1,1,117,0,0.593015," ","integrate((a+a*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{140} \, \sqrt{2} {\left(\frac{5 \, a^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)}{d} + \frac{49 \, a^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{245 \, a^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{1225 \, a^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/140*sqrt(2)*(5*a^3*sgn(cos(1/2*d*x + 1/2*c))*sin(7/2*d*x + 7/2*c)/d + 49*a^3*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 245*a^3*sgn(cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)/d + 1225*a^3*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
2,1,90,0,0.580980," ","integrate((a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(\frac{3 \, a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)}{d} + \frac{25 \, a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{150 \, a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(3*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c)/d + 25*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)/d + 150*a^2*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
3,1,58,0,0.453551," ","integrate((a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{2} {\left(\frac{a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} + \frac{9 \, a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/3*sqrt(2)*(a*sgn(cos(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c)/d + 9*a*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d)*sqrt(a)","A",0
4,1,30,0,0.391626," ","integrate((a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} \sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d","A",0
5,1,93,0,0.700146," ","integrate(1/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{4 \, d}"," ",0,"1/4*(sqrt(2)*log(abs(1/sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c) + 2))/(sqrt(a)*sgn(cos(1/2*d*x + 1/2*c))) - sqrt(2)*log(abs(1/sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c) - 2))/(sqrt(a)*sgn(cos(1/2*d*x + 1/2*c))))/d","B",0
6,1,81,0,1.115436," ","integrate(1/(a+a*cos(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{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}}} - \frac{\sqrt{2} \sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2}}}{4 \, d}"," ",0,"-1/4*(sqrt(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) - sqrt(2)*sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*tan(1/2*d*x + 1/2*c)/a^2)/d","A",0
7,1,103,0,1.964044," ","integrate(1/(a+a*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{3}} + \frac{5 \, \sqrt{2}}{a^{3}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{3 \, \sqrt{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{5}{2}}}}{32 \, d}"," ",0,"1/32*(sqrt(a*tan(1/2*d*x + 1/2*c)^2 + a)*(2*sqrt(2)*tan(1/2*d*x + 1/2*c)^2/a^3 + 5*sqrt(2)/a^3)*tan(1/2*d*x + 1/2*c) - 3*sqrt(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^(5/2))/d","A",0
8,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(4/3), x)","F",0
9,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(2/3), x)","F",0
10,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(1/3), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(-1/3), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(-2/3), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(-4/3), x)","F",0
14,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^n, x)","F",0
15,0,0,0,0.000000," ","integrate((a-a*cos(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-a \cos\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((-a*cos(d*x + c) + a)^n, x)","F",0
16,0,0,0,0.000000," ","integrate((2+2*cos(d*x+c))^n,x, algorithm=""giac"")","\int {\left(2 \, \cos\left(d x + c\right) + 2\right)}^{n}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 2)^n, x)","F",0
17,0,0,0,0.000000," ","integrate((2-2*cos(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-2 \, \cos\left(d x + c\right) + 2\right)}^{n}\,{d x}"," ",0,"integrate((-2*cos(d*x + c) + 2)^n, x)","F",0
18,1,30,0,0.371625," ","integrate(1/(5+3*cos(d*x+c)),x, algorithm=""giac"")","\frac{d x + c - 2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{4 \, d}"," ",0,"1/4*(d*x + c - 2*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
19,1,59,0,0.451383," ","integrate(1/(5+3*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, d x + 5 \, c - \frac{12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4} - 10 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{64 \, d}"," ",0,"1/64*(5*d*x + 5*c - 12*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 4) - 10*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
20,1,75,0,0.430585," ","integrate(1/(5+3*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{59 \, d x + 59 \, c - \frac{12 \, {\left(23 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 68 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4\right)}^{2}} - 118 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{2048 \, d}"," ",0,"1/2048*(59*d*x + 59*c - 12*(23*tan(1/2*d*x + 1/2*c)^3 + 68*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 4)^2 - 118*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
21,1,88,0,0.327344," ","integrate(1/(5+3*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{385 \, d x + 385 \, c - \frac{36 \, {\left(71 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 416 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 656 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4\right)}^{3}} - 770 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{32768 \, d}"," ",0,"1/32768*(385*d*x + 385*c - 36*(71*tan(1/2*d*x + 1/2*c)^5 + 416*tan(1/2*d*x + 1/2*c)^3 + 656*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 4)^3 - 770*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
22,1,30,0,0.371611," ","integrate(1/(5-3*cos(d*x+c)),x, algorithm=""giac"")","\frac{d x + c - 2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{4 \, d}"," ",0,"1/4*(d*x + c - 2*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
23,1,61,0,0.433567," ","integrate(1/(5-3*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, d x + 5 \, c + \frac{12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - 10 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{64 \, d}"," ",0,"1/64*(5*d*x + 5*c + 12*tan(1/2*d*x + 1/2*c)/(4*tan(1/2*d*x + 1/2*c)^2 + 1) - 10*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
24,1,77,0,0.429882," ","integrate(1/(5-3*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{59 \, d x + 59 \, c + \frac{12 \, {\left(68 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 23 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - 118 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{2048 \, d}"," ",0,"1/2048*(59*d*x + 59*c + 12*(68*tan(1/2*d*x + 1/2*c)^3 + 23*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 118*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
25,1,90,0,0.407317," ","integrate(1/(5-3*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{385 \, d x + 385 \, c + \frac{36 \, {\left(656 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 416 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 71 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} - 770 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{32768 \, d}"," ",0,"1/32768*(385*d*x + 385*c + 36*(656*tan(1/2*d*x + 1/2*c)^5 + 416*tan(1/2*d*x + 1/2*c)^3 + 71*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 + 1)^3 - 770*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
26,1,30,0,0.384106," ","integrate(1/(-5+3*cos(d*x+c)),x, algorithm=""giac"")","-\frac{d x + c - 2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{4 \, d}"," ",0,"-1/4*(d*x + c - 2*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
27,1,61,0,0.453617," ","integrate(1/(-5+3*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, d x + 5 \, c + \frac{12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1} - 10 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{64 \, d}"," ",0,"1/64*(5*d*x + 5*c + 12*tan(1/2*d*x + 1/2*c)/(4*tan(1/2*d*x + 1/2*c)^2 + 1) - 10*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
28,1,77,0,0.389585," ","integrate(1/(-5+3*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{59 \, d x + 59 \, c + \frac{12 \, {\left(68 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 23 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{2}} - 118 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{2048 \, d}"," ",0,"-1/2048*(59*d*x + 59*c + 12*(68*tan(1/2*d*x + 1/2*c)^3 + 23*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 + 1)^2 - 118*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
29,1,90,0,1.221145," ","integrate(1/(-5+3*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{385 \, d x + 385 \, c + \frac{36 \, {\left(656 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 416 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 71 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}} - 770 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) - 3}\right)}{32768 \, d}"," ",0,"1/32768*(385*d*x + 385*c + 36*(656*tan(1/2*d*x + 1/2*c)^5 + 416*tan(1/2*d*x + 1/2*c)^3 + 71*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 + 1)^3 - 770*arctan(sin(d*x + c)/(cos(d*x + c) - 3)))/d","A",0
30,1,30,0,0.372510," ","integrate(1/(-5-3*cos(d*x+c)),x, algorithm=""giac"")","-\frac{d x + c - 2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{4 \, d}"," ",0,"-1/4*(d*x + c - 2*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
31,1,59,0,0.596167," ","integrate(1/(-5-3*cos(d*x+c))^2,x, algorithm=""giac"")","\frac{5 \, d x + 5 \, c - \frac{12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4} - 10 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{64 \, d}"," ",0,"1/64*(5*d*x + 5*c - 12*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 + 4) - 10*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
32,1,75,0,0.416324," ","integrate(1/(-5-3*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{59 \, d x + 59 \, c - \frac{12 \, {\left(23 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 68 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4\right)}^{2}} - 118 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{2048 \, d}"," ",0,"-1/2048*(59*d*x + 59*c - 12*(23*tan(1/2*d*x + 1/2*c)^3 + 68*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 4)^2 - 118*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
33,1,88,0,0.443044," ","integrate(1/(-5-3*cos(d*x+c))^4,x, algorithm=""giac"")","\frac{385 \, d x + 385 \, c - \frac{36 \, {\left(71 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 416 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 656 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4\right)}^{3}} - 770 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 3}\right)}{32768 \, d}"," ",0,"1/32768*(385*d*x + 385*c - 36*(71*tan(1/2*d*x + 1/2*c)^5 + 416*tan(1/2*d*x + 1/2*c)^3 + 656*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 + 4)^3 - 770*arctan(sin(d*x + c)/(cos(d*x + c) + 3)))/d","A",0
34,1,34,0,0.396633," ","integrate(1/(3+5*cos(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{4 \, d}"," ",0,"1/4*(log(abs(tan(1/2*d*x + 1/2*c) + 2)) - log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
35,1,62,0,0.400276," ","integrate(1/(3+5*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4} + 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{64 \, d}"," ",0,"-1/64*(20*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 4) + 3*log(abs(tan(1/2*d*x + 1/2*c) + 2)) - 3*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
36,1,78,0,0.616634," ","integrate(1/(3+5*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{20 \, {\left(17 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4\right)}^{2}} + 43 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - 43 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{2048 \, d}"," ",0,"1/2048*(20*(17*tan(1/2*d*x + 1/2*c)^3 - 28*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 4)^2 + 43*log(abs(tan(1/2*d*x + 1/2*c) + 2)) - 43*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
37,1,91,0,0.388180," ","integrate(1/(3+5*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(447 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1696 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2832 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4\right)}^{3}} + 837 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - 837 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{98304 \, d}"," ",0,"-1/98304*(20*(447*tan(1/2*d*x + 1/2*c)^5 - 1696*tan(1/2*d*x + 1/2*c)^3 + 2832*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 4)^3 + 837*log(abs(tan(1/2*d*x + 1/2*c) + 2)) - 837*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
38,1,38,0,0.472604," ","integrate(1/(3-5*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{4 \, d}"," ",0,"-1/4*(log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) - log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
39,1,68,0,1.334716," ","integrate(1/(3-5*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 3 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{64 \, d}"," ",0,"-1/64*(20*tan(1/2*d*x + 1/2*c)/(4*tan(1/2*d*x + 1/2*c)^2 - 1) - 3*log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
40,1,84,0,0.397143," ","integrate(1/(3-5*cos(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{20 \, {\left(28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 17 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - 43 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 43 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{2048 \, d}"," ",0,"1/2048*(20*(28*tan(1/2*d*x + 1/2*c)^3 - 17*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 - 1)^2 - 43*log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) + 43*log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
41,1,97,0,0.453647," ","integrate(1/(3-5*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(2832 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1696 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 447 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} - 837 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 837 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{98304 \, d}"," ",0,"-1/98304*(20*(2832*tan(1/2*d*x + 1/2*c)^5 - 1696*tan(1/2*d*x + 1/2*c)^3 + 447*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 - 1)^3 - 837*log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) + 837*log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
42,1,38,0,0.467919," ","integrate(1/(-3+5*cos(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{4 \, d}"," ",0,"1/4*(log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) - log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
43,1,68,0,0.409031," ","integrate(1/(-3+5*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1} - 3 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 3 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{64 \, d}"," ",0,"-1/64*(20*tan(1/2*d*x + 1/2*c)/(4*tan(1/2*d*x + 1/2*c)^2 - 1) - 3*log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) + 3*log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
44,1,84,0,0.716504," ","integrate(1/(-3+5*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 17 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}} - 43 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 43 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{2048 \, d}"," ",0,"-1/2048*(20*(28*tan(1/2*d*x + 1/2*c)^3 - 17*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 - 1)^2 - 43*log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) + 43*log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
45,1,97,0,0.849251," ","integrate(1/(-3+5*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(2832 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1696 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 447 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}} - 837 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 837 \, \log\left({\left| 2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{98304 \, d}"," ",0,"-1/98304*(20*(2832*tan(1/2*d*x + 1/2*c)^5 - 1696*tan(1/2*d*x + 1/2*c)^3 + 447*tan(1/2*d*x + 1/2*c))/(4*tan(1/2*d*x + 1/2*c)^2 - 1)^3 - 837*log(abs(2*tan(1/2*d*x + 1/2*c) + 1)) + 837*log(abs(2*tan(1/2*d*x + 1/2*c) - 1)))/d","A",0
46,1,34,0,0.376587," ","integrate(1/(-3-5*cos(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{4 \, d}"," ",0,"-1/4*(log(abs(tan(1/2*d*x + 1/2*c) + 2)) - log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
47,1,62,0,0.507880," ","integrate(1/(-3-5*cos(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{20 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4} + 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{64 \, d}"," ",0,"-1/64*(20*tan(1/2*d*x + 1/2*c)/(tan(1/2*d*x + 1/2*c)^2 - 4) + 3*log(abs(tan(1/2*d*x + 1/2*c) + 2)) - 3*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
48,1,78,0,0.816230," ","integrate(1/(-3-5*cos(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(17 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 28 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4\right)}^{2}} + 43 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - 43 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{2048 \, d}"," ",0,"-1/2048*(20*(17*tan(1/2*d*x + 1/2*c)^3 - 28*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 4)^2 + 43*log(abs(tan(1/2*d*x + 1/2*c) + 2)) - 43*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
49,1,91,0,0.449336," ","integrate(1/(-3-5*cos(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{20 \, {\left(447 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1696 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2832 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4\right)}^{3}} + 837 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right) - 837 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{98304 \, d}"," ",0,"-1/98304*(20*(447*tan(1/2*d*x + 1/2*c)^5 - 1696*tan(1/2*d*x + 1/2*c)^3 + 2832*tan(1/2*d*x + 1/2*c))/(tan(1/2*d*x + 1/2*c)^2 - 4)^3 + 837*log(abs(tan(1/2*d*x + 1/2*c) + 2)) - 837*log(abs(tan(1/2*d*x + 1/2*c) - 2)))/d","A",0
50,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a), x)","F",0
53,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(d*x + c) + a), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-3/2), x)","F",0
55,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-5/2), x)","F",0
56,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(4/3), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(2/3), x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(1/3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-1/3), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-2/3), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-4/3), x)","F",0
62,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^n, x)","F",0
