1,1,240,0,0.977321," ","integrate((a+a*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\frac{1}{140} \, \sqrt{2} {\left(\frac{7 \, a^{3} \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{525 \, a^{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{5 \, a^{3} \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{175 \, a^{3} \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^{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{3}{2} \, d x + \frac{3}{2} \, c\right)}{d} - \frac{42 \, a^{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{700 \, a^{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{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}\right)} \sqrt{a}"," ",0,"1/140*sqrt(2)*(7*a^3*cos(1/4*pi + 5/2*d*x + 5/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 525*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 + 5*a^3*cos(-1/4*pi + 7/2*d*x + 7/2*c)*sgn(cos(-1/4*pi + 1/2*d*x + 1/2*c))/d - 175*a^3*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^3*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^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 + 700*a^3*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
2,1,174,0,2.430647," ","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
3,1,101,0,0.974437," ","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
4,1,36,0,0.477983," ","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
5,1,111,0,0.754930," ","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
6,1,293,0,1.463563," ","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
7,1,457,0,1.150126," ","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
8,0,0,0,0.000000," ","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
9,0,0,0,0.000000," ","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
10,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\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
11,0,0,0,0.000000," ","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
12,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\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
13,0,0,0,0.000000," ","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
14,0,0,0,0.000000," ","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
15,0,0,0,0.000000," ","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
16,0,0,0,0.000000," ","integrate((2+2*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(2 \, \sin\left(d x + c\right) + 2\right)}^{n}\,{d x}"," ",0,"integrate((2*sin(d*x + c) + 2)^n, x)","F",0
17,0,0,0,0.000000," ","integrate((2-2*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-2 \, \sin\left(d x + c\right) + 2\right)}^{n}\,{d x}"," ",0,"integrate((-2*sin(d*x + c) + 2)^n, x)","F",0
18,1,49,0,1.984278," ","integrate(1/(5+3*sin(d*x+c)),x, algorithm=""giac"")","\frac{d x + c + 2 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{4 \, d}"," ",0,"1/4*(d*x + c + 2*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
19,1,95,0,2.004108," ","integrate(1/(5+3*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{25 \, d x + 25 \, c + \frac{24 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5} + 50 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{320 \, d}"," ",0,"1/320*(25*d*x + 25*c + 24*(3*tan(1/2*d*x + 1/2*c) + 5)/(5*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) + 5) + 50*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
20,1,121,0,1.184314," ","integrate(1/(5+3*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{1475 \, d x + 1475 \, c + \frac{24 \, {\left(1605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3913 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3855 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2275\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{2}} + 2950 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{51200 \, d}"," ",0,"1/51200*(1475*d*x + 1475*c + 24*(1605*tan(1/2*d*x + 1/2*c)^3 + 3913*tan(1/2*d*x + 1/2*c)^2 + 3855*tan(1/2*d*x + 1/2*c) + 2275)/(5*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) + 5)^2 + 2950*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
21,1,147,0,0.542311," ","integrate(1/(5+3*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{48125 \, d x + 48125 \, c + \frac{72 \, {\left(110925 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 373735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 637794 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 672110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 403425 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 142875\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{3}} + 96250 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{4096000 \, d}"," ",0,"1/4096000*(48125*d*x + 48125*c + 72*(110925*tan(1/2*d*x + 1/2*c)^5 + 373735*tan(1/2*d*x + 1/2*c)^4 + 637794*tan(1/2*d*x + 1/2*c)^3 + 672110*tan(1/2*d*x + 1/2*c)^2 + 403425*tan(1/2*d*x + 1/2*c) + 142875)/(5*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) + 5)^3 + 96250*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
22,1,50,0,0.316821," ","integrate(1/(5-3*sin(d*x+c)),x, algorithm=""giac"")","\frac{d x + c + 2 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{4 \, d}"," ",0,"1/4*(d*x + c + 2*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
23,1,96,0,0.772468," ","integrate(1/(5-3*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{25 \, d x + 25 \, c + \frac{24 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5\right)}}{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5} + 50 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{320 \, d}"," ",0,"1/320*(25*d*x + 25*c + 24*(3*tan(1/2*d*x + 1/2*c) - 5)/(5*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 5) + 50*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
24,1,122,0,0.851570," ","integrate(1/(5-3*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{1475 \, d x + 1475 \, c + \frac{24 \, {\left(1605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3913 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3855 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2275\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{2}} + 2950 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{51200 \, d}"," ",0,"1/51200*(1475*d*x + 1475*c + 24*(1605*tan(1/2*d*x + 1/2*c)^3 - 3913*tan(1/2*d*x + 1/2*c)^2 + 3855*tan(1/2*d*x + 1/2*c) - 2275)/(5*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 5)^2 + 2950*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
25,1,148,0,1.308241," ","integrate(1/(5-3*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{48125 \, d x + 48125 \, c + \frac{72 \, {\left(110925 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 373735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 637794 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 672110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 403425 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 142875\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{3}} + 96250 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{4096000 \, d}"," ",0,"1/4096000*(48125*d*x + 48125*c + 72*(110925*tan(1/2*d*x + 1/2*c)^5 - 373735*tan(1/2*d*x + 1/2*c)^4 + 637794*tan(1/2*d*x + 1/2*c)^3 - 672110*tan(1/2*d*x + 1/2*c)^2 + 403425*tan(1/2*d*x + 1/2*c) - 142875)/(5*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 5)^3 + 96250*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
26,1,50,0,0.469909," ","integrate(1/(-5+3*sin(d*x+c)),x, algorithm=""giac"")","-\frac{d x + c + 2 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{4 \, d}"," ",0,"-1/4*(d*x + c + 2*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
27,1,96,0,0.511453," ","integrate(1/(-5+3*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{25 \, d x + 25 \, c + \frac{24 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5\right)}}{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5} + 50 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{320 \, d}"," ",0,"1/320*(25*d*x + 25*c + 24*(3*tan(1/2*d*x + 1/2*c) - 5)/(5*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 5) + 50*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
28,1,122,0,0.329448," ","integrate(1/(-5+3*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{1475 \, d x + 1475 \, c + \frac{24 \, {\left(1605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3913 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3855 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2275\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{2}} + 2950 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{51200 \, d}"," ",0,"-1/51200*(1475*d*x + 1475*c + 24*(1605*tan(1/2*d*x + 1/2*c)^3 - 3913*tan(1/2*d*x + 1/2*c)^2 + 3855*tan(1/2*d*x + 1/2*c) - 2275)/(5*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 5)^2 + 2950*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
29,1,148,0,0.392186," ","integrate(1/(-5+3*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{48125 \, d x + 48125 \, c + \frac{72 \, {\left(110925 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 373735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 637794 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 672110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 403425 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 142875\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{3}} + 96250 \, \arctan\left(\frac{3 \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) - 9}\right)}{4096000 \, d}"," ",0,"1/4096000*(48125*d*x + 48125*c + 72*(110925*tan(1/2*d*x + 1/2*c)^5 - 373735*tan(1/2*d*x + 1/2*c)^4 + 637794*tan(1/2*d*x + 1/2*c)^3 - 672110*tan(1/2*d*x + 1/2*c)^2 + 403425*tan(1/2*d*x + 1/2*c) - 142875)/(5*tan(1/2*d*x + 1/2*c)^2 - 6*tan(1/2*d*x + 1/2*c) + 5)^3 + 96250*arctan((3*cos(d*x + c) - sin(d*x + c) + 3)/(cos(d*x + c) + 3*sin(d*x + c) - 9)))/d","A",0
30,1,49,0,0.315575," ","integrate(1/(-5-3*sin(d*x+c)),x, algorithm=""giac"")","-\frac{d x + c + 2 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{4 \, d}"," ",0,"-1/4*(d*x + c + 2*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
31,1,95,0,3.439488," ","integrate(1/(-5-3*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{25 \, d x + 25 \, c + \frac{24 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}}{5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5} + 50 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{320 \, d}"," ",0,"1/320*(25*d*x + 25*c + 24*(3*tan(1/2*d*x + 1/2*c) + 5)/(5*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) + 5) + 50*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
32,1,121,0,1.432467," ","integrate(1/(-5-3*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{1475 \, d x + 1475 \, c + \frac{24 \, {\left(1605 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3913 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3855 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2275\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{2}} + 2950 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{51200 \, d}"," ",0,"-1/51200*(1475*d*x + 1475*c + 24*(1605*tan(1/2*d*x + 1/2*c)^3 + 3913*tan(1/2*d*x + 1/2*c)^2 + 3855*tan(1/2*d*x + 1/2*c) + 2275)/(5*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) + 5)^2 + 2950*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
33,1,147,0,2.472026," ","integrate(1/(-5-3*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{48125 \, d x + 48125 \, c + \frac{72 \, {\left(110925 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 373735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 637794 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 672110 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 403425 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 142875\right)}}{{\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5\right)}^{3}} + 96250 \, \arctan\left(-\frac{3 \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 3}{\cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) - 9}\right)}{4096000 \, d}"," ",0,"1/4096000*(48125*d*x + 48125*c + 72*(110925*tan(1/2*d*x + 1/2*c)^5 + 373735*tan(1/2*d*x + 1/2*c)^4 + 637794*tan(1/2*d*x + 1/2*c)^3 + 672110*tan(1/2*d*x + 1/2*c)^2 + 403425*tan(1/2*d*x + 1/2*c) + 142875)/(5*tan(1/2*d*x + 1/2*c)^2 + 6*tan(1/2*d*x + 1/2*c) + 5)^3 + 96250*arctan(-(3*cos(d*x + c) + sin(d*x + c) + 3)/(cos(d*x + c) - 3*sin(d*x + c) - 9)))/d","A",0
34,1,36,0,4.983846," ","integrate(1/(3+5*sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{4 \, d}"," ",0,"1/4*(log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) - log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
35,1,81,0,0.989547," ","integrate(1/(3+5*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}}{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3} + 9 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{192 \, d}"," ",0,"-1/192*(40*(5*tan(1/2*d*x + 1/2*c) + 3)/(3*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) + 3) + 9*log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) - 9*log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
36,1,107,0,0.548301," ","integrate(1/(3+5*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 649 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 99\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{2}} - 387 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 387 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{18432 \, d}"," ",0,"-1/18432*(40*(75*tan(1/2*d*x + 1/2*c)^3 - 649*tan(1/2*d*x + 1/2*c)^2 - 735*tan(1/2*d*x + 1/2*c) - 99)/(3*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) + 3)^2 - 387*log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) + 387*log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
37,1,133,0,0.423527," ","integrate(1/(3+5*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(84915 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 486441 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1218910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1066482 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 342495 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42741\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{3}} + 22599 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 22599 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{2654208 \, d}"," ",0,"-1/2654208*(40*(84915*tan(1/2*d*x + 1/2*c)^5 + 486441*tan(1/2*d*x + 1/2*c)^4 + 1218910*tan(1/2*d*x + 1/2*c)^3 + 1066482*tan(1/2*d*x + 1/2*c)^2 + 342495*tan(1/2*d*x + 1/2*c) + 42741)/(3*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) + 3)^3 + 22599*log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) - 22599*log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
38,1,36,0,0.663329," ","integrate(1/(3-5*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{4 \, d}"," ",0,"-1/4*(log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) - log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
39,1,81,0,0.403877," ","integrate(1/(3-5*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3\right)}}{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3} - 9 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 9 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{192 \, d}"," ",0,"-1/192*(40*(5*tan(1/2*d*x + 1/2*c) - 3)/(3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) + 3) - 9*log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) + 9*log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
40,1,107,0,0.477848," ","integrate(1/(3-5*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 649 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 99\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{2}} + 387 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 387 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{18432 \, d}"," ",0,"-1/18432*(40*(75*tan(1/2*d*x + 1/2*c)^3 + 649*tan(1/2*d*x + 1/2*c)^2 - 735*tan(1/2*d*x + 1/2*c) + 99)/(3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) + 3)^2 + 387*log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) - 387*log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
41,1,133,0,2.186606," ","integrate(1/(3-5*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(84915 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 486441 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1218910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1066482 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 342495 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42741\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{3}} - 22599 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 22599 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{2654208 \, d}"," ",0,"-1/2654208*(40*(84915*tan(1/2*d*x + 1/2*c)^5 - 486441*tan(1/2*d*x + 1/2*c)^4 + 1218910*tan(1/2*d*x + 1/2*c)^3 - 1066482*tan(1/2*d*x + 1/2*c)^2 + 342495*tan(1/2*d*x + 1/2*c) - 42741)/(3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) + 3)^3 - 22599*log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) + 22599*log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
42,1,36,0,1.865437," ","integrate(1/(-3+5*sin(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{4 \, d}"," ",0,"1/4*(log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) - log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
43,1,81,0,0.425221," ","integrate(1/(-3+5*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3\right)}}{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3} - 9 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 9 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{192 \, d}"," ",0,"-1/192*(40*(5*tan(1/2*d*x + 1/2*c) - 3)/(3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) + 3) - 9*log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) + 9*log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
44,1,107,0,0.444829," ","integrate(1/(-3+5*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{40 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 649 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 99\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{2}} + 387 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - 387 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{18432 \, d}"," ",0,"1/18432*(40*(75*tan(1/2*d*x + 1/2*c)^3 + 649*tan(1/2*d*x + 1/2*c)^2 - 735*tan(1/2*d*x + 1/2*c) + 99)/(3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) + 3)^2 + 387*log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) - 387*log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
45,1,133,0,0.379714," ","integrate(1/(-3+5*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(84915 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 486441 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1218910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1066482 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 342495 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 42741\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{3}} - 22599 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + 22599 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \right|}\right)}{2654208 \, d}"," ",0,"-1/2654208*(40*(84915*tan(1/2*d*x + 1/2*c)^5 - 486441*tan(1/2*d*x + 1/2*c)^4 + 1218910*tan(1/2*d*x + 1/2*c)^3 - 1066482*tan(1/2*d*x + 1/2*c)^2 + 342495*tan(1/2*d*x + 1/2*c) - 42741)/(3*tan(1/2*d*x + 1/2*c)^2 - 10*tan(1/2*d*x + 1/2*c) + 3)^3 - 22599*log(abs(3*tan(1/2*d*x + 1/2*c) - 1)) + 22599*log(abs(tan(1/2*d*x + 1/2*c) - 3)))/d","A",0
46,1,36,0,0.668425," ","integrate(1/(-3-5*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{4 \, d}"," ",0,"-1/4*(log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) - log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
47,1,81,0,0.564253," ","integrate(1/(-3-5*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(5 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}}{3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3} + 9 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 9 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{192 \, d}"," ",0,"-1/192*(40*(5*tan(1/2*d*x + 1/2*c) + 3)/(3*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) + 3) + 9*log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) - 9*log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
48,1,107,0,0.791450," ","integrate(1/(-3-5*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{40 \, {\left(75 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 649 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 99\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{2}} - 387 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) + 387 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{18432 \, d}"," ",0,"1/18432*(40*(75*tan(1/2*d*x + 1/2*c)^3 - 649*tan(1/2*d*x + 1/2*c)^2 - 735*tan(1/2*d*x + 1/2*c) - 99)/(3*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) + 3)^2 - 387*log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) + 387*log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
49,1,133,0,0.480819," ","integrate(1/(-3-5*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{40 \, {\left(84915 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 486441 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1218910 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1066482 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 342495 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 42741\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3\right)}^{3}} + 22599 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 22599 \, \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \right|}\right)}{2654208 \, d}"," ",0,"-1/2654208*(40*(84915*tan(1/2*d*x + 1/2*c)^5 + 486441*tan(1/2*d*x + 1/2*c)^4 + 1218910*tan(1/2*d*x + 1/2*c)^3 + 1066482*tan(1/2*d*x + 1/2*c)^2 + 342495*tan(1/2*d*x + 1/2*c) + 42741)/(3*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) + 3)^3 + 22599*log(abs(3*tan(1/2*d*x + 1/2*c) + 1)) - 22599*log(abs(tan(1/2*d*x + 1/2*c) + 3)))/d","A",0
50,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(7/2), x)","F",0
51,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sin(d*x + c) + a), x)","F",0
55,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(-3/2), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(-5/2), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(-7/2), x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(4/3), x)","F",0
59,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(2/3), x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(1/3), x)","F",0
61,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(-1/3), x)","F",0
62,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(-2/3), x)","F",0
63,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(-4/3), x)","F",0
64,0,0,0,0.000000," ","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
65,0,0,0,0.000000," ","integrate((3+4*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(4 \, \sin\left(d x + c\right) + 3\right)}^{n}\,{d x}"," ",0,"integrate((4*sin(d*x + c) + 3)^n, x)","F",0
66,0,0,0,0.000000," ","integrate((3-4*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-4 \, \sin\left(d x + c\right) + 3\right)}^{n}\,{d x}"," ",0,"integrate((-4*sin(d*x + c) + 3)^n, x)","F",0
67,0,0,0,0.000000," ","integrate((4+3*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(3 \, \sin\left(d x + c\right) + 4\right)}^{n}\,{d x}"," ",0,"integrate((3*sin(d*x + c) + 4)^n, x)","F",0
68,0,0,0,0.000000," ","integrate((4-3*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-3 \, \sin\left(d x + c\right) + 4\right)}^{n}\,{d x}"," ",0,"integrate((-3*sin(d*x + c) + 4)^n, x)","F",0
69,0,0,0,0.000000," ","integrate((-3+4*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(4 \, \sin\left(d x + c\right) - 3\right)}^{n}\,{d x}"," ",0,"integrate((4*sin(d*x + c) - 3)^n, x)","F",0
70,0,0,0,0.000000," ","integrate((-3-4*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-4 \, \sin\left(d x + c\right) - 3\right)}^{n}\,{d x}"," ",0,"integrate((-4*sin(d*x + c) - 3)^n, x)","F",0
71,0,0,0,0.000000," ","integrate((-4+3*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(3 \, \sin\left(d x + c\right) - 4\right)}^{n}\,{d x}"," ",0,"integrate((3*sin(d*x + c) - 4)^n, x)","F",0
72,0,0,0,0.000000," ","integrate((-4-3*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(-3 \, \sin\left(d x + c\right) - 4\right)}^{n}\,{d x}"," ",0,"integrate((-3*sin(d*x + c) - 4)^n, x)","F",0
