1,1,140,0,1.253854," ","integrate((a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{3} \cos\left(d x + c\right)^{4} + 27 \, a^{3} \cos\left(d x + c\right)^{3} - 54 \, a^{3} \cos\left(d x + c\right)^{2} - 204 \, a^{3} \cos\left(d x + c\right) - 128 \, a^{3} + {\left(5 \, a^{3} \cos\left(d x + c\right)^{3} - 22 \, a^{3} \cos\left(d x + c\right)^{2} - 76 \, a^{3} \cos\left(d x + c\right) + 128 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/35*(5*a^3*cos(d*x + c)^4 + 27*a^3*cos(d*x + c)^3 - 54*a^3*cos(d*x + c)^2 - 204*a^3*cos(d*x + c) - 128*a^3 + (5*a^3*cos(d*x + c)^3 - 22*a^3*cos(d*x + c)^2 - 76*a^3*cos(d*x + c) + 128*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
2,1,115,0,1.177561," ","integrate((a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{3} - 11 \, a^{2} \cos\left(d x + c\right)^{2} - 46 \, a^{2} \cos\left(d x + c\right) - 32 \, a^{2} - {\left(3 \, a^{2} \cos\left(d x + c\right)^{2} + 14 \, a^{2} \cos\left(d x + c\right) - 32 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*a^2*cos(d*x + c)^3 - 11*a^2*cos(d*x + c)^2 - 46*a^2*cos(d*x + c) - 32*a^2 - (3*a^2*cos(d*x + c)^2 + 14*a^2*cos(d*x + c) - 32*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
3,1,76,0,0.623926," ","integrate((a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a \cos\left(d x + c\right)^{2} + 5 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right) - 4 \, a\right)} \sin\left(d x + c\right) + 4 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/3*(a*cos(d*x + c)^2 + 5*a*cos(d*x + c) + (a*cos(d*x + c) - 4*a)*sin(d*x + c) + 4*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
4,1,50,0,1.234699," ","integrate((a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d}"," ",0,"-2*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","B",0
5,1,167,0,1.347190," ","integrate(1/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{2 \, \sqrt{a} d}, \frac{\sqrt{2} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{-\frac{1}{a}}}{\cos\left(d x + c\right)}\right)}{d}\right]"," ",0,"[1/2*sqrt(2)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/(sqrt(a)*d), sqrt(2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(-1/a)/cos(d*x + c))/d]","A",0
6,1,252,0,1.061928," ","integrate(1/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - 2 \, a^{2} d - {\left(a^{2} d \cos\left(d x + c\right) + 2 \, a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/8*(sqrt(2)*(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - 2*a^2*d - (a^2*d*cos(d*x + c) + 2*a^2*d)*sin(d*x + c))","B",0
7,1,320,0,1.264967," ","integrate(1/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 4\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(3 \, \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) + 7 \, \cos\left(d x + c\right) + 4\right)} \sqrt{a \sin\left(d x + c\right) + a}}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/64*(3*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 2*cos(d*x + c) - 4)*sin(d*x + c) - 2*cos(d*x + c) - 4)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(3*cos(d*x + c)^2 + (3*cos(d*x + c) - 4)*sin(d*x + c) + 7*cos(d*x + c) + 4)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
8,0,0,0,1.167567," ","integrate((a+a*sin(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^(4/3), x)","F",0
9,0,0,0,1.273360," ","integrate((a+a*sin(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^(2/3), x)","F",0
10,0,0,0,1.384551," ","integrate((a+a*sin(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^(1/3), x)","F",0
11,0,0,0,0.862654," ","integrate(1/(a+a*sin(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^(-1/3), x)","F",0
12,0,0,0,0.802718," ","integrate(1/(a+a*sin(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^(-2/3), x)","F",0
13,0,0,0,0.958930," ","integrate(1/(a+a*sin(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(a*sin(d*x + c) + a)^(2/3)/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
14,0,0,0,1.158972," ","integrate((a+a*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^n, x)","F",0
15,0,0,0,1.157243," ","integrate((a-a*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-a \sin\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((-a*sin(d*x + c) + a)^n, x)","F",0
16,0,0,0,1.221468," ","integrate((2+2*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, \sin\left(d x + c\right) + 2\right)}^{n}, x\right)"," ",0,"integral((2*sin(d*x + c) + 2)^n, x)","F",0
17,0,0,0,1.351226," ","integrate((2-2*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-2 \, \sin\left(d x + c\right) + 2\right)}^{n}, x\right)"," ",0,"integral((-2*sin(d*x + c) + 2)^n, x)","F",0
18,1,26,0,0.921405," ","integrate(1/(5+3*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right)}{4 \, d}"," ",0,"1/4*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c))/d","A",0
19,1,59,0,1.226341," ","integrate(1/(5+3*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, {\left(3 \, \sin\left(d x + c\right) + 5\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right) + 12 \, \cos\left(d x + c\right)}{64 \, {\left(3 \, d \sin\left(d x + c\right) + 5 \, d\right)}}"," ",0,"1/64*(5*(3*sin(d*x + c) + 5)*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c)) + 12*cos(d*x + c))/(3*d*sin(d*x + c) + 5*d)","A",0
20,1,94,0,1.373247," ","integrate(1/(5+3*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{59 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right) - 34\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right) - 540 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 1092 \, \cos\left(d x + c\right)}{2048 \, {\left(9 \, d \cos\left(d x + c\right)^{2} - 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"1/2048*(59*(9*cos(d*x + c)^2 - 30*sin(d*x + c) - 34)*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c)) - 540*cos(d*x + c)*sin(d*x + c) - 1092*cos(d*x + c))/(9*d*cos(d*x + c)^2 - 30*d*sin(d*x + c) - 34*d)","A",0
21,1,130,0,1.337919," ","integrate(1/(5+3*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{11196 \, \cos\left(d x + c\right)^{3} + 385 \, {\left(135 \, \cos\left(d x + c\right)^{2} + 9 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 28\right)} \sin\left(d x + c\right) - 260\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right) - 42120 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 52344 \, \cos\left(d x + c\right)}{32768 \, {\left(135 \, d \cos\left(d x + c\right)^{2} + 9 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - 28 \, d\right)} \sin\left(d x + c\right) - 260 \, d\right)}}"," ",0,"1/32768*(11196*cos(d*x + c)^3 + 385*(135*cos(d*x + c)^2 + 9*(3*cos(d*x + c)^2 - 28)*sin(d*x + c) - 260)*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c)) - 42120*cos(d*x + c)*sin(d*x + c) - 52344*cos(d*x + c))/(135*d*cos(d*x + c)^2 + 9*(3*d*cos(d*x + c)^2 - 28*d)*sin(d*x + c) - 260*d)","A",0
22,1,26,0,0.753403," ","integrate(1/(5-3*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right)}{4 \, d}"," ",0,"1/4*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c))/d","A",0
23,1,59,0,1.160697," ","integrate(1/(5-3*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, {\left(3 \, \sin\left(d x + c\right) - 5\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right) + 12 \, \cos\left(d x + c\right)}{64 \, {\left(3 \, d \sin\left(d x + c\right) - 5 \, d\right)}}"," ",0,"1/64*(5*(3*sin(d*x + c) - 5)*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c)) + 12*cos(d*x + c))/(3*d*sin(d*x + c) - 5*d)","A",0
24,1,94,0,1.373792," ","integrate(1/(5-3*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{59 \, {\left(9 \, \cos\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) - 34\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right) - 540 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 1092 \, \cos\left(d x + c\right)}{2048 \, {\left(9 \, d \cos\left(d x + c\right)^{2} + 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"1/2048*(59*(9*cos(d*x + c)^2 + 30*sin(d*x + c) - 34)*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c)) - 540*cos(d*x + c)*sin(d*x + c) + 1092*cos(d*x + c))/(9*d*cos(d*x + c)^2 + 30*d*sin(d*x + c) - 34*d)","A",0
25,1,130,0,1.352444," ","integrate(1/(5-3*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{11196 \, \cos\left(d x + c\right)^{3} - 385 \, {\left(135 \, \cos\left(d x + c\right)^{2} - 9 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 28\right)} \sin\left(d x + c\right) - 260\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right) + 42120 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 52344 \, \cos\left(d x + c\right)}{32768 \, {\left(135 \, d \cos\left(d x + c\right)^{2} - 9 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - 28 \, d\right)} \sin\left(d x + c\right) - 260 \, d\right)}}"," ",0,"-1/32768*(11196*cos(d*x + c)^3 - 385*(135*cos(d*x + c)^2 - 9*(3*cos(d*x + c)^2 - 28)*sin(d*x + c) - 260)*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c)) + 42120*cos(d*x + c)*sin(d*x + c) - 52344*cos(d*x + c))/(135*d*cos(d*x + c)^2 - 9*(3*d*cos(d*x + c)^2 - 28*d)*sin(d*x + c) - 260*d)","A",0
26,1,26,0,1.023463," ","integrate(1/(-5+3*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right)}{4 \, d}"," ",0,"-1/4*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c))/d","A",0
27,1,59,0,1.182235," ","integrate(1/(-5+3*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, {\left(3 \, \sin\left(d x + c\right) - 5\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right) + 12 \, \cos\left(d x + c\right)}{64 \, {\left(3 \, d \sin\left(d x + c\right) - 5 \, d\right)}}"," ",0,"1/64*(5*(3*sin(d*x + c) - 5)*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c)) + 12*cos(d*x + c))/(3*d*sin(d*x + c) - 5*d)","A",0
28,1,94,0,1.068195," ","integrate(1/(-5+3*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{59 \, {\left(9 \, \cos\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) - 34\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right) - 540 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 1092 \, \cos\left(d x + c\right)}{2048 \, {\left(9 \, d \cos\left(d x + c\right)^{2} + 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"-1/2048*(59*(9*cos(d*x + c)^2 + 30*sin(d*x + c) - 34)*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c)) - 540*cos(d*x + c)*sin(d*x + c) + 1092*cos(d*x + c))/(9*d*cos(d*x + c)^2 + 30*d*sin(d*x + c) - 34*d)","A",0
29,1,130,0,1.234016," ","integrate(1/(-5+3*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{11196 \, \cos\left(d x + c\right)^{3} - 385 \, {\left(135 \, \cos\left(d x + c\right)^{2} - 9 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 28\right)} \sin\left(d x + c\right) - 260\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) - 3}{4 \, \cos\left(d x + c\right)}\right) + 42120 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 52344 \, \cos\left(d x + c\right)}{32768 \, {\left(135 \, d \cos\left(d x + c\right)^{2} - 9 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - 28 \, d\right)} \sin\left(d x + c\right) - 260 \, d\right)}}"," ",0,"-1/32768*(11196*cos(d*x + c)^3 - 385*(135*cos(d*x + c)^2 - 9*(3*cos(d*x + c)^2 - 28)*sin(d*x + c) - 260)*arctan(1/4*(5*sin(d*x + c) - 3)/cos(d*x + c)) + 42120*cos(d*x + c)*sin(d*x + c) - 52344*cos(d*x + c))/(135*d*cos(d*x + c)^2 - 9*(3*d*cos(d*x + c)^2 - 28*d)*sin(d*x + c) - 260*d)","A",0
30,1,26,0,0.809081," ","integrate(1/(-5-3*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right)}{4 \, d}"," ",0,"-1/4*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c))/d","A",0
31,1,59,0,1.093851," ","integrate(1/(-5-3*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, {\left(3 \, \sin\left(d x + c\right) + 5\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right) + 12 \, \cos\left(d x + c\right)}{64 \, {\left(3 \, d \sin\left(d x + c\right) + 5 \, d\right)}}"," ",0,"1/64*(5*(3*sin(d*x + c) + 5)*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c)) + 12*cos(d*x + c))/(3*d*sin(d*x + c) + 5*d)","A",0
32,1,94,0,1.011996," ","integrate(1/(-5-3*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{59 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right) - 34\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right) - 540 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 1092 \, \cos\left(d x + c\right)}{2048 \, {\left(9 \, d \cos\left(d x + c\right)^{2} - 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"-1/2048*(59*(9*cos(d*x + c)^2 - 30*sin(d*x + c) - 34)*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c)) - 540*cos(d*x + c)*sin(d*x + c) - 1092*cos(d*x + c))/(9*d*cos(d*x + c)^2 - 30*d*sin(d*x + c) - 34*d)","A",0
33,1,130,0,1.048624," ","integrate(1/(-5-3*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{11196 \, \cos\left(d x + c\right)^{3} + 385 \, {\left(135 \, \cos\left(d x + c\right)^{2} + 9 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 28\right)} \sin\left(d x + c\right) - 260\right)} \arctan\left(\frac{5 \, \sin\left(d x + c\right) + 3}{4 \, \cos\left(d x + c\right)}\right) - 42120 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 52344 \, \cos\left(d x + c\right)}{32768 \, {\left(135 \, d \cos\left(d x + c\right)^{2} + 9 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - 28 \, d\right)} \sin\left(d x + c\right) - 260 \, d\right)}}"," ",0,"1/32768*(11196*cos(d*x + c)^3 + 385*(135*cos(d*x + c)^2 + 9*(3*cos(d*x + c)^2 - 28)*sin(d*x + c) - 260)*arctan(1/4*(5*sin(d*x + c) + 3)/cos(d*x + c)) - 42120*cos(d*x + c)*sin(d*x + c) - 52344*cos(d*x + c))/(135*d*cos(d*x + c)^2 + 9*(3*d*cos(d*x + c)^2 - 28*d)*sin(d*x + c) - 260*d)","A",0
34,1,46,0,1.113816," ","integrate(1/(3+5*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right)}{8 \, d}"," ",0,"-1/8*(log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) - log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5))/d","A",0
35,1,88,0,1.198620," ","integrate(1/(3+5*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, \sin\left(d x + c\right) + 3\right)} \log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 3 \, {\left(5 \, \sin\left(d x + c\right) + 3\right)} \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 40 \, \cos\left(d x + c\right)}{128 \, {\left(5 \, d \sin\left(d x + c\right) + 3 \, d\right)}}"," ",0,"1/128*(3*(5*sin(d*x + c) + 3)*log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 3*(5*sin(d*x + c) + 3)*log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 40*cos(d*x + c))/(5*d*sin(d*x + c) + 3*d)","A",0
36,1,133,0,0.746113," ","integrate(1/(3+5*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{43 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 43 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) + 1800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 440 \, \cos\left(d x + c\right)}{4096 \, {\left(25 \, d \cos\left(d x + c\right)^{2} - 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"-1/4096*(43*(25*cos(d*x + c)^2 - 30*sin(d*x + c) - 34)*log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 43*(25*cos(d*x + c)^2 - 30*sin(d*x + c) - 34)*log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5) + 1800*cos(d*x + c)*sin(d*x + c) + 440*cos(d*x + c))/(25*d*cos(d*x + c)^2 - 30*d*sin(d*x + c) - 34*d)","A",0
37,1,181,0,1.513106," ","integrate(1/(3+5*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{199000 \, \cos\left(d x + c\right)^{3} - 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) + 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 190800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 262320 \, \cos\left(d x + c\right)}{196608 \, {\left(225 \, d \cos\left(d x + c\right)^{2} + 5 \, {\left(25 \, d \cos\left(d x + c\right)^{2} - 52 \, d\right)} \sin\left(d x + c\right) - 252 \, d\right)}}"," ",0,"-1/196608*(199000*cos(d*x + c)^3 - 837*(225*cos(d*x + c)^2 + 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) + 837*(225*cos(d*x + c)^2 + 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 190800*cos(d*x + c)*sin(d*x + c) - 262320*cos(d*x + c))/(225*d*cos(d*x + c)^2 + 5*(25*d*cos(d*x + c)^2 - 52*d)*sin(d*x + c) - 252*d)","A",0
38,1,46,0,1.167214," ","integrate(1/(3-5*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right)}{8 \, d}"," ",0,"1/8*(log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) - log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5))/d","A",0
39,1,88,0,1.213428," ","integrate(1/(3-5*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(5 \, \sin\left(d x + c\right) - 3\right)} \log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - 3 \, {\left(5 \, \sin\left(d x + c\right) - 3\right)} \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) + 40 \, \cos\left(d x + c\right)}{128 \, {\left(5 \, d \sin\left(d x + c\right) - 3 \, d\right)}}"," ",0,"-1/128*(3*(5*sin(d*x + c) - 3)*log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) - 3*(5*sin(d*x + c) - 3)*log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5) + 40*cos(d*x + c))/(5*d*sin(d*x + c) - 3*d)","A",0
40,1,133,0,0.991131," ","integrate(1/(3-5*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{43 \, {\left(25 \, \cos\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - 43 \, {\left(25 \, \cos\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - 1800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 440 \, \cos\left(d x + c\right)}{4096 \, {\left(25 \, d \cos\left(d x + c\right)^{2} + 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"1/4096*(43*(25*cos(d*x + c)^2 + 30*sin(d*x + c) - 34)*log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) - 43*(25*cos(d*x + c)^2 + 30*sin(d*x + c) - 34)*log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5) - 1800*cos(d*x + c)*sin(d*x + c) + 440*cos(d*x + c))/(25*d*cos(d*x + c)^2 + 30*d*sin(d*x + c) - 34*d)","A",0
41,1,181,0,1.052704," ","integrate(1/(3-5*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{199000 \, \cos\left(d x + c\right)^{3} - 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} - 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) + 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} - 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) + 190800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 262320 \, \cos\left(d x + c\right)}{196608 \, {\left(225 \, d \cos\left(d x + c\right)^{2} - 5 \, {\left(25 \, d \cos\left(d x + c\right)^{2} - 52 \, d\right)} \sin\left(d x + c\right) - 252 \, d\right)}}"," ",0,"1/196608*(199000*cos(d*x + c)^3 - 837*(225*cos(d*x + c)^2 - 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) + 837*(225*cos(d*x + c)^2 - 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5) + 190800*cos(d*x + c)*sin(d*x + c) - 262320*cos(d*x + c))/(225*d*cos(d*x + c)^2 - 5*(25*d*cos(d*x + c)^2 - 52*d)*sin(d*x + c) - 252*d)","A",0
42,1,46,0,0.857055," ","integrate(1/(-3+5*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right)}{8 \, d}"," ",0,"-1/8*(log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) - log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5))/d","A",0
43,1,88,0,0.703794," ","integrate(1/(-3+5*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(5 \, \sin\left(d x + c\right) - 3\right)} \log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - 3 \, {\left(5 \, \sin\left(d x + c\right) - 3\right)} \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) + 40 \, \cos\left(d x + c\right)}{128 \, {\left(5 \, d \sin\left(d x + c\right) - 3 \, d\right)}}"," ",0,"-1/128*(3*(5*sin(d*x + c) - 3)*log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) - 3*(5*sin(d*x + c) - 3)*log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5) + 40*cos(d*x + c))/(5*d*sin(d*x + c) - 3*d)","A",0
44,1,133,0,1.073939," ","integrate(1/(-3+5*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{43 \, {\left(25 \, \cos\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - 43 \, {\left(25 \, \cos\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) - 1800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 440 \, \cos\left(d x + c\right)}{4096 \, {\left(25 \, d \cos\left(d x + c\right)^{2} + 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"-1/4096*(43*(25*cos(d*x + c)^2 + 30*sin(d*x + c) - 34)*log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) - 43*(25*cos(d*x + c)^2 + 30*sin(d*x + c) - 34)*log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5) - 1800*cos(d*x + c)*sin(d*x + c) + 440*cos(d*x + c))/(25*d*cos(d*x + c)^2 + 30*d*sin(d*x + c) - 34*d)","A",0
45,1,181,0,1.087845," ","integrate(1/(-3+5*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{199000 \, \cos\left(d x + c\right)^{3} - 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} - 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) + 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} - 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(-4 \, \cos\left(d x + c\right) - 3 \, \sin\left(d x + c\right) + 5\right) + 190800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 262320 \, \cos\left(d x + c\right)}{196608 \, {\left(225 \, d \cos\left(d x + c\right)^{2} - 5 \, {\left(25 \, d \cos\left(d x + c\right)^{2} - 52 \, d\right)} \sin\left(d x + c\right) - 252 \, d\right)}}"," ",0,"1/196608*(199000*cos(d*x + c)^3 - 837*(225*cos(d*x + c)^2 - 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(4*cos(d*x + c) - 3*sin(d*x + c) + 5) + 837*(225*cos(d*x + c)^2 - 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(-4*cos(d*x + c) - 3*sin(d*x + c) + 5) + 190800*cos(d*x + c)*sin(d*x + c) - 262320*cos(d*x + c))/(225*d*cos(d*x + c)^2 - 5*(25*d*cos(d*x + c)^2 - 52*d)*sin(d*x + c) - 252*d)","A",0
46,1,46,0,0.943336," ","integrate(1/(-3-5*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right)}{8 \, d}"," ",0,"1/8*(log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) - log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5))/d","A",0
47,1,88,0,1.080727," ","integrate(1/(-3-5*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, \sin\left(d x + c\right) + 3\right)} \log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 3 \, {\left(5 \, \sin\left(d x + c\right) + 3\right)} \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 40 \, \cos\left(d x + c\right)}{128 \, {\left(5 \, d \sin\left(d x + c\right) + 3 \, d\right)}}"," ",0,"1/128*(3*(5*sin(d*x + c) + 3)*log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 3*(5*sin(d*x + c) + 3)*log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 40*cos(d*x + c))/(5*d*sin(d*x + c) + 3*d)","A",0
48,1,133,0,1.012589," ","integrate(1/(-3-5*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{43 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 43 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right) - 34\right)} \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) + 1800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 440 \, \cos\left(d x + c\right)}{4096 \, {\left(25 \, d \cos\left(d x + c\right)^{2} - 30 \, d \sin\left(d x + c\right) - 34 \, d\right)}}"," ",0,"1/4096*(43*(25*cos(d*x + c)^2 - 30*sin(d*x + c) - 34)*log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 43*(25*cos(d*x + c)^2 - 30*sin(d*x + c) - 34)*log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5) + 1800*cos(d*x + c)*sin(d*x + c) + 440*cos(d*x + c))/(25*d*cos(d*x + c)^2 - 30*d*sin(d*x + c) - 34*d)","A",0
49,1,181,0,1.301790," ","integrate(1/(-3-5*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{199000 \, \cos\left(d x + c\right)^{3} - 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) + 837 \, {\left(225 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(25 \, \cos\left(d x + c\right)^{2} - 52\right)} \sin\left(d x + c\right) - 252\right)} \log\left(-4 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right) + 5\right) - 190800 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 262320 \, \cos\left(d x + c\right)}{196608 \, {\left(225 \, d \cos\left(d x + c\right)^{2} + 5 \, {\left(25 \, d \cos\left(d x + c\right)^{2} - 52 \, d\right)} \sin\left(d x + c\right) - 252 \, d\right)}}"," ",0,"-1/196608*(199000*cos(d*x + c)^3 - 837*(225*cos(d*x + c)^2 + 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(4*cos(d*x + c) + 3*sin(d*x + c) + 5) + 837*(225*cos(d*x + c)^2 + 5*(25*cos(d*x + c)^2 - 52)*sin(d*x + c) - 252)*log(-4*cos(d*x + c) + 3*sin(d*x + c) + 5) - 190800*cos(d*x + c)*sin(d*x + c) - 262320*cos(d*x + c))/(225*d*cos(d*x + c)^2 + 5*(25*d*cos(d*x + c)^2 - 52*d)*sin(d*x + c) - 252*d)","A",0
50,0,0,0,1.435830," ","integrate((a+b*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a), x)","F",0
51,0,0,0,0.913655," ","integrate((a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(b*sin(d*x + c) + a), x)","F",0
52,0,0,0,1.299602," ","integrate((a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(3/2), x)","F",0
53,0,0,0,1.063964," ","integrate((a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a), x)","F",0
54,0,0,0,1.134984," ","integrate(1/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*sin(d*x + c) + a), x)","F",0
55,0,0,0,0.987389," ","integrate(1/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
56,0,0,0,1.169405," ","integrate(1/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
57,0,0,0,1.073740," ","integrate(1/(a+b*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sin\left(d x + c\right) + a}}{b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)/(b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c)), x)","F",0
58,0,0,0,1.113495," ","integrate((a+b*sin(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{\frac{4}{3}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(4/3), x)","F",0
59,0,0,0,0.964958," ","integrate((a+b*sin(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(2/3), x)","F",0
60,0,0,0,0.697301," ","integrate((a+b*sin(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(1/3), x)","F",0
61,0,0,0,0.765317," ","integrate(1/(a+b*sin(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(-1/3), x)","F",0
62,0,0,0,1.114911," ","integrate(1/(a+b*sin(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(-2/3), x)","F",0
63,0,0,0,1.189368," ","integrate(1/(a+b*sin(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{2}{3}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(b*sin(d*x + c) + a)^(2/3)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
64,0,0,0,1.337367," ","integrate((a+b*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{n}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^n, x)","F",0
65,0,0,0,1.228747," ","integrate((3+4*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, \sin\left(d x + c\right) + 3\right)}^{n}, x\right)"," ",0,"integral((4*sin(d*x + c) + 3)^n, x)","F",0
66,0,0,0,0.800671," ","integrate((3-4*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-4 \, \sin\left(d x + c\right) + 3\right)}^{n}, x\right)"," ",0,"integral((-4*sin(d*x + c) + 3)^n, x)","F",0
67,0,0,0,1.059384," ","integrate((4+3*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, \sin\left(d x + c\right) + 4\right)}^{n}, x\right)"," ",0,"integral((3*sin(d*x + c) + 4)^n, x)","F",0
68,0,0,0,1.102353," ","integrate((4-3*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-3 \, \sin\left(d x + c\right) + 4\right)}^{n}, x\right)"," ",0,"integral((-3*sin(d*x + c) + 4)^n, x)","F",0
69,0,0,0,1.149158," ","integrate((-3+4*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, \sin\left(d x + c\right) - 3\right)}^{n}, x\right)"," ",0,"integral((4*sin(d*x + c) - 3)^n, x)","F",0
70,0,0,0,1.021723," ","integrate((-3-4*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-4 \, \sin\left(d x + c\right) - 3\right)}^{n}, x\right)"," ",0,"integral((-4*sin(d*x + c) - 3)^n, x)","F",0
71,0,0,0,1.032562," ","integrate((-4+3*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, \sin\left(d x + c\right) - 4\right)}^{n}, x\right)"," ",0,"integral((3*sin(d*x + c) - 4)^n, x)","F",0
72,0,0,0,0.866278," ","integrate((-4-3*sin(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-3 \, \sin\left(d x + c\right) - 4\right)}^{n}, x\right)"," ",0,"integral((-3*sin(d*x + c) - 4)^n, x)","F",0
