1,1,45,0,0.375867," ","integrate(sin(x)^4/(a+a*cos(x)),x, algorithm=""giac"")","\frac{x}{2 \, a} + \frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{5} - 8 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, x\right)}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3} a}"," ",0,"1/2*x/a + 1/3*(3*tan(1/2*x)^5 - 8*tan(1/2*x)^3 - 3*tan(1/2*x))/((tan(1/2*x)^2 + 1)^3*a)","A",0
2,1,14,0,2.406890," ","integrate(sin(x)^3/(a+a*cos(x)),x, algorithm=""giac"")","\frac{\cos\left(x\right)^{2} - 2 \, \cos\left(x\right)}{2 \, a}"," ",0,"1/2*(cos(x)^2 - 2*cos(x))/a","A",0
3,1,25,0,0.508465," ","integrate(sin(x)^2/(a+a*cos(x)),x, algorithm=""giac"")","\frac{x}{a} - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} a}"," ",0,"x/a - 2*tan(1/2*x)/((tan(1/2*x)^2 + 1)*a)","A",0
4,1,10,0,0.365180," ","integrate(sin(x)/(a+a*cos(x)),x, algorithm=""giac"")","-\frac{\log\left(\cos\left(x\right) + 1\right)}{a}"," ",0,"-log(cos(x) + 1)/a","A",0
5,1,8,0,0.347625," ","integrate(1/(a+a*cos(x)),x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, x\right)}{a}"," ",0,"tan(1/2*x)/a","A",0
6,1,34,0,0.372275," ","integrate(csc(x)/(a+a*cos(x)),x, algorithm=""giac"")","-\frac{\log\left(\cos\left(x\right) + 1\right)}{4 \, a} + \frac{\log\left(-\cos\left(x\right) + 1\right)}{4 \, a} + \frac{1}{2 \, a {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/4*log(cos(x) + 1)/a + 1/4*log(-cos(x) + 1)/a + 1/2/(a*(cos(x) + 1))","A",0
7,1,37,0,0.415678," ","integrate(csc(x)^2/(a+a*cos(x)),x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, x\right)}{12 \, a^{3}} - \frac{1}{4 \, a \tan\left(\frac{1}{2} \, x\right)}"," ",0,"1/12*(a^2*tan(1/2*x)^3 + 6*a^2*tan(1/2*x))/a^3 - 1/4/(a*tan(1/2*x))","A",0
8,1,52,0,0.594893," ","integrate(csc(x)^3/(a+a*cos(x)),x, algorithm=""giac"")","-\frac{3 \, \log\left(\cos\left(x\right) + 1\right)}{16 \, a} + \frac{3 \, \log\left(-\cos\left(x\right) + 1\right)}{16 \, a} + \frac{3 \, \cos\left(x\right)^{2} + 3 \, \cos\left(x\right) - 2}{8 \, a {\left(\cos\left(x\right) + 1\right)}^{2} {\left(\cos\left(x\right) - 1\right)}}"," ",0,"-3/16*log(cos(x) + 1)/a + 3/16*log(-cos(x) + 1)/a + 1/8*(3*cos(x)^2 + 3*cos(x) - 2)/(a*(cos(x) + 1)^2*(cos(x) - 1))","A",0
9,1,59,0,1.014916," ","integrate(csc(x)^4/(a+a*cos(x)),x, algorithm=""giac"")","-\frac{12 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}{48 \, a \tan\left(\frac{1}{2} \, x\right)^{3}} + \frac{3 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{5} + 20 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 90 \, a^{4} \tan\left(\frac{1}{2} \, x\right)}{240 \, a^{5}}"," ",0,"-1/48*(12*tan(1/2*x)^2 + 1)/(a*tan(1/2*x)^3) + 1/240*(3*a^4*tan(1/2*x)^5 + 20*a^4*tan(1/2*x)^3 + 90*a^4*tan(1/2*x))/a^5","A",0
10,1,9,0,0.300147," ","integrate(sin(2*x)/(1+cos(2*x)),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\cos\left(2 \, x\right) + 1\right)"," ",0,"-1/2*log(cos(2*x) + 1)","A",0
11,1,11,0,0.410607," ","integrate(sin(2*x)/(1-cos(2*x)),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(-\cos\left(2 \, x\right) + 1\right)"," ",0,"1/2*log(-cos(2*x) + 1)","B",0
12,1,6,0,0.483572," ","integrate(sin(x)/(1+cos(x))^2,x, algorithm=""giac"")","\frac{1}{\cos\left(x\right) + 1}"," ",0,"1/(cos(x) + 1)","A",0
13,1,6,0,0.527424," ","integrate(sin(x)/(1-cos(x))^2,x, algorithm=""giac"")","\frac{1}{\cos\left(x\right) - 1}"," ",0,"1/(cos(x) - 1)","A",0
14,1,10,0,0.461323," ","integrate(sin(x)^2/(1+cos(x))^2,x, algorithm=""giac"")","-x + 2 \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"-x + 2*tan(1/2*x)","A",0
15,1,12,0,0.371953," ","integrate(sin(x)^2/(1-cos(x))^2,x, algorithm=""giac"")","-x - \frac{2}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-x - 2/tan(1/2*x)","A",0
16,1,10,0,0.441406," ","integrate(sin(x)^3/(1+cos(x))^2,x, algorithm=""giac"")","\cos\left(x\right) - 2 \, \log\left(\cos\left(x\right) + 1\right)"," ",0,"cos(x) - 2*log(cos(x) + 1)","A",0
17,1,12,0,0.403675," ","integrate(sin(x)^3/(1-cos(x))^2,x, algorithm=""giac"")","\cos\left(x\right) + 2 \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"cos(x) + 2*log(-cos(x) + 1)","A",0
18,1,8,0,1.052634," ","integrate(sin(x)/(1+cos(x))^3,x, algorithm=""giac"")","\frac{1}{2 \, {\left(\cos\left(x\right) + 1\right)}^{2}}"," ",0,"1/2/(cos(x) + 1)^2","A",0
19,1,8,0,0.478056," ","integrate(sin(x)/(1-cos(x))^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(\cos\left(x\right) - 1\right)}^{2}}"," ",0,"-1/2/(cos(x) - 1)^2","A",0
20,1,8,0,0.426114," ","integrate(sin(x)^2/(1+cos(x))^3,x, algorithm=""giac"")","\frac{1}{3} \, \tan\left(\frac{1}{2} \, x\right)^{3}"," ",0,"1/3*tan(1/2*x)^3","A",0
21,1,8,0,0.979614," ","integrate(sin(x)^2/(1-cos(x))^3,x, algorithm=""giac"")","-\frac{1}{3 \, \tan\left(\frac{1}{2} \, x\right)^{3}}"," ",0,"-1/3/tan(1/2*x)^3","A",0
22,1,14,0,0.355089," ","integrate(sin(x)^3/(1+cos(x))^3,x, algorithm=""giac"")","\frac{2}{\cos\left(x\right) + 1} + \log\left(\cos\left(x\right) + 1\right)"," ",0,"2/(cos(x) + 1) + log(cos(x) + 1)","A",0
23,1,18,0,0.408757," ","integrate(sin(x)^3/(1-cos(x))^3,x, algorithm=""giac"")","\frac{2}{\cos\left(x\right) - 1} - \log\left(-\cos\left(x\right) + 1\right)"," ",0,"2/(cos(x) - 1) - log(-cos(x) + 1)","A",0
24,1,194,0,0.523771," ","integrate(sin(x)^4/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} x}{2 \, b^{4}} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}} b^{4}} + \frac{6 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{5} + 3 \, a b \tan\left(\frac{1}{2} \, x\right)^{5} - 6 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{5} + 12 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 20 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, a^{2} \tan\left(\frac{1}{2} \, x\right) - 3 \, a b \tan\left(\frac{1}{2} \, x\right) - 6 \, b^{2} \tan\left(\frac{1}{2} \, x\right)}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3} b^{3}}"," ",0,"-1/2*(2*a^3 - 3*a*b^2)*x/b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))/(sqrt(a^2 - b^2)*b^4) + 1/3*(6*a^2*tan(1/2*x)^5 + 3*a*b*tan(1/2*x)^5 - 6*b^2*tan(1/2*x)^5 + 12*a^2*tan(1/2*x)^3 - 20*b^2*tan(1/2*x)^3 + 6*a^2*tan(1/2*x) - 3*a*b*tan(1/2*x) - 6*b^2*tan(1/2*x))/((tan(1/2*x)^2 + 1)^3*b^3)","B",0
25,1,39,0,0.445744," ","integrate(sin(x)^3/(a+b*cos(x)),x, algorithm=""giac"")","\frac{b \cos\left(x\right)^{2} - 2 \, a \cos\left(x\right)}{2 \, b^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left({\left| b \cos\left(x\right) + a \right|}\right)}{b^{3}}"," ",0,"1/2*(b*cos(x)^2 - 2*a*cos(x))/b^2 + (a^2 - b^2)*log(abs(b*cos(x) + a))/b^3","A",0
26,1,90,0,0.353429," ","integrate(sin(x)^2/(a+b*cos(x)),x, algorithm=""giac"")","\frac{a x}{b^{2}} + \frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} \sqrt{a^{2} - b^{2}}}{b^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} b}"," ",0,"a*x/b^2 + 2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))*sqrt(a^2 - b^2)/b^2 - 2*tan(1/2*x)/((tan(1/2*x)^2 + 1)*b)","A",0
27,1,13,0,0.423444," ","integrate(sin(x)/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| b \cos\left(x\right) + a \right|}\right)}{b}"," ",0,"-log(abs(b*cos(x) + a))/b","A",0
28,1,61,0,0.924527," ","integrate(1/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2}}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))/sqrt(a^2 - b^2)","A",0
29,1,54,0,0.369785," ","integrate(csc(x)/(a+b*cos(x)),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| b \cos\left(x\right) + a \right|}\right)}{a^{2} b - b^{3}} - \frac{\log\left(\cos\left(x\right) + 1\right)}{2 \, {\left(a - b\right)}} + \frac{\log\left(-\cos\left(x\right) + 1\right)}{2 \, {\left(a + b\right)}}"," ",0,"b^2*log(abs(b*cos(x) + a))/(a^2*b - b^3) - 1/2*log(cos(x) + 1)/(a - b) + 1/2*log(-cos(x) + 1)/(a + b)","A",0
30,1,91,0,0.432976," ","integrate(csc(x)^2/(a+b*cos(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{2}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{\tan\left(\frac{1}{2} \, x\right)}{2 \, {\left(a - b\right)}} - \frac{1}{2 \, {\left(a + b\right)} \tan\left(\frac{1}{2} \, x\right)}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))*b^2/(a^2 - b^2)^(3/2) + 1/2*tan(1/2*x)/(a - b) - 1/2/((a + b)*tan(1/2*x))","A",0
31,1,136,0,0.440879," ","integrate(csc(x)^3/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{b^{4} \log\left({\left| b \cos\left(x\right) + a \right|}\right)}{a^{4} b - 2 \, a^{2} b^{3} + b^{5}} - \frac{{\left(a - 2 \, b\right)} \log\left(\cos\left(x\right) + 1\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)}} + \frac{{\left(a + 2 \, b\right)} \log\left(-\cos\left(x\right) + 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{a^{2} b - b^{3} - {\left(a^{3} - a b^{2}\right)} \cos\left(x\right)}{2 \, {\left(a + b\right)}^{2} {\left(a - b\right)}^{2} {\left(\cos\left(x\right) + 1\right)} {\left(\cos\left(x\right) - 1\right)}}"," ",0,"-b^4*log(abs(b*cos(x) + a))/(a^4*b - 2*a^2*b^3 + b^5) - 1/4*(a - 2*b)*log(cos(x) + 1)/(a^2 - 2*a*b + b^2) + 1/4*(a + 2*b)*log(-cos(x) + 1)/(a^2 + 2*a*b + b^2) - 1/2*(a^2*b - b^3 - (a^3 - a*b^2)*cos(x))/((a + b)^2*(a - b)^2*(cos(x) + 1)*(cos(x) - 1))","A",0
32,1,206,0,1.406102," ","integrate(csc(x)^4/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} b^{4}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 9 \, a^{2} \tan\left(\frac{1}{2} \, x\right) - 24 \, a b \tan\left(\frac{1}{2} \, x\right) + 15 \, b^{2} \tan\left(\frac{1}{2} \, x\right)}{24 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)}} - \frac{9 \, a \tan\left(\frac{1}{2} \, x\right)^{2} + 15 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + a + b}{24 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \tan\left(\frac{1}{2} \, x\right)^{3}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))*b^4/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + 1/24*(a^2*tan(1/2*x)^3 - 2*a*b*tan(1/2*x)^3 + b^2*tan(1/2*x)^3 + 9*a^2*tan(1/2*x) - 24*a*b*tan(1/2*x) + 15*b^2*tan(1/2*x))/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - 1/24*(9*a*tan(1/2*x)^2 + 15*b*tan(1/2*x)^2 + a + b)/((a^2 + 2*a*b + b^2)*tan(1/2*x)^3)","B",0
33,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)*(e*sin(d*x + c))^(7/2), x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)*(e*sin(d*x + c))^(5/2), x)","F",0
35,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)*(e*sin(d*x + c))^(3/2), x)","F",0
36,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)*sqrt(e*sin(d*x + c)), x)","F",0
37,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{b \cos\left(d x + c\right) + a}{\sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)/sqrt(e*sin(d*x + c)), x)","F",0
38,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{b \cos\left(d x + c\right) + a}{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)/(e*sin(d*x + c))^(3/2), x)","F",0
39,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{b \cos\left(d x + c\right) + a}{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)/(e*sin(d*x + c))^(5/2), x)","F",0
40,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{b \cos\left(d x + c\right) + a}{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)/(e*sin(d*x + c))^(7/2), x)","F",0
41,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*(e*sin(d*x + c))^(7/2), x)","F",0
42,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*(e*sin(d*x + c))^(5/2), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*(e*sin(d*x + c))^(3/2), x)","F",0
44,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{e \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sqrt(e*sin(d*x + c)), x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/sqrt(e*sin(d*x + c)), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/(e*sin(d*x + c))^(3/2), x)","F",0
47,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/(e*sin(d*x + c))^(5/2), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/(e*sin(d*x + c))^(7/2), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*(e*sin(d*x + c))^(7/2), x)","F",0
50,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*(e*sin(d*x + c))^(5/2), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*(e*sin(d*x + c))^(3/2), x)","F",0
52,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/sqrt(e*sin(d*x + c)), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/(e*sin(d*x + c))^(3/2), x)","F",0
55,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/(e*sin(d*x + c))^(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/(e*sin(d*x + c))^(7/2), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\left(e \sin\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/(e*sin(d*x + c))^(9/2), x)","F",0
58,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(7/2)/(b*cos(d*x + c) + a), x)","F",0
61,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(5/2)/(b*cos(d*x + c) + a), x)","F",0
62,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sin(d*x + c))^(3/2)/(b*cos(d*x + c) + a), x)","F",0
63,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*sqrt(e*sin(d*x + c))), x)","F",0
65,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*(e*sin(d*x + c))^(3/2)), x)","F",0
66,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*(e*sin(d*x + c))^(5/2)), x)","F",0
67,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*(e*sin(d*x + c))^(7/2)), x)","F",0
68,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
74,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*sqrt(e*sin(d*x + c))), x)","F",0
75,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*(e*sin(d*x + c))^(3/2)), x)","F",0
76,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*(e*sin(d*x + c))^(5/2)), x)","F",0
77,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*(e*sin(d*x + c))^(7/2)), x)","F",0
78,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(13/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,0,0,0,0.000000," ","integrate((e*sin(d*x+c))^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{e \sin\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(e*sin(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
85,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{e \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^3*sqrt(e*sin(d*x + c))), x)","F",0
86,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^3*(e*sin(d*x + c))^(3/2)), x)","F",0
87,-2,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 13.57Unable to divide, perhaps due to rounding error%%%{%%{[-268435456,0]:[1,0,-2]%%},[4,9,0,2,1]%%%}+%%%{%%{[805306368,0]:[1,0,-2]%%},[4,8,1,2,1]%%%}+%%%{%%{[-2147483648,0]:[1,0,-2]%%},[4,6,3,2,1]%%%}+%%%{%%{[1610612736,0]:[1,0,-2]%%},[4,5,4,2,1]%%%}+%%%{%%{[1610612736,0]:[1,0,-2]%%},[4,4,5,2,1]%%%}+%%%{%%{[-2147483648,0]:[1,0,-2]%%},[4,3,6,2,1]%%%}+%%%{%%{[805306368,0]:[1,0,-2]%%},[4,1,8,2,1]%%%}+%%%{%%{[-268435456,0]:[1,0,-2]%%},[4,0,9,2,1]%%%}+%%%{%%{[-536870912,0]:[1,0,-2]%%},[2,9,0,2,1]%%%}+%%%{%%{[536870912,0]:[1,0,-2]%%},[2,8,1,2,1]%%%}+%%%{%%{[2147483648,0]:[1,0,-2]%%},[2,7,2,2,1]%%%}+%%%{%%{[-2147483648,0]:[1,0,-2]%%},[2,6,3,2,1]%%%}+%%%{%%{[-3221225472,0]:[1,0,-2]%%},[2,5,4,2,1]%%%}+%%%{%%{[3221225472,0]:[1,0,-2]%%},[2,4,5,2,1]%%%}+%%%{%%{[2147483648,0]:[1,0,-2]%%},[2,3,6,2,1]%%%}+%%%{%%{[-2147483648,0]:[1,0,-2]%%},[2,2,7,2,1]%%%}+%%%{%%{[-536870912,0]:[1,0,-2]%%},[2,1,8,2,1]%%%}+%%%{%%{[536870912,0]:[1,0,-2]%%},[2,0,9,2,1]%%%}+%%%{%%{[-268435456,0]:[1,0,-2]%%},[0,9,0,2,1]%%%}+%%%{%%{[-268435456,0]:[1,0,-2]%%},[0,8,1,2,1]%%%}+%%%{%%{[1073741824,0]:[1,0,-2]%%},[0,7,2,2,1]%%%}+%%%{%%{[1073741824,0]:[1,0,-2]%%},[0,6,3,2,1]%%%}+%%%{%%{[-1610612736,0]:[1,0,-2]%%},[0,5,4,2,1]%%%}+%%%{%%{[-1610612736,0]:[1,0,-2]%%},[0,4,5,2,1]%%%}+%%%{%%{[1073741824,0]:[1,0,-2]%%},[0,3,6,2,1]%%%}+%%%{%%{[1073741824,0]:[1,0,-2]%%},[0,2,7,2,1]%%%}+%%%{%%{[-268435456,0]:[1,0,-2]%%},[0,1,8,2,1]%%%}+%%%{%%{[-268435456,0]:[1,0,-2]%%},[0,0,9,2,1]%%%} / %%%{1,[4,2,0,0,0]%%%}+%%%{-2,[4,1,1,0,0]%%%}+%%%{1,[4,0,2,0,0]%%%}+%%%{2,[2,2,0,0,0]%%%}+%%%{-2,[2,0,2,0,0]%%%}+%%%{1,[0,2,0,0,0]%%%}+%%%{2,[0,1,1,0,0]%%%}+%%%{1,[0,0,2,0,0]%%%} Error: Bad Argument Value","F(-2)",0
88,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \left(e \sin\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^3*(e*sin(d*x + c))^(7/2)), x)","F",0
