2*tan(1/4*exp(1))-53832089295912960*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^4*tan(1/4*exp(1))^2+54887620458577920*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^4*tan(1/4*exp(1))^3+53832089295912960*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^4*tan(1/4*exp(1))^4-16466286137573376*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^4*tan(1/4*exp(1))^5-3588805953060864*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^4*tan(1/4*exp(1))^6-16466286137573376*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^4*tan(1/4*exp(1))+1055531162664960*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^6*tan(1/4*exp(1))^2-7036874417766400*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^6*tan(1/4*exp(1))^3-1055531162664960*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^6*tan(1/4*exp(1))^4+2111062325329920*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^6*tan(1/4*exp(1))^5+70368744177664*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^6*tan(1/4*exp(1))^6+2111062325329920*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^6*tan(1/4*exp(1)))/(422212465065984*a*tan(1/2*exp(1))-140737488355328*a*tan(1/2*exp(1))^3*tan(1/4*exp(1))^6+422212465065984*a*tan(1/2*exp(1))^2*tan(1/4*exp(1))^6-422212465065984*a*tan(1/2*exp(1))^3*tan(1/4*exp(1))^4-140737488355328*a*tan(1/4*exp(1))^6+1266637395197952*a*tan(1/2*exp(1))^2*tan(1/4*exp(1))^4-422212465065984*a*tan(1/2*exp(1))^3*tan(1/4*exp(1))^2-422212465065984*a*tan(1/4*exp(1))^4+1266637395197952*a*tan(1/2*exp(1))^2*tan(1/4*exp(1))^2-140737488355328*a*tan(1/2*exp(1))^3+422212465065984*a*tan(1/2*exp(1))^2-422212465065984*a*tan(1/4*exp(1))^2+1266637395197952*a*tan(1/2*exp(1))*tan(1/4*exp(1))^2+1266637395197952*a*tan(1/2*exp(1))*tan(1/4*exp(1))^4+422212465065984*a*tan(1/2*exp(1))*tan(1/4*exp(1))^6-140737488355328*a)/(-2*tan(1/2*(1/2*f*x+2*exp(1)))^3-6*tan(1/2*(1/2*f*x+2*exp(1)))^3*tan(1/2*exp(1))+tan(1/2*(1/2*f*x+2*exp(1)))^4*tan(1/2*exp(1))^3+2*tan(1/2*(1/2*f*x+2*exp(1)))^3*tan(1/2*exp(1))^3-3*tan(1/2*(1/2*f*x+2*exp(1)))^4*tan(1/2*exp(1))^2+6*tan(1/2*(1/2*f*x+2*exp(1)))^3*tan(1/2*exp(1))^2+tan(1/2*(1/2*f*x+2*exp(1)))^4-tan(1/2*exp(1))^3+3*tan(1/2*exp(1))^2-3*tan(1/2*(1/2*f*x+2*exp(1)))^4*tan(1/2*exp(1))+6*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2+2*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^3-6*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))-2*tan(1/2*(1/2*f*x+2*exp(1)))+3*tan(1/2*exp(1))-1)+1/2*(158456325028528675187087900672*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^3-3169126500570573503741758013440*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^3+950737950171172051122527404032*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))^5-475368975085586025561263702016*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))+950737950171172051122527404032*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/4*exp(1))+9507379501711720511225274040320*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^3-2852213850513516153367582212096*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/4*exp(1))^5-2852213850513516153367582212096*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/4*exp(1))-2376844875427930127806318510080*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^3*tan(1/4*exp(1))^2+2376844875427930127806318510080*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^3*tan(1/4*exp(1))^4-158456325028528675187087900672*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^3*tan(1/4*exp(1))^6+7130534626283790383418955530240*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/4*exp(1))^2-7130534626283790383418955530240*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/4*exp(1))^4+475368975085586025561263702016*sqrt(2)*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/4*exp(1))^6)*ln(abs(2*tan(1/2*exp(1))^3-2*sqrt(2)*sqrt(tan(1/2*exp(1))^2+1)*(tan(1/2*exp(1))^2+1)+6*tan(1/2*exp(1))^2-6*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2+2*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^3-6*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))+2*tan(1/2*(1/2*f*x+2*exp(1)))-6*tan(1/2*exp(1))-2)/abs(2*tan(1/2*exp(1))^3+2*sqrt(2)*sqrt(tan(1/2*exp(1))^2+1)*(tan(1/2*exp(1))^2+1)+6*tan(1/2*exp(1))^2-6*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^2+2*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))^3-6*tan(1/2*(1/2*f*x+2*exp(1)))*tan(1/2*exp(1))+2*tan(1/2*(1/2*f*x+2*exp(1)))-6*tan(1/2*exp(1))-2))/sqrt(2)/sqrt(tan(1/2*exp(1))^2+1)/(tan(1/2*exp(1))^2+1)/(158456325028528675187087900672*a*tan(1/4*exp(1))^6+475368975085586025561263702016*a*tan(1/4*exp(1))^4+475368975085586025561263702016*a*tan(1/4*exp(1))^2+158456325028528675187087900672*a))/f","F(-2)",0
320,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)-2*sqrt(2*c)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))/a/f/((-cos(1/4*(2*f*x+2*exp(1)-pi))+1)/(cos(1/4*(2*f*x+2*exp(1)-pi))+1)-1)","F(-2)",0
321,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((2*c*sqrt(2)*atan(sqrt(c)/sqrt(-c))-2*c*atan(sqrt(c)/sqrt(-c))+sqrt(-c)*sqrt(c))/(2*a*c*sqrt(-c)*sqrt(2)-4*a*c*sqrt(-c))*sign(tan((f*x+exp(1))/2)-1)+2*(1/2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/a/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)/sign(tan((f*x+exp(1))/2)-1)+1/2*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/a/sign(tan((f*x+exp(1))/2)-1)))","F(-2)",0
322,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(-1/4*(sqrt(c)*tan((f*x+exp(1))/2)-sqrt(c)-sqrt(c*tan((f*x+exp(1))/2)^2+c))/a/c/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)/sign(tan((f*x+exp(1))/2)-1)+1/8*(-3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-sqrt(c)*c)/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^2/a/c/sign(tan((f*x+exp(1))/2)-1)+3/8*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/sqrt(-c)/a/c/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
323,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(-1/8*(sqrt(c)*tan((f*x+exp(1))/2)-sqrt(c)-sqrt(c*tan((f*x+exp(1))/2)^2+c))/c^2/a/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)/sign(tan((f*x+exp(1))/2)-1)+1/64*(-41*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7-127*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6-91*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5+143*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4-3*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+47*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-93*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-11*sqrt(c)*c^3)/c^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^4/a/sign(tan((f*x+exp(1))/2)-1)+15/64*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/c^2/sqrt(-c)/a/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
324,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)/3*(-3*((-cos(1/4*(2*f*x+2*exp(1)-pi))+1)/(cos(1/4*(2*f*x+2*exp(1)-pi))+1))^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))-sign(sin(1/2*(f*x+exp(1))-1/4*pi)))/a^2/((-cos(1/4*(2*f*x+2*exp(1)-pi))+1)/(cos(1/4*(2*f*x+2*exp(1)-pi))+1)-1)^3/f","F(-2)",0
329,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((30*c*sqrt(2)*atan(sqrt(c)/sqrt(-c))-42*c*atan(sqrt(c)/sqrt(-c))-15*sqrt(-c)*sqrt(2)*sqrt(c)+22*sqrt(-c)*sqrt(c))/(84*a^2*c*sqrt(-c)*sqrt(2)-120*a^2*c*sqrt(-c))*sign(tan((f*x+exp(1))/2)-1)+2*(1/12*(9*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-15*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4-10*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+21*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+30*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+5*sqrt(c)*c^2)/a^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^3/sign(tan((f*x+exp(1))/2)-1)+1/4*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/a^2/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1)))","F(-2)",0
330,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/16*(-3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-sqrt(c)*c)/a^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^2/c/sign(tan((f*x+exp(1))/2)-1)-1/6*(-3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5+6*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+4*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3-9*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-12*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*c^2)/a^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^3/c/sign(tan((f*x+exp(1))/2)-1)+5/16*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/a^2/sqrt(-c)/c/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
331,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(-1/48*(-15*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5+33*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+22*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3-51*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-66*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-11*sqrt(c)*c^2)/a^2/c^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^3/sign(tan((f*x+exp(1))/2)-1)+1/128*(-53*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7-179*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6-127*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5+195*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4-7*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+67*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))-121*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-15*sqrt(c)*c^3)/a^2/c^2/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2-2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^4/sign(tan((f*x+exp(1))/2)-1)+35/128*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/a^2/c^2/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1))","F(-2)",0
332,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*c)/10*(-10*((-cos(1/4*(2*f*x+2*exp(1)-pi))+1)/(cos(1/4*(2*f*x+2*exp(1)-pi))+1))^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))-5*((-cos(1/4*(2*f*x+2*exp(1)-pi))+1)/(cos(1/4*(2*f*x+2*exp(1)-pi))+1))^4*sign(sin(1/2*(f*x+exp(1))-1/4*pi))-sign(sin(1/2*(f*x+exp(1))-1/4*pi)))/a^3/((-cos(1/4*(2*f*x+2*exp(1)-pi))+1)/(cos(1/4*(2*f*x+2*exp(1)-pi))+1)-1)^5/f","F(-2)",0
337,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((870*c*sqrt(2)*atan(sqrt(c)/sqrt(-c))-1230*c*atan(sqrt(c)/sqrt(-c))-850*sqrt(-c)*sqrt(2)*sqrt(c)+1203*sqrt(-c)*sqrt(c))/(4920*a^3*c*sqrt(-c)*sqrt(2)-6960*a^3*c*sqrt(-c))*sign(tan((f*x+exp(1))/2)-1)+2*(1/120*(105*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^9-435*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^8+580*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^7+620*sqrt(c)*c*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^6-1258*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^5-490*sqrt(c)*c^2*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^4+900*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^3+265*c^4*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+860*sqrt(c)*c^3*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+37*sqrt(c)*c^4)/a^3/(-(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))^2+2*sqrt(c)*(-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c*tan((f*x+exp(1))/2)^2+c))+c)^5/sign(tan((f*x+exp(1))/2)-1)+1/8*atan((-sqrt(c)*tan((f*x+exp(1))/2)+sqrt(c)+sqrt(c*tan((f*x+exp(1))/2)^2+c))/sqrt(2)/sqrt(-c))/sqrt(2)/a^3/sqrt(-c)/sign(tan((f*x+exp(1))/2)-1)))","F(-2)",0
338,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (8*pi/t_nostep/2)>(-8*pi/t_nostep/2)Discontinuities at zeroes of sin((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep-1)]Not invertible Error: Bad Argument Value","F(-2)",0
339,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (8*pi/t_nostep/2)>(-8*pi/t_nostep/2)Discontinuities at zeroes of sin((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep-1)]Evaluation time: 0.44Not invertible Error: Bad Argument Value","F(-2)",0
340,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-56*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2+72*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2-480*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2+64*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(64*f)^2+32*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-32*f)^2)","F(-2)",0
341,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-40*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2+24*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2-4*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(4*f)^2)","F(-2)",0
342,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(2*f)^2-8*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(8*f)^2)","F(-2)",0
343,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/2*(f*x+exp(1))-1/4*pi)^2/f","F(-2)",0
344,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2)*(1/2*ln(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2)/sign(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^3+tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi))))-ln(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1)/sign(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^3+tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))/sqrt(c)/f","F(-2)",0
345,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)-sqrt(2*a)/8*(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1/tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2)*sign(cos(1/2*(f*x+exp(1))-1/4*pi))/sqrt(2)/sqrt(c)/c/f/sign(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^3+tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi))))","F(-2)",0
346,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-112*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-288*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2+160*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2-16*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(16*f)^2-32*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(32*f)^2-16*a*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-16*f)^2)","F(-2)",0
349,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-24*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2-24*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2-32*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2-64*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(64*f)^2-32*a*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-32*f)^2)","F(-2)",0
350,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-24*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2-24*a*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2)","F(-2)",0
351,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-2*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(2*f)^2+8*a*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(8*f)^2)","F(-2)",0
352,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)4*sqrt(2*a)*(a*sqrt(c*tan(1/2*exp(1))^2+c)*(-25165824*tan(1/2*exp(1))^5-75497472*tan(1/2*exp(1))^4+83886080*tan(1/2*exp(1))^3+50331648*tan(1/2*exp(1))^2-25165824*tan(1/2*exp(1))-8388608)+a*sqrt(c*tan(1/2*exp(1))^2+c)*(25165824*tan(1/2*exp(1))^5+75497472*tan(1/2*exp(1))^4-83886080*tan(1/2*exp(1))^3-50331648*tan(1/2*exp(1))^2+25165824*tan(1/2*exp(1))+8388608)*tan(1/4*exp(1))^6+a*sqrt(c*tan(1/2*exp(1))^2+c)*(167772160*tan(1/2*exp(1))^6+503316480*tan(1/2*exp(1))^5-1006632960*tan(1/2*exp(1))^4-1677721600*tan(1/2*exp(1))^3+1509949440*tan(1/2*exp(1))^2+503316480*tan(1/2*exp(1)))*tan(1/4*exp(1))^3+a*sqrt(c*tan(1/2*exp(1))^2+c)*(377487360*tan(1/2*exp(1))^5+1132462080*tan(1/2*exp(1))^4-1258291200*tan(1/2*exp(1))^3-754974720*tan(1/2*exp(1))^2+377487360*tan(1/2*exp(1))+125829120)*tan(1/4*exp(1))^2+a*sqrt(c*tan(1/2*exp(1))^2+c)*(-50331648*tan(1/2*exp(1))^6-150994944*tan(1/2*exp(1))^5+301989888*tan(1/2*exp(1))^4+503316480*tan(1/2*exp(1))^3-452984832*tan(1/2*exp(1))^2-150994944*tan(1/2*exp(1)))*tan(1/4*exp(1))^5+a*sqrt(c*tan(1/2*exp(1))^2+c)*(-50331648*tan(1/2*exp(1))^6-150994944*tan(1/2*exp(1))^5+301989888*tan(1/2*exp(1))^4+503316480*tan(1/2*exp(1))^3-452984832*tan(1/2*exp(1))^2-150994944*tan(1/2*exp(1)))*tan(1/4*exp(1))+a*sqrt(c*tan(1/2*exp(1))^2+c)*(-377487360*tan(1/2*exp(1))^5-1132462080*tan(1/2*exp(1))^4+1258291200*tan(1/2*exp(1))^3+754974720*tan(1/2*exp(1))^2-377487360*tan(1/2*exp(1))-125829120)*tan(1/4*exp(1))^4)*ln(abs(-2*tan(1/2*exp(1))^3+6*tan(1/2*exp(1))^2+(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(tan(1/2*exp(1))^3+3*tan(1/2*exp(1))^2-3*tan(1/2*exp(1))-1)+6*tan(1/2*exp(1))-2))/f/(-8388608*sqrt(2)*c*tan(1/2*exp(1))^7+8388608*sqrt(2)*c+(-8388608*sqrt(2)*c*tan(1/2*exp(1))^7-25165824*sqrt(2)*c*tan(1/2*exp(1))^6+8388608*sqrt(2)*c*tan(1/2*exp(1))^5-41943040*sqrt(2)*c*tan(1/2*exp(1))^4+41943040*sqrt(2)*c*tan(1/2*exp(1))^3-8388608*sqrt(2)*c*tan(1/2*exp(1))^2+8388608*sqrt(2)*c+25165824*sqrt(2)*c*tan(1/2*exp(1)))*tan(1/4*exp(1))^6+(-25165824*sqrt(2)*c*tan(1/2*exp(1))^7-75497472*sqrt(2)*c*tan(1/2*exp(1))^6+25165824*sqrt(2)*c*tan(1/2*exp(1))^5-125829120*sqrt(2)*c*tan(1/2*exp(1))^4+125829120*sqrt(2)*c*tan(1/2*exp(1))^3-25165824*sqrt(2)*c*tan(1/2*exp(1))^2+25165824*sqrt(2)*c+75497472*sqrt(2)*c*tan(1/2*exp(1)))*tan(1/4*exp(1))^2+(-25165824*sqrt(2)*c*tan(1/2*exp(1))^7-75497472*sqrt(2)*c*tan(1/2*exp(1))^6+25165824*sqrt(2)*c*tan(1/2*exp(1))^5-125829120*sqrt(2)*c*tan(1/2*exp(1))^4+125829120*sqrt(2)*c*tan(1/2*exp(1))^3-25165824*sqrt(2)*c*tan(1/2*exp(1))^2+25165824*sqrt(2)*c+75497472*sqrt(2)*c*tan(1/2*exp(1)))*tan(1/4*exp(1))^4-25165824*sqrt(2)*c*tan(1/2*exp(1))^6+8388608*sqrt(2)*c*tan(1/2*exp(1))^5-41943040*sqrt(2)*c*tan(1/2*exp(1))^4+41943040*sqrt(2)*c*tan(1/2*exp(1))^3-8388608*sqrt(2)*c*tan(1/2*exp(1))^2+25165824*sqrt(2)*c*tan(1/2*exp(1)))","F(-2)",0
353,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-80*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-480*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2-160*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2-64*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(64*f)^2-768*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(256*f)^2-384*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(384*f)^2-384*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-128*f)^2-256*a^2*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-256*f)^2)","F(-2)",0
359,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-80*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-480*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2-160*a^2*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2)","F(-2)",0
360,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-24*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2-24*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2+32*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2+64*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(64*f)^2+32*a^2*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-32*f)^2)","F(-2)",0
361,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-40*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2+24*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2+4*a^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(4*f)^2)","F(-2)",0
362,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-4480*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-8064*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-4480*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-896*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2-2560*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(512*f)^2-9216*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(1024*f)^2-7680*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(1536*f)^2-2048*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(8*f*x+8*exp(1))/(2048*f)^2-4608*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-512*f)^2-5120*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-1024*f)^2-1536*a^3*c^4*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-6*f*x-6*exp(1))/(-1536*f)^2)","F(-2)",0
370,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-4480*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(128*f)^2-8064*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(384*f)^2-4480*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(640*f)^2-896*a^3*c^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(7*f*x+7*exp(1))/(896*f)^2)","F(-2)",0
371,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-80*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-480*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2-160*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2+64*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(64*f)^2+768*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(256*f)^2+384*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(6*f*x+6*exp(1))/(384*f)^2+384*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-128*f)^2+256*a^3*c^2*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-4*f*x-4*exp(1))/(-256*f)^2)","F(-2)",0
372,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-112*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(16*f)^2-288*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(96*f)^2+160*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(5*f*x+5*exp(1))/(160*f)^2+16*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(16*f)^2+32*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(32*f)^2+16*a^3*c*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-16*f)^2)","F(-2)",0
373,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-56*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/(8*f)^2+72*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(3*f*x+3*exp(1))/(24*f)^2+480*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/(32*f)^2-64*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(4*f*x+4*exp(1))/(64*f)^2-32*a^3*f*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(-2*f*x-2*exp(1))/(-32*f)^2)","F(-2)",0
374,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)4*sqrt(2*c)*(c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(54043195528445952*tan(1/2*exp(1))^5-162129586585337856*tan(1/2*exp(1))^4-180143985094819840*tan(1/2*exp(1))^3+108086391056891904*tan(1/2*exp(1))^2+54043195528445952*tan(1/2*exp(1))-18014398509481984)+c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(108086391056891904*tan(1/2*exp(1))^6-324259173170675712*tan(1/2*exp(1))^5-648518346341351424*tan(1/2*exp(1))^4+1080863910568919040*tan(1/2*exp(1))^3+972777519512027136*tan(1/2*exp(1))^2-324259173170675712*tan(1/2*exp(1)))*tan(1/4*exp(1))^5+c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(108086391056891904*tan(1/2*exp(1))^6-324259173170675712*tan(1/2*exp(1))^5-648518346341351424*tan(1/2*exp(1))^4+1080863910568919040*tan(1/2*exp(1))^3+972777519512027136*tan(1/2*exp(1))^2-324259173170675712*tan(1/2*exp(1)))*tan(1/4*exp(1))+c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(810647932926689280*tan(1/2*exp(1))^5-2431943798780067840*tan(1/2*exp(1))^4-2702159776422297600*tan(1/2*exp(1))^3+1621295865853378560*tan(1/2*exp(1))^2+810647932926689280*tan(1/2*exp(1))-270215977642229760)*tan(1/4*exp(1))^4+c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(-54043195528445952*tan(1/2*exp(1))^5+162129586585337856*tan(1/2*exp(1))^4+180143985094819840*tan(1/2*exp(1))^3-108086391056891904*tan(1/2*exp(1))^2-54043195528445952*tan(1/2*exp(1))+18014398509481984)*tan(1/4*exp(1))^6+c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(-360287970189639680*tan(1/2*exp(1))^6+1080863910568919040*tan(1/2*exp(1))^5+2161727821137838080*tan(1/2*exp(1))^4-3602879701896396800*tan(1/2*exp(1))^3-3242591731706757120*tan(1/2*exp(1))^2+1080863910568919040*tan(1/2*exp(1)))*tan(1/4*exp(1))^3+c^2*sqrt(a*tan(1/2*exp(1))^2+a)*(-810647932926689280*tan(1/2*exp(1))^5+2431943798780067840*tan(1/2*exp(1))^4+2702159776422297600*tan(1/2*exp(1))^3-1621295865853378560*tan(1/2*exp(1))^2-810647932926689280*tan(1/2*exp(1))+270215977642229760)*tan(1/4*exp(1))^2)*ln(abs(2*tan(1/2*exp(1))^3+6*tan(1/2*exp(1))^2+(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(tan(1/2*exp(1))^3-3*tan(1/2*exp(1))^2-3*tan(1/2*exp(1))+1)-6*tan(1/2*exp(1))-2))/f/(-9007199254740992*sqrt(2)*a*tan(1/2*exp(1))^7-9007199254740992*sqrt(2)*a+(-9007199254740992*sqrt(2)*a*tan(1/2*exp(1))^7+27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^6+9007199254740992*sqrt(2)*a*tan(1/2*exp(1))^5+45035996273704960*sqrt(2)*a*tan(1/2*exp(1))^4+45035996273704960*sqrt(2)*a*tan(1/2*exp(1))^3+9007199254740992*sqrt(2)*a*tan(1/2*exp(1))^2-9007199254740992*sqrt(2)*a+27021597764222976*sqrt(2)*a*tan(1/2*exp(1)))*tan(1/4*exp(1))^6+(-27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^7+81064793292668928*sqrt(2)*a*tan(1/2*exp(1))^6+27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^5+135107988821114880*sqrt(2)*a*tan(1/2*exp(1))^4+135107988821114880*sqrt(2)*a*tan(1/2*exp(1))^3+27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^2-27021597764222976*sqrt(2)*a+81064793292668928*sqrt(2)*a*tan(1/2*exp(1)))*tan(1/4*exp(1))^2+(-27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^7+81064793292668928*sqrt(2)*a*tan(1/2*exp(1))^6+27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^5+135107988821114880*sqrt(2)*a*tan(1/2*exp(1))^4+135107988821114880*sqrt(2)*a*tan(1/2*exp(1))^3+27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^2-27021597764222976*sqrt(2)*a+81064793292668928*sqrt(2)*a*tan(1/2*exp(1)))*tan(1/4*exp(1))^4+27021597764222976*sqrt(2)*a*tan(1/2*exp(1))^6+9007199254740992*sqrt(2)*a*tan(1/2*exp(1))^5+45035996273704960*sqrt(2)*a*tan(1/2*exp(1))^4+45035996273704960*sqrt(2)*a*tan(1/2*exp(1))^3+9007199254740992*sqrt(2)*a*tan(1/2*exp(1))^2+27021597764222976*sqrt(2)*a*tan(1/2*exp(1)))","F(-2)",0
384,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)4*sqrt(2*c)*(c*sqrt(a*tan(1/2*exp(1))^2+a)*(25165824*tan(1/2*exp(1))^5-75497472*tan(1/2*exp(1))^4-83886080*tan(1/2*exp(1))^3+50331648*tan(1/2*exp(1))^2+25165824*tan(1/2*exp(1))-8388608)+c*sqrt(a*tan(1/2*exp(1))^2+a)*(50331648*tan(1/2*exp(1))^6-150994944*tan(1/2*exp(1))^5-301989888*tan(1/2*exp(1))^4+503316480*tan(1/2*exp(1))^3+452984832*tan(1/2*exp(1))^2-150994944*tan(1/2*exp(1)))*tan(1/4*exp(1))^5+c*sqrt(a*tan(1/2*exp(1))^2+a)*(50331648*tan(1/2*exp(1))^6-150994944*tan(1/2*exp(1))^5-301989888*tan(1/2*exp(1))^4+503316480*tan(1/2*exp(1))^3+452984832*tan(1/2*exp(1))^2-150994944*tan(1/2*exp(1)))*tan(1/4*exp(1))+c*sqrt(a*tan(1/2*exp(1))^2+a)*(377487360*tan(1/2*exp(1))^5-1132462080*tan(1/2*exp(1))^4-1258291200*tan(1/2*exp(1))^3+754974720*tan(1/2*exp(1))^2+377487360*tan(1/2*exp(1))-125829120)*tan(1/4*exp(1))^4+c*sqrt(a*tan(1/2*exp(1))^2+a)*(-25165824*tan(1/2*exp(1))^5+75497472*tan(1/2*exp(1))^4+83886080*tan(1/2*exp(1))^3-50331648*tan(1/2*exp(1))^2-25165824*tan(1/2*exp(1))+8388608)*tan(1/4*exp(1))^6+c*sqrt(a*tan(1/2*exp(1))^2+a)*(-167772160*tan(1/2*exp(1))^6+503316480*tan(1/2*exp(1))^5+1006632960*tan(1/2*exp(1))^4-1677721600*tan(1/2*exp(1))^3-1509949440*tan(1/2*exp(1))^2+503316480*tan(1/2*exp(1)))*tan(1/4*exp(1))^3+c*sqrt(a*tan(1/2*exp(1))^2+a)*(-377487360*tan(1/2*exp(1))^5+1132462080*tan(1/2*exp(1))^4+1258291200*tan(1/2*exp(1))^3-754974720*tan(1/2*exp(1))^2-377487360*tan(1/2*exp(1))+125829120)*tan(1/4*exp(1))^2)*ln(abs(2*tan(1/2*exp(1))^3+6*tan(1/2*exp(1))^2+(tan(1/2*(1/2*f*x+2*exp(1)))-1/tan(1/2*(1/2*f*x+2*exp(1))))*(tan(1/2*exp(1))^3-3*tan(1/2*exp(1))^2-3*tan(1/2*exp(1))+1)-6*tan(1/2*exp(1))-2))/f/(-8388608*sqrt(2)*a*tan(1/2*exp(1))^7-8388608*sqrt(2)*a+(-8388608*sqrt(2)*a*tan(1/2*exp(1))^7+25165824*sqrt(2)*a*tan(1/2*exp(1))^6+8388608*sqrt(2)*a*tan(1/2*exp(1))^5+41943040*sqrt(2)*a*tan(1/2*exp(1))^4+41943040*sqrt(2)*a*tan(1/2*exp(1))^3+8388608*sqrt(2)*a*tan(1/2*exp(1))^2-8388608*sqrt(2)*a+25165824*sqrt(2)*a*tan(1/2*exp(1)))*tan(1/4*exp(1))^6+(-25165824*sqrt(2)*a*tan(1/2*exp(1))^7+75497472*sqrt(2)*a*tan(1/2*exp(1))^6+25165824*sqrt(2)*a*tan(1/2*exp(1))^5+125829120*sqrt(2)*a*tan(1/2*exp(1))^4+125829120*sqrt(2)*a*tan(1/2*exp(1))^3+25165824*sqrt(2)*a*tan(1/2*exp(1))^2-25165824*sqrt(2)*a+75497472*sqrt(2)*a*tan(1/2*exp(1)))*tan(1/4*exp(1))^2+(-25165824*sqrt(2)*a*tan(1/2*exp(1))^7+75497472*sqrt(2)*a*tan(1/2*exp(1))^6+25165824*sqrt(2)*a*tan(1/2*exp(1))^5+125829120*sqrt(2)*a*tan(1/2*exp(1))^4+125829120*sqrt(2)*a*tan(1/2*exp(1))^3+25165824*sqrt(2)*a*tan(1/2*exp(1))^2-25165824*sqrt(2)*a+75497472*sqrt(2)*a*tan(1/2*exp(1)))*tan(1/4*exp(1))^4+25165824*sqrt(2)*a*tan(1/2*exp(1))^6+8388608*sqrt(2)*a*tan(1/2*exp(1))^5+41943040*sqrt(2)*a*tan(1/2*exp(1))^4+41943040*sqrt(2)*a*tan(1/2*exp(1))^3+8388608*sqrt(2)*a*tan(1/2*exp(1))^2+25165824*sqrt(2)*a*tan(1/2*exp(1)))","F(-2)",0
385,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)4*sqrt(2*c)*(-1/2*ln(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1)+1/2*ln(abs(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-1)))*sign(sin(1/2*(f*x+exp(1))-1/4*pi))/sqrt(2)/sqrt(a)/f/sign(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4-1)","F(-2)",0
386,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
387,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
389,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-2,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (8*pi/x/2)>(-8*pi/x/2)sqrt(2*c)*sqrt(2)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2/sqrt(a)/(tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-1)^2/a/f/sign(-tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+1)","F(-2)",0
393,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
394,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
395,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
396,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
402,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
403,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
404,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
405,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\int -{\left(c \sin\left(f x + e\right) - c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(-(c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
406,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(c \sin\left(f x + e\right) - c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
407,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""giac"")","\int -{\left(c \sin\left(f x + e\right) - c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(-(c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m, x)","F",0
408,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""giac"")","\int -\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}\,{d x}"," ",0,"integrate(-(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
409,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(c \sin\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^2, x)","F",0
410,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""giac"")","\int -\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(c \sin\left(f x + e\right) - c\right)}^{3}}\,{d x}"," ",0,"integrate(-(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^3, x)","F",0
411,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(5/2)*(a*sin(f*x + e) + a)^m, x)","F",0
412,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
413,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
414,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
415,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
416,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
417,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
418,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c \sin\left(f x + e\right) + c\right)}^{m}}{\sqrt{-a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((c*sin(f*x + e) + c)^m/sqrt(-a*sin(f*x + e) + a), x)","F",0
419,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3), x)","F",0
420,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
421,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1), x)","F",0
422,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^m, x)","F",0
423,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1), x)","F",0
424,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2), x)","F",0
425,1,272,0,0.176687," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","-\frac{a d^{4} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{a c d^{3} \cos\left(3 \, f x + 3 \, e\right)}{3 \, f} + \frac{a c d^{3} \sin\left(4 \, f x + 4 \, e\right)}{8 \, f} + \frac{a d^{4} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{8} \, {\left(8 \, a c^{4} + 24 \, a c^{2} d^{2} + 3 \, a d^{4}\right)} x + \frac{1}{2} \, {\left(4 \, a c^{3} d + 3 \, a c d^{3}\right)} x + \frac{{\left(24 \, a c^{2} d^{2} + 5 \, a d^{4}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(8 \, a c^{4} + 36 \, a c^{2} d^{2} + 5 \, a d^{4}\right)} \cos\left(f x + e\right)}{8 \, f} - \frac{{\left(4 \, a c^{3} d + 3 \, a c d^{3}\right)} \cos\left(f x + e\right)}{f} - \frac{{\left(a c^{3} d + a c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{f} - \frac{{\left(6 \, a c^{2} d^{2} + a d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-1/80*a*d^4*cos(5*f*x + 5*e)/f + 1/3*a*c*d^3*cos(3*f*x + 3*e)/f + 1/8*a*c*d^3*sin(4*f*x + 4*e)/f + 1/32*a*d^4*sin(4*f*x + 4*e)/f + 1/8*(8*a*c^4 + 24*a*c^2*d^2 + 3*a*d^4)*x + 1/2*(4*a*c^3*d + 3*a*c*d^3)*x + 1/48*(24*a*c^2*d^2 + 5*a*d^4)*cos(3*f*x + 3*e)/f - 1/8*(8*a*c^4 + 36*a*c^2*d^2 + 5*a*d^4)*cos(f*x + e)/f - (4*a*c^3*d + 3*a*c*d^3)*cos(f*x + e)/f - (a*c^3*d + a*c*d^3)*sin(2*f*x + 2*e)/f - 1/4*(6*a*c^2*d^2 + a*d^4)*sin(2*f*x + 2*e)/f","A",0
426,1,191,0,0.471320," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{a c d^{2} \cos\left(3 \, f x + 3 \, e\right)}{4 \, f} + \frac{a d^{3} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} + \frac{a d^{3} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{3 \, a c d^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{2} \, {\left(2 \, a c^{3} + 3 \, a c d^{2}\right)} x + \frac{3}{8} \, {\left(4 \, a c^{2} d + a d^{3}\right)} x - \frac{{\left(4 \, a c^{3} + 9 \, a c d^{2}\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{3 \, {\left(4 \, a c^{2} d + a d^{3}\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(3 \, a c^{2} d + a d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/4*a*c*d^2*cos(3*f*x + 3*e)/f + 1/12*a*d^3*cos(3*f*x + 3*e)/f + 1/32*a*d^3*sin(4*f*x + 4*e)/f - 3/4*a*c*d^2*sin(2*f*x + 2*e)/f + 1/2*(2*a*c^3 + 3*a*c*d^2)*x + 3/8*(4*a*c^2*d + a*d^3)*x - 1/4*(4*a*c^3 + 9*a*c*d^2)*cos(f*x + e)/f - 3/4*(4*a*c^2*d + a*d^3)*cos(f*x + e)/f - 1/4*(3*a*c^2*d + a*d^3)*sin(2*f*x + 2*e)/f","A",0
427,1,117,0,0.160088," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","a c d x + \frac{a d^{2} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{2 \, a c d \cos\left(f x + e\right)}{f} - \frac{a c d \sin\left(2 \, f x + 2 \, e\right)}{2 \, f} - \frac{a d^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{2} \, {\left(2 \, a c^{2} + a d^{2}\right)} x - \frac{{\left(4 \, a c^{2} + 3 \, a d^{2}\right)} \cos\left(f x + e\right)}{4 \, f}"," ",0,"a*c*d*x + 1/12*a*d^2*cos(3*f*x + 3*e)/f - 2*a*c*d*cos(f*x + e)/f - 1/2*a*c*d*sin(2*f*x + 2*e)/f - 1/4*a*d^2*sin(2*f*x + 2*e)/f + 1/2*(2*a*c^2 + a*d^2)*x - 1/4*(4*a*c^2 + 3*a*d^2)*cos(f*x + e)/f","A",0
428,1,55,0,0.224908," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""giac"")","a c x + \frac{1}{2} \, a d x - \frac{a c \cos\left(f x + e\right)}{f} - \frac{a d \cos\left(f x + e\right)}{f} - \frac{a d \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"a*c*x + 1/2*a*d*x - a*c*cos(f*x + e)/f - a*d*cos(f*x + e)/f - 1/4*a*d*sin(2*f*x + 2*e)/f","A",0
429,1,17,0,0.169002," ","integrate(a+a*sin(f*x+e),x, algorithm=""giac"")","a x - \frac{a \cos\left(f x + e\right)}{f}"," ",0,"a*x - a*cos(f*x + e)/f","A",0
430,1,86,0,0.222558," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} a}{d} - \frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} {\left(a c - a d\right)}}{\sqrt{c^{2} - d^{2}} d}}{f}"," ",0,"((f*x + e)*a/d - 2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*(a*c - a*d)/(sqrt(c^2 - d^2)*d))/f","A",0
431,1,129,0,0.339673," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} a}{\sqrt{c^{2} - d^{2}} {\left(c + d\right)}} - \frac{a d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a c}{{\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)} {\left(c^{2} + c d\right)}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*a/(sqrt(c^2 - d^2)*(c + d)) - (a*d*tan(1/2*f*x + 1/2*e) + a*c)/((c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)*(c^2 + c*d)))/f","A",0
432,1,384,0,0.361774," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} {\left(2 \, a c - a d\right)}}{{\left(c^{3} + c^{2} d - c d^{2} - d^{3}\right)} \sqrt{c^{2} - d^{2}}} - \frac{3 \, a c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, a c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 6 \, a c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a c^{4} - 2 \, a c^{3} d - a c^{2} d^{2}}{{\left(c^{5} + c^{4} d - c^{3} d^{2} - c^{2} d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*(2*a*c - a*d)/((c^3 + c^2*d - c*d^2 - d^3)*sqrt(c^2 - d^2)) - (3*a*c^3*d*tan(1/2*f*x + 1/2*e)^3 - 2*a*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 - 2*a*c*d^3*tan(1/2*f*x + 1/2*e)^3 + 2*a*c^4*tan(1/2*f*x + 1/2*e)^2 - 2*a*c^3*d*tan(1/2*f*x + 1/2*e)^2 + 3*a*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 - 4*a*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 2*a*d^4*tan(1/2*f*x + 1/2*e)^2 + 5*a*c^3*d*tan(1/2*f*x + 1/2*e) - 6*a*c^2*d^2*tan(1/2*f*x + 1/2*e) - 2*a*c*d^3*tan(1/2*f*x + 1/2*e) + 2*a*c^4 - 2*a*c^3*d - a*c^2*d^2)/((c^5 + c^4*d - c^3*d^2 - c^2*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
433,1,808,0,1.382293," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a c^{2} - 2 \, a c d + a d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{5} + c^{4} d - 2 \, c^{3} d^{2} - 2 \, c^{2} d^{3} + c d^{4} + d^{5}\right)} \sqrt{c^{2} - d^{2}}} - \frac{12 \, a c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 15 \, a c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 12 \, a c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 \, a c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 \, a c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 \, a c^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 12 \, a c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, a c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 51 \, a c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 18 \, a c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 18 \, a c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 36 \, a c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 72 \, a c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 30 \, a c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, a d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a c^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 24 \, a c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, a c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 84 \, a c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18 \, a c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 24 \, a c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 57 \, a c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 \, a c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a c^{7} - 12 \, a c^{6} d - 2 \, a c^{5} d^{2} + 3 \, a c^{4} d^{3} + 2 \, a c^{3} d^{4}}{{\left(c^{8} + c^{7} d - 2 \, c^{6} d^{2} - 2 \, c^{5} d^{3} + c^{4} d^{4} + c^{3} d^{5}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(2*a*c^2 - 2*a*c*d + a*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^5 + c^4*d - 2*c^3*d^2 - 2*c^2*d^3 + c*d^4 + d^5)*sqrt(c^2 - d^2)) - (12*a*c^6*d*tan(1/2*f*x + 1/2*e)^5 - 15*a*c^5*d^2*tan(1/2*f*x + 1/2*e)^5 - 12*a*c^4*d^3*tan(1/2*f*x + 1/2*e)^5 + 6*a*c^3*d^4*tan(1/2*f*x + 1/2*e)^5 + 6*a*c^2*d^5*tan(1/2*f*x + 1/2*e)^5 + 6*a*c^7*tan(1/2*f*x + 1/2*e)^4 - 12*a*c^6*d*tan(1/2*f*x + 1/2*e)^4 + 30*a*c^5*d^2*tan(1/2*f*x + 1/2*e)^4 - 51*a*c^4*d^3*tan(1/2*f*x + 1/2*e)^4 - 18*a*c^3*d^4*tan(1/2*f*x + 1/2*e)^4 + 18*a*c^2*d^5*tan(1/2*f*x + 1/2*e)^4 + 12*a*c*d^6*tan(1/2*f*x + 1/2*e)^4 + 36*a*c^6*d*tan(1/2*f*x + 1/2*e)^3 - 72*a*c^5*d^2*tan(1/2*f*x + 1/2*e)^3 + 12*a*c^4*d^3*tan(1/2*f*x + 1/2*e)^3 - 30*a*c^3*d^4*tan(1/2*f*x + 1/2*e)^3 + 4*a*c^2*d^5*tan(1/2*f*x + 1/2*e)^3 + 12*a*c*d^6*tan(1/2*f*x + 1/2*e)^3 + 8*a*d^7*tan(1/2*f*x + 1/2*e)^3 + 12*a*c^7*tan(1/2*f*x + 1/2*e)^2 - 24*a*c^6*d*tan(1/2*f*x + 1/2*e)^2 + 36*a*c^5*d^2*tan(1/2*f*x + 1/2*e)^2 - 84*a*c^4*d^3*tan(1/2*f*x + 1/2*e)^2 + 18*a*c^2*d^5*tan(1/2*f*x + 1/2*e)^2 + 12*a*c*d^6*tan(1/2*f*x + 1/2*e)^2 + 24*a*c^6*d*tan(1/2*f*x + 1/2*e) - 57*a*c^5*d^2*tan(1/2*f*x + 1/2*e) + 12*a*c^3*d^4*tan(1/2*f*x + 1/2*e) + 6*a*c^2*d^5*tan(1/2*f*x + 1/2*e) + 6*a*c^7 - 12*a*c^6*d - 2*a*c^5*d^2 + 3*a*c^4*d^3 + 2*a*c^3*d^4)/((c^8 + c^7*d - 2*c^6*d^2 - 2*c^5*d^3 + c^4*d^4 + c^3*d^5)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^3))/f","B",0
434,1,458,0,0.215094," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{a^{2} c d^{3} \cos\left(3 \, f x + 3 \, e\right)}{3 \, f} - \frac{a^{2} d^{4} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{a^{2} d^{4} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{16} \, {\left(8 \, a^{2} c^{4} + 64 \, a^{2} c^{3} d + 36 \, a^{2} c^{2} d^{2} + 48 \, a^{2} c d^{3} + 5 \, a^{2} d^{4}\right)} x + \frac{1}{8} \, {\left(8 \, a^{2} c^{4} + 24 \, a^{2} c^{2} d^{2} + 3 \, a^{2} d^{4}\right)} x - \frac{{\left(2 \, a^{2} c d^{3} + a^{2} d^{4}\right)} \cos\left(5 \, f x + 5 \, e\right)}{40 \, f} + \frac{{\left(8 \, a^{2} c^{3} d + 24 \, a^{2} c^{2} d^{2} + 10 \, a^{2} c d^{3} + 5 \, a^{2} d^{4}\right)} \cos\left(3 \, f x + 3 \, e\right)}{24 \, f} - \frac{{\left(8 \, a^{2} c^{4} + 12 \, a^{2} c^{3} d + 36 \, a^{2} c^{2} d^{2} + 10 \, a^{2} c d^{3} + 5 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(4 \, a^{2} c^{3} d + 3 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)}{f} + \frac{{\left(12 \, a^{2} c^{2} d^{2} + 16 \, a^{2} c d^{3} + 3 \, a^{2} d^{4}\right)} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} - \frac{{\left(16 \, a^{2} c^{4} + 128 \, a^{2} c^{3} d + 96 \, a^{2} c^{2} d^{2} + 128 \, a^{2} c d^{3} + 15 \, a^{2} d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f} - \frac{{\left(6 \, a^{2} c^{2} d^{2} + a^{2} d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/3*a^2*c*d^3*cos(3*f*x + 3*e)/f - 1/192*a^2*d^4*sin(6*f*x + 6*e)/f + 1/32*a^2*d^4*sin(4*f*x + 4*e)/f + 1/16*(8*a^2*c^4 + 64*a^2*c^3*d + 36*a^2*c^2*d^2 + 48*a^2*c*d^3 + 5*a^2*d^4)*x + 1/8*(8*a^2*c^4 + 24*a^2*c^2*d^2 + 3*a^2*d^4)*x - 1/40*(2*a^2*c*d^3 + a^2*d^4)*cos(5*f*x + 5*e)/f + 1/24*(8*a^2*c^3*d + 24*a^2*c^2*d^2 + 10*a^2*c*d^3 + 5*a^2*d^4)*cos(3*f*x + 3*e)/f - 1/4*(8*a^2*c^4 + 12*a^2*c^3*d + 36*a^2*c^2*d^2 + 10*a^2*c*d^3 + 5*a^2*d^4)*cos(f*x + e)/f - (4*a^2*c^3*d + 3*a^2*c*d^3)*cos(f*x + e)/f + 1/64*(12*a^2*c^2*d^2 + 16*a^2*c*d^3 + 3*a^2*d^4)*sin(4*f*x + 4*e)/f - 1/64*(16*a^2*c^4 + 128*a^2*c^3*d + 96*a^2*c^2*d^2 + 128*a^2*c*d^3 + 15*a^2*d^4)*sin(2*f*x + 2*e)/f - 1/4*(6*a^2*c^2*d^2 + a^2*d^4)*sin(2*f*x + 2*e)/f","A",0
435,1,324,0,0.212307," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{a^{2} d^{3} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{a^{2} d^{3} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{3 \, a^{2} c d^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{8} \, {\left(4 \, a^{2} c^{3} + 24 \, a^{2} c^{2} d + 9 \, a^{2} c d^{2} + 6 \, a^{2} d^{3}\right)} x + \frac{1}{2} \, {\left(2 \, a^{2} c^{3} + 3 \, a^{2} c d^{2}\right)} x + \frac{{\left(12 \, a^{2} c^{2} d + 24 \, a^{2} c d^{2} + 5 \, a^{2} d^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(16 \, a^{2} c^{3} + 18 \, a^{2} c^{2} d + 36 \, a^{2} c d^{2} + 5 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)}{8 \, f} - \frac{3 \, {\left(4 \, a^{2} c^{2} d + a^{2} d^{3}\right)} \cos\left(f x + e\right)}{4 \, f} + \frac{{\left(3 \, a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{{\left(a^{2} c^{3} + 6 \, a^{2} c^{2} d + 3 \, a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-1/80*a^2*d^3*cos(5*f*x + 5*e)/f + 1/12*a^2*d^3*cos(3*f*x + 3*e)/f - 3/4*a^2*c*d^2*sin(2*f*x + 2*e)/f + 1/8*(4*a^2*c^3 + 24*a^2*c^2*d + 9*a^2*c*d^2 + 6*a^2*d^3)*x + 1/2*(2*a^2*c^3 + 3*a^2*c*d^2)*x + 1/48*(12*a^2*c^2*d + 24*a^2*c*d^2 + 5*a^2*d^3)*cos(3*f*x + 3*e)/f - 1/8*(16*a^2*c^3 + 18*a^2*c^2*d + 36*a^2*c*d^2 + 5*a^2*d^3)*cos(f*x + e)/f - 3/4*(4*a^2*c^2*d + a^2*d^3)*cos(f*x + e)/f + 1/32*(3*a^2*c*d^2 + 2*a^2*d^3)*sin(4*f*x + 4*e)/f - 1/4*(a^2*c^3 + 6*a^2*c^2*d + 3*a^2*c*d^2 + 2*a^2*d^3)*sin(2*f*x + 2*e)/f","A",0
436,1,208,0,0.351657," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} c d \cos\left(f x + e\right)}{f} + \frac{a^{2} d^{2} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{a^{2} d^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{8} \, {\left(4 \, a^{2} c^{2} + 16 \, a^{2} c d + 3 \, a^{2} d^{2}\right)} x + \frac{1}{2} \, {\left(2 \, a^{2} c^{2} + a^{2} d^{2}\right)} x + \frac{{\left(a^{2} c d + a^{2} d^{2}\right)} \cos\left(3 \, f x + 3 \, e\right)}{6 \, f} - \frac{{\left(4 \, a^{2} c^{2} + 3 \, a^{2} c d + 3 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)}{2 \, f} - \frac{{\left(a^{2} c^{2} + 4 \, a^{2} c d + a^{2} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-2*a^2*c*d*cos(f*x + e)/f + 1/32*a^2*d^2*sin(4*f*x + 4*e)/f - 1/4*a^2*d^2*sin(2*f*x + 2*e)/f + 1/8*(4*a^2*c^2 + 16*a^2*c*d + 3*a^2*d^2)*x + 1/2*(2*a^2*c^2 + a^2*d^2)*x + 1/6*(a^2*c*d + a^2*d^2)*cos(3*f*x + 3*e)/f - 1/2*(4*a^2*c^2 + 3*a^2*c*d + 3*a^2*d^2)*cos(f*x + e)/f - 1/4*(a^2*c^2 + 4*a^2*c*d + a^2*d^2)*sin(2*f*x + 2*e)/f","A",0
437,1,109,0,0.170769," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e)),x, algorithm=""giac"")","a^{2} c x + \frac{a^{2} d \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{a^{2} d \cos\left(f x + e\right)}{f} + \frac{1}{2} \, {\left(a^{2} c + 2 \, a^{2} d\right)} x - \frac{{\left(8 \, a^{2} c + 3 \, a^{2} d\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(a^{2} c + 2 \, a^{2} d\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"a^2*c*x + 1/12*a^2*d*cos(3*f*x + 3*e)/f - a^2*d*cos(f*x + e)/f + 1/2*(a^2*c + 2*a^2*d)*x - 1/4*(8*a^2*c + 3*a^2*d)*cos(f*x + e)/f - 1/4*(a^2*c + 2*a^2*d)*sin(2*f*x + 2*e)/f","A",0
438,1,40,0,0.159619," ","integrate((a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{2} \, a^{2} x - \frac{2 \, a^{2} \cos\left(f x + e\right)}{f} - \frac{a^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"3/2*a^2*x - 2*a^2*cos(f*x + e)/f - 1/4*a^2*sin(2*f*x + 2*e)/f","A",0
439,1,136,0,0.208674," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} c - 2 \, a^{2} d\right)} {\left(f x + e\right)}}{d^{2}} + \frac{2 \, a^{2}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} d} - \frac{2 \, {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} d^{2}}}{f}"," ",0,"-((a^2*c - 2*a^2*d)*(f*x + e)/d^2 + 2*a^2/((tan(1/2*f*x + 1/2*e)^2 + 1)*d) - 2*(a^2*c^2 - 2*a^2*c*d + a^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*d^2))/f","A",0
440,1,205,0,0.219803," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} a^{2}}{d^{2}} - \frac{2 \, {\left(a^{2} c^{2} + a^{2} c d - 2 \, a^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c d^{2} + d^{3}\right)} \sqrt{c^{2} - d^{2}}} + \frac{2 \, {\left(a^{2} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{2} c^{2} - a^{2} c d\right)}}{{\left(c^{2} d + c d^{2}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}}}{f}"," ",0,"((f*x + e)*a^2/d^2 - 2*(a^2*c^2 + a^2*c*d - 2*a^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c*d^2 + d^3)*sqrt(c^2 - d^2)) + 2*(a^2*c*d*tan(1/2*f*x + 1/2*e) - a^2*d^2*tan(1/2*f*x + 1/2*e) + a^2*c^2 - a^2*c*d)/((c^2*d + c*d^2)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)))/f","A",0
441,1,348,0,0.260861," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} a^{2}}{{\left(c^{2} + 2 \, c d + d^{2}\right)} \sqrt{c^{2} - d^{2}}} + \frac{a^{2} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a^{2} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a^{2} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{2} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 8 \, a^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{2} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a^{2} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 4 \, a^{2} c^{3} - a^{2} c^{2} d}{{\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"(3*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*a^2/((c^2 + 2*c*d + d^2)*sqrt(c^2 - d^2)) + (a^2*c^3*tan(1/2*f*x + 1/2*e)^3 - 4*a^2*c^2*d*tan(1/2*f*x + 1/2*e)^3 - 2*a^2*c*d^2*tan(1/2*f*x + 1/2*e)^3 - 4*a^2*c^3*tan(1/2*f*x + 1/2*e)^2 - a^2*c^2*d*tan(1/2*f*x + 1/2*e)^2 - 8*a^2*c*d^2*tan(1/2*f*x + 1/2*e)^2 - 2*a^2*d^3*tan(1/2*f*x + 1/2*e)^2 - a^2*c^3*tan(1/2*f*x + 1/2*e) - 12*a^2*c^2*d*tan(1/2*f*x + 1/2*e) - 2*a^2*c*d^2*tan(1/2*f*x + 1/2*e) - 4*a^2*c^3 - a^2*c^2*d)/((c^4 + 2*c^3*d + c^2*d^2)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
442,1,781,0,0.589021," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, a^{2} c - 2 \, a^{2} d\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{4} + 2 \, c^{3} d - 2 \, c d^{3} - d^{4}\right)} \sqrt{c^{2} - d^{2}}} + \frac{3 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{2} c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 12 \, a^{2} c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 \, a^{2} c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 12 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 9 \, a^{2} c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 54 \, a^{2} c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 24 \, a^{2} c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 36 \, a^{2} c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a^{2} c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 72 \, a^{2} c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 42 \, a^{2} c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 12 \, a^{2} c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, a^{2} c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 24 \, a^{2} c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, a^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 24 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{2} c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 72 \, a^{2} c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 66 \, a^{2} c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, a^{2} c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{2} c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 54 \, a^{2} c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 42 \, a^{2} c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 24 \, a^{2} c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{2} c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a^{2} c^{6} + 7 \, a^{2} c^{5} d + 6 \, a^{2} c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3}}{{\left(c^{7} + 2 \, c^{6} d - 2 \, c^{4} d^{3} - c^{3} d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(3*a^2*c - 2*a^2*d)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^4 + 2*c^3*d - 2*c*d^3 - d^4)*sqrt(c^2 - d^2)) + (3*a^2*c^6*tan(1/2*f*x + 1/2*e)^5 - 18*a^2*c^5*d*tan(1/2*f*x + 1/2*e)^5 + 12*a^2*c^3*d^3*tan(1/2*f*x + 1/2*e)^5 + 6*a^2*c^2*d^4*tan(1/2*f*x + 1/2*e)^5 - 12*a^2*c^6*tan(1/2*f*x + 1/2*e)^4 + 9*a^2*c^5*d*tan(1/2*f*x + 1/2*e)^4 - 54*a^2*c^4*d^2*tan(1/2*f*x + 1/2*e)^4 + 24*a^2*c^3*d^3*tan(1/2*f*x + 1/2*e)^4 + 36*a^2*c^2*d^4*tan(1/2*f*x + 1/2*e)^4 + 12*a^2*c*d^5*tan(1/2*f*x + 1/2*e)^4 - 72*a^2*c^5*d*tan(1/2*f*x + 1/2*e)^3 + 42*a^2*c^4*d^2*tan(1/2*f*x + 1/2*e)^3 - 12*a^2*c^3*d^3*tan(1/2*f*x + 1/2*e)^3 + 40*a^2*c^2*d^4*tan(1/2*f*x + 1/2*e)^3 + 24*a^2*c*d^5*tan(1/2*f*x + 1/2*e)^3 + 8*a^2*d^6*tan(1/2*f*x + 1/2*e)^3 - 24*a^2*c^6*tan(1/2*f*x + 1/2*e)^2 + 12*a^2*c^5*d*tan(1/2*f*x + 1/2*e)^2 - 72*a^2*c^4*d^2*tan(1/2*f*x + 1/2*e)^2 + 66*a^2*c^3*d^3*tan(1/2*f*x + 1/2*e)^2 + 36*a^2*c^2*d^4*tan(1/2*f*x + 1/2*e)^2 + 12*a^2*c*d^5*tan(1/2*f*x + 1/2*e)^2 - 3*a^2*c^6*tan(1/2*f*x + 1/2*e) - 54*a^2*c^5*d*tan(1/2*f*x + 1/2*e) + 42*a^2*c^4*d^2*tan(1/2*f*x + 1/2*e) + 24*a^2*c^3*d^3*tan(1/2*f*x + 1/2*e) + 6*a^2*c^2*d^4*tan(1/2*f*x + 1/2*e) - 12*a^2*c^6 + 7*a^2*c^5*d + 6*a^2*c^4*d^2 + 2*a^2*c^3*d^3)/((c^7 + 2*c^6*d - 2*c^4*d^3 - c^3*d^4)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^3))/f","B",0
443,1,1555,0,2.323465," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^5,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(12 \, a^{2} c^{2} - 16 \, a^{2} c d + 7 \, a^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{6} + 2 \, c^{5} d - c^{4} d^{2} - 4 \, c^{3} d^{3} - c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} \sqrt{c^{2} - d^{2}}} + \frac{12 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 96 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 45 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 96 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 24 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 48 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 24 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 48 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 84 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 432 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 411 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 336 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 24 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 192 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 72 \, a^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 12 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 480 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 597 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 480 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 836 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 208 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 152 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 256 \, a^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 96 \, a^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 144 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 204 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 1104 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 1617 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 48 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 406 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 256 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 184 \, a^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 128 \, a^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 48 \, a^{2} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 12 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 672 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1035 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 672 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1220 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 80 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 152 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 256 \, a^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 96 \, a^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 144 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 188 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 656 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1201 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 16 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 120 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 192 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 72 \, a^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, a^{2} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 288 \, a^{2} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 499 \, a^{2} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 32 \, a^{2} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 64 \, a^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 80 \, a^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 24 \, a^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 48 \, a^{2} c^{9} + 68 \, a^{2} c^{8} d + 16 \, a^{2} c^{7} d^{2} - 5 \, a^{2} c^{6} d^{3} - 16 \, a^{2} c^{5} d^{4} - 6 \, a^{2} c^{4} d^{5}}{{\left(c^{10} + 2 \, c^{9} d - c^{8} d^{2} - 4 \, c^{7} d^{3} - c^{6} d^{4} + 2 \, c^{5} d^{5} + c^{4} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{4}}}{12 \, f}"," ",0,"1/12*(3*(12*a^2*c^2 - 16*a^2*c*d + 7*a^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^6 + 2*c^5*d - c^4*d^2 - 4*c^3*d^3 - c^2*d^4 + 2*c*d^5 + d^6)*sqrt(c^2 - d^2)) + (12*a^2*c^9*tan(1/2*f*x + 1/2*e)^7 - 96*a^2*c^8*d*tan(1/2*f*x + 1/2*e)^7 + 45*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e)^7 + 96*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e)^7 + 24*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^7 - 48*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^7 - 24*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^7 - 48*a^2*c^9*tan(1/2*f*x + 1/2*e)^6 + 84*a^2*c^8*d*tan(1/2*f*x + 1/2*e)^6 - 432*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e)^6 + 411*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e)^6 + 336*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^6 - 24*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^6 - 192*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^6 - 72*a^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^6 + 12*a^2*c^9*tan(1/2*f*x + 1/2*e)^5 - 480*a^2*c^8*d*tan(1/2*f*x + 1/2*e)^5 + 597*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e)^5 - 480*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e)^5 + 836*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^5 + 208*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^5 - 152*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^5 - 256*a^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^5 - 96*a^2*c*d^8*tan(1/2*f*x + 1/2*e)^5 - 144*a^2*c^9*tan(1/2*f*x + 1/2*e)^4 + 204*a^2*c^8*d*tan(1/2*f*x + 1/2*e)^4 - 1104*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e)^4 + 1617*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e)^4 - 48*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^4 + 406*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^4 - 256*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^4 - 184*a^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^4 - 128*a^2*c*d^8*tan(1/2*f*x + 1/2*e)^4 - 48*a^2*d^9*tan(1/2*f*x + 1/2*e)^4 - 12*a^2*c^9*tan(1/2*f*x + 1/2*e)^3 - 672*a^2*c^8*d*tan(1/2*f*x + 1/2*e)^3 + 1035*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e)^3 - 672*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e)^3 + 1220*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^3 - 80*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^3 - 152*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^3 - 256*a^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^3 - 96*a^2*c*d^8*tan(1/2*f*x + 1/2*e)^3 - 144*a^2*c^9*tan(1/2*f*x + 1/2*e)^2 + 188*a^2*c^8*d*tan(1/2*f*x + 1/2*e)^2 - 656*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e)^2 + 1201*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e)^2 - 16*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^2 - 120*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^2 - 192*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^2 - 72*a^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^2 - 12*a^2*c^9*tan(1/2*f*x + 1/2*e) - 288*a^2*c^8*d*tan(1/2*f*x + 1/2*e) + 499*a^2*c^7*d^2*tan(1/2*f*x + 1/2*e) + 32*a^2*c^6*d^3*tan(1/2*f*x + 1/2*e) - 64*a^2*c^5*d^4*tan(1/2*f*x + 1/2*e) - 80*a^2*c^4*d^5*tan(1/2*f*x + 1/2*e) - 24*a^2*c^3*d^6*tan(1/2*f*x + 1/2*e) - 48*a^2*c^9 + 68*a^2*c^8*d + 16*a^2*c^7*d^2 - 5*a^2*c^6*d^3 - 16*a^2*c^5*d^4 - 6*a^2*c^4*d^5)/((c^10 + 2*c^9*d - c^8*d^2 - 4*c^7*d^3 - c^6*d^4 + 2*c^5*d^5 + c^4*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^4))/f","B",0
444,1,373,0,0.272390," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{a^{3} d^{3} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{a^{3} d^{3} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} - \frac{3 \, a^{3} c d^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{16} \, {\left(24 \, a^{3} c^{3} + 90 \, a^{3} c^{2} d + 54 \, a^{3} c d^{2} + 23 \, a^{3} d^{3}\right)} x + \frac{1}{2} \, {\left(2 \, a^{3} c^{3} + 3 \, a^{3} c d^{2}\right)} x - \frac{3 \, {\left(a^{3} c d^{2} + a^{3} d^{3}\right)} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{{\left(4 \, a^{3} c^{3} + 36 \, a^{3} c^{2} d + 51 \, a^{3} c d^{2} + 15 \, a^{3} d^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{3 \, {\left(10 \, a^{3} c^{3} + 18 \, a^{3} c^{2} d + 23 \, a^{3} c d^{2} + 5 \, a^{3} d^{3}\right)} \cos\left(f x + e\right)}{8 \, f} - \frac{3 \, {\left(4 \, a^{3} c^{2} d + a^{3} d^{3}\right)} \cos\left(f x + e\right)}{4 \, f} + \frac{3 \, {\left(2 \, a^{3} c^{2} d + 6 \, a^{3} c d^{2} + 3 \, a^{3} d^{3}\right)} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} - \frac{3 \, {\left(16 \, a^{3} c^{3} + 64 \, a^{3} c^{2} d + 48 \, a^{3} c d^{2} + 21 \, a^{3} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"1/12*a^3*d^3*cos(3*f*x + 3*e)/f - 1/192*a^3*d^3*sin(6*f*x + 6*e)/f - 3/4*a^3*c*d^2*sin(2*f*x + 2*e)/f + 1/16*(24*a^3*c^3 + 90*a^3*c^2*d + 54*a^3*c*d^2 + 23*a^3*d^3)*x + 1/2*(2*a^3*c^3 + 3*a^3*c*d^2)*x - 3/80*(a^3*c*d^2 + a^3*d^3)*cos(5*f*x + 5*e)/f + 1/48*(4*a^3*c^3 + 36*a^3*c^2*d + 51*a^3*c*d^2 + 15*a^3*d^3)*cos(3*f*x + 3*e)/f - 3/8*(10*a^3*c^3 + 18*a^3*c^2*d + 23*a^3*c*d^2 + 5*a^3*d^3)*cos(f*x + e)/f - 3/4*(4*a^3*c^2*d + a^3*d^3)*cos(f*x + e)/f + 3/64*(2*a^3*c^2*d + 6*a^3*c*d^2 + 3*a^3*d^3)*sin(4*f*x + 4*e)/f - 3/64*(16*a^3*c^3 + 64*a^3*c^2*d + 48*a^3*c*d^2 + 21*a^3*d^3)*sin(2*f*x + 2*e)/f","A",0
445,1,251,0,0.206451," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{a^{3} d^{2} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} - \frac{2 \, a^{3} c d \cos\left(f x + e\right)}{f} - \frac{a^{3} d^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{3}{8} \, {\left(4 \, a^{3} c^{2} + 10 \, a^{3} c d + 3 \, a^{3} d^{2}\right)} x + \frac{1}{2} \, {\left(2 \, a^{3} c^{2} + a^{3} d^{2}\right)} x + \frac{{\left(4 \, a^{3} c^{2} + 24 \, a^{3} c d + 17 \, a^{3} d^{2}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(30 \, a^{3} c^{2} + 36 \, a^{3} c d + 23 \, a^{3} d^{2}\right)} \cos\left(f x + e\right)}{8 \, f} + \frac{{\left(2 \, a^{3} c d + 3 \, a^{3} d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{{\left(3 \, a^{3} c^{2} + 8 \, a^{3} c d + 3 \, a^{3} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-1/80*a^3*d^2*cos(5*f*x + 5*e)/f - 2*a^3*c*d*cos(f*x + e)/f - 1/4*a^3*d^2*sin(2*f*x + 2*e)/f + 3/8*(4*a^3*c^2 + 10*a^3*c*d + 3*a^3*d^2)*x + 1/2*(2*a^3*c^2 + a^3*d^2)*x + 1/48*(4*a^3*c^2 + 24*a^3*c*d + 17*a^3*d^2)*cos(3*f*x + 3*e)/f - 1/8*(30*a^3*c^2 + 36*a^3*c*d + 23*a^3*d^2)*cos(f*x + e)/f + 1/32*(2*a^3*c*d + 3*a^3*d^2)*sin(4*f*x + 4*e)/f - 1/4*(3*a^3*c^2 + 8*a^3*c*d + 3*a^3*d^2)*sin(2*f*x + 2*e)/f","A",0
446,1,138,0,0.201308," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e)),x, algorithm=""giac"")","a^{3} c x - \frac{a^{3} d \cos\left(f x + e\right)}{f} + \frac{a^{3} d \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{3}{8} \, {\left(4 \, a^{3} c + 5 \, a^{3} d\right)} x + \frac{{\left(a^{3} c + 3 \, a^{3} d\right)} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{3 \, {\left(5 \, a^{3} c + 3 \, a^{3} d\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(3 \, a^{3} c + 4 \, a^{3} d\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"a^3*c*x - a^3*d*cos(f*x + e)/f + 1/32*a^3*d*sin(4*f*x + 4*e)/f + 3/8*(4*a^3*c + 5*a^3*d)*x + 1/12*(a^3*c + 3*a^3*d)*cos(3*f*x + 3*e)/f - 3/4*(5*a^3*c + 3*a^3*d)*cos(f*x + e)/f - 1/4*(3*a^3*c + 4*a^3*d)*sin(2*f*x + 2*e)/f","A",0
447,1,58,0,0.509722," ","integrate((a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{5}{2} \, a^{3} x + \frac{a^{3} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{15 \, a^{3} \cos\left(f x + e\right)}{4 \, f} - \frac{3 \, a^{3} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"5/2*a^3*x + 1/12*a^3*cos(3*f*x + 3*e)/f - 15/4*a^3*cos(f*x + e)/f - 3/4*a^3*sin(2*f*x + 2*e)/f","A",0
448,1,239,0,0.261009," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{3} c^{2} - 6 \, a^{3} c d + 7 \, a^{3} d^{2}\right)} {\left(f x + e\right)}}{d^{3}} - \frac{4 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} d^{3}} + \frac{2 \, {\left(a^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a^{3} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a^{3} c - 6 \, a^{3} d\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} d^{2}}}{2 \, f}"," ",0,"1/2*((2*a^3*c^2 - 6*a^3*c*d + 7*a^3*d^2)*(f*x + e)/d^3 - 4*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*d^3) + 2*(a^3*d*tan(1/2*f*x + 1/2*e)^3 + 2*a^3*c*tan(1/2*f*x + 1/2*e)^2 - 6*a^3*d*tan(1/2*f*x + 1/2*e)^2 - a^3*d*tan(1/2*f*x + 1/2*e) + 2*a^3*c - 6*a^3*d)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*d^2))/f","A",0
449,1,395,0,0.246479," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, a^{3} c^{3} - a^{3} c^{2} d - 4 \, a^{3} c d^{2} + 3 \, a^{3} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c d^{3} + d^{4}\right)} \sqrt{c^{2} - d^{2}}} - \frac{2 \, {\left(a^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a^{3} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + a^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a^{3} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{3} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a^{3} c^{3} - a^{3} c^{2} d + a^{3} c d^{2}\right)}}{{\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)} {\left(c^{2} d^{2} + c d^{3}\right)}} - \frac{{\left(2 \, a^{3} c - 3 \, a^{3} d\right)} {\left(f x + e\right)}}{d^{3}}}{f}"," ",0,"(2*(2*a^3*c^3 - a^3*c^2*d - 4*a^3*c*d^2 + 3*a^3*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c*d^3 + d^4)*sqrt(c^2 - d^2)) - 2*(a^3*c^2*d*tan(1/2*f*x + 1/2*e)^3 - 2*a^3*c*d^2*tan(1/2*f*x + 1/2*e)^3 + a^3*d^3*tan(1/2*f*x + 1/2*e)^3 + 2*a^3*c^3*tan(1/2*f*x + 1/2*e)^2 - a^3*c^2*d*tan(1/2*f*x + 1/2*e)^2 + a^3*c*d^2*tan(1/2*f*x + 1/2*e)^2 + 3*a^3*c^2*d*tan(1/2*f*x + 1/2*e) + a^3*d^3*tan(1/2*f*x + 1/2*e) + 2*a^3*c^3 - a^3*c^2*d + a^3*c*d^2)/((c*tan(1/2*f*x + 1/2*e)^4 + 2*d*tan(1/2*f*x + 1/2*e)^3 + 2*c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)*(c^2*d^2 + c*d^3)) - (2*a^3*c - 3*a^3*d)*(f*x + e)/d^3)/f","B",0
450,1,522,0,0.409785," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} a^{3}}{d^{3}} - \frac{{\left(2 \, a^{3} c^{3} + 4 \, a^{3} c^{2} d + a^{3} c d^{2} - 7 \, a^{3} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} \sqrt{c^{2} - d^{2}}} + \frac{a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 5 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, a^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 11 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 16 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a^{3} c^{5} + 4 \, a^{3} c^{4} d - 5 \, a^{3} c^{3} d^{2} - a^{3} c^{2} d^{3}}{{\left(c^{4} d^{2} + 2 \, c^{3} d^{3} + c^{2} d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"((f*x + e)*a^3/d^3 - (2*a^3*c^3 + 4*a^3*c^2*d + a^3*c*d^2 - 7*a^3*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^2*d^3 + 2*c*d^4 + d^5)*sqrt(c^2 - d^2)) + (a^3*c^4*d*tan(1/2*f*x + 1/2*e)^3 + 5*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 - 4*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 2*a^3*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 2*a^3*c^5*tan(1/2*f*x + 1/2*e)^2 + 4*a^3*c^4*d*tan(1/2*f*x + 1/2*e)^2 - a^3*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 + 7*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 10*a^3*c*d^4*tan(1/2*f*x + 1/2*e)^2 - 2*a^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 7*a^3*c^4*d*tan(1/2*f*x + 1/2*e) + 11*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e) - 16*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e) - 2*a^3*c*d^4*tan(1/2*f*x + 1/2*e) + 2*a^3*c^5 + 4*a^3*c^4*d - 5*a^3*c^3*d^2 - a^3*c^2*d^3)/((c^4*d^2 + 2*c^3*d^3 + c^2*d^4)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
451,1,667,0,0.554167," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} a^{3}}{{\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} \sqrt{c^{2} - d^{2}}} + \frac{9 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 9 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 90 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 54 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 12 \, a^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 132 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 54 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 100 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 36 \, a^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, a^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 48 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 36 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 180 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 54 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, a^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 114 \, a^{3} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 36 \, a^{3} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 6 \, a^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 22 \, a^{3} c^{5} - 9 \, a^{3} c^{4} d - 2 \, a^{3} c^{3} d^{2}}{{\left(c^{6} + 3 \, c^{5} d + 3 \, c^{4} d^{2} + c^{3} d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{3}}}{3 \, f}"," ",0,"1/3*(15*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*a^3/((c^3 + 3*c^2*d + 3*c*d^2 + d^3)*sqrt(c^2 - d^2)) + (9*a^3*c^5*tan(1/2*f*x + 1/2*e)^5 - 18*a^3*c^4*d*tan(1/2*f*x + 1/2*e)^5 - 18*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e)^5 - 6*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^5 - 18*a^3*c^5*tan(1/2*f*x + 1/2*e)^4 + 9*a^3*c^4*d*tan(1/2*f*x + 1/2*e)^4 - 90*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e)^4 - 54*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^4 - 12*a^3*c*d^4*tan(1/2*f*x + 1/2*e)^4 - 132*a^3*c^4*d*tan(1/2*f*x + 1/2*e)^3 - 54*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 - 100*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 36*a^3*c*d^4*tan(1/2*f*x + 1/2*e)^3 - 8*a^3*d^5*tan(1/2*f*x + 1/2*e)^3 - 48*a^3*c^5*tan(1/2*f*x + 1/2*e)^2 - 36*a^3*c^4*d*tan(1/2*f*x + 1/2*e)^2 - 180*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 - 54*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 12*a^3*c*d^4*tan(1/2*f*x + 1/2*e)^2 - 9*a^3*c^5*tan(1/2*f*x + 1/2*e) - 114*a^3*c^4*d*tan(1/2*f*x + 1/2*e) - 36*a^3*c^3*d^2*tan(1/2*f*x + 1/2*e) - 6*a^3*c^2*d^3*tan(1/2*f*x + 1/2*e) - 22*a^3*c^5 - 9*a^3*c^4*d - 2*a^3*c^3*d^2)/((c^6 + 3*c^5*d + 3*c^4*d^2 + c^3*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^3))/f","B",0
452,1,1338,0,2.222327," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^5,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(4 \, a^{3} c - 3 \, a^{3} d\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{5} + 3 \, c^{4} d + 2 \, c^{3} d^{2} - 2 \, c^{2} d^{3} - 3 \, c d^{4} - d^{5}\right)} \sqrt{c^{2} - d^{2}}} + \frac{36 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 117 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 48 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 48 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 72 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 24 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 72 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 132 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 675 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 360 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 288 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 72 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 36 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 813 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 288 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 892 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 552 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 664 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 384 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 96 \, a^{3} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 264 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 108 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 2001 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 936 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 202 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 864 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 440 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 192 \, a^{3} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 48 \, a^{3} d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 36 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 1299 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 576 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 1036 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1176 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 664 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 384 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 96 \, a^{3} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 280 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1289 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 960 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 552 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 288 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 72 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 36 \, a^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 587 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 336 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 248 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 120 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 24 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 88 \, a^{3} c^{8} + 36 \, a^{3} c^{7} d + 37 \, a^{3} c^{6} d^{2} + 24 \, a^{3} c^{5} d^{3} + 6 \, a^{3} c^{4} d^{4}}{{\left(c^{9} + 3 \, c^{8} d + 2 \, c^{7} d^{2} - 2 \, c^{6} d^{3} - 3 \, c^{5} d^{4} - c^{4} d^{5}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{4}}}{12 \, f}"," ",0,"1/12*(15*(4*a^3*c - 3*a^3*d)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^5 + 3*c^4*d + 2*c^3*d^2 - 2*c^2*d^3 - 3*c*d^4 - d^5)*sqrt(c^2 - d^2)) + (36*a^3*c^8*tan(1/2*f*x + 1/2*e)^7 - 117*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^7 - 48*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^7 + 48*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^7 + 72*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^7 + 24*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^7 - 72*a^3*c^8*tan(1/2*f*x + 1/2*e)^6 + 132*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^6 - 675*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^6 + 360*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^6 + 288*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^6 + 72*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^6 + 36*a^3*c^8*tan(1/2*f*x + 1/2*e)^5 - 813*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^5 + 288*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^5 - 892*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^5 + 552*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^5 + 664*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^5 + 384*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^5 + 96*a^3*c*d^7*tan(1/2*f*x + 1/2*e)^5 - 264*a^3*c^8*tan(1/2*f*x + 1/2*e)^4 + 108*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^4 - 2001*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^4 + 936*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^4 + 202*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^4 + 864*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^4 + 440*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^4 + 192*a^3*c*d^7*tan(1/2*f*x + 1/2*e)^4 + 48*a^3*d^8*tan(1/2*f*x + 1/2*e)^4 - 36*a^3*c^8*tan(1/2*f*x + 1/2*e)^3 - 1299*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^3 + 576*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^3 - 1036*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^3 + 1176*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^3 + 664*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^3 + 384*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 + 96*a^3*c*d^7*tan(1/2*f*x + 1/2*e)^3 - 280*a^3*c^8*tan(1/2*f*x + 1/2*e)^2 + 12*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^2 - 1289*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^2 + 960*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^2 + 552*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^2 + 288*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 72*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^2 - 36*a^3*c^8*tan(1/2*f*x + 1/2*e) - 587*a^3*c^7*d*tan(1/2*f*x + 1/2*e) + 336*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e) + 248*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e) + 120*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e) + 24*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e) - 88*a^3*c^8 + 36*a^3*c^7*d + 37*a^3*c^6*d^2 + 24*a^3*c^5*d^3 + 6*a^3*c^4*d^4)/((c^9 + 3*c^8*d + 2*c^7*d^2 - 2*c^6*d^3 - 3*c^5*d^4 - c^4*d^5)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^4))/f","B",0
453,1,306,0,0.220829," ","integrate((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, c^{3} d - 12 \, c^{2} d^{2} + 12 \, c d^{3} - 3 \, d^{4}\right)} {\left(f x + e\right)}}{a} - \frac{12 \, {\left(c^{4} - 4 \, c^{3} d + 6 \, c^{2} d^{2} - 4 \, c d^{3} + d^{4}\right)}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{2 \, {\left(12 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 3 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 36 \, c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 24 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 6 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 72 \, c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 48 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 24 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 36 \, c^{2} d^{2} + 24 \, c d^{3} - 10 \, d^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{3} a}}{6 \, f}"," ",0,"1/6*(3*(8*c^3*d - 12*c^2*d^2 + 12*c*d^3 - 3*d^4)*(f*x + e)/a - 12*(c^4 - 4*c^3*d + 6*c^2*d^2 - 4*c*d^3 + d^4)/(a*(tan(1/2*f*x + 1/2*e) + 1)) + 2*(12*c*d^3*tan(1/2*f*x + 1/2*e)^5 - 3*d^4*tan(1/2*f*x + 1/2*e)^5 - 36*c^2*d^2*tan(1/2*f*x + 1/2*e)^4 + 24*c*d^3*tan(1/2*f*x + 1/2*e)^4 - 6*d^4*tan(1/2*f*x + 1/2*e)^4 - 72*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 48*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 24*d^4*tan(1/2*f*x + 1/2*e)^2 - 12*c*d^3*tan(1/2*f*x + 1/2*e) + 3*d^4*tan(1/2*f*x + 1/2*e) - 36*c^2*d^2 + 24*c*d^3 - 10*d^4)/((tan(1/2*f*x + 1/2*e)^2 + 1)^3*a))/f","A",0
454,1,172,0,0.193528," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, c^{2} d - 2 \, c d^{2} + d^{3}\right)} {\left(f x + e\right)}}{a} - \frac{4 \, {\left(c^{3} - 3 \, c^{2} d + 3 \, c d^{2} - d^{3}\right)}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}} + \frac{2 \, {\left(d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 6 \, c d^{2} + 2 \, d^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} a}}{2 \, f}"," ",0,"1/2*(3*(2*c^2*d - 2*c*d^2 + d^3)*(f*x + e)/a - 4*(c^3 - 3*c^2*d + 3*c*d^2 - d^3)/(a*(tan(1/2*f*x + 1/2*e) + 1)) + 2*(d^3*tan(1/2*f*x + 1/2*e)^3 - 6*c*d^2*tan(1/2*f*x + 1/2*e)^2 + 2*d^3*tan(1/2*f*x + 1/2*e)^2 - d^3*tan(1/2*f*x + 1/2*e) - 6*c*d^2 + 2*d^3)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*a))/f","A",0
455,1,143,0,0.151120," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, c d - d^{2}\right)} {\left(f x + e\right)}}{a} - \frac{2 \, {\left(c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c^{2} - 2 \, c d + 2 \, d^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)} a}}{f}"," ",0,"((2*c*d - d^2)*(f*x + e)/a - 2*(c^2*tan(1/2*f*x + 1/2*e)^2 - 2*c*d*tan(1/2*f*x + 1/2*e)^2 + d^2*tan(1/2*f*x + 1/2*e)^2 + d^2*tan(1/2*f*x + 1/2*e) + c^2 - 2*c*d + 2*d^2)/((tan(1/2*f*x + 1/2*e)^3 + tan(1/2*f*x + 1/2*e)^2 + tan(1/2*f*x + 1/2*e) + 1)*a))/f","B",0
456,1,40,0,0.153507," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} d}{a} - \frac{2 \, {\left(c - d\right)}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}}{f}"," ",0,"((f*x + e)*d/a - 2*(c - d)/(a*(tan(1/2*f*x + 1/2*e) + 1)))/f","A",0
457,1,22,0,0.408582," ","integrate(1/(a+a*sin(f*x+e)),x, algorithm=""giac"")","-\frac{2}{a f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}"," ",0,"-2/(a*f*(tan(1/2*f*x + 1/2*e) + 1))","A",0
458,1,100,0,1.212893," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} d}{{\left(a c - a d\right)} \sqrt{c^{2} - d^{2}}} + \frac{1}{{\left(a c - a d\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}\right)}}{f}"," ",0,"-2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*d/((a*c - a*d)*sqrt(c^2 - d^2)) + 1/((a*c - a*d)*(tan(1/2*f*x + 1/2*e) + 1)))/f","A",0
459,1,311,0,0.343702," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} {\left(2 \, c d + d^{2}\right)}}{{\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} \sqrt{c^{2} - d^{2}}} + \frac{c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c^{3} + c^{2} d + c d^{2}}{{\left(a c^{4} - a c^{3} d - a c^{2} d^{2} + a c d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}}\right)}}{f}"," ",0,"-2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*(2*c*d + d^2)/((a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*sqrt(c^2 - d^2)) + (c^3*tan(1/2*f*x + 1/2*e)^2 + c^2*d*tan(1/2*f*x + 1/2*e)^2 + d^3*tan(1/2*f*x + 1/2*e)^2 + 2*c^2*d*tan(1/2*f*x + 1/2*e) + 3*c*d^2*tan(1/2*f*x + 1/2*e) + d^3*tan(1/2*f*x + 1/2*e) + c^3 + c^2*d + c*d^2)/((a*c^4 - a*c^3*d - a*c^2*d^2 + a*c*d^3)*(c*tan(1/2*f*x + 1/2*e)^3 + c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e)^2 + c*tan(1/2*f*x + 1/2*e) + 2*d*tan(1/2*f*x + 1/2*e) + c)))/f","B",0
460,1,482,0,1.860738," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, c^{2} d + 2 \, c d^{2} + d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(a c^{5} - a c^{4} d - 2 \, a c^{3} d^{2} + 2 \, a c^{2} d^{3} + a c d^{4} - a d^{5}\right)} \sqrt{c^{2} - d^{2}}} + \frac{7 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 17 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, c^{4} d^{2} + 2 \, c^{3} d^{3} - c^{2} d^{4}}{{\left(a c^{7} - a c^{6} d - 2 \, a c^{5} d^{2} + 2 \, a c^{4} d^{3} + a c^{3} d^{4} - a c^{2} d^{5}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}} + \frac{2}{{\left(a c^{3} - 3 \, a c^{2} d + 3 \, a c d^{2} - a d^{3}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}}}{f}"," ",0,"-(3*(2*c^2*d + 2*c*d^2 + d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((a*c^5 - a*c^4*d - 2*a*c^3*d^2 + 2*a*c^2*d^3 + a*c*d^4 - a*d^5)*sqrt(c^2 - d^2)) + (7*c^3*d^3*tan(1/2*f*x + 1/2*e)^3 + 2*c^2*d^4*tan(1/2*f*x + 1/2*e)^3 - 2*c*d^5*tan(1/2*f*x + 1/2*e)^3 + 6*c^4*d^2*tan(1/2*f*x + 1/2*e)^2 + 2*c^3*d^3*tan(1/2*f*x + 1/2*e)^2 + 11*c^2*d^4*tan(1/2*f*x + 1/2*e)^2 + 4*c*d^5*tan(1/2*f*x + 1/2*e)^2 - 2*d^6*tan(1/2*f*x + 1/2*e)^2 + 17*c^3*d^3*tan(1/2*f*x + 1/2*e) + 6*c^2*d^4*tan(1/2*f*x + 1/2*e) - 2*c*d^5*tan(1/2*f*x + 1/2*e) + 6*c^4*d^2 + 2*c^3*d^3 - c^2*d^4)/((a*c^7 - a*c^6*d - 2*a*c^5*d^2 + 2*a*c^4*d^3 + a*c^3*d^4 - a*c^2*d^5)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2) + 2/((a*c^3 - 3*a*c^2*d + 3*a*c*d^2 - a*d^3)*(tan(1/2*f*x + 1/2*e) + 1)))/f","B",0
461,1,977,0,0.243612," ","integrate((c+d*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(4 \, c^{3} d^{2} - 8 \, c^{2} d^{3} + 7 \, c d^{4} - 2 \, d^{5}\right)} {\left(f x + e\right)}}{a^{2}} - \frac{2 \, {\left(6 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 60 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} + 120 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 105 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} + 30 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} + 6 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 30 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 180 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 360 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 315 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 90 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 22 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 10 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 260 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 680 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 595 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 170 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 18 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 90 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 540 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 1200 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 945 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 270 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 30 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 420 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 1200 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 975 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 306 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 18 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 90 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 540 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1320 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 1005 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 310 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 18 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 30 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 300 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 840 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 645 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 198 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 30 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 180 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 480 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 375 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 114 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, c^{5} + 10 \, c^{4} d - 80 \, c^{3} d^{2} + 200 \, c^{2} d^{3} - 160 \, c d^{4} + 48 \, d^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3} a^{2}}}{6 \, f}"," ",0,"1/6*(15*(4*c^3*d^2 - 8*c^2*d^3 + 7*c*d^4 - 2*d^5)*(f*x + e)/a^2 - 2*(6*c^5*tan(1/2*f*x + 1/2*e)^8 - 60*c^3*d^2*tan(1/2*f*x + 1/2*e)^8 + 120*c^2*d^3*tan(1/2*f*x + 1/2*e)^8 - 105*c*d^4*tan(1/2*f*x + 1/2*e)^8 + 30*d^5*tan(1/2*f*x + 1/2*e)^8 + 6*c^5*tan(1/2*f*x + 1/2*e)^7 + 30*c^4*d*tan(1/2*f*x + 1/2*e)^7 - 180*c^3*d^2*tan(1/2*f*x + 1/2*e)^7 + 360*c^2*d^3*tan(1/2*f*x + 1/2*e)^7 - 315*c*d^4*tan(1/2*f*x + 1/2*e)^7 + 90*d^5*tan(1/2*f*x + 1/2*e)^7 + 22*c^5*tan(1/2*f*x + 1/2*e)^6 + 10*c^4*d*tan(1/2*f*x + 1/2*e)^6 - 260*c^3*d^2*tan(1/2*f*x + 1/2*e)^6 + 680*c^2*d^3*tan(1/2*f*x + 1/2*e)^6 - 595*c*d^4*tan(1/2*f*x + 1/2*e)^6 + 170*d^5*tan(1/2*f*x + 1/2*e)^6 + 18*c^5*tan(1/2*f*x + 1/2*e)^5 + 90*c^4*d*tan(1/2*f*x + 1/2*e)^5 - 540*c^3*d^2*tan(1/2*f*x + 1/2*e)^5 + 1200*c^2*d^3*tan(1/2*f*x + 1/2*e)^5 - 945*c*d^4*tan(1/2*f*x + 1/2*e)^5 + 270*d^5*tan(1/2*f*x + 1/2*e)^5 + 30*c^5*tan(1/2*f*x + 1/2*e)^4 + 30*c^4*d*tan(1/2*f*x + 1/2*e)^4 - 420*c^3*d^2*tan(1/2*f*x + 1/2*e)^4 + 1200*c^2*d^3*tan(1/2*f*x + 1/2*e)^4 - 975*c*d^4*tan(1/2*f*x + 1/2*e)^4 + 306*d^5*tan(1/2*f*x + 1/2*e)^4 + 18*c^5*tan(1/2*f*x + 1/2*e)^3 + 90*c^4*d*tan(1/2*f*x + 1/2*e)^3 - 540*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 + 1320*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 1005*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 310*d^5*tan(1/2*f*x + 1/2*e)^3 + 18*c^5*tan(1/2*f*x + 1/2*e)^2 + 30*c^4*d*tan(1/2*f*x + 1/2*e)^2 - 300*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 + 840*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 645*c*d^4*tan(1/2*f*x + 1/2*e)^2 + 198*d^5*tan(1/2*f*x + 1/2*e)^2 + 6*c^5*tan(1/2*f*x + 1/2*e) + 30*c^4*d*tan(1/2*f*x + 1/2*e) - 180*c^3*d^2*tan(1/2*f*x + 1/2*e) + 480*c^2*d^3*tan(1/2*f*x + 1/2*e) - 375*c*d^4*tan(1/2*f*x + 1/2*e) + 114*d^5*tan(1/2*f*x + 1/2*e) + 4*c^5 + 10*c^4*d - 80*c^3*d^2 + 200*c^2*d^3 - 160*c*d^4 + 48*d^5)/((tan(1/2*f*x + 1/2*e)^3 + tan(1/2*f*x + 1/2*e)^2 + tan(1/2*f*x + 1/2*e) + 1)^3*a^2))/f","B",0
462,1,338,0,0.244974," ","integrate((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(12 \, c^{2} d^{2} - 16 \, c d^{3} + 7 \, d^{4}\right)} {\left(f x + e\right)}}{a^{2}} + \frac{6 \, {\left(d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 8 \, c d^{3} + 4 \, d^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} a^{2}} - \frac{4 \, {\left(3 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 18 \, c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 24 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 \, c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 54 \, c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 60 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 21 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c^{4} + 4 \, c^{3} d - 24 \, c^{2} d^{2} + 28 \, c d^{3} - 10 \, d^{4}\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{6 \, f}"," ",0,"1/6*(3*(12*c^2*d^2 - 16*c*d^3 + 7*d^4)*(f*x + e)/a^2 + 6*(d^4*tan(1/2*f*x + 1/2*e)^3 - 8*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 4*d^4*tan(1/2*f*x + 1/2*e)^2 - d^4*tan(1/2*f*x + 1/2*e) - 8*c*d^3 + 4*d^4)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*a^2) - 4*(3*c^4*tan(1/2*f*x + 1/2*e)^2 - 18*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 24*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 9*d^4*tan(1/2*f*x + 1/2*e)^2 + 3*c^4*tan(1/2*f*x + 1/2*e) + 12*c^3*d*tan(1/2*f*x + 1/2*e) - 54*c^2*d^2*tan(1/2*f*x + 1/2*e) + 60*c*d^3*tan(1/2*f*x + 1/2*e) - 21*d^4*tan(1/2*f*x + 1/2*e) + 2*c^4 + 4*c^3*d - 24*c^2*d^2 + 28*c*d^3 - 10*d^4)/(a^2*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
463,1,209,0,0.954540," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(3 \, c d^{2} - 2 \, d^{3}\right)} {\left(f x + e\right)}}{a^{2}} - \frac{6 \, d^{3}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} a^{2}} - \frac{2 \, {\left(3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 9 \, c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 27 \, c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 15 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c^{3} + 3 \, c^{2} d - 12 \, c d^{2} + 7 \, d^{3}\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(3*c*d^2 - 2*d^3)*(f*x + e)/a^2 - 6*d^3/((tan(1/2*f*x + 1/2*e)^2 + 1)*a^2) - 2*(3*c^3*tan(1/2*f*x + 1/2*e)^2 - 9*c*d^2*tan(1/2*f*x + 1/2*e)^2 + 6*d^3*tan(1/2*f*x + 1/2*e)^2 + 3*c^3*tan(1/2*f*x + 1/2*e) + 9*c^2*d*tan(1/2*f*x + 1/2*e) - 27*c*d^2*tan(1/2*f*x + 1/2*e) + 15*d^3*tan(1/2*f*x + 1/2*e) + 2*c^3 + 3*c^2*d - 12*c*d^2 + 7*d^3)/(a^2*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
464,1,132,0,0.173359," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(f x + e\right)} d^{2}}{a^{2}} - \frac{2 \, {\left(3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 9 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c^{2} + 2 \, c d - 4 \, d^{2}\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*d^2/a^2 - 2*(3*c^2*tan(1/2*f*x + 1/2*e)^2 - 3*d^2*tan(1/2*f*x + 1/2*e)^2 + 3*c^2*tan(1/2*f*x + 1/2*e) + 6*c*d*tan(1/2*f*x + 1/2*e) - 9*d^2*tan(1/2*f*x + 1/2*e) + 2*c^2 + 2*c*d - 4*d^2)/(a^2*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
465,1,68,0,0.217640," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c + d\right)}}{3 \, a^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}"," ",0,"-2/3*(3*c*tan(1/2*f*x + 1/2*e)^2 + 3*c*tan(1/2*f*x + 1/2*e) + 3*d*tan(1/2*f*x + 1/2*e) + 2*c + d)/(a^2*f*(tan(1/2*f*x + 1/2*e) + 1)^3)","A",0
466,1,50,0,0.163359," ","integrate(1/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2\right)}}{3 \, a^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}"," ",0,"-2/3*(3*tan(1/2*f*x + 1/2*e)^2 + 3*tan(1/2*f*x + 1/2*e) + 2)/(a^2*f*(tan(1/2*f*x + 1/2*e) + 1)^3)","A",0
467,1,195,0,0.188232," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} d^{2}}{{\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} \sqrt{c^{2} - d^{2}}} - \frac{3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 9 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c - 5 \, d}{{\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}\right)}}{3 \, f}"," ",0,"2/3*(3*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*d^2/((a^2*c^2 - 2*a^2*c*d + a^2*d^2)*sqrt(c^2 - d^2)) - (3*c*tan(1/2*f*x + 1/2*e)^2 - 6*d*tan(1/2*f*x + 1/2*e)^2 + 3*c*tan(1/2*f*x + 1/2*e) - 9*d*tan(1/2*f*x + 1/2*e) + 2*c - 5*d)/((a^2*c^2 - 2*a^2*c*d + a^2*d^2)*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
468,1,320,0,0.209847," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(3 \, c d^{2} + 2 \, d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} \sqrt{c^{2} - d^{2}}} + \frac{3 \, {\left(d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c d^{3}\right)}}{{\left(a^{2} c^{5} - 2 \, a^{2} c^{4} d + 2 \, a^{2} c^{2} d^{3} - a^{2} c d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}} - \frac{3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 15 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c - 8 \, d}{{\left(a^{2} c^{3} - 3 \, a^{2} c^{2} d + 3 \, a^{2} c d^{2} - a^{2} d^{3}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}\right)}}{3 \, f}"," ",0,"2/3*(3*(3*c*d^2 + 2*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*sqrt(c^2 - d^2)) + 3*(d^4*tan(1/2*f*x + 1/2*e) + c*d^3)/((a^2*c^5 - 2*a^2*c^4*d + 2*a^2*c^2*d^3 - a^2*c*d^4)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)) - (3*c*tan(1/2*f*x + 1/2*e)^2 - 9*d*tan(1/2*f*x + 1/2*e)^2 + 3*c*tan(1/2*f*x + 1/2*e) - 15*d*tan(1/2*f*x + 1/2*e) + 2*c - 8*d)/((a^2*c^3 - 3*a^2*c^2*d + 3*a^2*c*d^2 - a^2*d^3)*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","A",0
469,1,614,0,0.444364," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(12 \, c^{2} d^{2} + 16 \, c d^{3} + 7 \, d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(a^{2} c^{6} - 2 \, a^{2} c^{5} d - a^{2} c^{4} d^{2} + 4 \, a^{2} c^{3} d^{3} - a^{2} c^{2} d^{4} - 2 \, a^{2} c d^{5} + a^{2} d^{6}\right)} \sqrt{c^{2} - d^{2}}} + \frac{3 \, {\left(9 \, c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 15 \, c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 8 \, c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 23 \, c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 \, c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8 \, c^{4} d^{3} + 4 \, c^{3} d^{4} - c^{2} d^{5}\right)}}{{\left(a^{2} c^{8} - 2 \, a^{2} c^{7} d - a^{2} c^{6} d^{2} + 4 \, a^{2} c^{5} d^{3} - a^{2} c^{4} d^{4} - 2 \, a^{2} c^{3} d^{5} + a^{2} c^{2} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}} - \frac{2 \, {\left(3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 21 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, c - 11 \, d\right)}}{{\left(a^{2} c^{4} - 4 \, a^{2} c^{3} d + 6 \, a^{2} c^{2} d^{2} - 4 \, a^{2} c d^{3} + a^{2} d^{4}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(12*c^2*d^2 + 16*c*d^3 + 7*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((a^2*c^6 - 2*a^2*c^5*d - a^2*c^4*d^2 + 4*a^2*c^3*d^3 - a^2*c^2*d^4 - 2*a^2*c*d^5 + a^2*d^6)*sqrt(c^2 - d^2)) + 3*(9*c^3*d^4*tan(1/2*f*x + 1/2*e)^3 + 4*c^2*d^5*tan(1/2*f*x + 1/2*e)^3 - 2*c*d^6*tan(1/2*f*x + 1/2*e)^3 + 8*c^4*d^3*tan(1/2*f*x + 1/2*e)^2 + 4*c^3*d^4*tan(1/2*f*x + 1/2*e)^2 + 15*c^2*d^5*tan(1/2*f*x + 1/2*e)^2 + 8*c*d^6*tan(1/2*f*x + 1/2*e)^2 - 2*d^7*tan(1/2*f*x + 1/2*e)^2 + 23*c^3*d^4*tan(1/2*f*x + 1/2*e) + 12*c^2*d^5*tan(1/2*f*x + 1/2*e) - 2*c*d^6*tan(1/2*f*x + 1/2*e) + 8*c^4*d^3 + 4*c^3*d^4 - c^2*d^5)/((a^2*c^8 - 2*a^2*c^7*d - a^2*c^6*d^2 + 4*a^2*c^5*d^3 - a^2*c^4*d^4 - 2*a^2*c^3*d^5 + a^2*c^2*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2) - 2*(3*c*tan(1/2*f*x + 1/2*e)^2 - 12*d*tan(1/2*f*x + 1/2*e)^2 + 3*c*tan(1/2*f*x + 1/2*e) - 21*d*tan(1/2*f*x + 1/2*e) + 2*c - 11*d)/((a^2*c^4 - 4*a^2*c^3*d + 6*a^2*c^2*d^2 - 4*a^2*c*d^3 + a^2*d^4)*(tan(1/2*f*x + 1/2*e) + 1)^3))/f","B",0
470,1,776,0,0.292464," ","integrate((c+d*sin(f*x+e))^6/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(40 \, c^{3} d^{3} - 90 \, c^{2} d^{4} + 78 \, c d^{5} - 23 \, d^{6}\right)} {\left(f x + e\right)}}{a^{3}} + \frac{10 \, {\left(18 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 9 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 90 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 108 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 36 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 180 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 216 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 84 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 18 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 9 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 90 \, c^{2} d^{4} + 108 \, c d^{5} - 40 \, d^{6}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{3} a^{3}} - \frac{4 \, {\left(15 \, c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 300 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 675 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 540 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 150 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 90 \, c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 1500 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3150 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2430 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 660 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 90 \, c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 300 \, c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2900 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5400 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3990 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1060 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 90 \, c^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 150 \, c^{4} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1900 \, c^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3600 \, c^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2670 \, c d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 710 \, d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{6} + 18 \, c^{5} d + 30 \, c^{4} d^{2} - 440 \, c^{3} d^{3} + 855 \, c^{2} d^{4} - 642 \, c d^{5} + 172 \, d^{6}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{30 \, f}"," ",0,"1/30*(15*(40*c^3*d^3 - 90*c^2*d^4 + 78*c*d^5 - 23*d^6)*(f*x + e)/a^3 + 10*(18*c*d^5*tan(1/2*f*x + 1/2*e)^5 - 9*d^6*tan(1/2*f*x + 1/2*e)^5 - 90*c^2*d^4*tan(1/2*f*x + 1/2*e)^4 + 108*c*d^5*tan(1/2*f*x + 1/2*e)^4 - 36*d^6*tan(1/2*f*x + 1/2*e)^4 - 180*c^2*d^4*tan(1/2*f*x + 1/2*e)^2 + 216*c*d^5*tan(1/2*f*x + 1/2*e)^2 - 84*d^6*tan(1/2*f*x + 1/2*e)^2 - 18*c*d^5*tan(1/2*f*x + 1/2*e) + 9*d^6*tan(1/2*f*x + 1/2*e) - 90*c^2*d^4 + 108*c*d^5 - 40*d^6)/((tan(1/2*f*x + 1/2*e)^2 + 1)^3*a^3) - 4*(15*c^6*tan(1/2*f*x + 1/2*e)^4 - 300*c^3*d^3*tan(1/2*f*x + 1/2*e)^4 + 675*c^2*d^4*tan(1/2*f*x + 1/2*e)^4 - 540*c*d^5*tan(1/2*f*x + 1/2*e)^4 + 150*d^6*tan(1/2*f*x + 1/2*e)^4 + 30*c^6*tan(1/2*f*x + 1/2*e)^3 + 90*c^5*d*tan(1/2*f*x + 1/2*e)^3 - 1500*c^3*d^3*tan(1/2*f*x + 1/2*e)^3 + 3150*c^2*d^4*tan(1/2*f*x + 1/2*e)^3 - 2430*c*d^5*tan(1/2*f*x + 1/2*e)^3 + 660*d^6*tan(1/2*f*x + 1/2*e)^3 + 40*c^6*tan(1/2*f*x + 1/2*e)^2 + 90*c^5*d*tan(1/2*f*x + 1/2*e)^2 + 300*c^4*d^2*tan(1/2*f*x + 1/2*e)^2 - 2900*c^3*d^3*tan(1/2*f*x + 1/2*e)^2 + 5400*c^2*d^4*tan(1/2*f*x + 1/2*e)^2 - 3990*c*d^5*tan(1/2*f*x + 1/2*e)^2 + 1060*d^6*tan(1/2*f*x + 1/2*e)^2 + 20*c^6*tan(1/2*f*x + 1/2*e) + 90*c^5*d*tan(1/2*f*x + 1/2*e) + 150*c^4*d^2*tan(1/2*f*x + 1/2*e) - 1900*c^3*d^3*tan(1/2*f*x + 1/2*e) + 3600*c^2*d^4*tan(1/2*f*x + 1/2*e) - 2670*c*d^5*tan(1/2*f*x + 1/2*e) + 710*d^6*tan(1/2*f*x + 1/2*e) + 7*c^6 + 18*c^5*d + 30*c^4*d^2 - 440*c^3*d^3 + 855*c^2*d^4 - 642*c*d^5 + 172*d^6)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","B",0
471,1,564,0,0.249904," ","integrate((c+d*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(20 \, c^{2} d^{3} - 30 \, c d^{4} + 13 \, d^{5}\right)} {\left(f x + e\right)}}{a^{3}} + \frac{30 \, {\left(d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 10 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 10 \, c d^{4} + 6 \, d^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} a^{3}} - \frac{4 \, {\left(15 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 150 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 225 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 90 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 75 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 750 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 1050 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 405 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 75 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 200 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1450 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1800 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 665 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 75 \, c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 100 \, c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 950 \, c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1200 \, c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 445 \, d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{5} + 15 \, c^{4} d + 20 \, c^{3} d^{2} - 220 \, c^{2} d^{3} + 285 \, c d^{4} - 107 \, d^{5}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{30 \, f}"," ",0,"1/30*(15*(20*c^2*d^3 - 30*c*d^4 + 13*d^5)*(f*x + e)/a^3 + 30*(d^5*tan(1/2*f*x + 1/2*e)^3 - 10*c*d^4*tan(1/2*f*x + 1/2*e)^2 + 6*d^5*tan(1/2*f*x + 1/2*e)^2 - d^5*tan(1/2*f*x + 1/2*e) - 10*c*d^4 + 6*d^5)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*a^3) - 4*(15*c^5*tan(1/2*f*x + 1/2*e)^4 - 150*c^2*d^3*tan(1/2*f*x + 1/2*e)^4 + 225*c*d^4*tan(1/2*f*x + 1/2*e)^4 - 90*d^5*tan(1/2*f*x + 1/2*e)^4 + 30*c^5*tan(1/2*f*x + 1/2*e)^3 + 75*c^4*d*tan(1/2*f*x + 1/2*e)^3 - 750*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 + 1050*c*d^4*tan(1/2*f*x + 1/2*e)^3 - 405*d^5*tan(1/2*f*x + 1/2*e)^3 + 40*c^5*tan(1/2*f*x + 1/2*e)^2 + 75*c^4*d*tan(1/2*f*x + 1/2*e)^2 + 200*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 - 1450*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 + 1800*c*d^4*tan(1/2*f*x + 1/2*e)^2 - 665*d^5*tan(1/2*f*x + 1/2*e)^2 + 20*c^5*tan(1/2*f*x + 1/2*e) + 75*c^4*d*tan(1/2*f*x + 1/2*e) + 100*c^3*d^2*tan(1/2*f*x + 1/2*e) - 950*c^2*d^3*tan(1/2*f*x + 1/2*e) + 1200*c*d^4*tan(1/2*f*x + 1/2*e) - 445*d^5*tan(1/2*f*x + 1/2*e) + 7*c^5 + 15*c^4*d + 20*c^3*d^2 - 220*c^2*d^3 + 285*c*d^4 - 107*d^5)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","B",0
472,1,395,0,0.258456," ","integrate((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{30 \, d^{4}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} a^{3}} - \frac{15 \, {\left(4 \, c d^{3} - 3 \, d^{4}\right)} {\left(f x + e\right)}}{a^{3}} + \frac{2 \, {\left(15 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 60 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 60 \, c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 300 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 210 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 60 \, c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 120 \, c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 580 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 360 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 60 \, c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 60 \, c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 380 \, c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 240 \, d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{4} + 12 \, c^{3} d + 12 \, c^{2} d^{2} - 88 \, c d^{3} + 57 \, d^{4}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{15 \, f}"," ",0,"-1/15*(30*d^4/((tan(1/2*f*x + 1/2*e)^2 + 1)*a^3) - 15*(4*c*d^3 - 3*d^4)*(f*x + e)/a^3 + 2*(15*c^4*tan(1/2*f*x + 1/2*e)^4 - 60*c*d^3*tan(1/2*f*x + 1/2*e)^4 + 45*d^4*tan(1/2*f*x + 1/2*e)^4 + 30*c^4*tan(1/2*f*x + 1/2*e)^3 + 60*c^3*d*tan(1/2*f*x + 1/2*e)^3 - 300*c*d^3*tan(1/2*f*x + 1/2*e)^3 + 210*d^4*tan(1/2*f*x + 1/2*e)^3 + 40*c^4*tan(1/2*f*x + 1/2*e)^2 + 60*c^3*d*tan(1/2*f*x + 1/2*e)^2 + 120*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 - 580*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 360*d^4*tan(1/2*f*x + 1/2*e)^2 + 20*c^4*tan(1/2*f*x + 1/2*e) + 60*c^3*d*tan(1/2*f*x + 1/2*e) + 60*c^2*d^2*tan(1/2*f*x + 1/2*e) - 380*c*d^3*tan(1/2*f*x + 1/2*e) + 240*d^4*tan(1/2*f*x + 1/2*e) + 7*c^4 + 12*c^3*d + 12*c^2*d^2 - 88*c*d^3 + 57*d^4)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","B",0
473,1,280,0,0.227545," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(f x + e\right)} d^{3}}{a^{3}} - \frac{2 \, {\left(15 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 15 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 45 \, c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 75 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 45 \, c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 60 \, c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 145 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 45 \, c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 30 \, c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 95 \, d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{3} + 9 \, c^{2} d + 6 \, c d^{2} - 22 \, d^{3}\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{15 \, f}"," ",0,"1/15*(15*(f*x + e)*d^3/a^3 - 2*(15*c^3*tan(1/2*f*x + 1/2*e)^4 - 15*d^3*tan(1/2*f*x + 1/2*e)^4 + 30*c^3*tan(1/2*f*x + 1/2*e)^3 + 45*c^2*d*tan(1/2*f*x + 1/2*e)^3 - 75*d^3*tan(1/2*f*x + 1/2*e)^3 + 40*c^3*tan(1/2*f*x + 1/2*e)^2 + 45*c^2*d*tan(1/2*f*x + 1/2*e)^2 + 60*c*d^2*tan(1/2*f*x + 1/2*e)^2 - 145*d^3*tan(1/2*f*x + 1/2*e)^2 + 20*c^3*tan(1/2*f*x + 1/2*e) + 45*c^2*d*tan(1/2*f*x + 1/2*e) + 30*c*d^2*tan(1/2*f*x + 1/2*e) - 95*d^3*tan(1/2*f*x + 1/2*e) + 7*c^3 + 9*c^2*d + 6*c*d^2 - 22*d^3)/(a^3*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","B",0
474,1,181,0,2.208929," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 30 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 30 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 30 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 10 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{2} + 6 \, c d + 2 \, d^{2}\right)}}{15 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}"," ",0,"-2/15*(15*c^2*tan(1/2*f*x + 1/2*e)^4 + 30*c^2*tan(1/2*f*x + 1/2*e)^3 + 30*c*d*tan(1/2*f*x + 1/2*e)^3 + 40*c^2*tan(1/2*f*x + 1/2*e)^2 + 30*c*d*tan(1/2*f*x + 1/2*e)^2 + 20*d^2*tan(1/2*f*x + 1/2*e)^2 + 20*c^2*tan(1/2*f*x + 1/2*e) + 30*c*d*tan(1/2*f*x + 1/2*e) + 10*d^2*tan(1/2*f*x + 1/2*e) + 7*c^2 + 6*c*d + 2*d^2)/(a^3*f*(tan(1/2*f*x + 1/2*e) + 1)^5)","A",0
475,1,130,0,0.263607," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 15 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 15 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 15 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c + 3 \, d\right)}}{15 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}"," ",0,"-2/15*(15*c*tan(1/2*f*x + 1/2*e)^4 + 30*c*tan(1/2*f*x + 1/2*e)^3 + 15*d*tan(1/2*f*x + 1/2*e)^3 + 40*c*tan(1/2*f*x + 1/2*e)^2 + 15*d*tan(1/2*f*x + 1/2*e)^2 + 20*c*tan(1/2*f*x + 1/2*e) + 15*d*tan(1/2*f*x + 1/2*e) + 7*c + 3*d)/(a^3*f*(tan(1/2*f*x + 1/2*e) + 1)^5)","A",0
476,1,78,0,0.387967," ","integrate(1/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7\right)}}{15 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}"," ",0,"-2/15*(15*tan(1/2*f*x + 1/2*e)^4 + 30*tan(1/2*f*x + 1/2*e)^3 + 40*tan(1/2*f*x + 1/2*e)^2 + 20*tan(1/2*f*x + 1/2*e) + 7)/(a^3*f*(tan(1/2*f*x + 1/2*e) + 1)^5)","A",0
477,1,364,0,0.337394," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{15 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} d^{3}}{{\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} \sqrt{c^{2} - d^{2}}} + \frac{15 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 45 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 105 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 135 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 135 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 185 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 75 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 115 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{2} - 24 \, c d + 32 \, d^{2}}{{\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}\right)}}{15 \, f}"," ",0,"-2/15*(15*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*d^3/((a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*sqrt(c^2 - d^2)) + (15*c^2*tan(1/2*f*x + 1/2*e)^4 - 45*c*d*tan(1/2*f*x + 1/2*e)^4 + 45*d^2*tan(1/2*f*x + 1/2*e)^4 + 30*c^2*tan(1/2*f*x + 1/2*e)^3 - 105*c*d*tan(1/2*f*x + 1/2*e)^3 + 135*d^2*tan(1/2*f*x + 1/2*e)^3 + 40*c^2*tan(1/2*f*x + 1/2*e)^2 - 135*c*d*tan(1/2*f*x + 1/2*e)^2 + 185*d^2*tan(1/2*f*x + 1/2*e)^2 + 20*c^2*tan(1/2*f*x + 1/2*e) - 75*c*d*tan(1/2*f*x + 1/2*e) + 115*d^2*tan(1/2*f*x + 1/2*e) + 7*c^2 - 24*c*d + 32*d^2)/((a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","B",0
478,1,517,0,1.313493," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{15 \, {\left(4 \, c d^{3} + 3 \, d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} \sqrt{c^{2} - d^{2}}} + \frac{15 \, {\left(d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c d^{4}\right)}}{{\left(a^{3} c^{6} - 3 \, a^{3} c^{5} d + 2 \, a^{3} c^{4} d^{2} + 2 \, a^{3} c^{3} d^{3} - 3 \, a^{3} c^{2} d^{4} + a^{3} c d^{5}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}} + \frac{15 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 60 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 90 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 150 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 300 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 190 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 420 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 110 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 270 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{2} - 34 \, c d + 72 \, d^{2}}{{\left(a^{3} c^{4} - 4 \, a^{3} c^{3} d + 6 \, a^{3} c^{2} d^{2} - 4 \, a^{3} c d^{3} + a^{3} d^{4}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}\right)}}{15 \, f}"," ",0,"-2/15*(15*(4*c*d^3 + 3*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*sqrt(c^2 - d^2)) + 15*(d^5*tan(1/2*f*x + 1/2*e) + c*d^4)/((a^3*c^6 - 3*a^3*c^5*d + 2*a^3*c^4*d^2 + 2*a^3*c^3*d^3 - 3*a^3*c^2*d^4 + a^3*c*d^5)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)) + (15*c^2*tan(1/2*f*x + 1/2*e)^4 - 60*c*d*tan(1/2*f*x + 1/2*e)^4 + 90*d^2*tan(1/2*f*x + 1/2*e)^4 + 30*c^2*tan(1/2*f*x + 1/2*e)^3 - 150*c*d*tan(1/2*f*x + 1/2*e)^3 + 300*d^2*tan(1/2*f*x + 1/2*e)^3 + 40*c^2*tan(1/2*f*x + 1/2*e)^2 - 190*c*d*tan(1/2*f*x + 1/2*e)^2 + 420*d^2*tan(1/2*f*x + 1/2*e)^2 + 20*c^2*tan(1/2*f*x + 1/2*e) - 110*c*d*tan(1/2*f*x + 1/2*e) + 270*d^2*tan(1/2*f*x + 1/2*e) + 7*c^2 - 34*c*d + 72*d^2)/((a^3*c^4 - 4*a^3*c^3*d + 6*a^3*c^2*d^2 - 4*a^3*c*d^3 + a^3*d^4)*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","A",0
479,1,794,0,2.039297," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(20 \, c^{2} d^{3} + 30 \, c d^{4} + 13 \, d^{5}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(a^{3} c^{7} - 3 \, a^{3} c^{6} d + a^{3} c^{5} d^{2} + 5 \, a^{3} c^{4} d^{3} - 5 \, a^{3} c^{3} d^{4} - a^{3} c^{2} d^{5} + 3 \, a^{3} c d^{6} - a^{3} d^{7}\right)} \sqrt{c^{2} - d^{2}}} + \frac{15 \, {\left(11 \, c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 10 \, c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 19 \, c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 29 \, c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 18 \, c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 10 \, c^{4} d^{4} + 6 \, c^{3} d^{5} - c^{2} d^{6}\right)}}{{\left(a^{3} c^{9} - 3 \, a^{3} c^{8} d + a^{3} c^{7} d^{2} + 5 \, a^{3} c^{6} d^{3} - 5 \, a^{3} c^{5} d^{4} - a^{3} c^{4} d^{5} + 3 \, a^{3} c^{3} d^{6} - a^{3} c^{2} d^{7}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}} + \frac{2 \, {\left(15 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 75 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 150 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 30 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 195 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 525 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 245 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 745 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 145 \, c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 485 \, d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, c^{2} - 44 \, c d + 127 \, d^{2}\right)}}{{\left(a^{3} c^{5} - 5 \, a^{3} c^{4} d + 10 \, a^{3} c^{3} d^{2} - 10 \, a^{3} c^{2} d^{3} + 5 \, a^{3} c d^{4} - a^{3} d^{5}\right)} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}^{5}}}{15 \, f}"," ",0,"-1/15*(15*(20*c^2*d^3 + 30*c*d^4 + 13*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((a^3*c^7 - 3*a^3*c^6*d + a^3*c^5*d^2 + 5*a^3*c^4*d^3 - 5*a^3*c^3*d^4 - a^3*c^2*d^5 + 3*a^3*c*d^6 - a^3*d^7)*sqrt(c^2 - d^2)) + 15*(11*c^3*d^5*tan(1/2*f*x + 1/2*e)^3 + 6*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 - 2*c*d^7*tan(1/2*f*x + 1/2*e)^3 + 10*c^4*d^4*tan(1/2*f*x + 1/2*e)^2 + 6*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 19*c^2*d^6*tan(1/2*f*x + 1/2*e)^2 + 12*c*d^7*tan(1/2*f*x + 1/2*e)^2 - 2*d^8*tan(1/2*f*x + 1/2*e)^2 + 29*c^3*d^5*tan(1/2*f*x + 1/2*e) + 18*c^2*d^6*tan(1/2*f*x + 1/2*e) - 2*c*d^7*tan(1/2*f*x + 1/2*e) + 10*c^4*d^4 + 6*c^3*d^5 - c^2*d^6)/((a^3*c^9 - 3*a^3*c^8*d + a^3*c^7*d^2 + 5*a^3*c^6*d^3 - 5*a^3*c^5*d^4 - a^3*c^4*d^5 + 3*a^3*c^3*d^6 - a^3*c^2*d^7)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2) + 2*(15*c^2*tan(1/2*f*x + 1/2*e)^4 - 75*c*d*tan(1/2*f*x + 1/2*e)^4 + 150*d^2*tan(1/2*f*x + 1/2*e)^4 + 30*c^2*tan(1/2*f*x + 1/2*e)^3 - 195*c*d*tan(1/2*f*x + 1/2*e)^3 + 525*d^2*tan(1/2*f*x + 1/2*e)^3 + 40*c^2*tan(1/2*f*x + 1/2*e)^2 - 245*c*d*tan(1/2*f*x + 1/2*e)^2 + 745*d^2*tan(1/2*f*x + 1/2*e)^2 + 20*c^2*tan(1/2*f*x + 1/2*e) - 145*c*d*tan(1/2*f*x + 1/2*e) + 485*d^2*tan(1/2*f*x + 1/2*e) + 7*c^2 - 44*c*d + 127*d^2)/((a^3*c^5 - 5*a^3*c^4*d + 10*a^3*c^3*d^2 - 10*a^3*c^2*d^3 + 5*a^3*c*d^4 - a^3*d^5)*(tan(1/2*f*x + 1/2*e) + 1)^5))/f","B",0
480,1,112,0,0.197884," ","integrate((A+B*sin(x))/(1+sin(x))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, A \tan\left(\frac{1}{2} \, x\right)^{6} + 315 \, A \tan\left(\frac{1}{2} \, x\right)^{5} + 105 \, B \tan\left(\frac{1}{2} \, x\right)^{5} + 630 \, A \tan\left(\frac{1}{2} \, x\right)^{4} + 175 \, B \tan\left(\frac{1}{2} \, x\right)^{4} + 630 \, A \tan\left(\frac{1}{2} \, x\right)^{3} + 280 \, B \tan\left(\frac{1}{2} \, x\right)^{3} + 441 \, A \tan\left(\frac{1}{2} \, x\right)^{2} + 168 \, B \tan\left(\frac{1}{2} \, x\right)^{2} + 147 \, A \tan\left(\frac{1}{2} \, x\right) + 91 \, B \tan\left(\frac{1}{2} \, x\right) + 36 \, A + 13 \, B\right)}}{105 \, {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{7}}"," ",0,"-2/105*(105*A*tan(1/2*x)^6 + 315*A*tan(1/2*x)^5 + 105*B*tan(1/2*x)^5 + 630*A*tan(1/2*x)^4 + 175*B*tan(1/2*x)^4 + 630*A*tan(1/2*x)^3 + 280*B*tan(1/2*x)^3 + 441*A*tan(1/2*x)^2 + 168*B*tan(1/2*x)^2 + 147*A*tan(1/2*x) + 91*B*tan(1/2*x) + 36*A + 13*B)/(tan(1/2*x) + 1)^7","A",0
481,1,112,0,0.271556," ","integrate((A+B*sin(x))/(1-sin(x))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, A \tan\left(\frac{1}{2} \, x\right)^{6} - 315 \, A \tan\left(\frac{1}{2} \, x\right)^{5} + 105 \, B \tan\left(\frac{1}{2} \, x\right)^{5} + 630 \, A \tan\left(\frac{1}{2} \, x\right)^{4} - 175 \, B \tan\left(\frac{1}{2} \, x\right)^{4} - 630 \, A \tan\left(\frac{1}{2} \, x\right)^{3} + 280 \, B \tan\left(\frac{1}{2} \, x\right)^{3} + 441 \, A \tan\left(\frac{1}{2} \, x\right)^{2} - 168 \, B \tan\left(\frac{1}{2} \, x\right)^{2} - 147 \, A \tan\left(\frac{1}{2} \, x\right) + 91 \, B \tan\left(\frac{1}{2} \, x\right) + 36 \, A - 13 \, B\right)}}{105 \, {\left(\tan\left(\frac{1}{2} \, x\right) - 1\right)}^{7}}"," ",0,"-2/105*(105*A*tan(1/2*x)^6 - 315*A*tan(1/2*x)^5 + 105*B*tan(1/2*x)^5 + 630*A*tan(1/2*x)^4 - 175*B*tan(1/2*x)^4 - 630*A*tan(1/2*x)^3 + 280*B*tan(1/2*x)^3 + 441*A*tan(1/2*x)^2 - 168*B*tan(1/2*x)^2 - 147*A*tan(1/2*x) + 91*B*tan(1/2*x) + 36*A - 13*B)/(tan(1/2*x) - 1)^7","A",0
482,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
483,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
484,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
485,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{a \sin\left(f x + e\right) + a}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
486,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
487,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
488,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(7/2), x)","F",0
489,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(5/2), x)","F",0
490,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(3/2), x)","F",0
491,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c), x)","F",0
492,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/sqrt(d*sin(f*x + e) + c), x)","F",0
493,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(3/2), x)","F",0
494,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(5/2), x)","F",0
495,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(7/2), x)","F",0
496,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(5/2), x)","F",0
497,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(3/2), x)","F",0
498,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/sqrt(d*sin(f*x + e) + c), x)","F",0
500,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(3/2), x)","F",0
501,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(5/2), x)","F",0
502,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(7/2), x)","F",0
503,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(9/2), x)","F",0
504,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a), x)","F",0
505,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a), x)","F",0
506,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a), x)","F",0
507,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
508,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
509,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
510,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^2, x)","F",0
511,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^2, x)","F",0
512,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^2, x)","F",0
513,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c)), x)","F",0
514,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
515,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
516,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^3, x)","F",0
517,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^3, x)","F",0
518,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^3, x)","F",0
519,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{3} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^3*sqrt(d*sin(f*x + e) + c)), x)","F",0
520,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
521,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
522,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(2*f*(4*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2-8*f*(6*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+24*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2-24*f*(6*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+24*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2+80*d^3*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2+112*d^3*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2-72*c*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-120*c*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2)","F(-2)",0
523,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(2*f*(4*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2-2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x+2*exp(1)+pi))/f-24*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-6*c*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)-pi))/(3*f)^2)","F(-2)",0
524,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(2*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/f-4*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x+2*exp(1)+pi))/(2*f)^2-12*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)-pi))/(6*f)^2)","F(-2)",0
525,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2*sqrt(2*a)*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/2*(f*x+exp(1))-1/4*pi)/f","F(-2)",0
526,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)-sqrt(2*a)*sqrt(2)*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*atan(sqrt(2)*d*sin(1/4*(2*f*x+2*exp(1)-pi))/sqrt(-d^2-c*d))/sqrt(-d^2-c*d)/f","F(-2)",0
527,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)4*sqrt(2*a)*(-sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)-pi))/(-4*c-4*d)/(-2*d*sin(1/4*(2*f*x+2*exp(1)-pi))^2+c+d)-1/2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*atan(sqrt(2)*d*sin(1/4*(2*f*x+2*exp(1)-pi))/sqrt(-d^2-c*d))/sqrt(2)/sqrt(-d^2-c*d)/(2*c+2*d))/f","F(-2)",0
528,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)4*sqrt(2*a)*((-5*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)-pi))+6*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)-pi))^3-5*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x+2*exp(1)-pi)))/(2*d*sin(1/4*(2*f*x+2*exp(1)-pi))^2-c-d)^2/(-16*c^2-16*d^2-32*c*d)-3/2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*atan(sqrt(2)*d*sin(1/4*(2*f*x+2*exp(1)-pi))/sqrt(-d^2-c*d))/sqrt(2)/sqrt(-d^2-c*d)/(8*c^2+8*d^2+16*c*d))/f","F(-2)",0
529,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(-40*f*(-2*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-6*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2-56*f*(-2*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-6*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2+12*f*(-2*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-6*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-6*a*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+20*f*(-2*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-6*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-6*a*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-8*f*(8*a*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+18*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+24*a*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2-24*f*(8*a*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+18*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+24*a*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2+8*f*(16*a*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+24*a*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+24*a*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2+224*a*d^3*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2+288*a*d^3*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2)","F(-2)",0
530,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(12*f*(-2*a*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+20*f*(-2*a*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+2*f*(4*a*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*a*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+4*a*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2-8*f*(8*a*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+16*a*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2-24*f*(8*a*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+16*a*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2+80*a*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2+112*a*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2)","F(-2)",0
531,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(-2*f*(2*a*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*a*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(2*f)^2-6*f*(2*a*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*a*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(6*f)^2+2*f*(4*a*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*a*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2-24*a*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2)","F(-2)",0
532,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(2*a*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/f-4*a*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x+2*exp(1)+pi))/(2*f)^2-12*a*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)-pi))/(6*f)^2)","F(-2)",0
533,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*x+exp(1))/2-pi/4))]Evaluation time: 49.25Not invertible Error: Bad Argument Value","F(-2)",0
534,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(112*f*(4*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2+144*f*(4*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2-160*f*(-18*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-48*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-24*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(10*f*x+10*exp(1)+pi))/(160*f)^2-224*f*(-18*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-48*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-24*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(14*f*x+14*exp(1)-pi))/(224*f)^2+8*f*(24*a^2*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+12*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+42*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+48*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2-16*f*(32*a^2*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+22*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+72*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+84*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(16*f)^2-48*f*(32*a^2*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+22*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+72*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+84*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(48*f)^2+12*f*(-2*a^2*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-12*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-12*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+20*f*(-2*a^2*c^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a^2*d^3*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-12*a^2*c*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-12*a^2*c^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2-576*a^2*d^3*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(18*f*x+18*exp(1)+pi))/(288*f)^2-704*a^2*d^3*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(22*f*x+22*exp(1)-pi))/(352*f)^2)","F(-2)",0
537,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(-20*f*(-2*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-2*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(10*f*x+10*exp(1)+pi))/(20*f)^2-28*f*(-2*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-2*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(14*f*x+14*exp(1)-pi))/(28*f)^2-4*f*(8*a^2*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+14*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(4*f)^2-12*f*(8*a^2*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+6*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+14*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(12*f)^2+8*f*(24*a^2*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+14*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+32*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(8*f)^2+12*f*(-2*a^2*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-8*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+20*f*(-2*a^2*c^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a^2*d^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-8*a^2*c*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+224*a^2*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(14*f*x+14*exp(1)+pi))/(112*f)^2+288*a^2*d^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(18*f*x+18*exp(1)-pi))/(144*f)^2)","F(-2)",0
538,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(2*f*(6*a^2*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+4*a^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2-8*f*(16*a^2*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+14*a^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(2*f*x+2*exp(1)+pi))/(8*f)^2-24*f*(16*a^2*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+14*a^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(1/4*(6*f*x+6*exp(1)-pi))/(24*f)^2+12*f*(-2*a^2*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2+20*f*(-2*a^2*c*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-4*a^2*d*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+80*a^2*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(10*f*x+10*exp(1)+pi))/(40*f)^2+112*a^2*d*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(14*f*x+14*exp(1)-pi))/(56*f)^2)","F(-2)",0
539,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*(2*a^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/f-2*a^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(2*f*x+2*exp(1)+pi))/f-24*a^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(6*f*x+6*exp(1)+pi))/(12*f)^2-40*a^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(10*f*x+10*exp(1)-pi))/(20*f)^2+4*a^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(1/4*(2*f*x-pi)+1/2*exp(1))/(2*f)^2-6*a^2*f*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(1/4*(6*f*x+6*exp(1)-pi))/(3*f)^2)","F(-2)",0
540,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*x+exp(1))/2-pi/4))]Evaluation time: 109.9Not invertible Error: Bad Argument Value","F(-2)",0
541,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2/sqrt(a*tan((f*x+exp(1))/2)^2+a)/(a*tan((f*x+exp(1))/2)^2+a)^2*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(1/3600*tan((f*x+exp(1))/2)*(1560*a^2*d^3*sign(tan((f*x+exp(1))/2)+1)-1800*a^2*c*d^2*sign(tan((f*x+exp(1))/2)+1)+5400*a^2*c^2*d*sign(tan((f*x+exp(1))/2)+1))+1/3600*(-1800*a^2*d^3*sign(tan((f*x+exp(1))/2)+1)+5400*a^2*c*d^2*sign(tan((f*x+exp(1))/2)+1)-5400*a^2*c^2*d*sign(tan((f*x+exp(1))/2)+1)))+1/3600*(4800*a^2*d^3*sign(tan((f*x+exp(1))/2)+1)-7200*a^2*c*d^2*sign(tan((f*x+exp(1))/2)+1)+10800*a^2*c^2*d*sign(tan((f*x+exp(1))/2)+1)))+1/3600*(-4800*a^2*d^3*sign(tan((f*x+exp(1))/2)+1)+7200*a^2*c*d^2*sign(tan((f*x+exp(1))/2)+1)-10800*a^2*c^2*d*sign(tan((f*x+exp(1))/2)+1)))+1/3600*(1800*a^2*d^3*sign(tan((f*x+exp(1))/2)+1)-5400*a^2*c*d^2*sign(tan((f*x+exp(1))/2)+1)+5400*a^2*c^2*d*sign(tan((f*x+exp(1))/2)+1)))+1/3600*(-1560*a^2*d^3*sign(tan((f*x+exp(1))/2)+1)+1800*a^2*c*d^2*sign(tan((f*x+exp(1))/2)+1)-5400*a^2*c^2*d*sign(tan((f*x+exp(1))/2)+1)))+sqrt(2)*(c^3-d^3+3*c*d^2-3*c^2*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+(-15*a*c^3*sqrt(2)*atan(sqrt(a)/sqrt(-a))+45*a*c^2*d*sqrt(2)*atan(sqrt(a)/sqrt(-a))-45*a*c*d^2*sqrt(2)*atan(sqrt(a)/sqrt(-a))+15*a*d^3*sqrt(2)*atan(sqrt(a)/sqrt(-a))+45*c^2*d*sqrt(-a)*sqrt(2)*sqrt(a)-30*c*d^2*sqrt(-a)*sqrt(2)*sqrt(a)+17*d^3*sqrt(-a)*sqrt(2)*sqrt(a))/15/a/sqrt(-a)*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
544,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2/sqrt(a*tan((f*x+exp(1))/2)^2+a)/(a*tan((f*x+exp(1))/2)^2+a)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(-1/144*tan((f*x+exp(1))/2)*(24*a*d^2*sign(tan((f*x+exp(1))/2)+1)-144*a*c*d*sign(tan((f*x+exp(1))/2)+1))-1/144*(-72*a*d^2*sign(tan((f*x+exp(1))/2)+1)+144*a*c*d*sign(tan((f*x+exp(1))/2)+1)))-1/144*(72*a*d^2*sign(tan((f*x+exp(1))/2)+1)-144*a*c*d*sign(tan((f*x+exp(1))/2)+1)))-1/144*(-24*a*d^2*sign(tan((f*x+exp(1))/2)+1)+144*a*c*d*sign(tan((f*x+exp(1))/2)+1)))+sqrt(2)*(c^2+d^2-2*c*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+(-3*a*c^2*sqrt(2)*atan(sqrt(a)/sqrt(-a))+6*a*c*d*sqrt(2)*atan(sqrt(a)/sqrt(-a))-3*a*d^2*sqrt(2)*atan(sqrt(a)/sqrt(-a))+6*c*d*sqrt(-a)*sqrt(2)*sqrt(a)-2*d^2*sqrt(-a)*sqrt(2)*sqrt(a))/3/a/sqrt(-a)*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
545,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2*sqrt(a*tan((f*x+exp(1))/2)^2+a)*(-1/2*d/sign(tan((f*x+exp(1))/2)+1)+1/2*d*tan((f*x+exp(1))/2)/sign(tan((f*x+exp(1))/2)+1))/(a*tan((f*x+exp(1))/2)^2+a)+sqrt(2)*(c-d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)+(-a*c*sqrt(2)*atan(sqrt(a)/sqrt(-a))+a*d*sqrt(2)*atan(sqrt(a)/sqrt(-a))+d*sqrt(-a)*sqrt(2)*sqrt(a))/a/sqrt(-a)*sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
546,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)4*(1/8*sqrt(a)*ln(abs(sin(1/4*(2*f*x+2*exp(1)-pi))+1/sin(1/4*(2*f*x+2*exp(1)-pi))+2))/sqrt(2)/a/sign(cos(1/2*(f*x+exp(1))-1/4*pi))-1/8*sqrt(a)*ln(abs(sin(1/4*(2*f*x+2*exp(1)-pi))+1/sin(1/4*(2*f*x+2*exp(1)-pi))-2))/sqrt(2)/a/sign(cos(1/2*(f*x+exp(1))-1/4*pi)))/f","F(-2)",0
547,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
548,-1,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-49]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[8]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-6]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-13]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-14]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[45]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-35]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-29]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-4]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-62]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-43]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[96]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[98]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[72]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-41]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[72]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-52]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-42]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[1]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-38]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-96]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-63]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-85]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-32]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[64]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[24]Evaluation time: 0.76sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
550,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2/sqrt(a*tan((f*x+exp(1))/2)^2+a)/(a*tan((f*x+exp(1))/2)^2+a)*(tan((f*x+exp(1))/2)*(tan((f*x+exp(1))/2)*(-1/144*tan((f*x+exp(1))/2)*(96*d^3*sign(tan((f*x+exp(1))/2)+1)-216*c*d^2*sign(tan((f*x+exp(1))/2)+1))-1/144*(-144*d^3*sign(tan((f*x+exp(1))/2)+1)+216*c*d^2*sign(tan((f*x+exp(1))/2)+1)))-1/144*(144*d^3*sign(tan((f*x+exp(1))/2)+1)-216*c*d^2*sign(tan((f*x+exp(1))/2)+1)))-1/144*(-96*d^3*sign(tan((f*x+exp(1))/2)+1)+216*c*d^2*sign(tan((f*x+exp(1))/2)+1)))+2*(1/4*(-3*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+3*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-9*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+9*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+a*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-a*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+sqrt(a)*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-sqrt(a)*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+3*a*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-3*a*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+3*sqrt(a)*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-3*sqrt(a)*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*a*c^3-sqrt(a)*a*d^3+3*sqrt(a)*a*c*d^2-3*sqrt(a)*a*c^2*d)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^2/a/sign(tan((f*x+exp(1))/2)+1)+1/4*(c^3+11*d^3-21*c*d^2+9*c^2*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1)))","F(-2)",0
551,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2*sqrt(a*tan((f*x+exp(1))/2)^2+a)*(-1/2*d^2/a/sign(tan((f*x+exp(1))/2)+1)+1/2*d^2*tan((f*x+exp(1))/2)/a/sign(tan((f*x+exp(1))/2)+1))/(a*tan((f*x+exp(1))/2)^2+a)+2*(1/4*(-3*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-3*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+6*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+a*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+sqrt(a)*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-2*a*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-2*sqrt(a)*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*a*c^2+sqrt(a)*a*d^2-2*sqrt(a)*a*c*d)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^2/a/sign(tan((f*x+exp(1))/2)+1)+1/4*(c^2-7*d^2+6*c*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1)))","F(-2)",0
552,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/4*(-3*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+3*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+a*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-a*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+sqrt(a)*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-sqrt(a)*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*a*c-sqrt(a)*a*d)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^2/a/sign(tan((f*x+exp(1))/2)+1)+1/4*(c+3*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
553,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/4*(-3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+sqrt(a)*a)/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^2/a/sign(tan((f*x+exp(1))/2)+1)+1/4*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/sqrt(-a)/a/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
554,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 1.29sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
555,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.57Error: Bad Argument Type","F(-2)",0
556,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.62Unable to divide, perhaps due to rounding error%%%{%%%{1,[1]%%%},[18,1,3,0]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,1,3,0]%%%}+%%%{%%{[%%%{-12,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,1,2,1]%%%}+%%%{%%%{15,[2]%%%},[16,1,3,0]%%%}+%%%{%%%{72,[2]%%%},[16,1,2,1]%%%}+%%%{%%%{48,[2]%%%},[16,1,1,2]%%%}+%%%{%%{[%%%{-32,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,1,3,0]%%%}+%%%{%%{[%%%{-144,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,1,2,1]%%%}+%%%{%%{[%%%{-288,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,1,1,2]%%%}+%%%{%%{[%%%{-64,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,1,0,3]%%%}+%%%{%%%{60,[3]%%%},[14,1,3,0]%%%}+%%%{%%%{168,[3]%%%},[14,1,2,1]%%%}+%%%{%%%{432,[3]%%%},[14,1,1,2]%%%}+%%%{%%%{384,[3]%%%},[14,1,0,3]%%%}+%%%{%%{[%%%{-72,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,1,3,0]%%%}+%%%{%%{[%%%{-240,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,1,2,1]%%%}+%%%{%%{[%%%{192,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,1,1,2]%%%}+%%%{%%{[%%%{-384,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,1,0,3]%%%}+%%%{%%%{100,[4]%%%},[12,1,3,0]%%%}+%%%{%%%{72,[4]%%%},[12,1,2,1]%%%}+%%%{%%%{-528,[4]%%%},[12,1,1,2]%%%}+%%%{%%%{-1408,[4]%%%},[12,1,0,3]%%%}+%%%{%%{[%%%{-96,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,1,3,0]%%%}+%%%{%%{[%%%{144,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,1,2,1]%%%}+%%%{%%{[%%%{288,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,1,1,2]%%%}+%%%{%%{[%%%{2112,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,1,0,3]%%%}+%%%{%%%{54,[5]%%%},[10,1,3,0]%%%}+%%%{%%%{-24,[5]%%%},[10,1,2,1]%%%}+%%%{%%%{-912,[5]%%%},[10,1,1,2]%%%}+%%%{%%%{2304,[5]%%%},[10,1,0,3]%%%}+%%%{%%{[%%%{-100,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,1,3,0]%%%}+%%%{%%{[%%%{504,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,1,2,1]%%%}+%%%{%%{[%%%{-384,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,1,1,2]%%%}+%%%{%%{[%%%{-3328,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,1,0,3]%%%}+%%%{%%%{-54,[6]%%%},[8,1,3,0]%%%}+%%%{%%%{24,[6]%%%},[8,1,2,1]%%%}+%%%{%%%{912,[6]%%%},[8,1,1,2]%%%}+%%%{%%%{-2304,[6]%%%},[8,1,0,3]%%%}+%%%{%%{[%%%{-96,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,1,3,0]%%%}+%%%{%%{[%%%{144,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,1,2,1]%%%}+%%%{%%{[%%%{288,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,1,1,2]%%%}+%%%{%%{[%%%{2112,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,1,0,3]%%%}+%%%{%%%{-100,[7]%%%},[6,1,3,0]%%%}+%%%{%%%{-72,[7]%%%},[6,1,2,1]%%%}+%%%{%%%{528,[7]%%%},[6,1,1,2]%%%}+%%%{%%%{1408,[7]%%%},[6,1,0,3]%%%}+%%%{%%{[%%%{-72,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,3,0]%%%}+%%%{%%{[%%%{-240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,2,1]%%%}+%%%{%%{[%%%{192,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,1,2]%%%}+%%%{%%{[%%%{-384,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,0,3]%%%}+%%%{%%%{-60,[8]%%%},[4,1,3,0]%%%}+%%%{%%%{-168,[8]%%%},[4,1,2,1]%%%}+%%%{%%%{-432,[8]%%%},[4,1,1,2]%%%}+%%%{%%%{-384,[8]%%%},[4,1,0,3]%%%}+%%%{%%{[%%%{-32,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,3,0]%%%}+%%%{%%{[%%%{-144,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,2,1]%%%}+%%%{%%{[%%%{-288,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,1,2]%%%}+%%%{%%{[%%%{-64,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,3]%%%}+%%%{%%%{-15,[9]%%%},[2,1,3,0]%%%}+%%%{%%%{-72,[9]%%%},[2,1,2,1]%%%}+%%%{%%%{-48,[9]%%%},[2,1,1,2]%%%}+%%%{%%{[%%%{-6,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3,0]%%%}+%%%{%%{[%%%{-12,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,2,1]%%%}+%%%{%%%{-1,[10]%%%},[0,1,3,0]%%%} / %%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,0,3,0]%%%}+%%%{%%%{6,[2]%%%},[17,0,3,0]%%%}+%%%{%%%{12,[2]%%%},[17,0,2,1]%%%}+%%%{%%{poly1[%%%{-15,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,3,0]%%%}+%%%{%%{[%%%{-72,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,2,1]%%%}+%%%{%%{poly1[%%%{-48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,1,2]%%%}+%%%{%%%{32,[3]%%%},[15,0,3,0]%%%}+%%%{%%%{144,[3]%%%},[15,0,2,1]%%%}+%%%{%%%{288,[3]%%%},[15,0,1,2]%%%}+%%%{%%%{64,[3]%%%},[15,0,0,3]%%%}+%%%{%%{poly1[%%%{-60,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,3,0]%%%}+%%%{%%{[%%%{-168,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,2,1]%%%}+%%%{%%{poly1[%%%{-432,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,1,2]%%%}+%%%{%%{[%%%{-384,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,0,3]%%%}+%%%{%%%{72,[4]%%%},[13,0,3,0]%%%}+%%%{%%%{240,[4]%%%},[13,0,2,1]%%%}+%%%{%%%{-192,[4]%%%},[13,0,1,2]%%%}+%%%{%%%{384,[4]%%%},[13,0,0,3]%%%}+%%%{%%{poly1[%%%{-100,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,3,0]%%%}+%%%{%%{[%%%{-72,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,2,1]%%%}+%%%{%%{poly1[%%%{528,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,1,2]%%%}+%%%{%%{[%%%{1408,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,0,3]%%%}+%%%{%%%{96,[5]%%%},[11,0,3,0]%%%}+%%%{%%%{-144,[5]%%%},[11,0,2,1]%%%}+%%%{%%%{-288,[5]%%%},[11,0,1,2]%%%}+%%%{%%%{-2112,[5]%%%},[11,0,0,3]%%%}+%%%{%%{poly1[%%%{-54,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,3,0]%%%}+%%%{%%{[%%%{24,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,2,1]%%%}+%%%{%%{poly1[%%%{912,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,1,2]%%%}+%%%{%%{[%%%{-2304,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,0,3]%%%}+%%%{%%%{100,[6]%%%},[9,0,3,0]%%%}+%%%{%%%{-504,[6]%%%},[9,0,2,1]%%%}+%%%{%%%{384,[6]%%%},[9,0,1,2]%%%}+%%%{%%%{3328,[6]%%%},[9,0,0,3]%%%}+%%%{%%{poly1[%%%{54,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,3,0]%%%}+%%%{%%{[%%%{-24,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,2,1]%%%}+%%%{%%{poly1[%%%{-912,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,1,2]%%%}+%%%{%%{[%%%{2304,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,3]%%%}+%%%{%%%{96,[7]%%%},[7,0,3,0]%%%}+%%%{%%%{-144,[7]%%%},[7,0,2,1]%%%}+%%%{%%%{-288,[7]%%%},[7,0,1,2]%%%}+%%%{%%%{-2112,[7]%%%},[7,0,0,3]%%%}+%%%{%%{poly1[%%%{100,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,3,0]%%%}+%%%{%%{[%%%{72,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,2,1]%%%}+%%%{%%{poly1[%%%{-528,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,1,2]%%%}+%%%{%%{[%%%{-1408,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,3]%%%}+%%%{%%%{72,[8]%%%},[5,0,3,0]%%%}+%%%{%%%{240,[8]%%%},[5,0,2,1]%%%}+%%%{%%%{-192,[8]%%%},[5,0,1,2]%%%}+%%%{%%%{384,[8]%%%},[5,0,0,3]%%%}+%%%{%%{poly1[%%%{60,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,3,0]%%%}+%%%{%%{[%%%{168,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,1]%%%}+%%%{%%{poly1[%%%{432,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,2]%%%}+%%%{%%{[%%%{384,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,3]%%%}+%%%{%%%{32,[9]%%%},[3,0,3,0]%%%}+%%%{%%%{144,[9]%%%},[3,0,2,1]%%%}+%%%{%%%{288,[9]%%%},[3,0,1,2]%%%}+%%%{%%%{64,[9]%%%},[3,0,0,3]%%%}+%%%{%%{poly1[%%%{15,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,3,0]%%%}+%%%{%%{[%%%{72,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,1]%%%}+%%%{%%{poly1[%%%{48,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,2]%%%}+%%%{%%%{6,[10]%%%},[1,0,3,0]%%%}+%%%{%%%{12,[10]%%%},[1,0,2,1]%%%}+%%%{%%{poly1[%%%{1,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,3,0]%%%} Error: Bad Argument Value","F(-2)",0
557,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(2*sqrt(a*tan((f*x+exp(1))/2)^2+a)*(-1/2*d^3/a^2/sign(tan((f*x+exp(1))/2)+1)+1/2*d^3*tan((f*x+exp(1))/2)/a^2/sign(tan((f*x+exp(1))/2)+1))/(a*tan((f*x+exp(1))/2)^2+a)+2*(1/32*(-29*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7-43*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+57*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+15*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+75*sqrt(a)*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+237*sqrt(a)*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-399*sqrt(a)*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+87*sqrt(a)*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-55*a*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-161*a*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+267*a*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-51*a*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-91*sqrt(a)*a*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-221*sqrt(a)*a*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+351*sqrt(a)*a*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-39*sqrt(a)*a*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+a^2*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-25*a^2*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+51*a^2*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-27*a^2*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+27*a^3*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+93*a^3*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+65*sqrt(a)*a^2*c^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+103*sqrt(a)*a^2*d^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-159*a^3*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+39*a^3*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-141*sqrt(a)*a^2*c*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-27*sqrt(a)*a^2*c^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+7*sqrt(a)*a^3*c^3+17*sqrt(a)*a^3*d^3-27*sqrt(a)*a^3*c*d^2+3*sqrt(a)*a^3*c^2*d)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^4/sign(tan((f*x+exp(1))/2)+1)+1/32*(3*c^3-75*d^3+57*c*d^2+15*c^2*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1)))","F(-2)",0
558,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/32*(-29*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+19*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+10*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+75*sqrt(a)*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-133*sqrt(a)*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+58*sqrt(a)*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-55*a*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5+89*a*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-34*a*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-91*sqrt(a)*a*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+117*sqrt(a)*a*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-26*sqrt(a)*a*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+a^2*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+17*a^2*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-18*a^2*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+27*a^3*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-53*a^3*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+65*sqrt(a)*a^2*c^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-47*sqrt(a)*a^2*d^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+26*a^3*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))-18*sqrt(a)*a^2*c*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+7*sqrt(a)*a^3*c^2-9*sqrt(a)*a^3*d^2+2*sqrt(a)*a^3*c*d)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^4/sign(tan((f*x+exp(1))/2)+1)+1/32*(3*c^2+19*d^2+10*c*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
559,-2,0,0,0.000000," ","integrate((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/32*(-29*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+5*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+75*sqrt(a)*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6+29*sqrt(a)*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-55*a*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-17*a*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-91*sqrt(a)*a*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4-13*sqrt(a)*a*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+a^2*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3-9*a^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+27*a^3*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+13*a^3*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+65*sqrt(a)*a^2*c*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2-9*sqrt(a)*a^2*d*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+7*sqrt(a)*a^3*c+sqrt(a)*a^3*d)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^4/sign(tan((f*x+exp(1))/2)+1)+1/32*(3*c+5*d)*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
560,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*2*(1/32*(-29*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^7+75*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^6-55*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^5-91*sqrt(a)*a*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^4+a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^3+27*a^3*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+65*sqrt(a)*a^2*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+7*sqrt(a)*a^3)/a^2/(-(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))^2+2*sqrt(a)*(-sqrt(a)*tan((f*x+exp(1))/2)+sqrt(a*tan((f*x+exp(1))/2)^2+a))+a)^4/sign(tan((f*x+exp(1))/2)+1)+3/32*atan((-sqrt(a)*tan((f*x+exp(1))/2)-sqrt(a)+sqrt(a*tan((f*x+exp(1))/2)^2+a))/sqrt(2)/sqrt(-a))/sqrt(2)/a^2/sqrt(-a)/sign(tan((f*x+exp(1))/2)+1))","F(-2)",0
561,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 1.56sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
562,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 0.78Error: Bad Argument Type","F(-2)",0
563,-2,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(cos((f*t_nostep+exp(1))/2-pi/4))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of cos((f*t_nostep+exp(1))/2-pi/4) were not checkedUnable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep+1)]Evaluation time: 1.17index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
564,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
565,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
566,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
567,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
568,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)-8*sqrt(2*a)*(-1024*d^4+2048*c*d^3-1024*c^2*d^2)*sqrt(c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+2*c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6*d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+c+d)*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))/f/(2048*d^5-2048*c*d^4-2048*c^2*d^3+2048*c^3*d^2)/(c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+2*c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6*d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+c+d)","F(-2)",0
569,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)8*sqrt(2*a)*((-(21233664*d^10-42467328*c*d^9-21233664*c^2*d^8+84934656*c^3*d^7-21233664*c^4*d^6-42467328*c^5*d^5+21233664*c^6*d^4)*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2/(-42467328*d^11+42467328*c*d^10+127401984*c^2*d^9-127401984*c^3*d^8-127401984*c^4*d^7+127401984*c^5*d^6+42467328*c^6*d^5-42467328*c^7*d^4)-(-70778880*d^10+254803968*c*d^9-268959744*c^2*d^8-56623104*c^3*d^7+297271296*c^4*d^6-198180864*c^5*d^5+42467328*c^6*d^4)/(-42467328*d^11+42467328*c*d^10+127401984*c^2*d^9-127401984*c^3*d^8-127401984*c^4*d^7+127401984*c^5*d^6+42467328*c^6*d^5-42467328*c^7*d^4))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-(21233664*d^10-42467328*c*d^9-21233664*c^2*d^8+84934656*c^3*d^7-21233664*c^4*d^6-42467328*c^5*d^5+21233664*c^6*d^4)/(-42467328*d^11+42467328*c*d^10+127401984*c^2*d^9-127401984*c^3*d^8-127401984*c^4*d^7+127401984*c^5*d^6+42467328*c^6*d^5-42467328*c^7*d^4))/sqrt(c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+2*c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6*d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+c+d)/(c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+2*c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6*d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+c+d)*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))/f","F(-2)",0
570,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)8*sqrt(2*a)*((((-(54358179840000*d^16-108716359680000*c*d^15-163074539520000*c^2*d^14+434865438720000*c^3*d^13+108716359680000*c^4*d^12-652298158080000*c^5*d^11+108716359680000*c^6*d^10+434865438720000*c^7*d^9-163074539520000*c^8*d^8-108716359680000*c^9*d^7+54358179840000*c^10*d^6)*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2/(-108716359680000*d^17+108716359680000*c*d^16+543581798400000*c^2*d^15-543581798400000*c^3*d^14-1087163596800000*c^4*d^13+1087163596800000*c^5*d^12+1087163596800000*c^6*d^11-1087163596800000*c^7*d^10-543581798400000*c^8*d^9+543581798400000*c^9*d^8+108716359680000*c^10*d^7-108716359680000*c^11*d^6)-(-362387865600000*d^16+1304596316160000*c*d^15-652298158080000*c^2*d^14-2899102924800000*c^3*d^13+3913788948480000*c^4*d^12+869730877440000*c^5*d^11-4203699240960000*c^6*d^10+1739461754880000*c^7*d^9+1087163596800000*c^8*d^8-1014686023680000*c^9*d^7+217432719360000*c^10*d^6)/(-108716359680000*d^17+108716359680000*c*d^16+543581798400000*c^2*d^15-543581798400000*c^3*d^14-1087163596800000*c^4*d^13+1087163596800000*c^5*d^12+1087163596800000*c^6*d^11-1087163596800000*c^7*d^10-543581798400000*c^8*d^9+543581798400000*c^9*d^8+108716359680000*c^10*d^7-108716359680000*c^11*d^6))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-(1021933780992000*d^16-4595078135808000*c*d^15+6443256250368000*c^2*d^14+753766760448000*c^3*d^13-10944113541120000*c^4*d^12+10465761558528000*c^5*d^11-1203127713792000*c^6*d^10-4812510855168000*c^7*d^9+4355902144512000*c^8*d^8-1811939328000000*c^9*d^7+326149079040000*c^10*d^6)/(-108716359680000*d^17+108716359680000*c*d^16+543581798400000*c^2*d^15-543581798400000*c^3*d^14-1087163596800000*c^4*d^13+1087163596800000*c^5*d^12+1087163596800000*c^6*d^11-1087163596800000*c^7*d^10-543581798400000*c^8*d^9+543581798400000*c^9*d^8+108716359680000*c^10*d^7-108716359680000*c^11*d^6))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-(-362387865600000*d^16+1304596316160000*c*d^15-652298158080000*c^2*d^14-2899102924800000*c^3*d^13+3913788948480000*c^4*d^12+869730877440000*c^5*d^11-4203699240960000*c^6*d^10+1739461754880000*c^7*d^9+1087163596800000*c^8*d^8-1014686023680000*c^9*d^7+217432719360000*c^10*d^6)/(-108716359680000*d^17+108716359680000*c*d^16+543581798400000*c^2*d^15-543581798400000*c^3*d^14-1087163596800000*c^4*d^13+1087163596800000*c^5*d^12+1087163596800000*c^6*d^11-1087163596800000*c^7*d^10-543581798400000*c^8*d^9+543581798400000*c^9*d^8+108716359680000*c^10*d^7-108716359680000*c^11*d^6))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-(54358179840000*d^16-108716359680000*c*d^15-163074539520000*c^2*d^14+434865438720000*c^3*d^13+108716359680000*c^4*d^12-652298158080000*c^5*d^11+108716359680000*c^6*d^10+434865438720000*c^7*d^9-163074539520000*c^8*d^8-108716359680000*c^9*d^7+54358179840000*c^10*d^6)/(-108716359680000*d^17+108716359680000*c*d^16+543581798400000*c^2*d^15-543581798400000*c^3*d^14-1087163596800000*c^4*d^13+1087163596800000*c^5*d^12+1087163596800000*c^6*d^11-1087163596800000*c^7*d^10-543581798400000*c^8*d^9+543581798400000*c^9*d^8+108716359680000*c^10*d^7-108716359680000*c^11*d^6))/sqrt(c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+2*c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6*d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+c+d)/(c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^4+2*c*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2-6*d*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))^2+c+d)^2*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*(1/2*f*x+1/4*(2*exp(1)-pi)))/f","F(-2)",0
571,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
572,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
573,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
574,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
580,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
581,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
582,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
589,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
590,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
591,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
593,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
594,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
595,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
596,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
597,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
598,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
599,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
600,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
601,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
602,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
603,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
604,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
605,0,0,0,0.000000," ","integrate(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
606,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
607,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
608,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
609,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
610,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m, x)","F",0
611,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c), x)","F",0
612,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^2, x)","F",0
613,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^3, x)","F",0
614,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)*(a*sin(f*x + e) + a)^m, x)","F",0
615,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
616,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
617,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
618,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
619,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(5/2), x)","F",0
620,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+5*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((5*sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
621,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+4*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((4*sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
622,1,45,0,0.612736," ","integrate((1+sin(f*x+e))^m*(3+3*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\frac{3^{-m - 1} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3^{-m - 1}}{f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + f}"," ",0,"(3^(-m - 1)*tan(1/2*f*x + 1/2*e) - 3^(-m - 1))/(f*tan(1/2*f*x + 1/2*e) + f)","A",0
623,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+2*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((2*sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
624,0,0,0,0.000000," ","integrate((1+sin(f*x+e))^m*(3+sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 3\right)}^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate((sin(f*x + e) + 3)^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
625,0,0,0,0.000000," ","integrate(3^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int 3^{-m - 1} {\left(\sin\left(f x + e\right) + 1\right)}^{m}\,{d x}"," ",0,"integrate(3^(-m - 1)*(sin(f*x + e) + 1)^m, x)","F",0
626,0,0,0,0.000000," ","integrate((3-sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-\sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-sin(f*x + e) + 3)^(-m - 1), x)","F",0
627,0,0,0,0.000000," ","integrate((3-2*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-2*sin(f*x + e) + 3)^(-m - 1), x)","F",0
628,0,0,0,0.000000," ","integrate((3-3*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-3 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-3*sin(f*x + e) + 3)^(-m - 1), x)","F",0
629,0,0,0,0.000000," ","integrate((3-4*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-4*sin(f*x + e) + 3)^(-m - 1), x)","F",0
630,0,0,0,0.000000," ","integrate((3-5*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(\sin\left(f x + e\right) + 1\right)}^{m} {\left(-5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((sin(f*x + e) + 1)^m*(-5*sin(f*x + e) + 3)^(-m - 1), x)","F",0
631,0,0,0,0.000000," ","integrate((3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(5*sin(f*x + e) + 3)^(-m - 1), x)","F",0
632,0,0,0,0.000000," ","integrate((3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(4*sin(f*x + e) + 3)^(-m - 1), x)","F",0
633,1,827,0,2.575426," ","integrate((3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\frac{e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)}}{f \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + f \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + f \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + f \tan\left(-\frac{3}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{3}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + f}"," ",0,"(e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^3 + 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^2 - 2*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)*tan(1/2*f*x + 1/2*e)^3 - 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e) + 6*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)*tan(1/2*f*x + 1/2*e)^2 - e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(1/2*f*x + 1/2*e)^3 - e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2 + 6*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)*tan(1/2*f*x + 1/2*e) - 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(1/2*f*x + 1/2*e)^2 - 2*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e) + 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(1/2*f*x + 1/2*e) + e^(-m*log(3) + m*log(abs(a)) - log(3)))/(f*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^3 + f*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^2 + f*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e) + f*tan(1/2*f*x + 1/2*e)^3 + f*tan(-3/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 3/4*pi*m + 1/2*f*x + 1/2*e)^2 + f*tan(1/2*f*x + 1/2*e)^2 + f*tan(1/2*f*x + 1/2*e) + f)","B",0
634,0,0,0,0.000000," ","integrate((3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(2*sin(f*x + e) + 3)^(-m - 1), x)","F",0
635,0,0,0,0.000000," ","integrate((3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(\sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(sin(f*x + e) + 3)^(-m - 1), x)","F",0
636,0,0,0,0.000000," ","integrate(3^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int 3^{-m - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(3^(-m - 1)*(a*sin(f*x + e) + a)^m, x)","F",0
637,0,0,0,0.000000," ","integrate((3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-\sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-sin(f*x + e) + 3)^(-m - 1), x)","F",0
638,0,0,0,0.000000," ","integrate((3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-2 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-2*sin(f*x + e) + 3)^(-m - 1), x)","F",0
639,0,0,0,0.000000," ","integrate((3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-3 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-3*sin(f*x + e) + 3)^(-m - 1), x)","F",0
640,0,0,0,0.000000," ","integrate((3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-4 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-4*sin(f*x + e) + 3)^(-m - 1), x)","F",0
641,0,0,0,0.000000," ","integrate((3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-5 \, \sin\left(f x + e\right) + 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-5*sin(f*x + e) + 3)^(-m - 1), x)","F",0
642,0,0,0,0.000000," ","integrate((-3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(5 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(5*sin(f*x + e) - 3)^(-m - 1), x)","F",0
643,0,0,0,0.000000," ","integrate((-3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(4 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(4*sin(f*x + e) - 3)^(-m - 1), x)","F",0
644,0,0,0,0.000000," ","integrate((-3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(3 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(3*sin(f*x + e) - 3)^(-m - 1), x)","F",0
645,0,0,0,0.000000," ","integrate((-3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(2 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(2*sin(f*x + e) - 3)^(-m - 1), x)","F",0
646,0,0,0,0.000000," ","integrate((-3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(\sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(sin(f*x + e) - 3)^(-m - 1), x)","F",0
647,0,0,0,0.000000," ","integrate((-3)^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(-3\right)^{-m - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-3)^(-m - 1)*(a*sin(f*x + e) + a)^m, x)","F",0
648,0,0,0,0.000000," ","integrate((-3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-\sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-sin(f*x + e) - 3)^(-m - 1), x)","F",0
649,0,0,0,0.000000," ","integrate((-3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-2 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-2*sin(f*x + e) - 3)^(-m - 1), x)","F",0
650,1,827,0,1.257188," ","integrate((-3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\frac{e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + e^{\left(-m \log\left(3\right) + m \log\left({\left| a \right|}\right) - \log\left(3\right)\right)}}{f \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + f \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + f \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + f \tan\left(-\frac{5}{4} \, \pi - \pi m \left \lfloor -\frac{1}{4} \, \mathrm{sgn}\left(a\right) + \frac{1}{2} \right \rfloor - \frac{1}{4} \, \pi m \mathrm{sgn}\left(a\right) - \frac{5}{4} \, \pi m + \frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + f \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + f}"," ",0,"(e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^3 + 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^2 - 2*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)*tan(1/2*f*x + 1/2*e)^3 - 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e) + 6*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)*tan(1/2*f*x + 1/2*e)^2 - e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(1/2*f*x + 1/2*e)^3 - e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2 + 6*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)*tan(1/2*f*x + 1/2*e) - 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(1/2*f*x + 1/2*e)^2 - 2*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e) + 3*e^(-m*log(3) + m*log(abs(a)) - log(3))*tan(1/2*f*x + 1/2*e) + e^(-m*log(3) + m*log(abs(a)) - log(3)))/(f*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^3 + f*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e)^2 + f*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2*tan(1/2*f*x + 1/2*e) + f*tan(1/2*f*x + 1/2*e)^3 + f*tan(-5/4*pi - pi*m*floor(-1/4*sgn(a) + 1/2) - 1/4*pi*m*sgn(a) - 5/4*pi*m + 1/2*f*x + 1/2*e)^2 + f*tan(1/2*f*x + 1/2*e)^2 + f*tan(1/2*f*x + 1/2*e) + f)","B",0
651,0,0,0,0.000000," ","integrate((-3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-4 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-4*sin(f*x + e) - 3)^(-m - 1), x)","F",0
652,0,0,0,0.000000," ","integrate((-3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-5 \, \sin\left(f x + e\right) - 3\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-5*sin(f*x + e) - 3)^(-m - 1), x)","F",0
653,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^(-m - 1), x)","F",0
654,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 1), x)","F",0
655,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^n, x)","F",0
656,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n, x)","F",0
657,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
658,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n, x)","F",0
659,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
660,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
661,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^3, x)","F",0
662,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^n, x)","F",0
663,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^n, x)","F",0
664,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
665,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/sqrt(a*sin(f*x + e) + a), x)","F",0
666,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
667,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^(5/2), x)","F",0
668,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(1/3), x)","F",0
669,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(1/3), x)","F",0
670,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(4/3),x, algorithm=""giac"")","\int \frac{a \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(4/3), x)","F",0
671,1,152,0,0.193135," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{b d^{3} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{8} \, {\left(8 \, a c^{3} + 12 \, b c^{2} d + 12 \, a c d^{2} + 3 \, b d^{3}\right)} x + \frac{{\left(3 \, b c d^{2} + a d^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{{\left(4 \, b c^{3} + 12 \, a c^{2} d + 9 \, b c d^{2} + 3 \, a d^{3}\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(3 \, b c^{2} d + 3 \, a c d^{2} + b d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/32*b*d^3*sin(4*f*x + 4*e)/f + 1/8*(8*a*c^3 + 12*b*c^2*d + 12*a*c*d^2 + 3*b*d^3)*x + 1/12*(3*b*c*d^2 + a*d^3)*cos(3*f*x + 3*e)/f - 1/4*(4*b*c^3 + 12*a*c^2*d + 9*b*c*d^2 + 3*a*d^3)*cos(f*x + e)/f - 1/4*(3*b*c^2*d + 3*a*c*d^2 + b*d^3)*sin(2*f*x + 2*e)/f","A",0
672,1,96,0,0.194722," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{b d^{2} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} + \frac{1}{2} \, {\left(2 \, a c^{2} + 2 \, b c d + a d^{2}\right)} x - \frac{{\left(4 \, b c^{2} + 8 \, a c d + 3 \, b d^{2}\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(2 \, b c d + a d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/12*b*d^2*cos(3*f*x + 3*e)/f + 1/2*(2*a*c^2 + 2*b*c*d + a*d^2)*x - 1/4*(4*b*c^2 + 8*a*c*d + 3*b*d^2)*cos(f*x + e)/f - 1/4*(2*b*c*d + a*d^2)*sin(2*f*x + 2*e)/f","A",0
673,1,48,0,0.820285," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, a c + b d\right)} x - \frac{b d \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} - \frac{{\left(b c + a d\right)} \cos\left(f x + e\right)}{f}"," ",0,"1/2*(2*a*c + b*d)*x - 1/4*b*d*sin(2*f*x + 2*e)/f - (b*c + a*d)*cos(f*x + e)/f","A",0
674,1,17,0,0.236278," ","integrate(a+b*sin(f*x+e),x, algorithm=""giac"")","a x - \frac{b \cos\left(f x + e\right)}{f}"," ",0,"a*x - b*cos(f*x + e)/f","A",0
675,1,86,0,0.178927," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} b}{d} - \frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} {\left(b c - a d\right)}}{\sqrt{c^{2} - d^{2}} d}}{f}"," ",0,"((f*x + e)*b/d - 2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*(b*c - a*d)/(sqrt(c^2 - d^2)*d))/f","A",0
676,1,158,0,0.482486," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} {\left(a c - b d\right)}}{{\left(c^{2} - d^{2}\right)}^{\frac{3}{2}}} - \frac{b c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b c^{2} - a c d}{{\left(c^{3} - c d^{2}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*(a*c - b*d)/(c^2 - d^2)^(3/2) - (b*c*d*tan(1/2*f*x + 1/2*e) - a*d^2*tan(1/2*f*x + 1/2*e) + b*c^2 - a*c*d)/((c^3 - c*d^2)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)))/f","A",0
677,1,428,0,0.258677," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a c^{2} - 3 \, b c d + a d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{4} - 2 \, c^{2} d^{2} + d^{4}\right)} \sqrt{c^{2} - d^{2}}} - \frac{3 \, b c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 5 \, a c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, b c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, b c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 7 \, a c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, b c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 11 \, a c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, b c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, b c^{5} - 4 \, a c^{4} d + b c^{3} d^{2} + a c^{2} d^{3}}{{\left(c^{6} - 2 \, c^{4} d^{2} + c^{2} d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"((2*a*c^2 - 3*b*c*d + a*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^4 - 2*c^2*d^2 + d^4)*sqrt(c^2 - d^2)) - (3*b*c^4*d*tan(1/2*f*x + 1/2*e)^3 - 5*a*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 + 2*a*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 2*b*c^5*tan(1/2*f*x + 1/2*e)^2 - 4*a*c^4*d*tan(1/2*f*x + 1/2*e)^2 + 5*b*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 - 7*a*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 + 2*b*c*d^4*tan(1/2*f*x + 1/2*e)^2 + 2*a*d^5*tan(1/2*f*x + 1/2*e)^2 + 5*b*c^4*d*tan(1/2*f*x + 1/2*e) - 11*a*c^3*d^2*tan(1/2*f*x + 1/2*e) + 4*b*c^2*d^3*tan(1/2*f*x + 1/2*e) + 2*a*c*d^4*tan(1/2*f*x + 1/2*e) + 2*b*c^5 - 4*a*c^4*d + b*c^3*d^2 + a*c^2*d^3)/((c^6 - 2*c^4*d^2 + c^2*d^4)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
678,1,274,0,0.246858," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{b^{2} d^{3} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{1}{8} \, {\left(8 \, a^{2} c^{3} + 4 \, b^{2} c^{3} + 24 \, a b c^{2} d + 12 \, a^{2} c d^{2} + 9 \, b^{2} c d^{2} + 6 \, a b d^{3}\right)} x + \frac{{\left(12 \, b^{2} c^{2} d + 24 \, a b c d^{2} + 4 \, a^{2} d^{3} + 5 \, b^{2} d^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(16 \, a b c^{3} + 24 \, a^{2} c^{2} d + 18 \, b^{2} c^{2} d + 36 \, a b c d^{2} + 6 \, a^{2} d^{3} + 5 \, b^{2} d^{3}\right)} \cos\left(f x + e\right)}{8 \, f} + \frac{{\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{{\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2} + 3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-1/80*b^2*d^3*cos(5*f*x + 5*e)/f + 1/8*(8*a^2*c^3 + 4*b^2*c^3 + 24*a*b*c^2*d + 12*a^2*c*d^2 + 9*b^2*c*d^2 + 6*a*b*d^3)*x + 1/48*(12*b^2*c^2*d + 24*a*b*c*d^2 + 4*a^2*d^3 + 5*b^2*d^3)*cos(3*f*x + 3*e)/f - 1/8*(16*a*b*c^3 + 24*a^2*c^2*d + 18*b^2*c^2*d + 36*a*b*c*d^2 + 6*a^2*d^3 + 5*b^2*d^3)*cos(f*x + e)/f + 1/32*(3*b^2*c*d^2 + 2*a*b*d^3)*sin(4*f*x + 4*e)/f - 1/4*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2 + 3*b^2*c*d^2 + 2*a*b*d^3)*sin(2*f*x + 2*e)/f","A",0
679,1,176,0,0.214534," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{b^{2} d^{2} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{8} \, {\left(8 \, a^{2} c^{2} + 4 \, b^{2} c^{2} + 16 \, a b c d + 4 \, a^{2} d^{2} + 3 \, b^{2} d^{2}\right)} x + \frac{{\left(b^{2} c d + a b d^{2}\right)} \cos\left(3 \, f x + 3 \, e\right)}{6 \, f} - \frac{{\left(4 \, a b c^{2} + 4 \, a^{2} c d + 3 \, b^{2} c d + 3 \, a b d^{2}\right)} \cos\left(f x + e\right)}{2 \, f} - \frac{{\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2} + b^{2} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/32*b^2*d^2*sin(4*f*x + 4*e)/f + 1/8*(8*a^2*c^2 + 4*b^2*c^2 + 16*a*b*c*d + 4*a^2*d^2 + 3*b^2*d^2)*x + 1/6*(b^2*c*d + a*b*d^2)*cos(3*f*x + 3*e)/f - 1/2*(4*a*b*c^2 + 4*a^2*c*d + 3*b^2*c*d + 3*a*b*d^2)*cos(f*x + e)/f - 1/4*(b^2*c^2 + 4*a*b*c*d + a^2*d^2 + b^2*d^2)*sin(2*f*x + 2*e)/f","A",0
680,1,96,0,1.369502," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{b^{2} d \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} + \frac{1}{2} \, {\left(2 \, a^{2} c + b^{2} c + 2 \, a b d\right)} x - \frac{{\left(8 \, a b c + 4 \, a^{2} d + 3 \, b^{2} d\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(b^{2} c + 2 \, a b d\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/12*b^2*d*cos(3*f*x + 3*e)/f + 1/2*(2*a^2*c + b^2*c + 2*a*b*d)*x - 1/4*(8*a*b*c + 4*a^2*d + 3*b^2*d)*cos(f*x + e)/f - 1/4*(b^2*c + 2*a*b*d)*sin(2*f*x + 2*e)/f","A",0
681,1,45,0,0.164646," ","integrate((a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, a^{2} + b^{2}\right)} x - \frac{2 \, a b \cos\left(f x + e\right)}{f} - \frac{b^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/2*(2*a^2 + b^2)*x - 2*a*b*cos(f*x + e)/f - 1/4*b^2*sin(2*f*x + 2*e)/f","A",0
682,1,134,0,0.336822," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left(b^{2} c - 2 \, a b d\right)} {\left(f x + e\right)}}{d^{2}} + \frac{2 \, b^{2}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} d} - \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} d^{2}}}{f}"," ",0,"-((b^2*c - 2*a*b*d)*(f*x + e)/d^2 + 2*b^2/((tan(1/2*f*x + 1/2*e)^2 + 1)*d) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*d^2))/f","A",0
683,1,249,0,0.223958," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} b^{2}}{d^{2}} - \frac{2 \, {\left(b^{2} c^{3} - a^{2} c d^{2} - 2 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{2} d^{2} - d^{4}\right)} \sqrt{c^{2} - d^{2}}} + \frac{2 \, {\left(b^{2} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}}{{\left(c^{3} d - c d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}}}{f}"," ",0,"((f*x + e)*b^2/d^2 - 2*(b^2*c^3 - a^2*c*d^2 - 2*b^2*c*d^2 + 2*a*b*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^2*d^2 - d^4)*sqrt(c^2 - d^2)) + 2*(b^2*c^2*d*tan(1/2*f*x + 1/2*e) - 2*a*b*c*d^2*tan(1/2*f*x + 1/2*e) + a^2*d^3*tan(1/2*f*x + 1/2*e) + b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)/((c^3*d - c*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)))/f","B",0
684,1,609,0,0.290083," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{2} c^{2} + b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2} + 2 \, b^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{4} - 2 \, c^{2} d^{2} + d^{4}\right)} \sqrt{c^{2} - d^{2}}} + \frac{b^{2} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a b c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 5 \, a^{2} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, b^{2} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a^{2} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a b c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a^{2} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, b^{2} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, a b c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, b^{2} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - b^{2} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 10 \, a b c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 11 \, a^{2} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 10 \, b^{2} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 8 \, a b c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{2} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 4 \, a b c^{5} + 4 \, a^{2} c^{4} d + 3 \, b^{2} c^{4} d - 2 \, a b c^{3} d^{2} - a^{2} c^{2} d^{3}}{{\left(c^{6} - 2 \, c^{4} d^{2} + c^{2} d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"((2*a^2*c^2 + b^2*c^2 - 6*a*b*c*d + a^2*d^2 + 2*b^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^4 - 2*c^2*d^2 + d^4)*sqrt(c^2 - d^2)) + (b^2*c^5*tan(1/2*f*x + 1/2*e)^3 - 6*a*b*c^4*d*tan(1/2*f*x + 1/2*e)^3 + 5*a^2*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 + 2*b^2*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 - 2*a^2*c*d^4*tan(1/2*f*x + 1/2*e)^3 - 4*a*b*c^5*tan(1/2*f*x + 1/2*e)^2 + 4*a^2*c^4*d*tan(1/2*f*x + 1/2*e)^2 + 3*b^2*c^4*d*tan(1/2*f*x + 1/2*e)^2 - 10*a*b*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 + 6*b^2*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 4*a*b*c*d^4*tan(1/2*f*x + 1/2*e)^2 - 2*a^2*d^5*tan(1/2*f*x + 1/2*e)^2 - b^2*c^5*tan(1/2*f*x + 1/2*e) - 10*a*b*c^4*d*tan(1/2*f*x + 1/2*e) + 11*a^2*c^3*d^2*tan(1/2*f*x + 1/2*e) + 10*b^2*c^3*d^2*tan(1/2*f*x + 1/2*e) - 8*a*b*c^2*d^3*tan(1/2*f*x + 1/2*e) - 2*a^2*c*d^4*tan(1/2*f*x + 1/2*e) - 4*a*b*c^5 + 4*a^2*c^4*d + 3*b^2*c^4*d - 2*a*b*c^3*d^2 - a^2*c^2*d^3)/((c^6 - 2*c^4*d^2 + c^2*d^4)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
685,1,1316,0,3.152640," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{2} c^{3} + b^{2} c^{3} - 8 \, a b c^{2} d + 3 \, a^{2} c d^{2} + 4 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{6} - 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} - d^{6}\right)} \sqrt{c^{2} - d^{2}}} + \frac{3 \, b^{2} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 24 \, a b c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 27 \, a^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 12 \, b^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 \, a b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 \, a^{2} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 12 \, a b c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 18 \, a^{2} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 15 \, b^{2} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 84 \, a b c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 81 \, a^{2} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 60 \, b^{2} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 66 \, a b c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 36 \, a^{2} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a b c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a^{2} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 72 \, a b c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 108 \, a^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 78 \, b^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 168 \, a b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 42 \, a^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 64 \, b^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 68 \, a b c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, a^{2} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, b^{2} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, a b c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, a^{2} d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 24 \, a b c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, a^{2} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 24 \, b^{2} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 120 \, a b c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 120 \, a^{2} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 102 \, b^{2} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 168 \, a b c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 18 \, a^{2} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 24 \, b^{2} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a b c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{2} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, b^{2} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 48 \, a b c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 81 \, a^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 66 \, b^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 114 \, a b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 \, b^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 \, a b c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{2} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a b c^{8} + 18 \, a^{2} c^{7} d + 13 \, b^{2} c^{7} d - 20 \, a b c^{6} d^{2} - 5 \, a^{2} c^{5} d^{3} + 2 \, b^{2} c^{5} d^{3} + 2 \, a b c^{4} d^{4} + 2 \, a^{2} c^{3} d^{5}}{{\left(c^{9} - 3 \, c^{7} d^{2} + 3 \, c^{5} d^{4} - c^{3} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(2*a^2*c^3 + b^2*c^3 - 8*a*b*c^2*d + 3*a^2*c*d^2 + 4*b^2*c*d^2 - 2*a*b*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^6 - 3*c^4*d^2 + 3*c^2*d^4 - d^6)*sqrt(c^2 - d^2)) + (3*b^2*c^8*tan(1/2*f*x + 1/2*e)^5 - 24*a*b*c^7*d*tan(1/2*f*x + 1/2*e)^5 + 27*a^2*c^6*d^2*tan(1/2*f*x + 1/2*e)^5 + 12*b^2*c^6*d^2*tan(1/2*f*x + 1/2*e)^5 - 6*a*b*c^5*d^3*tan(1/2*f*x + 1/2*e)^5 - 18*a^2*c^4*d^4*tan(1/2*f*x + 1/2*e)^5 + 6*a^2*c^2*d^6*tan(1/2*f*x + 1/2*e)^5 - 12*a*b*c^8*tan(1/2*f*x + 1/2*e)^4 + 18*a^2*c^7*d*tan(1/2*f*x + 1/2*e)^4 + 15*b^2*c^7*d*tan(1/2*f*x + 1/2*e)^4 - 84*a*b*c^6*d^2*tan(1/2*f*x + 1/2*e)^4 + 81*a^2*c^5*d^3*tan(1/2*f*x + 1/2*e)^4 + 60*b^2*c^5*d^3*tan(1/2*f*x + 1/2*e)^4 - 66*a*b*c^4*d^4*tan(1/2*f*x + 1/2*e)^4 - 36*a^2*c^3*d^5*tan(1/2*f*x + 1/2*e)^4 + 12*a*b*c^2*d^6*tan(1/2*f*x + 1/2*e)^4 + 12*a^2*c*d^7*tan(1/2*f*x + 1/2*e)^4 - 72*a*b*c^7*d*tan(1/2*f*x + 1/2*e)^3 + 108*a^2*c^6*d^2*tan(1/2*f*x + 1/2*e)^3 + 78*b^2*c^6*d^2*tan(1/2*f*x + 1/2*e)^3 - 168*a*b*c^5*d^3*tan(1/2*f*x + 1/2*e)^3 + 42*a^2*c^4*d^4*tan(1/2*f*x + 1/2*e)^3 + 64*b^2*c^4*d^4*tan(1/2*f*x + 1/2*e)^3 - 68*a*b*c^3*d^5*tan(1/2*f*x + 1/2*e)^3 - 8*a^2*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 + 8*b^2*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 + 8*a*b*c*d^7*tan(1/2*f*x + 1/2*e)^3 + 8*a^2*d^8*tan(1/2*f*x + 1/2*e)^3 - 24*a*b*c^8*tan(1/2*f*x + 1/2*e)^2 + 36*a^2*c^7*d*tan(1/2*f*x + 1/2*e)^2 + 24*b^2*c^7*d*tan(1/2*f*x + 1/2*e)^2 - 120*a*b*c^6*d^2*tan(1/2*f*x + 1/2*e)^2 + 120*a^2*c^5*d^3*tan(1/2*f*x + 1/2*e)^2 + 102*b^2*c^5*d^3*tan(1/2*f*x + 1/2*e)^2 - 168*a*b*c^4*d^4*tan(1/2*f*x + 1/2*e)^2 - 18*a^2*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 24*b^2*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 12*a*b*c^2*d^6*tan(1/2*f*x + 1/2*e)^2 + 12*a^2*c*d^7*tan(1/2*f*x + 1/2*e)^2 - 3*b^2*c^8*tan(1/2*f*x + 1/2*e) - 48*a*b*c^7*d*tan(1/2*f*x + 1/2*e) + 81*a^2*c^6*d^2*tan(1/2*f*x + 1/2*e) + 66*b^2*c^6*d^2*tan(1/2*f*x + 1/2*e) - 114*a*b*c^5*d^3*tan(1/2*f*x + 1/2*e) - 12*a^2*c^4*d^4*tan(1/2*f*x + 1/2*e) + 12*b^2*c^4*d^4*tan(1/2*f*x + 1/2*e) + 12*a*b*c^3*d^5*tan(1/2*f*x + 1/2*e) + 6*a^2*c^2*d^6*tan(1/2*f*x + 1/2*e) - 12*a*b*c^8 + 18*a^2*c^7*d + 13*b^2*c^7*d - 20*a*b*c^6*d^2 - 5*a^2*c^5*d^3 + 2*b^2*c^5*d^3 + 2*a*b*c^4*d^4 + 2*a^2*c^3*d^5)/((c^9 - 3*c^7*d^2 + 3*c^5*d^4 - c^3*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^3))/f","B",0
686,1,416,0,0.217453," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","-\frac{b^{3} d^{3} \sin\left(6 \, f x + 6 \, e\right)}{192 \, f} + \frac{1}{16} \, {\left(16 \, a^{3} c^{3} + 24 \, a b^{2} c^{3} + 72 \, a^{2} b c^{2} d + 18 \, b^{3} c^{2} d + 24 \, a^{3} c d^{2} + 54 \, a b^{2} c d^{2} + 18 \, a^{2} b d^{3} + 5 \, b^{3} d^{3}\right)} x - \frac{3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{{\left(4 \, b^{3} c^{3} + 36 \, a b^{2} c^{2} d + 36 \, a^{2} b c d^{2} + 15 \, b^{3} c d^{2} + 4 \, a^{3} d^{3} + 15 \, a b^{2} d^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{3 \, {\left(8 \, a^{2} b c^{3} + 2 \, b^{3} c^{3} + 8 \, a^{3} c^{2} d + 18 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} + 5 \, b^{3} c d^{2} + 2 \, a^{3} d^{3} + 5 \, a b^{2} d^{3}\right)} \cos\left(f x + e\right)}{8 \, f} + \frac{3 \, {\left(2 \, b^{3} c^{2} d + 6 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3} + b^{3} d^{3}\right)} \sin\left(4 \, f x + 4 \, e\right)}{64 \, f} - \frac{3 \, {\left(16 \, a b^{2} c^{3} + 48 \, a^{2} b c^{2} d + 16 \, b^{3} c^{2} d + 16 \, a^{3} c d^{2} + 48 \, a b^{2} c d^{2} + 16 \, a^{2} b d^{3} + 5 \, b^{3} d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)}{64 \, f}"," ",0,"-1/192*b^3*d^3*sin(6*f*x + 6*e)/f + 1/16*(16*a^3*c^3 + 24*a*b^2*c^3 + 72*a^2*b*c^2*d + 18*b^3*c^2*d + 24*a^3*c*d^2 + 54*a*b^2*c*d^2 + 18*a^2*b*d^3 + 5*b^3*d^3)*x - 3/80*(b^3*c*d^2 + a*b^2*d^3)*cos(5*f*x + 5*e)/f + 1/48*(4*b^3*c^3 + 36*a*b^2*c^2*d + 36*a^2*b*c*d^2 + 15*b^3*c*d^2 + 4*a^3*d^3 + 15*a*b^2*d^3)*cos(3*f*x + 3*e)/f - 3/8*(8*a^2*b*c^3 + 2*b^3*c^3 + 8*a^3*c^2*d + 18*a*b^2*c^2*d + 18*a^2*b*c*d^2 + 5*b^3*c*d^2 + 2*a^3*d^3 + 5*a*b^2*d^3)*cos(f*x + e)/f + 3/64*(2*b^3*c^2*d + 6*a*b^2*c*d^2 + 2*a^2*b*d^3 + b^3*d^3)*sin(4*f*x + 4*e)/f - 3/64*(16*a*b^2*c^3 + 48*a^2*b*c^2*d + 16*b^3*c^2*d + 16*a^3*c*d^2 + 48*a*b^2*c*d^2 + 16*a^2*b*d^3 + 5*b^3*d^3)*sin(2*f*x + 2*e)/f","A",0
687,1,274,0,1.135609," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","-\frac{b^{3} d^{2} \cos\left(5 \, f x + 5 \, e\right)}{80 \, f} + \frac{1}{8} \, {\left(8 \, a^{3} c^{2} + 12 \, a b^{2} c^{2} + 24 \, a^{2} b c d + 6 \, b^{3} c d + 4 \, a^{3} d^{2} + 9 \, a b^{2} d^{2}\right)} x + \frac{{\left(4 \, b^{3} c^{2} + 24 \, a b^{2} c d + 12 \, a^{2} b d^{2} + 5 \, b^{3} d^{2}\right)} \cos\left(3 \, f x + 3 \, e\right)}{48 \, f} - \frac{{\left(24 \, a^{2} b c^{2} + 6 \, b^{3} c^{2} + 16 \, a^{3} c d + 36 \, a b^{2} c d + 18 \, a^{2} b d^{2} + 5 \, b^{3} d^{2}\right)} \cos\left(f x + e\right)}{8 \, f} + \frac{{\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} - \frac{{\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + 2 \, b^{3} c d + a^{3} d^{2} + 3 \, a b^{2} d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"-1/80*b^3*d^2*cos(5*f*x + 5*e)/f + 1/8*(8*a^3*c^2 + 12*a*b^2*c^2 + 24*a^2*b*c*d + 6*b^3*c*d + 4*a^3*d^2 + 9*a*b^2*d^2)*x + 1/48*(4*b^3*c^2 + 24*a*b^2*c*d + 12*a^2*b*d^2 + 5*b^3*d^2)*cos(3*f*x + 3*e)/f - 1/8*(24*a^2*b*c^2 + 6*b^3*c^2 + 16*a^3*c*d + 36*a*b^2*c*d + 18*a^2*b*d^2 + 5*b^3*d^2)*cos(f*x + e)/f + 1/32*(2*b^3*c*d + 3*a*b^2*d^2)*sin(4*f*x + 4*e)/f - 1/4*(3*a*b^2*c^2 + 6*a^2*b*c*d + 2*b^3*c*d + a^3*d^2 + 3*a*b^2*d^2)*sin(2*f*x + 2*e)/f","A",0
688,1,152,0,0.190530," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{b^{3} d \sin\left(4 \, f x + 4 \, e\right)}{32 \, f} + \frac{1}{8} \, {\left(8 \, a^{3} c + 12 \, a b^{2} c + 12 \, a^{2} b d + 3 \, b^{3} d\right)} x + \frac{{\left(b^{3} c + 3 \, a b^{2} d\right)} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{{\left(12 \, a^{2} b c + 3 \, b^{3} c + 4 \, a^{3} d + 9 \, a b^{2} d\right)} \cos\left(f x + e\right)}{4 \, f} - \frac{{\left(3 \, a b^{2} c + 3 \, a^{2} b d + b^{3} d\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f}"," ",0,"1/32*b^3*d*sin(4*f*x + 4*e)/f + 1/8*(8*a^3*c + 12*a*b^2*c + 12*a^2*b*d + 3*b^3*d)*x + 1/12*(b^3*c + 3*a*b^2*d)*cos(3*f*x + 3*e)/f - 1/4*(12*a^2*b*c + 3*b^3*c + 4*a^3*d + 9*a*b^2*d)*cos(f*x + e)/f - 1/4*(3*a*b^2*c + 3*a^2*b*d + b^3*d)*sin(2*f*x + 2*e)/f","A",0
689,1,75,0,0.147661," ","integrate((a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{b^{3} \cos\left(3 \, f x + 3 \, e\right)}{12 \, f} - \frac{3 \, a b^{2} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f} + \frac{1}{2} \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} x - \frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/12*b^3*cos(3*f*x + 3*e)/f - 3/4*a*b^2*sin(2*f*x + 2*e)/f + 1/2*(2*a^3 + 3*a*b^2)*x - 3/4*(4*a^2*b + b^3)*cos(f*x + e)/f","A",0
690,1,252,0,0.600771," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, b^{3} c^{2} - 6 \, a b^{2} c d + 6 \, a^{2} b d^{2} + b^{3} d^{2}\right)} {\left(f x + e\right)}}{d^{3}} - \frac{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} d^{3}} + \frac{2 \, {\left(b^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, b^{3} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a b^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - b^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, b^{3} c - 6 \, a b^{2} d\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} d^{2}}}{2 \, f}"," ",0,"1/2*((2*b^3*c^2 - 6*a*b^2*c*d + 6*a^2*b*d^2 + b^3*d^2)*(f*x + e)/d^3 - 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*d^3) + 2*(b^3*d*tan(1/2*f*x + 1/2*e)^3 + 2*b^3*c*tan(1/2*f*x + 1/2*e)^2 - 6*a*b^2*d*tan(1/2*f*x + 1/2*e)^2 - b^3*d*tan(1/2*f*x + 1/2*e) + 2*b^3*c - 6*a*b^2*d)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*d^2))/f","A",0
691,1,585,0,0.205834," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 3 \, b^{3} c^{2} d^{2} + a^{3} c d^{3} + 6 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{2} d^{3} - d^{5}\right)} \sqrt{c^{2} - d^{2}}} - \frac{2 \, {\left(b^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, a b^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, a^{2} b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - a^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, b^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, a b^{2} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a^{2} b c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - b^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, b^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, a b^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a^{2} b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, b^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - b^{3} c^{2} d^{2} - a^{3} c d^{3}\right)}}{{\left(c^{3} d^{2} - c d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}} - \frac{{\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} {\left(f x + e\right)}}{d^{3}}}{f}"," ",0,"(2*(2*b^3*c^4 - 3*a*b^2*c^3*d - 3*b^3*c^2*d^2 + a^3*c*d^3 + 6*a*b^2*c*d^3 - 3*a^2*b*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^2*d^3 - d^5)*sqrt(c^2 - d^2)) - 2*(b^3*c^3*d*tan(1/2*f*x + 1/2*e)^3 - 3*a*b^2*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 + 3*a^2*b*c*d^3*tan(1/2*f*x + 1/2*e)^3 - a^3*d^4*tan(1/2*f*x + 1/2*e)^3 + 2*b^3*c^4*tan(1/2*f*x + 1/2*e)^2 - 3*a*b^2*c^3*d*tan(1/2*f*x + 1/2*e)^2 + 3*a^2*b*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 - b^3*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 - a^3*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 3*b^3*c^3*d*tan(1/2*f*x + 1/2*e) - 3*a*b^2*c^2*d^2*tan(1/2*f*x + 1/2*e) + 3*a^2*b*c*d^3*tan(1/2*f*x + 1/2*e) - 2*b^3*c*d^3*tan(1/2*f*x + 1/2*e) - a^3*d^4*tan(1/2*f*x + 1/2*e) + 2*b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - b^3*c^2*d^2 - a^3*c*d^3)/((c^3*d^2 - c*d^4)*(c*tan(1/2*f*x + 1/2*e)^4 + 2*d*tan(1/2*f*x + 1/2*e)^3 + 2*c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)) - (2*b^3*c - 3*a*b^2*d)*(f*x + e)/d^3)/f","B",0
692,1,889,0,0.293389," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} b^{3}}{d^{3}} - \frac{{\left(2 \, b^{3} c^{5} - 5 \, b^{3} c^{3} d^{2} - 2 \, a^{3} c^{2} d^{3} - 3 \, a b^{2} c^{2} d^{3} + 9 \, a^{2} b c d^{4} + 6 \, b^{3} c d^{4} - a^{3} d^{5} - 6 \, a b^{2} d^{5}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{4} d^{3} - 2 \, c^{2} d^{5} + d^{7}\right)} \sqrt{c^{2} - d^{2}}} + \frac{b^{3} c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, a b^{2} c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 9 \, a^{2} b c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, b^{3} c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 5 \, a^{3} c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, a b^{2} c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a^{3} c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, b^{3} c^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a^{2} b c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - b^{3} c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a^{3} c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 9 \, a b^{2} c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 15 \, a^{2} b c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, b^{3} c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{3} c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18 \, a b^{2} c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a^{2} b c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{3} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, b^{3} c^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, a b^{2} c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 15 \, a^{2} b c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 16 \, b^{3} c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 11 \, a^{3} c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 30 \, a b^{2} c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a^{2} b c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{3} c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, b^{3} c^{7} - 6 \, a^{2} b c^{5} d^{2} - 5 \, b^{3} c^{5} d^{2} + 4 \, a^{3} c^{4} d^{3} + 9 \, a b^{2} c^{4} d^{3} - 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}}{{\left(c^{6} d^{2} - 2 \, c^{4} d^{4} + c^{2} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"((f*x + e)*b^3/d^3 - (2*b^3*c^5 - 5*b^3*c^3*d^2 - 2*a^3*c^2*d^3 - 3*a*b^2*c^2*d^3 + 9*a^2*b*c*d^4 + 6*b^3*c*d^4 - a^3*d^5 - 6*a*b^2*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^4*d^3 - 2*c^2*d^5 + d^7)*sqrt(c^2 - d^2)) + (b^3*c^6*d*tan(1/2*f*x + 1/2*e)^3 + 3*a*b^2*c^5*d^2*tan(1/2*f*x + 1/2*e)^3 - 9*a^2*b*c^4*d^3*tan(1/2*f*x + 1/2*e)^3 - 4*b^3*c^4*d^3*tan(1/2*f*x + 1/2*e)^3 + 5*a^3*c^3*d^4*tan(1/2*f*x + 1/2*e)^3 + 6*a*b^2*c^3*d^4*tan(1/2*f*x + 1/2*e)^3 - 2*a^3*c*d^6*tan(1/2*f*x + 1/2*e)^3 + 2*b^3*c^7*tan(1/2*f*x + 1/2*e)^2 - 6*a^2*b*c^5*d^2*tan(1/2*f*x + 1/2*e)^2 - b^3*c^5*d^2*tan(1/2*f*x + 1/2*e)^2 + 4*a^3*c^4*d^3*tan(1/2*f*x + 1/2*e)^2 + 9*a*b^2*c^4*d^3*tan(1/2*f*x + 1/2*e)^2 - 15*a^2*b*c^3*d^4*tan(1/2*f*x + 1/2*e)^2 - 10*b^3*c^3*d^4*tan(1/2*f*x + 1/2*e)^2 + 7*a^3*c^2*d^5*tan(1/2*f*x + 1/2*e)^2 + 18*a*b^2*c^2*d^5*tan(1/2*f*x + 1/2*e)^2 - 6*a^2*b*c*d^6*tan(1/2*f*x + 1/2*e)^2 - 2*a^3*d^7*tan(1/2*f*x + 1/2*e)^2 + 7*b^3*c^6*d*tan(1/2*f*x + 1/2*e) - 3*a*b^2*c^5*d^2*tan(1/2*f*x + 1/2*e) - 15*a^2*b*c^4*d^3*tan(1/2*f*x + 1/2*e) - 16*b^3*c^4*d^3*tan(1/2*f*x + 1/2*e) + 11*a^3*c^3*d^4*tan(1/2*f*x + 1/2*e) + 30*a*b^2*c^3*d^4*tan(1/2*f*x + 1/2*e) - 12*a^2*b*c^2*d^5*tan(1/2*f*x + 1/2*e) - 2*a^3*c*d^6*tan(1/2*f*x + 1/2*e) + 2*b^3*c^7 - 6*a^2*b*c^5*d^2 - 5*b^3*c^5*d^2 + 4*a^3*c^4*d^3 + 9*a*b^2*c^4*d^3 - 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)/((c^6*d^2 - 2*c^4*d^4 + c^2*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
693,1,1677,0,0.378664," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{3} c^{3} + 3 \, a b^{2} c^{3} - 12 \, a^{2} b c^{2} d - 3 \, b^{3} c^{2} d + 3 \, a^{3} c d^{2} + 12 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} - 2 \, b^{3} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(c^{6} - 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} - d^{6}\right)} \sqrt{c^{2} - d^{2}}} + \frac{9 \, a b^{2} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 36 \, a^{2} b c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 9 \, b^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 27 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 36 \, a b^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 9 \, a^{2} b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 \, b^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 18 \, a^{2} b c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 18 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, a b^{2} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 126 \, a^{2} b c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 45 \, b^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 81 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 180 \, a b^{2} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 99 \, a^{2} b c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 30 \, b^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 36 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 18 \, a^{2} b c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a^{3} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 108 \, a^{2} b c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 24 \, b^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 108 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 234 \, a b^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 252 \, a^{2} b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 82 \, b^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 42 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 192 \, a b^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 102 \, a^{2} b c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 44 \, b^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 24 \, a b^{2} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a^{2} b c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, a^{3} d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 36 \, a^{2} b c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, b^{3} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, a^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 72 \, a b^{2} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 180 \, a^{2} b c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 36 \, b^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 120 \, a^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 306 \, a b^{2} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 252 \, a^{2} b c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 102 \, b^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 18 \, a^{3} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 72 \, a b^{2} c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18 \, a^{2} b c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{3} c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, a b^{2} c^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 72 \, a^{2} b c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 15 \, b^{3} c^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 81 \, a^{3} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 198 \, a b^{2} c^{6} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 171 \, a^{2} b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 60 \, b^{3} c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a^{3} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 36 \, a b^{2} c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 18 \, a^{2} b c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{3} c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 18 \, a^{2} b c^{8} - 4 \, b^{3} c^{8} + 18 \, a^{3} c^{7} d + 39 \, a b^{2} c^{7} d - 30 \, a^{2} b c^{6} d^{2} - 11 \, b^{3} c^{6} d^{2} - 5 \, a^{3} c^{5} d^{3} + 6 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} + 2 \, a^{3} c^{3} d^{5}}{{\left(c^{9} - 3 \, c^{7} d^{2} + 3 \, c^{5} d^{4} - c^{3} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{3}}}{3 \, f}"," ",0,"1/3*(3*(2*a^3*c^3 + 3*a*b^2*c^3 - 12*a^2*b*c^2*d - 3*b^3*c^2*d + 3*a^3*c*d^2 + 12*a*b^2*c*d^2 - 3*a^2*b*d^3 - 2*b^3*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((c^6 - 3*c^4*d^2 + 3*c^2*d^4 - d^6)*sqrt(c^2 - d^2)) + (9*a*b^2*c^8*tan(1/2*f*x + 1/2*e)^5 - 36*a^2*b*c^7*d*tan(1/2*f*x + 1/2*e)^5 - 9*b^3*c^7*d*tan(1/2*f*x + 1/2*e)^5 + 27*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^5 + 36*a*b^2*c^6*d^2*tan(1/2*f*x + 1/2*e)^5 - 9*a^2*b*c^5*d^3*tan(1/2*f*x + 1/2*e)^5 - 6*b^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^5 - 18*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^5 + 6*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^5 - 18*a^2*b*c^8*tan(1/2*f*x + 1/2*e)^4 + 18*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^4 + 45*a*b^2*c^7*d*tan(1/2*f*x + 1/2*e)^4 - 126*a^2*b*c^6*d^2*tan(1/2*f*x + 1/2*e)^4 - 45*b^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^4 + 81*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^4 + 180*a*b^2*c^5*d^3*tan(1/2*f*x + 1/2*e)^4 - 99*a^2*b*c^4*d^4*tan(1/2*f*x + 1/2*e)^4 - 30*b^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^4 - 36*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^4 + 18*a^2*b*c^2*d^6*tan(1/2*f*x + 1/2*e)^4 + 12*a^3*c*d^7*tan(1/2*f*x + 1/2*e)^4 - 108*a^2*b*c^7*d*tan(1/2*f*x + 1/2*e)^3 - 24*b^3*c^7*d*tan(1/2*f*x + 1/2*e)^3 + 108*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^3 + 234*a*b^2*c^6*d^2*tan(1/2*f*x + 1/2*e)^3 - 252*a^2*b*c^5*d^3*tan(1/2*f*x + 1/2*e)^3 - 82*b^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^3 + 42*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^3 + 192*a*b^2*c^4*d^4*tan(1/2*f*x + 1/2*e)^3 - 102*a^2*b*c^3*d^5*tan(1/2*f*x + 1/2*e)^3 - 44*b^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^3 - 8*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 + 24*a*b^2*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 + 12*a^2*b*c*d^7*tan(1/2*f*x + 1/2*e)^3 + 8*a^3*d^8*tan(1/2*f*x + 1/2*e)^3 - 36*a^2*b*c^8*tan(1/2*f*x + 1/2*e)^2 - 12*b^3*c^8*tan(1/2*f*x + 1/2*e)^2 + 36*a^3*c^7*d*tan(1/2*f*x + 1/2*e)^2 + 72*a*b^2*c^7*d*tan(1/2*f*x + 1/2*e)^2 - 180*a^2*b*c^6*d^2*tan(1/2*f*x + 1/2*e)^2 - 36*b^3*c^6*d^2*tan(1/2*f*x + 1/2*e)^2 + 120*a^3*c^5*d^3*tan(1/2*f*x + 1/2*e)^2 + 306*a*b^2*c^5*d^3*tan(1/2*f*x + 1/2*e)^2 - 252*a^2*b*c^4*d^4*tan(1/2*f*x + 1/2*e)^2 - 102*b^3*c^4*d^4*tan(1/2*f*x + 1/2*e)^2 - 18*a^3*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 72*a*b^2*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 + 18*a^2*b*c^2*d^6*tan(1/2*f*x + 1/2*e)^2 + 12*a^3*c*d^7*tan(1/2*f*x + 1/2*e)^2 - 9*a*b^2*c^8*tan(1/2*f*x + 1/2*e) - 72*a^2*b*c^7*d*tan(1/2*f*x + 1/2*e) - 15*b^3*c^7*d*tan(1/2*f*x + 1/2*e) + 81*a^3*c^6*d^2*tan(1/2*f*x + 1/2*e) + 198*a*b^2*c^6*d^2*tan(1/2*f*x + 1/2*e) - 171*a^2*b*c^5*d^3*tan(1/2*f*x + 1/2*e) - 60*b^3*c^5*d^3*tan(1/2*f*x + 1/2*e) - 12*a^3*c^4*d^4*tan(1/2*f*x + 1/2*e) + 36*a*b^2*c^4*d^4*tan(1/2*f*x + 1/2*e) + 18*a^2*b*c^3*d^5*tan(1/2*f*x + 1/2*e) + 6*a^3*c^2*d^6*tan(1/2*f*x + 1/2*e) - 18*a^2*b*c^8 - 4*b^3*c^8 + 18*a^3*c^7*d + 39*a*b^2*c^7*d - 30*a^2*b*c^6*d^2 - 11*b^3*c^6*d^2 - 5*a^3*c^5*d^3 + 6*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 + 2*a^3*c^3*d^5)/((c^9 - 3*c^7*d^2 + 3*c^5*d^4 - c^3*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^3))/f","B",0
694,1,73,0,0.180349," ","integrate((b*B/a+B*sin(x))/(a+b*sin(x)),x, algorithm=""giac"")","\frac{B x}{b} - \frac{2 \, {\left(B a^{2} - B b^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} a b}"," ",0,"B*x/b - 2*(B*a^2 - B*b^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*a*b)","A",0
695,1,6,0,0.232088," ","integrate((a*B/b+B*sin(x))/(a+b*sin(x)),x, algorithm=""giac"")","\frac{B x}{b}"," ",0,"B*x/b","A",0
696,1,32,0,0.290467," ","integrate((a+b*sin(x))/(b+a*sin(x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(a \tan\left(\frac{1}{2} \, x\right) + b\right)}}{{\left(b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x\right) + b\right)} b}"," ",0,"-2*(a*tan(1/2*x) + b)/((b*tan(1/2*x)^2 + 2*a*tan(1/2*x) + b)*b)","B",0
697,1,51,0,0.357706," ","integrate((2-sin(x))/(2+sin(x)),x, algorithm=""giac"")","\frac{4}{3} \, \sqrt{3} {\left(x + 2 \, \arctan\left(-\frac{\sqrt{3} \sin\left(x\right) - \cos\left(x\right) - 2 \, \sin\left(x\right) - 1}{\sqrt{3} \cos\left(x\right) + \sqrt{3} - 2 \, \cos\left(x\right) + \sin\left(x\right) + 2}\right)\right)} - x"," ",0,"4/3*sqrt(3)*(x + 2*arctan(-(sqrt(3)*sin(x) - cos(x) - 2*sin(x) - 1)/(sqrt(3)*cos(x) + sqrt(3) - 2*cos(x) + sin(x) + 2))) - x","A",0
698,1,465,0,0.233879," ","integrate((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, b^{3} c^{3} d - 12 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} + 4 \, b^{3} c d^{3} - 2 \, a^{3} d^{4} - a b^{2} d^{4}\right)} {\left(f x + e\right)}}{b^{4}} + \frac{12 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{2 \, {\left(12 \, b^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 3 \, a b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 36 \, b^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 24 \, a b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 6 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 72 \, b^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 48 \, a b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, b^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, b^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 36 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 6 \, a^{2} d^{4} - 4 \, b^{2} d^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{3} b^{3}}}{6 \, f}"," ",0,"1/6*(3*(8*b^3*c^3*d - 12*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 + 4*b^3*c*d^3 - 2*a^3*d^4 - a*b^2*d^4)*(f*x + e)/b^4 + 12*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 2*(12*b^2*c*d^3*tan(1/2*f*x + 1/2*e)^5 - 3*a*b*d^4*tan(1/2*f*x + 1/2*e)^5 - 36*b^2*c^2*d^2*tan(1/2*f*x + 1/2*e)^4 + 24*a*b*c*d^3*tan(1/2*f*x + 1/2*e)^4 - 6*a^2*d^4*tan(1/2*f*x + 1/2*e)^4 - 72*b^2*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 48*a*b*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 12*a^2*d^4*tan(1/2*f*x + 1/2*e)^2 - 12*b^2*d^4*tan(1/2*f*x + 1/2*e)^2 - 12*b^2*c*d^3*tan(1/2*f*x + 1/2*e) + 3*a*b*d^4*tan(1/2*f*x + 1/2*e) - 36*b^2*c^2*d^2 + 24*a*b*c*d^3 - 6*a^2*d^4 - 4*b^2*d^4)/((tan(1/2*f*x + 1/2*e)^2 + 1)^3*b^3))/f","B",0
699,1,252,0,0.197011," ","integrate((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(6 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 2 \, a^{2} d^{3} + b^{2} d^{3}\right)} {\left(f x + e\right)}}{b^{3}} + \frac{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{3}} + \frac{2 \, {\left(b d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, b c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - b d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 6 \, b c d^{2} + 2 \, a d^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} b^{2}}}{2 \, f}"," ",0,"1/2*((6*b^2*c^2*d - 6*a*b*c*d^2 + 2*a^2*d^3 + b^2*d^3)*(f*x + e)/b^3 + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^3) + 2*(b*d^3*tan(1/2*f*x + 1/2*e)^3 - 6*b*c*d^2*tan(1/2*f*x + 1/2*e)^2 + 2*a*d^3*tan(1/2*f*x + 1/2*e)^2 - b*d^3*tan(1/2*f*x + 1/2*e) - 6*b*c*d^2 + 2*a*d^3)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*b^2))/f","A",0
700,1,134,0,0.303966," ","integrate((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, b c d - a d^{2}\right)} {\left(f x + e\right)}}{b^{2}} - \frac{2 \, d^{2}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} b} + \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{2}}}{f}"," ",0,"((2*b*c*d - a*d^2)*(f*x + e)/b^2 - 2*d^2/((tan(1/2*f*x + 1/2*e)^2 + 1)*b) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^2))/f","A",0
701,1,86,0,0.321739," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} d}{b} + \frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(b c - a d\right)}}{\sqrt{a^{2} - b^{2}} b}}{f}"," ",0,"((f*x + e)*d/b + 2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*(b*c - a*d)/(sqrt(a^2 - b^2)*b))/f","A",0
702,1,62,0,0.421203," ","integrate(1/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} f}"," ",0,"2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*f)","A",0
703,1,145,0,0.219345," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b}{\sqrt{a^{2} - b^{2}} {\left(b c - a d\right)}} - \frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} d}{{\left(b c - a d\right)} \sqrt{c^{2} - d^{2}}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*b/(sqrt(a^2 - b^2)*(b*c - a*d)) - (pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*d/((b*c - a*d)*sqrt(c^2 - d^2)))/f","A",0
704,1,308,0,0.223244," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{2}}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(2 \, b c^{2} d - a c d^{2} - b d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} - b^{2} c^{2} d^{2} + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \sqrt{c^{2} - d^{2}}} - \frac{d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c d^{2}}{{\left(b c^{4} - a c^{3} d - b c^{2} d^{2} + a c d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*b^2/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a^2 - b^2)) - (2*b*c^2*d - a*c*d^2 - b*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 - b^2*c^2*d^2 + 2*a*b*c*d^3 - a^2*d^4)*sqrt(c^2 - d^2)) - (d^3*tan(1/2*f*x + 1/2*e) + c*d^2)/((b*c^4 - a*c^3*d - b*c^2*d^2 + a*c*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)))/f","A",0
705,1,786,0,1.418436," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{3}}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(6 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} - 5 \, b^{2} c^{2} d^{3} + a^{2} d^{5} + 2 \, b^{2} d^{5}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - 2 \, b^{3} c^{5} d^{2} - a^{3} c^{4} d^{3} + 6 \, a b^{2} c^{4} d^{3} - 6 \, a^{2} b c^{3} d^{4} + b^{3} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{5} - 3 \, a b^{2} c^{2} d^{5} + 3 \, a^{2} b c d^{6} - a^{3} d^{7}\right)} \sqrt{c^{2} - d^{2}}} - \frac{7 \, b c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 5 \, a c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, b c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, b c^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 9 \, b c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 7 \, a c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, b c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 17 \, b c^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 11 \, a c^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 8 \, b c^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a c d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, b c^{5} d^{2} - 4 \, a c^{4} d^{3} - 3 \, b c^{3} d^{4} + a c^{2} d^{5}}{{\left(b^{2} c^{8} - 2 \, a b c^{7} d + a^{2} c^{6} d^{2} - 2 \, b^{2} c^{6} d^{2} + 4 \, a b c^{5} d^{3} - 2 \, a^{2} c^{4} d^{4} + b^{2} c^{4} d^{4} - 2 \, a b c^{3} d^{5} + a^{2} c^{2} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"(2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*b^3/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a^2 - b^2)) - (6*b^2*c^4*d - 6*a*b*c^3*d^2 + 2*a^2*c^2*d^3 - 5*b^2*c^2*d^3 + a^2*d^5 + 2*b^2*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - 2*b^3*c^5*d^2 - a^3*c^4*d^3 + 6*a*b^2*c^4*d^3 - 6*a^2*b*c^3*d^4 + b^3*c^3*d^4 + 2*a^3*c^2*d^5 - 3*a*b^2*c^2*d^5 + 3*a^2*b*c*d^6 - a^3*d^7)*sqrt(c^2 - d^2)) - (7*b*c^4*d^3*tan(1/2*f*x + 1/2*e)^3 - 5*a*c^3*d^4*tan(1/2*f*x + 1/2*e)^3 - 4*b*c^2*d^5*tan(1/2*f*x + 1/2*e)^3 + 2*a*c*d^6*tan(1/2*f*x + 1/2*e)^3 + 6*b*c^5*d^2*tan(1/2*f*x + 1/2*e)^2 - 4*a*c^4*d^3*tan(1/2*f*x + 1/2*e)^2 + 9*b*c^3*d^4*tan(1/2*f*x + 1/2*e)^2 - 7*a*c^2*d^5*tan(1/2*f*x + 1/2*e)^2 - 6*b*c*d^6*tan(1/2*f*x + 1/2*e)^2 + 2*a*d^7*tan(1/2*f*x + 1/2*e)^2 + 17*b*c^4*d^3*tan(1/2*f*x + 1/2*e) - 11*a*c^3*d^4*tan(1/2*f*x + 1/2*e) - 8*b*c^2*d^5*tan(1/2*f*x + 1/2*e) + 2*a*c*d^6*tan(1/2*f*x + 1/2*e) + 6*b*c^5*d^2 - 4*a*c^4*d^3 - 3*b*c^3*d^4 + a*c^2*d^5)/((b^2*c^8 - 2*a*b*c^7*d + a^2*c^6*d^2 - 2*b^2*c^6*d^2 + 4*a*b*c^5*d^3 - 2*a^2*c^4*d^4 + b^2*c^4*d^4 - 2*a*b*c^3*d^5 + a^2*c^2*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
706,1,517,0,0.409735," ","integrate((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(a b^{4} c^{4} - 4 \, b^{5} c^{3} d - 6 \, a^{3} b^{2} c^{2} d^{2} + 12 \, a b^{4} c^{2} d^{2} + 8 \, a^{4} b c d^{3} - 12 \, a^{2} b^{3} c d^{3} - 3 \, a^{5} d^{4} + 4 \, a^{3} b^{2} d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{4 \, {\left(b^{5} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 4 \, a b^{4} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{2} b^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 4 \, a^{3} b^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{4} b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}\right)}}{{\left(a^{3} b^{3} - a b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}} + \frac{{\left(12 \, b^{2} c^{2} d^{2} - 16 \, a b c d^{3} + 6 \, a^{2} d^{4} + b^{2} d^{4}\right)} {\left(f x + e\right)}}{b^{4}} + \frac{2 \, {\left(b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 8 \, b c d^{3} + 4 \, a d^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)}^{2} b^{3}}}{2 \, f}"," ",0,"1/2*(4*(a*b^4*c^4 - 4*b^5*c^3*d - 6*a^3*b^2*c^2*d^2 + 12*a*b^4*c^2*d^2 + 8*a^4*b*c*d^3 - 12*a^2*b^3*c*d^3 - 3*a^5*d^4 + 4*a^3*b^2*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 4*(b^5*c^4*tan(1/2*f*x + 1/2*e) - 4*a*b^4*c^3*d*tan(1/2*f*x + 1/2*e) + 6*a^2*b^3*c^2*d^2*tan(1/2*f*x + 1/2*e) - 4*a^3*b^2*c*d^3*tan(1/2*f*x + 1/2*e) + a^4*b*d^4*tan(1/2*f*x + 1/2*e) + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4)/((a^3*b^3 - a*b^5)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)) + (12*b^2*c^2*d^2 - 16*a*b*c*d^3 + 6*a^2*d^4 + b^2*d^4)*(f*x + e)/b^4 + 2*(b*d^4*tan(1/2*f*x + 1/2*e)^3 - 8*b*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 4*a*d^4*tan(1/2*f*x + 1/2*e)^2 - b*d^4*tan(1/2*f*x + 1/2*e) - 8*b*c*d^3 + 4*a*d^4)/((tan(1/2*f*x + 1/2*e)^2 + 1)^2*b^3))/f","A",0
707,1,579,0,0.250695," ","integrate((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a b^{3} c^{3} - 3 \, b^{4} c^{2} d - 3 \, a^{3} b c d^{2} + 6 \, a b^{3} c d^{2} + 2 \, a^{4} d^{3} - 3 \, a^{2} b^{2} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} - b^{5}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(b^{4} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, a b^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, a^{2} b^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - a^{3} b d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + a b^{3} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, a^{2} b^{2} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a^{3} b c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{2} b^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + b^{4} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, a b^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a^{2} b^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a b^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - 2 \, a^{4} d^{3} + a^{2} b^{2} d^{3}\right)}}{{\left(a^{3} b^{2} - a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}} + \frac{{\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} {\left(f x + e\right)}}{b^{3}}}{f}"," ",0,"(2*(a*b^3*c^3 - 3*b^4*c^2*d - 3*a^3*b*c*d^2 + 6*a*b^3*c*d^2 + 2*a^4*d^3 - 3*a^2*b^2*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^2*b^3 - b^5)*sqrt(a^2 - b^2)) + 2*(b^4*c^3*tan(1/2*f*x + 1/2*e)^3 - 3*a*b^3*c^2*d*tan(1/2*f*x + 1/2*e)^3 + 3*a^2*b^2*c*d^2*tan(1/2*f*x + 1/2*e)^3 - a^3*b*d^3*tan(1/2*f*x + 1/2*e)^3 + a*b^3*c^3*tan(1/2*f*x + 1/2*e)^2 - 3*a^2*b^2*c^2*d*tan(1/2*f*x + 1/2*e)^2 + 3*a^3*b*c*d^2*tan(1/2*f*x + 1/2*e)^2 - 2*a^4*d^3*tan(1/2*f*x + 1/2*e)^2 + a^2*b^2*d^3*tan(1/2*f*x + 1/2*e)^2 + b^4*c^3*tan(1/2*f*x + 1/2*e) - 3*a*b^3*c^2*d*tan(1/2*f*x + 1/2*e) + 3*a^2*b^2*c*d^2*tan(1/2*f*x + 1/2*e) - 3*a^3*b*d^3*tan(1/2*f*x + 1/2*e) + 2*a*b^3*d^3*tan(1/2*f*x + 1/2*e) + a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - 2*a^4*d^3 + a^2*b^2*d^3)/((a^3*b^2 - a*b^4)*(a*tan(1/2*f*x + 1/2*e)^4 + 2*b*tan(1/2*f*x + 1/2*e)^3 + 2*a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)) + (3*b*c*d^2 - 2*a*d^3)*(f*x + e)/b^3)/f","B",0
708,1,249,0,0.255043," ","integrate((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} d^{2}}{b^{2}} + \frac{2 \, {\left(a b^{2} c^{2} - 2 \, b^{3} c d - a^{3} d^{2} + 2 \, a b^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} - b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(b^{3} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{2} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{2} b d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}}{{\left(a^{3} b - a b^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}}}{f}"," ",0,"((f*x + e)*d^2/b^2 + 2*(a*b^2*c^2 - 2*b^3*c*d - a^3*d^2 + 2*a*b^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^2*b^2 - b^4)*sqrt(a^2 - b^2)) + 2*(b^3*c^2*tan(1/2*f*x + 1/2*e) - 2*a*b^2*c*d*tan(1/2*f*x + 1/2*e) + a^2*b*d^2*tan(1/2*f*x + 1/2*e) + a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)/((a^3*b - a*b^3)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)))/f","B",0
709,1,157,0,0.217250," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(a c - b d\right)}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{b^{2} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a b d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b c - a^{2} d}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*(a*c - b*d)/(a^2 - b^2)^(3/2) + (b^2*c*tan(1/2*f*x + 1/2*e) - a*b*d*tan(1/2*f*x + 1/2*e) + a*b*c - a^2*d)/((a^3 - a*b^2)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)))/f","A",0
710,1,127,0,0.323996," ","integrate(1/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{b^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b}{{\left(a^{3} - a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*a/(a^2 - b^2)^(3/2) + (b^2*tan(1/2*f*x + 1/2*e) + a*b)/((a^3 - a*b^2)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)))/f","A",0
711,1,304,0,0.240194," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} d^{2}}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c^{2} - d^{2}}} + \frac{{\left(a b^{2} c - 2 \, a^{2} b d + b^{3} d\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{2} c^{2} - b^{4} c^{2} - 2 \, a^{3} b c d + 2 \, a b^{3} c d + a^{4} d^{2} - a^{2} b^{2} d^{2}\right)} \sqrt{a^{2} - b^{2}}} + \frac{b^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b^{2}}{{\left(a^{3} b c - a b^{3} c - a^{4} d + a^{2} b^{2} d\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*d^2/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c^2 - d^2)) + (a*b^2*c - 2*a^2*b*d + b^3*d)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^2*b^2*c^2 - b^4*c^2 - 2*a^3*b*c*d + 2*a*b^3*c*d + a^4*d^2 - a^2*b^2*d^2)*sqrt(a^2 - b^2)) + (b^3*tan(1/2*f*x + 1/2*e) + a*b^2)/((a^3*b*c - a*b^3*c - a^4*d + a^2*b^2*d)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)))/f","A",0
712,1,1005,0,4.780168," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(a b^{3} c - 3 \, a^{2} b^{2} d + 2 \, b^{4} d\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{3} c^{3} - b^{5} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a b^{4} c^{2} d + 3 \, a^{4} b c d^{2} - 3 \, a^{2} b^{3} c d^{2} - a^{5} d^{3} + a^{3} b^{2} d^{3}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(3 \, b c^{2} d^{2} - a c d^{3} - 2 \, b d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - b^{3} c^{3} d^{2} - a^{3} c^{2} d^{3} + 3 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} \sqrt{c^{2} - d^{2}}} + \frac{b^{4} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - b^{4} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + a^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - a^{2} b^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + a b^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b^{4} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a b^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{4} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{2} b^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{4} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a^{3} b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a b^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + b^{4} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a b^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - b^{4} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a^{3} b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 4 \, a b^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a^{2} b^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b^{3} c^{4} - a b^{3} c^{2} d^{2} + a^{4} c d^{3} - a^{2} b^{2} c d^{3}}{{\left(a^{3} b^{2} c^{5} - a b^{4} c^{5} - 2 \, a^{4} b c^{4} d + 2 \, a^{2} b^{3} c^{4} d + a^{5} c^{3} d^{2} - 2 \, a^{3} b^{2} c^{3} d^{2} + a b^{4} c^{3} d^{2} + 2 \, a^{4} b c^{2} d^{3} - 2 \, a^{2} b^{3} c^{2} d^{3} - a^{5} c d^{4} + a^{3} b^{2} c d^{4}\right)} {\left(a c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 2 \, b c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, b d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a c\right)}}\right)}}{f}"," ",0,"2*((a*b^3*c - 3*a^2*b^2*d + 2*b^4*d)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^2*b^3*c^3 - b^5*c^3 - 3*a^3*b^2*c^2*d + 3*a*b^4*c^2*d + 3*a^4*b*c*d^2 - 3*a^2*b^3*c*d^2 - a^5*d^3 + a^3*b^2*d^3)*sqrt(a^2 - b^2)) + (3*b*c^2*d^2 - a*c*d^3 - 2*b*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - b^3*c^3*d^2 - a^3*c^2*d^3 + 3*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4 + a^3*d^5)*sqrt(c^2 - d^2)) + (b^4*c^4*tan(1/2*f*x + 1/2*e)^3 - b^4*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 + a^4*d^4*tan(1/2*f*x + 1/2*e)^3 - a^2*b^2*d^4*tan(1/2*f*x + 1/2*e)^3 + a*b^3*c^4*tan(1/2*f*x + 1/2*e)^2 + 2*b^4*c^3*d*tan(1/2*f*x + 1/2*e)^2 - a*b^3*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + a^4*c*d^3*tan(1/2*f*x + 1/2*e)^2 - a^2*b^2*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 2*b^4*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 2*a^3*b*d^4*tan(1/2*f*x + 1/2*e)^2 - 2*a*b^3*d^4*tan(1/2*f*x + 1/2*e)^2 + b^4*c^4*tan(1/2*f*x + 1/2*e) + 2*a*b^3*c^3*d*tan(1/2*f*x + 1/2*e) - b^4*c^2*d^2*tan(1/2*f*x + 1/2*e) + 2*a^3*b*c*d^3*tan(1/2*f*x + 1/2*e) - 4*a*b^3*c*d^3*tan(1/2*f*x + 1/2*e) + a^4*d^4*tan(1/2*f*x + 1/2*e) - a^2*b^2*d^4*tan(1/2*f*x + 1/2*e) + a*b^3*c^4 - a*b^3*c^2*d^2 + a^4*c*d^3 - a^2*b^2*c*d^3)/((a^3*b^2*c^5 - a*b^4*c^5 - 2*a^4*b*c^4*d + 2*a^2*b^3*c^4*d + a^5*c^3*d^2 - 2*a^3*b^2*c^3*d^2 + a*b^4*c^3*d^2 + 2*a^4*b*c^2*d^3 - 2*a^2*b^3*c^2*d^3 - a^5*c*d^4 + a^3*b^2*c*d^4)*(a*c*tan(1/2*f*x + 1/2*e)^4 + 2*b*c*tan(1/2*f*x + 1/2*e)^3 + 2*a*d*tan(1/2*f*x + 1/2*e)^3 + 2*a*c*tan(1/2*f*x + 1/2*e)^2 + 4*b*d*tan(1/2*f*x + 1/2*e)^2 + 2*b*c*tan(1/2*f*x + 1/2*e) + 2*a*d*tan(1/2*f*x + 1/2*e) + a*c)))/f","B",0
713,1,1109,0,0.417113," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a b^{4} c - 4 \, a^{2} b^{3} d + 3 \, b^{5} d\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} c^{4} - b^{6} c^{4} - 4 \, a^{3} b^{3} c^{3} d + 4 \, a b^{5} c^{3} d + 6 \, a^{4} b^{2} c^{2} d^{2} - 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + 4 \, a^{3} b^{3} c d^{3} + a^{6} d^{4} - a^{4} b^{2} d^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(12 \, b^{2} c^{4} d^{2} - 8 \, a b c^{3} d^{3} + 2 \, a^{2} c^{2} d^{4} - 15 \, b^{2} c^{2} d^{4} + 2 \, a b c d^{5} + a^{2} d^{6} + 6 \, b^{2} d^{6}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(b^{4} c^{8} - 4 \, a b^{3} c^{7} d + 6 \, a^{2} b^{2} c^{6} d^{2} - 2 \, b^{4} c^{6} d^{2} - 4 \, a^{3} b c^{5} d^{3} + 8 \, a b^{3} c^{5} d^{3} + a^{4} c^{4} d^{4} - 12 \, a^{2} b^{2} c^{4} d^{4} + b^{4} c^{4} d^{4} + 8 \, a^{3} b c^{3} d^{5} - 4 \, a b^{3} c^{3} d^{5} - 2 \, a^{4} c^{2} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{6} - 4 \, a^{3} b c d^{7} + a^{4} d^{8}\right)} \sqrt{c^{2} - d^{2}}} + \frac{2 \, {\left(b^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a b^{4}\right)}}{{\left(a^{3} b^{3} c^{3} - a b^{5} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{5} b c d^{2} - 3 \, a^{3} b^{3} c d^{2} - a^{6} d^{3} + a^{4} b^{2} d^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}} + \frac{9 \, b c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 5 \, a c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, b c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 8 \, b c^{5} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, b c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 7 \, a c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, b c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 23 \, b c^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 11 \, a c^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 14 \, b c^{2} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a c d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8 \, b c^{5} d^{3} - 4 \, a c^{4} d^{4} - 5 \, b c^{3} d^{5} + a c^{2} d^{6}}{{\left(b^{3} c^{9} - 3 \, a b^{2} c^{8} d + 3 \, a^{2} b c^{7} d^{2} - 2 \, b^{3} c^{7} d^{2} - a^{3} c^{6} d^{3} + 6 \, a b^{2} c^{6} d^{3} - 6 \, a^{2} b c^{5} d^{4} + b^{3} c^{5} d^{4} + 2 \, a^{3} c^{4} d^{5} - 3 \, a b^{2} c^{4} d^{5} + 3 \, a^{2} b c^{3} d^{6} - a^{3} c^{2} d^{7}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}^{2}}}{f}"," ",0,"(2*(a*b^4*c - 4*a^2*b^3*d + 3*b^5*d)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^2*b^4*c^4 - b^6*c^4 - 4*a^3*b^3*c^3*d + 4*a*b^5*c^3*d + 6*a^4*b^2*c^2*d^2 - 6*a^2*b^4*c^2*d^2 - 4*a^5*b*c*d^3 + 4*a^3*b^3*c*d^3 + a^6*d^4 - a^4*b^2*d^4)*sqrt(a^2 - b^2)) + (12*b^2*c^4*d^2 - 8*a*b*c^3*d^3 + 2*a^2*c^2*d^4 - 15*b^2*c^2*d^4 + 2*a*b*c*d^5 + a^2*d^6 + 6*b^2*d^6)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((b^4*c^8 - 4*a*b^3*c^7*d + 6*a^2*b^2*c^6*d^2 - 2*b^4*c^6*d^2 - 4*a^3*b*c^5*d^3 + 8*a*b^3*c^5*d^3 + a^4*c^4*d^4 - 12*a^2*b^2*c^4*d^4 + b^4*c^4*d^4 + 8*a^3*b*c^3*d^5 - 4*a*b^3*c^3*d^5 - 2*a^4*c^2*d^6 + 6*a^2*b^2*c^2*d^6 - 4*a^3*b*c*d^7 + a^4*d^8)*sqrt(c^2 - d^2)) + 2*(b^5*tan(1/2*f*x + 1/2*e) + a*b^4)/((a^3*b^3*c^3 - a*b^5*c^3 - 3*a^4*b^2*c^2*d + 3*a^2*b^4*c^2*d + 3*a^5*b*c*d^2 - 3*a^3*b^3*c*d^2 - a^6*d^3 + a^4*b^2*d^3)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)) + (9*b*c^4*d^4*tan(1/2*f*x + 1/2*e)^3 - 5*a*c^3*d^5*tan(1/2*f*x + 1/2*e)^3 - 6*b*c^2*d^6*tan(1/2*f*x + 1/2*e)^3 + 2*a*c*d^7*tan(1/2*f*x + 1/2*e)^3 + 8*b*c^5*d^3*tan(1/2*f*x + 1/2*e)^2 - 4*a*c^4*d^4*tan(1/2*f*x + 1/2*e)^2 + 11*b*c^3*d^5*tan(1/2*f*x + 1/2*e)^2 - 7*a*c^2*d^6*tan(1/2*f*x + 1/2*e)^2 - 10*b*c*d^7*tan(1/2*f*x + 1/2*e)^2 + 2*a*d^8*tan(1/2*f*x + 1/2*e)^2 + 23*b*c^4*d^4*tan(1/2*f*x + 1/2*e) - 11*a*c^3*d^5*tan(1/2*f*x + 1/2*e) - 14*b*c^2*d^6*tan(1/2*f*x + 1/2*e) + 2*a*c*d^7*tan(1/2*f*x + 1/2*e) + 8*b*c^5*d^3 - 4*a*c^4*d^4 - 5*b*c^3*d^5 + a*c^2*d^6)/((b^3*c^9 - 3*a*b^2*c^8*d + 3*a^2*b*c^7*d^2 - 2*b^3*c^7*d^2 - a^3*c^6*d^3 + 6*a*b^2*c^6*d^3 - 6*a^2*b*c^5*d^4 + b^3*c^5*d^4 + 2*a^3*c^4*d^5 - 3*a*b^2*c^4*d^5 + 3*a^2*b*c^3*d^6 - a^3*c^2*d^7)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)^2))/f","B",0
714,1,3162,0,0.376557," ","integrate((c+d*sin(f*x+e))^5/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(2 \, a^{2} b^{5} c^{5} + b^{7} c^{5} - 15 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} + 20 \, b^{7} c^{3} d^{2} - 20 \, a^{5} b^{2} c^{2} d^{3} + 50 \, a^{3} b^{4} c^{2} d^{3} - 60 \, a b^{6} c^{2} d^{3} + 30 \, a^{6} b c d^{4} - 75 \, a^{4} b^{3} c d^{4} + 60 \, a^{2} b^{5} c d^{4} - 12 \, a^{7} d^{5} + 29 \, a^{5} b^{2} d^{5} - 20 \, a^{3} b^{4} d^{5}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, {\left(5 \, a^{3} b^{6} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 2 \, a b^{8} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 15 \, a^{4} b^{5} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 10 \, a^{5} b^{4} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 20 \, a^{3} b^{6} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 10 \, a^{6} b^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 40 \, a^{4} b^{5} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 15 \, a^{7} b^{2} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 30 \, a^{5} b^{4} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 6 \, a^{8} b d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 10 \, a^{6} b^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + a^{4} b^{5} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 4 \, a^{4} b^{5} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 7 \, a^{2} b^{7} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 2 \, b^{9} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 10 \, a^{5} b^{4} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 25 \, a^{3} b^{6} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 10 \, a b^{8} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 30 \, a^{4} b^{5} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 60 \, a^{2} b^{7} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 20 \, a^{7} b^{2} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 10 \, a^{5} b^{4} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 100 \, a^{3} b^{6} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 30 \, a^{8} b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 15 \, a^{6} b^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 60 \, a^{4} b^{5} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 12 \, a^{9} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 5 \, a^{7} b^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 20 \, a^{5} b^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 4 \, a^{3} b^{6} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 21 \, a^{3} b^{6} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 \, a b^{8} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 55 \, a^{4} b^{5} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 20 \, a^{2} b^{7} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 10 \, a^{5} b^{4} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 140 \, a^{3} b^{6} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 90 \, a^{6} b^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 240 \, a^{4} b^{5} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 135 \, a^{7} b^{2} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 250 \, a^{5} b^{4} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 40 \, a^{3} b^{6} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 54 \, a^{8} b d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 90 \, a^{6} b^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 17 \, a^{4} b^{5} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 4 \, a^{2} b^{7} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 12 \, a^{4} b^{5} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 13 \, a^{2} b^{7} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4 \, b^{9} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 30 \, a^{5} b^{4} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 55 \, a^{3} b^{6} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 20 \, a b^{8} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 90 \, a^{4} b^{5} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 120 \, a^{2} b^{7} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 60 \, a^{7} b^{2} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 70 \, a^{5} b^{4} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 200 \, a^{3} b^{6} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 90 \, a^{8} b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, a^{6} b^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 190 \, a^{4} b^{5} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 40 \, a^{2} b^{7} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 36 \, a^{9} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 15 \, a^{7} b^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 66 \, a^{5} b^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 24 \, a^{3} b^{6} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 27 \, a^{3} b^{6} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a b^{8} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 65 \, a^{4} b^{5} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 40 \, a^{2} b^{7} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 10 \, a^{5} b^{4} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 220 \, a^{3} b^{6} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 150 \, a^{6} b^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 360 \, a^{4} b^{5} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 225 \, a^{7} b^{2} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 410 \, a^{5} b^{4} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 80 \, a^{3} b^{6} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 90 \, a^{8} b d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 162 \, a^{6} b^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 55 \, a^{4} b^{5} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a^{2} b^{7} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a^{4} b^{5} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, a^{2} b^{7} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{9} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 30 \, a^{5} b^{4} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 35 \, a^{3} b^{6} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, a b^{8} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 90 \, a^{4} b^{5} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 60 \, a^{2} b^{7} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 60 \, a^{7} b^{2} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 110 \, a^{5} b^{4} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 100 \, a^{3} b^{6} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 90 \, a^{8} b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 85 \, a^{6} b^{3} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 120 \, a^{4} b^{5} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 40 \, a^{2} b^{7} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, a^{9} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 31 \, a^{7} b^{2} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 40 \, a^{5} b^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, a^{3} b^{6} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{6} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{8} c^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 25 \, a^{4} b^{5} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 20 \, a^{2} b^{7} c^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 10 \, a^{5} b^{4} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 100 \, a^{3} b^{6} c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 70 \, a^{6} b^{3} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 160 \, a^{4} b^{5} c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 105 \, a^{7} b^{2} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 190 \, a^{5} b^{4} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 40 \, a^{3} b^{6} c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 42 \, a^{8} b d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 74 \, a^{6} b^{3} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 23 \, a^{4} b^{5} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b^{5} c^{5} - a^{2} b^{7} c^{5} - 10 \, a^{5} b^{4} c^{4} d - 5 \, a^{3} b^{6} c^{4} d + 30 \, a^{4} b^{5} c^{3} d^{2} + 20 \, a^{7} b^{2} c^{2} d^{3} - 50 \, a^{5} b^{4} c^{2} d^{3} - 30 \, a^{8} b c d^{4} + 55 \, a^{6} b^{3} c d^{4} - 10 \, a^{4} b^{5} c d^{4} + 12 \, a^{9} d^{5} - 21 \, a^{7} b^{2} d^{5} + 6 \, a^{5} b^{4} d^{5}\right)}}{{\left(a^{6} b^{4} - 2 \, a^{4} b^{6} + a^{2} b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}} + \frac{{\left(20 \, b^{2} c^{2} d^{3} - 30 \, a b c d^{4} + 12 \, a^{2} d^{5} + b^{2} d^{5}\right)} {\left(f x + e\right)}}{b^{5}}}{2 \, f}"," ",0,"1/2*(2*(2*a^2*b^5*c^5 + b^7*c^5 - 15*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 + 20*b^7*c^3*d^2 - 20*a^5*b^2*c^2*d^3 + 50*a^3*b^4*c^2*d^3 - 60*a*b^6*c^2*d^3 + 30*a^6*b*c*d^4 - 75*a^4*b^3*c*d^4 + 60*a^2*b^5*c*d^4 - 12*a^7*d^5 + 29*a^5*b^2*d^5 - 20*a^3*b^4*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4*b^5 - 2*a^2*b^7 + b^9)*sqrt(a^2 - b^2)) + 2*(5*a^3*b^6*c^5*tan(1/2*f*x + 1/2*e)^7 - 2*a*b^8*c^5*tan(1/2*f*x + 1/2*e)^7 - 15*a^4*b^5*c^4*d*tan(1/2*f*x + 1/2*e)^7 + 10*a^5*b^4*c^3*d^2*tan(1/2*f*x + 1/2*e)^7 + 20*a^3*b^6*c^3*d^2*tan(1/2*f*x + 1/2*e)^7 + 10*a^6*b^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^7 - 40*a^4*b^5*c^2*d^3*tan(1/2*f*x + 1/2*e)^7 - 15*a^7*b^2*c*d^4*tan(1/2*f*x + 1/2*e)^7 + 30*a^5*b^4*c*d^4*tan(1/2*f*x + 1/2*e)^7 + 6*a^8*b*d^5*tan(1/2*f*x + 1/2*e)^7 - 10*a^6*b^3*d^5*tan(1/2*f*x + 1/2*e)^7 + a^4*b^5*d^5*tan(1/2*f*x + 1/2*e)^7 + 4*a^4*b^5*c^5*tan(1/2*f*x + 1/2*e)^6 + 7*a^2*b^7*c^5*tan(1/2*f*x + 1/2*e)^6 - 2*b^9*c^5*tan(1/2*f*x + 1/2*e)^6 - 10*a^5*b^4*c^4*d*tan(1/2*f*x + 1/2*e)^6 - 25*a^3*b^6*c^4*d*tan(1/2*f*x + 1/2*e)^6 - 10*a*b^8*c^4*d*tan(1/2*f*x + 1/2*e)^6 + 30*a^4*b^5*c^3*d^2*tan(1/2*f*x + 1/2*e)^6 + 60*a^2*b^7*c^3*d^2*tan(1/2*f*x + 1/2*e)^6 + 20*a^7*b^2*c^2*d^3*tan(1/2*f*x + 1/2*e)^6 - 10*a^5*b^4*c^2*d^3*tan(1/2*f*x + 1/2*e)^6 - 100*a^3*b^6*c^2*d^3*tan(1/2*f*x + 1/2*e)^6 - 30*a^8*b*c*d^4*tan(1/2*f*x + 1/2*e)^6 + 15*a^6*b^3*c*d^4*tan(1/2*f*x + 1/2*e)^6 + 60*a^4*b^5*c*d^4*tan(1/2*f*x + 1/2*e)^6 + 12*a^9*d^5*tan(1/2*f*x + 1/2*e)^6 - 5*a^7*b^2*d^5*tan(1/2*f*x + 1/2*e)^6 - 20*a^5*b^4*d^5*tan(1/2*f*x + 1/2*e)^6 + 4*a^3*b^6*d^5*tan(1/2*f*x + 1/2*e)^6 + 21*a^3*b^6*c^5*tan(1/2*f*x + 1/2*e)^5 - 6*a*b^8*c^5*tan(1/2*f*x + 1/2*e)^5 - 55*a^4*b^5*c^4*d*tan(1/2*f*x + 1/2*e)^5 - 20*a^2*b^7*c^4*d*tan(1/2*f*x + 1/2*e)^5 + 10*a^5*b^4*c^3*d^2*tan(1/2*f*x + 1/2*e)^5 + 140*a^3*b^6*c^3*d^2*tan(1/2*f*x + 1/2*e)^5 + 90*a^6*b^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^5 - 240*a^4*b^5*c^2*d^3*tan(1/2*f*x + 1/2*e)^5 - 135*a^7*b^2*c*d^4*tan(1/2*f*x + 1/2*e)^5 + 250*a^5*b^4*c*d^4*tan(1/2*f*x + 1/2*e)^5 - 40*a^3*b^6*c*d^4*tan(1/2*f*x + 1/2*e)^5 + 54*a^8*b*d^5*tan(1/2*f*x + 1/2*e)^5 - 90*a^6*b^3*d^5*tan(1/2*f*x + 1/2*e)^5 + 17*a^4*b^5*d^5*tan(1/2*f*x + 1/2*e)^5 + 4*a^2*b^7*d^5*tan(1/2*f*x + 1/2*e)^5 + 12*a^4*b^5*c^5*tan(1/2*f*x + 1/2*e)^4 + 13*a^2*b^7*c^5*tan(1/2*f*x + 1/2*e)^4 - 4*b^9*c^5*tan(1/2*f*x + 1/2*e)^4 - 30*a^5*b^4*c^4*d*tan(1/2*f*x + 1/2*e)^4 - 55*a^3*b^6*c^4*d*tan(1/2*f*x + 1/2*e)^4 - 20*a*b^8*c^4*d*tan(1/2*f*x + 1/2*e)^4 + 90*a^4*b^5*c^3*d^2*tan(1/2*f*x + 1/2*e)^4 + 120*a^2*b^7*c^3*d^2*tan(1/2*f*x + 1/2*e)^4 + 60*a^7*b^2*c^2*d^3*tan(1/2*f*x + 1/2*e)^4 - 70*a^5*b^4*c^2*d^3*tan(1/2*f*x + 1/2*e)^4 - 200*a^3*b^6*c^2*d^3*tan(1/2*f*x + 1/2*e)^4 - 90*a^8*b*c*d^4*tan(1/2*f*x + 1/2*e)^4 + 45*a^6*b^3*c*d^4*tan(1/2*f*x + 1/2*e)^4 + 190*a^4*b^5*c*d^4*tan(1/2*f*x + 1/2*e)^4 - 40*a^2*b^7*c*d^4*tan(1/2*f*x + 1/2*e)^4 + 36*a^9*d^5*tan(1/2*f*x + 1/2*e)^4 - 15*a^7*b^2*d^5*tan(1/2*f*x + 1/2*e)^4 - 66*a^5*b^4*d^5*tan(1/2*f*x + 1/2*e)^4 + 24*a^3*b^6*d^5*tan(1/2*f*x + 1/2*e)^4 + 27*a^3*b^6*c^5*tan(1/2*f*x + 1/2*e)^3 - 6*a*b^8*c^5*tan(1/2*f*x + 1/2*e)^3 - 65*a^4*b^5*c^4*d*tan(1/2*f*x + 1/2*e)^3 - 40*a^2*b^7*c^4*d*tan(1/2*f*x + 1/2*e)^3 - 10*a^5*b^4*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 + 220*a^3*b^6*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 + 150*a^6*b^3*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 360*a^4*b^5*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 225*a^7*b^2*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 410*a^5*b^4*c*d^4*tan(1/2*f*x + 1/2*e)^3 - 80*a^3*b^6*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 90*a^8*b*d^5*tan(1/2*f*x + 1/2*e)^3 - 162*a^6*b^3*d^5*tan(1/2*f*x + 1/2*e)^3 + 55*a^4*b^5*d^5*tan(1/2*f*x + 1/2*e)^3 - 4*a^2*b^7*d^5*tan(1/2*f*x + 1/2*e)^3 + 12*a^4*b^5*c^5*tan(1/2*f*x + 1/2*e)^2 + 5*a^2*b^7*c^5*tan(1/2*f*x + 1/2*e)^2 - 2*b^9*c^5*tan(1/2*f*x + 1/2*e)^2 - 30*a^5*b^4*c^4*d*tan(1/2*f*x + 1/2*e)^2 - 35*a^3*b^6*c^4*d*tan(1/2*f*x + 1/2*e)^2 - 10*a*b^8*c^4*d*tan(1/2*f*x + 1/2*e)^2 + 90*a^4*b^5*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 + 60*a^2*b^7*c^3*d^2*tan(1/2*f*x + 1/2*e)^2 + 60*a^7*b^2*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 110*a^5*b^4*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 100*a^3*b^6*c^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 90*a^8*b*c*d^4*tan(1/2*f*x + 1/2*e)^2 + 85*a^6*b^3*c*d^4*tan(1/2*f*x + 1/2*e)^2 + 120*a^4*b^5*c*d^4*tan(1/2*f*x + 1/2*e)^2 - 40*a^2*b^7*c*d^4*tan(1/2*f*x + 1/2*e)^2 + 36*a^9*d^5*tan(1/2*f*x + 1/2*e)^2 - 31*a^7*b^2*d^5*tan(1/2*f*x + 1/2*e)^2 - 40*a^5*b^4*d^5*tan(1/2*f*x + 1/2*e)^2 + 20*a^3*b^6*d^5*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^6*c^5*tan(1/2*f*x + 1/2*e) - 2*a*b^8*c^5*tan(1/2*f*x + 1/2*e) - 25*a^4*b^5*c^4*d*tan(1/2*f*x + 1/2*e) - 20*a^2*b^7*c^4*d*tan(1/2*f*x + 1/2*e) - 10*a^5*b^4*c^3*d^2*tan(1/2*f*x + 1/2*e) + 100*a^3*b^6*c^3*d^2*tan(1/2*f*x + 1/2*e) + 70*a^6*b^3*c^2*d^3*tan(1/2*f*x + 1/2*e) - 160*a^4*b^5*c^2*d^3*tan(1/2*f*x + 1/2*e) - 105*a^7*b^2*c*d^4*tan(1/2*f*x + 1/2*e) + 190*a^5*b^4*c*d^4*tan(1/2*f*x + 1/2*e) - 40*a^3*b^6*c*d^4*tan(1/2*f*x + 1/2*e) + 42*a^8*b*d^5*tan(1/2*f*x + 1/2*e) - 74*a^6*b^3*d^5*tan(1/2*f*x + 1/2*e) + 23*a^4*b^5*d^5*tan(1/2*f*x + 1/2*e) + 4*a^4*b^5*c^5 - a^2*b^7*c^5 - 10*a^5*b^4*c^4*d - 5*a^3*b^6*c^4*d + 30*a^4*b^5*c^3*d^2 + 20*a^7*b^2*c^2*d^3 - 50*a^5*b^4*c^2*d^3 - 30*a^8*b*c*d^4 + 55*a^6*b^3*c*d^4 - 10*a^4*b^5*c*d^4 + 12*a^9*d^5 - 21*a^7*b^2*d^5 + 6*a^5*b^4*d^5)/((a^6*b^4 - 2*a^4*b^6 + a^2*b^8)*(a*tan(1/2*f*x + 1/2*e)^4 + 2*b*tan(1/2*f*x + 1/2*e)^3 + 2*a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2) + (20*b^2*c^2*d^3 - 30*a*b*c*d^4 + 12*a^2*d^5 + b^2*d^5)*(f*x + e)/b^5)/f","B",0
715,1,1159,0,2.209001," ","integrate((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{2} b^{4} c^{4} + b^{6} c^{4} - 12 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} + 12 \, b^{6} c^{2} d^{2} - 8 \, a^{5} b c d^{3} + 20 \, a^{3} b^{3} c d^{3} - 24 \, a b^{5} c d^{3} + 6 \, a^{6} d^{4} - 15 \, a^{4} b^{2} d^{4} + 12 \, a^{2} b^{4} d^{4}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, d^{4}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1\right)} b^{3}} + \frac{5 \, a^{3} b^{5} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{7} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 12 \, a^{4} b^{4} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, a^{5} b^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a^{3} b^{5} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{6} b^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 16 \, a^{4} b^{4} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, a^{7} b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, a^{5} b^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b^{4} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{6} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{8} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 8 \, a^{5} b^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 20 \, a^{3} b^{5} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 8 \, a b^{7} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18 \, a^{4} b^{4} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 36 \, a^{2} b^{6} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 8 \, a^{7} b c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a^{5} b^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 40 \, a^{3} b^{5} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a^{8} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{6} b^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 14 \, a^{4} b^{4} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{5} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{7} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 20 \, a^{4} b^{4} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 16 \, a^{2} b^{6} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 6 \, a^{5} b^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 60 \, a^{3} b^{5} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 28 \, a^{6} b^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 64 \, a^{4} b^{4} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 13 \, a^{7} b d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 22 \, a^{5} b^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b^{4} c^{4} - a^{2} b^{6} c^{4} - 8 \, a^{5} b^{3} c^{3} d - 4 \, a^{3} b^{5} c^{3} d + 18 \, a^{4} b^{4} c^{2} d^{2} + 8 \, a^{7} b c d^{3} - 20 \, a^{5} b^{3} c d^{3} - 4 \, a^{8} d^{4} + 7 \, a^{6} b^{2} d^{4}}{{\left(a^{6} b^{3} - 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}} + \frac{{\left(4 \, b c d^{3} - 3 \, a d^{4}\right)} {\left(f x + e\right)}}{b^{4}}}{f}"," ",0,"((2*a^2*b^4*c^4 + b^6*c^4 - 12*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 + 12*b^6*c^2*d^2 - 8*a^5*b*c*d^3 + 20*a^3*b^3*c*d^3 - 24*a*b^5*c*d^3 + 6*a^6*d^4 - 15*a^4*b^2*d^4 + 12*a^2*b^4*d^4)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) - 2*d^4/((tan(1/2*f*x + 1/2*e)^2 + 1)*b^3) + (5*a^3*b^5*c^4*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^7*c^4*tan(1/2*f*x + 1/2*e)^3 - 12*a^4*b^4*c^3*d*tan(1/2*f*x + 1/2*e)^3 + 6*a^5*b^3*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 + 12*a^3*b^5*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 + 4*a^6*b^2*c*d^3*tan(1/2*f*x + 1/2*e)^3 - 16*a^4*b^4*c*d^3*tan(1/2*f*x + 1/2*e)^3 - 3*a^7*b*d^4*tan(1/2*f*x + 1/2*e)^3 + 6*a^5*b^3*d^4*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b^4*c^4*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^6*c^4*tan(1/2*f*x + 1/2*e)^2 - 2*b^8*c^4*tan(1/2*f*x + 1/2*e)^2 - 8*a^5*b^3*c^3*d*tan(1/2*f*x + 1/2*e)^2 - 20*a^3*b^5*c^3*d*tan(1/2*f*x + 1/2*e)^2 - 8*a*b^7*c^3*d*tan(1/2*f*x + 1/2*e)^2 + 18*a^4*b^4*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 36*a^2*b^6*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 8*a^7*b*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 4*a^5*b^3*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 40*a^3*b^5*c*d^3*tan(1/2*f*x + 1/2*e)^2 - 4*a^8*d^4*tan(1/2*f*x + 1/2*e)^2 - a^6*b^2*d^4*tan(1/2*f*x + 1/2*e)^2 + 14*a^4*b^4*d^4*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^5*c^4*tan(1/2*f*x + 1/2*e) - 2*a*b^7*c^4*tan(1/2*f*x + 1/2*e) - 20*a^4*b^4*c^3*d*tan(1/2*f*x + 1/2*e) - 16*a^2*b^6*c^3*d*tan(1/2*f*x + 1/2*e) - 6*a^5*b^3*c^2*d^2*tan(1/2*f*x + 1/2*e) + 60*a^3*b^5*c^2*d^2*tan(1/2*f*x + 1/2*e) + 28*a^6*b^2*c*d^3*tan(1/2*f*x + 1/2*e) - 64*a^4*b^4*c*d^3*tan(1/2*f*x + 1/2*e) - 13*a^7*b*d^4*tan(1/2*f*x + 1/2*e) + 22*a^5*b^3*d^4*tan(1/2*f*x + 1/2*e) + 4*a^4*b^4*c^4 - a^2*b^6*c^4 - 8*a^5*b^3*c^3*d - 4*a^3*b^5*c^3*d + 18*a^4*b^4*c^2*d^2 + 8*a^7*b*c*d^3 - 20*a^5*b^3*c*d^3 - 4*a^8*d^4 + 7*a^6*b^2*d^4)/((a^6*b^3 - 2*a^4*b^5 + a^2*b^7)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2) + (4*b*c*d^3 - 3*a*d^4)*(f*x + e)/b^4)/f","B",0
716,1,887,0,1.188032," ","integrate((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(f x + e\right)} d^{3}}{b^{3}} + \frac{{\left(2 \, a^{2} b^{3} c^{3} + b^{5} c^{3} - 9 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} + 6 \, b^{5} c d^{2} - 2 \, a^{5} d^{3} + 5 \, a^{3} b^{2} d^{3} - 6 \, a b^{4} d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a^{2} - b^{2}}} + \frac{5 \, a^{3} b^{4} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{6} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 9 \, a^{4} b^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, a^{5} b^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, a^{3} b^{4} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + a^{6} b d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a^{4} b^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b^{3} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{5} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{7} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a^{5} b^{2} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 15 \, a^{3} b^{4} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a b^{6} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 9 \, a^{4} b^{3} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18 \, a^{2} b^{5} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a^{7} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{5} b^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, a^{3} b^{4} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{4} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{6} c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 15 \, a^{4} b^{3} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 12 \, a^{2} b^{5} c^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 \, a^{5} b^{2} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 30 \, a^{3} b^{4} c d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 7 \, a^{6} b d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 16 \, a^{4} b^{3} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b^{3} c^{3} - a^{2} b^{5} c^{3} - 6 \, a^{5} b^{2} c^{2} d - 3 \, a^{3} b^{4} c^{2} d + 9 \, a^{4} b^{3} c d^{2} + 2 \, a^{7} d^{3} - 5 \, a^{5} b^{2} d^{3}}{{\left(a^{6} b^{2} - 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}}}{f}"," ",0,"((f*x + e)*d^3/b^3 + (2*a^2*b^3*c^3 + b^5*c^3 - 9*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 + 6*b^5*c*d^2 - 2*a^5*d^3 + 5*a^3*b^2*d^3 - 6*a*b^4*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*sqrt(a^2 - b^2)) + (5*a^3*b^4*c^3*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^6*c^3*tan(1/2*f*x + 1/2*e)^3 - 9*a^4*b^3*c^2*d*tan(1/2*f*x + 1/2*e)^3 + 3*a^5*b^2*c*d^2*tan(1/2*f*x + 1/2*e)^3 + 6*a^3*b^4*c*d^2*tan(1/2*f*x + 1/2*e)^3 + a^6*b*d^3*tan(1/2*f*x + 1/2*e)^3 - 4*a^4*b^3*d^3*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b^3*c^3*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^5*c^3*tan(1/2*f*x + 1/2*e)^2 - 2*b^7*c^3*tan(1/2*f*x + 1/2*e)^2 - 6*a^5*b^2*c^2*d*tan(1/2*f*x + 1/2*e)^2 - 15*a^3*b^4*c^2*d*tan(1/2*f*x + 1/2*e)^2 - 6*a*b^6*c^2*d*tan(1/2*f*x + 1/2*e)^2 + 9*a^4*b^3*c*d^2*tan(1/2*f*x + 1/2*e)^2 + 18*a^2*b^5*c*d^2*tan(1/2*f*x + 1/2*e)^2 + 2*a^7*d^3*tan(1/2*f*x + 1/2*e)^2 - a^5*b^2*d^3*tan(1/2*f*x + 1/2*e)^2 - 10*a^3*b^4*d^3*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^4*c^3*tan(1/2*f*x + 1/2*e) - 2*a*b^6*c^3*tan(1/2*f*x + 1/2*e) - 15*a^4*b^3*c^2*d*tan(1/2*f*x + 1/2*e) - 12*a^2*b^5*c^2*d*tan(1/2*f*x + 1/2*e) - 3*a^5*b^2*c*d^2*tan(1/2*f*x + 1/2*e) + 30*a^3*b^4*c*d^2*tan(1/2*f*x + 1/2*e) + 7*a^6*b*d^3*tan(1/2*f*x + 1/2*e) - 16*a^4*b^3*d^3*tan(1/2*f*x + 1/2*e) + 4*a^4*b^3*c^3 - a^2*b^5*c^3 - 6*a^5*b^2*c^2*d - 3*a^3*b^4*c^2*d + 9*a^4*b^3*c*d^2 + 2*a^7*d^3 - 5*a^5*b^2*d^3)/((a^6*b^2 - 2*a^4*b^4 + a^2*b^6)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2))/f","B",0
717,1,609,0,0.273739," ","integrate((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{2} c^{2} + b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2} + 2 \, b^{2} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{5 \, a^{3} b^{2} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{4} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a^{4} b c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + a^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a^{3} b^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{3} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{5} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a^{5} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 10 \, a^{3} b^{2} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 4 \, a b^{4} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a^{4} b d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a^{2} b^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{2} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{4} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 10 \, a^{4} b c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 8 \, a^{2} b^{3} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a^{5} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 10 \, a^{3} b^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b c^{2} - a^{2} b^{3} c^{2} - 4 \, a^{5} c d - 2 \, a^{3} b^{2} c d + 3 \, a^{4} b d^{2}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}}}{f}"," ",0,"((2*a^2*c^2 + b^2*c^2 - 6*a*b*c*d + a^2*d^2 + 2*b^2*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (5*a^3*b^2*c^2*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^4*c^2*tan(1/2*f*x + 1/2*e)^3 - 6*a^4*b*c*d*tan(1/2*f*x + 1/2*e)^3 + a^5*d^2*tan(1/2*f*x + 1/2*e)^3 + 2*a^3*b^2*d^2*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b*c^2*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^3*c^2*tan(1/2*f*x + 1/2*e)^2 - 2*b^5*c^2*tan(1/2*f*x + 1/2*e)^2 - 4*a^5*c*d*tan(1/2*f*x + 1/2*e)^2 - 10*a^3*b^2*c*d*tan(1/2*f*x + 1/2*e)^2 - 4*a*b^4*c*d*tan(1/2*f*x + 1/2*e)^2 + 3*a^4*b*d^2*tan(1/2*f*x + 1/2*e)^2 + 6*a^2*b^3*d^2*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^2*c^2*tan(1/2*f*x + 1/2*e) - 2*a*b^4*c^2*tan(1/2*f*x + 1/2*e) - 10*a^4*b*c*d*tan(1/2*f*x + 1/2*e) - 8*a^2*b^3*c*d*tan(1/2*f*x + 1/2*e) - a^5*d^2*tan(1/2*f*x + 1/2*e) + 10*a^3*b^2*d^2*tan(1/2*f*x + 1/2*e) + 4*a^4*b*c^2 - a^2*b^3*c^2 - 4*a^5*c*d - 2*a^3*b^2*c*d + 3*a^4*b*d^2)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2))/f","B",0
718,1,429,0,0.237087," ","integrate((c+d*sin(f*x+e))/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{2} c + b^{2} c - 3 \, a b d\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{5 \, a^{3} b^{2} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{4} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, a^{4} b d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{3} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{5} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 5 \, a^{3} b^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a b^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{2} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{4} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 5 \, a^{4} b d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 4 \, a^{2} b^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b c - a^{2} b^{3} c - 2 \, a^{5} d - a^{3} b^{2} d}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}}}{f}"," ",0,"((2*a^2*c + b^2*c - 3*a*b*d)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (5*a^3*b^2*c*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^4*c*tan(1/2*f*x + 1/2*e)^3 - 3*a^4*b*d*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b*c*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^3*c*tan(1/2*f*x + 1/2*e)^2 - 2*b^5*c*tan(1/2*f*x + 1/2*e)^2 - 2*a^5*d*tan(1/2*f*x + 1/2*e)^2 - 5*a^3*b^2*d*tan(1/2*f*x + 1/2*e)^2 - 2*a*b^4*d*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^2*c*tan(1/2*f*x + 1/2*e) - 2*a*b^4*c*tan(1/2*f*x + 1/2*e) - 5*a^4*b*d*tan(1/2*f*x + 1/2*e) - 4*a^2*b^3*d*tan(1/2*f*x + 1/2*e) + 4*a^4*b*c - a^2*b^3*c - 2*a^5*d - a^3*b^2*d)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2))/f","B",0
719,1,284,0,0.175458," ","integrate(1/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(2 \, a^{2} + b^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b - a^{2} b^{3}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}}}{f}"," ",0,"((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))*(2*a^2 + b^2)/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (5*a^3*b^2*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^4*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^3*tan(1/2*f*x + 1/2*e)^2 - 2*b^5*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^2*tan(1/2*f*x + 1/2*e) - 2*a*b^4*tan(1/2*f*x + 1/2*e) + 4*a^4*b - a^2*b^3)/((a^6 - 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2))/f","B",0
720,1,788,0,1.344561," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)} d^{3}}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{c^{2} - d^{2}}} - \frac{{\left(2 \, a^{2} b^{3} c^{2} + b^{5} c^{2} - 6 \, a^{3} b^{2} c d + 6 \, a^{4} b d^{2} - 5 \, a^{2} b^{3} d^{2} + 2 \, b^{5} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{3} c^{3} - 2 \, a^{2} b^{5} c^{3} + b^{7} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 6 \, a^{3} b^{4} c^{2} d - 3 \, a b^{6} c^{2} d + 3 \, a^{6} b c d^{2} - 6 \, a^{4} b^{3} c d^{2} + 3 \, a^{2} b^{5} c d^{2} - a^{7} d^{3} + 2 \, a^{5} b^{2} d^{3} - a^{3} b^{4} d^{3}\right)} \sqrt{a^{2} - b^{2}}} - \frac{5 \, a^{3} b^{4} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{6} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 7 \, a^{4} b^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{2} b^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b^{3} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{5} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{7} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 6 \, a^{5} b^{2} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 9 \, a^{3} b^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a b^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{4} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{6} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 17 \, a^{4} b^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8 \, a^{2} b^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b^{3} c - a^{2} b^{5} c - 6 \, a^{5} b^{2} d + 3 \, a^{3} b^{4} d}{{\left(a^{6} b^{2} c^{2} - 2 \, a^{4} b^{4} c^{2} + a^{2} b^{6} c^{2} - 2 \, a^{7} b c d + 4 \, a^{5} b^{3} c d - 2 \, a^{3} b^{5} c d + a^{8} d^{2} - 2 \, a^{6} b^{2} d^{2} + a^{4} b^{4} d^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}}}{f}"," ",0,"-(2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))*d^3/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c^2 - d^2)) - (2*a^2*b^3*c^2 + b^5*c^2 - 6*a^3*b^2*c*d + 6*a^4*b*d^2 - 5*a^2*b^3*d^2 + 2*b^5*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4*b^3*c^3 - 2*a^2*b^5*c^3 + b^7*c^3 - 3*a^5*b^2*c^2*d + 6*a^3*b^4*c^2*d - 3*a*b^6*c^2*d + 3*a^6*b*c*d^2 - 6*a^4*b^3*c*d^2 + 3*a^2*b^5*c*d^2 - a^7*d^3 + 2*a^5*b^2*d^3 - a^3*b^4*d^3)*sqrt(a^2 - b^2)) - (5*a^3*b^4*c*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^6*c*tan(1/2*f*x + 1/2*e)^3 - 7*a^4*b^3*d*tan(1/2*f*x + 1/2*e)^3 + 4*a^2*b^5*d*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b^3*c*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^5*c*tan(1/2*f*x + 1/2*e)^2 - 2*b^7*c*tan(1/2*f*x + 1/2*e)^2 - 6*a^5*b^2*d*tan(1/2*f*x + 1/2*e)^2 - 9*a^3*b^4*d*tan(1/2*f*x + 1/2*e)^2 + 6*a*b^6*d*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^4*c*tan(1/2*f*x + 1/2*e) - 2*a*b^6*c*tan(1/2*f*x + 1/2*e) - 17*a^4*b^3*d*tan(1/2*f*x + 1/2*e) + 8*a^2*b^5*d*tan(1/2*f*x + 1/2*e) + 4*a^4*b^3*c - a^2*b^5*c - 6*a^5*b^2*d + 3*a^3*b^4*d)/((a^6*b^2*c^2 - 2*a^4*b^4*c^2 + a^2*b^6*c^2 - 2*a^7*b*c*d + 4*a^5*b^3*c*d - 2*a^3*b^5*c*d + a^8*d^2 - 2*a^6*b^2*d^2 + a^4*b^4*d^2)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2))/f","B",0
721,1,1111,0,1.377211," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{2} b^{4} c^{2} + b^{6} c^{2} - 8 \, a^{3} b^{3} c d + 2 \, a b^{5} c d + 12 \, a^{4} b^{2} d^{2} - 15 \, a^{2} b^{4} d^{2} + 6 \, b^{6} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{4} c^{4} - 2 \, a^{2} b^{6} c^{4} + b^{8} c^{4} - 4 \, a^{5} b^{3} c^{3} d + 8 \, a^{3} b^{5} c^{3} d - 4 \, a b^{7} c^{3} d + 6 \, a^{6} b^{2} c^{2} d^{2} - 12 \, a^{4} b^{4} c^{2} d^{2} + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{7} b c d^{3} + 8 \, a^{5} b^{3} c d^{3} - 4 \, a^{3} b^{5} c d^{3} + a^{8} d^{4} - 2 \, a^{6} b^{2} d^{4} + a^{4} b^{4} d^{4}\right)} \sqrt{a^{2} - b^{2}}} - \frac{2 \, {\left(4 \, b c^{2} d^{3} - a c d^{4} - 3 \, b d^{5}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - b^{4} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + 4 \, a b^{3} c^{3} d^{3} + a^{4} c^{2} d^{4} - 6 \, a^{2} b^{2} c^{2} d^{4} + 4 \, a^{3} b c d^{5} - a^{4} d^{6}\right)} \sqrt{c^{2} - d^{2}}} - \frac{2 \, {\left(d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c d^{4}\right)}}{{\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - b^{3} c^{4} d^{2} - a^{3} c^{3} d^{3} + 3 \, a b^{2} c^{3} d^{3} - 3 \, a^{2} b c^{2} d^{4} + a^{3} c d^{5}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + c\right)}} + \frac{5 \, a^{3} b^{5} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a b^{7} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 9 \, a^{4} b^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 \, a^{2} b^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 4 \, a^{4} b^{4} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 7 \, a^{2} b^{6} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{8} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 8 \, a^{5} b^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 11 \, a^{3} b^{5} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 10 \, a b^{7} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{5} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{7} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 23 \, a^{4} b^{4} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 14 \, a^{2} b^{6} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b^{4} c - a^{2} b^{6} c - 8 \, a^{5} b^{3} d + 5 \, a^{3} b^{5} d}{{\left(a^{6} b^{3} c^{3} - 2 \, a^{4} b^{5} c^{3} + a^{2} b^{7} c^{3} - 3 \, a^{7} b^{2} c^{2} d + 6 \, a^{5} b^{4} c^{2} d - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{8} b c d^{2} - 6 \, a^{6} b^{3} c d^{2} + 3 \, a^{4} b^{5} c d^{2} - a^{9} d^{3} + 2 \, a^{7} b^{2} d^{3} - a^{5} b^{4} d^{3}\right)} {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a\right)}^{2}}}{f}"," ",0,"((2*a^2*b^4*c^2 + b^6*c^2 - 8*a^3*b^3*c*d + 2*a*b^5*c*d + 12*a^4*b^2*d^2 - 15*a^2*b^4*d^2 + 6*b^6*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4*b^4*c^4 - 2*a^2*b^6*c^4 + b^8*c^4 - 4*a^5*b^3*c^3*d + 8*a^3*b^5*c^3*d - 4*a*b^7*c^3*d + 6*a^6*b^2*c^2*d^2 - 12*a^4*b^4*c^2*d^2 + 6*a^2*b^6*c^2*d^2 - 4*a^7*b*c*d^3 + 8*a^5*b^3*c*d^3 - 4*a^3*b^5*c*d^3 + a^8*d^4 - 2*a^6*b^2*d^4 + a^4*b^4*d^4)*sqrt(a^2 - b^2)) - 2*(4*b*c^2*d^3 - a*c*d^4 - 3*b*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - b^4*c^4*d^2 - 4*a^3*b*c^3*d^3 + 4*a*b^3*c^3*d^3 + a^4*c^2*d^4 - 6*a^2*b^2*c^2*d^4 + 4*a^3*b*c*d^5 - a^4*d^6)*sqrt(c^2 - d^2)) - 2*(d^5*tan(1/2*f*x + 1/2*e) + c*d^4)/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - b^3*c^4*d^2 - a^3*c^3*d^3 + 3*a*b^2*c^3*d^3 - 3*a^2*b*c^2*d^4 + a^3*c*d^5)*(c*tan(1/2*f*x + 1/2*e)^2 + 2*d*tan(1/2*f*x + 1/2*e) + c)) + (5*a^3*b^5*c*tan(1/2*f*x + 1/2*e)^3 - 2*a*b^7*c*tan(1/2*f*x + 1/2*e)^3 - 9*a^4*b^4*d*tan(1/2*f*x + 1/2*e)^3 + 6*a^2*b^6*d*tan(1/2*f*x + 1/2*e)^3 + 4*a^4*b^4*c*tan(1/2*f*x + 1/2*e)^2 + 7*a^2*b^6*c*tan(1/2*f*x + 1/2*e)^2 - 2*b^8*c*tan(1/2*f*x + 1/2*e)^2 - 8*a^5*b^3*d*tan(1/2*f*x + 1/2*e)^2 - 11*a^3*b^5*d*tan(1/2*f*x + 1/2*e)^2 + 10*a*b^7*d*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^5*c*tan(1/2*f*x + 1/2*e) - 2*a*b^7*c*tan(1/2*f*x + 1/2*e) - 23*a^4*b^4*d*tan(1/2*f*x + 1/2*e) + 14*a^2*b^6*d*tan(1/2*f*x + 1/2*e) + 4*a^4*b^4*c - a^2*b^6*c - 8*a^5*b^3*d + 5*a^3*b^5*d)/((a^6*b^3*c^3 - 2*a^4*b^5*c^3 + a^2*b^7*c^3 - 3*a^7*b^2*c^2*d + 6*a^5*b^4*c^2*d - 3*a^3*b^6*c^2*d + 3*a^8*b*c*d^2 - 6*a^6*b^3*c*d^2 + 3*a^4*b^5*c*d^2 - a^9*d^3 + 2*a^7*b^2*d^3 - a^5*b^4*d^3)*(a*tan(1/2*f*x + 1/2*e)^2 + 2*b*tan(1/2*f*x + 1/2*e) + a)^2))/f","B",0
722,1,7128,0,16.259968," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, a^{2} b^{5} c^{2} + b^{7} c^{2} - 10 \, a^{3} b^{4} c d + 4 \, a b^{6} c d + 20 \, a^{4} b^{3} d^{2} - 29 \, a^{2} b^{5} d^{2} + 12 \, b^{7} d^{2}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} b^{5} c^{5} - 2 \, a^{2} b^{7} c^{5} + b^{9} c^{5} - 5 \, a^{5} b^{4} c^{4} d + 10 \, a^{3} b^{6} c^{4} d - 5 \, a b^{8} c^{4} d + 10 \, a^{6} b^{3} c^{3} d^{2} - 20 \, a^{4} b^{5} c^{3} d^{2} + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{7} b^{2} c^{2} d^{3} + 20 \, a^{5} b^{4} c^{2} d^{3} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{8} b c d^{4} - 10 \, a^{6} b^{3} c d^{4} + 5 \, a^{4} b^{5} c d^{4} - a^{9} d^{5} + 2 \, a^{7} b^{2} d^{5} - a^{5} b^{4} d^{5}\right)} \sqrt{a^{2} - b^{2}}} - \frac{{\left(20 \, b^{2} c^{4} d^{3} - 10 \, a b c^{3} d^{4} + 2 \, a^{2} c^{2} d^{5} - 29 \, b^{2} c^{2} d^{5} + 4 \, a b c d^{6} + a^{2} d^{7} + 12 \, b^{2} d^{7}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{{\left(b^{5} c^{9} - 5 \, a b^{4} c^{8} d + 10 \, a^{2} b^{3} c^{7} d^{2} - 2 \, b^{5} c^{7} d^{2} - 10 \, a^{3} b^{2} c^{6} d^{3} + 10 \, a b^{4} c^{6} d^{3} + 5 \, a^{4} b c^{5} d^{4} - 20 \, a^{2} b^{3} c^{5} d^{4} + b^{5} c^{5} d^{4} - a^{5} c^{4} d^{5} + 20 \, a^{3} b^{2} c^{4} d^{5} - 5 \, a b^{4} c^{4} d^{5} - 10 \, a^{4} b c^{3} d^{6} + 10 \, a^{2} b^{3} c^{3} d^{6} + 2 \, a^{5} c^{2} d^{7} - 10 \, a^{3} b^{2} c^{2} d^{7} + 5 \, a^{4} b c d^{8} - a^{5} d^{9}\right)} \sqrt{c^{2} - d^{2}}} + \frac{5 \, a^{3} b^{6} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 2 \, a b^{8} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 11 \, a^{4} b^{5} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 8 \, a^{2} b^{7} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 10 \, a^{3} b^{6} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 4 \, a b^{8} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 22 \, a^{4} b^{5} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 16 \, a^{2} b^{7} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 5 \, a^{3} b^{6} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 2 \, a b^{8} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 11 \, a^{8} b c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 22 \, a^{6} b^{3} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 22 \, a^{4} b^{5} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 8 \, a^{2} b^{7} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 5 \, a^{9} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 10 \, a^{7} b^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 5 \, a^{5} b^{4} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 8 \, a^{8} b c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 16 \, a^{6} b^{3} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 8 \, a^{4} b^{5} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 2 \, a^{9} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 4 \, a^{7} b^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 2 \, a^{5} b^{4} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 4 \, a^{4} b^{5} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 7 \, a^{2} b^{7} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 2 \, b^{9} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 10 \, a^{5} b^{4} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 7 \, a^{3} b^{6} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 6 \, a b^{8} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 52 \, a^{4} b^{5} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 18 \, a^{2} b^{7} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 4 \, b^{9} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 20 \, a^{5} b^{4} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 14 \, a^{3} b^{6} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 12 \, a b^{8} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 10 \, a^{8} b c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 20 \, a^{6} b^{3} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 82 \, a^{4} b^{5} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 57 \, a^{2} b^{7} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 2 \, b^{9} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 4 \, a^{9} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 52 \, a^{7} b^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 82 \, a^{5} b^{4} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 37 \, a^{3} b^{6} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 6 \, a b^{8} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 7 \, a^{8} b c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 14 \, a^{6} b^{3} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 37 \, a^{4} b^{5} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 32 \, a^{2} b^{7} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 7 \, a^{9} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 18 \, a^{7} b^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 57 \, a^{5} b^{4} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 32 \, a^{3} b^{6} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 6 \, a^{8} b c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 12 \, a^{6} b^{3} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 6 \, a^{4} b^{5} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 2 \, a^{9} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 4 \, a^{7} b^{2} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 2 \, a^{5} b^{4} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 21 \, a^{3} b^{6} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 \, a b^{8} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 35 \, a^{4} b^{5} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 64 \, a^{2} b^{7} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 8 \, b^{9} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 40 \, a^{5} b^{4} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 74 \, a^{3} b^{6} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 60 \, a b^{8} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 26 \, a^{4} b^{5} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 96 \, a^{2} b^{7} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 16 \, b^{9} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 40 \, a^{7} b^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 160 \, a^{5} b^{4} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 45 \, a^{3} b^{6} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 102 \, a b^{8} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 35 \, a^{8} b c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 26 \, a^{6} b^{3} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 106 \, a^{4} b^{5} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 44 \, a^{2} b^{7} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 8 \, b^{9} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 21 \, a^{9} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 74 \, a^{7} b^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 45 \, a^{5} b^{4} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 64 \, a^{3} b^{6} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 48 \, a b^{8} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 64 \, a^{8} b c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 96 \, a^{6} b^{3} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 44 \, a^{4} b^{5} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 64 \, a^{2} b^{7} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 \, a^{9} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 60 \, a^{7} b^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 102 \, a^{5} b^{4} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 48 \, a^{3} b^{6} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 8 \, a^{8} b d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 16 \, a^{6} b^{3} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 8 \, a^{4} b^{5} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 12 \, a^{4} b^{5} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 13 \, a^{2} b^{7} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4 \, b^{9} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 30 \, a^{5} b^{4} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, a^{3} b^{6} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a b^{8} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 168 \, a^{4} b^{5} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 114 \, a^{2} b^{7} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 20 \, a^{5} b^{4} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 142 \, a^{3} b^{6} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 32 \, a b^{8} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 30 \, a^{8} b c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 20 \, a^{6} b^{3} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 350 \, a^{4} b^{5} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 307 \, a^{2} b^{7} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, b^{9} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a^{9} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 168 \, a^{7} b^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 350 \, a^{5} b^{4} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 5 \, a^{3} b^{6} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 100 \, a b^{8} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 45 \, a^{8} b c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 142 \, a^{6} b^{3} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 5 \, a^{4} b^{5} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 88 \, a^{2} b^{7} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 8 \, b^{9} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 13 \, a^{9} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 114 \, a^{7} b^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 307 \, a^{5} b^{4} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 88 \, a^{3} b^{6} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 56 \, a b^{8} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a^{8} b c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 32 \, a^{6} b^{3} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 100 \, a^{4} b^{5} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 56 \, a^{2} b^{7} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4 \, a^{9} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 12 \, a^{5} b^{4} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 8 \, a^{3} b^{6} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 27 \, a^{3} b^{6} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a b^{8} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 37 \, a^{4} b^{5} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 72 \, a^{2} b^{7} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, b^{9} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 80 \, a^{5} b^{4} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 34 \, a^{3} b^{6} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 60 \, a b^{8} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 42 \, a^{4} b^{5} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 64 \, a^{2} b^{7} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 16 \, b^{9} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 80 \, a^{7} b^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 320 \, a^{5} b^{4} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 93 \, a^{3} b^{6} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 102 \, a b^{8} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 37 \, a^{8} b c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 42 \, a^{6} b^{3} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 390 \, a^{4} b^{5} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 204 \, a^{2} b^{7} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, b^{9} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 27 \, a^{9} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 34 \, a^{7} b^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 93 \, a^{5} b^{4} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 40 \, a^{3} b^{6} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 48 \, a b^{8} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 72 \, a^{8} b c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 64 \, a^{6} b^{3} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 204 \, a^{4} b^{5} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 160 \, a^{2} b^{7} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a^{9} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 60 \, a^{7} b^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 102 \, a^{5} b^{4} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 48 \, a^{3} b^{6} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, a^{8} b d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 16 \, a^{6} b^{3} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 8 \, a^{4} b^{5} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 12 \, a^{4} b^{5} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, a^{2} b^{7} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{9} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 30 \, a^{5} b^{4} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 45 \, a^{3} b^{6} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a b^{8} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 124 \, a^{4} b^{5} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 66 \, a^{2} b^{7} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, b^{9} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, a^{5} b^{4} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 62 \, a^{3} b^{6} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, a b^{8} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 30 \, a^{8} b c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 20 \, a^{6} b^{3} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 262 \, a^{4} b^{5} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 187 \, a^{2} b^{7} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, b^{9} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{9} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 124 \, a^{7} b^{2} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 262 \, a^{5} b^{4} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 111 \, a^{3} b^{6} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a b^{8} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 45 \, a^{8} b c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 62 \, a^{6} b^{3} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 111 \, a^{4} b^{5} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 104 \, a^{2} b^{7} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, a^{9} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 66 \, a^{7} b^{2} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 187 \, a^{5} b^{4} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 104 \, a^{3} b^{6} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a^{8} b c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 12 \, a^{6} b^{3} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a^{4} b^{5} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{9} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a^{7} b^{2} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{5} b^{4} d^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 11 \, a^{3} b^{6} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{8} c^{9} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 13 \, a^{4} b^{5} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 16 \, a^{2} b^{7} c^{8} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 40 \, a^{5} b^{4} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{3} b^{6} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a b^{8} c^{7} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 26 \, a^{4} b^{5} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 32 \, a^{2} b^{7} c^{6} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 40 \, a^{7} b^{2} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 160 \, a^{5} b^{4} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 85 \, a^{3} b^{6} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a b^{8} c^{5} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 13 \, a^{8} b c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 26 \, a^{6} b^{3} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 26 \, a^{4} b^{5} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 16 \, a^{2} b^{7} c^{4} d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 11 \, a^{9} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 \, a^{7} b^{2} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 85 \, a^{5} b^{4} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 56 \, a^{3} b^{6} c^{3} d^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 16 \, a^{8} b c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 32 \, a^{6} b^{3} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 16 \, a^{4} b^{5} c^{2} d^{7} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{9} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{7} b^{2} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{5} b^{4} c d^{8} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a^{4} b^{5} c^{9} - a^{2} b^{7} c^{9} - 10 \, a^{5} b^{4} c^{8} d + 7 \, a^{3} b^{6} c^{8} d - 8 \, a^{4} b^{5} c^{7} d^{2} + 2 \, a^{2} b^{7} c^{7} d^{2} + 20 \, a^{5} b^{4} c^{6} d^{3} - 14 \, a^{3} b^{6} c^{6} d^{3} - 10 \, a^{8} b c^{5} d^{4} + 20 \, a^{6} b^{3} c^{5} d^{4} - 6 \, a^{4} b^{5} c^{5} d^{4} - a^{2} b^{7} c^{5} d^{4} + 4 \, a^{9} c^{4} d^{5} - 8 \, a^{7} b^{2} c^{4} d^{5} - 6 \, a^{5} b^{4} c^{4} d^{5} + 7 \, a^{3} b^{6} c^{4} d^{5} + 7 \, a^{8} b c^{3} d^{6} - 14 \, a^{6} b^{3} c^{3} d^{6} + 7 \, a^{4} b^{5} c^{3} d^{6} - a^{9} c^{2} d^{7} + 2 \, a^{7} b^{2} c^{2} d^{7} - a^{5} b^{4} c^{2} d^{7}}{{\left(a^{6} b^{4} c^{10} - 2 \, a^{4} b^{6} c^{10} + a^{2} b^{8} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 8 \, a^{5} b^{5} c^{9} d - 4 \, a^{3} b^{7} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 14 \, a^{6} b^{4} c^{8} d^{2} + 10 \, a^{4} b^{6} c^{8} d^{2} - 2 \, a^{2} b^{8} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + 16 \, a^{7} b^{3} c^{7} d^{3} - 20 \, a^{5} b^{5} c^{7} d^{3} + 8 \, a^{3} b^{7} c^{7} d^{3} + a^{10} c^{6} d^{4} - 14 \, a^{8} b^{2} c^{6} d^{4} + 26 \, a^{6} b^{4} c^{6} d^{4} - 14 \, a^{4} b^{6} c^{6} d^{4} + a^{2} b^{8} c^{6} d^{4} + 8 \, a^{9} b c^{5} d^{5} - 20 \, a^{7} b^{3} c^{5} d^{5} + 16 \, a^{5} b^{5} c^{5} d^{5} - 4 \, a^{3} b^{7} c^{5} d^{5} - 2 \, a^{10} c^{4} d^{6} + 10 \, a^{8} b^{2} c^{4} d^{6} - 14 \, a^{6} b^{4} c^{4} d^{6} + 6 \, a^{4} b^{6} c^{4} d^{6} - 4 \, a^{9} b c^{3} d^{7} + 8 \, a^{7} b^{3} c^{3} d^{7} - 4 \, a^{5} b^{5} c^{3} d^{7} + a^{10} c^{2} d^{8} - 2 \, a^{8} b^{2} c^{2} d^{8} + a^{6} b^{4} c^{2} d^{8}\right)} {\left(a c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 2 \, b c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, b d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, b c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a c\right)}^{2}}}{f}"," ",0,"((2*a^2*b^5*c^2 + b^7*c^2 - 10*a^3*b^4*c*d + 4*a*b^6*c*d + 20*a^4*b^3*d^2 - 29*a^2*b^5*d^2 + 12*b^7*d^2)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*f*x + 1/2*e) + b)/sqrt(a^2 - b^2)))/((a^4*b^5*c^5 - 2*a^2*b^7*c^5 + b^9*c^5 - 5*a^5*b^4*c^4*d + 10*a^3*b^6*c^4*d - 5*a*b^8*c^4*d + 10*a^6*b^3*c^3*d^2 - 20*a^4*b^5*c^3*d^2 + 10*a^2*b^7*c^3*d^2 - 10*a^7*b^2*c^2*d^3 + 20*a^5*b^4*c^2*d^3 - 10*a^3*b^6*c^2*d^3 + 5*a^8*b*c*d^4 - 10*a^6*b^3*c*d^4 + 5*a^4*b^5*c*d^4 - a^9*d^5 + 2*a^7*b^2*d^5 - a^5*b^4*d^5)*sqrt(a^2 - b^2)) - (20*b^2*c^4*d^3 - 10*a*b*c^3*d^4 + 2*a^2*c^2*d^5 - 29*b^2*c^2*d^5 + 4*a*b*c*d^6 + a^2*d^7 + 12*b^2*d^7)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*f*x + 1/2*e) + d)/sqrt(c^2 - d^2)))/((b^5*c^9 - 5*a*b^4*c^8*d + 10*a^2*b^3*c^7*d^2 - 2*b^5*c^7*d^2 - 10*a^3*b^2*c^6*d^3 + 10*a*b^4*c^6*d^3 + 5*a^4*b*c^5*d^4 - 20*a^2*b^3*c^5*d^4 + b^5*c^5*d^4 - a^5*c^4*d^5 + 20*a^3*b^2*c^4*d^5 - 5*a*b^4*c^4*d^5 - 10*a^4*b*c^3*d^6 + 10*a^2*b^3*c^3*d^6 + 2*a^5*c^2*d^7 - 10*a^3*b^2*c^2*d^7 + 5*a^4*b*c*d^8 - a^5*d^9)*sqrt(c^2 - d^2)) + (5*a^3*b^6*c^9*tan(1/2*f*x + 1/2*e)^7 - 2*a*b^8*c^9*tan(1/2*f*x + 1/2*e)^7 - 11*a^4*b^5*c^8*d*tan(1/2*f*x + 1/2*e)^7 + 8*a^2*b^7*c^8*d*tan(1/2*f*x + 1/2*e)^7 - 10*a^3*b^6*c^7*d^2*tan(1/2*f*x + 1/2*e)^7 + 4*a*b^8*c^7*d^2*tan(1/2*f*x + 1/2*e)^7 + 22*a^4*b^5*c^6*d^3*tan(1/2*f*x + 1/2*e)^7 - 16*a^2*b^7*c^6*d^3*tan(1/2*f*x + 1/2*e)^7 + 5*a^3*b^6*c^5*d^4*tan(1/2*f*x + 1/2*e)^7 - 2*a*b^8*c^5*d^4*tan(1/2*f*x + 1/2*e)^7 - 11*a^8*b*c^4*d^5*tan(1/2*f*x + 1/2*e)^7 + 22*a^6*b^3*c^4*d^5*tan(1/2*f*x + 1/2*e)^7 - 22*a^4*b^5*c^4*d^5*tan(1/2*f*x + 1/2*e)^7 + 8*a^2*b^7*c^4*d^5*tan(1/2*f*x + 1/2*e)^7 + 5*a^9*c^3*d^6*tan(1/2*f*x + 1/2*e)^7 - 10*a^7*b^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^7 + 5*a^5*b^4*c^3*d^6*tan(1/2*f*x + 1/2*e)^7 + 8*a^8*b*c^2*d^7*tan(1/2*f*x + 1/2*e)^7 - 16*a^6*b^3*c^2*d^7*tan(1/2*f*x + 1/2*e)^7 + 8*a^4*b^5*c^2*d^7*tan(1/2*f*x + 1/2*e)^7 - 2*a^9*c*d^8*tan(1/2*f*x + 1/2*e)^7 + 4*a^7*b^2*c*d^8*tan(1/2*f*x + 1/2*e)^7 - 2*a^5*b^4*c*d^8*tan(1/2*f*x + 1/2*e)^7 + 4*a^4*b^5*c^9*tan(1/2*f*x + 1/2*e)^6 + 7*a^2*b^7*c^9*tan(1/2*f*x + 1/2*e)^6 - 2*b^9*c^9*tan(1/2*f*x + 1/2*e)^6 - 10*a^5*b^4*c^8*d*tan(1/2*f*x + 1/2*e)^6 + 7*a^3*b^6*c^8*d*tan(1/2*f*x + 1/2*e)^6 + 6*a*b^8*c^8*d*tan(1/2*f*x + 1/2*e)^6 - 52*a^4*b^5*c^7*d^2*tan(1/2*f*x + 1/2*e)^6 + 18*a^2*b^7*c^7*d^2*tan(1/2*f*x + 1/2*e)^6 + 4*b^9*c^7*d^2*tan(1/2*f*x + 1/2*e)^6 + 20*a^5*b^4*c^6*d^3*tan(1/2*f*x + 1/2*e)^6 - 14*a^3*b^6*c^6*d^3*tan(1/2*f*x + 1/2*e)^6 - 12*a*b^8*c^6*d^3*tan(1/2*f*x + 1/2*e)^6 - 10*a^8*b*c^5*d^4*tan(1/2*f*x + 1/2*e)^6 + 20*a^6*b^3*c^5*d^4*tan(1/2*f*x + 1/2*e)^6 + 82*a^4*b^5*c^5*d^4*tan(1/2*f*x + 1/2*e)^6 - 57*a^2*b^7*c^5*d^4*tan(1/2*f*x + 1/2*e)^6 - 2*b^9*c^5*d^4*tan(1/2*f*x + 1/2*e)^6 + 4*a^9*c^4*d^5*tan(1/2*f*x + 1/2*e)^6 - 52*a^7*b^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^6 + 82*a^5*b^4*c^4*d^5*tan(1/2*f*x + 1/2*e)^6 - 37*a^3*b^6*c^4*d^5*tan(1/2*f*x + 1/2*e)^6 + 6*a*b^8*c^4*d^5*tan(1/2*f*x + 1/2*e)^6 + 7*a^8*b*c^3*d^6*tan(1/2*f*x + 1/2*e)^6 - 14*a^6*b^3*c^3*d^6*tan(1/2*f*x + 1/2*e)^6 - 37*a^4*b^5*c^3*d^6*tan(1/2*f*x + 1/2*e)^6 + 32*a^2*b^7*c^3*d^6*tan(1/2*f*x + 1/2*e)^6 + 7*a^9*c^2*d^7*tan(1/2*f*x + 1/2*e)^6 + 18*a^7*b^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^6 - 57*a^5*b^4*c^2*d^7*tan(1/2*f*x + 1/2*e)^6 + 32*a^3*b^6*c^2*d^7*tan(1/2*f*x + 1/2*e)^6 + 6*a^8*b*c*d^8*tan(1/2*f*x + 1/2*e)^6 - 12*a^6*b^3*c*d^8*tan(1/2*f*x + 1/2*e)^6 + 6*a^4*b^5*c*d^8*tan(1/2*f*x + 1/2*e)^6 - 2*a^9*d^9*tan(1/2*f*x + 1/2*e)^6 + 4*a^7*b^2*d^9*tan(1/2*f*x + 1/2*e)^6 - 2*a^5*b^4*d^9*tan(1/2*f*x + 1/2*e)^6 + 21*a^3*b^6*c^9*tan(1/2*f*x + 1/2*e)^5 - 6*a*b^8*c^9*tan(1/2*f*x + 1/2*e)^5 - 35*a^4*b^5*c^8*d*tan(1/2*f*x + 1/2*e)^5 + 64*a^2*b^7*c^8*d*tan(1/2*f*x + 1/2*e)^5 - 8*b^9*c^8*d*tan(1/2*f*x + 1/2*e)^5 - 40*a^5*b^4*c^7*d^2*tan(1/2*f*x + 1/2*e)^5 - 74*a^3*b^6*c^7*d^2*tan(1/2*f*x + 1/2*e)^5 + 60*a*b^8*c^7*d^2*tan(1/2*f*x + 1/2*e)^5 + 26*a^4*b^5*c^6*d^3*tan(1/2*f*x + 1/2*e)^5 - 96*a^2*b^7*c^6*d^3*tan(1/2*f*x + 1/2*e)^5 + 16*b^9*c^6*d^3*tan(1/2*f*x + 1/2*e)^5 - 40*a^7*b^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^5 + 160*a^5*b^4*c^5*d^4*tan(1/2*f*x + 1/2*e)^5 + 45*a^3*b^6*c^5*d^4*tan(1/2*f*x + 1/2*e)^5 - 102*a*b^8*c^5*d^4*tan(1/2*f*x + 1/2*e)^5 - 35*a^8*b*c^4*d^5*tan(1/2*f*x + 1/2*e)^5 + 26*a^6*b^3*c^4*d^5*tan(1/2*f*x + 1/2*e)^5 + 106*a^4*b^5*c^4*d^5*tan(1/2*f*x + 1/2*e)^5 - 44*a^2*b^7*c^4*d^5*tan(1/2*f*x + 1/2*e)^5 - 8*b^9*c^4*d^5*tan(1/2*f*x + 1/2*e)^5 + 21*a^9*c^3*d^6*tan(1/2*f*x + 1/2*e)^5 - 74*a^7*b^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^5 + 45*a^5*b^4*c^3*d^6*tan(1/2*f*x + 1/2*e)^5 - 64*a^3*b^6*c^3*d^6*tan(1/2*f*x + 1/2*e)^5 + 48*a*b^8*c^3*d^6*tan(1/2*f*x + 1/2*e)^5 + 64*a^8*b*c^2*d^7*tan(1/2*f*x + 1/2*e)^5 - 96*a^6*b^3*c^2*d^7*tan(1/2*f*x + 1/2*e)^5 - 44*a^4*b^5*c^2*d^7*tan(1/2*f*x + 1/2*e)^5 + 64*a^2*b^7*c^2*d^7*tan(1/2*f*x + 1/2*e)^5 - 6*a^9*c*d^8*tan(1/2*f*x + 1/2*e)^5 + 60*a^7*b^2*c*d^8*tan(1/2*f*x + 1/2*e)^5 - 102*a^5*b^4*c*d^8*tan(1/2*f*x + 1/2*e)^5 + 48*a^3*b^6*c*d^8*tan(1/2*f*x + 1/2*e)^5 - 8*a^8*b*d^9*tan(1/2*f*x + 1/2*e)^5 + 16*a^6*b^3*d^9*tan(1/2*f*x + 1/2*e)^5 - 8*a^4*b^5*d^9*tan(1/2*f*x + 1/2*e)^5 + 12*a^4*b^5*c^9*tan(1/2*f*x + 1/2*e)^4 + 13*a^2*b^7*c^9*tan(1/2*f*x + 1/2*e)^4 - 4*b^9*c^9*tan(1/2*f*x + 1/2*e)^4 - 30*a^5*b^4*c^8*d*tan(1/2*f*x + 1/2*e)^4 + 45*a^3*b^6*c^8*d*tan(1/2*f*x + 1/2*e)^4 + 12*a*b^8*c^8*d*tan(1/2*f*x + 1/2*e)^4 - 168*a^4*b^5*c^7*d^2*tan(1/2*f*x + 1/2*e)^4 + 114*a^2*b^7*c^7*d^2*tan(1/2*f*x + 1/2*e)^4 + 20*a^5*b^4*c^6*d^3*tan(1/2*f*x + 1/2*e)^4 - 142*a^3*b^6*c^6*d^3*tan(1/2*f*x + 1/2*e)^4 + 32*a*b^8*c^6*d^3*tan(1/2*f*x + 1/2*e)^4 - 30*a^8*b*c^5*d^4*tan(1/2*f*x + 1/2*e)^4 + 20*a^6*b^3*c^5*d^4*tan(1/2*f*x + 1/2*e)^4 + 350*a^4*b^5*c^5*d^4*tan(1/2*f*x + 1/2*e)^4 - 307*a^2*b^7*c^5*d^4*tan(1/2*f*x + 1/2*e)^4 + 12*b^9*c^5*d^4*tan(1/2*f*x + 1/2*e)^4 + 12*a^9*c^4*d^5*tan(1/2*f*x + 1/2*e)^4 - 168*a^7*b^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^4 + 350*a^5*b^4*c^4*d^5*tan(1/2*f*x + 1/2*e)^4 + 5*a^3*b^6*c^4*d^5*tan(1/2*f*x + 1/2*e)^4 - 100*a*b^8*c^4*d^5*tan(1/2*f*x + 1/2*e)^4 + 45*a^8*b*c^3*d^6*tan(1/2*f*x + 1/2*e)^4 - 142*a^6*b^3*c^3*d^6*tan(1/2*f*x + 1/2*e)^4 + 5*a^4*b^5*c^3*d^6*tan(1/2*f*x + 1/2*e)^4 + 88*a^2*b^7*c^3*d^6*tan(1/2*f*x + 1/2*e)^4 - 8*b^9*c^3*d^6*tan(1/2*f*x + 1/2*e)^4 + 13*a^9*c^2*d^7*tan(1/2*f*x + 1/2*e)^4 + 114*a^7*b^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^4 - 307*a^5*b^4*c^2*d^7*tan(1/2*f*x + 1/2*e)^4 + 88*a^3*b^6*c^2*d^7*tan(1/2*f*x + 1/2*e)^4 + 56*a*b^8*c^2*d^7*tan(1/2*f*x + 1/2*e)^4 + 12*a^8*b*c*d^8*tan(1/2*f*x + 1/2*e)^4 + 32*a^6*b^3*c*d^8*tan(1/2*f*x + 1/2*e)^4 - 100*a^4*b^5*c*d^8*tan(1/2*f*x + 1/2*e)^4 + 56*a^2*b^7*c*d^8*tan(1/2*f*x + 1/2*e)^4 - 4*a^9*d^9*tan(1/2*f*x + 1/2*e)^4 + 12*a^5*b^4*d^9*tan(1/2*f*x + 1/2*e)^4 - 8*a^3*b^6*d^9*tan(1/2*f*x + 1/2*e)^4 + 27*a^3*b^6*c^9*tan(1/2*f*x + 1/2*e)^3 - 6*a*b^8*c^9*tan(1/2*f*x + 1/2*e)^3 - 37*a^4*b^5*c^8*d*tan(1/2*f*x + 1/2*e)^3 + 72*a^2*b^7*c^8*d*tan(1/2*f*x + 1/2*e)^3 - 8*b^9*c^8*d*tan(1/2*f*x + 1/2*e)^3 - 80*a^5*b^4*c^7*d^2*tan(1/2*f*x + 1/2*e)^3 - 34*a^3*b^6*c^7*d^2*tan(1/2*f*x + 1/2*e)^3 + 60*a*b^8*c^7*d^2*tan(1/2*f*x + 1/2*e)^3 - 42*a^4*b^5*c^6*d^3*tan(1/2*f*x + 1/2*e)^3 - 64*a^2*b^7*c^6*d^3*tan(1/2*f*x + 1/2*e)^3 + 16*b^9*c^6*d^3*tan(1/2*f*x + 1/2*e)^3 - 80*a^7*b^2*c^5*d^4*tan(1/2*f*x + 1/2*e)^3 + 320*a^5*b^4*c^5*d^4*tan(1/2*f*x + 1/2*e)^3 - 93*a^3*b^6*c^5*d^4*tan(1/2*f*x + 1/2*e)^3 - 102*a*b^8*c^5*d^4*tan(1/2*f*x + 1/2*e)^3 - 37*a^8*b*c^4*d^5*tan(1/2*f*x + 1/2*e)^3 - 42*a^6*b^3*c^4*d^5*tan(1/2*f*x + 1/2*e)^3 + 390*a^4*b^5*c^4*d^5*tan(1/2*f*x + 1/2*e)^3 - 204*a^2*b^7*c^4*d^5*tan(1/2*f*x + 1/2*e)^3 - 8*b^9*c^4*d^5*tan(1/2*f*x + 1/2*e)^3 + 27*a^9*c^3*d^6*tan(1/2*f*x + 1/2*e)^3 - 34*a^7*b^2*c^3*d^6*tan(1/2*f*x + 1/2*e)^3 - 93*a^5*b^4*c^3*d^6*tan(1/2*f*x + 1/2*e)^3 + 40*a^3*b^6*c^3*d^6*tan(1/2*f*x + 1/2*e)^3 + 48*a*b^8*c^3*d^6*tan(1/2*f*x + 1/2*e)^3 + 72*a^8*b*c^2*d^7*tan(1/2*f*x + 1/2*e)^3 - 64*a^6*b^3*c^2*d^7*tan(1/2*f*x + 1/2*e)^3 - 204*a^4*b^5*c^2*d^7*tan(1/2*f*x + 1/2*e)^3 + 160*a^2*b^7*c^2*d^7*tan(1/2*f*x + 1/2*e)^3 - 6*a^9*c*d^8*tan(1/2*f*x + 1/2*e)^3 + 60*a^7*b^2*c*d^8*tan(1/2*f*x + 1/2*e)^3 - 102*a^5*b^4*c*d^8*tan(1/2*f*x + 1/2*e)^3 + 48*a^3*b^6*c*d^8*tan(1/2*f*x + 1/2*e)^3 - 8*a^8*b*d^9*tan(1/2*f*x + 1/2*e)^3 + 16*a^6*b^3*d^9*tan(1/2*f*x + 1/2*e)^3 - 8*a^4*b^5*d^9*tan(1/2*f*x + 1/2*e)^3 + 12*a^4*b^5*c^9*tan(1/2*f*x + 1/2*e)^2 + 5*a^2*b^7*c^9*tan(1/2*f*x + 1/2*e)^2 - 2*b^9*c^9*tan(1/2*f*x + 1/2*e)^2 - 30*a^5*b^4*c^8*d*tan(1/2*f*x + 1/2*e)^2 + 45*a^3*b^6*c^8*d*tan(1/2*f*x + 1/2*e)^2 + 6*a*b^8*c^8*d*tan(1/2*f*x + 1/2*e)^2 - 124*a^4*b^5*c^7*d^2*tan(1/2*f*x + 1/2*e)^2 + 66*a^2*b^7*c^7*d^2*tan(1/2*f*x + 1/2*e)^2 + 4*b^9*c^7*d^2*tan(1/2*f*x + 1/2*e)^2 + 20*a^5*b^4*c^6*d^3*tan(1/2*f*x + 1/2*e)^2 - 62*a^3*b^6*c^6*d^3*tan(1/2*f*x + 1/2*e)^2 - 12*a*b^8*c^6*d^3*tan(1/2*f*x + 1/2*e)^2 - 30*a^8*b*c^5*d^4*tan(1/2*f*x + 1/2*e)^2 + 20*a^6*b^3*c^5*d^4*tan(1/2*f*x + 1/2*e)^2 + 262*a^4*b^5*c^5*d^4*tan(1/2*f*x + 1/2*e)^2 - 187*a^2*b^7*c^5*d^4*tan(1/2*f*x + 1/2*e)^2 - 2*b^9*c^5*d^4*tan(1/2*f*x + 1/2*e)^2 + 12*a^9*c^4*d^5*tan(1/2*f*x + 1/2*e)^2 - 124*a^7*b^2*c^4*d^5*tan(1/2*f*x + 1/2*e)^2 + 262*a^5*b^4*c^4*d^5*tan(1/2*f*x + 1/2*e)^2 - 111*a^3*b^6*c^4*d^5*tan(1/2*f*x + 1/2*e)^2 + 6*a*b^8*c^4*d^5*tan(1/2*f*x + 1/2*e)^2 + 45*a^8*b*c^3*d^6*tan(1/2*f*x + 1/2*e)^2 - 62*a^6*b^3*c^3*d^6*tan(1/2*f*x + 1/2*e)^2 - 111*a^4*b^5*c^3*d^6*tan(1/2*f*x + 1/2*e)^2 + 104*a^2*b^7*c^3*d^6*tan(1/2*f*x + 1/2*e)^2 + 5*a^9*c^2*d^7*tan(1/2*f*x + 1/2*e)^2 + 66*a^7*b^2*c^2*d^7*tan(1/2*f*x + 1/2*e)^2 - 187*a^5*b^4*c^2*d^7*tan(1/2*f*x + 1/2*e)^2 + 104*a^3*b^6*c^2*d^7*tan(1/2*f*x + 1/2*e)^2 + 6*a^8*b*c*d^8*tan(1/2*f*x + 1/2*e)^2 - 12*a^6*b^3*c*d^8*tan(1/2*f*x + 1/2*e)^2 + 6*a^4*b^5*c*d^8*tan(1/2*f*x + 1/2*e)^2 - 2*a^9*d^9*tan(1/2*f*x + 1/2*e)^2 + 4*a^7*b^2*d^9*tan(1/2*f*x + 1/2*e)^2 - 2*a^5*b^4*d^9*tan(1/2*f*x + 1/2*e)^2 + 11*a^3*b^6*c^9*tan(1/2*f*x + 1/2*e) - 2*a*b^8*c^9*tan(1/2*f*x + 1/2*e) - 13*a^4*b^5*c^8*d*tan(1/2*f*x + 1/2*e) + 16*a^2*b^7*c^8*d*tan(1/2*f*x + 1/2*e) - 40*a^5*b^4*c^7*d^2*tan(1/2*f*x + 1/2*e) + 6*a^3*b^6*c^7*d^2*tan(1/2*f*x + 1/2*e) + 4*a*b^8*c^7*d^2*tan(1/2*f*x + 1/2*e) + 26*a^4*b^5*c^6*d^3*tan(1/2*f*x + 1/2*e) - 32*a^2*b^7*c^6*d^3*tan(1/2*f*x + 1/2*e) - 40*a^7*b^2*c^5*d^4*tan(1/2*f*x + 1/2*e) + 160*a^5*b^4*c^5*d^4*tan(1/2*f*x + 1/2*e) - 85*a^3*b^6*c^5*d^4*tan(1/2*f*x + 1/2*e) - 2*a*b^8*c^5*d^4*tan(1/2*f*x + 1/2*e) - 13*a^8*b*c^4*d^5*tan(1/2*f*x + 1/2*e) + 26*a^6*b^3*c^4*d^5*tan(1/2*f*x + 1/2*e) - 26*a^4*b^5*c^4*d^5*tan(1/2*f*x + 1/2*e) + 16*a^2*b^7*c^4*d^5*tan(1/2*f*x + 1/2*e) + 11*a^9*c^3*d^6*tan(1/2*f*x + 1/2*e) + 6*a^7*b^2*c^3*d^6*tan(1/2*f*x + 1/2*e) - 85*a^5*b^4*c^3*d^6*tan(1/2*f*x + 1/2*e) + 56*a^3*b^6*c^3*d^6*tan(1/2*f*x + 1/2*e) + 16*a^8*b*c^2*d^7*tan(1/2*f*x + 1/2*e) - 32*a^6*b^3*c^2*d^7*tan(1/2*f*x + 1/2*e) + 16*a^4*b^5*c^2*d^7*tan(1/2*f*x + 1/2*e) - 2*a^9*c*d^8*tan(1/2*f*x + 1/2*e) + 4*a^7*b^2*c*d^8*tan(1/2*f*x + 1/2*e) - 2*a^5*b^4*c*d^8*tan(1/2*f*x + 1/2*e) + 4*a^4*b^5*c^9 - a^2*b^7*c^9 - 10*a^5*b^4*c^8*d + 7*a^3*b^6*c^8*d - 8*a^4*b^5*c^7*d^2 + 2*a^2*b^7*c^7*d^2 + 20*a^5*b^4*c^6*d^3 - 14*a^3*b^6*c^6*d^3 - 10*a^8*b*c^5*d^4 + 20*a^6*b^3*c^5*d^4 - 6*a^4*b^5*c^5*d^4 - a^2*b^7*c^5*d^4 + 4*a^9*c^4*d^5 - 8*a^7*b^2*c^4*d^5 - 6*a^5*b^4*c^4*d^5 + 7*a^3*b^6*c^4*d^5 + 7*a^8*b*c^3*d^6 - 14*a^6*b^3*c^3*d^6 + 7*a^4*b^5*c^3*d^6 - a^9*c^2*d^7 + 2*a^7*b^2*c^2*d^7 - a^5*b^4*c^2*d^7)/((a^6*b^4*c^10 - 2*a^4*b^6*c^10 + a^2*b^8*c^10 - 4*a^7*b^3*c^9*d + 8*a^5*b^5*c^9*d - 4*a^3*b^7*c^9*d + 6*a^8*b^2*c^8*d^2 - 14*a^6*b^4*c^8*d^2 + 10*a^4*b^6*c^8*d^2 - 2*a^2*b^8*c^8*d^2 - 4*a^9*b*c^7*d^3 + 16*a^7*b^3*c^7*d^3 - 20*a^5*b^5*c^7*d^3 + 8*a^3*b^7*c^7*d^3 + a^10*c^6*d^4 - 14*a^8*b^2*c^6*d^4 + 26*a^6*b^4*c^6*d^4 - 14*a^4*b^6*c^6*d^4 + a^2*b^8*c^6*d^4 + 8*a^9*b*c^5*d^5 - 20*a^7*b^3*c^5*d^5 + 16*a^5*b^5*c^5*d^5 - 4*a^3*b^7*c^5*d^5 - 2*a^10*c^4*d^6 + 10*a^8*b^2*c^4*d^6 - 14*a^6*b^4*c^4*d^6 + 6*a^4*b^6*c^4*d^6 - 4*a^9*b*c^3*d^7 + 8*a^7*b^3*c^3*d^7 - 4*a^5*b^5*c^3*d^7 + a^10*c^2*d^8 - 2*a^8*b^2*c^2*d^8 + a^6*b^4*c^2*d^8)*(a*c*tan(1/2*f*x + 1/2*e)^4 + 2*b*c*tan(1/2*f*x + 1/2*e)^3 + 2*a*d*tan(1/2*f*x + 1/2*e)^3 + 2*a*c*tan(1/2*f*x + 1/2*e)^2 + 4*b*d*tan(1/2*f*x + 1/2*e)^2 + 2*b*c*tan(1/2*f*x + 1/2*e) + 2*a*d*tan(1/2*f*x + 1/2*e) + a*c)^2))/f","B",0
723,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
725,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
726,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{b \sin\left(f x + e\right) + a}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
727,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{b \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
728,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{b \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
729,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{b \sin\left(f x + e\right) + a}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(7/2), x)","F",0
730,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c), x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/sqrt(d*sin(f*x + e) + c), x)","F",0
734,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(3/2), x)","F",0
735,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(5/2), x)","F",0
736,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/(d*sin(f*x + e) + c)^(7/2), x)","F",0
737,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
738,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(3/2), x)","F",0
739,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/sqrt(d*sin(f*x + e) + c), x)","F",0
741,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(3/2), x)","F",0
742,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(5/2), x)","F",0
743,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(7/2), x)","F",0
744,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3/(d*sin(f*x + e) + c)^(9/2), x)","F",0
745,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a), x)","F",0
746,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a), x)","F",0
747,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a), x)","F",0
748,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
749,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
750,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
751,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(7/2)/(b*sin(f*x + e) + a)^2, x)","F",0
752,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^2, x)","F",0
753,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^2, x)","F",0
754,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^2, x)","F",0
755,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e) + c)), x)","F",0
756,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
757,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
758,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(9/2)/(b*sin(f*x + e) + a)^3, x)","F",0
759,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(7/2)/(b*sin(f*x + e) + a)^3, x)","F",0
760,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^3, x)","F",0
761,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^3, x)","F",0
762,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^3, x)","F",0
763,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{3} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^3*sqrt(d*sin(f*x + e) + c)), x)","F",0
764,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{3} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^3*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
765,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
766,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
767,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c), x)","F",0
768,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/sqrt(d*sin(f*x + e) + c), x)","F",0
769,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
770,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
771,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2), x)","F",0
772,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
774,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)/sqrt(d*sin(f*x + e) + c), x)","F",0
775,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
776,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
777,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2), x)","F",0
779,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c), x)","F",0
780,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)/sqrt(d*sin(f*x + e) + c), x)","F",0
781,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^(3/2), x)","F",0
782,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^(5/2), x)","F",0
783,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/sqrt(b*sin(f*x + e) + a), x)","F",0
784,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/sqrt(b*sin(f*x + e) + a), x)","F",0
785,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/sqrt(b*sin(f*x + e) + a), x)","F",0
786,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
787,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
788,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
789,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
790,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
791,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
792,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
793,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
794,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
795,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)/(b*sin(f*x + e) + a)^(5/2), x)","F",0
796,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^(5/2), x)","F",0
797,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^(5/2), x)","F",0
798,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
799,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
800,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
801,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
802,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^2*(b*sin(f*x + e) + a)^m, x)","F",0
803,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)*(b*sin(f*x + e) + a)^m, x)","F",0
804,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m, x)","F",0
805,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c), x)","F",0
806,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^2, x)","F",0
807,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^3, x)","F",0
808,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(5/2)*(b*sin(f*x + e) + a)^m, x)","F",0
809,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(3/2)*(b*sin(f*x + e) + a)^m, x)","F",0
810,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{d \sin\left(f x + e\right) + c} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)*(b*sin(f*x + e) + a)^m, x)","F",0
811,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
812,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
813,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(5/2), x)","F",0
814,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*(d*csc(f*x + e))^n, x)","F",0
815,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*csc(f*x + e))^n, x)","F",0
816,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*csc(f*x + e))^n, x)","F",0
817,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(a*sin(f*x + e) + a), x)","F",0
818,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(a*sin(f*x + e) + a)^2, x)","F",0
819,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n*(a*sin(f*x + e) + a)^m, x)","F",0
820,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^3,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^3*((d*sin(f*x + e))^p*c)^n, x)","F",0
821,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*((d*sin(f*x + e))^p*c)^n, x)","F",0
822,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(a \sin\left(f x + e\right) + a\right)} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*((d*sin(f*x + e))^p*c)^n, x)","F",0
823,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(a*sin(f*x + e) + a), x)","F",0
824,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
825,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*(d*csc(f*x + e))^n, x)","F",0
826,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*csc(f*x + e))^n, x)","F",0
827,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(d \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*csc(f*x + e))^n, x)","F",0
828,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(b*sin(f*x + e) + a), x)","F",0
829,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(b*sin(f*x + e) + a)^2, x)","F",0
830,0,0,0,0.000000," ","integrate((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(d \csc\left(f x + e\right)\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*csc(f*x + e))^n/(b*sin(f*x + e) + a)^3, x)","F",0
831,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^m,x, algorithm=""giac"")","\int \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n} {\left(b \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n*(b*sin(f*x + e) + a)^m, x)","F",0
832,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{3} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^3*((d*sin(f*x + e))^p*c)^n, x)","F",0
833,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*((d*sin(f*x + e))^p*c)^n, x)","F",0
834,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int {\left(b \sin\left(f x + e\right) + a\right)} \left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*((d*sin(f*x + e))^p*c)^n, x)","F",0
835,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(b*sin(f*x + e) + a), x)","F",0
836,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(b*sin(f*x + e) + a)^2, x)","F",0
837,0,0,0,0.000000," ","integrate((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(\left(d \sin\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(b \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(((d*sin(f*x + e))^p*c)^n/(b*sin(f*x + e) + a)^3, x)","F",0
