1,1,25,44,0.308386,"\text{Not used}","int(cos(x)^4/(a + a/sin(x)),x)","-\frac{3\,x+2\,\cos\left(3\,x\right)-\frac{3\,\sin\left(4\,x\right)}{4}+6\,\cos\left(x\right)}{24\,a}","Not used",1,"-(3*x + 2*cos(3*x) - (3*sin(4*x))/4 + 6*cos(x))/(24*a)","B"
2,1,15,23,0.043958,"\text{Not used}","int(cos(x)^3/(a + a/sin(x)),x)","-\frac{{\sin\left(x\right)}^2\,\left(2\,\sin\left(x\right)-3\right)}{6\,a}","Not used",1,"-(sin(x)^2*(2*sin(x) - 3))/(6*a)","B"
3,1,17,27,0.235241,"\text{Not used}","int(cos(x)^2/(a + a/sin(x)),x)","-\frac{\frac{x}{2}-\frac{\sin\left(2\,x\right)}{4}+\cos\left(x\right)}{a}","Not used",1,"-(x/2 - sin(2*x)/4 + cos(x))/a","B"
4,1,15,17,0.066099,"\text{Not used}","int(cos(x)/(a + a/sin(x)),x)","-\frac{\ln\left(\sin\left(x\right)+1\right)-\sin\left(x\right)}{a}","Not used",1,"-(log(sin(x) + 1) - sin(x))/a","B"
5,1,20,33,0.206873,"\text{Not used}","int(1/(cos(x)*(a + a/sin(x))),x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{2\,a}+\frac{1}{2\,a\,\left(\sin\left(x\right)+1\right)}","Not used",1,"atanh(sin(x))/(2*a) + 1/(2*a*(sin(x) + 1))","B"
6,1,37,23,0.267255,"\text{Not used}","int(1/(cos(x)^2*(a + a/sin(x))),x)","-\frac{2\,\left(3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{3\,a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}","Not used",1,"-(2*(2*tan(x/2) + 3*tan(x/2)^2 + 1))/(3*a*(tan(x/2) - 1)*(tan(x/2) + 1)^3)","B"
7,1,44,46,0.218222,"\text{Not used}","int(1/(cos(x)^3*(a + a/sin(x))),x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{8\,a}+\frac{\frac{{\sin\left(x\right)}^2}{8}+\frac{\sin\left(x\right)}{8}+\frac{1}{4}}{-a\,{\sin\left(x\right)}^3-a\,{\sin\left(x\right)}^2+a\,\sin\left(x\right)+a}","Not used",1,"atanh(sin(x))/(8*a) + (sin(x)/8 + sin(x)^2/8 + 1/4)/(a - a*sin(x)^2 - a*sin(x)^3 + a*sin(x))","B"
8,1,69,34,0.303613,"\text{Not used}","int(1/(cos(x)^4*(a + a/sin(x))),x)","-\frac{2\,\left(15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+9\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+6\,\mathrm{tan}\left(\frac{x}{2}\right)+3\right)}{15\,a\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"-(2*(6*tan(x/2) + 9*tan(x/2)^2 - 8*tan(x/2)^3 + 5*tan(x/2)^4 + 10*tan(x/2)^5 + 15*tan(x/2)^6 + 3))/(15*a*(tan(x/2) - 1)^3*(tan(x/2) + 1)^5)","B"
9,1,2055,130,1.066143,"\text{Not used}","int(cos(x)^4/(a + b/sin(x)),x)","\frac{2\,b\,\mathrm{atanh}\left(\frac{18\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{26\,b^5-9\,a^2\,b^3-\frac{25\,b^7}{a^2}+\frac{8\,b^9}{a^4}-18\,a^3\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{50\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{16\,b^8\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^3}+52\,a\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{8\,b^5\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{16\,b^8\,\mathrm{tan}\left(\frac{x}{2}\right)-25\,a\,b^7+26\,a^3\,b^5-9\,a^5\,b^3+\frac{8\,b^9}{a}-50\,a^2\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)+52\,a^4\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)-18\,a^6\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{9\,b^3\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{50\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)-26\,a\,b^5+9\,a^3\,b^3+\frac{25\,b^7}{a}-\frac{8\,b^9}{a^3}-52\,a^2\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+18\,a^4\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{16\,b^8\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}}+\frac{25\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{25\,b^7-26\,a^2\,b^5+9\,a^4\,b^3-\frac{8\,b^9}{a^2}-52\,a^3\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+18\,a^5\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{16\,b^8\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+50\,a\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}+\frac{8\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{-18\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^7\,b^2-9\,a^6\,b^3+52\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^5\,b^4+26\,a^4\,b^5-50\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,b^6-25\,a^2\,b^7+16\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^8+8\,b^9}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^5}-\frac{\frac{2\,\left(4\,a^2\,b-3\,b^3\right)}{3\,a^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(5\,a^2-4\,b^2\right)}{4\,a^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(3\,a^2+4\,b^2\right)}{4\,a^3}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(3\,a^2+4\,b^2\right)}{4\,a^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(5\,a^2-4\,b^2\right)}{4\,a^3}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(2\,a^2\,b-b^3\right)}{a^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(4\,a^2\,b-3\,b^3\right)}{a^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(10\,a^2\,b-9\,b^3\right)}{3\,a^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{9\,a^{12}\,b^2}{2}-36\,a^{10}\,b^4+96\,a^8\,b^6-96\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}-\frac{\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(\frac{12\,a^{14}\,b-28\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}-\frac{\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{14}\,b^2-256\,a^{12}\,b^4+128\,a^{10}\,b^6\right)}{2\,a^{12}}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b-217\,a^{12}\,b^3+712\,a^{10}\,b^5-960\,a^8\,b^7+576\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^5}+\frac{\left(\frac{\frac{9\,a^{12}\,b^2}{2}-36\,a^{10}\,b^4+96\,a^8\,b^6-96\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}+\frac{\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(\frac{12\,a^{14}\,b-28\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}+\frac{\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{14}\,b^2-256\,a^{12}\,b^4+128\,a^{10}\,b^6\right)}{2\,a^{12}}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b-217\,a^{12}\,b^3+712\,a^{10}\,b^5-960\,a^8\,b^7+576\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^5}}{\frac{-15\,a^{10}\,b^3+102\,a^8\,b^5-247\,a^6\,b^7+280\,a^4\,b^9-152\,a^2\,b^{11}+32\,b^{13}}{a^{11}}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{12}\,b^2-180\,a^{10}\,b^4+690\,a^8\,b^6-1296\,a^6\,b^8+1280\,a^4\,b^{10}-640\,a^2\,b^{12}+128\,b^{14}\right)}{a^{12}}-\frac{\left(\frac{\frac{9\,a^{12}\,b^2}{2}-36\,a^{10}\,b^4+96\,a^8\,b^6-96\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}-\frac{\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(\frac{12\,a^{14}\,b-28\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}-\frac{\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{14}\,b^2-256\,a^{12}\,b^4+128\,a^{10}\,b^6\right)}{2\,a^{12}}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b-217\,a^{12}\,b^3+712\,a^{10}\,b^5-960\,a^8\,b^7+576\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\left(\frac{\frac{9\,a^{12}\,b^2}{2}-36\,a^{10}\,b^4+96\,a^8\,b^6-96\,a^6\,b^8+32\,a^4\,b^{10}}{a^{11}}+\frac{\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(\frac{12\,a^{14}\,b-28\,a^{12}\,b^3+16\,a^{10}\,b^5}{a^{11}}+\frac{\left(32\,a^3\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(192\,a^{16}\,b-128\,a^{14}\,b^3\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{14}\,b^2-256\,a^{12}\,b^4+128\,a^{10}\,b^6\right)}{2\,a^{12}}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(18\,a^{14}\,b-217\,a^{12}\,b^3+712\,a^{10}\,b^5-960\,a^8\,b^7+576\,a^6\,b^9-128\,a^4\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,12{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,a^5}","Not used",1,"(atan(((((32*a^4*b^10 - 96*a^6*b^8 + 96*a^8*b^6 - 36*a^10*b^4 + (9*a^12*b^2)/2)/a^11 - ((a^4*3i + b^4*8i - a^2*b^2*12i)*((12*a^14*b + 16*a^10*b^5 - 28*a^12*b^3)/a^11 - ((32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i))/(8*a^5) + (tan(x/2)*(128*a^10*b^6 - 256*a^12*b^4 + 128*a^14*b^2))/(2*a^12)))/(8*a^5) + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 576*a^6*b^9 - 960*a^8*b^7 + 712*a^10*b^5 - 217*a^12*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i)*1i)/(8*a^5) + (((32*a^4*b^10 - 96*a^6*b^8 + 96*a^8*b^6 - 36*a^10*b^4 + (9*a^12*b^2)/2)/a^11 + ((a^4*3i + b^4*8i - a^2*b^2*12i)*((12*a^14*b + 16*a^10*b^5 - 28*a^12*b^3)/a^11 + ((32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i))/(8*a^5) + (tan(x/2)*(128*a^10*b^6 - 256*a^12*b^4 + 128*a^14*b^2))/(2*a^12)))/(8*a^5) + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 576*a^6*b^9 - 960*a^8*b^7 + 712*a^10*b^5 - 217*a^12*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i)*1i)/(8*a^5))/((32*b^13 - 152*a^2*b^11 + 280*a^4*b^9 - 247*a^6*b^7 + 102*a^8*b^5 - 15*a^10*b^3)/a^11 + (tan(x/2)*(128*b^14 - 640*a^2*b^12 + 1280*a^4*b^10 - 1296*a^6*b^8 + 690*a^8*b^6 - 180*a^10*b^4 + 18*a^12*b^2))/a^12 - (((32*a^4*b^10 - 96*a^6*b^8 + 96*a^8*b^6 - 36*a^10*b^4 + (9*a^12*b^2)/2)/a^11 - ((a^4*3i + b^4*8i - a^2*b^2*12i)*((12*a^14*b + 16*a^10*b^5 - 28*a^12*b^3)/a^11 - ((32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i))/(8*a^5) + (tan(x/2)*(128*a^10*b^6 - 256*a^12*b^4 + 128*a^14*b^2))/(2*a^12)))/(8*a^5) + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 576*a^6*b^9 - 960*a^8*b^7 + 712*a^10*b^5 - 217*a^12*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i))/(8*a^5) + (((32*a^4*b^10 - 96*a^6*b^8 + 96*a^8*b^6 - 36*a^10*b^4 + (9*a^12*b^2)/2)/a^11 + ((a^4*3i + b^4*8i - a^2*b^2*12i)*((12*a^14*b + 16*a^10*b^5 - 28*a^12*b^3)/a^11 + ((32*a^3*b^2 + (tan(x/2)*(192*a^16*b - 128*a^14*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i))/(8*a^5) + (tan(x/2)*(128*a^10*b^6 - 256*a^12*b^4 + 128*a^14*b^2))/(2*a^12)))/(8*a^5) + (tan(x/2)*(18*a^14*b - 128*a^4*b^11 + 576*a^6*b^9 - 960*a^8*b^7 + 712*a^10*b^5 - 217*a^12*b^3))/(2*a^12))*(a^4*3i + b^4*8i - a^2*b^2*12i))/(8*a^5)))*(a^4*3i + b^4*8i - a^2*b^2*12i)*1i)/(4*a^5) - ((2*(4*a^2*b - 3*b^3))/(3*a^4) - (tan(x/2)*(5*a^2 - 4*b^2))/(4*a^3) + (tan(x/2)^3*(3*a^2 + 4*b^2))/(4*a^3) - (tan(x/2)^5*(3*a^2 + 4*b^2))/(4*a^3) + (tan(x/2)^7*(5*a^2 - 4*b^2))/(4*a^3) + (2*tan(x/2)^6*(2*a^2*b - b^3))/a^4 + (2*tan(x/2)^4*(4*a^2*b - 3*b^3))/a^4 + (2*tan(x/2)^2*(10*a^2*b - 9*b^3))/(3*a^4))/(4*tan(x/2)^2 + 6*tan(x/2)^4 + 4*tan(x/2)^6 + tan(x/2)^8 + 1) + (2*b*atanh((18*b^2*tan(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(26*b^5 - 9*a^2*b^3 - (25*b^7)/a^2 + (8*b^9)/a^4 - 18*a^3*b^2*tan(x/2) - (50*b^6*tan(x/2))/a + (16*b^8*tan(x/2))/a^3 + 52*a*b^4*tan(x/2)) - (8*b^5*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(16*b^8*tan(x/2) - 25*a*b^7 + 26*a^3*b^5 - 9*a^5*b^3 + (8*b^9)/a - 50*a^2*b^6*tan(x/2) + 52*a^4*b^4*tan(x/2) - 18*a^6*b^2*tan(x/2)) - (9*b^3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(50*b^6*tan(x/2) - 26*a*b^5 + 9*a^3*b^3 + (25*b^7)/a - (8*b^9)/a^3 - 52*a^2*b^4*tan(x/2) + 18*a^4*b^2*tan(x/2) - (16*b^8*tan(x/2))/a^2) + (25*b^4*tan(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(25*b^7 - 26*a^2*b^5 + 9*a^4*b^3 - (8*b^9)/a^2 - 52*a^3*b^4*tan(x/2) + 18*a^5*b^2*tan(x/2) - (16*b^8*tan(x/2))/a + 50*a*b^6*tan(x/2)) + (8*b^6*tan(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(8*b^9 - 25*a^2*b^7 + 26*a^4*b^5 - 9*a^6*b^3 - 50*a^3*b^6*tan(x/2) + 52*a^5*b^4*tan(x/2) - 18*a^7*b^2*tan(x/2) + 16*a*b^8*tan(x/2)))*((a + b)^3*(a - b)^3)^(1/2))/a^5","B"
10,1,58,61,0.084346,"\text{Not used}","int(cos(x)^3/(a + b/sin(x)),x)","\sin\left(x\right)\,\left(\frac{1}{a}-\frac{b^2}{a^3}\right)-\frac{{\sin\left(x\right)}^3}{3\,a}+\frac{b\,{\sin\left(x\right)}^2}{2\,a^2}-\frac{\ln\left(b+a\,\sin\left(x\right)\right)\,\left(a^2\,b-b^3\right)}{a^4}","Not used",1,"sin(x)*(1/a - b^2/a^3) - sin(x)^3/(3*a) + (b*sin(x)^2)/(2*a^2) - (log(b + a*sin(x))*(a^2*b - b^3))/a^4","B"
11,1,362,80,0.539809,"\text{Not used}","int(cos(x)^2/(a + b/sin(x)),x)","-\frac{\frac{2\,b}{a^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{2\,b\,\mathrm{atanh}\left(\frac{32\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}}{16\,b^3-\frac{16\,b^5}{a^2}-\frac{32\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+32\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{16\,b^3\,\sqrt{a^2-b^2}}{32\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)-16\,a\,b^3+\frac{16\,b^5}{a}-32\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}+\frac{16\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}}{-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,b^2-16\,a^2\,b^3+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^4+16\,b^5}\right)\,\sqrt{a^2-b^2}}{a^3}-\frac{\mathrm{atan}\left(\frac{16\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^4\,b-24\,a^2\,b^3+16\,b^5}-\frac{24\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a^2\,b-24\,b^3+\frac{16\,b^5}{a^2}}+\frac{8\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a\,b-\frac{24\,b^3}{a}+\frac{16\,b^5}{a^3}}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^3}","Not used",1,"- ((2*b)/a^2 - tan(x/2)/a + tan(x/2)^3/a + (2*b*tan(x/2)^2)/a^2)/(2*tan(x/2)^2 + tan(x/2)^4 + 1) - (atan((16*b^5*tan(x/2))/(8*a^4*b + 16*b^5 - 24*a^2*b^3) - (24*b^3*tan(x/2))/(8*a^2*b - 24*b^3 + (16*b^5)/a^2) + (8*a*b*tan(x/2))/(8*a*b - (24*b^3)/a + (16*b^5)/a^3))*(a^2*1i - b^2*2i)*1i)/a^3 - (2*b*atanh((32*b^2*tan(x/2)*(a^2 - b^2)^(1/2))/(16*b^3 - (16*b^5)/a^2 - (32*b^4*tan(x/2))/a + 32*a*b^2*tan(x/2)) - (16*b^3*(a^2 - b^2)^(1/2))/(32*b^4*tan(x/2) - 16*a*b^3 + (16*b^5)/a - 32*a^2*b^2*tan(x/2)) + (16*b^4*tan(x/2)*(a^2 - b^2)^(1/2))/(16*b^5 - 16*a^2*b^3 - 32*a^3*b^2*tan(x/2) + 32*a*b^4*tan(x/2)))*(a^2 - b^2)^(1/2))/a^3","B"
12,1,20,20,0.067313,"\text{Not used}","int(cos(x)/(a + b/sin(x)),x)","-\frac{b\,\ln\left(b+a\,\sin\left(x\right)\right)-a\,\sin\left(x\right)}{a^2}","Not used",1,"-(b*log(b + a*sin(x)) - a*sin(x))/a^2","B"
13,1,53,54,0.185375,"\text{Not used}","int(1/(cos(x)*(a + b/sin(x))),x)","\frac{\ln\left(\sin\left(x\right)+1\right)}{2\,\left(a-b\right)}-\frac{\ln\left(\sin\left(x\right)-1\right)}{2\,\left(a+b\right)}-\frac{b\,\ln\left(b+a\,\sin\left(x\right)\right)}{a^2-b^2}","Not used",1,"log(sin(x) + 1)/(2*(a - b)) - log(sin(x) - 1)/(2*(a + b)) - (b*log(b + a*sin(x)))/(a^2 - b^2)","B"
14,1,104,65,0.403255,"\text{Not used}","int(1/(cos(x)^2*(a + b/sin(x))),x)","\frac{\frac{2\,b}{a^2-b^2}-\frac{2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2-b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-1}+\frac{2\,a\,b\,\mathrm{atanh}\left(\frac{2\,a^3-2\,a\,b^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-b^2\right)}{2\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"((2*b)/(a^2 - b^2) - (2*a*tan(x/2))/(a^2 - b^2))/(tan(x/2)^2 - 1) + (2*a*b*atanh((2*a^3 - 2*a*b^2 + 2*b*tan(x/2)*(a^2 - b^2))/(2*(a + b)^(3/2)*(a - b)^(3/2))))/((a + b)^(3/2)*(a - b)^(3/2))","B"
15,1,96,85,0.376258,"\text{Not used}","int(1/(cos(x)^3*(a + b/sin(x))),x)","\ln\left(b+a\,\sin\left(x\right)\right)\,\left(\frac{a}{4\,{\left(a+b\right)}^2}-\frac{a}{4\,{\left(a-b\right)}^2}\right)-\frac{\frac{b}{2\,\left(a^2-b^2\right)}-\frac{a\,\sin\left(x\right)}{2\,\left(a^2-b^2\right)}}{{\cos\left(x\right)}^2}+\frac{a\,\ln\left(\sin\left(x\right)+1\right)}{4\,{\left(a-b\right)}^2}-\frac{a\,\ln\left(\sin\left(x\right)-1\right)}{4\,{\left(a+b\right)}^2}","Not used",1,"log(b + a*sin(x))*(a/(4*(a + b)^2) - a/(4*(a - b)^2)) - (b/(2*(a^2 - b^2)) - (a*sin(x))/(2*(a^2 - b^2)))/cos(x)^2 + (a*log(sin(x) + 1))/(4*(a - b)^2) - (a*log(sin(x) - 1))/(4*(a + b)^2)","B"
16,1,298,109,0.650904,"\text{Not used}","int(1/(cos(x)^4*(a + b/sin(x))),x)","\frac{\frac{2\,\left(4\,a^2\,b-b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(2\,a^2\,b-b^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^4-2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\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\,a^3\,b\,\mathrm{atanh}\left(\frac{2\,a\,b^4+2\,a^5-4\,a^3\,b^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{2\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*(4*a^2*b - b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*tan(x/2)^4*(2*a^2*b - b^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*a^3*tan(x/2))/(a^4 + b^4 - 2*a^2*b^2) - (2*a^3*tan(x/2)^5)/(a^4 + b^4 - 2*a^2*b^2) - (4*a^2*b*tan(x/2)^2)/(a^4 + b^4 - 2*a^2*b^2) + (4*a*tan(x/2)^3*(a^2 + 2*b^2))/(3*(a^4 + b^4 - 2*a^2*b^2)))/(3*tan(x/2)^2 - 3*tan(x/2)^4 + tan(x/2)^6 - 1) + (2*a^3*b*atanh((2*a*b^4 + 2*a^5 - 4*a^3*b^2 + 2*b*tan(x/2)*(a^4 + b^4 - 2*a^2*b^2))/(2*(a + b)^(5/2)*(a - b)^(5/2))))/((a + b)^(5/2)*(a - b)^(5/2))","B"