1,1,1779,54,18.464227,"\text{Not used}","int((A + B*cos(x))/(a + b*sin(x)),x)","\frac{\ln\left(\frac{a+b\,\sin\left(x\right)}{\cos\left(x\right)+1}\right)\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{2\,\left(b^4-a^2\,b^2\right)}-\frac{2\,A\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(\frac{\left(\frac{\left(\frac{A\,\left(\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,A\,a\,b^3+32\,B\,a\,b^3\right)}{\sqrt{a^2-b^2}}+\frac{A\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{2\,\left(b^4-a^2\,b^2\right)}-\frac{A^3\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{{\left(a^2-b^2\right)}^{3/2}}+\frac{A\,\left(64\,B^2\,a^3-32\,A^2\,a\,b^2-96\,B^2\,a\,b^2+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,A\,a\,b^3+32\,B\,a\,b^3\right)}{2\,\left(b^4-a^2\,b^2\right)}+128\,A\,B\,a\,b^2\right)}{\sqrt{a^2-b^2}}\right)\,\left(-A^2\,a^2\,b^2+2\,A^2\,b^4-8\,A\,B\,a^2\,b^2+8\,A\,B\,b^4+4\,B^2\,a^4-12\,B^2\,a^2\,b^2+8\,B^2\,b^4\right)}{a^3\,\sqrt{a^2-b^2}\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}-\frac{2\,b\,\left(A+2\,B\right)\,\left(A\,b^2-2\,B\,a^2+2\,B\,b^2\right)\,\left(\frac{A\,\left(\frac{A\,\left(\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,A\,a\,b^3+32\,B\,a\,b^3\right)}{\sqrt{a^2-b^2}}+\frac{A\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+32\,B^3\,a\,b-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,B^2\,a^3-32\,A^2\,a\,b^2-96\,B^2\,a\,b^2+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,A\,a\,b^3+32\,B\,a\,b^3\right)}{2\,\left(b^4-a^2\,b^2\right)}+128\,A\,B\,a\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,A\,B^2\,a\,b+32\,A^2\,B\,a\,b+\frac{A^2\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{a^3\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}\right)}{32\,A\,a}+\frac{\left(a^2-b^2\right)\,\left(\frac{A\,\left(\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(32\,A\,a^2\,b^2+32\,B\,a^2\,b^2+\frac{16\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{b^4-a^2\,b^2}\right)}{2\,\left(b^4-a^2\,b^2\right)}-32\,B^2\,a^2\,b+64\,A\,B\,a^2\,b\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(\frac{A\,\left(32\,A\,a^2\,b^2+32\,B\,a^2\,b^2+\frac{16\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{b^4-a^2\,b^2}\right)}{\sqrt{a^2-b^2}}+\frac{16\,A\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{2\,\left(b^4-a^2\,b^2\right)}-\frac{32\,A^3\,a^2\,b^3}{{\left(a^2-b^2\right)}^{3/2}}\right)\,\left(-A^2\,a^2\,b^2+2\,A^2\,b^4-8\,A\,B\,a^2\,b^2+8\,A\,B\,b^4+4\,B^2\,a^4-12\,B^2\,a^2\,b^2+8\,B^2\,b^4\right)}{32\,A\,a^4\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}-\frac{b\,{\left(a^2-b^2\right)}^{3/2}\,\left(A+2\,B\right)\,\left(A\,b^2-2\,B\,a^2+2\,B\,b^2\right)\,\left(32\,B^3\,a^2-32\,A\,B^2\,a^2-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(32\,A\,a^2\,b^2+32\,B\,a^2\,b^2+\frac{16\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{b^4-a^2\,b^2}\right)}{2\,\left(b^4-a^2\,b^2\right)}-32\,B^2\,a^2\,b+64\,A\,B\,a^2\,b\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{A\,\left(\frac{A\,\left(32\,A\,a^2\,b^2+32\,B\,a^2\,b^2+\frac{16\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{b^4-a^2\,b^2}\right)}{\sqrt{a^2-b^2}}+\frac{16\,A\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{16\,A^2\,a^2\,b^3\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)}{\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{16\,A\,a^4\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}\right)}{\sqrt{a^2-b^2}}-\frac{B\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{b}","Not used",1,"(log((a + b*sin(x))/(cos(x) + 1))*(2*B*b^3 - 2*B*a^2*b))/(2*(b^4 - a^2*b^2)) - (2*A*atan((tan(x/2)*(a^2 - b^2)^(3/2)*((((((A*(((2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*A*a*b^3 + 32*B*a*b^3))/(a^2 - b^2)^(1/2) + (A*(2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2)))*(2*B*b^3 - 2*B*a^2*b))/(2*(b^4 - a^2*b^2)) - (A^3*(96*a*b^4 - 64*a^3*b^2))/(a^2 - b^2)^(3/2) + (A*(64*B^2*a^3 - 32*A^2*a*b^2 - 96*B^2*a*b^2 + ((2*B*b^3 - 2*B*a^2*b)*(((2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*A*a*b^3 + 32*B*a*b^3))/(2*(b^4 - a^2*b^2)) + 128*A*B*a*b^2))/(a^2 - b^2)^(1/2))*(2*A^2*b^4 + 4*B^2*a^4 + 8*B^2*b^4 - A^2*a^2*b^2 - 12*B^2*a^2*b^2 + 8*A*B*b^4 - 8*A*B*a^2*b^2))/(a^3*(a^2 - b^2)^(1/2)*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2) - (2*b*(A + 2*B)*(A*b^2 - 2*B*a^2 + 2*B*b^2)*((A*((A*(((2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*A*a*b^3 + 32*B*a*b^3))/(a^2 - b^2)^(1/2) + (A*(2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) + 32*B^3*a*b - ((2*B*b^3 - 2*B*a^2*b)*(64*B^2*a^3 - 32*A^2*a*b^2 - 96*B^2*a*b^2 + ((2*B*b^3 - 2*B*a^2*b)*(((2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*A*a*b^3 + 32*B*a*b^3))/(2*(b^4 - a^2*b^2)) + 128*A*B*a*b^2))/(2*(b^4 - a^2*b^2)) - 64*A*B^2*a*b + 32*A^2*B*a*b + (A^2*(2*B*b^3 - 2*B*a^2*b)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2))))/(a^3*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2)))/(32*A*a) + ((a^2 - b^2)*((A*(((2*B*b^3 - 2*B*a^2*b)*(32*A*a^2*b^2 + 32*B*a^2*b^2 + (16*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/(b^4 - a^2*b^2)))/(2*(b^4 - a^2*b^2)) - 32*B^2*a^2*b + 64*A*B*a^2*b))/(a^2 - b^2)^(1/2) + ((2*B*b^3 - 2*B*a^2*b)*((A*(32*A*a^2*b^2 + 32*B*a^2*b^2 + (16*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/(b^4 - a^2*b^2)))/(a^2 - b^2)^(1/2) + (16*A*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/((b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(2*(b^4 - a^2*b^2)) - (32*A^3*a^2*b^3)/(a^2 - b^2)^(3/2))*(2*A^2*b^4 + 4*B^2*a^4 + 8*B^2*b^4 - A^2*a^2*b^2 - 12*B^2*a^2*b^2 + 8*A*B*b^4 - 8*A*B*a^2*b^2))/(32*A*a^4*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2) - (b*(a^2 - b^2)^(3/2)*(A + 2*B)*(A*b^2 - 2*B*a^2 + 2*B*b^2)*(32*B^3*a^2 - 32*A*B^2*a^2 - ((2*B*b^3 - 2*B*a^2*b)*(((2*B*b^3 - 2*B*a^2*b)*(32*A*a^2*b^2 + 32*B*a^2*b^2 + (16*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/(b^4 - a^2*b^2)))/(2*(b^4 - a^2*b^2)) - 32*B^2*a^2*b + 64*A*B*a^2*b))/(2*(b^4 - a^2*b^2)) + (A*((A*(32*A*a^2*b^2 + 32*B*a^2*b^2 + (16*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/(b^4 - a^2*b^2)))/(a^2 - b^2)^(1/2) + (16*A*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/((b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) + (16*A^2*a^2*b^3*(2*B*b^3 - 2*B*a^2*b))/((b^4 - a^2*b^2)*(a^2 - b^2))))/(16*A*a^4*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2)))/(a^2 - b^2)^(1/2) - (B*log(1/(cos(x) + 1)))/b","B"
2,1,34,19,15.153076,"\text{Not used}","int((A + B*cos(x))/(sin(x) + 1),x)","2\,B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)-\frac{2\,A}{\mathrm{tan}\left(\frac{x}{2}\right)+1}-B\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"2*B*log(tan(x/2) + 1) - (2*A)/(tan(x/2) + 1) - B*log(tan(x/2)^2 + 1)","B"
3,1,33,23,15.314516,"\text{Not used}","int(-(A + B*cos(x))/(sin(x) - 1),x)","B\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\frac{2\,A}{\mathrm{tan}\left(\frac{x}{2}\right)-1}-2\,B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)","Not used",1,"B*log(tan(x/2)^2 + 1) - (2*A)/(tan(x/2) - 1) - 2*B*log(tan(x/2) - 1)","B"
4,1,1955,55,24.220554,"\text{Not used}","int((b + c + cos(x))/(a + b*sin(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{{\left(b+c\right)}^3\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{{\left(a^2-b^2\right)}^{3/2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{\left(b+c\right)\,\left(96\,a\,b^2-128\,a\,b^3+32\,a\,b^4-64\,a^3+32\,a\,b^2\,c^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,a\,b^2\,c+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}\right)\,\left(4\,a^4-a^2\,b^4-2\,a^2\,b^3\,c-8\,a^2\,b^3-a^2\,b^2\,c^2-8\,a^2\,b^2\,c-12\,a^2\,b^2+2\,b^6+4\,b^5\,c+8\,b^5+2\,b^4\,c^2+8\,b^4\,c+8\,b^4\right)}{a^3\,\sqrt{a^2-b^2}\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}+\frac{2\,b\,\left(b+c+2\right)\,\left(b^2\,c-2\,a^2+2\,b^2+b^3\right)\,\left(32\,a\,b-64\,a\,b^2+32\,a\,b^3-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^2-128\,a\,b^3+32\,a\,b^4-64\,a^3+32\,a\,b^2\,c^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,a\,b^2\,c+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,a\,b\,c+\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+32\,a\,b\,c^2+64\,a\,b^2\,c-\frac{\left(2\,a^2\,b-2\,b^3\right)\,{\left(b+c\right)}^2\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{a^3\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}\right)\,{\left(a^2-b^2\right)}^{3/2}}{32\,a\,b+32\,a\,c}+\frac{\left(a^2-b^2\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a^2\,b-64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,a^2\,b\,c\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{\sqrt{a^2-b^2}}-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)}{\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{32\,a^2\,b^3\,{\left(b+c\right)}^3}{{\left(a^2-b^2\right)}^{3/2}}\right)\,\left(4\,a^4-a^2\,b^4-2\,a^2\,b^3\,c-8\,a^2\,b^3-a^2\,b^2\,c^2-8\,a^2\,b^2\,c-12\,a^2\,b^2+2\,b^6+4\,b^5\,c+8\,b^5+2\,b^4\,c^2+8\,b^4\,c+8\,b^4\right)}{a^3\,\left(32\,a\,b+32\,a\,c\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}-\frac{2\,b\,{\left(a^2-b^2\right)}^{3/2}\,\left(b+c+2\right)\,\left(b^2\,c-2\,a^2+2\,b^2+b^3\right)\,\left(32\,a^2\,b+32\,a^2\,c-32\,a^2-\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{\sqrt{a^2-b^2}}-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)}{\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b-64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,a^2\,b\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)\,{\left(b+c\right)}^2}{\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{a^3\,\left(32\,a\,b+32\,a\,c\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}\right)\,\left(b+c\right)}{\sqrt{a^2-b^2}}-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{b}-\frac{\ln\left(\frac{a+b\,\sin\left(x\right)}{\cos\left(x\right)+1}\right)\,\left(2\,a^2\,b-2\,b^3\right)}{2\,\left(b^4-a^2\,b^2\right)}","Not used",1,"(2*atan((tan(x/2)*(((((b + c)^3*(96*a*b^4 - 64*a^3*b^2))/(a^2 - b^2)^(3/2) + ((2*a^2*b - 2*b^3)*(((b + c)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(2*(b^4 - a^2*b^2)) + ((b + c)*(96*a*b^2 - 128*a*b^3 + 32*a*b^4 - 64*a^3 + 32*a*b^2*c^2 + ((2*a^2*b - 2*b^3)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 128*a*b^2*c + 64*a*b^3*c))/(a^2 - b^2)^(1/2))*(8*b^4*c + 4*b^5*c + 4*a^4 + 8*b^4 + 8*b^5 + 2*b^6 - 12*a^2*b^2 - 8*a^2*b^3 - a^2*b^4 + 2*b^4*c^2 - 8*a^2*b^2*c - 2*a^2*b^3*c - a^2*b^2*c^2))/(a^3*(a^2 - b^2)^(1/2)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) + (2*b*(b + c + 2)*(b^2*c - 2*a^2 + 2*b^2 + b^3)*(32*a*b - 64*a*b^2 + 32*a*b^3 - ((2*a^2*b - 2*b^3)*(96*a*b^2 - 128*a*b^3 + 32*a*b^4 - 64*a^3 + 32*a*b^2*c^2 + ((2*a^2*b - 2*b^3)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 128*a*b^2*c + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 64*a*b*c + ((b + c)*(((b + c)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) + 32*a*b*c^2 + 64*a*b^2*c - ((2*a^2*b - 2*b^3)*(b + c)^2*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2))))/(a^3*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2))*(a^2 - b^2)^(3/2))/(32*a*b + 32*a*c) + ((a^2 - b^2)*(((b + c)*(32*a^2*b - 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(2*(b^4 - a^2*b^2)) - 64*a^2*b*c))/(a^2 - b^2)^(1/2) + ((2*a^2*b - 2*b^3)*(((b + c)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(a^2 - b^2)^(1/2) - (16*a^2*b^3*(2*a^2*b - 2*b^3)*(b + c))/((b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(2*(b^4 - a^2*b^2)) + (32*a^2*b^3*(b + c)^3)/(a^2 - b^2)^(3/2))*(8*b^4*c + 4*b^5*c + 4*a^4 + 8*b^4 + 8*b^5 + 2*b^6 - 12*a^2*b^2 - 8*a^2*b^3 - a^2*b^4 + 2*b^4*c^2 - 8*a^2*b^2*c - 2*a^2*b^3*c - a^2*b^2*c^2))/(a^3*(32*a*b + 32*a*c)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) - (2*b*(a^2 - b^2)^(3/2)*(b + c + 2)*(b^2*c - 2*a^2 + 2*b^2 + b^3)*(32*a^2*b + 32*a^2*c - 32*a^2 - ((b + c)*(((b + c)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(a^2 - b^2)^(1/2) - (16*a^2*b^3*(2*a^2*b - 2*b^3)*(b + c))/((b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) + ((2*a^2*b - 2*b^3)*(32*a^2*b - 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(2*(b^4 - a^2*b^2)) - 64*a^2*b*c))/(2*(b^4 - a^2*b^2)) + (16*a^2*b^3*(2*a^2*b - 2*b^3)*(b + c)^2)/((b^4 - a^2*b^2)*(a^2 - b^2))))/(a^3*(32*a*b + 32*a*c)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2))*(b + c))/(a^2 - b^2)^(1/2) - log(tan(x/2)^2 + 1)/b - (log((a + b*sin(x))/(cos(x) + 1))*(2*a^2*b - 2*b^3))/(2*(b^4 - a^2*b^2))","B"
5,1,1955,58,24.705860,"\text{Not used}","int((b + c + cos(x))/(a - b*sin(x)),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{b}+\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{{\left(b+c\right)}^3\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{{\left(a^2-b^2\right)}^{3/2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{\left(b+c\right)\,\left(96\,a\,b^2-128\,a\,b^3+32\,a\,b^4-64\,a^3+32\,a\,b^2\,c^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,a\,b^2\,c+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}\right)\,\left(4\,a^4-a^2\,b^4-2\,a^2\,b^3\,c-8\,a^2\,b^3-a^2\,b^2\,c^2-8\,a^2\,b^2\,c-12\,a^2\,b^2+2\,b^6+4\,b^5\,c+8\,b^5+2\,b^4\,c^2+8\,b^4\,c+8\,b^4\right)}{a^3\,\sqrt{a^2-b^2}\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}+\frac{2\,b\,\left(b+c+2\right)\,\left(b^2\,c-2\,a^2+2\,b^2+b^3\right)\,\left(32\,a\,b-64\,a\,b^2+32\,a\,b^3-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^2-128\,a\,b^3+32\,a\,b^4-64\,a^3+32\,a\,b^2\,c^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,a\,b^2\,c+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,a\,b\,c+\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a\,b^3+64\,a\,b^4-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+32\,a\,b\,c^2+64\,a\,b^2\,c-\frac{\left(2\,a^2\,b-2\,b^3\right)\,{\left(b+c\right)}^2\,\left(96\,a\,b^4-64\,a^3\,b^2\right)}{2\,\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{a^3\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}\right)\,{\left(a^2-b^2\right)}^{3/2}}{32\,a\,b+32\,a\,c}-\frac{\left(a^2-b^2\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a^2\,b-64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,a^2\,b\,c\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{\sqrt{a^2-b^2}}-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)}{\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{32\,a^2\,b^3\,{\left(b+c\right)}^3}{{\left(a^2-b^2\right)}^{3/2}}\right)\,\left(4\,a^4-a^2\,b^4-2\,a^2\,b^3\,c-8\,a^2\,b^3-a^2\,b^2\,c^2-8\,a^2\,b^2\,c-12\,a^2\,b^2+2\,b^6+4\,b^5\,c+8\,b^5+2\,b^4\,c^2+8\,b^4\,c+8\,b^4\right)}{a^3\,\left(32\,a\,b+32\,a\,c\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}+\frac{2\,b\,{\left(a^2-b^2\right)}^{3/2}\,\left(b+c+2\right)\,\left(b^2\,c-2\,a^2+2\,b^2+b^3\right)\,\left(32\,a^2\,b+32\,a^2\,c-32\,a^2-\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{\sqrt{a^2-b^2}}-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)}{\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b-64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^2+32\,a^2\,b^3+32\,a^2\,b^2\,c-\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)}{b^4-a^2\,b^2}\right)}{2\,\left(b^4-a^2\,b^2\right)}-64\,a^2\,b\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}+\frac{16\,a^2\,b^3\,\left(2\,a^2\,b-2\,b^3\right)\,{\left(b+c\right)}^2}{\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{a^3\,\left(32\,a\,b+32\,a\,c\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}\right)\,\left(b+c\right)}{\sqrt{a^2-b^2}}+\frac{\ln\left(\frac{a-b\,\sin\left(x\right)}{\cos\left(x\right)+1}\right)\,\left(2\,a^2\,b-2\,b^3\right)}{2\,\left(b^4-a^2\,b^2\right)}","Not used",1,"log(tan(x/2)^2 + 1)/b + (2*atan((tan(x/2)*(((((b + c)^3*(96*a*b^4 - 64*a^3*b^2))/(a^2 - b^2)^(3/2) + ((2*a^2*b - 2*b^3)*(((b + c)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(2*(b^4 - a^2*b^2)) + ((b + c)*(96*a*b^2 - 128*a*b^3 + 32*a*b^4 - 64*a^3 + 32*a*b^2*c^2 + ((2*a^2*b - 2*b^3)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 128*a*b^2*c + 64*a*b^3*c))/(a^2 - b^2)^(1/2))*(8*b^4*c + 4*b^5*c + 4*a^4 + 8*b^4 + 8*b^5 + 2*b^6 - 12*a^2*b^2 - 8*a^2*b^3 - a^2*b^4 + 2*b^4*c^2 - 8*a^2*b^2*c - 2*a^2*b^3*c - a^2*b^2*c^2))/(a^3*(a^2 - b^2)^(1/2)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) + (2*b*(b + c + 2)*(b^2*c - 2*a^2 + 2*b^2 + b^3)*(32*a*b - 64*a*b^2 + 32*a*b^3 - ((2*a^2*b - 2*b^3)*(96*a*b^2 - 128*a*b^3 + 32*a*b^4 - 64*a^3 + 32*a*b^2*c^2 + ((2*a^2*b - 2*b^3)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 128*a*b^2*c + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 64*a*b*c + ((b + c)*(((b + c)*(32*a*b^3 + 64*a*b^4 - ((2*a^2*b - 2*b^3)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)) + 64*a*b^3*c))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) + 32*a*b*c^2 + 64*a*b^2*c - ((2*a^2*b - 2*b^3)*(b + c)^2*(96*a*b^4 - 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2))))/(a^3*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2))*(a^2 - b^2)^(3/2))/(32*a*b + 32*a*c) - ((a^2 - b^2)*(((b + c)*(32*a^2*b - 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(2*(b^4 - a^2*b^2)) - 64*a^2*b*c))/(a^2 - b^2)^(1/2) + ((2*a^2*b - 2*b^3)*(((b + c)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(a^2 - b^2)^(1/2) - (16*a^2*b^3*(2*a^2*b - 2*b^3)*(b + c))/((b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(2*(b^4 - a^2*b^2)) + (32*a^2*b^3*(b + c)^3)/(a^2 - b^2)^(3/2))*(8*b^4*c + 4*b^5*c + 4*a^4 + 8*b^4 + 8*b^5 + 2*b^6 - 12*a^2*b^2 - 8*a^2*b^3 - a^2*b^4 + 2*b^4*c^2 - 8*a^2*b^2*c - 2*a^2*b^3*c - a^2*b^2*c^2))/(a^3*(32*a*b + 32*a*c)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) + (2*b*(a^2 - b^2)^(3/2)*(b + c + 2)*(b^2*c - 2*a^2 + 2*b^2 + b^3)*(32*a^2*b + 32*a^2*c - 32*a^2 - ((b + c)*(((b + c)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(a^2 - b^2)^(1/2) - (16*a^2*b^3*(2*a^2*b - 2*b^3)*(b + c))/((b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) + ((2*a^2*b - 2*b^3)*(32*a^2*b - 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(32*a^2*b^2 + 32*a^2*b^3 + 32*a^2*b^2*c - (16*a^2*b^3*(2*a^2*b - 2*b^3))/(b^4 - a^2*b^2)))/(2*(b^4 - a^2*b^2)) - 64*a^2*b*c))/(2*(b^4 - a^2*b^2)) + (16*a^2*b^3*(2*a^2*b - 2*b^3)*(b + c)^2)/((b^4 - a^2*b^2)*(a^2 - b^2))))/(a^3*(32*a*b + 32*a*c)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2))*(b + c))/(a^2 - b^2)^(1/2) + (log((a - b*sin(x))/(cos(x) + 1))*(2*a^2*b - 2*b^3))/(2*(b^4 - a^2*b^2))","B"
6,1,752,97,20.113250,"\text{Not used}","int((A + B*tan(x))/(a + b*sin(x)),x)","\frac{\ln\left(-32\,A\,B^2\,a^2-\frac{\left(B\,a^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a\,b^2\right)\,\left(64\,A^2\,a^2\,b-32\,B^2\,a^2\,b-\frac{\left(B\,a^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a\,b^2\right)\,\left(32\,A\,a^2\,b^2-32\,A\,a^4+32\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,B\,a^3-2\,A\,a^2\,b+B\,a\,b^2+2\,A\,b^3\right)+32\,B\,a\,b^3+64\,B\,a^3\,b-\frac{96\,a\,b\,\left(a+b\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(B\,a^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a\,b^2\right)}{a^2-b^2}\right)}{{\left(a^2-b^2\right)}^2}+32\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,a^2+A^2\,b^2+4\,A\,B\,a\,b+2\,B^2\,b^2\right)+64\,A\,B\,a^3\right)}{{\left(a^2-b^2\right)}^2}-32\,A^2\,B\,a\,b-32\,B\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a\,A^2+2\,b\,A\,B+2\,a\,B^2\right)\right)\,\left(B\,a^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{\ln\left(\frac{\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^3+B\,a\,b^2\right)\,\left(64\,A^2\,a^2\,b-32\,B^2\,a^2\,b+\frac{\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^3+B\,a\,b^2\right)\,\left(32\,A\,a^2\,b^2-32\,A\,a^4+32\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,B\,a^3-2\,A\,a^2\,b+B\,a\,b^2+2\,A\,b^3\right)+32\,B\,a\,b^3+64\,B\,a^3\,b+\frac{96\,a\,b\,\left(a+b\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^3+B\,a\,b^2\right)}{a^2-b^2}\right)}{{\left(a^2-b^2\right)}^2}+32\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,a^2+A^2\,b^2+4\,A\,B\,a\,b+2\,B^2\,b^2\right)+64\,A\,B\,a^3\right)}{{\left(a^2-b^2\right)}^2}-32\,A\,B^2\,a^2-32\,A^2\,B\,a\,b-32\,B\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a\,A^2+2\,b\,A\,B+2\,a\,B^2\right)\right)\,\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^3+B\,a\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{a+b}-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{a-b}","Not used",1,"(log(- 32*A*B^2*a^2 - ((B*a^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a*b^2)*(64*A^2*a^2*b - 32*B^2*a^2*b - ((B*a^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a*b^2)*(32*A*a^2*b^2 - 32*A*a^4 + 32*a*tan(x/2)*(2*A*b^3 + 2*B*a^3 - 2*A*a^2*b + B*a*b^2) + 32*B*a*b^3 + 64*B*a^3*b - (96*a*b*(a + b*tan(x/2))*(B*a^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a*b^2))/(a^2 - b^2)))/(a^2 - b^2)^2 + 32*a*tan(x/2)*(A^2*a^2 + A^2*b^2 + 2*B^2*b^2 + 4*A*B*a*b) + 64*A*B*a^3))/(a^2 - b^2)^2 - 32*A^2*B*a*b - 32*B*a*tan(x/2)*(A^2*a + 2*B^2*a + 2*A*B*b))*(B*a^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a*b^2))/(a^4 + b^4 - 2*a^2*b^2) - (log(((A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^3 + B*a*b^2)*(64*A^2*a^2*b - 32*B^2*a^2*b + ((A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^3 + B*a*b^2)*(32*A*a^2*b^2 - 32*A*a^4 + 32*a*tan(x/2)*(2*A*b^3 + 2*B*a^3 - 2*A*a^2*b + B*a*b^2) + 32*B*a*b^3 + 64*B*a^3*b + (96*a*b*(a + b*tan(x/2))*(A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^3 + B*a*b^2))/(a^2 - b^2)))/(a^2 - b^2)^2 + 32*a*tan(x/2)*(A^2*a^2 + A^2*b^2 + 2*B^2*b^2 + 4*A*B*a*b) + 64*A*B*a^3))/(a^2 - b^2)^2 - 32*A*B^2*a^2 - 32*A^2*B*a*b - 32*B*a*tan(x/2)*(A^2*a + 2*B^2*a + 2*A*B*b))*(A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^3 + B*a*b^2))/(a^4 + b^4 - 2*a^2*b^2) - (B*log(tan(x/2) - 1))/(a + b) - (B*log(tan(x/2) + 1))/(a - b)","B"
7,1,124,63,16.060507,"\text{Not used}","int((A + B*cot(x))/(a + b*sin(x)),x)","\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}-\ln\left(b+a\,\mathrm{tan}\left(\frac{x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(\frac{B}{a}+\frac{A\,a\,\sqrt{b^2-a^2}}{a\,b^2-a^3}\right)-\ln\left(b+a\,\mathrm{tan}\left(\frac{x}{2}\right)-\sqrt{b^2-a^2}\right)\,\left(\frac{B}{a}-\frac{A\,a\,\sqrt{b^2-a^2}}{a\,b^2-a^3}\right)","Not used",1,"(B*log(tan(x/2)))/a - log(b + a*tan(x/2) + (b^2 - a^2)^(1/2))*(B/a + (A*a*(b^2 - a^2)^(1/2))/(a*b^2 - a^3)) - log(b + a*tan(x/2) - (b^2 - a^2)^(1/2))*(B/a - (A*a*(b^2 - a^2)^(1/2))/(a*b^2 - a^3))","B"
8,1,755,98,20.280818,"\text{Not used}","int((A + B/cos(x))/(a + b*sin(x)),x)","\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{a-b}-\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{a+b}-\frac{\ln\left(32\,A\,B^2\,a^2-32\,A^2\,B\,a^2+\frac{\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,b^3+B\,a^2\,b\right)\,\left(32\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,a^2+A^2\,b^2-4\,A\,B\,b^2+B^2\,a^2+3\,B^2\,b^2\right)+64\,A^2\,a^2\,b+32\,B^2\,a^2\,b-\frac{\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,b^3+B\,a^2\,b\right)\,\left(32\,A\,a^4+32\,B\,a^4-32\,A\,a^2\,b^2+64\,B\,a^2\,b^2+32\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,A\,a^2-2\,A\,b^2+4\,B\,a^2-B\,b^2\right)-\frac{96\,a\,b\,\left(a+b\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,b^3+B\,a^2\,b\right)}{a^2-b^2}\right)}{{\left(a^2-b^2\right)}^2}-64\,A\,B\,a^2\,b\right)}{{\left(a^2-b^2\right)}^2}-32\,B\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(A-B\right)}^2\right)\,\left(A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,b^3+B\,a^2\,b\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{\ln\left(32\,A\,B^2\,a^2-32\,A^2\,B\,a^2-\frac{\left(B\,b^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^2\,b\right)\,\left(32\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(A^2\,a^2+A^2\,b^2-4\,A\,B\,b^2+B^2\,a^2+3\,B^2\,b^2\right)+64\,A^2\,a^2\,b+32\,B^2\,a^2\,b+\frac{\left(B\,b^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^2\,b\right)\,\left(32\,A\,a^4+32\,B\,a^4-32\,A\,a^2\,b^2+64\,B\,a^2\,b^2+32\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,A\,a^2-2\,A\,b^2+4\,B\,a^2-B\,b^2\right)+\frac{96\,a\,b\,\left(a+b\,\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(B\,b^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^2\,b\right)}{a^2-b^2}\right)}{{\left(a^2-b^2\right)}^2}-64\,A\,B\,a^2\,b\right)}{{\left(a^2-b^2\right)}^2}-32\,B\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(A-B\right)}^2\right)\,\left(B\,b^3+A\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,a^2\,b\right)}{a^4-2\,a^2\,b^2+b^4}","Not used",1,"(B*log(tan(x/2) + 1))/(a - b) - (B*log(tan(x/2) - 1))/(a + b) - (log(32*A*B^2*a^2 - 32*A^2*B*a^2 + ((A*(-(a + b)^3*(a - b)^3)^(1/2) - B*b^3 + B*a^2*b)*(32*a*tan(x/2)*(A^2*a^2 + A^2*b^2 + B^2*a^2 + 3*B^2*b^2 - 4*A*B*b^2) + 64*A^2*a^2*b + 32*B^2*a^2*b - ((A*(-(a + b)^3*(a - b)^3)^(1/2) - B*b^3 + B*a^2*b)*(32*A*a^4 + 32*B*a^4 - 32*A*a^2*b^2 + 64*B*a^2*b^2 + 32*a*b*tan(x/2)*(2*A*a^2 - 2*A*b^2 + 4*B*a^2 - B*b^2) - (96*a*b*(a + b*tan(x/2))*(A*(-(a + b)^3*(a - b)^3)^(1/2) - B*b^3 + B*a^2*b))/(a^2 - b^2)))/(a^2 - b^2)^2 - 64*A*B*a^2*b))/(a^2 - b^2)^2 - 32*B*a*b*tan(x/2)*(A - B)^2)*(A*(-(a + b)^3*(a - b)^3)^(1/2) - B*b^3 + B*a^2*b))/(a^4 + b^4 - 2*a^2*b^2) + (log(32*A*B^2*a^2 - 32*A^2*B*a^2 - ((B*b^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^2*b)*(32*a*tan(x/2)*(A^2*a^2 + A^2*b^2 + B^2*a^2 + 3*B^2*b^2 - 4*A*B*b^2) + 64*A^2*a^2*b + 32*B^2*a^2*b + ((B*b^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^2*b)*(32*A*a^4 + 32*B*a^4 - 32*A*a^2*b^2 + 64*B*a^2*b^2 + 32*a*b*tan(x/2)*(2*A*a^2 - 2*A*b^2 + 4*B*a^2 - B*b^2) + (96*a*b*(a + b*tan(x/2))*(B*b^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^2*b))/(a^2 - b^2)))/(a^2 - b^2)^2 - 64*A*B*a^2*b))/(a^2 - b^2)^2 - 32*B*a*b*tan(x/2)*(A - B)^2)*(B*b^3 + A*(-(a + b)^3*(a - b)^3)^(1/2) - B*a^2*b))/(a^4 + b^4 - 2*a^2*b^2)","B"
9,1,134,61,15.623041,"\text{Not used}","int((A + B/sin(x))/(a + b*sin(x)),x)","\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}-\frac{\ln\left(b+a\,\mathrm{tan}\left(\frac{x}{2}\right)+\sqrt{b^2-a^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,a-B\,b\right)}{a\,b^2-a^3}-\frac{\ln\left(b+a\,\mathrm{tan}\left(\frac{x}{2}\right)-\sqrt{b^2-a^2}\right)\,\left(A\,a\,\sqrt{b^2-a^2}-B\,b\,\sqrt{b^2-a^2}\right)}{a\,\left(a^2-b^2\right)}","Not used",1,"(B*log(tan(x/2)))/a - (log(b + a*tan(x/2) + (b^2 - a^2)^(1/2))*(-(a + b)*(a - b))^(1/2)*(A*a - B*b))/(a*b^2 - a^3) - (log(b + a*tan(x/2) - (b^2 - a^2)^(1/2))*(A*a*(b^2 - a^2)^(1/2) - B*b*(b^2 - a^2)^(1/2)))/(a*(a^2 - b^2))","B"