1,1,1537,57,5.571707,"\text{Not used}","int((A + B*sin(x))/(a + b*cos(x)),x)","\frac{B\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{b}-\frac{\ln\left(\frac{a+b\,\cos\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{\left(a^2-b^2\right)\,\left(\frac{A\,\left(64\,A\,B\,b^3+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(32\,A\,a^2\,b^2-64\,A\,a\,b^3+32\,A\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,A\,B\,a\,b^2+64\,A\,B\,a^2\,b\right)}{\sqrt{a^2-b^2}}+\frac{A\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(32\,A\,a^2\,b^2-64\,A\,a\,b^3+32\,A\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)\,\left(A^2\,b^2-4\,B^2\,a^2+4\,B^2\,b^2\right)}{\left(32\,A\,a-32\,A\,b\right)\,\left(a-b\right)\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(\frac{\left(\frac{A^3\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{{\left(a^2-b^2\right)}^{3/2}}+\frac{\left(\frac{A\,\left(64\,B\,b^4+64\,B\,a^2\,b^2-128\,B\,a\,b^3-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}-\frac{A\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\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\,\left(32\,A^2\,b^3+64\,B^2\,a^3-32\,A^2\,a\,b^2+64\,B^2\,a\,b^2-128\,B^2\,a^2\,b+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,B\,b^4+64\,B\,a^2\,b^2-128\,B\,a\,b^3-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}\right)\,\left(A^2\,b^2-4\,B^2\,a^2+4\,B^2\,b^2\right)}{\sqrt{a^2-b^2}\,\left(a-b\right)\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}-\frac{4\,A\,B\,b\,\left(64\,B^3\,a^2+64\,B^3\,b^2-32\,A^2\,B\,b^2+\frac{A\,\left(\frac{A\,\left(64\,B\,b^4+64\,B\,a^2\,b^2-128\,B\,a\,b^3-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}-\frac{A\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(32\,A^2\,b^3+64\,B^2\,a^3-32\,A^2\,a\,b^2+64\,B^2\,a\,b^2-128\,B^2\,a^2\,b+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,B\,b^4+64\,B\,a^2\,b^2-128\,B\,a\,b^3-\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,B^3\,a\,b+32\,A^2\,B\,a\,b-\frac{A^2\,\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{\left(a-b\right)\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}\right)}{32\,A\,a-32\,A\,b}+\frac{4\,A\,B\,b\,{\left(a^2-b^2\right)}^{3/2}\,\left(32\,A\,B^2\,a^2+32\,A\,B^2\,b^2+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(64\,A\,B\,b^3+\frac{\left(2\,B\,b^3-2\,B\,a^2\,b\right)\,\left(32\,A\,a^2\,b^2-64\,A\,a\,b^3+32\,A\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,A\,B\,a\,b^2+64\,A\,B\,a^2\,b\right)}{2\,\left(b^4-a^2\,b^2\right)}-\frac{A^2\,\left(32\,A\,a^2\,b^2-64\,A\,a\,b^3+32\,A\,b^4\right)}{a^2-b^2}-64\,A\,B^2\,a\,b\right)}{\left(32\,A\,a-32\,A\,b\right)\,\left(a-b\right)\,{\left(A^2\,b^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}\right)}{\sqrt{a^2-b^2}}","Not used",1,"(B*log(1/(cos(x) + 1)))/b - (log((a + b*cos(x))/(cos(x) + 1))*(2*B*b^3 - 2*B*a^2*b))/(2*(b^4 - a^2*b^2)) - (2*A*atan(((a^2 - b^2)*((A*(64*A*B*b^3 + ((2*B*b^3 - 2*B*a^2*b)*(32*A*b^4 + 32*A*a^2*b^2 - 64*A*a*b^3))/(2*(b^4 - a^2*b^2)) - 128*A*B*a*b^2 + 64*A*B*a^2*b))/(a^2 - b^2)^(1/2) + (A*(2*B*b^3 - 2*B*a^2*b)*(32*A*b^4 + 32*A*a^2*b^2 - 64*A*a*b^3))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2)))*(A^2*b^2 - 4*B^2*a^2 + 4*B^2*b^2))/((32*A*a - 32*A*b)*(a - b)*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2) - (tan(x/2)*(a^2 - b^2)^(3/2)*((((A^3*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(a^2 - b^2)^(3/2) + (((A*(64*B*b^4 + 64*B*a^2*b^2 - 128*B*a*b^3 - ((2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) - (A*(2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 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*(32*A^2*b^3 + 64*B^2*a^3 - 32*A^2*a*b^2 + 64*B^2*a*b^2 - 128*B^2*a^2*b + ((2*B*b^3 - 2*B*a^2*b)*(64*B*b^4 + 64*B*a^2*b^2 - 128*B*a*b^3 - ((2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2))*(A^2*b^2 - 4*B^2*a^2 + 4*B^2*b^2))/((a^2 - b^2)^(1/2)*(a - b)*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2) - (4*A*B*b*(64*B^3*a^2 + 64*B^3*b^2 - 32*A^2*B*b^2 + (A*((A*(64*B*b^4 + 64*B*a^2*b^2 - 128*B*a*b^3 - ((2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) - (A*(2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) - ((2*B*b^3 - 2*B*a^2*b)*(32*A^2*b^3 + 64*B^2*a^3 - 32*A^2*a*b^2 + 64*B^2*a*b^2 - 128*B^2*a^2*b + ((2*B*b^3 - 2*B*a^2*b)*(64*B*b^4 + 64*B*a^2*b^2 - 128*B*a*b^3 - ((2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2)) - 128*B^3*a*b + 32*A^2*B*a*b - (A^2*(2*B*b^3 - 2*B*a^2*b)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2))))/((a - b)*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2)))/(32*A*a - 32*A*b) + (4*A*B*b*(a^2 - b^2)^(3/2)*(32*A*B^2*a^2 + 32*A*B^2*b^2 + ((2*B*b^3 - 2*B*a^2*b)*(64*A*B*b^3 + ((2*B*b^3 - 2*B*a^2*b)*(32*A*b^4 + 32*A*a^2*b^2 - 64*A*a*b^3))/(2*(b^4 - a^2*b^2)) - 128*A*B*a*b^2 + 64*A*B*a^2*b))/(2*(b^4 - a^2*b^2)) - (A^2*(32*A*b^4 + 32*A*a^2*b^2 - 64*A*a*b^3))/(a^2 - b^2) - 64*A*B^2*a*b))/((32*A*a - 32*A*b)*(a - b)*(A^2*b^2 + 4*B^2*a^2 - 4*B^2*b^2)^2)))/(a^2 - b^2)^(1/2)","B"
2,1,18,19,2.176914,"\text{Not used}","int((A + B*sin(x))/(cos(x) + 1),x)","B\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+A\,\mathrm{tan}\left(\frac{x}{2}\right)","Not used",1,"B*log(tan(x/2)^2 + 1) + A*tan(x/2)","B"
3,1,30,23,2.214610,"\text{Not used}","int(-(A + B*sin(x))/(cos(x) - 1),x)","2\,B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\frac{A}{\mathrm{tan}\left(\frac{x}{2}\right)}-B\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"2*B*log(tan(x/2)) - A/tan(x/2) - B*log(tan(x/2)^2 + 1)","B"
4,1,2219,58,11.809608,"\text{Not used}","int((b + c + sin(x))/(a + b*cos(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{4\,b\,\left(b+c\right)\,\left(32\,a\,b^3-128\,a\,b-64\,b^3\,c+64\,a^2+64\,b^2-32\,b^4-32\,b^2\,c^2+\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(64\,b^4-128\,a\,b^3+64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\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(64\,a\,b^2-128\,a^2\,b-32\,a\,b^4+64\,b^4\,c+64\,a^3+32\,b^5+32\,b^3\,c^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,b^4-128\,a\,b^3+64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}-32\,a\,b^2\,c^2-64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}+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(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{\left(a-b\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}-\frac{\left(\frac{{\left(b+c\right)}^3\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\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(64\,b^4-128\,a\,b^3+64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\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(64\,a\,b^2-128\,a^2\,b-32\,a\,b^4+64\,b^4\,c+64\,a^3+32\,b^5+32\,b^3\,c^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,b^4-128\,a\,b^3+64\,a^2\,b^2+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2-128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}-32\,a\,b^2\,c^2-64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}\right)\,\left(-4\,a^2+b^4+2\,b^3\,c+b^2\,c^2+4\,b^2\right)}{\sqrt{a^2-b^2}\,\left(a-b\right)\,{\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-32\,b\,c-32\,b^2}+\frac{\left(\frac{\left(b+c\right)\,\left(64\,b^3\,c-128\,a\,b^3+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2-64\,a\,b^4-64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,a\,b^2\,c+64\,a^2\,b\,c\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2-64\,a\,b^4-64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)\,\left(a^2-b^2\right)\,\left(-4\,a^2+b^4+2\,b^3\,c+b^2\,c^2+4\,b^2\right)}{\left(a-b\right)\,\left(32\,a\,b+32\,a\,c-32\,b\,c-32\,b^2\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}-\frac{4\,b\,\left(b+c\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(64\,a\,b^2-32\,a^2\,b-32\,a^2\,c-32\,b^2\,c-32\,b^3+\frac{{\left(b+c\right)}^2\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2-64\,a\,b^4-64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{a^2-b^2}+\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,b^3\,c-128\,a\,b^3+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2-64\,a\,b^4-64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}-128\,a\,b^2\,c+64\,a^2\,b\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b\,c\right)}{\left(a-b\right)\,\left(32\,a\,b+32\,a\,c-32\,b\,c-32\,b^2\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(\left(32\,a^2\,b-64\,a\,b^2+32\,a^2\,c+32\,b^2\,c+32\,b^3+\frac{\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}+1\right)\,\left(64\,b^3\,c-128\,a\,b^3+64\,b^4+64\,a^2\,b^2-128\,a\,b^2\,c+64\,a^2\,b\,c+32\,\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}+1\right)\,{\left(a-b\right)}^2\,\left(2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+b\,c+b^2+2\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}\right)+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,a^2+2\,a\,b+b^4+2\,b^3\,c+b^2\,c^2\right)\right)}{b}-64\,a\,b\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(b^3+2\,b^2\,c+b\,c^2-2\,b+2\,a\right)\right)\,\left(32\,a^2\,b-64\,a\,b^2+32\,a^2\,c+32\,b^2\,c+32\,b^3-\frac{\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}-1\right)\,\left(64\,b^3\,c-128\,a\,b^3+64\,b^4+64\,a^2\,b^2-128\,a\,b^2\,c+64\,a^2\,b\,c-32\,\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}-1\right)\,{\left(a-b\right)}^2\,\left(2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+b\,c+b^2-2\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}\right)+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(-2\,a^2+2\,a\,b+b^4+2\,b^3\,c+b^2\,c^2\right)\right)}{b}-64\,a\,b\,c+32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-b\right)\,\left(b^3+2\,b^2\,c+b\,c^2-2\,b+2\,a\right)\right)\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)*((4*b*(b + c)*(32*a*b^3 - 128*a*b - 64*b^3*c + 64*a^2 + 64*b^2 - 32*b^4 - 32*b^2*c^2 + ((b + c)*(((b + c)*(64*b^4 - 128*a*b^3 + 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) + ((2*a^2*b - 2*b^3)*(b + c)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(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)*(64*a*b^2 - 128*a^2*b - 32*a*b^4 + 64*b^4*c + 64*a^3 + 32*b^5 + 32*b^3*c^2 - ((2*a^2*b - 2*b^3)*(64*b^4 - 128*a*b^3 + 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2)) - 32*a*b^2*c^2 - 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) + 32*a*b*c^2 + 64*a*b^2*c + ((2*a^2*b - 2*b^3)*(b + c)^2*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2))))/((a - b)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) - ((((b + c)^3*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(a^2 - b^2)^(3/2) - ((2*a^2*b - 2*b^3)*(((b + c)*(64*b^4 - 128*a*b^3 + 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) + ((2*a^2*b - 2*b^3)*(b + c)*(64*a*b^4 - 128*a^2*b^3 + 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)*(64*a*b^2 - 128*a^2*b - 32*a*b^4 + 64*b^4*c + 64*a^3 + 32*b^5 + 32*b^3*c^2 - ((2*a^2*b - 2*b^3)*(64*b^4 - 128*a*b^3 + 64*a^2*b^2 + ((2*a^2*b - 2*b^3)*(64*a*b^4 - 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2)) - 32*a*b^2*c^2 - 64*a*b^3*c))/(a^2 - b^2)^(1/2))*(2*b^3*c - 4*a^2 + 4*b^2 + b^4 + b^2*c^2))/((a^2 - b^2)^(1/2)*(a - b)*(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 - 32*b*c - 32*b^2) + ((((b + c)*(64*b^3*c - 128*a*b^3 + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(32*b^4*c - 64*a*b^4 + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c - 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 128*a*b^2*c + 64*a^2*b*c))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(32*b^4*c - 64*a*b^4 + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c - 64*a*b^3*c))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2)))*(a^2 - b^2)*(2*b^3*c - 4*a^2 + 4*b^2 + b^4 + b^2*c^2))/((a - b)*(32*a*b + 32*a*c - 32*b*c - 32*b^2)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) - (4*b*(b + c)*(a^2 - b^2)^(3/2)*(64*a*b^2 - 32*a^2*b - 32*a^2*c - 32*b^2*c - 32*b^3 + ((b + c)^2*(32*b^4*c - 64*a*b^4 + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c - 64*a*b^3*c))/(a^2 - b^2) + ((2*a^2*b - 2*b^3)*(64*b^3*c - 128*a*b^3 + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(32*b^4*c - 64*a*b^4 + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c - 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) - 128*a*b^2*c + 64*a^2*b*c))/(2*(b^4 - a^2*b^2)) + 64*a*b*c))/((a - b)*(32*a*b + 32*a*c - 32*b*c - 32*b^2)*(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((32*a^2*b - 64*a*b^2 + 32*a^2*c + 32*b^2*c + 32*b^3 + ((b*(-(b + c)^2/(a^2 - b^2))^(1/2) + 1)*(64*b^3*c - 128*a*b^3 + 64*b^4 + 64*a^2*b^2 - 128*a*b^2*c + 64*a^2*b*c + 32*(b*(-(b + c)^2/(a^2 - b^2))^(1/2) + 1)*(a - b)^2*(2*a*tan(x/2) - 2*b*tan(x/2) + b*c + b^2 + 2*a*b*tan(x/2)*(-(b + c)^2/(a^2 - b^2))^(1/2)) + 32*tan(x/2)*(a - b)*(2*a*b + 2*b^3*c - 2*a^2 + b^4 + b^2*c^2)))/b - 64*a*b*c + 32*tan(x/2)*(a - b)*(2*a - 2*b + b*c^2 + 2*b^2*c + b^3))*(32*a^2*b - 64*a*b^2 + 32*a^2*c + 32*b^2*c + 32*b^3 - ((b*(-(b + c)^2/(a^2 - b^2))^(1/2) - 1)*(64*b^3*c - 128*a*b^3 + 64*b^4 + 64*a^2*b^2 - 128*a*b^2*c + 64*a^2*b*c - 32*(b*(-(b + c)^2/(a^2 - b^2))^(1/2) - 1)*(a - b)^2*(2*a*tan(x/2) - 2*b*tan(x/2) + b*c + b^2 - 2*a*b*tan(x/2)*(-(b + c)^2/(a^2 - b^2))^(1/2)) + 32*tan(x/2)*(a - b)*(2*a*b + 2*b^3*c - 2*a^2 + b^4 + b^2*c^2)))/b - 64*a*b*c + 32*tan(x/2)*(a - b)*(2*a - 2*b + b*c^2 + 2*b^2*c + b^3)))*(2*a^2*b - 2*b^3))/(2*(b^4 - a^2*b^2))","B"
5,1,2213,58,11.903556,"\text{Not used}","int((b + c + sin(x))/(a - b*cos(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{\left(\frac{\left(b+c\right)\,\left(128\,a\,b^3+64\,b^3\,c+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2+64\,a\,b^4+64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}+128\,a\,b^2\,c+64\,a^2\,b\,c\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2+64\,a\,b^4+64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)\,\left(a^2-b^2\right)\,\left(-4\,a^2+b^4+2\,b^3\,c+b^2\,c^2+4\,b^2\right)}{\left(a+b\right)\,\left(32\,a\,b+32\,a\,c+32\,b\,c+32\,b^2\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(\frac{4\,b\,\left(b+c\right)\,\left(32\,a\,b^3-128\,a\,b+64\,b^3\,c-64\,a^2-64\,b^2+32\,b^4+32\,b^2\,c^2-\frac{\left(b+c\right)\,\left(\frac{\left(b+c\right)\,\left(128\,a\,b^3+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\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\,b^4-128\,a^2\,b-64\,a\,b^2+64\,b^4\,c-64\,a^3+32\,b^5+32\,b^3\,c^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(128\,a\,b^3+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}+32\,a\,b^2\,c^2+64\,a\,b^3\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}+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(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{\left(a+b\right)\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}-\frac{\left(\frac{{\left(b+c\right)}^3\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\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(128\,a\,b^3+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(b+c\right)\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\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(32\,a\,b^4-128\,a^2\,b-64\,a\,b^2+64\,b^4\,c-64\,a^3+32\,b^5+32\,b^3\,c^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(128\,a\,b^3+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(64\,a^3\,b^2+128\,a^2\,b^3+64\,a\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}\right)}{2\,\left(b^4-a^2\,b^2\right)}+32\,a\,b^2\,c^2+64\,a\,b^3\,c\right)}{\sqrt{a^2-b^2}}\right)\,\left(-4\,a^2+b^4+2\,b^3\,c+b^2\,c^2+4\,b^2\right)}{\left(a+b\right)\,\sqrt{a^2-b^2}\,{\left(4\,a^2+b^4+2\,b^3\,c+b^2\,c^2-4\,b^2\right)}^2}\right)}{32\,a\,b+32\,a\,c+32\,b\,c+32\,b^2}+\frac{4\,b\,\left(b+c\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(64\,a\,b^2+32\,a^2\,b+32\,a^2\,c+32\,b^2\,c+32\,b^3-\frac{{\left(b+c\right)}^2\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2+64\,a\,b^4+64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{a^2-b^2}-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(128\,a\,b^3+64\,b^3\,c+64\,b^4+64\,a^2\,b^2-\frac{\left(2\,a^2\,b-2\,b^3\right)\,\left(32\,a^2\,b^3+32\,c\,a^2\,b^2+64\,a\,b^4+64\,c\,a\,b^3+32\,b^5+32\,c\,b^4\right)}{2\,\left(b^4-a^2\,b^2\right)}+128\,a\,b^2\,c+64\,a^2\,b\,c\right)}{2\,\left(b^4-a^2\,b^2\right)}+64\,a\,b\,c\right)}{\left(a+b\right)\,\left(32\,a\,b+32\,a\,c+32\,b\,c+32\,b^2\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(\left(64\,a\,b^2+32\,a^2\,b+32\,a^2\,c+32\,b^2\,c+32\,b^3-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(b^3+2\,b^2\,c+b\,c^2-2\,b-2\,a\right)-\frac{\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}-1\right)\,\left(128\,a\,b^3+64\,b^3\,c+64\,b^4+64\,a^2\,b^2-32\,\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}-1\right)\,{\left(a+b\right)}^2\,\left(b\,c-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b^2+2\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}\right)-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(-2\,a^2-2\,a\,b+b^4+2\,b^3\,c+b^2\,c^2\right)+128\,a\,b^2\,c+64\,a^2\,b\,c\right)}{b}+64\,a\,b\,c\right)\,\left(64\,a\,b^2+32\,a^2\,b+32\,a^2\,c+32\,b^2\,c+32\,b^3-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(b^3+2\,b^2\,c+b\,c^2-2\,b-2\,a\right)+64\,a\,b\,c+\frac{\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}+1\right)\,\left(128\,a\,b^3+64\,b^3\,c+64\,b^4+64\,a^2\,b^2-32\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(-2\,a^2-2\,a\,b+b^4+2\,b^3\,c+b^2\,c^2\right)+128\,a\,b^2\,c+64\,a^2\,b\,c-32\,\left(b\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}+1\right)\,{\left(a+b\right)}^2\,\left(2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-b\,c-b^2+2\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{{\left(b+c\right)}^2}{a^2-b^2}}\right)\right)}{b}\right)\right)\,\left(2\,a^2\,b-2\,b^3\right)}{2\,\left(b^4-a^2\,b^2\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{b}","Not used",1,"(2*atan(((((b + c)*(128*a*b^3 + 64*b^3*c + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(64*a*b^4 + 32*b^4*c + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) + 128*a*b^2*c + 64*a^2*b*c))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(64*a*b^4 + 32*b^4*c + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)*(a^2 - b^2)^(1/2)))*(a^2 - b^2)*(2*b^3*c - 4*a^2 + 4*b^2 + b^4 + b^2*c^2))/((a + b)*(32*a*b + 32*a*c + 32*b*c + 32*b^2)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) - (tan(x/2)*(a^2 - b^2)^(3/2)*((4*b*(b + c)*(32*a*b^3 - 128*a*b + 64*b^3*c - 64*a^2 - 64*b^2 + 32*b^4 + 32*b^2*c^2 - ((b + c)*(((b + c)*(128*a*b^3 + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(2*(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*b^4 - 128*a^2*b - 64*a*b^2 + 64*b^4*c - 64*a^3 + 32*b^5 + 32*b^3*c^2 - ((2*a^2*b - 2*b^3)*(128*a*b^3 + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2)) + 32*a*b^2*c^2 + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) + 32*a*b*c^2 + 64*a*b^2*c + ((2*a^2*b - 2*b^3)*(b + c)^2*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2)*(a^2 - b^2))))/((a + b)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2) - ((((b + c)^3*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(a^2 - b^2)^(3/2) + ((2*a^2*b - 2*b^3)*(((b + c)*(128*a*b^3 + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) - ((2*a^2*b - 2*b^3)*(b + c)*(64*a*b^4 + 128*a^2*b^3 + 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)*(32*a*b^4 - 128*a^2*b - 64*a*b^2 + 64*b^4*c - 64*a^3 + 32*b^5 + 32*b^3*c^2 - ((2*a^2*b - 2*b^3)*(128*a*b^3 + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(64*a*b^4 + 128*a^2*b^3 + 64*a^3*b^2))/(2*(b^4 - a^2*b^2))))/(2*(b^4 - a^2*b^2)) + 32*a*b^2*c^2 + 64*a*b^3*c))/(a^2 - b^2)^(1/2))*(2*b^3*c - 4*a^2 + 4*b^2 + b^4 + b^2*c^2))/((a + b)*(a^2 - b^2)^(1/2)*(2*b^3*c + 4*a^2 - 4*b^2 + b^4 + b^2*c^2)^2)))/(32*a*b + 32*a*c + 32*b*c + 32*b^2) + (4*b*(b + c)*(a^2 - b^2)^(3/2)*(64*a*b^2 + 32*a^2*b + 32*a^2*c + 32*b^2*c + 32*b^3 - ((b + c)^2*(64*a*b^4 + 32*b^4*c + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c + 64*a*b^3*c))/(a^2 - b^2) - ((2*a^2*b - 2*b^3)*(128*a*b^3 + 64*b^3*c + 64*b^4 + 64*a^2*b^2 - ((2*a^2*b - 2*b^3)*(64*a*b^4 + 32*b^4*c + 32*b^5 + 32*a^2*b^3 + 32*a^2*b^2*c + 64*a*b^3*c))/(2*(b^4 - a^2*b^2)) + 128*a*b^2*c + 64*a^2*b*c))/(2*(b^4 - a^2*b^2)) + 64*a*b*c))/((a + b)*(32*a*b + 32*a*c + 32*b*c + 32*b^2)*(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((64*a*b^2 + 32*a^2*b + 32*a^2*c + 32*b^2*c + 32*b^3 - 32*tan(x/2)*(a + b)*(b*c^2 - 2*b - 2*a + 2*b^2*c + b^3) - ((b*(-(b + c)^2/(a^2 - b^2))^(1/2) - 1)*(128*a*b^3 + 64*b^3*c + 64*b^4 + 64*a^2*b^2 - 32*(b*(-(b + c)^2/(a^2 - b^2))^(1/2) - 1)*(a + b)^2*(b*c - 2*b*tan(x/2) - 2*a*tan(x/2) + b^2 + 2*a*b*tan(x/2)*(-(b + c)^2/(a^2 - b^2))^(1/2)) - 32*tan(x/2)*(a + b)*(2*b^3*c - 2*a*b - 2*a^2 + b^4 + b^2*c^2) + 128*a*b^2*c + 64*a^2*b*c))/b + 64*a*b*c)*(64*a*b^2 + 32*a^2*b + 32*a^2*c + 32*b^2*c + 32*b^3 - 32*tan(x/2)*(a + b)*(b*c^2 - 2*b - 2*a + 2*b^2*c + b^3) + 64*a*b*c + ((b*(-(b + c)^2/(a^2 - b^2))^(1/2) + 1)*(128*a*b^3 + 64*b^3*c + 64*b^4 + 64*a^2*b^2 - 32*tan(x/2)*(a + b)*(2*b^3*c - 2*a*b - 2*a^2 + b^4 + b^2*c^2) + 128*a*b^2*c + 64*a^2*b*c - 32*(b*(-(b + c)^2/(a^2 - b^2))^(1/2) + 1)*(a + b)^2*(2*a*tan(x/2) + 2*b*tan(x/2) - b*c - b^2 + 2*a*b*tan(x/2)*(-(b + c)^2/(a^2 - b^2))^(1/2))))/b))*(2*a^2*b - 2*b^3))/(2*(b^4 - a^2*b^2)) - log(tan(x/2)^2 + 1)/b","B"
6,1,1540,65,5.658924,"\text{Not used}","int((A + B*tan(x))/(a + b*cos(x)),x)","\frac{\ln\left(\frac{a+b\,\cos\left(x\right)}{\cos\left(x\right)+1}\right)\,\left(2\,B\,a^3-2\,B\,a\,b^2\right)}{2\,\left(a^4-a^2\,b^2\right)}+\frac{2\,A\,\mathrm{atan}\left(\frac{\left(a^2-b^2\right)\,\left(\frac{A\,\left(64\,A\,B\,a^3+\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(32\,A\,a^4-64\,A\,a^3\,b+32\,A\,a^2\,b^2\right)}{2\,\left(a^4-a^2\,b^2\right)}+64\,A\,B\,a\,b^2-128\,A\,B\,a^2\,b\right)}{\sqrt{a^2-b^2}}+\frac{A\,\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(32\,A\,a^4-64\,A\,a^3\,b+32\,A\,a^2\,b^2\right)}{2\,\left(a^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)\,\left(A^2\,a^2-4\,B^2\,a^2+4\,B^2\,b^2\right)}{\left(32\,A\,a-32\,A\,b\right)\,\left(a-b\right)\,{\left(A^2\,a^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,\left(\frac{\left(\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(\frac{A\,\left(64\,B\,a^4+64\,B\,a^2\,b^2-128\,B\,a^3\,b-\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}-\frac{A\,\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{2\,\left(a^4-a^2\,b^2\right)}+\frac{A^3\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{{\left(a^2-b^2\right)}^{3/2}}+\frac{A\,\left(64\,B^2\,b^3-32\,A^2\,a^3+32\,A^2\,a^2\,b-128\,B^2\,a\,b^2+64\,B^2\,a^2\,b+\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,B\,a^4+64\,B\,a^2\,b^2-128\,B\,a^3\,b-\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)}\right)}{2\,\left(a^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}\right)\,\left(A^2\,a^2-4\,B^2\,a^2+4\,B^2\,b^2\right)}{\sqrt{a^2-b^2}\,\left(a-b\right)\,{\left(A^2\,a^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}-\frac{4\,A\,B\,a\,\left(64\,B^3\,a^2+64\,B^3\,b^2+32\,A^2\,B\,a^2+\frac{A\,\left(\frac{A\,\left(64\,B\,a^4+64\,B\,a^2\,b^2-128\,B\,a^3\,b-\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)}\right)}{\sqrt{a^2-b^2}}-\frac{A\,\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)\,\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,B^2\,b^3-32\,A^2\,a^3+32\,A^2\,a^2\,b-128\,B^2\,a\,b^2+64\,B^2\,a^2\,b+\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,B\,a^4+64\,B\,a^2\,b^2-128\,B\,a^3\,b-\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)}\right)}{2\,\left(a^4-a^2\,b^2\right)}\right)}{2\,\left(a^4-a^2\,b^2\right)}-128\,B^3\,a\,b-32\,A^2\,B\,a\,b-\frac{A^2\,\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,a^4\,b-128\,a^3\,b^2+64\,a^2\,b^3\right)}{2\,\left(a^4-a^2\,b^2\right)\,\left(a^2-b^2\right)}\right)}{\left(a-b\right)\,{\left(A^2\,a^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}\right)}{32\,A\,a-32\,A\,b}+\frac{4\,A\,B\,a\,{\left(a^2-b^2\right)}^{3/2}\,\left(32\,A\,B^2\,a^2+32\,A\,B^2\,b^2+\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(64\,A\,B\,a^3+\frac{\left(2\,B\,a^3-2\,B\,a\,b^2\right)\,\left(32\,A\,a^4-64\,A\,a^3\,b+32\,A\,a^2\,b^2\right)}{2\,\left(a^4-a^2\,b^2\right)}+64\,A\,B\,a\,b^2-128\,A\,B\,a^2\,b\right)}{2\,\left(a^4-a^2\,b^2\right)}-\frac{A^2\,\left(32\,A\,a^4-64\,A\,a^3\,b+32\,A\,a^2\,b^2\right)}{a^2-b^2}-64\,A\,B^2\,a\,b\right)}{\left(32\,A\,a-32\,A\,b\right)\,\left(a-b\right)\,{\left(A^2\,a^2+4\,B^2\,a^2-4\,B^2\,b^2\right)}^2}\right)}{\sqrt{a^2-b^2}}-\frac{B\,\ln\left(\frac{\cos\left(x\right)}{\cos\left(x\right)+1}\right)}{a}","Not used",1,"(log((a + b*cos(x))/(cos(x) + 1))*(2*B*a^3 - 2*B*a*b^2))/(2*(a^4 - a^2*b^2)) + (2*A*atan(((a^2 - b^2)*((A*(64*A*B*a^3 + ((2*B*a^3 - 2*B*a*b^2)*(32*A*a^4 + 32*A*a^2*b^2 - 64*A*a^3*b))/(2*(a^4 - a^2*b^2)) + 64*A*B*a*b^2 - 128*A*B*a^2*b))/(a^2 - b^2)^(1/2) + (A*(2*B*a^3 - 2*B*a*b^2)*(32*A*a^4 + 32*A*a^2*b^2 - 64*A*a^3*b))/(2*(a^4 - a^2*b^2)*(a^2 - b^2)^(1/2)))*(A^2*a^2 - 4*B^2*a^2 + 4*B^2*b^2))/((32*A*a - 32*A*b)*(a - b)*(A^2*a^2 + 4*B^2*a^2 - 4*B^2*b^2)^2) - (tan(x/2)*(a^2 - b^2)^(3/2)*(((((2*B*a^3 - 2*B*a*b^2)*((A*(64*B*a^4 + 64*B*a^2*b^2 - 128*B*a^3*b - ((2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) - (A*(2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(2*(a^4 - a^2*b^2)) + (A^3*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(a^2 - b^2)^(3/2) + (A*(64*B^2*b^3 - 32*A^2*a^3 + 32*A^2*a^2*b - 128*B^2*a*b^2 + 64*B^2*a^2*b + ((2*B*a^3 - 2*B*a*b^2)*(64*B*a^4 + 64*B*a^2*b^2 - 128*B*a^3*b - ((2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2))))/(2*(a^4 - a^2*b^2))))/(a^2 - b^2)^(1/2))*(A^2*a^2 - 4*B^2*a^2 + 4*B^2*b^2))/((a^2 - b^2)^(1/2)*(a - b)*(A^2*a^2 + 4*B^2*a^2 - 4*B^2*b^2)^2) - (4*A*B*a*(64*B^3*a^2 + 64*B^3*b^2 + 32*A^2*B*a^2 + (A*((A*(64*B*a^4 + 64*B*a^2*b^2 - 128*B*a^3*b - ((2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2))))/(a^2 - b^2)^(1/2) - (A*(2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2)*(a^2 - b^2)^(1/2))))/(a^2 - b^2)^(1/2) - ((2*B*a^3 - 2*B*a*b^2)*(64*B^2*b^3 - 32*A^2*a^3 + 32*A^2*a^2*b - 128*B^2*a*b^2 + 64*B^2*a^2*b + ((2*B*a^3 - 2*B*a*b^2)*(64*B*a^4 + 64*B*a^2*b^2 - 128*B*a^3*b - ((2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2))))/(2*(a^4 - a^2*b^2))))/(2*(a^4 - a^2*b^2)) - 128*B^3*a*b - 32*A^2*B*a*b - (A^2*(2*B*a^3 - 2*B*a*b^2)*(64*a^4*b + 64*a^2*b^3 - 128*a^3*b^2))/(2*(a^4 - a^2*b^2)*(a^2 - b^2))))/((a - b)*(A^2*a^2 + 4*B^2*a^2 - 4*B^2*b^2)^2)))/(32*A*a - 32*A*b) + (4*A*B*a*(a^2 - b^2)^(3/2)*(32*A*B^2*a^2 + 32*A*B^2*b^2 + ((2*B*a^3 - 2*B*a*b^2)*(64*A*B*a^3 + ((2*B*a^3 - 2*B*a*b^2)*(32*A*a^4 + 32*A*a^2*b^2 - 64*A*a^3*b))/(2*(a^4 - a^2*b^2)) + 64*A*B*a*b^2 - 128*A*B*a^2*b))/(2*(a^4 - a^2*b^2)) - (A^2*(32*A*a^4 + 32*A*a^2*b^2 - 64*A*a^3*b))/(a^2 - b^2) - 64*A*B^2*a*b))/((32*A*a - 32*A*b)*(a - b)*(A^2*a^2 + 4*B^2*a^2 - 4*B^2*b^2)^2)))/(a^2 - b^2)^(1/2) - (B*log(cos(x)/(cos(x) + 1)))/a","B"
7,1,419,100,3.580738,"\text{Not used}","int((A + B*cot(x))/(a + b*cos(x)),x)","\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a+b}+\frac{\ln\left(3\,B\,a^2\,b^2-B\,b^4-2\,B\,a^4+A\,a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+A\,b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+A\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)+A\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+B\,a\,b^3-B\,a^3\,b-2\,A\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+2\,B\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\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{\ln\left(2\,B\,a^4+B\,b^4-3\,B\,a^2\,b^2+A\,a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+A\,b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-A\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)-A\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)-B\,a\,b^3+B\,a^3\,b+2\,A\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+2\,B\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-B\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\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}","Not used",1,"(B*log(tan(x/2)))/(a + b) + (log(3*B*a^2*b^2 - B*b^4 - 2*B*a^4 + A*a*(-(a + b)^3*(a - b)^3)^(1/2) + A*b*(-(a + b)^3*(a - b)^3)^(1/2) + A*a^4*tan(x/2) + A*b^4*tan(x/2) + B*a*b^3 - B*a^3*b - 2*A*a^2*b^2*tan(x/2) + 2*B*a*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2) - B*b*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2))*(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) - (log(2*B*a^4 + B*b^4 - 3*B*a^2*b^2 + A*a*(-(a + b)^3*(a - b)^3)^(1/2) + A*b*(-(a + b)^3*(a - b)^3)^(1/2) - A*a^4*tan(x/2) - A*b^4*tan(x/2) - B*a*b^3 + B*a^3*b + 2*A*a^2*b^2*tan(x/2) + 2*B*a*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2) - B*b*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2))*(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)","B"
8,1,417,99,3.543566,"\text{Not used}","int((A + B/sin(x))/(a + b*cos(x)),x)","\frac{B\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a+b}+\frac{\ln\left(3\,B\,a^2\,b^2-2\,B\,b^4-B\,a^4+A\,a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+A\,b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+A\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)+A\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)-B\,a\,b^3+B\,a^3\,b-2\,A\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+B\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-2\,B\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\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(B\,a^4+2\,B\,b^4-3\,B\,a^2\,b^2+A\,a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+A\,b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-A\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)-A\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+B\,a\,b^3-B\,a^3\,b+2\,A\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+B\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}-2\,B\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\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)))/(a + b) + (log(3*B*a^2*b^2 - 2*B*b^4 - B*a^4 + A*a*(-(a + b)^3*(a - b)^3)^(1/2) + A*b*(-(a + b)^3*(a - b)^3)^(1/2) + A*a^4*tan(x/2) + A*b^4*tan(x/2) - B*a*b^3 + B*a^3*b - 2*A*a^2*b^2*tan(x/2) + B*a*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2) - 2*B*b*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2))*(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(B*a^4 + 2*B*b^4 - 3*B*a^2*b^2 + A*a*(-(a + b)^3*(a - b)^3)^(1/2) + A*b*(-(a + b)^3*(a - b)^3)^(1/2) - A*a^4*tan(x/2) - A*b^4*tan(x/2) + B*a*b^3 - B*a^3*b + 2*A*a^2*b^2*tan(x/2) + B*a*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2) - 2*B*b*tan(x/2)*(-(a + b)^3*(a - b)^3)^(1/2))*(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"
9,1,9992,247,11.819132,"\text{Not used}","int((c + d/cos(e + f*x))^4/(a + b*cos(e + f*x)),x)","-\frac{\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,a^2\,c^2\,d^2+4\,a^2\,c\,d^3+2\,a^2\,d^4-8\,a\,b\,c\,d^3-a\,b\,d^4+2\,b^2\,d^4\right)}{a^3}-\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(18\,a^2\,c^2\,d^2+a^2\,d^4-12\,a\,b\,c\,d^3+3\,b^2\,d^4\right)}{3\,a^3}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(12\,a^2\,c^2\,d^2-4\,a^2\,c\,d^3+2\,a^2\,d^4-8\,a\,b\,c\,d^3+a\,b\,d^4+2\,b^2\,d^4\right)}{a^3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^{10}}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(\frac{\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^{10}}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(16\,a^{11}\,c^{11}\,d-64\,a^{11}\,c^{10}\,d^2+8\,a^{11}\,c^9\,d^3-64\,a^{11}\,c^8\,d^4-16\,a^{11}\,c^6\,d^6-16\,a^{10}\,b\,c^{11}\,d-24\,a^{10}\,b\,c^{10}\,d^2+440\,a^{10}\,b\,c^9\,d^3+62\,a^{10}\,b\,c^8\,d^4+368\,a^{10}\,b\,c^7\,d^5+32\,a^{10}\,b\,c^6\,d^6+72\,a^{10}\,b\,c^5\,d^7+88\,a^9\,b^2\,c^{10}\,d^2-240\,a^9\,b^2\,c^9\,d^3-1422\,a^9\,b^2\,c^8\,d^4-496\,a^9\,b^2\,c^7\,d^5-936\,a^9\,b^2\,c^6\,d^6-144\,a^9\,b^2\,c^5\,d^7-129\,a^9\,b^2\,c^4\,d^8-208\,a^8\,b^3\,c^9\,d^3+1148\,a^8\,b^3\,c^8\,d^4+2848\,a^8\,b^3\,c^7\,d^5+1336\,a^8\,b^3\,c^6\,d^6+1384\,a^8\,b^3\,c^5\,d^7+258\,a^8\,b^3\,c^4\,d^8+116\,a^8\,b^3\,c^3\,d^9+276\,a^7\,b^4\,c^8\,d^4-2496\,a^7\,b^4\,c^7\,d^5-3888\,a^7\,b^4\,c^6\,d^6-1952\,a^7\,b^4\,c^5\,d^7-1301\,a^7\,b^4\,c^4\,d^8-232\,a^7\,b^4\,c^3\,d^9-54\,a^7\,b^4\,c^2\,d^{10}-224\,a^6\,b^5\,c^7\,d^5+3360\,a^6\,b^5\,c^6\,d^6+3744\,a^6\,b^5\,c^5\,d^7+1756\,a^6\,b^5\,c^4\,d^8+788\,a^6\,b^5\,c^3\,d^9+108\,a^6\,b^5\,c^2\,d^{10}+12\,a^6\,b^5\,c\,d^{11}+112\,a^5\,b^6\,c^6\,d^6-3072\,a^5\,b^6\,c^5\,d^7-2556\,a^5\,b^6\,c^4\,d^8-1008\,a^5\,b^6\,c^3\,d^9-294\,a^5\,b^6\,c^2\,d^{10}-24\,a^5\,b^6\,c\,d^{11}-a^5\,b^6\,d^{12}-32\,a^4\,b^7\,c^5\,d^7+1968\,a^4\,b^7\,c^4\,d^8+1216\,a^4\,b^7\,c^3\,d^9+360\,a^4\,b^7\,c^2\,d^{10}+60\,a^4\,b^7\,c\,d^{11}+2\,a^4\,b^7\,d^{12}+4\,a^3\,b^8\,c^4\,d^8-880\,a^3\,b^8\,c^3\,d^9-384\,a^3\,b^8\,c^2\,d^{10}-72\,a^3\,b^8\,c\,d^{11}-5\,a^3\,b^8\,d^{12}+264\,a^2\,b^9\,c^2\,d^{10}+72\,a^2\,b^9\,c\,d^{11}+6\,a^2\,b^9\,d^{12}-48\,a\,b^{10}\,c\,d^{11}-6\,a\,b^{10}\,d^{12}+4\,b^{11}\,d^{12}\right)}{a^9}+\frac{\left(\frac{\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^{10}}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^4}+\frac{\left(\frac{\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^{10}}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)}{a^4}}\right)\,\left(a^2\,\left(6\,b\,c^2\,d^2+\frac{b\,d^4}{2}\right)-a^3\,\left(4\,c^3\,d+2\,c\,d^3\right)+b^3\,d^4-4\,a\,b^2\,c\,d^3\right)\,2{}\mathrm{i}}{a^4\,f}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,{\left(a\,c-b\,d\right)}^4\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,{\left(a\,c-b\,d\right)}^4\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(16\,a^{11}\,c^{11}\,d-64\,a^{11}\,c^{10}\,d^2+8\,a^{11}\,c^9\,d^3-64\,a^{11}\,c^8\,d^4-16\,a^{11}\,c^6\,d^6-16\,a^{10}\,b\,c^{11}\,d-24\,a^{10}\,b\,c^{10}\,d^2+440\,a^{10}\,b\,c^9\,d^3+62\,a^{10}\,b\,c^8\,d^4+368\,a^{10}\,b\,c^7\,d^5+32\,a^{10}\,b\,c^6\,d^6+72\,a^{10}\,b\,c^5\,d^7+88\,a^9\,b^2\,c^{10}\,d^2-240\,a^9\,b^2\,c^9\,d^3-1422\,a^9\,b^2\,c^8\,d^4-496\,a^9\,b^2\,c^7\,d^5-936\,a^9\,b^2\,c^6\,d^6-144\,a^9\,b^2\,c^5\,d^7-129\,a^9\,b^2\,c^4\,d^8-208\,a^8\,b^3\,c^9\,d^3+1148\,a^8\,b^3\,c^8\,d^4+2848\,a^8\,b^3\,c^7\,d^5+1336\,a^8\,b^3\,c^6\,d^6+1384\,a^8\,b^3\,c^5\,d^7+258\,a^8\,b^3\,c^4\,d^8+116\,a^8\,b^3\,c^3\,d^9+276\,a^7\,b^4\,c^8\,d^4-2496\,a^7\,b^4\,c^7\,d^5-3888\,a^7\,b^4\,c^6\,d^6-1952\,a^7\,b^4\,c^5\,d^7-1301\,a^7\,b^4\,c^4\,d^8-232\,a^7\,b^4\,c^3\,d^9-54\,a^7\,b^4\,c^2\,d^{10}-224\,a^6\,b^5\,c^7\,d^5+3360\,a^6\,b^5\,c^6\,d^6+3744\,a^6\,b^5\,c^5\,d^7+1756\,a^6\,b^5\,c^4\,d^8+788\,a^6\,b^5\,c^3\,d^9+108\,a^6\,b^5\,c^2\,d^{10}+12\,a^6\,b^5\,c\,d^{11}+112\,a^5\,b^6\,c^6\,d^6-3072\,a^5\,b^6\,c^5\,d^7-2556\,a^5\,b^6\,c^4\,d^8-1008\,a^5\,b^6\,c^3\,d^9-294\,a^5\,b^6\,c^2\,d^{10}-24\,a^5\,b^6\,c\,d^{11}-a^5\,b^6\,d^{12}-32\,a^4\,b^7\,c^5\,d^7+1968\,a^4\,b^7\,c^4\,d^8+1216\,a^4\,b^7\,c^3\,d^9+360\,a^4\,b^7\,c^2\,d^{10}+60\,a^4\,b^7\,c\,d^{11}+2\,a^4\,b^7\,d^{12}+4\,a^3\,b^8\,c^4\,d^8-880\,a^3\,b^8\,c^3\,d^9-384\,a^3\,b^8\,c^2\,d^{10}-72\,a^3\,b^8\,c\,d^{11}-5\,a^3\,b^8\,d^{12}+264\,a^2\,b^9\,c^2\,d^{10}+72\,a^2\,b^9\,c\,d^{11}+6\,a^2\,b^9\,d^{12}-48\,a\,b^{10}\,c\,d^{11}-6\,a\,b^{10}\,d^{12}+4\,b^{11}\,d^{12}\right)}{a^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,{\left(a\,c-b\,d\right)}^4}{a^6-a^4\,b^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^9\,c^8+64\,a^9\,c^6\,d^2+64\,a^9\,c^4\,d^4+16\,a^9\,c^2\,d^6-4\,a^8\,b\,c^8-32\,a^8\,b\,c^7\,d-192\,a^8\,b\,c^6\,d^2-192\,a^8\,b\,c^5\,d^3-192\,a^8\,b\,c^4\,d^4-112\,a^8\,b\,c^3\,d^5-48\,a^8\,b\,c^2\,d^6-8\,a^8\,b\,c\,d^7+32\,a^7\,b^2\,c^7\,d+304\,a^7\,b^2\,c^6\,d^2+576\,a^7\,b^2\,c^5\,d^3+464\,a^7\,b^2\,c^4\,d^4+336\,a^7\,b^2\,c^3\,d^5+136\,a^7\,b^2\,c^2\,d^6+24\,a^7\,b^2\,c\,d^7+a^7\,b^2\,d^8-176\,a^6\,b^3\,c^6\,d^2-800\,a^6\,b^3\,c^5\,d^3-880\,a^6\,b^3\,c^4\,d^4-560\,a^6\,b^3\,c^3\,d^5-280\,a^6\,b^3\,c^2\,d^6-56\,a^6\,b^3\,c\,d^7-3\,a^6\,b^3\,d^8+416\,a^5\,b^4\,c^5\,d^3+1096\,a^5\,b^4\,c^4\,d^4+784\,a^5\,b^4\,c^3\,d^5+376\,a^5\,b^4\,c^2\,d^6+104\,a^5\,b^4\,c\,d^7+7\,a^5\,b^4\,d^8-552\,a^4\,b^5\,c^4\,d^4-896\,a^4\,b^5\,c^3\,d^5-424\,a^4\,b^5\,c^2\,d^6-128\,a^4\,b^5\,c\,d^7-13\,a^4\,b^5\,d^8+448\,a^3\,b^6\,c^3\,d^5+448\,a^3\,b^6\,c^2\,d^6+128\,a^3\,b^6\,c\,d^7+16\,a^3\,b^6\,d^8-224\,a^2\,b^7\,c^2\,d^6-128\,a^2\,b^7\,c\,d^7-16\,a^2\,b^7\,d^8+64\,a\,b^8\,c\,d^7+16\,a\,b^8\,d^8-8\,b^9\,d^8\right)}{a^6}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(\frac{8\,\left(4\,a^{13}\,c^4+16\,a^{13}\,c^3\,d+8\,a^{13}\,c\,d^3-8\,a^{12}\,b\,c^4-32\,a^{12}\,b\,c^3\,d-24\,a^{12}\,b\,c^2\,d^2-8\,a^{12}\,b\,c\,d^3-2\,a^{12}\,b\,d^4+4\,a^{11}\,b^2\,c^4+16\,a^{11}\,b^2\,c^3\,d+48\,a^{11}\,b^2\,c^2\,d^2+8\,a^{11}\,b^2\,c\,d^3+2\,a^{11}\,b^2\,d^4-24\,a^{10}\,b^3\,c^2\,d^2-24\,a^{10}\,b^3\,c\,d^3-2\,a^{10}\,b^3\,d^4+16\,a^9\,b^4\,c\,d^3+6\,a^9\,b^4\,d^4-4\,a^8\,b^5\,d^4\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,{\left(a\,c-b\,d\right)}^4}{a^6-a^4\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^4\,2{}\mathrm{i}}{f\,\left(a^6-a^4\,b^2\right)}","Not used",1,"(atan(((((((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 - (8*tan(e/2 + (f*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^10)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^4 - (8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3)*1i)/a^4 - (((((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 + (8*tan(e/2 + (f*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^10)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^4 + (8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3)*1i)/a^4)/((16*(4*b^11*d^12 - 6*a*b^10*d^12 + 16*a^11*c^11*d + 6*a^2*b^9*d^12 - 5*a^3*b^8*d^12 + 2*a^4*b^7*d^12 - a^5*b^6*d^12 - 16*a^11*c^6*d^6 - 64*a^11*c^8*d^4 + 8*a^11*c^9*d^3 - 64*a^11*c^10*d^2 + 72*a^2*b^9*c*d^11 - 72*a^3*b^8*c*d^11 + 60*a^4*b^7*c*d^11 - 24*a^5*b^6*c*d^11 + 12*a^6*b^5*c*d^11 + 72*a^10*b*c^5*d^7 + 32*a^10*b*c^6*d^6 + 368*a^10*b*c^7*d^5 + 62*a^10*b*c^8*d^4 + 440*a^10*b*c^9*d^3 - 24*a^10*b*c^10*d^2 + 264*a^2*b^9*c^2*d^10 - 384*a^3*b^8*c^2*d^10 - 880*a^3*b^8*c^3*d^9 + 4*a^3*b^8*c^4*d^8 + 360*a^4*b^7*c^2*d^10 + 1216*a^4*b^7*c^3*d^9 + 1968*a^4*b^7*c^4*d^8 - 32*a^4*b^7*c^5*d^7 - 294*a^5*b^6*c^2*d^10 - 1008*a^5*b^6*c^3*d^9 - 2556*a^5*b^6*c^4*d^8 - 3072*a^5*b^6*c^5*d^7 + 112*a^5*b^6*c^6*d^6 + 108*a^6*b^5*c^2*d^10 + 788*a^6*b^5*c^3*d^9 + 1756*a^6*b^5*c^4*d^8 + 3744*a^6*b^5*c^5*d^7 + 3360*a^6*b^5*c^6*d^6 - 224*a^6*b^5*c^7*d^5 - 54*a^7*b^4*c^2*d^10 - 232*a^7*b^4*c^3*d^9 - 1301*a^7*b^4*c^4*d^8 - 1952*a^7*b^4*c^5*d^7 - 3888*a^7*b^4*c^6*d^6 - 2496*a^7*b^4*c^7*d^5 + 276*a^7*b^4*c^8*d^4 + 116*a^8*b^3*c^3*d^9 + 258*a^8*b^3*c^4*d^8 + 1384*a^8*b^3*c^5*d^7 + 1336*a^8*b^3*c^6*d^6 + 2848*a^8*b^3*c^7*d^5 + 1148*a^8*b^3*c^8*d^4 - 208*a^8*b^3*c^9*d^3 - 129*a^9*b^2*c^4*d^8 - 144*a^9*b^2*c^5*d^7 - 936*a^9*b^2*c^6*d^6 - 496*a^9*b^2*c^7*d^5 - 1422*a^9*b^2*c^8*d^4 - 240*a^9*b^2*c^9*d^3 + 88*a^9*b^2*c^10*d^2 - 48*a*b^10*c*d^11 - 16*a^10*b*c^11*d))/a^9 + (((((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 - (8*tan(e/2 + (f*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^10)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^4 - (8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^4 + (((((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 + (8*tan(e/2 + (f*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^10)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^4 + (8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6)*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3))/a^4))*(a^2*((b*d^4)/2 + 6*b*c^2*d^2) - a^3*(2*c*d^3 + 4*c^3*d) + b^3*d^4 - 4*a*b^2*c*d^3)*2i)/(a^4*f) - ((tan(e/2 + (f*x)/2)*(2*a^2*d^4 + 2*b^2*d^4 + 4*a^2*c*d^3 + 12*a^2*c^2*d^2 - a*b*d^4 - 8*a*b*c*d^3))/a^3 - (4*tan(e/2 + (f*x)/2)^3*(a^2*d^4 + 3*b^2*d^4 + 18*a^2*c^2*d^2 - 12*a*b*c*d^3))/(3*a^3) + (tan(e/2 + (f*x)/2)^5*(2*a^2*d^4 + 2*b^2*d^4 - 4*a^2*c*d^3 + 12*a^2*c^2*d^2 + a*b*d^4 - 8*a*b*c*d^3))/a^3)/(f*(3*tan(e/2 + (f*x)/2)^2 - 3*tan(e/2 + (f*x)/2)^4 + tan(e/2 + (f*x)/2)^6 - 1)) - (atan((((-(a + b)*(a - b))^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6 + ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 + (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*(a*c - b*d)^4*1i)/(a^6 - a^4*b^2) + ((-(a + b)*(a - b))^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6 - ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 - (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*(a*c - b*d)^4*1i)/(a^6 - a^4*b^2))/((16*(4*b^11*d^12 - 6*a*b^10*d^12 + 16*a^11*c^11*d + 6*a^2*b^9*d^12 - 5*a^3*b^8*d^12 + 2*a^4*b^7*d^12 - a^5*b^6*d^12 - 16*a^11*c^6*d^6 - 64*a^11*c^8*d^4 + 8*a^11*c^9*d^3 - 64*a^11*c^10*d^2 + 72*a^2*b^9*c*d^11 - 72*a^3*b^8*c*d^11 + 60*a^4*b^7*c*d^11 - 24*a^5*b^6*c*d^11 + 12*a^6*b^5*c*d^11 + 72*a^10*b*c^5*d^7 + 32*a^10*b*c^6*d^6 + 368*a^10*b*c^7*d^5 + 62*a^10*b*c^8*d^4 + 440*a^10*b*c^9*d^3 - 24*a^10*b*c^10*d^2 + 264*a^2*b^9*c^2*d^10 - 384*a^3*b^8*c^2*d^10 - 880*a^3*b^8*c^3*d^9 + 4*a^3*b^8*c^4*d^8 + 360*a^4*b^7*c^2*d^10 + 1216*a^4*b^7*c^3*d^9 + 1968*a^4*b^7*c^4*d^8 - 32*a^4*b^7*c^5*d^7 - 294*a^5*b^6*c^2*d^10 - 1008*a^5*b^6*c^3*d^9 - 2556*a^5*b^6*c^4*d^8 - 3072*a^5*b^6*c^5*d^7 + 112*a^5*b^6*c^6*d^6 + 108*a^6*b^5*c^2*d^10 + 788*a^6*b^5*c^3*d^9 + 1756*a^6*b^5*c^4*d^8 + 3744*a^6*b^5*c^5*d^7 + 3360*a^6*b^5*c^6*d^6 - 224*a^6*b^5*c^7*d^5 - 54*a^7*b^4*c^2*d^10 - 232*a^7*b^4*c^3*d^9 - 1301*a^7*b^4*c^4*d^8 - 1952*a^7*b^4*c^5*d^7 - 3888*a^7*b^4*c^6*d^6 - 2496*a^7*b^4*c^7*d^5 + 276*a^7*b^4*c^8*d^4 + 116*a^8*b^3*c^3*d^9 + 258*a^8*b^3*c^4*d^8 + 1384*a^8*b^3*c^5*d^7 + 1336*a^8*b^3*c^6*d^6 + 2848*a^8*b^3*c^7*d^5 + 1148*a^8*b^3*c^8*d^4 - 208*a^8*b^3*c^9*d^3 - 129*a^9*b^2*c^4*d^8 - 144*a^9*b^2*c^5*d^7 - 936*a^9*b^2*c^6*d^6 - 496*a^9*b^2*c^7*d^5 - 1422*a^9*b^2*c^8*d^4 - 240*a^9*b^2*c^9*d^3 + 88*a^9*b^2*c^10*d^2 - 48*a*b^10*c*d^11 - 16*a^10*b*c^11*d))/a^9 + ((-(a + b)*(a - b))^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6 + ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 + (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*(a*c - b*d)^4)/(a^6 - a^4*b^2) - ((-(a + b)*(a - b))^(1/2)*((8*tan(e/2 + (f*x)/2)*(4*a^9*c^8 - 8*b^9*d^8 - 4*a^8*b*c^8 + 16*a*b^8*d^8 - 16*a^2*b^7*d^8 + 16*a^3*b^6*d^8 - 13*a^4*b^5*d^8 + 7*a^5*b^4*d^8 - 3*a^6*b^3*d^8 + a^7*b^2*d^8 + 16*a^9*c^2*d^6 + 64*a^9*c^4*d^4 + 64*a^9*c^6*d^2 - 128*a^2*b^7*c*d^7 + 128*a^3*b^6*c*d^7 - 128*a^4*b^5*c*d^7 + 104*a^5*b^4*c*d^7 - 56*a^6*b^3*c*d^7 + 24*a^7*b^2*c*d^7 + 32*a^7*b^2*c^7*d - 48*a^8*b*c^2*d^6 - 112*a^8*b*c^3*d^5 - 192*a^8*b*c^4*d^4 - 192*a^8*b*c^5*d^3 - 192*a^8*b*c^6*d^2 - 224*a^2*b^7*c^2*d^6 + 448*a^3*b^6*c^2*d^6 + 448*a^3*b^6*c^3*d^5 - 424*a^4*b^5*c^2*d^6 - 896*a^4*b^5*c^3*d^5 - 552*a^4*b^5*c^4*d^4 + 376*a^5*b^4*c^2*d^6 + 784*a^5*b^4*c^3*d^5 + 1096*a^5*b^4*c^4*d^4 + 416*a^5*b^4*c^5*d^3 - 280*a^6*b^3*c^2*d^6 - 560*a^6*b^3*c^3*d^5 - 880*a^6*b^3*c^4*d^4 - 800*a^6*b^3*c^5*d^3 - 176*a^6*b^3*c^6*d^2 + 136*a^7*b^2*c^2*d^6 + 336*a^7*b^2*c^3*d^5 + 464*a^7*b^2*c^4*d^4 + 576*a^7*b^2*c^5*d^3 + 304*a^7*b^2*c^6*d^2 + 64*a*b^8*c*d^7 - 8*a^8*b*c*d^7 - 32*a^8*b*c^7*d))/a^6 - ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*((8*(4*a^13*c^4 - 8*a^12*b*c^4 - 2*a^12*b*d^4 + 8*a^13*c*d^3 + 16*a^13*c^3*d + 4*a^11*b^2*c^4 - 4*a^8*b^5*d^4 + 6*a^9*b^4*d^4 - 2*a^10*b^3*d^4 + 2*a^11*b^2*d^4 + 16*a^9*b^4*c*d^3 - 24*a^10*b^3*c*d^3 + 8*a^11*b^2*c*d^3 + 16*a^11*b^2*c^3*d - 24*a^12*b*c^2*d^2 - 24*a^10*b^3*c^2*d^2 + 48*a^11*b^2*c^2*d^2 - 8*a^12*b*c*d^3 - 32*a^12*b*c^3*d))/a^9 - (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*(a*c - b*d)^4)/(a^6 - a^4*b^2)))*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^4*2i)/(f*(a^6 - a^4*b^2))","B"
10,1,6735,170,9.929971,"\text{Not used}","int((c + d/cos(e + f*x))^3/(a + b*cos(e + f*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,d^3-2\,b\,d^3+6\,a\,c\,d^2\right)}{a^2}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(a\,d^3+2\,b\,d^3-6\,a\,c\,d^2\right)}{a^2}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}+\frac{\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^7}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^3}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)\,1{}\mathrm{i}}{a^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}-\frac{\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^7}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^3}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)\,1{}\mathrm{i}}{a^3}}{\frac{16\,\left(-12\,a^8\,c^8\,d+36\,a^8\,c^7\,d^2-2\,a^8\,c^6\,d^3+12\,a^8\,c^5\,d^4+a^8\,c^3\,d^6+12\,a^7\,b\,c^8\,d+12\,a^7\,b\,c^7\,d^2-178\,a^7\,b\,c^6\,d^3-12\,a^7\,b\,c^5\,d^4-48\,a^7\,b\,c^4\,d^5-2\,a^7\,b\,c^3\,d^6-3\,a^7\,b\,c^2\,d^7-48\,a^6\,b^2\,c^7\,d^2+104\,a^6\,b^2\,c^6\,d^3+384\,a^6\,b^2\,c^5\,d^4+66\,a^6\,b^2\,c^4\,d^5+77\,a^6\,b^2\,c^3\,d^6+6\,a^6\,b^2\,c^2\,d^7+3\,a^6\,b^2\,c\,d^8+76\,a^5\,b^3\,c^6\,d^3-324\,a^5\,b^3\,c^5\,d^4-474\,a^5\,b^3\,c^4\,d^5-112\,a^5\,b^3\,c^3\,d^6-63\,a^5\,b^3\,c^2\,d^7-6\,a^5\,b^3\,c\,d^8-a^5\,b^3\,d^9-60\,a^4\,b^4\,c^5\,d^4+432\,a^4\,b^4\,c^4\,d^5+364\,a^4\,b^4\,c^3\,d^6+90\,a^4\,b^4\,c^2\,d^7+27\,a^4\,b^4\,c\,d^8+2\,a^4\,b^4\,d^9+24\,a^3\,b^5\,c^4\,d^5-324\,a^3\,b^5\,c^3\,d^6-174\,a^3\,b^5\,c^2\,d^7-36\,a^3\,b^5\,c\,d^8-5\,a^3\,b^5\,d^9-4\,a^2\,b^6\,c^3\,d^6+144\,a^2\,b^6\,c^2\,d^7+48\,a^2\,b^6\,c\,d^8+6\,a^2\,b^6\,d^9-36\,a\,b^7\,c\,d^8-6\,a\,b^7\,d^9+4\,b^8\,d^9\right)}{a^6}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}+\frac{\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^7}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^3}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}-\frac{\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^7}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^3}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)}{a^3}}\right)\,\left(a^2\,\left(3\,c^2\,d+\frac{d^3}{2}\right)+b^2\,d^3-3\,a\,b\,c\,d^2\right)\,2{}\mathrm{i}}{a^3\,f}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}}{\frac{16\,\left(-12\,a^8\,c^8\,d+36\,a^8\,c^7\,d^2-2\,a^8\,c^6\,d^3+12\,a^8\,c^5\,d^4+a^8\,c^3\,d^6+12\,a^7\,b\,c^8\,d+12\,a^7\,b\,c^7\,d^2-178\,a^7\,b\,c^6\,d^3-12\,a^7\,b\,c^5\,d^4-48\,a^7\,b\,c^4\,d^5-2\,a^7\,b\,c^3\,d^6-3\,a^7\,b\,c^2\,d^7-48\,a^6\,b^2\,c^7\,d^2+104\,a^6\,b^2\,c^6\,d^3+384\,a^6\,b^2\,c^5\,d^4+66\,a^6\,b^2\,c^4\,d^5+77\,a^6\,b^2\,c^3\,d^6+6\,a^6\,b^2\,c^2\,d^7+3\,a^6\,b^2\,c\,d^8+76\,a^5\,b^3\,c^6\,d^3-324\,a^5\,b^3\,c^5\,d^4-474\,a^5\,b^3\,c^4\,d^5-112\,a^5\,b^3\,c^3\,d^6-63\,a^5\,b^3\,c^2\,d^7-6\,a^5\,b^3\,c\,d^8-a^5\,b^3\,d^9-60\,a^4\,b^4\,c^5\,d^4+432\,a^4\,b^4\,c^4\,d^5+364\,a^4\,b^4\,c^3\,d^6+90\,a^4\,b^4\,c^2\,d^7+27\,a^4\,b^4\,c\,d^8+2\,a^4\,b^4\,d^9+24\,a^3\,b^5\,c^4\,d^5-324\,a^3\,b^5\,c^3\,d^6-174\,a^3\,b^5\,c^2\,d^7-36\,a^3\,b^5\,c\,d^8-5\,a^3\,b^5\,d^9-4\,a^2\,b^6\,c^3\,d^6+144\,a^2\,b^6\,c^2\,d^7+48\,a^2\,b^6\,c\,d^8+6\,a^2\,b^6\,d^9-36\,a\,b^7\,c\,d^8-6\,a\,b^7\,d^9+4\,b^8\,d^9\right)}{a^6}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,a^7\,c^6+36\,a^7\,c^4\,d^2+12\,a^7\,c^2\,d^4+a^7\,d^6-4\,a^6\,b\,c^6-24\,a^6\,b\,c^5\,d-108\,a^6\,b\,c^4\,d^2-72\,a^6\,b\,c^3\,d^3-36\,a^6\,b\,c^2\,d^4-12\,a^6\,b\,c\,d^5-3\,a^6\,b\,d^6+24\,a^5\,b^2\,c^5\,d+168\,a^5\,b^2\,c^4\,d^2+216\,a^5\,b^2\,c^3\,d^3+96\,a^5\,b^2\,c^2\,d^4+36\,a^5\,b^2\,c\,d^5+7\,a^5\,b^2\,d^6-96\,a^4\,b^3\,c^4\,d^2-296\,a^4\,b^3\,c^3\,d^3-192\,a^4\,b^3\,c^2\,d^4-60\,a^4\,b^3\,c\,d^5-13\,a^4\,b^3\,d^6+152\,a^3\,b^4\,c^3\,d^3+240\,a^3\,b^4\,c^2\,d^4+84\,a^3\,b^4\,c\,d^5+16\,a^3\,b^4\,d^6-120\,a^2\,b^5\,c^2\,d^4-96\,a^2\,b^5\,c\,d^5-16\,a^2\,b^5\,d^6+48\,a\,b^6\,c\,d^5+16\,a\,b^6\,d^6-8\,b^7\,d^6\right)}{a^4}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(\frac{8\,\left(4\,a^{10}\,c^3+12\,a^{10}\,c^2\,d+2\,a^{10}\,d^3-8\,a^9\,b\,c^3-24\,a^9\,b\,c^2\,d-12\,a^9\,b\,c\,d^2-2\,a^9\,b\,d^3+4\,a^8\,b^2\,c^3+12\,a^8\,b^2\,c^2\,d+24\,a^8\,b^2\,c\,d^2+2\,a^8\,b^2\,d^3-12\,a^7\,b^3\,c\,d^2-6\,a^7\,b^3\,d^3+4\,a^6\,b^4\,d^3\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^3\,2{}\mathrm{i}}{f\,\left(a^5-a^3\,b^2\right)}","Not used",1,"((tan(e/2 + (f*x)/2)*(a*d^3 - 2*b*d^3 + 6*a*c*d^2))/a^2 + (tan(e/2 + (f*x)/2)^3*(a*d^3 + 2*b*d^3 - 6*a*c*d^2))/a^2)/(f*(tan(e/2 + (f*x)/2)^4 - 2*tan(e/2 + (f*x)/2)^2 + 1)) + (atan(((((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 + (((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 + (8*tan(e/2 + (f*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^7)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^3)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2)*1i)/a^3 + (((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 - (((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 - (8*tan(e/2 + (f*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^7)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^3)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2)*1i)/a^3)/((16*(4*b^8*d^9 - 6*a*b^7*d^9 - 12*a^8*c^8*d + 6*a^2*b^6*d^9 - 5*a^3*b^5*d^9 + 2*a^4*b^4*d^9 - a^5*b^3*d^9 + a^8*c^3*d^6 + 12*a^8*c^5*d^4 - 2*a^8*c^6*d^3 + 36*a^8*c^7*d^2 + 48*a^2*b^6*c*d^8 - 36*a^3*b^5*c*d^8 + 27*a^4*b^4*c*d^8 - 6*a^5*b^3*c*d^8 + 3*a^6*b^2*c*d^8 - 3*a^7*b*c^2*d^7 - 2*a^7*b*c^3*d^6 - 48*a^7*b*c^4*d^5 - 12*a^7*b*c^5*d^4 - 178*a^7*b*c^6*d^3 + 12*a^7*b*c^7*d^2 + 144*a^2*b^6*c^2*d^7 - 4*a^2*b^6*c^3*d^6 - 174*a^3*b^5*c^2*d^7 - 324*a^3*b^5*c^3*d^6 + 24*a^3*b^5*c^4*d^5 + 90*a^4*b^4*c^2*d^7 + 364*a^4*b^4*c^3*d^6 + 432*a^4*b^4*c^4*d^5 - 60*a^4*b^4*c^5*d^4 - 63*a^5*b^3*c^2*d^7 - 112*a^5*b^3*c^3*d^6 - 474*a^5*b^3*c^4*d^5 - 324*a^5*b^3*c^5*d^4 + 76*a^5*b^3*c^6*d^3 + 6*a^6*b^2*c^2*d^7 + 77*a^6*b^2*c^3*d^6 + 66*a^6*b^2*c^4*d^5 + 384*a^6*b^2*c^5*d^4 + 104*a^6*b^2*c^6*d^3 - 48*a^6*b^2*c^7*d^2 - 36*a*b^7*c*d^8 + 12*a^7*b*c^8*d))/a^6 - (((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 + (((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 + (8*tan(e/2 + (f*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^7)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^3)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^3 + (((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 - (((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 - (8*tan(e/2 + (f*x)/2)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^7)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^3)*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2))/a^3))*(a^2*(3*c^2*d + d^3/2) + b^2*d^3 - 3*a*b*c*d^2)*2i)/(a^3*f) + (atan((((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 + ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 + (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*1i)/(a^5 - a^3*b^2) + ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 - ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 - (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*1i)/(a^5 - a^3*b^2))/((16*(4*b^8*d^9 - 6*a*b^7*d^9 - 12*a^8*c^8*d + 6*a^2*b^6*d^9 - 5*a^3*b^5*d^9 + 2*a^4*b^4*d^9 - a^5*b^3*d^9 + a^8*c^3*d^6 + 12*a^8*c^5*d^4 - 2*a^8*c^6*d^3 + 36*a^8*c^7*d^2 + 48*a^2*b^6*c*d^8 - 36*a^3*b^5*c*d^8 + 27*a^4*b^4*c*d^8 - 6*a^5*b^3*c*d^8 + 3*a^6*b^2*c*d^8 - 3*a^7*b*c^2*d^7 - 2*a^7*b*c^3*d^6 - 48*a^7*b*c^4*d^5 - 12*a^7*b*c^5*d^4 - 178*a^7*b*c^6*d^3 + 12*a^7*b*c^7*d^2 + 144*a^2*b^6*c^2*d^7 - 4*a^2*b^6*c^3*d^6 - 174*a^3*b^5*c^2*d^7 - 324*a^3*b^5*c^3*d^6 + 24*a^3*b^5*c^4*d^5 + 90*a^4*b^4*c^2*d^7 + 364*a^4*b^4*c^3*d^6 + 432*a^4*b^4*c^4*d^5 - 60*a^4*b^4*c^5*d^4 - 63*a^5*b^3*c^2*d^7 - 112*a^5*b^3*c^3*d^6 - 474*a^5*b^3*c^4*d^5 - 324*a^5*b^3*c^5*d^4 + 76*a^5*b^3*c^6*d^3 + 6*a^6*b^2*c^2*d^7 + 77*a^6*b^2*c^3*d^6 + 66*a^6*b^2*c^4*d^5 + 384*a^6*b^2*c^5*d^4 + 104*a^6*b^2*c^6*d^3 - 48*a^6*b^2*c^7*d^2 - 36*a*b^7*c*d^8 + 12*a^7*b*c^8*d))/a^6 - ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 + ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 + (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2) + ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*tan(e/2 + (f*x)/2)*(4*a^7*c^6 + a^7*d^6 - 8*b^7*d^6 - 4*a^6*b*c^6 + 16*a*b^6*d^6 - 3*a^6*b*d^6 - 16*a^2*b^5*d^6 + 16*a^3*b^4*d^6 - 13*a^4*b^3*d^6 + 7*a^5*b^2*d^6 + 12*a^7*c^2*d^4 + 36*a^7*c^4*d^2 - 96*a^2*b^5*c*d^5 + 84*a^3*b^4*c*d^5 - 60*a^4*b^3*c*d^5 + 36*a^5*b^2*c*d^5 + 24*a^5*b^2*c^5*d - 36*a^6*b*c^2*d^4 - 72*a^6*b*c^3*d^3 - 108*a^6*b*c^4*d^2 - 120*a^2*b^5*c^2*d^4 + 240*a^3*b^4*c^2*d^4 + 152*a^3*b^4*c^3*d^3 - 192*a^4*b^3*c^2*d^4 - 296*a^4*b^3*c^3*d^3 - 96*a^4*b^3*c^4*d^2 + 96*a^5*b^2*c^2*d^4 + 216*a^5*b^2*c^3*d^3 + 168*a^5*b^2*c^4*d^2 + 48*a*b^6*c*d^5 - 12*a^6*b*c*d^5 - 24*a^6*b*c^5*d))/a^4 - ((-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*((8*(4*a^10*c^3 + 2*a^10*d^3 - 8*a^9*b*c^3 - 2*a^9*b*d^3 + 12*a^10*c^2*d + 4*a^8*b^2*c^3 + 4*a^6*b^4*d^3 - 6*a^7*b^3*d^3 + 2*a^8*b^2*d^3 - 12*a^7*b^3*c*d^2 + 24*a^8*b^2*c*d^2 + 12*a^8*b^2*c^2*d - 12*a^9*b*c*d^2 - 24*a^9*b*c^2*d))/a^6 - (8*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2)))/(a^5 - a^3*b^2)))*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^3*2i)/(f*(a^5 - a^3*b^2))","B"
11,1,3577,103,7.465286,"\text{Not used}","int((c + d/cos(e + f*x))^2/(a + b*cos(e + f*x)),x)","\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^2\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,{\left(a\,c-b\,d\right)}^2}{a^4-a^2\,b^2}\right)\,{\left(a\,c-b\,d\right)}^2\,1{}\mathrm{i}}{a^4-a^2\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^2\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,{\left(a\,c-b\,d\right)}^2}{a^4-a^2\,b^2}\right)\,{\left(a\,c-b\,d\right)}^2\,1{}\mathrm{i}}{a^4-a^2\,b^2}}{\frac{64\,\left(-2\,a^5\,c^5\,d+4\,a^5\,c^4\,d^2+2\,a^4\,b\,c^5\,d+a^4\,b\,c^4\,d^2-12\,a^4\,b\,c^3\,d^3-5\,a^3\,b^2\,c^4\,d^2+8\,a^3\,b^2\,c^3\,d^3+13\,a^3\,b^2\,c^2\,d^4+4\,a^2\,b^3\,c^3\,d^3-12\,a^2\,b^3\,c^2\,d^4-6\,a^2\,b^3\,c\,d^5-a\,b^4\,c^2\,d^4+6\,a\,b^4\,c\,d^5+a\,b^4\,d^6-b^5\,d^6\right)}{a^3}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^2\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,{\left(a\,c-b\,d\right)}^2}{a^4-a^2\,b^2}\right)\,{\left(a\,c-b\,d\right)}^2}{a^4-a^2\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^2\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,{\left(a\,c-b\,d\right)}^2}{a^4-a^2\,b^2}\right)\,{\left(a\,c-b\,d\right)}^2}{a^4-a^2\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,{\left(a\,c-b\,d\right)}^2\,2{}\mathrm{i}}{f\,\left(a^4-a^2\,b^2\right)}-\frac{2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{a\,f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}+\frac{d\,\mathrm{atan}\left(\frac{\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}+\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}+\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a\,c-b\,d\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}-\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}-\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a\,c-b\,d\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{\frac{64\,\left(-2\,a^5\,c^5\,d+4\,a^5\,c^4\,d^2+2\,a^4\,b\,c^5\,d+a^4\,b\,c^4\,d^2-12\,a^4\,b\,c^3\,d^3-5\,a^3\,b^2\,c^4\,d^2+8\,a^3\,b^2\,c^3\,d^3+13\,a^3\,b^2\,c^2\,d^4+4\,a^2\,b^3\,c^3\,d^3-12\,a^2\,b^3\,c^2\,d^4-6\,a^2\,b^3\,c\,d^5-a\,b^4\,c^2\,d^4+6\,a\,b^4\,c\,d^5+a\,b^4\,d^6-b^5\,d^6\right)}{a^3}-\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}+\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}+\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a\,c-b\,d\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)}{a^2}+\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^4+4\,a^5\,c^2\,d^2-a^4\,b\,c^4-4\,a^4\,b\,c^3\,d-12\,a^4\,b\,c^2\,d^2-4\,a^4\,b\,c\,d^3+4\,a^3\,b^2\,c^3\,d+18\,a^3\,b^2\,c^2\,d^2+12\,a^3\,b^2\,c\,d^3+a^3\,b^2\,d^4-10\,a^2\,b^3\,c^2\,d^2-16\,a^2\,b^3\,c\,d^3-3\,a^2\,b^3\,d^4+8\,a\,b^4\,c\,d^3+4\,a\,b^4\,d^4-2\,b^5\,d^4\right)}{a^2}-\frac{d\,\left(2\,a\,c-b\,d\right)\,\left(\frac{32\,\left(a^7\,c^2+2\,a^7\,c\,d-2\,a^6\,b\,c^2-4\,a^6\,b\,c\,d-a^6\,b\,d^2+a^5\,b^2\,c^2+2\,a^5\,b^2\,c\,d+2\,a^5\,b^2\,d^2-a^4\,b^3\,d^2\right)}{a^3}-\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a\,c-b\,d\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)}{a^2}}\right)\,\left(2\,a\,c-b\,d\right)\,2{}\mathrm{i}}{a^2\,f}","Not used",1,"(atan((((-(a + b)*(a - b))^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 + ((-(a + b)*(a - b))^(1/2)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 + (32*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^2*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(a*c - b*d)^2)/(a^4 - a^2*b^2))*(a*c - b*d)^2*1i)/(a^4 - a^2*b^2) + ((-(a + b)*(a - b))^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 - ((-(a + b)*(a - b))^(1/2)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 - (32*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^2*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(a*c - b*d)^2)/(a^4 - a^2*b^2))*(a*c - b*d)^2*1i)/(a^4 - a^2*b^2))/((64*(a*b^4*d^6 - b^5*d^6 - 2*a^5*c^5*d + 4*a^5*c^4*d^2 - a*b^4*c^2*d^4 - 6*a^2*b^3*c*d^5 - 12*a^4*b*c^3*d^3 + a^4*b*c^4*d^2 - 12*a^2*b^3*c^2*d^4 + 4*a^2*b^3*c^3*d^3 + 13*a^3*b^2*c^2*d^4 + 8*a^3*b^2*c^3*d^3 - 5*a^3*b^2*c^4*d^2 + 6*a*b^4*c*d^5 + 2*a^4*b*c^5*d))/a^3 - ((-(a + b)*(a - b))^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 + ((-(a + b)*(a - b))^(1/2)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 + (32*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^2*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(a*c - b*d)^2)/(a^4 - a^2*b^2))*(a*c - b*d)^2)/(a^4 - a^2*b^2) + ((-(a + b)*(a - b))^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 - ((-(a + b)*(a - b))^(1/2)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 - (32*tan(e/2 + (f*x)/2)*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^2*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(a*c - b*d)^2)/(a^4 - a^2*b^2))*(a*c - b*d)^2)/(a^4 - a^2*b^2)))*(-(a + b)*(a - b))^(1/2)*(a*c - b*d)^2*2i)/(f*(a^4 - a^2*b^2)) - (2*d^2*tan(e/2 + (f*x)/2))/(a*f*(tan(e/2 + (f*x)/2)^2 - 1)) + (d*atan(((d*(2*a*c - b*d)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 + (d*(2*a*c - b*d)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 + (32*d*tan(e/2 + (f*x)/2)*(2*a*c - b*d)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2)*1i)/a^2 + (d*(2*a*c - b*d)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 - (d*(2*a*c - b*d)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 - (32*d*tan(e/2 + (f*x)/2)*(2*a*c - b*d)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2)*1i)/a^2)/((64*(a*b^4*d^6 - b^5*d^6 - 2*a^5*c^5*d + 4*a^5*c^4*d^2 - a*b^4*c^2*d^4 - 6*a^2*b^3*c*d^5 - 12*a^4*b*c^3*d^3 + a^4*b*c^4*d^2 - 12*a^2*b^3*c^2*d^4 + 4*a^2*b^3*c^3*d^3 + 13*a^3*b^2*c^2*d^4 + 8*a^3*b^2*c^3*d^3 - 5*a^3*b^2*c^4*d^2 + 6*a*b^4*c*d^5 + 2*a^4*b*c^5*d))/a^3 - (d*(2*a*c - b*d)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 + (d*(2*a*c - b*d)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 + (32*d*tan(e/2 + (f*x)/2)*(2*a*c - b*d)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2))/a^2 + (d*(2*a*c - b*d)*((32*tan(e/2 + (f*x)/2)*(a^5*c^4 - 2*b^5*d^4 - a^4*b*c^4 + 4*a*b^4*d^4 - 3*a^2*b^3*d^4 + a^3*b^2*d^4 + 4*a^5*c^2*d^2 - 16*a^2*b^3*c*d^3 + 12*a^3*b^2*c*d^3 + 4*a^3*b^2*c^3*d - 12*a^4*b*c^2*d^2 - 10*a^2*b^3*c^2*d^2 + 18*a^3*b^2*c^2*d^2 + 8*a*b^4*c*d^3 - 4*a^4*b*c*d^3 - 4*a^4*b*c^3*d))/a^2 - (d*(2*a*c - b*d)*((32*(a^7*c^2 - 2*a^6*b*c^2 - a^6*b*d^2 + a^5*b^2*c^2 - a^4*b^3*d^2 + 2*a^5*b^2*d^2 + 2*a^7*c*d - 4*a^6*b*c*d + 2*a^5*b^2*c*d))/a^3 - (32*d*tan(e/2 + (f*x)/2)*(2*a*c - b*d)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2))/a^2))*(2*a*c - b*d)*2i)/(a^2*f)","B"
12,1,345,76,3.552594,"\text{Not used}","int((c + d/cos(e + f*x))/(a + b*cos(e + f*x)),x)","\frac{2\,d\,\mathrm{atanh}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{a\,f}-\frac{b\,\left(d\,\ln\left(\frac{a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}-d\,\ln\left(\frac{b\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}\right)+a\,c\,\ln\left(\frac{b\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-a\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}-a\,c\,\ln\left(\frac{a\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+b\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}}{a\,f\,\left(a^2-b^2\right)}","Not used",1,"(2*d*atanh(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(a*f) - (b*(d*log((a*cos(e/2 + (f*x)/2) + b*cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(-(a + b)*(a - b))^(1/2) - d*log((b*sin(e/2 + (f*x)/2) - a*sin(e/2 + (f*x)/2) + cos(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(b^2 - a^2)^(1/2)) + a*c*log((b*sin(e/2 + (f*x)/2) - a*sin(e/2 + (f*x)/2) + cos(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(b^2 - a^2)^(1/2) - a*c*log((a*cos(e/2 + (f*x)/2) + b*cos(e/2 + (f*x)/2) - sin(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2))/cos(e/2 + (f*x)/2))*(-(a + b)*(a - b))^(1/2))/(a*f*(a^2 - b^2))","B"
13,1,2665,121,4.788539,"\text{Not used}","int(1/((c + d/cos(e + f*x))*(a + b*cos(e + f*x))),x)","\frac{a\,c^2\,\mathrm{atan}\left(\frac{a^5\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+a^5\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-b^5\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^2\,b^3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^3\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^2\,b^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^3\,b^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}-a^3\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-a^5\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a^2\,b\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+a^4\,b\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a\,b^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^2\,b^3\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a^3\,b^2\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^2\,b\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-a^4\,b\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^6\,c^2-2\,a^4\,b^2\,c^2-a^4\,b^2\,d^2+a^2\,b^4\,c^2+2\,a^2\,b^4\,d^2-b^6\,d^2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(a^3\,c^3-a^3\,c\,d^2-a^2\,b\,c^2\,d+a^2\,b\,d^3-a\,b^2\,c^3+a\,b^2\,c\,d^2+b^3\,c^2\,d-b^3\,d^3\right)}-\frac{a\,d^2\,\mathrm{atan}\left(\frac{a^5\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+a^5\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-b^5\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^2\,b^3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^3\,b^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^2\,b^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^3\,b^2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}-a^3\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-a^5\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a^2\,b\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+a^4\,b\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a\,b^4\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+a^2\,b^3\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+a^3\,b^2\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^2\,b\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-a^4\,b\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^6\,c^2-2\,a^4\,b^2\,c^2-a^4\,b^2\,d^2+a^2\,b^4\,c^2+2\,a^2\,b^4\,d^2-b^6\,d^2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(a^3\,c^3-a^3\,c\,d^2-a^2\,b\,c^2\,d+a^2\,b\,d^3-a\,b^2\,c^3+a\,b^2\,c\,d^2+b^3\,c^2\,d-b^3\,d^3\right)}-\frac{a^2\,d\,\mathrm{atan}\left(\frac{-a^2\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}+a^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}+b^2\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-a^2\,c^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,3{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-b^2\,c^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-b^2\,c^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-a\,b\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}-a\,b\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}+a^2\,c^4\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}-a\,b\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}-a\,b\,c\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}}{a^2\,c^6-2\,a^2\,c^4\,d^2+a^2\,c^2\,d^4-b^2\,c^4\,d^2+2\,b^2\,c^2\,d^4-b^2\,d^6}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}}{f\,\left(a^3\,c^3-a^3\,c\,d^2-a^2\,b\,c^2\,d+a^2\,b\,d^3-a\,b^2\,c^3+a\,b^2\,c\,d^2+b^3\,c^2\,d-b^3\,d^3\right)}+\frac{b^2\,d\,\mathrm{atan}\left(\frac{-a^2\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}+a^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}+a^2\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}+b^2\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-a^2\,c^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,3{}\mathrm{i}+a^2\,c^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-b^2\,c^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-b^2\,c^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}-a\,b\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}-a\,b\,d^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}+a^2\,c^4\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}+b^2\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}+b^2\,c\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,1{}\mathrm{i}+a\,b\,c^2\,d^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}+a\,b\,c^3\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}-a\,b\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(c^2-d^2\right)}^{3/2}\,2{}\mathrm{i}-a\,b\,c\,d^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}}{a^2\,c^6-2\,a^2\,c^4\,d^2+a^2\,c^2\,d^4-b^2\,c^4\,d^2+2\,b^2\,c^2\,d^4-b^2\,d^6}\right)\,\sqrt{c^2-d^2}\,2{}\mathrm{i}}{f\,\left(a^3\,c^3-a^3\,c\,d^2-a^2\,b\,c^2\,d+a^2\,b\,d^3-a\,b^2\,c^3+a\,b^2\,c\,d^2+b^3\,c^2\,d-b^3\,d^3\right)}","Not used",1,"(a*c^2*atan((a^5*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^3*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i + a^5*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i - b^5*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^2*b^3*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^3*b^2*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^2*b^3*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^3*b^2*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*3i - a^3*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i - a^5*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i + a^2*b*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i + a^4*b*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a*b^4*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^2*b^3*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i + a^3*b^2*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i - a^2*b*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i - a^4*b*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i)/(a^6*c^2 - b^6*d^2 + a^2*b^4*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*d^2 - a^4*b^2*d^2))*(b^2 - a^2)^(1/2)*2i)/(f*(a^3*c^3 - b^3*d^3 - a*b^2*c^3 + a^2*b*d^3 - a^3*c*d^2 + b^3*c^2*d + a*b^2*c*d^2 - a^2*b*c^2*d)) - (a*d^2*atan((a^5*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^3*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i + a^5*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i - b^5*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^2*b^3*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^3*b^2*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^2*b^3*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i - a^3*b^2*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*3i - a^3*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i - a^5*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i + a^2*b*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i + a^4*b*c^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a*b^4*d^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*1i + a^2*b^3*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i + a^3*b^2*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i - a^2*b*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(3/2)*2i - a^4*b*c*d*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*2i)/(a^6*c^2 - b^6*d^2 + a^2*b^4*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*d^2 - a^4*b^2*d^2))*(b^2 - a^2)^(1/2)*2i)/(f*(a^3*c^3 - b^3*d^3 - a*b^2*c^3 + a^2*b*d^3 - a^3*c*d^2 + b^3*c^2*d + a*b^2*c*d^2 - a^2*b*c^2*d)) - (a^2*d*atan((a^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i - a^2*c^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i + a^2*d^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i + b^2*d^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - a^2*c^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*3i + a^2*c^3*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - b^2*c^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - b^2*c^3*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - a*b*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i - a*b*d^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i + a^2*c^4*d*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i + b^2*c*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i + b^2*c*d^4*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i + a*b*c^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i + a*b*c^3*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i - a*b*c*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i - a*b*c*d^4*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i)/(a^2*c^6 - b^2*d^6 + a^2*c^2*d^4 - 2*a^2*c^4*d^2 + 2*b^2*c^2*d^4 - b^2*c^4*d^2))*(c^2 - d^2)^(1/2)*2i)/(f*(a^3*c^3 - b^3*d^3 - a*b^2*c^3 + a^2*b*d^3 - a^3*c*d^2 + b^3*c^2*d + a*b^2*c*d^2 - a^2*b*c^2*d)) + (b^2*d*atan((a^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i - a^2*c^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i + a^2*d^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i + b^2*d^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - a^2*c^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*3i + a^2*c^3*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - b^2*c^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - b^2*c^3*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i - a*b*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i - a*b*d^5*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i + a^2*c^4*d*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i + b^2*c*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i + b^2*c*d^4*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*1i + a*b*c^2*d^3*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i + a*b*c^3*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i - a*b*c*d^2*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(3/2)*2i - a*b*c*d^4*tan(e/2 + (f*x)/2)*(c^2 - d^2)^(1/2)*2i)/(a^2*c^6 - b^2*d^6 + a^2*c^2*d^4 - 2*a^2*c^4*d^2 + 2*b^2*c^2*d^4 - b^2*c^4*d^2))*(c^2 - d^2)^(1/2)*2i)/(f*(a^3*c^3 - b^3*d^3 - a*b^2*c^3 + a^2*b*d^3 - a^3*c*d^2 + b^3*c^2*d + a*b^2*c*d^2 - a^2*b*c^2*d))","B"
14,1,20827,187,15.227753,"\text{Not used}","int(1/((c + d/cos(e + f*x))^2*(a + b*cos(e + f*x))),x)","\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}+\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2\right)\,\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)}\right)}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}\right)\,1{}\mathrm{i}}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}+\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}-\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2\right)\,\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)}\right)}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}\right)\,1{}\mathrm{i}}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}}{\frac{64\,\left(2\,a^5\,c^4\,d+2\,a^5\,c^3\,d^2-3\,a^5\,c^2\,d^3-a^5\,c\,d^4+a^5\,d^5-2\,a^4\,b\,c^4\,d-5\,a^4\,b\,c^3\,d^2+2\,a^4\,b\,c^2\,d^3+3\,a^4\,b\,c\,d^4-a^4\,b\,d^5+3\,a^3\,b^2\,c^3\,d^2+2\,a^3\,b^2\,c^2\,d^3-2\,a^3\,b^2\,c\,d^4-a^2\,b^3\,c^2\,d^3\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}+\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}+\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2\right)\,\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)}\right)}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}\right)}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}-\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}-\frac{a^2\,\sqrt{b^2-a^2}\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2\right)\,\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)}\right)}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}\right)}{a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2}}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{f\,\left(a^4\,c^2-2\,a^3\,b\,c\,d-a^2\,b^2\,c^2+a^2\,b^2\,d^2+2\,a\,b^3\,c\,d-b^4\,d^2\right)}+\frac{2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{f\,\left(c+d\right)\,\left(\left(d-c\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+c+d\right)\,\left(a\,c^2+b\,d^2-a\,c\,d-b\,c\,d\right)}+\frac{d\,\mathrm{atan}\left(\frac{\frac{d\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}+\frac{d\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}+\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)\,\left(a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8\right)}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,1{}\mathrm{i}}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}+\frac{d\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}-\frac{d\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}-\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)\,\left(a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8\right)}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,1{}\mathrm{i}}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}}{\frac{64\,\left(2\,a^5\,c^4\,d+2\,a^5\,c^3\,d^2-3\,a^5\,c^2\,d^3-a^5\,c\,d^4+a^5\,d^5-2\,a^4\,b\,c^4\,d-5\,a^4\,b\,c^3\,d^2+2\,a^4\,b\,c^2\,d^3+3\,a^4\,b\,c\,d^4-a^4\,b\,d^5+3\,a^3\,b^2\,c^3\,d^2+2\,a^3\,b^2\,c^2\,d^3-2\,a^3\,b^2\,c\,d^4-a^2\,b^3\,c^2\,d^3\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}+\frac{d\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}+\frac{d\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}+\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)\,\left(a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8\right)}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}-\frac{d\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^5\,c^6-2\,a^5\,c^5\,d+3\,a^5\,c^4\,d^2+4\,a^5\,c^3\,d^3-5\,a^5\,c^2\,d^4-2\,a^5\,c\,d^5+2\,a^5\,d^6-a^4\,b\,c^6+2\,a^4\,b\,c^5\,d-11\,a^4\,b\,c^4\,d^2-8\,a^4\,b\,c^3\,d^3+13\,a^4\,b\,c^2\,d^4+4\,a^4\,b\,c\,d^5-4\,a^4\,b\,d^6+12\,a^3\,b^2\,c^4\,d^2+12\,a^3\,b^2\,c^3\,d^3-11\,a^3\,b^2\,c^2\,d^4-6\,a^3\,b^2\,c\,d^5+3\,a^3\,b^2\,d^6-4\,a^2\,b^3\,c^4\,d^2-12\,a^2\,b^3\,c^3\,d^3+a^2\,b^3\,c^2\,d^4+6\,a^2\,b^3\,c\,d^5-a^2\,b^3\,d^6+4\,a\,b^4\,c^3\,d^3+3\,a\,b^4\,c^2\,d^4-2\,a\,b^4\,c\,d^5-b^5\,c^2\,d^4\right)}{a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5}-\frac{d\,\left(\frac{32\,\left(-a^7\,c^9+2\,a^7\,c^8\,d+a^7\,c^7\,d^2-3\,a^7\,c^6\,d^3+a^7\,c^4\,d^5+2\,a^6\,b\,c^9+a^6\,b\,c^8\,d-11\,a^6\,b\,c^7\,d^2+a^6\,b\,c^6\,d^3+13\,a^6\,b\,c^5\,d^4-2\,a^6\,b\,c^4\,d^5-4\,a^6\,b\,c^3\,d^6-a^5\,b^2\,c^9-8\,a^5\,b^2\,c^8\,d+9\,a^5\,b^2\,c^7\,d^2+23\,a^5\,b^2\,c^6\,d^3-16\,a^5\,b^2\,c^5\,d^4-21\,a^5\,b^2\,c^4\,d^5+8\,a^5\,b^2\,c^3\,d^6+6\,a^5\,b^2\,c^2\,d^7+5\,a^4\,b^3\,c^8\,d+11\,a^4\,b^3\,c^7\,d^2-27\,a^4\,b^3\,c^6\,d^3-21\,a^4\,b^3\,c^5\,d^4+34\,a^4\,b^3\,c^4\,d^5+14\,a^4\,b^3\,c^3\,d^6-12\,a^4\,b^3\,c^2\,d^7-4\,a^4\,b^3\,c\,d^8-10\,a^3\,b^4\,c^7\,d^2-4\,a^3\,b^4\,c^6\,d^3+33\,a^3\,b^4\,c^5\,d^4+4\,a^3\,b^4\,c^4\,d^5-31\,a^3\,b^4\,c^3\,d^6-a^3\,b^4\,c^2\,d^7+8\,a^3\,b^4\,c\,d^8+a^3\,b^4\,d^9+10\,a^2\,b^5\,c^6\,d^3-4\,a^2\,b^5\,c^5\,d^4-21\,a^2\,b^5\,c^4\,d^5+7\,a^2\,b^5\,c^3\,d^6+13\,a^2\,b^5\,c^2\,d^7-3\,a^2\,b^5\,c\,d^8-2\,a^2\,b^5\,d^9-5\,a\,b^6\,c^5\,d^4+4\,a\,b^6\,c^4\,d^5+7\,a\,b^6\,c^3\,d^6-5\,a\,b^6\,c^2\,d^7-2\,a\,b^6\,c\,d^8+a\,b^6\,d^9+b^7\,c^4\,d^5-b^7\,c^3\,d^6-b^7\,c^2\,d^7+b^7\,c\,d^8\right)}{a^3\,c^6+a^3\,c^5\,d-a^3\,c^4\,d^2-a^3\,c^3\,d^3-3\,a^2\,b\,c^5\,d-3\,a^2\,b\,c^4\,d^2+3\,a^2\,b\,c^3\,d^3+3\,a^2\,b\,c^2\,d^4+3\,a\,b^2\,c^4\,d^2+3\,a\,b^2\,c^3\,d^3-3\,a\,b^2\,c^2\,d^4-3\,a\,b^2\,c\,d^5-b^3\,c^3\,d^3-b^3\,c^2\,d^4+b^3\,c\,d^5+b^3\,d^6}-\frac{32\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,\left(-2\,a^7\,c^9\,d+2\,a^7\,c^8\,d^2+4\,a^7\,c^7\,d^3-4\,a^7\,c^6\,d^4-2\,a^7\,c^5\,d^5+2\,a^7\,c^4\,d^6+2\,a^6\,b\,c^{10}+2\,a^6\,b\,c^9\,d-12\,a^6\,b\,c^7\,d^3-6\,a^6\,b\,c^6\,d^4+18\,a^6\,b\,c^5\,d^5+4\,a^6\,b\,c^4\,d^6-8\,a^6\,b\,c^3\,d^7-4\,a^5\,b^2\,c^{10}-6\,a^5\,b^2\,c^9\,d+2\,a^5\,b^2\,c^8\,d^2+16\,a^5\,b^2\,c^7\,d^3+20\,a^5\,b^2\,c^6\,d^4-14\,a^5\,b^2\,c^5\,d^5-30\,a^5\,b^2\,c^4\,d^6+4\,a^5\,b^2\,c^3\,d^7+12\,a^5\,b^2\,c^2\,d^8+2\,a^4\,b^3\,c^{10}+14\,a^4\,b^3\,c^9\,d-24\,a^4\,b^3\,c^7\,d^3-22\,a^4\,b^3\,c^6\,d^4-2\,a^4\,b^3\,c^5\,d^5+36\,a^4\,b^3\,c^4\,d^6+20\,a^4\,b^3\,c^3\,d^7-16\,a^4\,b^3\,c^2\,d^8-8\,a^4\,b^3\,c\,d^9-8\,a^3\,b^4\,c^9\,d-16\,a^3\,b^4\,c^8\,d^2+20\,a^3\,b^4\,c^7\,d^3+36\,a^3\,b^4\,c^6\,d^4-2\,a^3\,b^4\,c^5\,d^5-22\,a^3\,b^4\,c^4\,d^6-24\,a^3\,b^4\,c^3\,d^7+14\,a^3\,b^4\,c\,d^9+2\,a^3\,b^4\,d^{10}+12\,a^2\,b^5\,c^8\,d^2+4\,a^2\,b^5\,c^7\,d^3-30\,a^2\,b^5\,c^6\,d^4-14\,a^2\,b^5\,c^5\,d^5+20\,a^2\,b^5\,c^4\,d^6+16\,a^2\,b^5\,c^3\,d^7+2\,a^2\,b^5\,c^2\,d^8-6\,a^2\,b^5\,c\,d^9-4\,a^2\,b^5\,d^{10}-8\,a\,b^6\,c^7\,d^3+4\,a\,b^6\,c^6\,d^4+18\,a\,b^6\,c^5\,d^5-6\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7+2\,a\,b^6\,c\,d^9+2\,a\,b^6\,d^{10}+2\,b^7\,c^6\,d^4-2\,b^7\,c^5\,d^5-4\,b^7\,c^4\,d^6+4\,b^7\,c^3\,d^7+2\,b^7\,c^2\,d^8-2\,b^7\,c\,d^9\right)}{\left(a^2\,c^5+a^2\,c^4\,d-a^2\,c^3\,d^2-a^2\,c^2\,d^3-2\,a\,b\,c^4\,d-2\,a\,b\,c^3\,d^2+2\,a\,b\,c^2\,d^3+2\,a\,b\,c\,d^4+b^2\,c^3\,d^2+b^2\,c^2\,d^3-b^2\,c\,d^4-b^2\,d^5\right)\,\left(a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8\right)}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)}{a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8}}\right)\,\sqrt{{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(-2\,a\,c^2+b\,c\,d+a\,d^2\right)\,2{}\mathrm{i}}{f\,\left(a^2\,c^8-3\,a^2\,c^6\,d^2+3\,a^2\,c^4\,d^4-a^2\,c^2\,d^6-2\,a\,b\,c^7\,d+6\,a\,b\,c^5\,d^3-6\,a\,b\,c^3\,d^5+2\,a\,b\,c\,d^7+b^2\,c^6\,d^2-3\,b^2\,c^4\,d^4+3\,b^2\,c^2\,d^6-b^2\,d^8\right)}","Not used",1,"(a^2*atan(((a^2*(b^2 - a^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) + (a^2*(b^2 - a^2)^(1/2)*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) + (32*a^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)*(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2))))/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d))*1i)/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d) + (a^2*(b^2 - a^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) - (a^2*(b^2 - a^2)^(1/2)*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) - (32*a^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)*(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2))))/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d))*1i)/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d))/((64*(a^5*d^5 - a^4*b*d^5 - a^5*c*d^4 + 2*a^5*c^4*d - 3*a^5*c^2*d^3 + 2*a^5*c^3*d^2 - 2*a^3*b^2*c*d^4 + 2*a^4*b*c^2*d^3 - 5*a^4*b*c^3*d^2 - a^2*b^3*c^2*d^3 + 2*a^3*b^2*c^2*d^3 + 3*a^3*b^2*c^3*d^2 + 3*a^4*b*c*d^4 - 2*a^4*b*c^4*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) + (a^2*(b^2 - a^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) + (a^2*(b^2 - a^2)^(1/2)*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) + (32*a^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)*(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2))))/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d) - (a^2*(b^2 - a^2)^(1/2)*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) - (a^2*(b^2 - a^2)^(1/2)*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) - (32*a^2*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)*(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2))))/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))/(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^4*c^2 - b^4*d^2 - a^2*b^2*c^2 + a^2*b^2*d^2 + 2*a*b^3*c*d - 2*a^3*b*c*d)) + (2*d^2*tan(e/2 + (f*x)/2))/(f*(c + d)*(c + d - tan(e/2 + (f*x)/2)^2*(c - d))*(a*c^2 + b*d^2 - a*c*d - b*c*d)) + (d*atan(((d*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) + (d*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) + (32*d*tan(e/2 + (f*x)/2)*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2)*(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3)))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d))/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*1i)/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3) + (d*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) - (d*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) - (32*d*tan(e/2 + (f*x)/2)*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2)*(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3)))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d))/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*1i)/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3))/((64*(a^5*d^5 - a^4*b*d^5 - a^5*c*d^4 + 2*a^5*c^4*d - 3*a^5*c^2*d^3 + 2*a^5*c^3*d^2 - 2*a^3*b^2*c*d^4 + 2*a^4*b*c^2*d^3 - 5*a^4*b*c^3*d^2 - a^2*b^3*c^2*d^3 + 2*a^3*b^2*c^2*d^3 + 3*a^3*b^2*c^3*d^2 + 3*a^4*b*c*d^4 - 2*a^4*b*c^4*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) + (d*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) + (d*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) + (32*d*tan(e/2 + (f*x)/2)*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2)*(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3)))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d))/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d))/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3) - (d*((32*tan(e/2 + (f*x)/2)*(a^5*c^6 + 2*a^5*d^6 - a^4*b*c^6 - 4*a^4*b*d^6 - 2*a^5*c*d^5 - 2*a^5*c^5*d - a^2*b^3*d^6 + 3*a^3*b^2*d^6 - 5*a^5*c^2*d^4 + 4*a^5*c^3*d^3 + 3*a^5*c^4*d^2 - b^5*c^2*d^4 + 3*a*b^4*c^2*d^4 + 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c*d^5 - 6*a^3*b^2*c*d^5 + 13*a^4*b*c^2*d^4 - 8*a^4*b*c^3*d^3 - 11*a^4*b*c^4*d^2 + a^2*b^3*c^2*d^4 - 12*a^2*b^3*c^3*d^3 - 4*a^2*b^3*c^4*d^2 - 11*a^3*b^2*c^2*d^4 + 12*a^3*b^2*c^3*d^3 + 12*a^3*b^2*c^4*d^2 - 2*a*b^4*c*d^5 + 4*a^4*b*c*d^5 + 2*a^4*b*c^5*d))/(a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2) - (d*((32*(2*a^6*b*c^9 - a^7*c^9 + a*b^6*d^9 + 2*a^7*c^8*d + b^7*c*d^8 - a^5*b^2*c^9 - 2*a^2*b^5*d^9 + a^3*b^4*d^9 + a^7*c^4*d^5 - 3*a^7*c^6*d^3 + a^7*c^7*d^2 - b^7*c^2*d^7 - b^7*c^3*d^6 + b^7*c^4*d^5 - 5*a*b^6*c^2*d^7 + 7*a*b^6*c^3*d^6 + 4*a*b^6*c^4*d^5 - 5*a*b^6*c^5*d^4 - 3*a^2*b^5*c*d^8 + 8*a^3*b^4*c*d^8 - 4*a^4*b^3*c*d^8 + 5*a^4*b^3*c^8*d - 8*a^5*b^2*c^8*d - 4*a^6*b*c^3*d^6 - 2*a^6*b*c^4*d^5 + 13*a^6*b*c^5*d^4 + a^6*b*c^6*d^3 - 11*a^6*b*c^7*d^2 + 13*a^2*b^5*c^2*d^7 + 7*a^2*b^5*c^3*d^6 - 21*a^2*b^5*c^4*d^5 - 4*a^2*b^5*c^5*d^4 + 10*a^2*b^5*c^6*d^3 - a^3*b^4*c^2*d^7 - 31*a^3*b^4*c^3*d^6 + 4*a^3*b^4*c^4*d^5 + 33*a^3*b^4*c^5*d^4 - 4*a^3*b^4*c^6*d^3 - 10*a^3*b^4*c^7*d^2 - 12*a^4*b^3*c^2*d^7 + 14*a^4*b^3*c^3*d^6 + 34*a^4*b^3*c^4*d^5 - 21*a^4*b^3*c^5*d^4 - 27*a^4*b^3*c^6*d^3 + 11*a^4*b^3*c^7*d^2 + 6*a^5*b^2*c^2*d^7 + 8*a^5*b^2*c^3*d^6 - 21*a^5*b^2*c^4*d^5 - 16*a^5*b^2*c^5*d^4 + 23*a^5*b^2*c^6*d^3 + 9*a^5*b^2*c^7*d^2 - 2*a*b^6*c*d^8 + a^6*b*c^8*d))/(a^3*c^6 + b^3*d^6 + a^3*c^5*d + b^3*c*d^5 - a^3*c^3*d^3 - a^3*c^4*d^2 - b^3*c^2*d^4 - b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a*b^2*c^3*d^3 + 3*a*b^2*c^4*d^2 + 3*a^2*b*c^2*d^4 + 3*a^2*b*c^3*d^3 - 3*a^2*b*c^4*d^2 - 3*a*b^2*c*d^5 - 3*a^2*b*c^5*d) - (32*d*tan(e/2 + (f*x)/2)*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*(2*a^6*b*c^10 + 2*a*b^6*d^10 - 2*a^7*c^9*d - 2*b^7*c*d^9 + 2*a^4*b^3*c^10 - 4*a^5*b^2*c^10 - 4*a^2*b^5*d^10 + 2*a^3*b^4*d^10 + 2*a^7*c^4*d^6 - 2*a^7*c^5*d^5 - 4*a^7*c^6*d^4 + 4*a^7*c^7*d^3 + 2*a^7*c^8*d^2 + 2*b^7*c^2*d^8 + 4*b^7*c^3*d^7 - 4*b^7*c^4*d^6 - 2*b^7*c^5*d^5 + 2*b^7*c^6*d^4 - 12*a*b^6*c^3*d^7 - 6*a*b^6*c^4*d^6 + 18*a*b^6*c^5*d^5 + 4*a*b^6*c^6*d^4 - 8*a*b^6*c^7*d^3 - 6*a^2*b^5*c*d^9 + 14*a^3*b^4*c*d^9 - 8*a^3*b^4*c^9*d - 8*a^4*b^3*c*d^9 + 14*a^4*b^3*c^9*d - 6*a^5*b^2*c^9*d - 8*a^6*b*c^3*d^7 + 4*a^6*b*c^4*d^6 + 18*a^6*b*c^5*d^5 - 6*a^6*b*c^6*d^4 - 12*a^6*b*c^7*d^3 + 2*a^2*b^5*c^2*d^8 + 16*a^2*b^5*c^3*d^7 + 20*a^2*b^5*c^4*d^6 - 14*a^2*b^5*c^5*d^5 - 30*a^2*b^5*c^6*d^4 + 4*a^2*b^5*c^7*d^3 + 12*a^2*b^5*c^8*d^2 - 24*a^3*b^4*c^3*d^7 - 22*a^3*b^4*c^4*d^6 - 2*a^3*b^4*c^5*d^5 + 36*a^3*b^4*c^6*d^4 + 20*a^3*b^4*c^7*d^3 - 16*a^3*b^4*c^8*d^2 - 16*a^4*b^3*c^2*d^8 + 20*a^4*b^3*c^3*d^7 + 36*a^4*b^3*c^4*d^6 - 2*a^4*b^3*c^5*d^5 - 22*a^4*b^3*c^6*d^4 - 24*a^4*b^3*c^7*d^3 + 12*a^5*b^2*c^2*d^8 + 4*a^5*b^2*c^3*d^7 - 30*a^5*b^2*c^4*d^6 - 14*a^5*b^2*c^5*d^5 + 20*a^5*b^2*c^6*d^4 + 16*a^5*b^2*c^7*d^3 + 2*a^5*b^2*c^8*d^2 + 2*a*b^6*c*d^9 + 2*a^6*b*c^9*d))/((a^2*c^5 - b^2*d^5 + a^2*c^4*d - b^2*c*d^4 - a^2*c^2*d^3 - a^2*c^3*d^2 + b^2*c^2*d^3 + b^2*c^3*d^2 + 2*a*b*c*d^4 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - 2*a*b*c^3*d^2)*(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3)))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d))/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d))/(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3)))*((c + d)^3*(c - d)^3)^(1/2)*(a*d^2 - 2*a*c^2 + b*c*d)*2i)/(f*(a^2*c^8 - b^2*d^8 - a^2*c^2*d^6 + 3*a^2*c^4*d^4 - 3*a^2*c^6*d^2 + 3*b^2*c^2*d^6 - 3*b^2*c^4*d^4 + b^2*c^6*d^2 + 2*a*b*c*d^7 - 2*a*b*c^7*d - 6*a*b*c^3*d^5 + 6*a*b*c^5*d^3))","B"
15,1,52103,458,20.251357,"\text{Not used}","int(1/((c + d/cos(e + f*x))^3*(a + b*cos(e + f*x))),x)","\frac{\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,a\,d^4+b\,d^4-6\,a\,c^2\,d^2-a\,c\,d^3+4\,b\,c\,d^3\right)}{{\left(c+d\right)}^2\,\left(a^2\,c^3-a^2\,c^2\,d-2\,a\,b\,c^2\,d+2\,a\,b\,c\,d^2+b^2\,c\,d^2-b^2\,d^3\right)}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,a\,d^4-b\,d^4-6\,a\,c^2\,d^2+a\,c\,d^3+4\,b\,c\,d^3\right)}{\left(c+d\right)\,\left(a^2\,c^4-2\,a^2\,c^3\,d+a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+4\,a\,b\,c^2\,d^2-2\,a\,b\,c\,d^3+b^2\,c^2\,d^2-2\,b^2\,c\,d^3+b^2\,d^4\right)}}{f\,\left(2\,c\,d-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2-2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(c^2-2\,c\,d+d^2\right)+c^2+d^2\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,c^{10}+8\,a^7\,c^9\,d-24\,a^7\,c^8\,d^2-32\,a^7\,c^7\,d^3+52\,a^7\,c^6\,d^4+48\,a^7\,c^5\,d^5-57\,a^7\,c^4\,d^6-32\,a^7\,c^3\,d^7+32\,a^7\,c^2\,d^8+8\,a^7\,c\,d^9-8\,a^7\,d^{10}+4\,a^6\,b\,c^{10}-8\,a^6\,b\,c^9\,d+96\,a^6\,b\,c^8\,d^2+104\,a^6\,b\,c^7\,d^3-172\,a^6\,b\,c^6\,d^4-108\,a^6\,b\,c^5\,d^5+155\,a^6\,b\,c^4\,d^6+56\,a^6\,b\,c^3\,d^7-72\,a^6\,b\,c^2\,d^8-8\,a^6\,b\,c\,d^9+16\,a^6\,b\,d^{10}-108\,a^5\,b^2\,c^8\,d^2-216\,a^5\,b^2\,c^7\,d^3+120\,a^5\,b^2\,c^6\,d^4+180\,a^5\,b^2\,c^5\,d^5-139\,a^5\,b^2\,c^4\,d^6-72\,a^5\,b^2\,c^3\,d^7+62\,a^5\,b^2\,c^2\,d^8-16\,a^5\,b^2\,d^{10}+36\,a^4\,b^3\,c^8\,d^2+216\,a^4\,b^3\,c^7\,d^3+120\,a^4\,b^3\,c^6\,d^4-156\,a^4\,b^3\,c^5\,d^5+25\,a^4\,b^3\,c^4\,d^6+84\,a^4\,b^3\,c^3\,d^7-26\,a^4\,b^3\,c^2\,d^8+16\,a^4\,b^3\,d^{10}-72\,a^3\,b^4\,c^7\,d^3-180\,a^3\,b^4\,c^6\,d^4-12\,a^3\,b^4\,c^5\,d^5+20\,a^3\,b^4\,c^4\,d^6-60\,a^3\,b^4\,c^3\,d^7+2\,a^3\,b^4\,c^2\,d^8-13\,a^3\,b^4\,d^{10}+60\,a^2\,b^5\,c^6\,d^4+72\,a^2\,b^5\,c^5\,d^5+4\,a^2\,b^5\,c^4\,d^6+36\,a^2\,b^5\,c^3\,d^7+10\,a^2\,b^5\,c^2\,d^8+7\,a^2\,b^5\,d^{10}-24\,a\,b^6\,c^5\,d^5-12\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7-12\,a\,b^6\,c^2\,d^8-3\,a\,b^6\,d^{10}+4\,b^7\,c^4\,d^6+4\,b^7\,c^2\,d^8+b^7\,d^{10}\right)}{a^4\,c^{11}+a^4\,c^{10}\,d-3\,a^4\,c^9\,d^2-3\,a^4\,c^8\,d^3+3\,a^4\,c^7\,d^4+3\,a^4\,c^6\,d^5-a^4\,c^5\,d^6-a^4\,c^4\,d^7-4\,a^3\,b\,c^{10}\,d-4\,a^3\,b\,c^9\,d^2+12\,a^3\,b\,c^8\,d^3+12\,a^3\,b\,c^7\,d^4-12\,a^3\,b\,c^6\,d^5-12\,a^3\,b\,c^5\,d^6+4\,a^3\,b\,c^4\,d^7+4\,a^3\,b\,c^3\,d^8+6\,a^2\,b^2\,c^9\,d^2+6\,a^2\,b^2\,c^8\,d^3-18\,a^2\,b^2\,c^7\,d^4-18\,a^2\,b^2\,c^6\,d^5+18\,a^2\,b^2\,c^5\,d^6+18\,a^2\,b^2\,c^4\,d^7-6\,a^2\,b^2\,c^3\,d^8-6\,a^2\,b^2\,c^2\,d^9-4\,a\,b^3\,c^8\,d^3-4\,a\,b^3\,c^7\,d^4+12\,a\,b^3\,c^6\,d^5+12\,a\,b^3\,c^5\,d^6-12\,a\,b^3\,c^4\,d^7-12\,a\,b^3\,c^3\,d^8+4\,a\,b^3\,c^2\,d^9+4\,a\,b^3\,c\,d^{10}+b^4\,c^7\,d^4+b^4\,c^6\,d^5-3\,b^4\,c^5\,d^6-3\,b^4\,c^4\,d^7+3\,b^4\,c^3\,d^8+3\,b^4\,c^2\,d^9-b^4\,c\,d^{10}-b^4\,d^{11}}+\frac{a^3\,\sqrt{b^2-a^2}\,\left(\frac{8\,\left(-4\,a^{10}\,c^{15}+12\,a^{10}\,c^{14}\,d+8\,a^{10}\,c^{13}\,d^2-34\,a^{10}\,c^{12}\,d^3-6\,a^{10}\,c^{11}\,d^4+36\,a^{10}\,c^{10}\,d^5+4\,a^{10}\,c^9\,d^6-18\,a^{10}\,c^8\,d^7-2\,a^{10}\,c^7\,d^8+4\,a^{10}\,c^6\,d^9+8\,a^9\,b\,c^{15}+8\,a^9\,b\,c^{14}\,d-100\,a^9\,b\,c^{13}\,d^2+6\,a^9\,b\,c^{12}\,d^3+240\,a^9\,b\,c^{11}\,d^4-30\,a^9\,b\,c^{10}\,d^5-236\,a^9\,b\,c^9\,d^6+10\,a^9\,b\,c^8\,d^7+112\,a^9\,b\,c^7\,d^8+6\,a^9\,b\,c^6\,d^9-24\,a^9\,b\,c^5\,d^{10}-4\,a^8\,b^2\,c^{15}-52\,a^8\,b^2\,c^{14}\,d+64\,a^8\,b^2\,c^{13}\,d^2+346\,a^8\,b^2\,c^{12}\,d^3-252\,a^8\,b^2\,c^{11}\,d^4-708\,a^8\,b^2\,c^{10}\,d^5+334\,a^8\,b^2\,c^9\,d^6+646\,a^8\,b^2\,c^8\,d^7-148\,a^8\,b^2\,c^7\,d^8-292\,a^8\,b^2\,c^6\,d^9+6\,a^8\,b^2\,c^5\,d^{10}+60\,a^8\,b^2\,c^4\,d^{11}+32\,a^7\,b^3\,c^{14}\,d+140\,a^7\,b^3\,c^{13}\,d^2-350\,a^7\,b^3\,c^{12}\,d^3-636\,a^7\,b^3\,c^{11}\,d^4+956\,a^7\,b^3\,c^{10}\,d^5+1100\,a^7\,b^3\,c^9\,d^6-1040\,a^7\,b^3\,c^8\,d^7-932\,a^7\,b^3\,c^7\,d^8+452\,a^7\,b^3\,c^6\,d^9+408\,a^7\,b^3\,c^5\,d^{10}-50\,a^7\,b^3\,c^4\,d^{11}-80\,a^7\,b^3\,c^3\,d^{12}-112\,a^6\,b^4\,c^{13}\,d^2-192\,a^6\,b^4\,c^{12}\,d^3+818\,a^6\,b^4\,c^{11}\,d^4+632\,a^6\,b^4\,c^{10}\,d^5-1788\,a^6\,b^4\,c^9\,d^6-888\,a^6\,b^4\,c^8\,d^7+1660\,a^6\,b^4\,c^7\,d^8+708\,a^6\,b^4\,c^6\,d^9-668\,a^6\,b^4\,c^5\,d^{10}-320\,a^6\,b^4\,c^4\,d^{11}+90\,a^6\,b^4\,c^3\,d^{12}+60\,a^6\,b^4\,c^2\,d^{13}+224\,a^5\,b^5\,c^{12}\,d^3+116\,a^5\,b^5\,c^{11}\,d^4-1142\,a^5\,b^5\,c^{10}\,d^5-236\,a^5\,b^5\,c^9\,d^6+1992\,a^5\,b^5\,c^8\,d^7+204\,a^5\,b^5\,c^7\,d^8-1532\,a^5\,b^5\,c^6\,d^9-188\,a^5\,b^5\,c^5\,d^{10}+536\,a^5\,b^5\,c^4\,d^{11}+128\,a^5\,b^5\,c^3\,d^{12}-78\,a^5\,b^5\,c^2\,d^{13}-24\,a^5\,b^5\,c\,d^{14}-280\,a^4\,b^6\,c^{11}\,d^4+32\,a^4\,b^6\,c^{10}\,d^5+1042\,a^4\,b^6\,c^9\,d^6-180\,a^4\,b^6\,c^8\,d^7-1396\,a^4\,b^6\,c^7\,d^8+260\,a^4\,b^6\,c^6\,d^9+820\,a^4\,b^6\,c^5\,d^{10}-104\,a^4\,b^6\,c^4\,d^{11}-220\,a^4\,b^6\,c^3\,d^{12}-12\,a^4\,b^6\,c^2\,d^{13}+34\,a^4\,b^6\,c\,d^{14}+4\,a^4\,b^6\,d^{15}+224\,a^3\,b^7\,c^{10}\,d^5-108\,a^3\,b^7\,c^9\,d^6-634\,a^3\,b^7\,c^8\,d^7+284\,a^3\,b^7\,c^7\,d^8+612\,a^3\,b^7\,c^6\,d^9-252\,a^3\,b^7\,c^5\,d^{10}-224\,a^3\,b^7\,c^4\,d^{11}+84\,a^3\,b^7\,c^3\,d^{12}+28\,a^3\,b^7\,c^2\,d^{13}-8\,a^3\,b^7\,c\,d^{14}-6\,a^3\,b^7\,d^{15}-112\,a^2\,b^8\,c^9\,d^6+80\,a^2\,b^8\,c^8\,d^7+250\,a^2\,b^8\,c^7\,d^8-164\,a^2\,b^8\,c^6\,d^9-156\,a^2\,b^8\,c^5\,d^{10}+90\,a^2\,b^8\,c^4\,d^{11}+10\,a^2\,b^8\,c^3\,d^{12}-8\,a^2\,b^8\,c^2\,d^{13}+8\,a^2\,b^8\,c\,d^{14}+2\,a^2\,b^8\,d^{15}+32\,a\,b^9\,c^8\,d^7-28\,a\,b^9\,c^7\,d^8-58\,a\,b^9\,c^6\,d^9+48\,a\,b^9\,c^5\,d^{10}+18\,a\,b^9\,c^4\,d^{11}-12\,a\,b^9\,c^3\,d^{12}+10\,a\,b^9\,c^2\,d^{13}-8\,a\,b^9\,c\,d^{14}-2\,a\,b^9\,d^{15}-4\,b^{10}\,c^7\,d^8+4\,b^{10}\,c^6\,d^9+6\,b^{10}\,c^5\,d^{10}-6\,b^{10}\,c^4\,d^{11}-2\,b^{10}\,c\,d^{14}+2\,b^{10}\,d^{15}\right)}{a^6\,c^{13}+a^6\,c^{12}\,d-3\,a^6\,c^{11}\,d^2-3\,a^6\,c^{10}\,d^3+3\,a^6\,c^9\,d^4+3\,a^6\,c^8\,d^5-a^6\,c^7\,d^6-a^6\,c^6\,d^7-6\,a^5\,b\,c^{12}\,d-6\,a^5\,b\,c^{11}\,d^2+18\,a^5\,b\,c^{10}\,d^3+18\,a^5\,b\,c^9\,d^4-18\,a^5\,b\,c^8\,d^5-18\,a^5\,b\,c^7\,d^6+6\,a^5\,b\,c^6\,d^7+6\,a^5\,b\,c^5\,d^8+15\,a^4\,b^2\,c^{11}\,d^2+15\,a^4\,b^2\,c^{10}\,d^3-45\,a^4\,b^2\,c^9\,d^4-45\,a^4\,b^2\,c^8\,d^5+45\,a^4\,b^2\,c^7\,d^6+45\,a^4\,b^2\,c^6\,d^7-15\,a^4\,b^2\,c^5\,d^8-15\,a^4\,b^2\,c^4\,d^9-20\,a^3\,b^3\,c^{10}\,d^3-20\,a^3\,b^3\,c^9\,d^4+60\,a^3\,b^3\,c^8\,d^5+60\,a^3\,b^3\,c^7\,d^6-60\,a^3\,b^3\,c^6\,d^7-60\,a^3\,b^3\,c^5\,d^8+20\,a^3\,b^3\,c^4\,d^9+20\,a^3\,b^3\,c^3\,d^{10}+15\,a^2\,b^4\,c^9\,d^4+15\,a^2\,b^4\,c^8\,d^5-45\,a^2\,b^4\,c^7\,d^6-45\,a^2\,b^4\,c^6\,d^7+45\,a^2\,b^4\,c^5\,d^8+45\,a^2\,b^4\,c^4\,d^9-15\,a^2\,b^4\,c^3\,d^{10}-15\,a^2\,b^4\,c^2\,d^{11}-6\,a\,b^5\,c^8\,d^5-6\,a\,b^5\,c^7\,d^6+18\,a\,b^5\,c^6\,d^7+18\,a\,b^5\,c^5\,d^8-18\,a\,b^5\,c^4\,d^9-18\,a\,b^5\,c^3\,d^{10}+6\,a\,b^5\,c^2\,d^{11}+6\,a\,b^5\,c\,d^{12}+b^6\,c^7\,d^6+b^6\,c^6\,d^7-3\,b^6\,c^5\,d^8-3\,b^6\,c^4\,d^9+3\,b^6\,c^3\,d^{10}+3\,b^6\,c^2\,d^{11}-b^6\,c\,d^{12}-b^6\,d^{13}}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{b^2-a^2}\,\left(-8\,a^9\,c^{15}\,d+8\,a^9\,c^{14}\,d^2+32\,a^9\,c^{13}\,d^3-32\,a^9\,c^{12}\,d^4-48\,a^9\,c^{11}\,d^5+48\,a^9\,c^{10}\,d^6+32\,a^9\,c^9\,d^7-32\,a^9\,c^8\,d^8-8\,a^9\,c^7\,d^9+8\,a^9\,c^6\,d^{10}+8\,a^8\,b\,c^{16}+8\,a^8\,b\,c^{15}\,d-80\,a^8\,b\,c^{13}\,d^3-80\,a^8\,b\,c^{12}\,d^4+240\,a^8\,b\,c^{11}\,d^5+160\,a^8\,b\,c^{10}\,d^6-320\,a^8\,b\,c^9\,d^7-120\,a^8\,b\,c^8\,d^8+200\,a^8\,b\,c^7\,d^9+32\,a^8\,b\,c^6\,d^{10}-48\,a^8\,b\,c^5\,d^{11}-16\,a^7\,b^2\,c^{16}-40\,a^7\,b^2\,c^{15}\,d+24\,a^7\,b^2\,c^{14}\,d^2+136\,a^7\,b^2\,c^{13}\,d^3+184\,a^7\,b^2\,c^{12}\,d^4-144\,a^7\,b^2\,c^{11}\,d^5-656\,a^7\,b^2\,c^{10}\,d^6+16\,a^7\,b^2\,c^9\,d^7+864\,a^7\,b^2\,c^8\,d^8+56\,a^7\,b^2\,c^7\,d^9-520\,a^7\,b^2\,c^6\,d^{10}-24\,a^7\,b^2\,c^5\,d^{11}+120\,a^7\,b^2\,c^4\,d^{12}+8\,a^6\,b^3\,c^{16}+88\,a^6\,b^3\,c^{15}\,d+40\,a^6\,b^3\,c^{14}\,d^2-280\,a^6\,b^3\,c^{13}\,d^3-320\,a^6\,b^3\,c^{12}\,d^4+80\,a^6\,b^3\,c^{11}\,d^5+720\,a^6\,b^3\,c^{10}\,d^6+720\,a^6\,b^3\,c^9\,d^7-760\,a^6\,b^3\,c^8\,d^8-1160\,a^6\,b^3\,c^7\,d^9+392\,a^6\,b^3\,c^6\,d^{10}+712\,a^6\,b^3\,c^5\,d^{11}-80\,a^6\,b^3\,c^4\,d^{12}-160\,a^6\,b^3\,c^3\,d^{13}-48\,a^5\,b^4\,c^{15}\,d-192\,a^5\,b^4\,c^{14}\,d^2+152\,a^5\,b^4\,c^{13}\,d^3+728\,a^5\,b^4\,c^{12}\,d^4+72\,a^5\,b^4\,c^{11}\,d^5-872\,a^5\,b^4\,c^{10}\,d^6-848\,a^5\,b^4\,c^9\,d^7+48\,a^5\,b^4\,c^8\,d^8+1312\,a^5\,b^4\,c^7\,d^9+688\,a^5\,b^4\,c^6\,d^{10}-840\,a^5\,b^4\,c^5\,d^{11}-520\,a^5\,b^4\,c^4\,d^{12}+200\,a^5\,b^4\,c^3\,d^{13}+120\,a^5\,b^4\,c^2\,d^{14}+120\,a^4\,b^5\,c^{14}\,d^2+200\,a^4\,b^5\,c^{13}\,d^3-520\,a^4\,b^5\,c^{12}\,d^4-840\,a^4\,b^5\,c^{11}\,d^5+688\,a^4\,b^5\,c^{10}\,d^6+1312\,a^4\,b^5\,c^9\,d^7+48\,a^4\,b^5\,c^8\,d^8-848\,a^4\,b^5\,c^7\,d^9-872\,a^4\,b^5\,c^6\,d^{10}+72\,a^4\,b^5\,c^5\,d^{11}+728\,a^4\,b^5\,c^4\,d^{12}+152\,a^4\,b^5\,c^3\,d^{13}-192\,a^4\,b^5\,c^2\,d^{14}-48\,a^4\,b^5\,c\,d^{15}-160\,a^3\,b^6\,c^{13}\,d^3-80\,a^3\,b^6\,c^{12}\,d^4+712\,a^3\,b^6\,c^{11}\,d^5+392\,a^3\,b^6\,c^{10}\,d^6-1160\,a^3\,b^6\,c^9\,d^7-760\,a^3\,b^6\,c^8\,d^8+720\,a^3\,b^6\,c^7\,d^9+720\,a^3\,b^6\,c^6\,d^{10}+80\,a^3\,b^6\,c^5\,d^{11}-320\,a^3\,b^6\,c^4\,d^{12}-280\,a^3\,b^6\,c^3\,d^{13}+40\,a^3\,b^6\,c^2\,d^{14}+88\,a^3\,b^6\,c\,d^{15}+8\,a^3\,b^6\,d^{16}+120\,a^2\,b^7\,c^{12}\,d^4-24\,a^2\,b^7\,c^{11}\,d^5-520\,a^2\,b^7\,c^{10}\,d^6+56\,a^2\,b^7\,c^9\,d^7+864\,a^2\,b^7\,c^8\,d^8+16\,a^2\,b^7\,c^7\,d^9-656\,a^2\,b^7\,c^6\,d^{10}-144\,a^2\,b^7\,c^5\,d^{11}+184\,a^2\,b^7\,c^4\,d^{12}+136\,a^2\,b^7\,c^3\,d^{13}+24\,a^2\,b^7\,c^2\,d^{14}-40\,a^2\,b^7\,c\,d^{15}-16\,a^2\,b^7\,d^{16}-48\,a\,b^8\,c^{11}\,d^5+32\,a\,b^8\,c^{10}\,d^6+200\,a\,b^8\,c^9\,d^7-120\,a\,b^8\,c^8\,d^8-320\,a\,b^8\,c^7\,d^9+160\,a\,b^8\,c^6\,d^{10}+240\,a\,b^8\,c^5\,d^{11}-80\,a\,b^8\,c^4\,d^{12}-80\,a\,b^8\,c^3\,d^{13}+8\,a\,b^8\,c\,d^{15}+8\,a\,b^8\,d^{16}+8\,b^9\,c^{10}\,d^6-8\,b^9\,c^9\,d^7-32\,b^9\,c^8\,d^8+32\,b^9\,c^7\,d^9+48\,b^9\,c^6\,d^{10}-48\,b^9\,c^5\,d^{11}-32\,b^9\,c^4\,d^{12}+32\,b^9\,c^3\,d^{13}+8\,b^9\,c^2\,d^{14}-8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\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)\,\left(a^4\,c^{11}+a^4\,c^{10}\,d-3\,a^4\,c^9\,d^2-3\,a^4\,c^8\,d^3+3\,a^4\,c^7\,d^4+3\,a^4\,c^6\,d^5-a^4\,c^5\,d^6-a^4\,c^4\,d^7-4\,a^3\,b\,c^{10}\,d-4\,a^3\,b\,c^9\,d^2+12\,a^3\,b\,c^8\,d^3+12\,a^3\,b\,c^7\,d^4-12\,a^3\,b\,c^6\,d^5-12\,a^3\,b\,c^5\,d^6+4\,a^3\,b\,c^4\,d^7+4\,a^3\,b\,c^3\,d^8+6\,a^2\,b^2\,c^9\,d^2+6\,a^2\,b^2\,c^8\,d^3-18\,a^2\,b^2\,c^7\,d^4-18\,a^2\,b^2\,c^6\,d^5+18\,a^2\,b^2\,c^5\,d^6+18\,a^2\,b^2\,c^4\,d^7-6\,a^2\,b^2\,c^3\,d^8-6\,a^2\,b^2\,c^2\,d^9-4\,a\,b^3\,c^8\,d^3-4\,a\,b^3\,c^7\,d^4+12\,a\,b^3\,c^6\,d^5+12\,a\,b^3\,c^5\,d^6-12\,a\,b^3\,c^4\,d^7-12\,a\,b^3\,c^3\,d^8+4\,a\,b^3\,c^2\,d^9+4\,a\,b^3\,c\,d^{10}+b^4\,c^7\,d^4+b^4\,c^6\,d^5-3\,b^4\,c^5\,d^6-3\,b^4\,c^4\,d^7+3\,b^4\,c^3\,d^8+3\,b^4\,c^2\,d^9-b^4\,c\,d^{10}-b^4\,d^{11}\right)}\right)\,\left(6\,a^2\,c^4-5\,a^2\,c^2\,d^2+2\,a^2\,d^4-6\,a\,b\,c^3\,d+2\,b^2\,c^2\,d^2+b^2\,d^4\right)}{2\,\left(a^3\,c^{13}-5\,a^3\,c^{11}\,d^2+10\,a^3\,c^9\,d^4-10\,a^3\,c^7\,d^6+5\,a^3\,c^5\,d^8-a^3\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)}\right)\,\left(6\,a^2\,c^4-5\,a^2\,c^2\,d^2+2\,a^2\,d^4-6\,a\,b\,c^3\,d+2\,b^2\,c^2\,d^2+b^2\,d^4\right)}{2\,\left(a^3\,c^{13}-5\,a^3\,c^{11}\,d^2+10\,a^3\,c^9\,d^4-10\,a^3\,c^7\,d^6+5\,a^3\,c^5\,d^8-a^3\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)}+\frac{d\,\sqrt{{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,a^7\,c^{10}+8\,a^7\,c^9\,d-24\,a^7\,c^8\,d^2-32\,a^7\,c^7\,d^3+52\,a^7\,c^6\,d^4+48\,a^7\,c^5\,d^5-57\,a^7\,c^4\,d^6-32\,a^7\,c^3\,d^7+32\,a^7\,c^2\,d^8+8\,a^7\,c\,d^9-8\,a^7\,d^{10}+4\,a^6\,b\,c^{10}-8\,a^6\,b\,c^9\,d+96\,a^6\,b\,c^8\,d^2+104\,a^6\,b\,c^7\,d^3-172\,a^6\,b\,c^6\,d^4-108\,a^6\,b\,c^5\,d^5+155\,a^6\,b\,c^4\,d^6+56\,a^6\,b\,c^3\,d^7-72\,a^6\,b\,c^2\,d^8-8\,a^6\,b\,c\,d^9+16\,a^6\,b\,d^{10}-108\,a^5\,b^2\,c^8\,d^2-216\,a^5\,b^2\,c^7\,d^3+120\,a^5\,b^2\,c^6\,d^4+180\,a^5\,b^2\,c^5\,d^5-139\,a^5\,b^2\,c^4\,d^6-72\,a^5\,b^2\,c^3\,d^7+62\,a^5\,b^2\,c^2\,d^8-16\,a^5\,b^2\,d^{10}+36\,a^4\,b^3\,c^8\,d^2+216\,a^4\,b^3\,c^7\,d^3+120\,a^4\,b^3\,c^6\,d^4-156\,a^4\,b^3\,c^5\,d^5+25\,a^4\,b^3\,c^4\,d^6+84\,a^4\,b^3\,c^3\,d^7-26\,a^4\,b^3\,c^2\,d^8+16\,a^4\,b^3\,d^{10}-72\,a^3\,b^4\,c^7\,d^3-180\,a^3\,b^4\,c^6\,d^4-12\,a^3\,b^4\,c^5\,d^5+20\,a^3\,b^4\,c^4\,d^6-60\,a^3\,b^4\,c^3\,d^7+2\,a^3\,b^4\,c^2\,d^8-13\,a^3\,b^4\,d^{10}+60\,a^2\,b^5\,c^6\,d^4+72\,a^2\,b^5\,c^5\,d^5+4\,a^2\,b^5\,c^4\,d^6+36\,a^2\,b^5\,c^3\,d^7+10\,a^2\,b^5\,c^2\,d^8+7\,a^2\,b^5\,d^{10}-24\,a\,b^6\,c^5\,d^5-12\,a\,b^6\,c^4\,d^6-12\,a\,b^6\,c^3\,d^7-12\,a\,b^6\,c^2\,d^8-3\,a\,b^6\,d^{10}+4\,b^7\,c^4\,d^6+4\,b^7\,c^2\,d^8+b^7\,d^{10}\right)}{a^4\,c^{11}+a^4\,c^{10}\,d-3\,a^4\,c^9\,d^2-3\,a^4\,c^8\,d^3+3\,a^4\,c^7\,d^4+3\,a^4\,c^6\,d^5-a^4\,c^5\,d^6-a^4\,c^4\,d^7-4\,a^3\,b\,c^{10}\,d-4\,a^3\,b\,c^9\,d^2+12\,a^3\,b\,c^8\,d^3+12\,a^3\,b\,c^7\,d^4-12\,a^3\,b\,c^6\,d^5-12\,a^3\,b\,c^5\,d^6+4\,a^3\,b\,c^4\,d^7+4\,a^3\,b\,c^3\,d^8+6\,a^2\,b^2\,c^9\,d^2+6\,a^2\,b^2\,c^8\,d^3-18\,a^2\,b^2\,c^7\,d^4-18\,a^2\,b^2\,c^6\,d^5+18\,a^2\,b^2\,c^5\,d^6+18\,a^2\,b^2\,c^4\,d^7-6\,a^2\,b^2\,c^3\,d^8-6\,a^2\,b^2\,c^2\,d^9-4\,a\,b^3\,c^8\,d^3-4\,a\,b^3\,c^7\,d^4+12\,a\,b^3\,c^6\,d^5+12\,a\,b^3\,c^5\,d^6-12\,a\,b^3\,c^4\,d^7-12\,a\,b^3\,c^3\,d^8+4\,a\,b^3\,c^2\,d^9+4\,a\,b^3\,c\,d^{10}+b^4\,c^7\,d^4+b^4\,c^6\,d^5-3\,b^4\,c^5\,d^6-3\,b^4\,c^4\,d^7+3\,b^4\,c^3\,d^8+3\,b^4\,c^2\,d^9-b^4\,c\,d^{10}-b^4\,d^{11}}-\frac{d\,\sqrt{{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(-4\,a^{10}\,c^{15}+12\,a^{10}\,c^{14}\,d+8\,a^{10}\,c^{13}\,d^2-34\,a^{10}\,c^{12}\,d^3-6\,a^{10}\,c^{11}\,d^4+36\,a^{10}\,c^{10}\,d^5+4\,a^{10}\,c^9\,d^6-18\,a^{10}\,c^8\,d^7-2\,a^{10}\,c^7\,d^8+4\,a^{10}\,c^6\,d^9+8\,a^9\,b\,c^{15}+8\,a^9\,b\,c^{14}\,d-100\,a^9\,b\,c^{13}\,d^2+6\,a^9\,b\,c^{12}\,d^3+240\,a^9\,b\,c^{11}\,d^4-30\,a^9\,b\,c^{10}\,d^5-236\,a^9\,b\,c^9\,d^6+10\,a^9\,b\,c^8\,d^7+112\,a^9\,b\,c^7\,d^8+6\,a^9\,b\,c^6\,d^9-24\,a^9\,b\,c^5\,d^{10}-4\,a^8\,b^2\,c^{15}-52\,a^8\,b^2\,c^{14}\,d+64\,a^8\,b^2\,c^{13}\,d^2+346\,a^8\,b^2\,c^{12}\,d^3-252\,a^8\,b^2\,c^{11}\,d^4-708\,a^8\,b^2\,c^{10}\,d^5+334\,a^8\,b^2\,c^9\,d^6+646\,a^8\,b^2\,c^8\,d^7-148\,a^8\,b^2\,c^7\,d^8-292\,a^8\,b^2\,c^6\,d^9+6\,a^8\,b^2\,c^5\,d^{10}+60\,a^8\,b^2\,c^4\,d^{11}+32\,a^7\,b^3\,c^{14}\,d+140\,a^7\,b^3\,c^{13}\,d^2-350\,a^7\,b^3\,c^{12}\,d^3-636\,a^7\,b^3\,c^{11}\,d^4+956\,a^7\,b^3\,c^{10}\,d^5+1100\,a^7\,b^3\,c^9\,d^6-1040\,a^7\,b^3\,c^8\,d^7-932\,a^7\,b^3\,c^7\,d^8+452\,a^7\,b^3\,c^6\,d^9+408\,a^7\,b^3\,c^5\,d^{10}-50\,a^7\,b^3\,c^4\,d^{11}-80\,a^7\,b^3\,c^3\,d^{12}-112\,a^6\,b^4\,c^{13}\,d^2-192\,a^6\,b^4\,c^{12}\,d^3+818\,a^6\,b^4\,c^{11}\,d^4+632\,a^6\,b^4\,c^{10}\,d^5-1788\,a^6\,b^4\,c^9\,d^6-888\,a^6\,b^4\,c^8\,d^7+1660\,a^6\,b^4\,c^7\,d^8+708\,a^6\,b^4\,c^6\,d^9-668\,a^6\,b^4\,c^5\,d^{10}-320\,a^6\,b^4\,c^4\,d^{11}+90\,a^6\,b^4\,c^3\,d^{12}+60\,a^6\,b^4\,c^2\,d^{13}+224\,a^5\,b^5\,c^{12}\,d^3+116\,a^5\,b^5\,c^{11}\,d^4-1142\,a^5\,b^5\,c^{10}\,d^5-236\,a^5\,b^5\,c^9\,d^6+1992\,a^5\,b^5\,c^8\,d^7+204\,a^5\,b^5\,c^7\,d^8-1532\,a^5\,b^5\,c^6\,d^9-188\,a^5\,b^5\,c^5\,d^{10}+536\,a^5\,b^5\,c^4\,d^{11}+128\,a^5\,b^5\,c^3\,d^{12}-78\,a^5\,b^5\,c^2\,d^{13}-24\,a^5\,b^5\,c\,d^{14}-280\,a^4\,b^6\,c^{11}\,d^4+32\,a^4\,b^6\,c^{10}\,d^5+1042\,a^4\,b^6\,c^9\,d^6-180\,a^4\,b^6\,c^8\,d^7-1396\,a^4\,b^6\,c^7\,d^8+260\,a^4\,b^6\,c^6\,d^9+820\,a^4\,b^6\,c^5\,d^{10}-104\,a^4\,b^6\,c^4\,d^{11}-220\,a^4\,b^6\,c^3\,d^{12}-12\,a^4\,b^6\,c^2\,d^{13}+34\,a^4\,b^6\,c\,d^{14}+4\,a^4\,b^6\,d^{15}+224\,a^3\,b^7\,c^{10}\,d^5-108\,a^3\,b^7\,c^9\,d^6-634\,a^3\,b^7\,c^8\,d^7+284\,a^3\,b^7\,c^7\,d^8+612\,a^3\,b^7\,c^6\,d^9-252\,a^3\,b^7\,c^5\,d^{10}-224\,a^3\,b^7\,c^4\,d^{11}+84\,a^3\,b^7\,c^3\,d^{12}+28\,a^3\,b^7\,c^2\,d^{13}-8\,a^3\,b^7\,c\,d^{14}-6\,a^3\,b^7\,d^{15}-112\,a^2\,b^8\,c^9\,d^6+80\,a^2\,b^8\,c^8\,d^7+250\,a^2\,b^8\,c^7\,d^8-164\,a^2\,b^8\,c^6\,d^9-156\,a^2\,b^8\,c^5\,d^{10}+90\,a^2\,b^8\,c^4\,d^{11}+10\,a^2\,b^8\,c^3\,d^{12}-8\,a^2\,b^8\,c^2\,d^{13}+8\,a^2\,b^8\,c\,d^{14}+2\,a^2\,b^8\,d^{15}+32\,a\,b^9\,c^8\,d^7-28\,a\,b^9\,c^7\,d^8-58\,a\,b^9\,c^6\,d^9+48\,a\,b^9\,c^5\,d^{10}+18\,a\,b^9\,c^4\,d^{11}-12\,a\,b^9\,c^3\,d^{12}+10\,a\,b^9\,c^2\,d^{13}-8\,a\,b^9\,c\,d^{14}-2\,a\,b^9\,d^{15}-4\,b^{10}\,c^7\,d^8+4\,b^{10}\,c^6\,d^9+6\,b^{10}\,c^5\,d^{10}-6\,b^{10}\,c^4\,d^{11}-2\,b^{10}\,c\,d^{14}+2\,b^{10}\,d^{15}\right)}{a^6\,c^{13}+a^6\,c^{12}\,d-3\,a^6\,c^{11}\,d^2-3\,a^6\,c^{10}\,d^3+3\,a^6\,c^9\,d^4+3\,a^6\,c^8\,d^5-a^6\,c^7\,d^6-a^6\,c^6\,d^7-6\,a^5\,b\,c^{12}\,d-6\,a^5\,b\,c^{11}\,d^2+18\,a^5\,b\,c^{10}\,d^3+18\,a^5\,b\,c^9\,d^4-18\,a^5\,b\,c^8\,d^5-18\,a^5\,b\,c^7\,d^6+6\,a^5\,b\,c^6\,d^7+6\,a^5\,b\,c^5\,d^8+15\,a^4\,b^2\,c^{11}\,d^2+15\,a^4\,b^2\,c^{10}\,d^3-45\,a^4\,b^2\,c^9\,d^4-45\,a^4\,b^2\,c^8\,d^5+45\,a^4\,b^2\,c^7\,d^6+45\,a^4\,b^2\,c^6\,d^7-15\,a^4\,b^2\,c^5\,d^8-15\,a^4\,b^2\,c^4\,d^9-20\,a^3\,b^3\,c^{10}\,d^3-20\,a^3\,b^3\,c^9\,d^4+60\,a^3\,b^3\,c^8\,d^5+60\,a^3\,b^3\,c^7\,d^6-60\,a^3\,b^3\,c^6\,d^7-60\,a^3\,b^3\,c^5\,d^8+20\,a^3\,b^3\,c^4\,d^9+20\,a^3\,b^3\,c^3\,d^{10}+15\,a^2\,b^4\,c^9\,d^4+15\,a^2\,b^4\,c^8\,d^5-45\,a^2\,b^4\,c^7\,d^6-45\,a^2\,b^4\,c^6\,d^7+45\,a^2\,b^4\,c^5\,d^8+45\,a^2\,b^4\,c^4\,d^9-15\,a^2\,b^4\,c^3\,d^{10}-15\,a^2\,b^4\,c^2\,d^{11}-6\,a\,b^5\,c^8\,d^5-6\,a\,b^5\,c^7\,d^6+18\,a\,b^5\,c^6\,d^7+18\,a\,b^5\,c^5\,d^8-18\,a\,b^5\,c^4\,d^9-18\,a\,b^5\,c^3\,d^{10}+6\,a\,b^5\,c^2\,d^{11}+6\,a\,b^5\,c\,d^{12}+b^6\,c^7\,d^6+b^6\,c^6\,d^7-3\,b^6\,c^5\,d^8-3\,b^6\,c^4\,d^9+3\,b^6\,c^3\,d^{10}+3\,b^6\,c^2\,d^{11}-b^6\,c\,d^{12}-b^6\,d^{13}}+\frac{4\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(6\,a^2\,c^4-5\,a^2\,c^2\,d^2+2\,a^2\,d^4-6\,a\,b\,c^3\,d+2\,b^2\,c^2\,d^2+b^2\,d^4\right)\,\left(-8\,a^9\,c^{15}\,d+8\,a^9\,c^{14}\,d^2+32\,a^9\,c^{13}\,d^3-32\,a^9\,c^{12}\,d^4-48\,a^9\,c^{11}\,d^5+48\,a^9\,c^{10}\,d^6+32\,a^9\,c^9\,d^7-32\,a^9\,c^8\,d^8-8\,a^9\,c^7\,d^9+8\,a^9\,c^6\,d^{10}+8\,a^8\,b\,c^{16}+8\,a^8\,b\,c^{15}\,d-80\,a^8\,b\,c^{13}\,d^3-80\,a^8\,b\,c^{12}\,d^4+240\,a^8\,b\,c^{11}\,d^5+160\,a^8\,b\,c^{10}\,d^6-320\,a^8\,b\,c^9\,d^7-120\,a^8\,b\,c^8\,d^8+200\,a^8\,b\,c^7\,d^9+32\,a^8\,b\,c^6\,d^{10}-48\,a^8\,b\,c^5\,d^{11}-16\,a^7\,b^2\,c^{16}-40\,a^7\,b^2\,c^{15}\,d+24\,a^7\,b^2\,c^{14}\,d^2+136\,a^7\,b^2\,c^{13}\,d^3+184\,a^7\,b^2\,c^{12}\,d^4-144\,a^7\,b^2\,c^{11}\,d^5-656\,a^7\,b^2\,c^{10}\,d^6+16\,a^7\,b^2\,c^9\,d^7+864\,a^7\,b^2\,c^8\,d^8+56\,a^7\,b^2\,c^7\,d^9-520\,a^7\,b^2\,c^6\,d^{10}-24\,a^7\,b^2\,c^5\,d^{11}+120\,a^7\,b^2\,c^4\,d^{12}+8\,a^6\,b^3\,c^{16}+88\,a^6\,b^3\,c^{15}\,d+40\,a^6\,b^3\,c^{14}\,d^2-280\,a^6\,b^3\,c^{13}\,d^3-320\,a^6\,b^3\,c^{12}\,d^4+80\,a^6\,b^3\,c^{11}\,d^5+720\,a^6\,b^3\,c^{10}\,d^6+720\,a^6\,b^3\,c^9\,d^7-760\,a^6\,b^3\,c^8\,d^8-1160\,a^6\,b^3\,c^7\,d^9+392\,a^6\,b^3\,c^6\,d^{10}+712\,a^6\,b^3\,c^5\,d^{11}-80\,a^6\,b^3\,c^4\,d^{12}-160\,a^6\,b^3\,c^3\,d^{13}-48\,a^5\,b^4\,c^{15}\,d-192\,a^5\,b^4\,c^{14}\,d^2+152\,a^5\,b^4\,c^{13}\,d^3+728\,a^5\,b^4\,c^{12}\,d^4+72\,a^5\,b^4\,c^{11}\,d^5-872\,a^5\,b^4\,c^{10}\,d^6-848\,a^5\,b^4\,c^9\,d^7+48\,a^5\,b^4\,c^8\,d^8+1312\,a^5\,b^4\,c^7\,d^9+688\,a^5\,b^4\,c^6\,d^{10}-840\,a^5\,b^4\,c^5\,d^{11}-520\,a^5\,b^4\,c^4\,d^{12}+200\,a^5\,b^4\,c^3\,d^{13}+120\,a^5\,b^4\,c^2\,d^{14}+120\,a^4\,b^5\,c^{14}\,d^2+200\,a^4\,b^5\,c^{13}\,d^3-520\,a^4\,b^5\,c^{12}\,d^4-840\,a^4\,b^5\,c^{11}\,d^5+688\,a^4\,b^5\,c^{10}\,d^6+1312\,a^4\,b^5\,c^9\,d^7+48\,a^4\,b^5\,c^8\,d^8-848\,a^4\,b^5\,c^7\,d^9-872\,a^4\,b^5\,c^6\,d^{10}+72\,a^4\,b^5\,c^5\,d^{11}+728\,a^4\,b^5\,c^4\,d^{12}+152\,a^4\,b^5\,c^3\,d^{13}-192\,a^4\,b^5\,c^2\,d^{14}-48\,a^4\,b^5\,c\,d^{15}-160\,a^3\,b^6\,c^{13}\,d^3-80\,a^3\,b^6\,c^{12}\,d^4+712\,a^3\,b^6\,c^{11}\,d^5+392\,a^3\,b^6\,c^{10}\,d^6-1160\,a^3\,b^6\,c^9\,d^7-760\,a^3\,b^6\,c^8\,d^8+720\,a^3\,b^6\,c^7\,d^9+720\,a^3\,b^6\,c^6\,d^{10}+80\,a^3\,b^6\,c^5\,d^{11}-320\,a^3\,b^6\,c^4\,d^{12}-280\,a^3\,b^6\,c^3\,d^{13}+40\,a^3\,b^6\,c^2\,d^{14}+88\,a^3\,b^6\,c\,d^{15}+8\,a^3\,b^6\,d^{16}+120\,a^2\,b^7\,c^{12}\,d^4-24\,a^2\,b^7\,c^{11}\,d^5-520\,a^2\,b^7\,c^{10}\,d^6+56\,a^2\,b^7\,c^9\,d^7+864\,a^2\,b^7\,c^8\,d^8+16\,a^2\,b^7\,c^7\,d^9-656\,a^2\,b^7\,c^6\,d^{10}-144\,a^2\,b^7\,c^5\,d^{11}+184\,a^2\,b^7\,c^4\,d^{12}+136\,a^2\,b^7\,c^3\,d^{13}+24\,a^2\,b^7\,c^2\,d^{14}-40\,a^2\,b^7\,c\,d^{15}-16\,a^2\,b^7\,d^{16}-48\,a\,b^8\,c^{11}\,d^5+32\,a\,b^8\,c^{10}\,d^6+200\,a\,b^8\,c^9\,d^7-120\,a\,b^8\,c^8\,d^8-320\,a\,b^8\,c^7\,d^9+160\,a\,b^8\,c^6\,d^{10}+240\,a\,b^8\,c^5\,d^{11}-80\,a\,b^8\,c^4\,d^{12}-80\,a\,b^8\,c^3\,d^{13}+8\,a\,b^8\,c\,d^{15}+8\,a\,b^8\,d^{16}+8\,b^9\,c^{10}\,d^6-8\,b^9\,c^9\,d^7-32\,b^9\,c^8\,d^8+32\,b^9\,c^7\,d^9+48\,b^9\,c^6\,d^{10}-48\,b^9\,c^5\,d^{11}-32\,b^9\,c^4\,d^{12}+32\,b^9\,c^3\,d^{13}+8\,b^9\,c^2\,d^{14}-8\,b^9\,c\,d^{15}\right)}{\left(a^3\,c^{13}-5\,a^3\,c^{11}\,d^2+10\,a^3\,c^9\,d^4-10\,a^3\,c^7\,d^6+5\,a^3\,c^5\,d^8-a^3\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)\,\left(a^4\,c^{11}+a^4\,c^{10}\,d-3\,a^4\,c^9\,d^2-3\,a^4\,c^8\,d^3+3\,a^4\,c^7\,d^4+3\,a^4\,c^6\,d^5-a^4\,c^5\,d^6-a^4\,c^4\,d^7-4\,a^3\,b\,c^{10}\,d-4\,a^3\,b\,c^9\,d^2+12\,a^3\,b\,c^8\,d^3+12\,a^3\,b\,c^7\,d^4-12\,a^3\,b\,c^6\,d^5-12\,a^3\,b\,c^5\,d^6+4\,a^3\,b\,c^4\,d^7+4\,a^3\,b\,c^3\,d^8+6\,a^2\,b^2\,c^9\,d^2+6\,a^2\,b^2\,c^8\,d^3-18\,a^2\,b^2\,c^7\,d^4-18\,a^2\,b^2\,c^6\,d^5+18\,a^2\,b^2\,c^5\,d^6+18\,a^2\,b^2\,c^4\,d^7-6\,a^2\,b^2\,c^3\,d^8-6\,a^2\,b^2\,c^2\,d^9-4\,a\,b^3\,c^8\,d^3-4\,a\,b^3\,c^7\,d^4+12\,a\,b^3\,c^6\,d^5+12\,a\,b^3\,c^5\,d^6-12\,a\,b^3\,c^4\,d^7-12\,a\,b^3\,c^3\,d^8+4\,a\,b^3\,c^2\,d^9+4\,a\,b^3\,c\,d^{10}+b^4\,c^7\,d^4+b^4\,c^6\,d^5-3\,b^4\,c^5\,d^6-3\,b^4\,c^4\,d^7+3\,b^4\,c^3\,d^8+3\,b^4\,c^2\,d^9-b^4\,c\,d^{10}-b^4\,d^{11}\right)}\right)\,\left(6\,a^2\,c^4-5\,a^2\,c^2\,d^2+2\,a^2\,d^4-6\,a\,b\,c^3\,d+2\,b^2\,c^2\,d^2+b^2\,d^4\right)}{2\,\left(a^3\,c^{13}-5\,a^3\,c^{11}\,d^2+10\,a^3\,c^9\,d^4-10\,a^3\,c^7\,d^6+5\,a^3\,c^5\,d^8-a^3\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)}\right)\,\left(6\,a^2\,c^4-5\,a^2\,c^2\,d^2+2\,a^2\,d^4-6\,a\,b\,c^3\,d+2\,b^2\,c^2\,d^2+b^2\,d^4\right)}{2\,\left(a^3\,c^{13}-5\,a^3\,c^{11}\,d^2+10\,a^3\,c^9\,d^4-10\,a^3\,c^7\,d^6+5\,a^3\,c^5\,d^8-a^3\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)}}\right)\,\sqrt{{\left(c+d\right)}^5\,{\left(c-d\right)}^5}\,\left(6\,a^2\,c^4-5\,a^2\,c^2\,d^2+2\,a^2\,d^4-6\,a\,b\,c^3\,d+2\,b^2\,c^2\,d^2+b^2\,d^4\right)\,1{}\mathrm{i}}{f\,\left(a^3\,c^{13}-5\,a^3\,c^{11}\,d^2+10\,a^3\,c^9\,d^4-10\,a^3\,c^7\,d^6+5\,a^3\,c^5\,d^8-a^3\,c^3\,d^{10}-3\,a^2\,b\,c^{12}\,d+15\,a^2\,b\,c^{10}\,d^3-30\,a^2\,b\,c^8\,d^5+30\,a^2\,b\,c^6\,d^7-15\,a^2\,b\,c^4\,d^9+3\,a^2\,b\,c^2\,d^{11}+3\,a\,b^2\,c^{11}\,d^2-15\,a\,b^2\,c^9\,d^4+30\,a\,b^2\,c^7\,d^6-30\,a\,b^2\,c^5\,d^8+15\,a\,b^2\,c^3\,d^{10}-3\,a\,b^2\,c\,d^{12}-b^3\,c^{10}\,d^3+5\,b^3\,c^8\,d^5-10\,b^3\,c^6\,d^7+10\,b^3\,c^4\,d^9-5\,b^3\,c^2\,d^{11}+b^3\,d^{13}\right)}","Not used",1,"((tan(e/2 + (f*x)/2)^3*(2*a*d^4 + b*d^4 - 6*a*c^2*d^2 - a*c*d^3 + 4*b*c*d^3))/((c + d)^2*(a^2*c^3 - b^2*d^3 - a^2*c^2*d + b^2*c*d^2 + 2*a*b*c*d^2 - 2*a*b*c^2*d)) - (tan(e/2 + (f*x)/2)*(2*a*d^4 - b*d^4 - 6*a*c^2*d^2 + a*c*d^3 + 4*b*c*d^3))/((c + d)*(a^2*c^4 + b^2*d^4 - 2*a^2*c^3*d - 2*b^2*c*d^3 + a^2*c^2*d^2 + b^2*c^2*d^2 - 2*a*b*c*d^3 - 2*a*b*c^3*d + 4*a*b*c^2*d^2)))/(f*(2*c*d - tan(e/2 + (f*x)/2)^2*(2*c^2 - 2*d^2) + tan(e/2 + (f*x)/2)^4*(c^2 - 2*c*d + d^2) + c^2 + d^2)) + (a^3*atan(((a^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) + (a^3*(b^2 - a^2)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) - (8*a^3*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d))))/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d))*1i)/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d) + (a^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) - (a^3*(b^2 - a^2)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) + (8*a^3*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d))))/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d))*1i)/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d))/((16*(6*a^7*b*d^9 - 4*a^8*d^9 + 2*a^8*c*d^8 - 12*a^8*c^8*d + a^3*b^5*d^9 - 2*a^4*b^4*d^9 + 5*a^5*b^3*d^9 - 6*a^6*b^2*d^9 + 18*a^8*c^2*d^7 - 13*a^8*c^3*d^6 - 36*a^8*c^4*d^5 + 26*a^8*c^5*d^4 + 34*a^8*c^6*d^3 - 24*a^8*c^7*d^2 + a^4*b^4*c*d^8 - 2*a^5*b^3*c*d^8 + 3*a^6*b^2*c*d^8 - 19*a^7*b*c^2*d^7 + 38*a^7*b*c^3*d^6 + 26*a^7*b*c^4*d^5 - 76*a^7*b*c^5*d^4 + 2*a^7*b*c^6*d^3 + 60*a^7*b*c^7*d^2 + 4*a^3*b^5*c^2*d^7 + 4*a^3*b^5*c^4*d^5 - 8*a^4*b^4*c^2*d^7 - 8*a^4*b^4*c^3*d^6 - 8*a^4*b^4*c^4*d^5 - 20*a^4*b^4*c^5*d^4 + 3*a^5*b^3*c^2*d^7 + 16*a^5*b^3*c^3*d^6 - 12*a^5*b^3*c^4*d^5 + 40*a^5*b^3*c^5*d^4 + 40*a^5*b^3*c^6*d^3 + 2*a^6*b^2*c^2*d^7 - 33*a^6*b^2*c^3*d^6 + 26*a^6*b^2*c^4*d^5 + 30*a^6*b^2*c^5*d^4 - 76*a^6*b^2*c^6*d^3 - 36*a^6*b^2*c^7*d^2 - 4*a^7*b*c*d^8 + 12*a^7*b*c^8*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) - (a^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) + (a^3*(b^2 - a^2)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) - (8*a^3*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d))))/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)))/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d) + (a^3*(b^2 - a^2)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) - (a^3*(b^2 - a^2)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) + (8*a^3*tan(e/2 + (f*x)/2)*(b^2 - a^2)^(1/2)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d))))/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)))/(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)))*(b^2 - a^2)^(1/2)*2i)/(f*(a^5*c^3 + b^5*d^3 - a^3*b^2*c^3 - a^2*b^3*d^3 + 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - 3*a*b^4*c*d^2 - 3*a^4*b*c^2*d)) + (d*atan(((d*((c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) + (d*((c + d)^5*(c - d)^5)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) - (4*d*tan(e/2 + (f*x)/2)*((c + d)^5*(c - d)^5)^(1/2)*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)) + (d*((c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 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4*a^3*b*c^10*d) - (d*((c + d)^5*(c - d)^5)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) + (4*d*tan(e/2 + (f*x)/2)*((c + d)^5*(c - d)^5)^(1/2)*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)))/((16*(6*a^7*b*d^9 - 4*a^8*d^9 + 2*a^8*c*d^8 - 12*a^8*c^8*d + a^3*b^5*d^9 - 2*a^4*b^4*d^9 + 5*a^5*b^3*d^9 - 6*a^6*b^2*d^9 + 18*a^8*c^2*d^7 - 13*a^8*c^3*d^6 - 36*a^8*c^4*d^5 + 26*a^8*c^5*d^4 + 34*a^8*c^6*d^3 - 24*a^8*c^7*d^2 + a^4*b^4*c*d^8 - 2*a^5*b^3*c*d^8 + 3*a^6*b^2*c*d^8 - 19*a^7*b*c^2*d^7 + 38*a^7*b*c^3*d^6 + 26*a^7*b*c^4*d^5 - 76*a^7*b*c^5*d^4 + 2*a^7*b*c^6*d^3 + 60*a^7*b*c^7*d^2 + 4*a^3*b^5*c^2*d^7 + 4*a^3*b^5*c^4*d^5 - 8*a^4*b^4*c^2*d^7 - 8*a^4*b^4*c^3*d^6 - 8*a^4*b^4*c^4*d^5 - 20*a^4*b^4*c^5*d^4 + 3*a^5*b^3*c^2*d^7 + 16*a^5*b^3*c^3*d^6 - 12*a^5*b^3*c^4*d^5 + 40*a^5*b^3*c^5*d^4 + 40*a^5*b^3*c^6*d^3 + 2*a^6*b^2*c^2*d^7 - 33*a^6*b^2*c^3*d^6 + 26*a^6*b^2*c^4*d^5 + 30*a^6*b^2*c^5*d^4 - 76*a^6*b^2*c^6*d^3 - 36*a^6*b^2*c^7*d^2 - 4*a^7*b*c*d^8 + 12*a^7*b*c^8*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) - (d*((c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) + (d*((c + d)^5*(c - d)^5)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) - (4*d*tan(e/2 + (f*x)/2)*((c + d)^5*(c - d)^5)^(1/2)*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)) + (d*((c + d)^5*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(b^7*d^10 - 8*a^7*d^10 - 4*a^7*c^10 + 4*a^6*b*c^10 - 3*a*b^6*d^10 + 16*a^6*b*d^10 + 8*a^7*c*d^9 + 8*a^7*c^9*d + 7*a^2*b^5*d^10 - 13*a^3*b^4*d^10 + 16*a^4*b^3*d^10 - 16*a^5*b^2*d^10 + 32*a^7*c^2*d^8 - 32*a^7*c^3*d^7 - 57*a^7*c^4*d^6 + 48*a^7*c^5*d^5 + 52*a^7*c^6*d^4 - 32*a^7*c^7*d^3 - 24*a^7*c^8*d^2 + 4*b^7*c^2*d^8 + 4*b^7*c^4*d^6 - 12*a*b^6*c^2*d^8 - 12*a*b^6*c^3*d^7 - 12*a*b^6*c^4*d^6 - 24*a*b^6*c^5*d^5 - 72*a^6*b*c^2*d^8 + 56*a^6*b*c^3*d^7 + 155*a^6*b*c^4*d^6 - 108*a^6*b*c^5*d^5 - 172*a^6*b*c^6*d^4 + 104*a^6*b*c^7*d^3 + 96*a^6*b*c^8*d^2 + 10*a^2*b^5*c^2*d^8 + 36*a^2*b^5*c^3*d^7 + 4*a^2*b^5*c^4*d^6 + 72*a^2*b^5*c^5*d^5 + 60*a^2*b^5*c^6*d^4 + 2*a^3*b^4*c^2*d^8 - 60*a^3*b^4*c^3*d^7 + 20*a^3*b^4*c^4*d^6 - 12*a^3*b^4*c^5*d^5 - 180*a^3*b^4*c^6*d^4 - 72*a^3*b^4*c^7*d^3 - 26*a^4*b^3*c^2*d^8 + 84*a^4*b^3*c^3*d^7 + 25*a^4*b^3*c^4*d^6 - 156*a^4*b^3*c^5*d^5 + 120*a^4*b^3*c^6*d^4 + 216*a^4*b^3*c^7*d^3 + 36*a^4*b^3*c^8*d^2 + 62*a^5*b^2*c^2*d^8 - 72*a^5*b^2*c^3*d^7 - 139*a^5*b^2*c^4*d^6 + 180*a^5*b^2*c^5*d^5 + 120*a^5*b^2*c^6*d^4 - 216*a^5*b^2*c^7*d^3 - 108*a^5*b^2*c^8*d^2 - 8*a^6*b*c*d^9 - 8*a^6*b*c^9*d))/(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d) - (d*((c + d)^5*(c - d)^5)^(1/2)*((8*(2*b^10*d^15 - 4*a^10*c^15 + 8*a^9*b*c^15 - 2*a*b^9*d^15 + 12*a^10*c^14*d - 2*b^10*c*d^14 - 4*a^8*b^2*c^15 + 2*a^2*b^8*d^15 - 6*a^3*b^7*d^15 + 4*a^4*b^6*d^15 + 4*a^10*c^6*d^9 - 2*a^10*c^7*d^8 - 18*a^10*c^8*d^7 + 4*a^10*c^9*d^6 + 36*a^10*c^10*d^5 - 6*a^10*c^11*d^4 - 34*a^10*c^12*d^3 + 8*a^10*c^13*d^2 - 6*b^10*c^4*d^11 + 6*b^10*c^5*d^10 + 4*b^10*c^6*d^9 - 4*b^10*c^7*d^8 + 10*a*b^9*c^2*d^13 - 12*a*b^9*c^3*d^12 + 18*a*b^9*c^4*d^11 + 48*a*b^9*c^5*d^10 - 58*a*b^9*c^6*d^9 - 28*a*b^9*c^7*d^8 + 32*a*b^9*c^8*d^7 + 8*a^2*b^8*c*d^14 - 8*a^3*b^7*c*d^14 + 34*a^4*b^6*c*d^14 - 24*a^5*b^5*c*d^14 + 32*a^7*b^3*c^14*d - 52*a^8*b^2*c^14*d - 24*a^9*b*c^5*d^10 + 6*a^9*b*c^6*d^9 + 112*a^9*b*c^7*d^8 + 10*a^9*b*c^8*d^7 - 236*a^9*b*c^9*d^6 - 30*a^9*b*c^10*d^5 + 240*a^9*b*c^11*d^4 + 6*a^9*b*c^12*d^3 - 100*a^9*b*c^13*d^2 - 8*a^2*b^8*c^2*d^13 + 10*a^2*b^8*c^3*d^12 + 90*a^2*b^8*c^4*d^11 - 156*a^2*b^8*c^5*d^10 - 164*a^2*b^8*c^6*d^9 + 250*a^2*b^8*c^7*d^8 + 80*a^2*b^8*c^8*d^7 - 112*a^2*b^8*c^9*d^6 + 28*a^3*b^7*c^2*d^13 + 84*a^3*b^7*c^3*d^12 - 224*a^3*b^7*c^4*d^11 - 252*a^3*b^7*c^5*d^10 + 612*a^3*b^7*c^6*d^9 + 284*a^3*b^7*c^7*d^8 - 634*a^3*b^7*c^8*d^7 - 108*a^3*b^7*c^9*d^6 + 224*a^3*b^7*c^10*d^5 - 12*a^4*b^6*c^2*d^13 - 220*a^4*b^6*c^3*d^12 - 104*a^4*b^6*c^4*d^11 + 820*a^4*b^6*c^5*d^10 + 260*a^4*b^6*c^6*d^9 - 1396*a^4*b^6*c^7*d^8 - 180*a^4*b^6*c^8*d^7 + 1042*a^4*b^6*c^9*d^6 + 32*a^4*b^6*c^10*d^5 - 280*a^4*b^6*c^11*d^4 - 78*a^5*b^5*c^2*d^13 + 128*a^5*b^5*c^3*d^12 + 536*a^5*b^5*c^4*d^11 - 188*a^5*b^5*c^5*d^10 - 1532*a^5*b^5*c^6*d^9 + 204*a^5*b^5*c^7*d^8 + 1992*a^5*b^5*c^8*d^7 - 236*a^5*b^5*c^9*d^6 - 1142*a^5*b^5*c^10*d^5 + 116*a^5*b^5*c^11*d^4 + 224*a^5*b^5*c^12*d^3 + 60*a^6*b^4*c^2*d^13 + 90*a^6*b^4*c^3*d^12 - 320*a^6*b^4*c^4*d^11 - 668*a^6*b^4*c^5*d^10 + 708*a^6*b^4*c^6*d^9 + 1660*a^6*b^4*c^7*d^8 - 888*a^6*b^4*c^8*d^7 - 1788*a^6*b^4*c^9*d^6 + 632*a^6*b^4*c^10*d^5 + 818*a^6*b^4*c^11*d^4 - 192*a^6*b^4*c^12*d^3 - 112*a^6*b^4*c^13*d^2 - 80*a^7*b^3*c^3*d^12 - 50*a^7*b^3*c^4*d^11 + 408*a^7*b^3*c^5*d^10 + 452*a^7*b^3*c^6*d^9 - 932*a^7*b^3*c^7*d^8 - 1040*a^7*b^3*c^8*d^7 + 1100*a^7*b^3*c^9*d^6 + 956*a^7*b^3*c^10*d^5 - 636*a^7*b^3*c^11*d^4 - 350*a^7*b^3*c^12*d^3 + 140*a^7*b^3*c^13*d^2 + 60*a^8*b^2*c^4*d^11 + 6*a^8*b^2*c^5*d^10 - 292*a^8*b^2*c^6*d^9 - 148*a^8*b^2*c^7*d^8 + 646*a^8*b^2*c^8*d^7 + 334*a^8*b^2*c^9*d^6 - 708*a^8*b^2*c^10*d^5 - 252*a^8*b^2*c^11*d^4 + 346*a^8*b^2*c^12*d^3 + 64*a^8*b^2*c^13*d^2 - 8*a*b^9*c*d^14 + 8*a^9*b*c^14*d))/(a^6*c^13 - b^6*d^13 + a^6*c^12*d - b^6*c*d^12 - a^6*c^6*d^7 - a^6*c^7*d^6 + 3*a^6*c^8*d^5 + 3*a^6*c^9*d^4 - 3*a^6*c^10*d^3 - 3*a^6*c^11*d^2 + 3*b^6*c^2*d^11 + 3*b^6*c^3*d^10 - 3*b^6*c^4*d^9 - 3*b^6*c^5*d^8 + b^6*c^6*d^7 + b^6*c^7*d^6 + 6*a*b^5*c^2*d^11 - 18*a*b^5*c^3*d^10 - 18*a*b^5*c^4*d^9 + 18*a*b^5*c^5*d^8 + 18*a*b^5*c^6*d^7 - 6*a*b^5*c^7*d^6 - 6*a*b^5*c^8*d^5 + 6*a^5*b*c^5*d^8 + 6*a^5*b*c^6*d^7 - 18*a^5*b*c^7*d^6 - 18*a^5*b*c^8*d^5 + 18*a^5*b*c^9*d^4 + 18*a^5*b*c^10*d^3 - 6*a^5*b*c^11*d^2 - 15*a^2*b^4*c^2*d^11 - 15*a^2*b^4*c^3*d^10 + 45*a^2*b^4*c^4*d^9 + 45*a^2*b^4*c^5*d^8 - 45*a^2*b^4*c^6*d^7 - 45*a^2*b^4*c^7*d^6 + 15*a^2*b^4*c^8*d^5 + 15*a^2*b^4*c^9*d^4 + 20*a^3*b^3*c^3*d^10 + 20*a^3*b^3*c^4*d^9 - 60*a^3*b^3*c^5*d^8 - 60*a^3*b^3*c^6*d^7 + 60*a^3*b^3*c^7*d^6 + 60*a^3*b^3*c^8*d^5 - 20*a^3*b^3*c^9*d^4 - 20*a^3*b^3*c^10*d^3 - 15*a^4*b^2*c^4*d^9 - 15*a^4*b^2*c^5*d^8 + 45*a^4*b^2*c^6*d^7 + 45*a^4*b^2*c^7*d^6 - 45*a^4*b^2*c^8*d^5 - 45*a^4*b^2*c^9*d^4 + 15*a^4*b^2*c^10*d^3 + 15*a^4*b^2*c^11*d^2 + 6*a*b^5*c*d^12 - 6*a^5*b*c^12*d) + (4*d*tan(e/2 + (f*x)/2)*((c + d)^5*(c - d)^5)^(1/2)*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*(8*a^8*b*c^16 + 8*a*b^8*d^16 - 8*a^9*c^15*d - 8*b^9*c*d^15 + 8*a^6*b^3*c^16 - 16*a^7*b^2*c^16 - 16*a^2*b^7*d^16 + 8*a^3*b^6*d^16 + 8*a^9*c^6*d^10 - 8*a^9*c^7*d^9 - 32*a^9*c^8*d^8 + 32*a^9*c^9*d^7 + 48*a^9*c^10*d^6 - 48*a^9*c^11*d^5 - 32*a^9*c^12*d^4 + 32*a^9*c^13*d^3 + 8*a^9*c^14*d^2 + 8*b^9*c^2*d^14 + 32*b^9*c^3*d^13 - 32*b^9*c^4*d^12 - 48*b^9*c^5*d^11 + 48*b^9*c^6*d^10 + 32*b^9*c^7*d^9 - 32*b^9*c^8*d^8 - 8*b^9*c^9*d^7 + 8*b^9*c^10*d^6 - 80*a*b^8*c^3*d^13 - 80*a*b^8*c^4*d^12 + 240*a*b^8*c^5*d^11 + 160*a*b^8*c^6*d^10 - 320*a*b^8*c^7*d^9 - 120*a*b^8*c^8*d^8 + 200*a*b^8*c^9*d^7 + 32*a*b^8*c^10*d^6 - 48*a*b^8*c^11*d^5 - 40*a^2*b^7*c*d^15 + 88*a^3*b^6*c*d^15 - 48*a^4*b^5*c*d^15 - 48*a^5*b^4*c^15*d + 88*a^6*b^3*c^15*d - 40*a^7*b^2*c^15*d - 48*a^8*b*c^5*d^11 + 32*a^8*b*c^6*d^10 + 200*a^8*b*c^7*d^9 - 120*a^8*b*c^8*d^8 - 320*a^8*b*c^9*d^7 + 160*a^8*b*c^10*d^6 + 240*a^8*b*c^11*d^5 - 80*a^8*b*c^12*d^4 - 80*a^8*b*c^13*d^3 + 24*a^2*b^7*c^2*d^14 + 136*a^2*b^7*c^3*d^13 + 184*a^2*b^7*c^4*d^12 - 144*a^2*b^7*c^5*d^11 - 656*a^2*b^7*c^6*d^10 + 16*a^2*b^7*c^7*d^9 + 864*a^2*b^7*c^8*d^8 + 56*a^2*b^7*c^9*d^7 - 520*a^2*b^7*c^10*d^6 - 24*a^2*b^7*c^11*d^5 + 120*a^2*b^7*c^12*d^4 + 40*a^3*b^6*c^2*d^14 - 280*a^3*b^6*c^3*d^13 - 320*a^3*b^6*c^4*d^12 + 80*a^3*b^6*c^5*d^11 + 720*a^3*b^6*c^6*d^10 + 720*a^3*b^6*c^7*d^9 - 760*a^3*b^6*c^8*d^8 - 1160*a^3*b^6*c^9*d^7 + 392*a^3*b^6*c^10*d^6 + 712*a^3*b^6*c^11*d^5 - 80*a^3*b^6*c^12*d^4 - 160*a^3*b^6*c^13*d^3 - 192*a^4*b^5*c^2*d^14 + 152*a^4*b^5*c^3*d^13 + 728*a^4*b^5*c^4*d^12 + 72*a^4*b^5*c^5*d^11 - 872*a^4*b^5*c^6*d^10 - 848*a^4*b^5*c^7*d^9 + 48*a^4*b^5*c^8*d^8 + 1312*a^4*b^5*c^9*d^7 + 688*a^4*b^5*c^10*d^6 - 840*a^4*b^5*c^11*d^5 - 520*a^4*b^5*c^12*d^4 + 200*a^4*b^5*c^13*d^3 + 120*a^4*b^5*c^14*d^2 + 120*a^5*b^4*c^2*d^14 + 200*a^5*b^4*c^3*d^13 - 520*a^5*b^4*c^4*d^12 - 840*a^5*b^4*c^5*d^11 + 688*a^5*b^4*c^6*d^10 + 1312*a^5*b^4*c^7*d^9 + 48*a^5*b^4*c^8*d^8 - 848*a^5*b^4*c^9*d^7 - 872*a^5*b^4*c^10*d^6 + 72*a^5*b^4*c^11*d^5 + 728*a^5*b^4*c^12*d^4 + 152*a^5*b^4*c^13*d^3 - 192*a^5*b^4*c^14*d^2 - 160*a^6*b^3*c^3*d^13 - 80*a^6*b^3*c^4*d^12 + 712*a^6*b^3*c^5*d^11 + 392*a^6*b^3*c^6*d^10 - 1160*a^6*b^3*c^7*d^9 - 760*a^6*b^3*c^8*d^8 + 720*a^6*b^3*c^9*d^7 + 720*a^6*b^3*c^10*d^6 + 80*a^6*b^3*c^11*d^5 - 320*a^6*b^3*c^12*d^4 - 280*a^6*b^3*c^13*d^3 + 40*a^6*b^3*c^14*d^2 + 120*a^7*b^2*c^4*d^12 - 24*a^7*b^2*c^5*d^11 - 520*a^7*b^2*c^6*d^10 + 56*a^7*b^2*c^7*d^9 + 864*a^7*b^2*c^8*d^8 + 16*a^7*b^2*c^9*d^7 - 656*a^7*b^2*c^10*d^6 - 144*a^7*b^2*c^11*d^5 + 184*a^7*b^2*c^12*d^4 + 136*a^7*b^2*c^13*d^3 + 24*a^7*b^2*c^14*d^2 + 8*a*b^8*c*d^15 + 8*a^8*b*c^15*d))/((a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)*(a^4*c^11 - b^4*d^11 + a^4*c^10*d - b^4*c*d^10 - a^4*c^4*d^7 - a^4*c^5*d^6 + 3*a^4*c^6*d^5 + 3*a^4*c^7*d^4 - 3*a^4*c^8*d^3 - 3*a^4*c^9*d^2 + 3*b^4*c^2*d^9 + 3*b^4*c^3*d^8 - 3*b^4*c^4*d^7 - 3*b^4*c^5*d^6 + b^4*c^6*d^5 + b^4*c^7*d^4 + 4*a*b^3*c^2*d^9 - 12*a*b^3*c^3*d^8 - 12*a*b^3*c^4*d^7 + 12*a*b^3*c^5*d^6 + 12*a*b^3*c^6*d^5 - 4*a*b^3*c^7*d^4 - 4*a*b^3*c^8*d^3 + 4*a^3*b*c^3*d^8 + 4*a^3*b*c^4*d^7 - 12*a^3*b*c^5*d^6 - 12*a^3*b*c^6*d^5 + 12*a^3*b*c^7*d^4 + 12*a^3*b*c^8*d^3 - 4*a^3*b*c^9*d^2 - 6*a^2*b^2*c^2*d^9 - 6*a^2*b^2*c^3*d^8 + 18*a^2*b^2*c^4*d^7 + 18*a^2*b^2*c^5*d^6 - 18*a^2*b^2*c^6*d^5 - 18*a^2*b^2*c^7*d^4 + 6*a^2*b^2*c^8*d^3 + 6*a^2*b^2*c^9*d^2 + 4*a*b^3*c*d^10 - 4*a^3*b*c^10*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d)))*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d))/(2*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d))))*((c + d)^5*(c - d)^5)^(1/2)*(6*a^2*c^4 + 2*a^2*d^4 + b^2*d^4 - 5*a^2*c^2*d^2 + 2*b^2*c^2*d^2 - 6*a*b*c^3*d)*1i)/(f*(a^3*c^13 + b^3*d^13 - a^3*c^3*d^10 + 5*a^3*c^5*d^8 - 10*a^3*c^7*d^6 + 10*a^3*c^9*d^4 - 5*a^3*c^11*d^2 - 5*b^3*c^2*d^11 + 10*b^3*c^4*d^9 - 10*b^3*c^6*d^7 + 5*b^3*c^8*d^5 - b^3*c^10*d^3 + 15*a*b^2*c^3*d^10 - 30*a*b^2*c^5*d^8 + 30*a*b^2*c^7*d^6 - 15*a*b^2*c^9*d^4 + 3*a*b^2*c^11*d^2 + 3*a^2*b*c^2*d^11 - 15*a^2*b*c^4*d^9 + 30*a^2*b*c^6*d^7 - 30*a^2*b*c^8*d^5 + 15*a^2*b*c^10*d^3 - 3*a*b^2*c*d^12 - 3*a^2*b*c^12*d))","B"
16,0,-1,213,0.000000,"\text{Not used}","int((c + d/cos(e + f*x))^(1/2)/(a + b*cos(e + f*x)),x)","\int \frac{\sqrt{c+\frac{d}{\cos\left(e+f\,x\right)}}}{a+b\,\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((c + d/cos(e + f*x))^(1/2)/(a + b*cos(e + f*x)), x)","F"
17,0,-1,102,0.000000,"\text{Not used}","int(1/((c + d/cos(e + f*x))^(1/2)*(a + b*cos(e + f*x))),x)","\int \frac{1}{\sqrt{c+\frac{d}{\cos\left(e+f\,x\right)}}\,\left(a+b\,\cos\left(e+f\,x\right)\right)} \,d x","Not used",1,"int(1/((c + d/cos(e + f*x))^(1/2)*(a + b*cos(e + f*x))), x)","F"
18,1,886,87,4.164833,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + b*cos(d + e*x)),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-\mathrm{i}\right)\,\left(-C+B\,1{}\mathrm{i}\right)}{b\,e}+\frac{\ln\left(\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(C+B\,1{}\mathrm{i}\right)}{b\,e}-\frac{\ln\left(A^2\,b^3+B^2\,b^3-4\,C^2\,a^3+4\,C^2\,b^3+A^2\,a\,b^2+B^2\,a\,b^2+4\,C^2\,a\,b^2-4\,C^2\,a^2\,b-2\,A\,B\,a\,b^2-2\,A\,B\,a^2\,b+A^2\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}+B^2\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,b^2\,\sqrt{b^2-a^2}+4\,B\,C\,a^2\,\sqrt{b^2-a^2}-4\,A\,C\,b^3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-4\,B\,C\,a^3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-4\,A\,C\,a\,b\,\sqrt{b^2-a^2}+4\,B\,C\,a\,b\,\sqrt{b^2-a^2}+4\,A\,C\,a^2\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+4\,B\,C\,a\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-2\,A\,B\,a\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,\left(C\,a^2-C\,b^2+A\,b\,\sqrt{b^2-a^2}-B\,a\,\sqrt{b^2-a^2}\right)}{b\,e\,\left(a^2-b^2\right)}-\frac{\ln\left(A^2\,b^3+B^2\,b^3-4\,C^2\,a^3+4\,C^2\,b^3+A^2\,a\,b^2+B^2\,a\,b^2+4\,C^2\,a\,b^2-4\,C^2\,a^2\,b-2\,A\,B\,a\,b^2-2\,A\,B\,a^2\,b-A^2\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}-B^2\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,b^2\,\sqrt{b^2-a^2}-4\,B\,C\,a^2\,\sqrt{b^2-a^2}-4\,A\,C\,b^3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)-4\,B\,C\,a^3\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+4\,A\,C\,a\,b\,\sqrt{b^2-a^2}-4\,B\,C\,a\,b\,\sqrt{b^2-a^2}+4\,A\,C\,a^2\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+4\,B\,C\,a\,b^2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)+2\,A\,B\,a\,b\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,\left(C\,a^2-C\,b^2-A\,b\,\sqrt{b^2-a^2}+B\,a\,\sqrt{b^2-a^2}\right)}{b\,e\,\left(a^2-b^2\right)}","Not used",1,"(log(tan(d/2 + (e*x)/2) + 1i)*(B*1i + C))/(b*e) - (log(tan(d/2 + (e*x)/2) - 1i)*(B*1i - C))/(b*e) - (log(A^2*b^3 + B^2*b^3 - 4*C^2*a^3 + 4*C^2*b^3 + A^2*a*b^2 + B^2*a*b^2 + 4*C^2*a*b^2 - 4*C^2*a^2*b - 2*A*B*a*b^2 - 2*A*B*a^2*b + A^2*b^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) + B^2*b^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*b^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*b^2*(b^2 - a^2)^(1/2) + 4*B*C*a^2*(b^2 - a^2)^(1/2) - 4*A*C*b^3*tan(d/2 + (e*x)/2) - 4*B*C*a^3*tan(d/2 + (e*x)/2) - 4*A*C*a*b*(b^2 - a^2)^(1/2) + 4*B*C*a*b*(b^2 - a^2)^(1/2) + 4*A*C*a^2*b*tan(d/2 + (e*x)/2) + 4*B*C*a*b^2*tan(d/2 + (e*x)/2) - 2*A*B*a*b*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2))*(C*a^2 - C*b^2 + A*b*(b^2 - a^2)^(1/2) - B*a*(b^2 - a^2)^(1/2)))/(b*e*(a^2 - b^2)) - (log(A^2*b^3 + B^2*b^3 - 4*C^2*a^3 + 4*C^2*b^3 + A^2*a*b^2 + B^2*a*b^2 + 4*C^2*a*b^2 - 4*C^2*a^2*b - 2*A*B*a*b^2 - 2*A*B*a^2*b - A^2*b^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) - B^2*b^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*b^2*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*b^2*(b^2 - a^2)^(1/2) - 4*B*C*a^2*(b^2 - a^2)^(1/2) - 4*A*C*b^3*tan(d/2 + (e*x)/2) - 4*B*C*a^3*tan(d/2 + (e*x)/2) + 4*A*C*a*b*(b^2 - a^2)^(1/2) - 4*B*C*a*b*(b^2 - a^2)^(1/2) + 4*A*C*a^2*b*tan(d/2 + (e*x)/2) + 4*B*C*a*b^2*tan(d/2 + (e*x)/2) + 2*A*B*a*b*tan(d/2 + (e*x)/2)*(b^2 - a^2)^(1/2))*(C*a^2 - C*b^2 - A*b*(b^2 - a^2)^(1/2) + B*a*(b^2 - a^2)^(1/2)))/(b*e*(a^2 - b^2))","B"
19,1,126,120,2.565575,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + b*cos(d + e*x))^2,x)","\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)\,\left(A\,a-B\,b\right)}{e\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{\frac{2\,C}{a-b}+\frac{2\,\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(A\,b-B\,a\right)}{\left(a+b\right)\,\left(a-b\right)}}{e\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*atan((tan(d/2 + (e*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2)))*(A*a - B*b))/(e*(a + b)^(3/2)*(a - b)^(3/2)) - ((2*C)/(a - b) + (2*tan(d/2 + (e*x)/2)*(A*b - B*a))/((a + b)*(a - b)))/(e*(a + b + tan(d/2 + (e*x)/2)^2*(a - b)))","B"
20,1,283,187,5.495348,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + b*cos(d + e*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,A\,a^2-3\,B\,a\,b+A\,b^2\right)}{e\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{2\,C\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2}{a-b}+\frac{2\,C\,a}{{\left(a-b\right)}^2}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(2\,B\,a^2-A\,b^2+2\,B\,b^2-4\,A\,a\,b+B\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(A\,b^2+2\,B\,a^2+2\,B\,b^2-4\,A\,a\,b-B\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{e\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(atan((tan(d/2 + (e*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*A*a^2 + A*b^2 - 3*B*a*b))/(e*(a + b)^(5/2)*(a - b)^(5/2)) - ((2*C*tan(d/2 + (e*x)/2)^2)/(a - b) + (2*C*a)/(a - b)^2 - (tan(d/2 + (e*x)/2)^3*(2*B*a^2 - A*b^2 + 2*B*b^2 - 4*A*a*b + B*a*b))/((a + b)^2*(a - b)) - (tan(d/2 + (e*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 - 4*A*a*b - B*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(e*(2*a*b + tan(d/2 + (e*x)/2)^2*(2*a^2 - 2*b^2) + tan(d/2 + (e*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
21,1,502,260,5.219557,"\text{Not used}","int((A + B*cos(d + e*x) + C*sin(d + e*x))/(a + b*cos(d + e*x))^4,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(2\,A\,a^3-4\,B\,a^2\,b+3\,A\,a\,b^2-B\,b^3\right)}{e\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{2\,C\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4}{a-b}+\frac{2\,C\,\left(3\,a^2+b^2\right)}{3\,{\left(a-b\right)}^3}+\frac{4\,C\,a\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2}{{\left(a-b\right)}^2}+\frac{4\,{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^3\,\left(-3\,B\,a^3+9\,A\,a^2\,b-7\,B\,a\,b^2+A\,b^3\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}-\frac{{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^5\,\left(2\,B\,a^3-2\,A\,b^3+B\,b^3-3\,A\,a\,b^2-6\,A\,a^2\,b+6\,B\,a\,b^2+2\,B\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)\,\left(2\,A\,b^3-2\,B\,a^3+B\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2+2\,B\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{e\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{d}{2}+\frac{e\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(atan((tan(d/2 + (e*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(a + b)^(1/2)*(a - b)^(7/2)))*(2*A*a^3 - B*b^3 + 3*A*a*b^2 - 4*B*a^2*b))/(e*(a + b)^(7/2)*(a - b)^(7/2)) - ((2*C*tan(d/2 + (e*x)/2)^4)/(a - b) + (2*C*(3*a^2 + b^2))/(3*(a - b)^3) + (4*C*a*tan(d/2 + (e*x)/2)^2)/(a - b)^2 + (4*tan(d/2 + (e*x)/2)^3*(A*b^3 - 3*B*a^3 + 9*A*a^2*b - 7*B*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) - (tan(d/2 + (e*x)/2)^5*(2*B*a^3 - 2*A*b^3 + B*b^3 - 3*A*a*b^2 - 6*A*a^2*b + 6*B*a*b^2 + 2*B*a^2*b))/((a + b)^3*(a - b)) + (tan(d/2 + (e*x)/2)*(2*A*b^3 - 2*B*a^3 + B*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 + 2*B*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(e*(3*a*b^2 - tan(d/2 + (e*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(d/2 + (e*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(d/2 + (e*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))","B"