1,1,34,31,0.381780,"\text{Not used}","int(sin(x)^4/(a + a*cos(x)),x)","\frac{x}{2\,a}-\frac{\sin\left(x\right)}{3\,a}+\frac{{\cos\left(x\right)}^2\,\sin\left(x\right)}{3\,a}-\frac{\cos\left(x\right)\,\sin\left(x\right)}{2\,a}","Not used",1,"x/(2*a) - sin(x)/(3*a) + (cos(x)^2*sin(x))/(3*a) - (cos(x)*sin(x))/(2*a)","B"
2,1,11,19,0.249488,"\text{Not used}","int(sin(x)^3/(a + a*cos(x)),x)","\frac{\cos\left(x\right)\,\left(\cos\left(x\right)-2\right)}{2\,a}","Not used",1,"(cos(x)*(cos(x) - 2))/(2*a)","B"
3,1,10,13,0.292232,"\text{Not used}","int(sin(x)^2/(a + a*cos(x)),x)","\frac{x-\sin\left(x\right)}{a}","Not used",1,"(x - sin(x))/a","B"
4,1,10,10,0.056953,"\text{Not used}","int(sin(x)/(a + a*cos(x)),x)","-\frac{\ln\left(\cos\left(x\right)+1\right)}{a}","Not used",1,"-log(cos(x) + 1)/a","B"
5,1,8,11,0.293013,"\text{Not used}","int(1/(a + a*cos(x)),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{a}","Not used",1,"tan(x/2)/a","B"
6,1,20,23,0.284602,"\text{Not used}","int(1/(sin(x)*(a + a*cos(x))),x)","\frac{1}{2\,a\,\left(\cos\left(x\right)+1\right)}-\frac{\mathrm{atanh}\left(\cos\left(x\right)\right)}{2\,a}","Not used",1,"1/(2*a*(cos(x) + 1)) - atanh(cos(x))/(2*a)","B"
7,1,35,24,0.319744,"\text{Not used}","int(1/(sin(x)^2*(a + a*cos(x))),x)","\frac{-8\,{\cos\left(\frac{x}{2}\right)}^4+4\,{\cos\left(\frac{x}{2}\right)}^2+1}{12\,a\,{\cos\left(\frac{x}{2}\right)}^3\,\sin\left(\frac{x}{2}\right)}","Not used",1,"(4*cos(x/2)^2 - 8*cos(x/2)^4 + 1)/(12*a*cos(x/2)^3*sin(x/2))","B"
8,1,45,49,0.288582,"\text{Not used}","int(1/(sin(x)^3*(a + a*cos(x))),x)","-\frac{\frac{3\,{\cos\left(x\right)}^2}{8}+\frac{3\,\cos\left(x\right)}{8}-\frac{1}{4}}{-a\,{\cos\left(x\right)}^3-a\,{\cos\left(x\right)}^2+a\,\cos\left(x\right)+a}-\frac{3\,\mathrm{atanh}\left(\cos\left(x\right)\right)}{8\,a}","Not used",1,"- ((3*cos(x))/8 + (3*cos(x)^2)/8 - 1/4)/(a + a*cos(x) - a*cos(x)^2 - a*cos(x)^3) - (3*atanh(cos(x)))/(8*a)","B"
9,1,45,37,0.372264,"\text{Not used}","int(1/(sin(x)^4*(a + a*cos(x))),x)","\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+90\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-60\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-5}{240\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}","Not used",1,"(90*tan(x/2)^4 - 60*tan(x/2)^2 + 20*tan(x/2)^6 + 3*tan(x/2)^8 - 5)/(240*a*tan(x/2)^3)","B"
10,1,7,5,0.264215,"\text{Not used}","int(sin(2*x)/(cos(2*x) + 1),x)","-\frac{\ln\left({\cos\left(x\right)}^2\right)}{2}","Not used",1,"-log(cos(x)^2)/2","B"
11,1,9,3,0.076505,"\text{Not used}","int(-sin(2*x)/(cos(2*x) - 1),x)","\frac{\ln\left(-{\sin\left(x\right)}^2\right)}{2}","Not used",1,"log(-sin(x)^2)/2","B"
12,1,6,6,0.251154,"\text{Not used}","int(sin(x)/(cos(x) + 1)^2,x)","\frac{1}{\cos\left(x\right)+1}","Not used",1,"1/(cos(x) + 1)","B"
13,1,6,10,0.247768,"\text{Not used}","int(sin(x)/(cos(x) - 1)^2,x)","\frac{1}{\cos\left(x\right)-1}","Not used",1,"1/(cos(x) - 1)","B"
14,1,10,14,0.298446,"\text{Not used}","int(sin(x)^2/(cos(x) + 1)^2,x)","2\,\mathrm{tan}\left(\frac{x}{2}\right)-x","Not used",1,"2*tan(x/2) - x","B"
15,1,10,16,0.305262,"\text{Not used}","int(sin(x)^2/(cos(x) - 1)^2,x)","-x-2\,\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"- x - 2*cot(x/2)","B"
16,1,10,10,0.247473,"\text{Not used}","int(sin(x)^3/(cos(x) + 1)^2,x)","\cos\left(x\right)-2\,\ln\left(\cos\left(x\right)+1\right)","Not used",1,"cos(x) - 2*log(cos(x) + 1)","B"
17,1,10,12,0.043593,"\text{Not used}","int(sin(x)^3/(cos(x) - 1)^2,x)","2\,\ln\left(\cos\left(x\right)-1\right)+\cos\left(x\right)","Not used",1,"2*log(cos(x) - 1) + cos(x)","B"
18,1,8,10,0.035410,"\text{Not used}","int(sin(x)/(cos(x) + 1)^3,x)","\frac{1}{2\,{\left(\cos\left(x\right)+1\right)}^2}","Not used",1,"1/(2*(cos(x) + 1)^2)","B"
19,1,8,12,0.036093,"\text{Not used}","int(-sin(x)/(cos(x) - 1)^3,x)","-\frac{1}{2\,{\left(\cos\left(x\right)-1\right)}^2}","Not used",1,"-1/(2*(cos(x) - 1)^2)","B"
20,1,8,14,0.258950,"\text{Not used}","int(sin(x)^2/(cos(x) + 1)^3,x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3}","Not used",1,"tan(x/2)^3/3","B"
21,1,8,16,0.352742,"\text{Not used}","int(-sin(x)^2/(cos(x) - 1)^3,x)","-\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^3}{3}","Not used",1,"-cot(x/2)^3/3","B"
22,1,14,14,0.043261,"\text{Not used}","int(sin(x)^3/(cos(x) + 1)^3,x)","\ln\left(\cos\left(x\right)+1\right)+\frac{2}{\cos\left(x\right)+1}","Not used",1,"log(cos(x) + 1) + 2/(cos(x) + 1)","B"
23,1,16,20,0.043540,"\text{Not used}","int(-sin(x)^3/(cos(x) - 1)^3,x)","\frac{2}{\cos\left(x\right)-1}-\ln\left(\cos\left(x\right)-1\right)","Not used",1,"2/(cos(x) - 1) - log(cos(x) - 1)","B"
24,1,1677,104,1.112405,"\text{Not used}","int(sin(x)^4/(a + b*cos(x)),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(3\,a^2-5\,b^2\right)}{3\,b^3}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(-2\,a^2+a\,b+2\,b^2\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(2\,a^2+a\,b-2\,b^2\right)}{b^3}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{2\,\mathrm{atanh}\left(\frac{64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a\,b^2+112\,a^2\,b-352\,a^3-64\,b^3+\frac{16\,a^4}{b}+\frac{320\,a^5}{b^2}-\frac{112\,a^6}{b^3}-\frac{96\,a^7}{b^4}+\frac{48\,a^8}{b^5}}+\frac{144\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a\,b^4+16\,a^4\,b+320\,a^5-64\,b^5+112\,a^2\,b^3-352\,a^3\,b^2-\frac{112\,a^6}{b}-\frac{96\,a^7}{b^2}+\frac{48\,a^8}{b^3}}+\frac{80\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a\,b^5+320\,a^5\,b-112\,a^6-64\,b^6+112\,a^2\,b^4-352\,a^3\,b^3+16\,a^4\,b^2-\frac{96\,a^7}{b}+\frac{48\,a^8}{b^2}}-\frac{144\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a\,b^6-112\,a^6\,b-96\,a^7-64\,b^7+112\,a^2\,b^5-352\,a^3\,b^4+16\,a^4\,b^3+320\,a^5\,b^2+\frac{48\,a^8}{b}}+\frac{48\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{48\,a^8-96\,a^7\,b-112\,a^6\,b^2+320\,a^5\,b^3+16\,a^4\,b^4-352\,a^3\,b^5+112\,a^2\,b^6+128\,a\,b^7-64\,b^8}-\frac{192\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a\,b^3-352\,a^3\,b+16\,a^4-64\,b^4+112\,a^2\,b^2+\frac{320\,a^5}{b}-\frac{112\,a^6}{b^2}-\frac{96\,a^7}{b^3}+\frac{48\,a^8}{b^4}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{b^4}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^9-16\,a^8\,b-16\,a^7\,b^2+48\,a^6\,b^3-3\,a^5\,b^4-39\,a^4\,b^5+11\,a^3\,b^6+7\,a^2\,b^7+4\,a\,b^8-4\,b^9\right)}{b^6}-\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^8-6\,a^4\,b^9-6\,a^3\,b^{10}+10\,a^2\,b^{11}+2\,a\,b^{12}-4\,b^{13}\right)}{b^9}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^9-16\,a^8\,b-16\,a^7\,b^2+48\,a^6\,b^3-3\,a^5\,b^4-39\,a^4\,b^5+11\,a^3\,b^6+7\,a^2\,b^7+4\,a\,b^8-4\,b^9\right)}{b^6}+\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^8-6\,a^4\,b^9-6\,a^3\,b^{10}+10\,a^2\,b^{11}+2\,a\,b^{12}-4\,b^{13}\right)}{b^9}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}}{\frac{16\,\left(-4\,a^{11}+6\,a^{10}\,b+18\,a^9\,b^2-31\,a^8\,b^3-26\,a^7\,b^4+59\,a^6\,b^5+8\,a^5\,b^6-49\,a^4\,b^7+10\,a^3\,b^8+15\,a^2\,b^9-6\,a\,b^{10}\right)}{b^9}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^9-16\,a^8\,b-16\,a^7\,b^2+48\,a^6\,b^3-3\,a^5\,b^4-39\,a^4\,b^5+11\,a^3\,b^6+7\,a^2\,b^7+4\,a\,b^8-4\,b^9\right)}{b^6}-\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^8-6\,a^4\,b^9-6\,a^3\,b^{10}+10\,a^2\,b^{11}+2\,a\,b^{12}-4\,b^{13}\right)}{b^9}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^9-16\,a^8\,b-16\,a^7\,b^2+48\,a^6\,b^3-3\,a^5\,b^4-39\,a^4\,b^5+11\,a^3\,b^6+7\,a^2\,b^7+4\,a\,b^8-4\,b^9\right)}{b^6}+\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^8-6\,a^4\,b^9-6\,a^3\,b^{10}+10\,a^2\,b^{11}+2\,a\,b^{12}-4\,b^{13}\right)}{b^9}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}}\right)\,\left(2\,a^2-3\,b^2\right)}{b^4}","Not used",1,"((4*tan(x/2)^3*(3*a^2 - 5*b^2))/(3*b^3) - (tan(x/2)*(a*b - 2*a^2 + 2*b^2))/b^3 + (tan(x/2)^5*(a*b + 2*a^2 - 2*b^2))/b^3)/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1) - (2*atanh((64*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a*b^2 + 112*a^2*b - 352*a^3 - 64*b^3 + (16*a^4)/b + (320*a^5)/b^2 - (112*a^6)/b^3 - (96*a^7)/b^4 + (48*a^8)/b^5) + (144*a^2*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a*b^4 + 16*a^4*b + 320*a^5 - 64*b^5 + 112*a^2*b^3 - 352*a^3*b^2 - (112*a^6)/b - (96*a^7)/b^2 + (48*a^8)/b^3) + (80*a^3*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a*b^5 + 320*a^5*b - 112*a^6 - 64*b^6 + 112*a^2*b^4 - 352*a^3*b^3 + 16*a^4*b^2 - (96*a^7)/b + (48*a^8)/b^2) - (144*a^4*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a*b^6 - 112*a^6*b - 96*a^7 - 64*b^7 + 112*a^2*b^5 - 352*a^3*b^4 + 16*a^4*b^3 + 320*a^5*b^2 + (48*a^8)/b) + (48*a^5*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a*b^7 - 96*a^7*b + 48*a^8 - 64*b^8 + 112*a^2*b^6 - 352*a^3*b^5 + 16*a^4*b^4 + 320*a^5*b^3 - 112*a^6*b^2) - (192*a*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a*b^3 - 352*a^3*b + 16*a^4 - 64*b^4 + 112*a^2*b^2 + (320*a^5)/b - (112*a^6)/b^2 - (96*a^7)/b^3 + (48*a^8)/b^4))*(-(a + b)^3*(a - b)^3)^(1/2))/b^4 + (a*atan(((a*(2*a^2 - 3*b^2)*((8*tan(x/2)*(4*a*b^8 - 16*a^8*b + 8*a^9 - 4*b^9 + 7*a^2*b^7 + 11*a^3*b^6 - 39*a^4*b^5 - 3*a^5*b^4 + 48*a^6*b^3 - 16*a^7*b^2))/b^6 - (a*((8*(2*a*b^12 - 4*b^13 + 10*a^2*b^11 - 6*a^3*b^10 - 6*a^4*b^9 + 4*a^5*b^8))/b^9 - (a*tan(x/2)*(2*a^2 - 3*b^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 - 3*b^2)*1i)/(2*b^4)))/(2*b^4) + (a*(2*a^2 - 3*b^2)*((8*tan(x/2)*(4*a*b^8 - 16*a^8*b + 8*a^9 - 4*b^9 + 7*a^2*b^7 + 11*a^3*b^6 - 39*a^4*b^5 - 3*a^5*b^4 + 48*a^6*b^3 - 16*a^7*b^2))/b^6 + (a*((8*(2*a*b^12 - 4*b^13 + 10*a^2*b^11 - 6*a^3*b^10 - 6*a^4*b^9 + 4*a^5*b^8))/b^9 + (a*tan(x/2)*(2*a^2 - 3*b^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 - 3*b^2)*1i)/(2*b^4)))/(2*b^4))/((16*(6*a^10*b - 6*a*b^10 - 4*a^11 + 15*a^2*b^9 + 10*a^3*b^8 - 49*a^4*b^7 + 8*a^5*b^6 + 59*a^6*b^5 - 26*a^7*b^4 - 31*a^8*b^3 + 18*a^9*b^2))/b^9 + (a*(2*a^2 - 3*b^2)*((8*tan(x/2)*(4*a*b^8 - 16*a^8*b + 8*a^9 - 4*b^9 + 7*a^2*b^7 + 11*a^3*b^6 - 39*a^4*b^5 - 3*a^5*b^4 + 48*a^6*b^3 - 16*a^7*b^2))/b^6 - (a*((8*(2*a*b^12 - 4*b^13 + 10*a^2*b^11 - 6*a^3*b^10 - 6*a^4*b^9 + 4*a^5*b^8))/b^9 - (a*tan(x/2)*(2*a^2 - 3*b^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 - 3*b^2)*1i)/(2*b^4))*1i)/(2*b^4) - (a*(2*a^2 - 3*b^2)*((8*tan(x/2)*(4*a*b^8 - 16*a^8*b + 8*a^9 - 4*b^9 + 7*a^2*b^7 + 11*a^3*b^6 - 39*a^4*b^5 - 3*a^5*b^4 + 48*a^6*b^3 - 16*a^7*b^2))/b^6 + (a*((8*(2*a*b^12 - 4*b^13 + 10*a^2*b^11 - 6*a^3*b^10 - 6*a^4*b^9 + 4*a^5*b^8))/b^9 + (a*tan(x/2)*(2*a^2 - 3*b^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 - 3*b^2)*1i)/(2*b^4))*1i)/(2*b^4)))*(2*a^2 - 3*b^2))/b^4","B"
25,1,38,40,0.091654,"\text{Not used}","int(sin(x)^3/(a + b*cos(x)),x)","\frac{{\cos\left(x\right)}^2}{2\,b}+\frac{\ln\left(a+b\,\cos\left(x\right)\right)\,\left(a^2-b^2\right)}{b^3}-\frac{a\,\cos\left(x\right)}{b^2}","Not used",1,"cos(x)^2/(2*b) + (log(a + b*cos(x))*(a^2 - b^2))/b^3 - (a*cos(x))/b^2","B"
26,1,74,59,0.487503,"\text{Not used}","int(sin(x)^2/(a + b*cos(x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}}{a\,\cos\left(\frac{x}{2}\right)+b\,\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{b^2}-\frac{\sin\left(x\right)}{b}+\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{b^2}","Not used",1,"(2*atanh((sin(x/2)*(b^2 - a^2)^(1/2))/(a*cos(x/2) + b*cos(x/2)))*(b^2 - a^2)^(1/2))/b^2 - sin(x)/b + (2*a*atan(sin(x/2)/cos(x/2)))/b^2","B"
27,1,12,12,0.043380,"\text{Not used}","int(sin(x)/(a + b*cos(x)),x)","-\frac{\ln\left(a+b\,\cos\left(x\right)\right)}{b}","Not used",1,"-log(a + b*cos(x))/b","B"
28,1,38,42,0.483467,"\text{Not used}","int(1/(a + b*cos(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}","Not used",1,"(2*atan((tan(x/2)*(2*a - 2*b))/(2*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2)","B"
29,1,52,53,0.212193,"\text{Not used}","int(1/(sin(x)*(a + b*cos(x))),x)","\frac{\ln\left(\cos\left(x\right)-1\right)}{2\,\left(a+b\right)}-\frac{\ln\left(\cos\left(x\right)+1\right)}{2\,\left(a-b\right)}+\frac{b\,\ln\left(a+b\,\cos\left(x\right)\right)}{a^2-b^2}","Not used",1,"log(cos(x) - 1)/(2*(a + b)) - log(cos(x) + 1)/(2*(a - b)) + (b*log(a + b*cos(x)))/(a^2 - b^2)","B"
30,1,86,67,0.472092,"\text{Not used}","int(1/(sin(x)^2*(a + b*cos(x))),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a-2\,b}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-b^2\right)}{{\left(a+b\right)}^{3/2}\,\sqrt{a-b}}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{a-b}{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(2\,a-2\,b\right)}","Not used",1,"tan(x/2)/(2*a - 2*b) - (2*b^2*atan((tan(x/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(1/2))))/((a + b)^(3/2)*(a - b)^(3/2)) - (a - b)/(tan(x/2)*(a + b)*(2*a - 2*b))","B"
31,1,112,92,0.507701,"\text{Not used}","int(1/(sin(x)^3*(a + b*cos(x))),x)","\ln\left(\cos\left(x\right)-1\right)\,\left(\frac{b}{4\,{\left(a+b\right)}^2}+\frac{1}{4\,\left(a+b\right)}\right)+\frac{\frac{b}{2\,\left(a^2-b^2\right)}-\frac{a\,\cos\left(x\right)}{2\,\left(a^2-b^2\right)}}{{\sin\left(x\right)}^2}-\frac{b^3\,\ln\left(a+b\,\cos\left(x\right)\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{\ln\left(\cos\left(x\right)+1\right)\,\left(a-2\,b\right)}{4\,{\left(a-b\right)}^2}","Not used",1,"log(cos(x) - 1)*(b/(4*(a + b)^2) + 1/(4*(a + b))) + (b/(2*(a^2 - b^2)) - (a*cos(x))/(2*(a^2 - b^2)))/sin(x)^2 - (b^3*log(a + b*cos(x)))/(a^4 + b^4 - 2*a^2*b^2) - (log(cos(x) + 1)*(a - 2*b))/(4*(a - b)^2)","B"
32,1,184,110,0.558254,"\text{Not used}","int(1/(sin(x)^4*(a + b*cos(x))),x)","\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{4}{8\,a-8\,b}-\frac{8\,a+8\,b}{{\left(8\,a-8\,b\right)}^2}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3\,\left(8\,a-8\,b\right)}-\frac{\frac{a^2-2\,a\,b+b^2}{3\,\left(a+b\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-3\,a^3+a^2\,b+7\,a\,b^2-5\,b^3\right)}{{\left(a+b\right)}^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(8\,a^2-16\,a\,b+8\,b^2\right)}+\frac{2\,b^4\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"tan(x/2)*(4/(8*a - 8*b) - (8*a + 8*b)/(8*a - 8*b)^2) + tan(x/2)^3/(3*(8*a - 8*b)) - ((a^2 - 2*a*b + b^2)/(3*(a + b)) - (tan(x/2)^2*(7*a*b^2 + a^2*b - 3*a^3 - 5*b^3))/(a + b)^2)/(tan(x/2)^3*(8*a^2 - 16*a*b + 8*b^2)) + (2*b^4*atan((tan(x/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(3/2))))/((a + b)^(5/2)*(a - b)^(5/2))","B"
33,0,-1,129,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x)),x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x)), x)","F"
34,0,-1,100,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x)),x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x)), x)","F"
35,0,-1,100,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x)),x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x)), x)","F"
36,1,60,68,0.493993,"\text{Not used}","int((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x)),x)","\frac{2\,b\,\sin\left(c+d\,x\right)\,\sqrt{e\,\sin\left(c+d\,x\right)}}{3\,d}+\frac{2\,a\,\sqrt{e\,\sin\left(c+d\,x\right)}\,\mathrm{E}\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\middle|2\right)}{d\,\sqrt{\sin\left(c+d\,x\right)}}","Not used",1,"(2*b*sin(c + d*x)*(e*sin(c + d*x))^(1/2))/(3*d) + (2*a*(e*sin(c + d*x))^(1/2)*ellipticE(c/2 - pi/4 + (d*x)/2, 2))/(d*sin(c + d*x)^(1/2))","B"
37,1,50,66,0.724067,"\text{Not used}","int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(1/2),x)","-\frac{2\,\sqrt{\sin\left(c+d\,x\right)}\,\left(a\,\mathrm{F}\left(\frac{\pi }{4}-\frac{c}{2}-\frac{d\,x}{2}\middle|2\right)-b\,\sqrt{\sin\left(c+d\,x\right)}\right)}{d\,\sqrt{e\,\sin\left(c+d\,x\right)}}","Not used",1,"-(2*sin(c + d*x)^(1/2)*(a*ellipticF(pi/4 - c/2 - (d*x)/2, 2) - b*sin(c + d*x)^(1/2)))/(d*(e*sin(c + d*x))^(1/2))","B"
38,0,-1,96,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(3/2),x)","\int \frac{a+b\,\cos\left(c+d\,x\right)}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(3/2), x)","F"
39,0,-1,102,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(5/2),x)","\int \frac{a+b\,\cos\left(c+d\,x\right)}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(5/2), x)","F"
40,0,-1,131,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(7/2),x)","\int \frac{a+b\,\cos\left(c+d\,x\right)}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))/(e*sin(c + d*x))^(7/2), x)","F"
41,0,-1,193,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2, x)","F"
42,0,-1,154,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2, x)","F"
43,0,-1,154,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2, x)","F"
44,0,-1,114,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2,x)","\int \sqrt{e\,\sin\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2, x)","F"
45,0,-1,114,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{\sqrt{e\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(1/2), x)","F"
46,0,-1,118,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(3/2), x)","F"
47,0,-1,124,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(5/2), x)","F"
48,0,-1,165,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(7/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(e*sin(c + d*x))^(7/2), x)","F"
49,0,-1,242,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3, x)","F"
50,0,-1,202,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3, x)","F"
51,0,-1,202,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3, x)","F"
52,0,-1,161,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3,x)","\int \sqrt{e\,\sin\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3, x)","F"
53,0,-1,157,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{\sqrt{e\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(1/2), x)","F"
54,0,-1,165,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(3/2), x)","F"
55,0,-1,169,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(5/2), x)","F"
56,0,-1,192,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(7/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(7/2), x)","F"
57,0,-1,193,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(9/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(e*sin(c + d*x))^(9/2), x)","F"
58,0,-1,544,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(11/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{11/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*sin(c + d*x))^(11/2)/(a + b*cos(c + d*x)), x)","F"
59,0,-1,461,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(9/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{9/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*sin(c + d*x))^(9/2)/(a + b*cos(c + d*x)), x)","F"
60,0,-1,474,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*sin(c + d*x))^(7/2)/(a + b*cos(c + d*x)), x)","F"
61,0,-1,399,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*sin(c + d*x))^(5/2)/(a + b*cos(c + d*x)), x)","F"
62,0,-1,410,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*sin(c + d*x))^(3/2)/(a + b*cos(c + d*x)), x)","F"
63,0,-1,302,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{e\,\sin\left(c+d\,x\right)}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)/(a + b*cos(c + d*x)), x)","F"
64,0,-1,307,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{\sqrt{e\,\sin\left(c+d\,x\right)}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))), x)","F"
65,0,-1,426,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))), x)","F"
66,0,-1,447,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))), x)","F"
67,0,-1,501,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))), x)","F"
68,0,-1,557,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(11/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*sin(c + d*x))^(11/2)/(a + b*cos(c + d*x))^2, x)","F"
69,0,-1,473,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(9/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*sin(c + d*x))^(9/2)/(a + b*cos(c + d*x))^2, x)","F"
70,0,-1,487,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*sin(c + d*x))^(7/2)/(a + b*cos(c + d*x))^2, x)","F"
71,0,-1,404,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*sin(c + d*x))^(5/2)/(a + b*cos(c + d*x))^2, x)","F"
72,0,-1,418,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*sin(c + d*x))^(3/2)/(a + b*cos(c + d*x))^2, x)","F"
73,0,-1,438,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{e\,\sin\left(c+d\,x\right)}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)/(a + b*cos(c + d*x))^2, x)","F"
74,0,-1,445,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{\sqrt{e\,\sin\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
75,0,-1,507,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
76,0,-1,530,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
77,0,-1,590,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2), x)","F"
78,0,-1,590,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(13/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{13/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(13/2)/(a + b*cos(c + d*x))^3, x)","F"
79,0,-1,604,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(11/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{11/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(11/2)/(a + b*cos(c + d*x))^3, x)","F"
80,0,-1,498,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(9/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{9/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(9/2)/(a + b*cos(c + d*x))^3, x)","F"
81,0,-1,512,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(7/2)/(a + b*cos(c + d*x))^3, x)","F"
82,0,-1,520,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(5/2)/(a + b*cos(c + d*x))^3, x)","F"
83,0,-1,534,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(3/2)/(a + b*cos(c + d*x))^3, x)","F"
84,0,-1,529,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{\sqrt{e\,\sin\left(c+d\,x\right)}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)/(a + b*cos(c + d*x))^3, x)","F"
85,0,-1,535,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{\sqrt{e\,\sin\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
86,0,-1,611,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
87,0,-1,629,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
88,0,-1,700,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/((e*sin(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3), x)","F"