1,0,-1,373,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3, x)","F"
2,0,-1,277,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2, x)","F"
3,0,-1,191,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x)),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x)), x)","F"
4,0,-1,202,0.000000,"\text{Not used}","int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x)),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x)), x)","F"
5,0,-1,279,0.000000,"\text{Not used}","int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^2, x)","F"
6,0,-1,362,0.000000,"\text{Not used}","int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^3, x)","F"
7,0,-1,336,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2), x)","F"
8,0,-1,229,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2), x)","F"
9,0,-1,137,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2), x)","F"
10,0,-1,152,0.000000,"\text{Not used}","int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^(1/2), x)","F"
11,0,-1,226,0.000000,"\text{Not used}","int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((d*sin(e + f*x))^n*(A + B*sin(e + f*x)))/(a + a*sin(e + f*x))^(3/2), x)","F"
12,0,-1,221,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((d*sin(e + f*x))^n*(A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
13,0,-1,114,0.000000,"\text{Not used}","int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^m*(a - a*sin(e + f*x)),x)","\int {\left(d\,\sin\left(e+f\,x\right)\right)}^n\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(a-a\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((d*sin(e + f*x))^n*(a + a*sin(e + f*x))^m*(a - a*sin(e + f*x)), x)","F"
14,1,61,37,12.982373,"\text{Not used}","int(-(sin(c + d*x)^n*(n - sin(c + d*x)*(n + 2) + 1))/(a + a*sin(c + d*x))^(n + 2),x)","-\frac{{\sin\left(c+d\,x\right)}^n\,\sin\left(2\,c+2\,d\,x\right)}{a^2\,d\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^n\,\left(2\,{\sin\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)+2\right)}","Not used",1,"-(sin(c + d*x)^n*sin(2*c + 2*d*x))/(a^2*d*(a*(sin(c + d*x) + 1))^n*(4*sin(c + d*x) + 2*sin(c + d*x)^2 + 2))","B"
15,1,38,35,12.847509,"\text{Not used}","int(((a + a*sin(c + d*x))^m*(m - m*sin(c + d*x) + 1))/sin(c + d*x)^(m + 2),x)","-\frac{\sin\left(2\,c+2\,d\,x\right)\,{\left(a\,\left(\sin\left(c+d\,x\right)+1\right)\right)}^m}{2\,d\,{\sin\left(c+d\,x\right)}^{m+2}}","Not used",1,"-(sin(2*c + 2*d*x)*(a*(sin(c + d*x) + 1))^m)/(2*d*sin(c + d*x)^(m + 2))","B"
16,1,3718,153,17.181616,"\text{Not used}","int((sin(e + f*x)^2*(A + B*sin(e + f*x)))/(a + b*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(-2\,B\,a^3+A\,a^2\,b+B\,a\,b^2\right)}{b^2\,\left(a^2-b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(B\,a^2-A\,a\,b\right)}{b\,\left(a^2-b^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-3\,B\,a^2+A\,a\,b+2\,B\,b^2\right)}{b\,\left(a^2-b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-2\,B\,a^3+A\,a^2\,b+B\,a\,b^2\right)}{b^2\,\left(a^2-b^2\right)}}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(A\,b-2\,B\,a\right)\,1{}\mathrm{i}}{b^3\,f}-\frac{\ln\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-\mathrm{i}\right)\,\left(A\,b\,1{}\mathrm{i}-B\,a\,2{}\mathrm{i}\right)}{b^3\,f}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(A^2\,a^6\,b^4-2\,A^2\,a^4\,b^6+A^2\,a^2\,b^8-4\,A\,B\,a^7\,b^3+8\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+4\,B^2\,a^8\,b^2-8\,B^2\,a^6\,b^4+4\,B^2\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^7\,b^4+8\,A^2\,a^5\,b^6-9\,A^2\,a^3\,b^8+2\,A^2\,a\,b^{10}+8\,A\,B\,a^8\,b^3-30\,A\,B\,a^6\,b^5+32\,A\,B\,a^4\,b^7-8\,A\,B\,a^2\,b^9-8\,B^2\,a^9\,b^2+28\,B^2\,a^7\,b^4-29\,B^2\,a^5\,b^6+8\,B^2\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,B\,a^7\,b^6+2\,A\,a^6\,b^7+10\,B\,a^5\,b^8-6\,A\,a^4\,b^9-6\,B\,a^3\,b^{10}+4\,A\,a^2\,b^{11}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{32\,\left(B\,a^6\,b^6-3\,B\,a^4\,b^8+A\,a^3\,b^9+2\,B\,a^2\,b^{10}-A\,a\,b^{11}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{a\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(A^2\,a^6\,b^4-2\,A^2\,a^4\,b^6+A^2\,a^2\,b^8-4\,A\,B\,a^7\,b^3+8\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+4\,B^2\,a^8\,b^2-8\,B^2\,a^6\,b^4+4\,B^2\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^7\,b^4+8\,A^2\,a^5\,b^6-9\,A^2\,a^3\,b^8+2\,A^2\,a\,b^{10}+8\,A\,B\,a^8\,b^3-30\,A\,B\,a^6\,b^5+32\,A\,B\,a^4\,b^7-8\,A\,B\,a^2\,b^9-8\,B^2\,a^9\,b^2+28\,B^2\,a^7\,b^4-29\,B^2\,a^5\,b^6+8\,B^2\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(B\,a^6\,b^6-3\,B\,a^4\,b^8+A\,a^3\,b^9+2\,B\,a^2\,b^{10}-A\,a\,b^{11}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,B\,a^7\,b^6+2\,A\,a^6\,b^7+10\,B\,a^5\,b^8-6\,A\,a^4\,b^9-6\,B\,a^3\,b^{10}+4\,A\,a^2\,b^{11}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(-A^3\,a^5\,b^3+2\,A^3\,a^3\,b^5+5\,A^2\,B\,a^6\,b^2-9\,A^2\,B\,a^4\,b^4-8\,A\,B^2\,a^7\,b+13\,A\,B^2\,a^5\,b^3+4\,B^3\,a^8-6\,B^3\,a^6\,b^2\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^3\,a^6\,b^3+6\,A^3\,a^4\,b^5-4\,A^3\,a^2\,b^7+12\,A^2\,B\,a^7\,b^2-34\,A^2\,B\,a^5\,b^4+22\,A^2\,B\,a^3\,b^6-24\,A\,B^2\,a^8\,b+64\,A\,B^2\,a^6\,b^3-40\,A\,B^2\,a^4\,b^5+16\,B^3\,a^9-40\,B^3\,a^7\,b^2+24\,B^3\,a^5\,b^4\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(A^2\,a^6\,b^4-2\,A^2\,a^4\,b^6+A^2\,a^2\,b^8-4\,A\,B\,a^7\,b^3+8\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+4\,B^2\,a^8\,b^2-8\,B^2\,a^6\,b^4+4\,B^2\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^7\,b^4+8\,A^2\,a^5\,b^6-9\,A^2\,a^3\,b^8+2\,A^2\,a\,b^{10}+8\,A\,B\,a^8\,b^3-30\,A\,B\,a^6\,b^5+32\,A\,B\,a^4\,b^7-8\,A\,B\,a^2\,b^9-8\,B^2\,a^9\,b^2+28\,B^2\,a^7\,b^4-29\,B^2\,a^5\,b^6+8\,B^2\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,B\,a^7\,b^6+2\,A\,a^6\,b^7+10\,B\,a^5\,b^8-6\,A\,a^4\,b^9-6\,B\,a^3\,b^{10}+4\,A\,a^2\,b^{11}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}-\frac{32\,\left(B\,a^6\,b^6-3\,B\,a^4\,b^8+A\,a^3\,b^9+2\,B\,a^2\,b^{10}-A\,a\,b^{11}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{a\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(A^2\,a^6\,b^4-2\,A^2\,a^4\,b^6+A^2\,a^2\,b^8-4\,A\,B\,a^7\,b^3+8\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+4\,B^2\,a^8\,b^2-8\,B^2\,a^6\,b^4+4\,B^2\,a^4\,b^6\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^7\,b^4+8\,A^2\,a^5\,b^6-9\,A^2\,a^3\,b^8+2\,A^2\,a\,b^{10}+8\,A\,B\,a^8\,b^3-30\,A\,B\,a^6\,b^5+32\,A\,B\,a^4\,b^7-8\,A\,B\,a^2\,b^9-8\,B^2\,a^9\,b^2+28\,B^2\,a^7\,b^4-29\,B^2\,a^5\,b^6+8\,B^2\,a^3\,b^8\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\left(B\,a^6\,b^6-3\,B\,a^4\,b^8+A\,a^3\,b^9+2\,B\,a^2\,b^{10}-A\,a\,b^{11}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-4\,B\,a^7\,b^6+2\,A\,a^6\,b^7+10\,B\,a^5\,b^8-6\,A\,a^4\,b^9-6\,B\,a^3\,b^{10}+4\,A\,a^2\,b^{11}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{32\,\left(a^6\,b^8-2\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^4\,b^5-2\,a^2\,b^7+b^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,a^7\,b^8+7\,a^5\,b^{10}-8\,a^3\,b^{12}+3\,a\,b^{14}\right)}{a^4\,b^6-2\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)\,2{}\mathrm{i}}{f\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((2*(A*a^2*b - 2*B*a^3 + B*a*b^2))/(b^2*(a^2 - b^2)) - (2*tan(e/2 + (f*x)/2)^3*(B*a^2 - A*a*b))/(b*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)*(2*B*b^2 - 3*B*a^2 + A*a*b))/(b*(a^2 - b^2)) + (2*tan(e/2 + (f*x)/2)^2*(A*a^2*b - 2*B*a^3 + B*a*b^2))/(b^2*(a^2 - b^2)))/(f*(a + 2*b*tan(e/2 + (f*x)/2) + 2*a*tan(e/2 + (f*x)/2)^2 + a*tan(e/2 + (f*x)/2)^4 + 2*b*tan(e/2 + (f*x)/2)^3)) + (log(tan(e/2 + (f*x)/2) + 1i)*(A*b - 2*B*a)*1i)/(b^3*f) - (log(tan(e/2 + (f*x)/2) - 1i)*(A*b*1i - B*a*2i))/(b^3*f) - (a*atan(((a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(A^2*a^2*b^8 - 2*A^2*a^4*b^6 + A^2*a^6*b^4 + 4*B^2*a^4*b^6 - 8*B^2*a^6*b^4 + 4*B^2*a^8*b^2 - 4*A*B*a^3*b^7 + 8*A*B*a^5*b^5 - 4*A*B*a^7*b^3))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(2*A^2*a*b^10 - 9*A^2*a^3*b^8 + 8*A^2*a^5*b^6 - 2*A^2*a^7*b^4 + 8*B^2*a^3*b^8 - 29*B^2*a^5*b^6 + 28*B^2*a^7*b^4 - 8*B^2*a^9*b^2 - 8*A*B*a^2*b^9 + 32*A*B*a^4*b^7 - 30*A*B*a^6*b^5 + 8*A*B*a^8*b^3))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(4*A*a^2*b^11 - 6*A*a^4*b^9 + 2*A*a^6*b^7 - 6*B*a^3*b^10 + 10*B*a^5*b^8 - 4*B*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (32*(A*a^3*b^9 + 2*B*a^2*b^10 - 3*B*a^4*b^8 + B*a^6*b^6 - A*a*b^11))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (a*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(A^2*a^2*b^8 - 2*A^2*a^4*b^6 + A^2*a^6*b^4 + 4*B^2*a^4*b^6 - 8*B^2*a^6*b^4 + 4*B^2*a^8*b^2 - 4*A*B*a^3*b^7 + 8*A*B*a^5*b^5 - 4*A*B*a^7*b^3))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(2*A^2*a*b^10 - 9*A^2*a^3*b^8 + 8*A^2*a^5*b^6 - 2*A^2*a^7*b^4 + 8*B^2*a^3*b^8 - 29*B^2*a^5*b^6 + 28*B^2*a^7*b^4 - 8*B^2*a^9*b^2 - 8*A*B*a^2*b^9 + 32*A*B*a^4*b^7 - 30*A*B*a^6*b^5 + 8*A*B*a^8*b^3))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(A*a^3*b^9 + 2*B*a^2*b^10 - 3*B*a^4*b^8 + B*a^6*b^6 - A*a*b^11))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(4*A*a^2*b^11 - 6*A*a^4*b^9 + 2*A*a^6*b^7 - 6*B*a^3*b^10 + 10*B*a^5*b^8 - 4*B*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(4*B^3*a^8 + 2*A^3*a^3*b^5 - A^3*a^5*b^3 - 6*B^3*a^6*b^2 - 8*A*B^2*a^7*b + 13*A*B^2*a^5*b^3 - 9*A^2*B*a^4*b^4 + 5*A^2*B*a^6*b^2))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (64*tan(e/2 + (f*x)/2)*(16*B^3*a^9 - 4*A^3*a^2*b^7 + 6*A^3*a^4*b^5 - 2*A^3*a^6*b^3 + 24*B^3*a^5*b^4 - 40*B^3*a^7*b^2 - 24*A*B^2*a^8*b - 40*A*B^2*a^4*b^5 + 64*A*B^2*a^6*b^3 + 22*A^2*B*a^3*b^6 - 34*A^2*B*a^5*b^4 + 12*A^2*B*a^7*b^2))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(A^2*a^2*b^8 - 2*A^2*a^4*b^6 + A^2*a^6*b^4 + 4*B^2*a^4*b^6 - 8*B^2*a^6*b^4 + 4*B^2*a^8*b^2 - 4*A*B*a^3*b^7 + 8*A*B*a^5*b^5 - 4*A*B*a^7*b^3))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(2*A^2*a*b^10 - 9*A^2*a^3*b^8 + 8*A^2*a^5*b^6 - 2*A^2*a^7*b^4 + 8*B^2*a^3*b^8 - 29*B^2*a^5*b^6 + 28*B^2*a^7*b^4 - 8*B^2*a^9*b^2 - 8*A*B*a^2*b^9 + 32*A*B*a^4*b^7 - 30*A*B*a^6*b^5 + 8*A*B*a^8*b^3))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(4*A*a^2*b^11 - 6*A*a^4*b^9 + 2*A*a^6*b^7 - 6*B*a^3*b^10 + 10*B*a^5*b^8 - 4*B*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) - (32*(A*a^3*b^9 + 2*B*a^2*b^10 - 3*B*a^4*b^8 + B*a^6*b^6 - A*a*b^11))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (a*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(A^2*a^2*b^8 - 2*A^2*a^4*b^6 + A^2*a^6*b^4 + 4*B^2*a^4*b^6 - 8*B^2*a^6*b^4 + 4*B^2*a^8*b^2 - 4*A*B*a^3*b^7 + 8*A*B*a^5*b^5 - 4*A*B*a^7*b^3))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(2*A^2*a*b^10 - 9*A^2*a^3*b^8 + 8*A^2*a^5*b^6 - 2*A^2*a^7*b^4 + 8*B^2*a^3*b^8 - 29*B^2*a^5*b^6 + 28*B^2*a^7*b^4 - 8*B^2*a^9*b^2 - 8*A*B*a^2*b^9 + 32*A*B*a^4*b^7 - 30*A*B*a^6*b^5 + 8*A*B*a^8*b^3))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*(A*a^3*b^9 + 2*B*a^2*b^10 - 3*B*a^4*b^8 + B*a^6*b^6 - A*a*b^11))/(b^9 - 2*a^2*b^7 + a^4*b^5) - (32*tan(e/2 + (f*x)/2)*(4*A*a^2*b^11 - 6*A*a^4*b^9 + 2*A*a^6*b^7 - 6*B*a^3*b^10 + 10*B*a^5*b^8 - 4*B*a^7*b^6))/(b^10 - 2*a^2*b^8 + a^4*b^6) + (a*((32*(a^2*b^12 - 2*a^4*b^10 + a^6*b^8))/(b^9 - 2*a^2*b^7 + a^4*b^5) + (32*tan(e/2 + (f*x)/2)*(3*a*b^14 - 8*a^3*b^12 + 7*a^5*b^10 - 2*a^7*b^8))/(b^10 - 2*a^2*b^8 + a^4*b^6))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*2i)/(f*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
17,1,454,182,14.832536,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^4,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{A\,a\,c^4}{4}+\frac{7\,B\,a\,c^4}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(6\,A\,a\,c^4-2\,B\,a\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(12\,A\,a\,c^4-4\,B\,a\,c^4\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{A\,a\,c^4}{4}+\frac{7\,B\,a\,c^4}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(22\,A\,a\,c^4-18\,B\,a\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{13\,A\,a\,c^4}{2}-\frac{37\,B\,a\,c^4}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{13\,A\,a\,c^4}{2}-\frac{37\,B\,a\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{38\,A\,a\,c^4}{5}-\frac{34\,B\,a\,c^4}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{68\,A\,a\,c^4}{3}-\frac{44\,B\,a\,c^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{27\,A\,a\,c^4}{4}-\frac{73\,B\,a\,c^4}{24}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{27\,A\,a\,c^4}{4}-\frac{73\,B\,a\,c^4}{24}\right)+\frac{34\,A\,a\,c^4}{15}-\frac{22\,B\,a\,c^4}{15}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{7\,a\,c^4\,\mathrm{atan}\left(\frac{7\,a\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A-B\right)}{8\,\left(\frac{7\,A\,a\,c^4}{4}-\frac{7\,B\,a\,c^4}{8}\right)}\right)\,\left(2\,A-B\right)}{8\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*((A*a*c^4)/4 + (7*B*a*c^4)/8) + tan(e/2 + (f*x)/2)^10*(6*A*a*c^4 - 2*B*a*c^4) + tan(e/2 + (f*x)/2)^4*(12*A*a*c^4 - 4*B*a*c^4) - tan(e/2 + (f*x)/2)^11*((A*a*c^4)/4 + (7*B*a*c^4)/8) + tan(e/2 + (f*x)/2)^8*(22*A*a*c^4 - 18*B*a*c^4) + tan(e/2 + (f*x)/2)^5*((13*A*a*c^4)/2 - (37*B*a*c^4)/4) - tan(e/2 + (f*x)/2)^7*((13*A*a*c^4)/2 - (37*B*a*c^4)/4) + tan(e/2 + (f*x)/2)^2*((38*A*a*c^4)/5 - (34*B*a*c^4)/5) + tan(e/2 + (f*x)/2)^6*((68*A*a*c^4)/3 - (44*B*a*c^4)/3) + tan(e/2 + (f*x)/2)^3*((27*A*a*c^4)/4 - (73*B*a*c^4)/24) - tan(e/2 + (f*x)/2)^9*((27*A*a*c^4)/4 - (73*B*a*c^4)/24) + (34*A*a*c^4)/15 - (22*B*a*c^4)/15)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1)) + (7*a*c^4*atan((7*a*c^4*tan(e/2 + (f*x)/2)*(2*A - B))/(8*((7*A*a*c^4)/4 - (7*B*a*c^4)/8)))*(2*A - B))/(8*f)","B"
18,1,389,142,13.800276,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^3,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{3\,A\,a\,c^3}{4}+\frac{B\,a\,c^3}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(4\,A\,a\,c^3-2\,B\,a\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{7\,A\,a\,c^3}{2}-3\,B\,a\,c^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{7\,A\,a\,c^3}{2}-3\,B\,a\,c^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{3\,A\,a\,c^3}{4}+\frac{B\,a\,c^3}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(8\,A\,a\,c^3-8\,B\,a\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{8\,A\,a\,c^3}{3}-\frac{8\,B\,a\,c^3}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{16\,A\,a\,c^3}{3}-\frac{4\,B\,a\,c^3}{3}\right)+\frac{4\,A\,a\,c^3}{3}-\frac{14\,B\,a\,c^3}{15}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{a\,c^3\,\mathrm{atan}\left(\frac{a\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,A-2\,B\right)}{4\,\left(\frac{5\,A\,a\,c^3}{4}-\frac{B\,a\,c^3}{2}\right)}\right)\,\left(5\,A-2\,B\right)}{4\,f}-\frac{a\,c^3\,\left(5\,A-2\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*((3*A*a*c^3)/4 + (B*a*c^3)/2) + tan(e/2 + (f*x)/2)^8*(4*A*a*c^3 - 2*B*a*c^3) + tan(e/2 + (f*x)/2)^3*((7*A*a*c^3)/2 - 3*B*a*c^3) - tan(e/2 + (f*x)/2)^7*((7*A*a*c^3)/2 - 3*B*a*c^3) - tan(e/2 + (f*x)/2)^9*((3*A*a*c^3)/4 + (B*a*c^3)/2) + tan(e/2 + (f*x)/2)^6*(8*A*a*c^3 - 8*B*a*c^3) + tan(e/2 + (f*x)/2)^2*((8*A*a*c^3)/3 - (8*B*a*c^3)/3) + tan(e/2 + (f*x)/2)^4*((16*A*a*c^3)/3 - (4*B*a*c^3)/3) + (4*A*a*c^3)/3 - (14*B*a*c^3)/15)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1)) + (a*c^3*atan((a*c^3*tan(e/2 + (f*x)/2)*(5*A - 2*B))/(4*((5*A*a*c^3)/4 - (B*a*c^3)/2)))*(5*A - 2*B))/(4*f) - (a*c^3*(5*A - 2*B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
19,1,345,97,13.380926,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^2,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a\,c^2+\frac{B\,a\,c^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,a\,c^2-2\,B\,a\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,A\,a\,c^2-2\,B\,a\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{2\,A\,a\,c^2}{3}-\frac{2\,B\,a\,c^2}{3}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(A\,a\,c^2+\frac{B\,a\,c^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a\,c^2-\frac{7\,B\,a\,c^2}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(A\,a\,c^2-\frac{7\,B\,a\,c^2}{4}\right)+\frac{2\,A\,a\,c^2}{3}-\frac{2\,B\,a\,c^2}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{a\,c^2\,\mathrm{atan}\left(\frac{a\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A-B\right)}{4\,\left(A\,a\,c^2-\frac{B\,a\,c^2}{4}\right)}\right)\,\left(4\,A-B\right)}{4\,f}-\frac{a\,c^2\,\left(4\,A-B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*(A*a*c^2 + (B*a*c^2)/4) + tan(e/2 + (f*x)/2)^4*(2*A*a*c^2 - 2*B*a*c^2) + tan(e/2 + (f*x)/2)^6*(2*A*a*c^2 - 2*B*a*c^2) + tan(e/2 + (f*x)/2)^2*((2*A*a*c^2)/3 - (2*B*a*c^2)/3) - tan(e/2 + (f*x)/2)^7*(A*a*c^2 + (B*a*c^2)/4) + tan(e/2 + (f*x)/2)^3*(A*a*c^2 - (7*B*a*c^2)/4) - tan(e/2 + (f*x)/2)^5*(A*a*c^2 - (7*B*a*c^2)/4) + (2*A*a*c^2)/3 - (2*B*a*c^2)/3)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1)) + (a*c^2*atan((a*c^2*tan(e/2 + (f*x)/2)*(4*A - B))/(4*(A*a*c^2 - (B*a*c^2)/4)))*(4*A - B))/(4*f) - (a*c^2*(4*A - B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
20,1,122,49,14.328807,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x)),x)","\frac{A\,a\,c\,x}{2}-\frac{A\,a\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+\left(\frac{a\,c\,\left(12\,B-9\,A\,\left(e+f\,x\right)\right)}{6}+\frac{3\,A\,a\,c\,\left(e+f\,x\right)}{2}\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-A\,a\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{a\,c\,\left(4\,B-3\,A\,\left(e+f\,x\right)\right)}{6}+\frac{A\,a\,c\,\left(e+f\,x\right)}{2}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(A*a*c*x)/2 - (tan(e/2 + (f*x)/2)^4*((a*c*(12*B - 9*A*(e + f*x)))/6 + (3*A*a*c*(e + f*x))/2) + (a*c*(4*B - 3*A*(e + f*x)))/6 - A*a*c*tan(e/2 + (f*x)/2) + (A*a*c*(e + f*x))/2 + A*a*c*tan(e/2 + (f*x)/2)^5)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^3)","B"
21,1,111,56,12.636466,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x)),x)","\frac{\left(4\,A\,a+4\,B\,a\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-2\,B\,a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A\,a+6\,B\,a}{f\,\left(-c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{A\,a\,f\,x+2\,B\,a\,f\,x}{c\,f}","Not used",1,"(4*A*a + 6*B*a + tan(e/2 + (f*x)/2)^2*(4*A*a + 4*B*a) - 2*B*a*tan(e/2 + (f*x)/2))/(f*(c - c*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2 - c*tan(e/2 + (f*x)/2)^3)) - (A*a*f*x + 2*B*a*f*x)/(c*f)","B"
22,1,132,72,12.506022,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^2,x)","\frac{B\,a\,x}{c^2}-\frac{\left(\frac{a\,\left(6\,A-6\,B+9\,B\,\left(e+f\,x\right)\right)}{3}-3\,B\,a\,\left(e+f\,x\right)\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(\frac{a\,\left(24\,B-9\,B\,\left(e+f\,x\right)\right)}{3}+3\,B\,a\,\left(e+f\,x\right)\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{a\,\left(2\,A-10\,B+3\,B\,\left(e+f\,x\right)\right)}{3}-B\,a\,\left(e+f\,x\right)}{c^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^3}","Not used",1,"(B*a*x)/c^2 - ((a*(2*A - 10*B + 3*B*(e + f*x)))/3 + tan(e/2 + (f*x)/2)^2*((a*(6*A - 6*B + 9*B*(e + f*x)))/3 - 3*B*a*(e + f*x)) + tan(e/2 + (f*x)/2)*((a*(24*B - 9*B*(e + f*x)))/3 + 3*B*a*(e + f*x)) - B*a*(e + f*x))/(c^2*f*(tan(e/2 + (f*x)/2) - 1)^3)","B"
23,1,172,104,12.981000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^3,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{11\,A\,a\,\cos\left(e+f\,x\right)}{2}-\frac{B\,a}{4}-\frac{41\,A\,a}{4}+\frac{B\,a\,\cos\left(e+f\,x\right)}{2}+5\,A\,a\,\sin\left(e+f\,x\right)-5\,B\,a\,\sin\left(e+f\,x\right)+\frac{3\,A\,a\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{3\,B\,a\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{5\,A\,a\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{5\,B\,a\,\sin\left(2\,e+2\,f\,x\right)}{4}\right)}{15\,c^3\,f\,\left(\frac{5\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{5\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}+\frac{\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((11*A*a*cos(e + f*x))/2 - (B*a)/4 - (41*A*a)/4 + (B*a*cos(e + f*x))/2 + 5*A*a*sin(e + f*x) - 5*B*a*sin(e + f*x) + (3*A*a*cos(2*e + 2*f*x))/4 + (3*B*a*cos(2*e + 2*f*x))/4 - (5*A*a*sin(2*e + 2*f*x))/4 + (5*B*a*sin(2*e + 2*f*x))/4))/(15*c^3*f*((5*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/4 - (5*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/2 + (2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/4))","B"
24,1,228,142,13.222756,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^4,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{15\,B\,a}{4}-\frac{171\,A\,a}{2}+\frac{353\,A\,a\,\cos\left(e+f\,x\right)}{8}+\frac{5\,B\,a\,\cos\left(e+f\,x\right)}{4}+\frac{595\,A\,a\,\sin\left(e+f\,x\right)}{8}-35\,B\,a\,\sin\left(e+f\,x\right)+\frac{43\,A\,a\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{25\,A\,a\,\cos\left(3\,e+3\,f\,x\right)}{8}-\frac{5\,B\,a\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{5\,B\,a\,\cos\left(3\,e+3\,f\,x\right)}{4}-\frac{77\,A\,a\,\sin\left(2\,e+2\,f\,x\right)}{4}-\frac{21\,A\,a\,\sin\left(3\,e+3\,f\,x\right)}{8}+\frac{35\,B\,a\,\sin\left(2\,e+2\,f\,x\right)}{4}\right)}{105\,c^4\,f\,\left(\frac{35\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{8}-\frac{21\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{8}-\frac{7\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{8}+\frac{\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{8}\right)}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*((15*B*a)/4 - (171*A*a)/2 + (353*A*a*cos(e + f*x))/8 + (5*B*a*cos(e + f*x))/4 + (595*A*a*sin(e + f*x))/8 - 35*B*a*sin(e + f*x) + (43*A*a*cos(2*e + 2*f*x))/2 - (25*A*a*cos(3*e + 3*f*x))/8 - (5*B*a*cos(2*e + 2*f*x))/4 + (5*B*a*cos(3*e + 3*f*x))/4 - (77*A*a*sin(2*e + 2*f*x))/4 - (21*A*a*sin(3*e + 3*f*x))/8 + (35*B*a*sin(2*e + 2*f*x))/4))/(105*c^4*f*((35*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/8 - (21*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/8 - (7*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/8 + (2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/8))","B"
25,1,310,176,13.344727,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^5,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{1357\,A\,a}{4}-\frac{461\,B\,a}{16}-\frac{635\,A\,a\,\cos\left(e+f\,x\right)}{4}+\frac{5\,B\,a\,\cos\left(e+f\,x\right)}{2}-\frac{1575\,A\,a\,\sin\left(e+f\,x\right)}{4}+\frac{945\,B\,a\,\sin\left(e+f\,x\right)}{8}-\frac{625\,A\,a\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{121\,A\,a\,\cos\left(3\,e+3\,f\,x\right)}{4}+\frac{7\,A\,a\,\cos\left(4\,e+4\,f\,x\right)}{2}+\frac{95\,B\,a\,\cos\left(2\,e+2\,f\,x\right)}{4}-8\,B\,a\,\cos\left(3\,e+3\,f\,x\right)-\frac{7\,B\,a\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{399\,A\,a\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{141\,A\,a\,\sin\left(3\,e+3\,f\,x\right)}{4}-\frac{15\,A\,a\,\sin\left(4\,e+4\,f\,x\right)}{4}-\frac{231\,B\,a\,\sin\left(2\,e+2\,f\,x\right)}{8}-\frac{39\,B\,a\,\sin\left(3\,e+3\,f\,x\right)}{8}+\frac{15\,B\,a\,\sin\left(4\,e+4\,f\,x\right)}{16}\right)}{315\,c^5\,f\,\left(\frac{63\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{8}-\frac{21\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{9\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}+\frac{9\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{16}+\frac{\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{16}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((1357*A*a)/4 - (461*B*a)/16 - (635*A*a*cos(e + f*x))/4 + (5*B*a*cos(e + f*x))/2 - (1575*A*a*sin(e + f*x))/4 + (945*B*a*sin(e + f*x))/8 - (625*A*a*cos(2*e + 2*f*x))/4 + (121*A*a*cos(3*e + 3*f*x))/4 + (7*A*a*cos(4*e + 4*f*x))/2 + (95*B*a*cos(2*e + 2*f*x))/4 - 8*B*a*cos(3*e + 3*f*x) - (7*B*a*cos(4*e + 4*f*x))/16 + (399*A*a*sin(2*e + 2*f*x))/4 + (141*A*a*sin(3*e + 3*f*x))/4 - (15*A*a*sin(4*e + 4*f*x))/4 - (231*B*a*sin(2*e + 2*f*x))/8 - (39*B*a*sin(3*e + 3*f*x))/8 + (15*B*a*sin(4*e + 4*f*x))/16))/(315*c^5*f*((63*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/8 - (21*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/4 - (9*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/4 + (9*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/16 + (2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/16))","B"
26,1,661,229,15.132410,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^5,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}\,\left(6\,A\,a^2\,c^5-2\,B\,a^2\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(30\,A\,a^2\,c^5-10\,B\,a^2\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(22\,A\,a^2\,c^5-18\,B\,a^2\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(46\,A\,a^2\,c^5-26\,B\,a^2\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{74\,A\,a^2\,c^5}{5}-\frac{14\,B\,a^2\,c^5}{5}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{15}\,\left(\frac{7\,A\,a^2\,c^5}{8}+\frac{27\,B\,a^2\,c^5}{64}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{158\,A\,a^2\,c^5}{35}-\frac{138\,B\,a^2\,c^5}{35}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{218\,A\,a^2\,c^5}{5}-\frac{158\,B\,a^2\,c^5}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{75\,A\,a^2\,c^5}{8}-\frac{305\,B\,a^2\,c^5}{64}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}\,\left(\frac{75\,A\,a^2\,c^5}{8}-\frac{305\,B\,a^2\,c^5}{64}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{55\,A\,a^2\,c^5}{8}-\frac{437\,B\,a^2\,c^5}{64}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{55\,A\,a^2\,c^5}{8}-\frac{437\,B\,a^2\,c^5}{64}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{13\,A\,a^2\,c^5}{8}-\frac{919\,B\,a^2\,c^5}{64}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{13\,A\,a^2\,c^5}{8}-\frac{919\,B\,a^2\,c^5}{64}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{7\,A\,a^2\,c^5}{8}+\frac{27\,B\,a^2\,c^5}{64}\right)+\frac{46\,A\,a^2\,c^5}{35}-\frac{26\,B\,a^2\,c^5}{35}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{9\,a^2\,c^5\,\mathrm{atan}\left(\frac{9\,a^2\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A-3\,B\right)}{64\,\left(\frac{9\,A\,a^2\,c^5}{8}-\frac{27\,B\,a^2\,c^5}{64}\right)}\right)\,\left(8\,A-3\,B\right)}{64\,f}","Not used",1,"(tan(e/2 + (f*x)/2)^14*(6*A*a^2*c^5 - 2*B*a^2*c^5) + tan(e/2 + (f*x)/2)^10*(30*A*a^2*c^5 - 10*B*a^2*c^5) + tan(e/2 + (f*x)/2)^12*(22*A*a^2*c^5 - 18*B*a^2*c^5) + tan(e/2 + (f*x)/2)^8*(46*A*a^2*c^5 - 26*B*a^2*c^5) + tan(e/2 + (f*x)/2)^4*((74*A*a^2*c^5)/5 - (14*B*a^2*c^5)/5) - tan(e/2 + (f*x)/2)^15*((7*A*a^2*c^5)/8 + (27*B*a^2*c^5)/64) + tan(e/2 + (f*x)/2)^2*((158*A*a^2*c^5)/35 - (138*B*a^2*c^5)/35) + tan(e/2 + (f*x)/2)^6*((218*A*a^2*c^5)/5 - (158*B*a^2*c^5)/5) + tan(e/2 + (f*x)/2)^3*((75*A*a^2*c^5)/8 - (305*B*a^2*c^5)/64) - tan(e/2 + (f*x)/2)^13*((75*A*a^2*c^5)/8 - (305*B*a^2*c^5)/64) + tan(e/2 + (f*x)/2)^5*((55*A*a^2*c^5)/8 - (437*B*a^2*c^5)/64) - tan(e/2 + (f*x)/2)^11*((55*A*a^2*c^5)/8 - (437*B*a^2*c^5)/64) - tan(e/2 + (f*x)/2)^7*((13*A*a^2*c^5)/8 - (919*B*a^2*c^5)/64) + tan(e/2 + (f*x)/2)^9*((13*A*a^2*c^5)/8 - (919*B*a^2*c^5)/64) + tan(e/2 + (f*x)/2)*((7*A*a^2*c^5)/8 + (27*B*a^2*c^5)/64) + (46*A*a^2*c^5)/35 - (26*B*a^2*c^5)/35)/(f*(8*tan(e/2 + (f*x)/2)^2 + 28*tan(e/2 + (f*x)/2)^4 + 56*tan(e/2 + (f*x)/2)^6 + 70*tan(e/2 + (f*x)/2)^8 + 56*tan(e/2 + (f*x)/2)^10 + 28*tan(e/2 + (f*x)/2)^12 + 8*tan(e/2 + (f*x)/2)^14 + tan(e/2 + (f*x)/2)^16 + 1)) + (9*a^2*c^5*atan((9*a^2*c^5*tan(e/2 + (f*x)/2)*(8*A - 3*B))/(64*((9*A*a^2*c^5)/8 - (27*B*a^2*c^5)/64)))*(8*A - 3*B))/(64*f)","B"
27,1,553,189,14.887705,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(4\,A\,a^2\,c^4-2\,B\,a^2\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(12\,A\,a^2\,c^4-2\,B\,a^2\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(8\,A\,a^2\,c^4-8\,B\,a^2\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^2\,c^4}{5}-\frac{8\,B\,a^2\,c^4}{5}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}\,\left(\frac{9\,A\,a^2\,c^4}{8}+\frac{B\,a^2\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(16\,A\,a^2\,c^4-16\,B\,a^2\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{29\,A\,a^2\,c^4}{6}-\frac{11\,B\,a^2\,c^4}{3}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{29\,A\,a^2\,c^4}{6}-\frac{11\,B\,a^2\,c^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{44\,A\,a^2\,c^4}{5}-\frac{14\,B\,a^2\,c^4}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{23\,A\,a^2\,c^4}{24}+\frac{31\,B\,a^2\,c^4}{12}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{23\,A\,a^2\,c^4}{24}+\frac{31\,B\,a^2\,c^4}{12}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{9\,A\,a^2\,c^4}{8}+\frac{B\,a^2\,c^4}{4}\right)+\frac{4\,A\,a^2\,c^4}{5}-\frac{18\,B\,a^2\,c^4}{35}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{a^2\,c^4\,\mathrm{atan}\left(\frac{a^2\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(7\,A-2\,B\right)}{8\,\left(\frac{7\,A\,a^2\,c^4}{8}-\frac{B\,a^2\,c^4}{4}\right)}\right)\,\left(7\,A-2\,B\right)}{8\,f}","Not used",1,"(tan(e/2 + (f*x)/2)^12*(4*A*a^2*c^4 - 2*B*a^2*c^4) + tan(e/2 + (f*x)/2)^8*(12*A*a^2*c^4 - 2*B*a^2*c^4) + tan(e/2 + (f*x)/2)^10*(8*A*a^2*c^4 - 8*B*a^2*c^4) + tan(e/2 + (f*x)/2)^2*((8*A*a^2*c^4)/5 - (8*B*a^2*c^4)/5) - tan(e/2 + (f*x)/2)^13*((9*A*a^2*c^4)/8 + (B*a^2*c^4)/4) + tan(e/2 + (f*x)/2)^6*(16*A*a^2*c^4 - 16*B*a^2*c^4) + tan(e/2 + (f*x)/2)^3*((29*A*a^2*c^4)/6 - (11*B*a^2*c^4)/3) - tan(e/2 + (f*x)/2)^11*((29*A*a^2*c^4)/6 - (11*B*a^2*c^4)/3) + tan(e/2 + (f*x)/2)^4*((44*A*a^2*c^4)/5 - (14*B*a^2*c^4)/5) + tan(e/2 + (f*x)/2)^5*((23*A*a^2*c^4)/24 + (31*B*a^2*c^4)/12) - tan(e/2 + (f*x)/2)^9*((23*A*a^2*c^4)/24 + (31*B*a^2*c^4)/12) + tan(e/2 + (f*x)/2)*((9*A*a^2*c^4)/8 + (B*a^2*c^4)/4) + (4*A*a^2*c^4)/5 - (18*B*a^2*c^4)/35)/(f*(7*tan(e/2 + (f*x)/2)^2 + 21*tan(e/2 + (f*x)/2)^4 + 35*tan(e/2 + (f*x)/2)^6 + 35*tan(e/2 + (f*x)/2)^8 + 21*tan(e/2 + (f*x)/2)^10 + 7*tan(e/2 + (f*x)/2)^12 + tan(e/2 + (f*x)/2)^14 + 1)) + (a^2*c^4*atan((a^2*c^4*tan(e/2 + (f*x)/2)*(7*A - 2*B))/(8*((7*A*a^2*c^4)/8 - (B*a^2*c^4)/4)))*(7*A - 2*B))/(8*f)","B"
28,1,542,147,14.154120,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(4\,A\,a^2\,c^3-4\,B\,a^2\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,A\,a^2\,c^3-2\,B\,a^2\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,A\,a^2\,c^3-4\,B\,a^2\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(2\,A\,a^2\,c^3-2\,B\,a^2\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{2\,A\,a^2\,c^3}{5}-\frac{2\,B\,a^2\,c^3}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{A\,a^2\,c^3}{2}+\frac{13\,B\,a^2\,c^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{A\,a^2\,c^3}{2}+\frac{13\,B\,a^2\,c^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{5\,A\,a^2\,c^3}{4}+\frac{B\,a^2\,c^3}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{7\,A\,a^2\,c^3}{4}-\frac{47\,B\,a^2\,c^3}{24}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{7\,A\,a^2\,c^3}{4}-\frac{47\,B\,a^2\,c^3}{24}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{5\,A\,a^2\,c^3}{4}+\frac{B\,a^2\,c^3}{8}\right)+\frac{2\,A\,a^2\,c^3}{5}-\frac{2\,B\,a^2\,c^3}{5}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{a^2\,c^3\,\mathrm{atan}\left(\frac{a^2\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,A-B\right)}{8\,\left(\frac{3\,A\,a^2\,c^3}{4}-\frac{B\,a^2\,c^3}{8}\right)}\right)\,\left(6\,A-B\right)}{8\,f}-\frac{a^2\,c^3\,\left(6\,A-B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{8\,f}","Not used",1,"(tan(e/2 + (f*x)/2)^4*(4*A*a^2*c^3 - 4*B*a^2*c^3) + tan(e/2 + (f*x)/2)^8*(2*A*a^2*c^3 - 2*B*a^2*c^3) + tan(e/2 + (f*x)/2)^6*(4*A*a^2*c^3 - 4*B*a^2*c^3) + tan(e/2 + (f*x)/2)^10*(2*A*a^2*c^3 - 2*B*a^2*c^3) + tan(e/2 + (f*x)/2)^2*((2*A*a^2*c^3)/5 - (2*B*a^2*c^3)/5) + tan(e/2 + (f*x)/2)^5*((A*a^2*c^3)/2 + (13*B*a^2*c^3)/4) - tan(e/2 + (f*x)/2)^7*((A*a^2*c^3)/2 + (13*B*a^2*c^3)/4) - tan(e/2 + (f*x)/2)^11*((5*A*a^2*c^3)/4 + (B*a^2*c^3)/8) + tan(e/2 + (f*x)/2)^3*((7*A*a^2*c^3)/4 - (47*B*a^2*c^3)/24) - tan(e/2 + (f*x)/2)^9*((7*A*a^2*c^3)/4 - (47*B*a^2*c^3)/24) + tan(e/2 + (f*x)/2)*((5*A*a^2*c^3)/4 + (B*a^2*c^3)/8) + (2*A*a^2*c^3)/5 - (2*B*a^2*c^3)/5)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1)) + (a^2*c^3*atan((a^2*c^3*tan(e/2 + (f*x)/2)*(6*A - B))/(8*((3*A*a^2*c^3)/4 - (B*a^2*c^3)/8)))*(6*A - B))/(8*f) - (a^2*c^3*(6*A - B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(8*f)","B"
29,1,238,89,14.205017,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^2,x)","\frac{3\,A\,a^2\,c^2\,x}{8}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a^2\,c^2\,\left(80\,B-75\,A\,\left(e+f\,x\right)\right)}{40}+\frac{15\,A\,a^2\,c^2\,\left(e+f\,x\right)}{8}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^2\,c^2\,\left(160\,B-150\,A\,\left(e+f\,x\right)\right)}{40}+\frac{15\,A\,a^2\,c^2\,\left(e+f\,x\right)}{4}\right)+\frac{a^2\,c^2\,\left(16\,B-15\,A\,\left(e+f\,x\right)\right)}{40}+\frac{3\,A\,a^2\,c^2\,\left(e+f\,x\right)}{8}-\frac{A\,a^2\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{2}+\frac{A\,a^2\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7}{2}+\frac{5\,A\,a^2\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{4}-\frac{5\,A\,a^2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{4}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*A*a^2*c^2*x)/8 - (tan(e/2 + (f*x)/2)^8*((a^2*c^2*(80*B - 75*A*(e + f*x)))/40 + (15*A*a^2*c^2*(e + f*x))/8) + tan(e/2 + (f*x)/2)^4*((a^2*c^2*(160*B - 150*A*(e + f*x)))/40 + (15*A*a^2*c^2*(e + f*x))/4) + (a^2*c^2*(16*B - 15*A*(e + f*x)))/40 + (3*A*a^2*c^2*(e + f*x))/8 - (A*a^2*c^2*tan(e/2 + (f*x)/2)^3)/2 + (A*a^2*c^2*tan(e/2 + (f*x)/2)^7)/2 + (5*A*a^2*c^2*tan(e/2 + (f*x)/2)^9)/4 - (5*A*a^2*c^2*tan(e/2 + (f*x)/2))/4)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^5)","B"
30,1,339,98,13.704614,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x)),x)","\frac{a^2\,c\,\mathrm{atan}\left(\frac{a^2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A+B\right)}{4\,\left(A\,a^2\,c+\frac{B\,a^2\,c}{4}\right)}\right)\,\left(4\,A+B\right)}{4\,f}-\frac{a^2\,c\,\left(4\,A+B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,a^2\,c+2\,B\,a^2\,c\right)-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a^2\,c-\frac{B\,a^2\,c}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,A\,a^2\,c+2\,B\,a^2\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{2\,A\,a^2\,c}{3}+\frac{2\,B\,a^2\,c}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(A\,a^2\,c-\frac{B\,a^2\,c}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a^2\,c+\frac{7\,B\,a^2\,c}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(A\,a^2\,c+\frac{7\,B\,a^2\,c}{4}\right)+\frac{2\,A\,a^2\,c}{3}+\frac{2\,B\,a^2\,c}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^2*c*atan((a^2*c*tan(e/2 + (f*x)/2)*(4*A + B))/(4*(A*a^2*c + (B*a^2*c)/4)))*(4*A + B))/(4*f) - (a^2*c*(4*A + B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f) - (tan(e/2 + (f*x)/2)^4*(2*A*a^2*c + 2*B*a^2*c) - tan(e/2 + (f*x)/2)*(A*a^2*c - (B*a^2*c)/4) + tan(e/2 + (f*x)/2)^6*(2*A*a^2*c + 2*B*a^2*c) + tan(e/2 + (f*x)/2)^2*((2*A*a^2*c)/3 + (2*B*a^2*c)/3) + tan(e/2 + (f*x)/2)^7*(A*a^2*c - (B*a^2*c)/4) - tan(e/2 + (f*x)/2)^3*(A*a^2*c + (7*B*a^2*c)/4) + tan(e/2 + (f*x)/2)^5*(A*a^2*c + (7*B*a^2*c)/4) + (2*A*a^2*c)/3 + (2*B*a^2*c)/3)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1))","B"
31,1,244,117,14.701059,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x)),x)","\frac{10\,A\,a^2-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a^2+5\,B\,a^2\right)+14\,B\,a^2-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,a^2+7\,B\,a^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(8\,A\,a^2+9\,B\,a^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(18\,A\,a^2+21\,B\,a^2\right)}{f\,\left(-c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{3\,a^2\,\mathrm{atan}\left(\frac{3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A+3\,B\right)}{6\,A\,a^2+9\,B\,a^2}\right)\,\left(2\,A+3\,B\right)}{c\,f}","Not used",1,"(10*A*a^2 - tan(e/2 + (f*x)/2)*(2*A*a^2 + 5*B*a^2) + 14*B*a^2 - tan(e/2 + (f*x)/2)^3*(2*A*a^2 + 7*B*a^2) + tan(e/2 + (f*x)/2)^4*(8*A*a^2 + 9*B*a^2) + tan(e/2 + (f*x)/2)^2*(18*A*a^2 + 21*B*a^2))/(f*(c - c*tan(e/2 + (f*x)/2) + 2*c*tan(e/2 + (f*x)/2)^2 - 2*c*tan(e/2 + (f*x)/2)^3 + c*tan(e/2 + (f*x)/2)^4 - c*tan(e/2 + (f*x)/2)^5)) - (3*a^2*atan((3*a^2*tan(e/2 + (f*x)/2)*(2*A + 3*B))/(6*A*a^2 + 9*B*a^2))*(2*A + 3*B))/(c*f)","B"
32,1,246,109,14.150020,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^2,x)","\frac{2\,a^2\,\mathrm{atan}\left(\frac{2\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A+4\,B\right)}{2\,A\,a^2+8\,B\,a^2}\right)\,\left(A+4\,B\right)}{c^2\,f}-\frac{\frac{8\,A\,a^2}{3}-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2+30\,B\,a^2\right)+\frac{38\,B\,a^2}{3}-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(8\,A\,a^2+26\,B\,a^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^2}{3}+\frac{74\,B\,a^2}{3}\right)+8\,B\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{f\,\left(-c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-4\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c^2\right)}","Not used",1,"(2*a^2*atan((2*a^2*tan(e/2 + (f*x)/2)*(A + 4*B))/(2*A*a^2 + 8*B*a^2))*(A + 4*B))/(c^2*f) - ((8*A*a^2)/3 - tan(e/2 + (f*x)/2)*(8*A*a^2 + 30*B*a^2) + (38*B*a^2)/3 - tan(e/2 + (f*x)/2)^3*(8*A*a^2 + 26*B*a^2) + tan(e/2 + (f*x)/2)^2*((8*A*a^2)/3 + (74*B*a^2)/3) + 8*B*a^2*tan(e/2 + (f*x)/2)^4)/(f*(4*c^2*tan(e/2 + (f*x)/2)^2 - 4*c^2*tan(e/2 + (f*x)/2)^3 + 3*c^2*tan(e/2 + (f*x)/2)^4 - c^2*tan(e/2 + (f*x)/2)^5 + c^2 - 3*c^2*tan(e/2 + (f*x)/2)))","B"
33,1,233,112,14.679242,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^3,x)","-\frac{B\,a^2\,x}{c^3}-\frac{\frac{a^2\,\left(6\,A+46\,B-15\,B\,\left(e+f\,x\right)\right)}{15}-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{a^2\,\left(120\,B-150\,B\,\left(e+f\,x\right)\right)}{15}+10\,B\,a^2\,\left(e+f\,x\right)\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^2\,\left(30\,A+30\,B-75\,B\,\left(e+f\,x\right)\right)}{15}+5\,B\,a^2\,\left(e+f\,x\right)\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^2\,\left(60\,A+340\,B-150\,B\,\left(e+f\,x\right)\right)}{15}+10\,B\,a^2\,\left(e+f\,x\right)\right)-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{a^2\,\left(200\,B-75\,B\,\left(e+f\,x\right)\right)}{15}+5\,B\,a^2\,\left(e+f\,x\right)\right)+B\,a^2\,\left(e+f\,x\right)}{c^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^5}","Not used",1,"- (B*a^2*x)/c^3 - ((a^2*(6*A + 46*B - 15*B*(e + f*x)))/15 - tan(e/2 + (f*x)/2)^3*((a^2*(120*B - 150*B*(e + f*x)))/15 + 10*B*a^2*(e + f*x)) + tan(e/2 + (f*x)/2)^4*((a^2*(30*A + 30*B - 75*B*(e + f*x)))/15 + 5*B*a^2*(e + f*x)) + tan(e/2 + (f*x)/2)^2*((a^2*(60*A + 340*B - 150*B*(e + f*x)))/15 + 10*B*a^2*(e + f*x)) - tan(e/2 + (f*x)/2)*((a^2*(200*B - 75*B*(e + f*x)))/15 + 5*B*a^2*(e + f*x)) + B*a^2*(e + f*x))/(c^3*f*(tan(e/2 + (f*x)/2) - 1)^5)","B"
34,1,269,75,13.350764,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^4,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{109\,A\,a^2}{4}+\frac{11\,B\,a^2}{4}-\frac{27\,A\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{5\,A\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{8}-\frac{13\,B\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{5\,B\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{8}+\frac{7\,A\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{7\,A\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{8}-\frac{7\,B\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{7\,B\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{8}-\frac{121\,A\,a^2\,\cos\left(e+f\,x\right)}{8}-\frac{9\,B\,a^2\,\cos\left(e+f\,x\right)}{8}-\frac{105\,A\,a^2\,\sin\left(e+f\,x\right)}{8}+\frac{105\,B\,a^2\,\sin\left(e+f\,x\right)}{8}\right)}{35\,c^4\,f\,\left(\frac{35\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{8}-\frac{21\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{8}-\frac{7\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{8}+\frac{\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{8}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((109*A*a^2)/4 + (11*B*a^2)/4 - (27*A*a^2*cos(2*e + 2*f*x))/4 + (5*A*a^2*cos(3*e + 3*f*x))/8 - (13*B*a^2*cos(2*e + 2*f*x))/4 + (5*B*a^2*cos(3*e + 3*f*x))/8 + (7*A*a^2*sin(2*e + 2*f*x))/2 + (7*A*a^2*sin(3*e + 3*f*x))/8 - (7*B*a^2*sin(2*e + 2*f*x))/2 - (7*B*a^2*sin(3*e + 3*f*x))/8 - (121*A*a^2*cos(e + f*x))/8 - (9*B*a^2*cos(e + f*x))/8 - (105*A*a^2*sin(e + f*x))/8 + (105*B*a^2*sin(e + f*x))/8))/(35*c^4*f*((35*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/8 - (21*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/8 - (7*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/8 + (2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/8))","B"
35,1,331,115,13.358172,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^5,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{265\,A\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{49\,B\,a^2}{8}-\frac{4967\,A\,a^2}{16}-\frac{89\,A\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{4}-\frac{49\,A\,a^2\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{35\,B\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{7\,B\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{8}+\frac{7\,B\,a^2\,\cos\left(4\,e+4\,f\,x\right)}{8}-\frac{567\,A\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{8}-\frac{243\,A\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{8}+\frac{45\,A\,a^2\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{63\,B\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{63\,B\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{8}+\frac{625\,A\,a^2\,\cos\left(e+f\,x\right)}{4}+\frac{35\,B\,a^2\,\cos\left(e+f\,x\right)}{8}+\frac{2205\,A\,a^2\,\sin\left(e+f\,x\right)}{8}-\frac{945\,B\,a^2\,\sin\left(e+f\,x\right)}{8}\right)}{315\,c^5\,f\,\left(\frac{63\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{8}-\frac{21\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{9\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}+\frac{9\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{16}+\frac{\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{16}\right)}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*((265*A*a^2*cos(2*e + 2*f*x))/2 - (49*B*a^2)/8 - (4967*A*a^2)/16 - (89*A*a^2*cos(3*e + 3*f*x))/4 - (49*A*a^2*cos(4*e + 4*f*x))/16 + (35*B*a^2*cos(2*e + 2*f*x))/4 - (7*B*a^2*cos(3*e + 3*f*x))/8 + (7*B*a^2*cos(4*e + 4*f*x))/8 - (567*A*a^2*sin(2*e + 2*f*x))/8 - (243*A*a^2*sin(3*e + 3*f*x))/8 + (45*A*a^2*sin(4*e + 4*f*x))/16 + (63*B*a^2*sin(2*e + 2*f*x))/2 + (63*B*a^2*sin(3*e + 3*f*x))/8 + (625*A*a^2*cos(e + f*x))/4 + (35*B*a^2*cos(e + f*x))/8 + (2205*A*a^2*sin(e + f*x))/8 - (945*B*a^2*sin(e + f*x))/8))/(315*c^5*f*((63*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/8 - (21*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/4 - (9*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/4 + (9*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/16 + (2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/16))","B"
36,1,423,156,13.544393,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^6,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{38163\,A\,a^2}{8}-\frac{1283\,B\,a^2}{8}-\frac{11931\,A\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{9609\,A\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{16}+\frac{1383\,A\,a^2\,\cos\left(4\,e+4\,f\,x\right)}{8}-\frac{225\,A\,a^2\,\cos\left(5\,e+5\,f\,x\right)}{16}+\frac{631\,B\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{1583\,B\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{32}-\frac{223\,B\,a^2\,\cos\left(4\,e+4\,f\,x\right)}{8}+\frac{45\,B\,a^2\,\cos\left(5\,e+5\,f\,x\right)}{32}+1386\,A\,a^2\,\sin\left(2\,e+2\,f\,x\right)+\frac{14949\,A\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{16}-\frac{561\,A\,a^2\,\sin\left(4\,e+4\,f\,x\right)}{4}-\frac{231\,A\,a^2\,\sin\left(5\,e+5\,f\,x\right)}{16}-\frac{3003\,B\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{8}-\frac{4653\,B\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{32}+\frac{209\,B\,a^2\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{77\,B\,a^2\,\sin\left(5\,e+5\,f\,x\right)}{32}-2091\,A\,a^2\,\cos\left(e+f\,x\right)+\frac{281\,B\,a^2\,\cos\left(e+f\,x\right)}{16}-\frac{22869\,A\,a^2\,\sin\left(e+f\,x\right)}{4}+\frac{23331\,B\,a^2\,\sin\left(e+f\,x\right)}{16}\right)}{3465\,c^6\,f\,\left(\frac{231\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{16}-\frac{165\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{16}-\frac{165\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{32}+\frac{55\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{32}+\frac{11\,\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{32}-\frac{\sqrt{2}\,\cos\left(\frac{11\,e}{2}-\frac{\pi }{4}+\frac{11\,f\,x}{2}\right)}{32}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((38163*A*a^2)/8 - (1283*B*a^2)/8 - (11931*A*a^2*cos(2*e + 2*f*x))/4 + (9609*A*a^2*cos(3*e + 3*f*x))/16 + (1383*A*a^2*cos(4*e + 4*f*x))/8 - (225*A*a^2*cos(5*e + 5*f*x))/16 + (631*B*a^2*cos(2*e + 2*f*x))/4 - (1583*B*a^2*cos(3*e + 3*f*x))/32 - (223*B*a^2*cos(4*e + 4*f*x))/8 + (45*B*a^2*cos(5*e + 5*f*x))/32 + 1386*A*a^2*sin(2*e + 2*f*x) + (14949*A*a^2*sin(3*e + 3*f*x))/16 - (561*A*a^2*sin(4*e + 4*f*x))/4 - (231*A*a^2*sin(5*e + 5*f*x))/16 - (3003*B*a^2*sin(2*e + 2*f*x))/8 - (4653*B*a^2*sin(3*e + 3*f*x))/32 + (209*B*a^2*sin(4*e + 4*f*x))/16 + (77*B*a^2*sin(5*e + 5*f*x))/32 - 2091*A*a^2*cos(e + f*x) + (281*B*a^2*cos(e + f*x))/16 - (22869*A*a^2*sin(e + f*x))/4 + (23331*B*a^2*sin(e + f*x))/16))/(3465*c^6*f*((231*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/16 - (165*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/16 - (165*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/32 + (55*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/32 + (11*2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/32 - (2^(1/2)*cos((11*e)/2 - pi/4 + (11*f*x)/2))/32))","B"
37,1,500,197,14.053151,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^7,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{994249\,A\,a^2}{32}-\frac{63639\,B\,a^2}{32}-\frac{1609013\,A\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{64}+\frac{85687\,A\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{16}+\frac{79591\,A\,a^2\,\cos\left(4\,e+4\,f\,x\right)}{32}-\frac{5261\,A\,a^2\,\cos\left(5\,e+5\,f\,x\right)}{16}-\frac{1771\,A\,a^2\,\cos\left(6\,e+6\,f\,x\right)}{64}+\frac{140553\,B\,a^2\,\cos\left(2\,e+2\,f\,x\right)}{64}-\frac{4431\,B\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{8}-\frac{10161\,B\,a^2\,\cos\left(4\,e+4\,f\,x\right)}{32}+36\,B\,a^2\,\cos\left(5\,e+5\,f\,x\right)+\frac{231\,B\,a^2\,\cos\left(6\,e+6\,f\,x\right)}{64}+\frac{636207\,A\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{64}+\frac{309309\,A\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{32}-\frac{7007\,A\,a^2\,\sin\left(4\,e+4\,f\,x\right)}{4}-\frac{12389\,A\,a^2\,\sin\left(5\,e+5\,f\,x\right)}{32}+\frac{1755\,A\,a^2\,\sin\left(6\,e+6\,f\,x\right)}{64}-\frac{121407\,B\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{64}-\frac{39039\,B\,a^2\,\sin\left(3\,e+3\,f\,x\right)}{32}+\frac{3003\,B\,a^2\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{1599\,B\,a^2\,\sin\left(5\,e+5\,f\,x\right)}{32}-\frac{195\,B\,a^2\,\sin\left(6\,e+6\,f\,x\right)}{64}-\frac{93221\,A\,a^2\,\cos\left(e+f\,x\right)}{8}+\frac{3291\,B\,a^2\,\cos\left(e+f\,x\right)}{8}-\frac{704847\,A\,a^2\,\sin\left(e+f\,x\right)}{16}+\frac{125697\,B\,a^2\,\sin\left(e+f\,x\right)}{16}\right)}{15015\,c^7\,f\,\left(\frac{1287\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{64}-\frac{429\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{16}+\frac{715\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{64}-\frac{143\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{32}-\frac{39\,\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{32}+\frac{13\,\sqrt{2}\,\cos\left(\frac{11\,e}{2}-\frac{\pi }{4}+\frac{11\,f\,x}{2}\right)}{64}+\frac{\sqrt{2}\,\cos\left(\frac{13\,e}{2}+\frac{\pi }{4}+\frac{13\,f\,x}{2}\right)}{64}\right)}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*((994249*A*a^2)/32 - (63639*B*a^2)/32 - (1609013*A*a^2*cos(2*e + 2*f*x))/64 + (85687*A*a^2*cos(3*e + 3*f*x))/16 + (79591*A*a^2*cos(4*e + 4*f*x))/32 - (5261*A*a^2*cos(5*e + 5*f*x))/16 - (1771*A*a^2*cos(6*e + 6*f*x))/64 + (140553*B*a^2*cos(2*e + 2*f*x))/64 - (4431*B*a^2*cos(3*e + 3*f*x))/8 - (10161*B*a^2*cos(4*e + 4*f*x))/32 + 36*B*a^2*cos(5*e + 5*f*x) + (231*B*a^2*cos(6*e + 6*f*x))/64 + (636207*A*a^2*sin(2*e + 2*f*x))/64 + (309309*A*a^2*sin(3*e + 3*f*x))/32 - (7007*A*a^2*sin(4*e + 4*f*x))/4 - (12389*A*a^2*sin(5*e + 5*f*x))/32 + (1755*A*a^2*sin(6*e + 6*f*x))/64 - (121407*B*a^2*sin(2*e + 2*f*x))/64 - (39039*B*a^2*sin(3*e + 3*f*x))/32 + (3003*B*a^2*sin(4*e + 4*f*x))/16 + (1599*B*a^2*sin(5*e + 5*f*x))/32 - (195*B*a^2*sin(6*e + 6*f*x))/64 - (93221*A*a^2*cos(e + f*x))/8 + (3291*B*a^2*cos(e + f*x))/8 - (704847*A*a^2*sin(e + f*x))/16 + (125697*B*a^2*sin(e + f*x))/16))/(15015*c^7*f*((1287*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/64 - (429*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/16 + (715*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/64 - (143*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/32 - (39*2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/32 + (13*2^(1/2)*cos((11*e)/2 - pi/4 + (11*f*x)/2))/64 + (2^(1/2)*cos((13*e)/2 + pi/4 + (13*f*x)/2))/64))","B"
38,1,812,265,14.869203,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^6,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{18}\,\left(6\,A\,a^3\,c^6-2\,B\,a^3\,c^6\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}\,\left(22\,A\,a^3\,c^6-18\,B\,a^3\,c^6\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(84\,A\,a^3\,c^6-28\,B\,a^3\,c^6\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}\,\left(\frac{136\,A\,a^3\,c^6}{3}-8\,B\,a^3\,c^6\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{136\,A\,a^3\,c^6}{7}-\frac{24\,B\,a^3\,c^6}{7}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(116\,A\,a^3\,c^6-60\,B\,a^3\,c^6\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{19}\,\left(\frac{73\,A\,a^3\,c^6}{64}+\frac{33\,B\,a^3\,c^6}{128}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{202\,A\,a^3\,c^6}{63}-\frac{58\,B\,a^3\,c^6}{21}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(\frac{328\,A\,a^3\,c^6}{3}-72\,B\,a^3\,c^6\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{341\,A\,a^3\,c^6}{16}+\frac{333\,B\,a^3\,c^6}{32}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}\,\left(\frac{341\,A\,a^3\,c^6}{16}+\frac{333\,B\,a^3\,c^6}{32}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{456\,A\,a^3\,c^6}{7}-\frac{344\,B\,a^3\,c^6}{7}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{449\,A\,a^3\,c^6}{48}-\frac{577\,B\,a^3\,c^6}{160}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{15}\,\left(\frac{449\,A\,a^3\,c^6}{48}-\frac{577\,B\,a^3\,c^6}{160}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{2117\,A\,a^3\,c^6}{192}-\frac{705\,B\,a^3\,c^6}{128}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{17}\,\left(\frac{2117\,A\,a^3\,c^6}{192}-\frac{705\,B\,a^3\,c^6}{128}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{699\,A\,a^3\,c^6}{32}-\frac{2749\,B\,a^3\,c^6}{64}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{699\,A\,a^3\,c^6}{32}-\frac{2749\,B\,a^3\,c^6}{64}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{73\,A\,a^3\,c^6}{64}+\frac{33\,B\,a^3\,c^6}{128}\right)+\frac{58\,A\,a^3\,c^6}{63}-\frac{10\,B\,a^3\,c^6}{21}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{20}+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{18}+45\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}+120\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}+210\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+252\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+210\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+120\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+45\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{11\,a^3\,c^6\,\mathrm{atan}\left(\frac{11\,a^3\,c^6\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(10\,A-3\,B\right)}{128\,\left(\frac{55\,A\,a^3\,c^6}{64}-\frac{33\,B\,a^3\,c^6}{128}\right)}\right)\,\left(10\,A-3\,B\right)}{128\,f}","Not used",1,"(tan(e/2 + (f*x)/2)^18*(6*A*a^3*c^6 - 2*B*a^3*c^6) + tan(e/2 + (f*x)/2)^16*(22*A*a^3*c^6 - 18*B*a^3*c^6) + tan(e/2 + (f*x)/2)^8*(84*A*a^3*c^6 - 28*B*a^3*c^6) + tan(e/2 + (f*x)/2)^14*((136*A*a^3*c^6)/3 - 8*B*a^3*c^6) + tan(e/2 + (f*x)/2)^4*((136*A*a^3*c^6)/7 - (24*B*a^3*c^6)/7) + tan(e/2 + (f*x)/2)^10*(116*A*a^3*c^6 - 60*B*a^3*c^6) - tan(e/2 + (f*x)/2)^19*((73*A*a^3*c^6)/64 + (33*B*a^3*c^6)/128) + tan(e/2 + (f*x)/2)^2*((202*A*a^3*c^6)/63 - (58*B*a^3*c^6)/21) + tan(e/2 + (f*x)/2)^12*((328*A*a^3*c^6)/3 - 72*B*a^3*c^6) + tan(e/2 + (f*x)/2)^7*((341*A*a^3*c^6)/16 + (333*B*a^3*c^6)/32) - tan(e/2 + (f*x)/2)^13*((341*A*a^3*c^6)/16 + (333*B*a^3*c^6)/32) + tan(e/2 + (f*x)/2)^6*((456*A*a^3*c^6)/7 - (344*B*a^3*c^6)/7) + tan(e/2 + (f*x)/2)^5*((449*A*a^3*c^6)/48 - (577*B*a^3*c^6)/160) - tan(e/2 + (f*x)/2)^15*((449*A*a^3*c^6)/48 - (577*B*a^3*c^6)/160) + tan(e/2 + (f*x)/2)^3*((2117*A*a^3*c^6)/192 - (705*B*a^3*c^6)/128) - tan(e/2 + (f*x)/2)^17*((2117*A*a^3*c^6)/192 - (705*B*a^3*c^6)/128) + tan(e/2 + (f*x)/2)^9*((699*A*a^3*c^6)/32 - (2749*B*a^3*c^6)/64) - tan(e/2 + (f*x)/2)^11*((699*A*a^3*c^6)/32 - (2749*B*a^3*c^6)/64) + tan(e/2 + (f*x)/2)*((73*A*a^3*c^6)/64 + (33*B*a^3*c^6)/128) + (58*A*a^3*c^6)/63 - (10*B*a^3*c^6)/21)/(f*(10*tan(e/2 + (f*x)/2)^2 + 45*tan(e/2 + (f*x)/2)^4 + 120*tan(e/2 + (f*x)/2)^6 + 210*tan(e/2 + (f*x)/2)^8 + 252*tan(e/2 + (f*x)/2)^10 + 210*tan(e/2 + (f*x)/2)^12 + 120*tan(e/2 + (f*x)/2)^14 + 45*tan(e/2 + (f*x)/2)^16 + 10*tan(e/2 + (f*x)/2)^18 + tan(e/2 + (f*x)/2)^20 + 1)) + (11*a^3*c^6*atan((11*a^3*c^6*tan(e/2 + (f*x)/2)*(10*A - 3*B))/(128*((55*A*a^3*c^6)/64 - (33*B*a^3*c^6)/128)))*(10*A - 3*B))/(128*f)","B"
39,1,705,222,14.928906,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^5,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}\,\left(4\,A\,a^3\,c^5-2\,B\,a^3\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}\,\left(8\,A\,a^3\,c^5-8\,B\,a^3\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^3\,c^5}{7}-\frac{8\,B\,a^3\,c^5}{7}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(32\,A\,a^3\,c^5-4\,B\,a^3\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(24\,A\,a^3\,c^5-24\,B\,a^3\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(24\,A\,a^3\,c^5-\frac{16\,B\,a^3\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(40\,A\,a^3\,c^5-40\,B\,a^3\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{88\,A\,a^3\,c^5}{7}-\frac{32\,B\,a^3\,c^5}{7}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{17}\,\left(\frac{83\,A\,a^3\,c^5}{64}+\frac{5\,B\,a^3\,c^5}{32}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{149\,A\,a^3\,c^5}{32}+\frac{83\,B\,a^3\,c^5}{16}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}\,\left(\frac{149\,A\,a^3\,c^5}{32}+\frac{83\,B\,a^3\,c^5}{16}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{189\,A\,a^3\,c^5}{32}-\frac{191\,B\,a^3\,c^5}{48}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{15}\,\left(\frac{189\,A\,a^3\,c^5}{32}-\frac{191\,B\,a^3\,c^5}{48}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{409\,A\,a^3\,c^5}{32}-\frac{145\,B\,a^3\,c^5}{16}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{409\,A\,a^3\,c^5}{32}-\frac{145\,B\,a^3\,c^5}{16}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{83\,A\,a^3\,c^5}{64}+\frac{5\,B\,a^3\,c^5}{32}\right)+\frac{4\,A\,a^3\,c^5}{7}-\frac{22\,B\,a^3\,c^5}{63}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{18}+9\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}+84\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+126\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+36\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+9\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{5\,a^3\,c^5\,\mathrm{atan}\left(\frac{5\,a^3\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(9\,A-2\,B\right)}{64\,\left(\frac{45\,A\,a^3\,c^5}{64}-\frac{5\,B\,a^3\,c^5}{32}\right)}\right)\,\left(9\,A-2\,B\right)}{64\,f}","Not used",1,"(tan(e/2 + (f*x)/2)^16*(4*A*a^3*c^5 - 2*B*a^3*c^5) + tan(e/2 + (f*x)/2)^14*(8*A*a^3*c^5 - 8*B*a^3*c^5) + tan(e/2 + (f*x)/2)^2*((8*A*a^3*c^5)/7 - (8*B*a^3*c^5)/7) + tan(e/2 + (f*x)/2)^8*(32*A*a^3*c^5 - 4*B*a^3*c^5) + tan(e/2 + (f*x)/2)^6*(24*A*a^3*c^5 - 24*B*a^3*c^5) + tan(e/2 + (f*x)/2)^12*(24*A*a^3*c^5 - (16*B*a^3*c^5)/3) + tan(e/2 + (f*x)/2)^10*(40*A*a^3*c^5 - 40*B*a^3*c^5) + tan(e/2 + (f*x)/2)^4*((88*A*a^3*c^5)/7 - (32*B*a^3*c^5)/7) - tan(e/2 + (f*x)/2)^17*((83*A*a^3*c^5)/64 + (5*B*a^3*c^5)/32) + tan(e/2 + (f*x)/2)^5*((149*A*a^3*c^5)/32 + (83*B*a^3*c^5)/16) - tan(e/2 + (f*x)/2)^13*((149*A*a^3*c^5)/32 + (83*B*a^3*c^5)/16) + tan(e/2 + (f*x)/2)^3*((189*A*a^3*c^5)/32 - (191*B*a^3*c^5)/48) - tan(e/2 + (f*x)/2)^15*((189*A*a^3*c^5)/32 - (191*B*a^3*c^5)/48) + tan(e/2 + (f*x)/2)^7*((409*A*a^3*c^5)/32 - (145*B*a^3*c^5)/16) - tan(e/2 + (f*x)/2)^11*((409*A*a^3*c^5)/32 - (145*B*a^3*c^5)/16) + tan(e/2 + (f*x)/2)*((83*A*a^3*c^5)/64 + (5*B*a^3*c^5)/32) + (4*A*a^3*c^5)/7 - (22*B*a^3*c^5)/63)/(f*(9*tan(e/2 + (f*x)/2)^2 + 36*tan(e/2 + (f*x)/2)^4 + 84*tan(e/2 + (f*x)/2)^6 + 126*tan(e/2 + (f*x)/2)^8 + 126*tan(e/2 + (f*x)/2)^10 + 84*tan(e/2 + (f*x)/2)^12 + 36*tan(e/2 + (f*x)/2)^14 + 9*tan(e/2 + (f*x)/2)^16 + tan(e/2 + (f*x)/2)^18 + 1)) + (5*a^3*c^5*atan((5*a^3*c^5*tan(e/2 + (f*x)/2)*(9*A - 2*B))/(64*((45*A*a^3*c^5)/64 - (5*B*a^3*c^5)/32)))*(9*A - 2*B))/(64*f)","B"
40,1,661,181,14.782138,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,A\,a^3\,c^4-6\,B\,a^3\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(2\,A\,a^3\,c^4-2\,B\,a^3\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(6\,A\,a^3\,c^4-6\,B\,a^3\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}\,\left(2\,A\,a^3\,c^4-2\,B\,a^3\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{2\,A\,a^3\,c^4}{7}-\frac{2\,B\,a^3\,c^4}{7}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(10\,A\,a^3\,c^4-10\,B\,a^3\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(10\,A\,a^3\,c^4-10\,B\,a^3\,c^4\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{15}\,\left(\frac{11\,A\,a^3\,c^4}{8}+\frac{5\,B\,a^3\,c^4}{64}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{61\,A\,a^3\,c^4}{24}-\frac{397\,B\,a^3\,c^4}{192}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}\,\left(\frac{61\,A\,a^3\,c^4}{24}-\frac{397\,B\,a^3\,c^4}{192}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{113\,A\,a^3\,c^4}{24}+\frac{895\,B\,a^3\,c^4}{192}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{113\,A\,a^3\,c^4}{24}+\frac{895\,B\,a^3\,c^4}{192}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{85\,A\,a^3\,c^4}{24}-\frac{1765\,B\,a^3\,c^4}{192}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{85\,A\,a^3\,c^4}{24}-\frac{1765\,B\,a^3\,c^4}{192}\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{11\,A\,a^3\,c^4}{8}+\frac{5\,B\,a^3\,c^4}{64}\right)+\frac{2\,A\,a^3\,c^4}{7}-\frac{2\,B\,a^3\,c^4}{7}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}+\frac{5\,a^3\,c^4\,\mathrm{atan}\left(\frac{5\,a^3\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A-B\right)}{64\,\left(\frac{5\,A\,a^3\,c^4}{8}-\frac{5\,B\,a^3\,c^4}{64}\right)}\right)\,\left(8\,A-B\right)}{64\,f}","Not used",1,"(tan(e/2 + (f*x)/2)^4*(6*A*a^3*c^4 - 6*B*a^3*c^4) + tan(e/2 + (f*x)/2)^12*(2*A*a^3*c^4 - 2*B*a^3*c^4) + tan(e/2 + (f*x)/2)^6*(6*A*a^3*c^4 - 6*B*a^3*c^4) + tan(e/2 + (f*x)/2)^14*(2*A*a^3*c^4 - 2*B*a^3*c^4) + tan(e/2 + (f*x)/2)^2*((2*A*a^3*c^4)/7 - (2*B*a^3*c^4)/7) + tan(e/2 + (f*x)/2)^8*(10*A*a^3*c^4 - 10*B*a^3*c^4) + tan(e/2 + (f*x)/2)^10*(10*A*a^3*c^4 - 10*B*a^3*c^4) - tan(e/2 + (f*x)/2)^15*((11*A*a^3*c^4)/8 + (5*B*a^3*c^4)/64) + tan(e/2 + (f*x)/2)^3*((61*A*a^3*c^4)/24 - (397*B*a^3*c^4)/192) - tan(e/2 + (f*x)/2)^13*((61*A*a^3*c^4)/24 - (397*B*a^3*c^4)/192) + tan(e/2 + (f*x)/2)^5*((113*A*a^3*c^4)/24 + (895*B*a^3*c^4)/192) - tan(e/2 + (f*x)/2)^11*((113*A*a^3*c^4)/24 + (895*B*a^3*c^4)/192) + tan(e/2 + (f*x)/2)^7*((85*A*a^3*c^4)/24 - (1765*B*a^3*c^4)/192) - tan(e/2 + (f*x)/2)^9*((85*A*a^3*c^4)/24 - (1765*B*a^3*c^4)/192) + tan(e/2 + (f*x)/2)*((11*A*a^3*c^4)/8 + (5*B*a^3*c^4)/64) + (2*A*a^3*c^4)/7 - (2*B*a^3*c^4)/7)/(f*(8*tan(e/2 + (f*x)/2)^2 + 28*tan(e/2 + (f*x)/2)^4 + 56*tan(e/2 + (f*x)/2)^6 + 70*tan(e/2 + (f*x)/2)^8 + 56*tan(e/2 + (f*x)/2)^10 + 28*tan(e/2 + (f*x)/2)^12 + 8*tan(e/2 + (f*x)/2)^14 + tan(e/2 + (f*x)/2)^16 + 1)) + (5*a^3*c^4*atan((5*a^3*c^4*tan(e/2 + (f*x)/2)*(8*A - B))/(64*((5*A*a^3*c^4)/8 - (5*B*a^3*c^4)/64)))*(8*A - B))/(64*f)","B"
41,1,325,117,14.288450,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^3,x)","\frac{5\,A\,a^3\,c^3\,x}{16}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(\frac{a^3\,c^3\,\left(672\,B-735\,A\,\left(e+f\,x\right)\right)}{336}+\frac{35\,A\,a^3\,c^3\,\left(e+f\,x\right)}{16}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^3\,c^3\,\left(2016\,B-2205\,A\,\left(e+f\,x\right)\right)}{336}+\frac{105\,A\,a^3\,c^3\,\left(e+f\,x\right)}{16}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{a^3\,c^3\,\left(3360\,B-3675\,A\,\left(e+f\,x\right)\right)}{336}+\frac{175\,A\,a^3\,c^3\,\left(e+f\,x\right)}{16}\right)+\frac{a^3\,c^3\,\left(96\,B-105\,A\,\left(e+f\,x\right)\right)}{336}+\frac{5\,A\,a^3\,c^3\,\left(e+f\,x\right)}{16}-\frac{7\,A\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{6}-\frac{85\,A\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5}{24}+\frac{85\,A\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9}{24}+\frac{7\,A\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}}{6}+\frac{11\,A\,a^3\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}}{8}-\frac{11\,A\,a^3\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{8}}{f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(5*A*a^3*c^3*x)/16 - (tan(e/2 + (f*x)/2)^12*((a^3*c^3*(672*B - 735*A*(e + f*x)))/336 + (35*A*a^3*c^3*(e + f*x))/16) + tan(e/2 + (f*x)/2)^4*((a^3*c^3*(2016*B - 2205*A*(e + f*x)))/336 + (105*A*a^3*c^3*(e + f*x))/16) + tan(e/2 + (f*x)/2)^8*((a^3*c^3*(3360*B - 3675*A*(e + f*x)))/336 + (175*A*a^3*c^3*(e + f*x))/16) + (a^3*c^3*(96*B - 105*A*(e + f*x)))/336 + (5*A*a^3*c^3*(e + f*x))/16 - (7*A*a^3*c^3*tan(e/2 + (f*x)/2)^3)/6 - (85*A*a^3*c^3*tan(e/2 + (f*x)/2)^5)/24 + (85*A*a^3*c^3*tan(e/2 + (f*x)/2)^9)/24 + (7*A*a^3*c^3*tan(e/2 + (f*x)/2)^11)/6 + (11*A*a^3*c^3*tan(e/2 + (f*x)/2)^13)/8 - (11*A*a^3*c^3*tan(e/2 + (f*x)/2))/8)/(f*(tan(e/2 + (f*x)/2)^2 + 1)^7)","B"
42,1,536,138,14.166082,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^2,x)","\frac{a^3\,c^2\,\mathrm{atan}\left(\frac{a^3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,A+B\right)}{8\,\left(\frac{3\,A\,a^3\,c^2}{4}+\frac{B\,a^3\,c^2}{8}\right)}\right)\,\left(6\,A+B\right)}{8\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(4\,A\,a^3\,c^2+4\,B\,a^3\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,A\,a^3\,c^2+2\,B\,a^3\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,A\,a^3\,c^2+4\,B\,a^3\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(2\,A\,a^3\,c^2+2\,B\,a^3\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{2\,A\,a^3\,c^2}{5}+\frac{2\,B\,a^3\,c^2}{5}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{A\,a^3\,c^2}{2}-\frac{13\,B\,a^3\,c^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{A\,a^3\,c^2}{2}-\frac{13\,B\,a^3\,c^2}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(\frac{5\,A\,a^3\,c^2}{4}-\frac{B\,a^3\,c^2}{8}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{7\,A\,a^3\,c^2}{4}+\frac{47\,B\,a^3\,c^2}{24}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{7\,A\,a^3\,c^2}{4}+\frac{47\,B\,a^3\,c^2}{24}\right)-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{5\,A\,a^3\,c^2}{4}-\frac{B\,a^3\,c^2}{8}\right)+\frac{2\,A\,a^3\,c^2}{5}+\frac{2\,B\,a^3\,c^2}{5}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{a^3\,c^2\,\left(6\,A+B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{8\,f}","Not used",1,"(a^3*c^2*atan((a^3*c^2*tan(e/2 + (f*x)/2)*(6*A + B))/(8*((3*A*a^3*c^2)/4 + (B*a^3*c^2)/8)))*(6*A + B))/(8*f) - (tan(e/2 + (f*x)/2)^4*(4*A*a^3*c^2 + 4*B*a^3*c^2) + tan(e/2 + (f*x)/2)^8*(2*A*a^3*c^2 + 2*B*a^3*c^2) + tan(e/2 + (f*x)/2)^6*(4*A*a^3*c^2 + 4*B*a^3*c^2) + tan(e/2 + (f*x)/2)^10*(2*A*a^3*c^2 + 2*B*a^3*c^2) + tan(e/2 + (f*x)/2)^2*((2*A*a^3*c^2)/5 + (2*B*a^3*c^2)/5) - tan(e/2 + (f*x)/2)^5*((A*a^3*c^2)/2 - (13*B*a^3*c^2)/4) + tan(e/2 + (f*x)/2)^7*((A*a^3*c^2)/2 - (13*B*a^3*c^2)/4) + tan(e/2 + (f*x)/2)^11*((5*A*a^3*c^2)/4 - (B*a^3*c^2)/8) - tan(e/2 + (f*x)/2)^3*((7*A*a^3*c^2)/4 + (47*B*a^3*c^2)/24) + tan(e/2 + (f*x)/2)^9*((7*A*a^3*c^2)/4 + (47*B*a^3*c^2)/24) - tan(e/2 + (f*x)/2)*((5*A*a^3*c^2)/4 - (B*a^3*c^2)/8) + (2*A*a^3*c^2)/5 + (2*B*a^3*c^2)/5)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1)) - (a^3*c^2*(6*A + B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(8*f)","B"
43,1,390,140,13.664286,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x)),x)","\frac{a^3\,c\,\mathrm{atan}\left(\frac{a^3\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,A+2\,B\right)}{4\,\left(\frac{5\,A\,a^3\,c}{4}+\frac{B\,a^3\,c}{2}\right)}\right)\,\left(5\,A+2\,B\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(4\,A\,a^3\,c+2\,B\,a^3\,c\right)-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{3\,A\,a^3\,c}{4}-\frac{B\,a^3\,c}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{7\,A\,a^3\,c}{2}+3\,B\,a^3\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{7\,A\,a^3\,c}{2}+3\,B\,a^3\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{3\,A\,a^3\,c}{4}-\frac{B\,a^3\,c}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(8\,A\,a^3\,c+8\,B\,a^3\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{8\,A\,a^3\,c}{3}+\frac{8\,B\,a^3\,c}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{16\,A\,a^3\,c}{3}+\frac{4\,B\,a^3\,c}{3}\right)+\frac{4\,A\,a^3\,c}{3}+\frac{14\,B\,a^3\,c}{15}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{a^3\,c\,\left(5\,A+2\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(a^3*c*atan((a^3*c*tan(e/2 + (f*x)/2)*(5*A + 2*B))/(4*((5*A*a^3*c)/4 + (B*a^3*c)/2)))*(5*A + 2*B))/(4*f) - (tan(e/2 + (f*x)/2)^8*(4*A*a^3*c + 2*B*a^3*c) - tan(e/2 + (f*x)/2)*((3*A*a^3*c)/4 - (B*a^3*c)/2) - tan(e/2 + (f*x)/2)^3*((7*A*a^3*c)/2 + 3*B*a^3*c) + tan(e/2 + (f*x)/2)^7*((7*A*a^3*c)/2 + 3*B*a^3*c) + tan(e/2 + (f*x)/2)^9*((3*A*a^3*c)/4 - (B*a^3*c)/2) + tan(e/2 + (f*x)/2)^6*(8*A*a^3*c + 8*B*a^3*c) + tan(e/2 + (f*x)/2)^2*((8*A*a^3*c)/3 + (8*B*a^3*c)/3) + tan(e/2 + (f*x)/2)^4*((16*A*a^3*c)/3 + (4*B*a^3*c)/3) + (4*A*a^3*c)/3 + (14*B*a^3*c)/15)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1)) - (a^3*c*(5*A + 2*B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
44,1,323,156,14.119763,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x)),x)","\frac{24\,A\,a^3-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(7\,A\,a^3+\frac{34\,B\,a^3}{3}\right)+\frac{94\,B\,a^3}{3}-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(9\,A\,a^3+18\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(17\,A\,a^3+20\,B\,a^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(16\,A\,a^3+32\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(56\,A\,a^3+62\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(63\,A\,a^3+76\,B\,a^3\right)}{f\,\left(-c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{5\,a^3\,\mathrm{atan}\left(\frac{5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A+4\,B\right)}{15\,A\,a^3+20\,B\,a^3}\right)\,\left(3\,A+4\,B\right)}{c\,f}","Not used",1,"(24*A*a^3 - tan(e/2 + (f*x)/2)*(7*A*a^3 + (34*B*a^3)/3) + (94*B*a^3)/3 - tan(e/2 + (f*x)/2)^5*(9*A*a^3 + 18*B*a^3) + tan(e/2 + (f*x)/2)^6*(17*A*a^3 + 20*B*a^3) - tan(e/2 + (f*x)/2)^3*(16*A*a^3 + 32*B*a^3) + tan(e/2 + (f*x)/2)^4*(56*A*a^3 + 62*B*a^3) + tan(e/2 + (f*x)/2)^2*(63*A*a^3 + 76*B*a^3))/(f*(c - c*tan(e/2 + (f*x)/2) + 3*c*tan(e/2 + (f*x)/2)^2 - 3*c*tan(e/2 + (f*x)/2)^3 + 3*c*tan(e/2 + (f*x)/2)^4 - 3*c*tan(e/2 + (f*x)/2)^5 + c*tan(e/2 + (f*x)/2)^6 - c*tan(e/2 + (f*x)/2)^7)) - (5*a^3*atan((5*a^3*tan(e/2 + (f*x)/2)*(3*A + 4*B))/(15*A*a^3 + 20*B*a^3))*(3*A + 4*B))/(c*f)","B"
45,1,341,163,14.004803,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^2,x)","\frac{5\,a^3\,\mathrm{atan}\left(\frac{5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A+5\,B\right)}{10\,A\,a^3+25\,B\,a^3}\right)\,\left(2\,A+5\,B\right)}{c^2\,f}-\frac{\frac{46\,A\,a^3}{3}-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(38\,A\,a^3+93\,B\,a^3\right)+\frac{118\,B\,a^3}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(8\,A\,a^3+25\,B\,a^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(34\,A\,a^3+77\,B\,a^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(72\,A\,a^3+166\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{106\,A\,a^3}{3}+\frac{328\,B\,a^3}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{128\,A\,a^3}{3}+\frac{359\,B\,a^3}{3}\right)}{f\,\left(-c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-5\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+7\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-7\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+5\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c^2\right)}","Not used",1,"(5*a^3*atan((5*a^3*tan(e/2 + (f*x)/2)*(2*A + 5*B))/(10*A*a^3 + 25*B*a^3))*(2*A + 5*B))/(c^2*f) - ((46*A*a^3)/3 - tan(e/2 + (f*x)/2)*(38*A*a^3 + 93*B*a^3) + (118*B*a^3)/3 + tan(e/2 + (f*x)/2)^6*(8*A*a^3 + 25*B*a^3) - tan(e/2 + (f*x)/2)^5*(34*A*a^3 + 77*B*a^3) - tan(e/2 + (f*x)/2)^3*(72*A*a^3 + 166*B*a^3) + tan(e/2 + (f*x)/2)^4*((106*A*a^3)/3 + (328*B*a^3)/3) + tan(e/2 + (f*x)/2)^2*((128*A*a^3)/3 + (359*B*a^3)/3))/(f*(5*c^2*tan(e/2 + (f*x)/2)^2 - 7*c^2*tan(e/2 + (f*x)/2)^3 + 7*c^2*tan(e/2 + (f*x)/2)^4 - 5*c^2*tan(e/2 + (f*x)/2)^5 + 3*c^2*tan(e/2 + (f*x)/2)^6 - c^2*tan(e/2 + (f*x)/2)^7 + c^2 - 3*c^2*tan(e/2 + (f*x)/2)))","B"
46,1,336,153,14.002227,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^3,x)","\frac{\frac{52\,A\,a^3}{15}-\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{40\,A\,a^3}{3}+82\,B\,a^3\right)+\frac{94\,B\,a^3}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,A\,a^3+12\,B\,a^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(8\,A\,a^3+58\,B\,a^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{64\,A\,a^3}{3}+148\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{92\,A\,a^3}{3}+134\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{452\,A\,a^3}{15}+\frac{744\,B\,a^3}{5}\right)}{f\,\left(-c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+5\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6-11\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+15\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-15\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+11\,c^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-5\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c^3\right)}-\frac{2\,a^3\,\mathrm{atan}\left(\frac{2\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A+6\,B\right)}{2\,A\,a^3+12\,B\,a^3}\right)\,\left(A+6\,B\right)}{c^3\,f}","Not used",1,"((52*A*a^3)/15 - tan(e/2 + (f*x)/2)*((40*A*a^3)/3 + 82*B*a^3) + (94*B*a^3)/5 + tan(e/2 + (f*x)/2)^6*(4*A*a^3 + 12*B*a^3) - tan(e/2 + (f*x)/2)^5*(8*A*a^3 + 58*B*a^3) - tan(e/2 + (f*x)/2)^3*((64*A*a^3)/3 + 148*B*a^3) + tan(e/2 + (f*x)/2)^4*((92*A*a^3)/3 + 134*B*a^3) + tan(e/2 + (f*x)/2)^2*((452*A*a^3)/15 + (744*B*a^3)/5))/(f*(11*c^3*tan(e/2 + (f*x)/2)^2 - 15*c^3*tan(e/2 + (f*x)/2)^3 + 15*c^3*tan(e/2 + (f*x)/2)^4 - 11*c^3*tan(e/2 + (f*x)/2)^5 + 5*c^3*tan(e/2 + (f*x)/2)^6 - c^3*tan(e/2 + (f*x)/2)^7 + c^3 - 5*c^3*tan(e/2 + (f*x)/2))) - (2*a^3*atan((2*a^3*tan(e/2 + (f*x)/2)*(A + 6*B))/(2*A*a^3 + 12*B*a^3))*(A + 6*B))/(c^3*f)","B"
47,1,316,151,15.977925,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^4,x)","\frac{B\,a^3\,x}{c^4}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{a^3\,\left(1680\,B-2205\,B\,\left(e+f\,x\right)\right)}{105}+21\,B\,a^3\,\left(e+f\,x\right)\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{a^3\,\left(7840\,B-3675\,B\,\left(e+f\,x\right)\right)}{105}+35\,B\,a^3\,\left(e+f\,x\right)\right)+\frac{a^3\,\left(30\,A-334\,B+105\,B\,\left(e+f\,x\right)\right)}{105}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{a^3\,\left(210\,A-210\,B+735\,B\,\left(e+f\,x\right)\right)}{105}-7\,B\,a^3\,\left(e+f\,x\right)\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{a^3\,\left(630\,A-5334\,B+2205\,B\,\left(e+f\,x\right)\right)}{105}-21\,B\,a^3\,\left(e+f\,x\right)\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{a^3\,\left(1050\,A-3850\,B+3675\,B\,\left(e+f\,x\right)\right)}{105}-35\,B\,a^3\,\left(e+f\,x\right)\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{a^3\,\left(2128\,B-735\,B\,\left(e+f\,x\right)\right)}{105}+7\,B\,a^3\,\left(e+f\,x\right)\right)-B\,a^3\,\left(e+f\,x\right)}{c^4\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)-1\right)}^7}","Not used",1,"(B*a^3*x)/c^4 - (tan(e/2 + (f*x)/2)^5*((a^3*(1680*B - 2205*B*(e + f*x)))/105 + 21*B*a^3*(e + f*x)) + tan(e/2 + (f*x)/2)^3*((a^3*(7840*B - 3675*B*(e + f*x)))/105 + 35*B*a^3*(e + f*x)) + (a^3*(30*A - 334*B + 105*B*(e + f*x)))/105 + tan(e/2 + (f*x)/2)^6*((a^3*(210*A - 210*B + 735*B*(e + f*x)))/105 - 7*B*a^3*(e + f*x)) + tan(e/2 + (f*x)/2)^2*((a^3*(630*A - 5334*B + 2205*B*(e + f*x)))/105 - 21*B*a^3*(e + f*x)) + tan(e/2 + (f*x)/2)^4*((a^3*(1050*A - 3850*B + 3675*B*(e + f*x)))/105 - 35*B*a^3*(e + f*x)) + tan(e/2 + (f*x)/2)*((a^3*(2128*B - 735*B*(e + f*x)))/105 + 7*B*a^3*(e + f*x)) - B*a^3*(e + f*x))/(c^4*f*(tan(e/2 + (f*x)/2) - 1)^7)","B"
48,1,346,77,13.391561,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^5,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{1013\,A\,a^3}{16}+\frac{149\,B\,a^3}{16}-\frac{113\,A\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{37\,A\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{8}+\frac{7\,A\,a^3\,\cos\left(4\,e+4\,f\,x\right)}{16}-\frac{41\,B\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{19\,B\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{8}+\frac{7\,B\,a^3\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{63\,A\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{8}+\frac{9\,A\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{2}-\frac{9\,A\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{16}-\frac{63\,B\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{8}-\frac{9\,B\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{2}+\frac{9\,B\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{16}-\frac{257\,A\,a^3\,\cos\left(e+f\,x\right)}{8}-\frac{23\,B\,a^3\,\cos\left(e+f\,x\right)}{8}-\frac{63\,A\,a^3\,\sin\left(e+f\,x\right)}{2}+\frac{63\,B\,a^3\,\sin\left(e+f\,x\right)}{2}\right)}{63\,c^5\,f\,\left(\frac{63\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{8}-\frac{21\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{9\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}+\frac{9\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{16}+\frac{\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{16}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((1013*A*a^3)/16 + (149*B*a^3)/16 - (113*A*a^3*cos(2*e + 2*f*x))/4 + (37*A*a^3*cos(3*e + 3*f*x))/8 + (7*A*a^3*cos(4*e + 4*f*x))/16 - (41*B*a^3*cos(2*e + 2*f*x))/4 + (19*B*a^3*cos(3*e + 3*f*x))/8 + (7*B*a^3*cos(4*e + 4*f*x))/16 + (63*A*a^3*sin(2*e + 2*f*x))/8 + (9*A*a^3*sin(3*e + 3*f*x))/2 - (9*A*a^3*sin(4*e + 4*f*x))/16 - (63*B*a^3*sin(2*e + 2*f*x))/8 - (9*B*a^3*sin(3*e + 3*f*x))/2 + (9*B*a^3*sin(4*e + 4*f*x))/16 - (257*A*a^3*cos(e + f*x))/8 - (23*B*a^3*cos(e + f*x))/8 - (63*A*a^3*sin(e + f*x))/2 + (63*B*a^3*sin(e + f*x))/2))/(63*c^5*f*((63*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/8 - (21*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/4 - (9*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/4 + (9*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/16 + (2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/16))","B"
49,1,408,118,13.544180,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^6,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(565\,A\,a^3\,\cos\left(2\,e+2\,f\,x\right)-\frac{837\,B\,a^3}{16}-922\,A\,a^3-\frac{3527\,A\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{32}-29\,A\,a^3\,\cos\left(4\,e+4\,f\,x\right)+\frac{81\,A\,a^3\,\cos\left(5\,e+5\,f\,x\right)}{32}+\frac{225\,B\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{207\,B\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{16}+\frac{9\,B\,a^3\,\cos\left(4\,e+4\,f\,x\right)}{16}-\frac{9\,B\,a^3\,\cos\left(5\,e+5\,f\,x\right)}{16}-\frac{1617\,A\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{8}-\frac{5049\,A\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{32}+\frac{407\,A\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{77\,A\,a^3\,\sin\left(5\,e+5\,f\,x\right)}{32}+\frac{693\,B\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{8}+\frac{99\,B\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{2}-\frac{99\,B\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{6635\,A\,a^3\,\cos\left(e+f\,x\right)}{16}+18\,B\,a^3\,\cos\left(e+f\,x\right)+\frac{13629\,A\,a^3\,\sin\left(e+f\,x\right)}{16}-\frac{693\,B\,a^3\,\sin\left(e+f\,x\right)}{2}\right)}{693\,c^6\,f\,\left(\frac{231\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{16}-\frac{165\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{16}-\frac{165\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{32}+\frac{55\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{32}+\frac{11\,\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{32}-\frac{\sqrt{2}\,\cos\left(\frac{11\,e}{2}-\frac{\pi }{4}+\frac{11\,f\,x}{2}\right)}{32}\right)}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*(565*A*a^3*cos(2*e + 2*f*x) - (837*B*a^3)/16 - 922*A*a^3 - (3527*A*a^3*cos(3*e + 3*f*x))/32 - 29*A*a^3*cos(4*e + 4*f*x) + (81*A*a^3*cos(5*e + 5*f*x))/32 + (225*B*a^3*cos(2*e + 2*f*x))/4 - (207*B*a^3*cos(3*e + 3*f*x))/16 + (9*B*a^3*cos(4*e + 4*f*x))/16 - (9*B*a^3*cos(5*e + 5*f*x))/16 - (1617*A*a^3*sin(2*e + 2*f*x))/8 - (5049*A*a^3*sin(3*e + 3*f*x))/32 + (407*A*a^3*sin(4*e + 4*f*x))/16 + (77*A*a^3*sin(5*e + 5*f*x))/32 + (693*B*a^3*sin(2*e + 2*f*x))/8 + (99*B*a^3*sin(3*e + 3*f*x))/2 - (99*B*a^3*sin(4*e + 4*f*x))/16 + (6635*A*a^3*cos(e + f*x))/16 + 18*B*a^3*cos(e + f*x) + (13629*A*a^3*sin(e + f*x))/16 - (693*B*a^3*sin(e + f*x))/2))/(693*c^6*f*((231*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/16 - (165*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/16 - (165*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/32 + (55*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/32 + (11*2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/32 - (2^(1/2)*cos((11*e)/2 - pi/4 + (11*f*x)/2))/32))","B"
50,1,500,156,13.793596,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^7,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{2363\,B\,a^3}{32}-\frac{279183\,A\,a^3}{16}+\frac{220269\,A\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{16}-\frac{46095\,A\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{16}-\frac{20829\,A\,a^3\,\cos\left(4\,e+4\,f\,x\right)}{16}+\frac{2811\,A\,a^3\,\cos\left(5\,e+5\,f\,x\right)}{16}+\frac{231\,A\,a^3\,\cos\left(6\,e+6\,f\,x\right)}{16}-\frac{8995\,B\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{64}+\frac{497\,B\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{16}+\frac{3725\,B\,a^3\,\cos\left(4\,e+4\,f\,x\right)}{32}-\frac{361\,B\,a^3\,\cos\left(5\,e+5\,f\,x\right)}{16}-\frac{77\,B\,a^3\,\cos\left(6\,e+6\,f\,x\right)}{64}-\frac{19305\,A\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{4}-\frac{81081\,A\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{16}+\frac{15015\,A\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{16}+\frac{3237\,A\,a^3\,\sin\left(5\,e+5\,f\,x\right)}{16}-\frac{117\,A\,a^3\,\sin\left(6\,e+6\,f\,x\right)}{8}+\frac{77649\,B\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{64}+\frac{27027\,B\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{32}-\frac{1001\,B\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{8}-\frac{559\,B\,a^3\,\sin\left(5\,e+5\,f\,x\right)}{32}+\frac{117\,B\,a^3\,\sin\left(6\,e+6\,f\,x\right)}{64}+\frac{26979\,A\,a^3\,\cos\left(e+f\,x\right)}{4}+40\,B\,a^3\,\cos\left(e+f\,x\right)+\frac{173745\,A\,a^3\,\sin\left(e+f\,x\right)}{8}-\frac{80223\,B\,a^3\,\sin\left(e+f\,x\right)}{16}\right)}{9009\,c^7\,f\,\left(\frac{1287\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{64}-\frac{429\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{16}+\frac{715\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{64}-\frac{143\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{32}-\frac{39\,\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{32}+\frac{13\,\sqrt{2}\,\cos\left(\frac{11\,e}{2}-\frac{\pi }{4}+\frac{11\,f\,x}{2}\right)}{64}+\frac{\sqrt{2}\,\cos\left(\frac{13\,e}{2}+\frac{\pi }{4}+\frac{13\,f\,x}{2}\right)}{64}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((2363*B*a^3)/32 - (279183*A*a^3)/16 + (220269*A*a^3*cos(2*e + 2*f*x))/16 - (46095*A*a^3*cos(3*e + 3*f*x))/16 - (20829*A*a^3*cos(4*e + 4*f*x))/16 + (2811*A*a^3*cos(5*e + 5*f*x))/16 + (231*A*a^3*cos(6*e + 6*f*x))/16 - (8995*B*a^3*cos(2*e + 2*f*x))/64 + (497*B*a^3*cos(3*e + 3*f*x))/16 + (3725*B*a^3*cos(4*e + 4*f*x))/32 - (361*B*a^3*cos(5*e + 5*f*x))/16 - (77*B*a^3*cos(6*e + 6*f*x))/64 - (19305*A*a^3*sin(2*e + 2*f*x))/4 - (81081*A*a^3*sin(3*e + 3*f*x))/16 + (15015*A*a^3*sin(4*e + 4*f*x))/16 + (3237*A*a^3*sin(5*e + 5*f*x))/16 - (117*A*a^3*sin(6*e + 6*f*x))/8 + (77649*B*a^3*sin(2*e + 2*f*x))/64 + (27027*B*a^3*sin(3*e + 3*f*x))/32 - (1001*B*a^3*sin(4*e + 4*f*x))/8 - (559*B*a^3*sin(5*e + 5*f*x))/32 + (117*B*a^3*sin(6*e + 6*f*x))/64 + (26979*A*a^3*cos(e + f*x))/4 + 40*B*a^3*cos(e + f*x) + (173745*A*a^3*sin(e + f*x))/8 - (80223*B*a^3*sin(e + f*x))/16))/(9009*c^7*f*((1287*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/64 - (429*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/16 + (715*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/64 - (143*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/32 - (39*2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/32 + (13*2^(1/2)*cos((11*e)/2 - pi/4 + (11*f*x)/2))/64 + (2^(1/2)*cos((13*e)/2 + pi/4 + (13*f*x)/2))/64))","B"
51,1,577,197,13.963389,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^8,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{544369\,A\,a^3}{4}-\frac{21791\,B\,a^3}{4}-\frac{257861\,A\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{2}+\frac{3497111\,A\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{128}+\frac{72047\,A\,a^3\,\cos\left(4\,e+4\,f\,x\right)}{4}-\frac{378579\,A\,a^3\,\cos\left(5\,e+5\,f\,x\right)}{128}-\frac{1059\,A\,a^3\,\cos\left(6\,e+6\,f\,x\right)}{2}+\frac{4251\,A\,a^3\,\cos\left(7\,e+7\,f\,x\right)}{128}+\frac{219769\,B\,a^3\,\cos\left(2\,e+2\,f\,x\right)}{32}-\frac{191389\,B\,a^3\,\cos\left(3\,e+3\,f\,x\right)}{128}-1672\,B\,a^3\,\cos\left(4\,e+4\,f\,x\right)+\frac{38841\,B\,a^3\,\cos\left(5\,e+5\,f\,x\right)}{128}+\frac{1551\,B\,a^3\,\cos\left(6\,e+6\,f\,x\right)}{32}-\frac{429\,B\,a^3\,\cos\left(7\,e+7\,f\,x\right)}{128}+\frac{2633345\,A\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{64}+\frac{7210775\,A\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{128}-\frac{89375\,A\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{8}-\frac{504205\,A\,a^3\,\sin\left(5\,e+5\,f\,x\right)}{128}+\frac{29765\,A\,a^3\,\sin\left(6\,e+6\,f\,x\right)}{64}+\frac{4235\,A\,a^3\,\sin\left(7\,e+7\,f\,x\right)}{128}-\frac{451165\,B\,a^3\,\sin\left(2\,e+2\,f\,x\right)}{64}-\frac{854425\,B\,a^3\,\sin\left(3\,e+3\,f\,x\right)}{128}+\frac{9295\,B\,a^3\,\sin\left(4\,e+4\,f\,x\right)}{8}+\frac{46475\,B\,a^3\,\sin\left(5\,e+5\,f\,x\right)}{128}-\frac{3025\,B\,a^3\,\sin\left(6\,e+6\,f\,x\right)}{64}-\frac{385\,B\,a^3\,\sin\left(7\,e+7\,f\,x\right)}{128}-\frac{5734111\,A\,a^3\,\cos\left(e+f\,x\right)}{128}+\frac{126929\,B\,a^3\,\cos\left(e+f\,x\right)}{128}-\frac{25501905\,A\,a^3\,\sin\left(e+f\,x\right)}{128}+\frac{3970395\,B\,a^3\,\sin\left(e+f\,x\right)}{128}\right)}{45045\,c^8\,f\,\left(\frac{6435\,\sqrt{2}\,\cos\left(\frac{e}{2}+\frac{\pi }{4}+\frac{f\,x}{2}\right)}{128}-\frac{5005\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}-\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{128}-\frac{3003\,\sqrt{2}\,\cos\left(\frac{5\,e}{2}+\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{128}+\frac{1365\,\sqrt{2}\,\cos\left(\frac{7\,e}{2}-\frac{\pi }{4}+\frac{7\,f\,x}{2}\right)}{128}+\frac{455\,\sqrt{2}\,\cos\left(\frac{9\,e}{2}+\frac{\pi }{4}+\frac{9\,f\,x}{2}\right)}{128}-\frac{105\,\sqrt{2}\,\cos\left(\frac{11\,e}{2}-\frac{\pi }{4}+\frac{11\,f\,x}{2}\right)}{128}-\frac{15\,\sqrt{2}\,\cos\left(\frac{13\,e}{2}+\frac{\pi }{4}+\frac{13\,f\,x}{2}\right)}{128}+\frac{\sqrt{2}\,\cos\left(\frac{15\,e}{2}-\frac{\pi }{4}+\frac{15\,f\,x}{2}\right)}{128}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((544369*A*a^3)/4 - (21791*B*a^3)/4 - (257861*A*a^3*cos(2*e + 2*f*x))/2 + (3497111*A*a^3*cos(3*e + 3*f*x))/128 + (72047*A*a^3*cos(4*e + 4*f*x))/4 - (378579*A*a^3*cos(5*e + 5*f*x))/128 - (1059*A*a^3*cos(6*e + 6*f*x))/2 + (4251*A*a^3*cos(7*e + 7*f*x))/128 + (219769*B*a^3*cos(2*e + 2*f*x))/32 - (191389*B*a^3*cos(3*e + 3*f*x))/128 - 1672*B*a^3*cos(4*e + 4*f*x) + (38841*B*a^3*cos(5*e + 5*f*x))/128 + (1551*B*a^3*cos(6*e + 6*f*x))/32 - (429*B*a^3*cos(7*e + 7*f*x))/128 + (2633345*A*a^3*sin(2*e + 2*f*x))/64 + (7210775*A*a^3*sin(3*e + 3*f*x))/128 - (89375*A*a^3*sin(4*e + 4*f*x))/8 - (504205*A*a^3*sin(5*e + 5*f*x))/128 + (29765*A*a^3*sin(6*e + 6*f*x))/64 + (4235*A*a^3*sin(7*e + 7*f*x))/128 - (451165*B*a^3*sin(2*e + 2*f*x))/64 - (854425*B*a^3*sin(3*e + 3*f*x))/128 + (9295*B*a^3*sin(4*e + 4*f*x))/8 + (46475*B*a^3*sin(5*e + 5*f*x))/128 - (3025*B*a^3*sin(6*e + 6*f*x))/64 - (385*B*a^3*sin(7*e + 7*f*x))/128 - (5734111*A*a^3*cos(e + f*x))/128 + (126929*B*a^3*cos(e + f*x))/128 - (25501905*A*a^3*sin(e + f*x))/128 + (3970395*B*a^3*sin(e + f*x))/128))/(45045*c^8*f*((6435*2^(1/2)*cos(e/2 + pi/4 + (f*x)/2))/128 - (5005*2^(1/2)*cos((3*e)/2 - pi/4 + (3*f*x)/2))/128 - (3003*2^(1/2)*cos((5*e)/2 + pi/4 + (5*f*x)/2))/128 + (1365*2^(1/2)*cos((7*e)/2 - pi/4 + (7*f*x)/2))/128 + (455*2^(1/2)*cos((9*e)/2 + pi/4 + (9*f*x)/2))/128 - (105*2^(1/2)*cos((11*e)/2 - pi/4 + (11*f*x)/2))/128 - (15*2^(1/2)*cos((13*e)/2 + pi/4 + (13*f*x)/2))/128 + (2^(1/2)*cos((15*e)/2 - pi/4 + (15*f*x)/2))/128))","B"
52,1,397,190,14.778201,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^4)/(a + a*sin(e + f*x)),x)","-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{55\,A\,c^4}{3}-\frac{299\,B\,c^4}{12}\right)+\frac{166\,A\,c^4}{3}-\frac{206\,B\,c^4}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(27\,A\,c^4-\frac{167\,B\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(37\,A\,c^4-\frac{175\,B\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(75\,A\,c^4-\frac{495\,B\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(155\,A\,c^4-\frac{687\,B\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(257\,A\,c^4-\frac{1153\,B\,c^4}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{199\,A\,c^4}{3}-\frac{1235\,B\,c^4}{12}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{583\,A\,c^4}{3}-\frac{2795\,B\,c^4}{12}\right)}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+4\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+6\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}-\frac{35\,c^4\,\mathrm{atan}\left(\frac{35\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A-5\,B\right)}{140\,A\,c^4-175\,B\,c^4}\right)\,\left(4\,A-5\,B\right)}{4\,a\,f}","Not used",1,"- (tan(e/2 + (f*x)/2)*((55*A*c^4)/3 - (299*B*c^4)/12) + (166*A*c^4)/3 - (206*B*c^4)/3 + tan(e/2 + (f*x)/2)^7*(27*A*c^4 - (167*B*c^4)/4) + tan(e/2 + (f*x)/2)^8*(37*A*c^4 - (175*B*c^4)/4) + tan(e/2 + (f*x)/2)^5*(75*A*c^4 - (495*B*c^4)/4) + tan(e/2 + (f*x)/2)^6*(155*A*c^4 - (687*B*c^4)/4) + tan(e/2 + (f*x)/2)^4*(257*A*c^4 - (1153*B*c^4)/4) + tan(e/2 + (f*x)/2)^3*((199*A*c^4)/3 - (1235*B*c^4)/12) + tan(e/2 + (f*x)/2)^2*((583*A*c^4)/3 - (2795*B*c^4)/12))/(f*(a + a*tan(e/2 + (f*x)/2) + 4*a*tan(e/2 + (f*x)/2)^2 + 4*a*tan(e/2 + (f*x)/2)^3 + 6*a*tan(e/2 + (f*x)/2)^4 + 6*a*tan(e/2 + (f*x)/2)^5 + 4*a*tan(e/2 + (f*x)/2)^6 + 4*a*tan(e/2 + (f*x)/2)^7 + a*tan(e/2 + (f*x)/2)^8 + a*tan(e/2 + (f*x)/2)^9)) - (35*c^4*atan((35*c^4*tan(e/2 + (f*x)/2)*(4*A - 5*B))/(140*A*c^4 - 175*B*c^4))*(4*A - 5*B))/(4*a*f)","B"
53,1,319,157,14.011636,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^3)/(a + a*sin(e + f*x)),x)","-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(7\,A\,c^3-\frac{34\,B\,c^3}{3}\right)+24\,A\,c^3-\frac{94\,B\,c^3}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(9\,A\,c^3-18\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(17\,A\,c^3-20\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(16\,A\,c^3-32\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(56\,A\,c^3-62\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(63\,A\,c^3-76\,B\,c^3\right)}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}-\frac{5\,c^3\,\mathrm{atan}\left(\frac{5\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A-4\,B\right)}{15\,A\,c^3-20\,B\,c^3}\right)\,\left(3\,A-4\,B\right)}{a\,f}","Not used",1,"- (tan(e/2 + (f*x)/2)*(7*A*c^3 - (34*B*c^3)/3) + 24*A*c^3 - (94*B*c^3)/3 + tan(e/2 + (f*x)/2)^5*(9*A*c^3 - 18*B*c^3) + tan(e/2 + (f*x)/2)^6*(17*A*c^3 - 20*B*c^3) + tan(e/2 + (f*x)/2)^3*(16*A*c^3 - 32*B*c^3) + tan(e/2 + (f*x)/2)^4*(56*A*c^3 - 62*B*c^3) + tan(e/2 + (f*x)/2)^2*(63*A*c^3 - 76*B*c^3))/(f*(a + a*tan(e/2 + (f*x)/2) + 3*a*tan(e/2 + (f*x)/2)^2 + 3*a*tan(e/2 + (f*x)/2)^3 + 3*a*tan(e/2 + (f*x)/2)^4 + 3*a*tan(e/2 + (f*x)/2)^5 + a*tan(e/2 + (f*x)/2)^6 + a*tan(e/2 + (f*x)/2)^7)) - (5*c^3*atan((5*c^3*tan(e/2 + (f*x)/2)*(3*A - 4*B))/(15*A*c^3 - 20*B*c^3))*(3*A - 4*B))/(a*f)","B"
54,1,241,118,14.576543,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^2)/(a + a*sin(e + f*x)),x)","-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,c^2-5\,B\,c^2\right)+10\,A\,c^2-14\,B\,c^2+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,c^2-7\,B\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(8\,A\,c^2-9\,B\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(18\,A\,c^2-21\,B\,c^2\right)}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}-\frac{3\,c^2\,\mathrm{atan}\left(\frac{3\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A-3\,B\right)}{6\,A\,c^2-9\,B\,c^2}\right)\,\left(2\,A-3\,B\right)}{a\,f}","Not used",1,"- (tan(e/2 + (f*x)/2)*(2*A*c^2 - 5*B*c^2) + 10*A*c^2 - 14*B*c^2 + tan(e/2 + (f*x)/2)^3*(2*A*c^2 - 7*B*c^2) + tan(e/2 + (f*x)/2)^4*(8*A*c^2 - 9*B*c^2) + tan(e/2 + (f*x)/2)^2*(18*A*c^2 - 21*B*c^2))/(f*(a + a*tan(e/2 + (f*x)/2) + 2*a*tan(e/2 + (f*x)/2)^2 + 2*a*tan(e/2 + (f*x)/2)^3 + a*tan(e/2 + (f*x)/2)^4 + a*tan(e/2 + (f*x)/2)^5)) - (3*c^2*atan((3*c^2*tan(e/2 + (f*x)/2)*(2*A - 3*B))/(6*A*c^2 - 9*B*c^2))*(2*A - 3*B))/(a*f)","B"
55,1,110,57,12.940532,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x)))/(a + a*sin(e + f*x)),x)","-\frac{\left(4\,A\,c-4\,B\,c\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-2\,B\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A\,c-6\,B\,c}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}-\frac{A\,c\,f\,x-2\,B\,c\,f\,x}{a\,f}","Not used",1,"- (4*A*c - 6*B*c + tan(e/2 + (f*x)/2)^2*(4*A*c - 4*B*c) - 2*B*c*tan(e/2 + (f*x)/2))/(f*(a + a*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2 + a*tan(e/2 + (f*x)/2)^3)) - (A*c*f*x - 2*B*c*f*x)/(a*f)","B"
56,1,39,35,12.554070,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))),x)","-\frac{2\,\left(B+A\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}{a\,c\,f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}","Not used",1,"-(2*(B + A*tan(e/2 + (f*x)/2)))/(a*c*f*(tan(e/2 + (f*x)/2)^2 - 1))","B"
57,1,118,63,12.323244,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^2),x)","\frac{2\,\left(\frac{3\,B}{2}+A\,\cos\left(e+f\,x\right)+B\,\cos\left(e+f\,x\right)+2\,A\,\sin\left(e+f\,x\right)-B\,\sin\left(e+f\,x\right)+A\,\cos\left(2\,e+2\,f\,x\right)-\frac{B\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{A\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{B\,\sin\left(2\,e+2\,f\,x\right)}{2}\right)}{3\,a\,c^2\,f\,\left(2\,\cos\left(e+f\,x\right)-\sin\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"(2*((3*B)/2 + A*cos(e + f*x) + B*cos(e + f*x) + 2*A*sin(e + f*x) - B*sin(e + f*x) + A*cos(2*e + 2*f*x) - (B*cos(2*e + 2*f*x))/2 - (A*sin(2*e + 2*f*x))/2 - (B*sin(2*e + 2*f*x))/2))/(3*a*c^2*f*(2*cos(e + f*x) - sin(2*e + 2*f*x)))","B"
58,1,178,102,12.469297,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^3),x)","\frac{2\,\left(\frac{5\,B\,\sin\left(e+f\,x\right)}{2}-\frac{15\,A\,\cos\left(e+f\,x\right)}{4}-\frac{5\,B\,\cos\left(e+f\,x\right)}{8}-\frac{15\,A\,\sin\left(e+f\,x\right)}{4}-\frac{5\,B}{2}-3\,A\,\cos\left(2\,e+2\,f\,x\right)+\frac{3\,A\,\cos\left(3\,e+3\,f\,x\right)}{4}+2\,B\,\cos\left(2\,e+2\,f\,x\right)+\frac{B\,\cos\left(3\,e+3\,f\,x\right)}{8}+3\,A\,\sin\left(2\,e+2\,f\,x\right)+\frac{3\,A\,\sin\left(3\,e+3\,f\,x\right)}{4}+\frac{B\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{B\,\sin\left(3\,e+3\,f\,x\right)}{2}\right)}{15\,a\,c^3\,f\,\left(\frac{\cos\left(3\,e+3\,f\,x\right)}{4}-\frac{5\,\cos\left(e+f\,x\right)}{4}+\sin\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"(2*((5*B*sin(e + f*x))/2 - (15*A*cos(e + f*x))/4 - (5*B*cos(e + f*x))/8 - (15*A*sin(e + f*x))/4 - (5*B)/2 - 3*A*cos(2*e + 2*f*x) + (3*A*cos(3*e + 3*f*x))/4 + 2*B*cos(2*e + 2*f*x) + (B*cos(3*e + 3*f*x))/8 + 3*A*sin(2*e + 2*f*x) + (3*A*sin(3*e + 3*f*x))/4 + (B*sin(2*e + 2*f*x))/2 - (B*sin(3*e + 3*f*x))/2))/(15*a*c^3*f*(cos(3*e + 3*f*x)/4 - (5*cos(e + f*x))/4 + sin(2*e + 2*f*x)))","B"
59,1,239,142,13.232897,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^4),x)","\frac{2\,\left(\frac{35\,B}{4}+\frac{91\,A\,\cos\left(e+f\,x\right)}{4}-\frac{7\,B\,\cos\left(e+f\,x\right)}{4}+14\,A\,\sin\left(e+f\,x\right)-\frac{21\,B\,\sin\left(e+f\,x\right)}{2}+14\,A\,\cos\left(2\,e+2\,f\,x\right)-\frac{39\,A\,\cos\left(3\,e+3\,f\,x\right)}{4}-A\,\cos\left(4\,e+4\,f\,x\right)-\frac{21\,B\,\cos\left(2\,e+2\,f\,x\right)}{2}+\frac{3\,B\,\cos\left(3\,e+3\,f\,x\right)}{4}+\frac{3\,B\,\cos\left(4\,e+4\,f\,x\right)}{4}-\frac{91\,A\,\sin\left(2\,e+2\,f\,x\right)}{4}-6\,A\,\sin\left(3\,e+3\,f\,x\right)+\frac{13\,A\,\sin\left(4\,e+4\,f\,x\right)}{8}+\frac{7\,B\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{9\,B\,\sin\left(3\,e+3\,f\,x\right)}{2}-\frac{B\,\sin\left(4\,e+4\,f\,x\right)}{8}\right)}{35\,a\,c^4\,f\,\left(\frac{7\,\cos\left(e+f\,x\right)}{2}-\frac{3\,\cos\left(3\,e+3\,f\,x\right)}{2}-\frac{7\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{\sin\left(4\,e+4\,f\,x\right)}{4}\right)}","Not used",1,"(2*((35*B)/4 + (91*A*cos(e + f*x))/4 - (7*B*cos(e + f*x))/4 + 14*A*sin(e + f*x) - (21*B*sin(e + f*x))/2 + 14*A*cos(2*e + 2*f*x) - (39*A*cos(3*e + 3*f*x))/4 - A*cos(4*e + 4*f*x) - (21*B*cos(2*e + 2*f*x))/2 + (3*B*cos(3*e + 3*f*x))/4 + (3*B*cos(4*e + 4*f*x))/4 - (91*A*sin(2*e + 2*f*x))/4 - 6*A*sin(3*e + 3*f*x) + (13*A*sin(4*e + 4*f*x))/8 + (7*B*sin(2*e + 2*f*x))/4 + (9*B*sin(3*e + 3*f*x))/2 - (B*sin(4*e + 4*f*x))/8))/(35*a*c^4*f*((7*cos(e + f*x))/2 - (3*cos(3*e + 3*f*x))/2 - (7*sin(2*e + 2*f*x))/2 + sin(4*e + 4*f*x)/4))","B"
60,1,500,240,14.825430,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^5)/(a + a*sin(e + f*x))^2,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(391\,A\,c^5-\frac{2729\,B\,c^5}{4}\right)+\frac{494\,A\,c^5}{3}-\frac{866\,B\,c^5}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(103\,A\,c^5-\frac{735\,B\,c^5}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(323\,A\,c^5-\frac{2213\,B\,c^5}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(1332\,A\,c^5-2253\,B\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(1632\,A\,c^5-2943\,B\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{2002\,A\,c^5}{3}-\frac{3637\,B\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{4420\,A\,c^5}{3}-\frac{7621\,B\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{2489\,A\,c^5}{3}-\frac{17609\,B\,c^5}{12}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{4594\,A\,c^5}{3}-\frac{16805\,B\,c^5}{6}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{6274\,A\,c^5}{3}-\frac{21299\,B\,c^5}{6}\right)}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+13\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+18\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+22\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+22\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+18\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+13\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}+\frac{105\,c^5\,\mathrm{atan}\left(\frac{105\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A-7\,B\right)}{420\,A\,c^5-735\,B\,c^5}\right)\,\left(4\,A-7\,B\right)}{4\,a^2\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*(391*A*c^5 - (2729*B*c^5)/4) + (494*A*c^5)/3 - (866*B*c^5)/3 + tan(e/2 + (f*x)/2)^10*(103*A*c^5 - (735*B*c^5)/4) + tan(e/2 + (f*x)/2)^9*(323*A*c^5 - (2213*B*c^5)/4) + tan(e/2 + (f*x)/2)^7*(1332*A*c^5 - 2253*B*c^5) + tan(e/2 + (f*x)/2)^4*(1632*A*c^5 - 2943*B*c^5) + tan(e/2 + (f*x)/2)^8*((2002*A*c^5)/3 - (3637*B*c^5)/3) + tan(e/2 + (f*x)/2)^3*((4420*A*c^5)/3 - (7621*B*c^5)/3) + tan(e/2 + (f*x)/2)^2*((2489*A*c^5)/3 - (17609*B*c^5)/12) + tan(e/2 + (f*x)/2)^6*((4594*A*c^5)/3 - (16805*B*c^5)/6) + tan(e/2 + (f*x)/2)^5*((6274*A*c^5)/3 - (21299*B*c^5)/6))/(f*(7*a^2*tan(e/2 + (f*x)/2)^2 + 13*a^2*tan(e/2 + (f*x)/2)^3 + 18*a^2*tan(e/2 + (f*x)/2)^4 + 22*a^2*tan(e/2 + (f*x)/2)^5 + 22*a^2*tan(e/2 + (f*x)/2)^6 + 18*a^2*tan(e/2 + (f*x)/2)^7 + 13*a^2*tan(e/2 + (f*x)/2)^8 + 7*a^2*tan(e/2 + (f*x)/2)^9 + 3*a^2*tan(e/2 + (f*x)/2)^10 + a^2*tan(e/2 + (f*x)/2)^11 + a^2 + 3*a^2*tan(e/2 + (f*x)/2))) + (105*c^5*atan((105*c^5*tan(e/2 + (f*x)/2)*(4*A - 7*B))/(420*A*c^5 - 735*B*c^5))*(4*A - 7*B))/(4*a^2*f)","B"
61,1,414,180,14.952062,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^4)/(a + a*sin(e + f*x))^2,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(131\,A\,c^4-260\,B\,c^4\right)+\frac{164\,A\,c^4}{3}-110\,B\,c^4+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(33\,A\,c^4-70\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(111\,A\,c^4-212\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(217\,A\,c^4-448\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(307\,A\,c^4-660\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(349\,A\,c^4-660\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{533\,A\,c^4}{3}-\frac{1160\,B\,c^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(369\,A\,c^4-\frac{2140\,B\,c^4}{3}\right)}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+6\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+10\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+12\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+12\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+6\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}+\frac{35\,c^4\,\mathrm{atan}\left(\frac{35\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A-2\,B\right)}{35\,A\,c^4-70\,B\,c^4}\right)\,\left(A-2\,B\right)}{a^2\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*(131*A*c^4 - 260*B*c^4) + (164*A*c^4)/3 - 110*B*c^4 + tan(e/2 + (f*x)/2)^8*(33*A*c^4 - 70*B*c^4) + tan(e/2 + (f*x)/2)^7*(111*A*c^4 - 212*B*c^4) + tan(e/2 + (f*x)/2)^2*(217*A*c^4 - 448*B*c^4) + tan(e/2 + (f*x)/2)^4*(307*A*c^4 - 660*B*c^4) + tan(e/2 + (f*x)/2)^5*(349*A*c^4 - 660*B*c^4) + tan(e/2 + (f*x)/2)^6*((533*A*c^4)/3 - (1160*B*c^4)/3) + tan(e/2 + (f*x)/2)^3*(369*A*c^4 - (2140*B*c^4)/3))/(f*(6*a^2*tan(e/2 + (f*x)/2)^2 + 10*a^2*tan(e/2 + (f*x)/2)^3 + 12*a^2*tan(e/2 + (f*x)/2)^4 + 12*a^2*tan(e/2 + (f*x)/2)^5 + 10*a^2*tan(e/2 + (f*x)/2)^6 + 6*a^2*tan(e/2 + (f*x)/2)^7 + 3*a^2*tan(e/2 + (f*x)/2)^8 + a^2*tan(e/2 + (f*x)/2)^9 + a^2 + 3*a^2*tan(e/2 + (f*x)/2))) + (35*c^4*atan((35*c^4*tan(e/2 + (f*x)/2)*(A - 2*B))/(35*A*c^4 - 70*B*c^4))*(A - 2*B))/(a^2*f)","B"
62,1,336,162,14.340542,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^3)/(a + a*sin(e + f*x))^2,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(38\,A\,c^3-93\,B\,c^3\right)+\frac{46\,A\,c^3}{3}-\frac{118\,B\,c^3}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(8\,A\,c^3-25\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(34\,A\,c^3-77\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(72\,A\,c^3-166\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{106\,A\,c^3}{3}-\frac{328\,B\,c^3}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{128\,A\,c^3}{3}-\frac{359\,B\,c^3}{3}\right)}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+5\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+5\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}+\frac{5\,c^3\,\mathrm{atan}\left(\frac{5\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A-5\,B\right)}{10\,A\,c^3-25\,B\,c^3}\right)\,\left(2\,A-5\,B\right)}{a^2\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*(38*A*c^3 - 93*B*c^3) + (46*A*c^3)/3 - (118*B*c^3)/3 + tan(e/2 + (f*x)/2)^6*(8*A*c^3 - 25*B*c^3) + tan(e/2 + (f*x)/2)^5*(34*A*c^3 - 77*B*c^3) + tan(e/2 + (f*x)/2)^3*(72*A*c^3 - 166*B*c^3) + tan(e/2 + (f*x)/2)^4*((106*A*c^3)/3 - (328*B*c^3)/3) + tan(e/2 + (f*x)/2)^2*((128*A*c^3)/3 - (359*B*c^3)/3))/(f*(5*a^2*tan(e/2 + (f*x)/2)^2 + 7*a^2*tan(e/2 + (f*x)/2)^3 + 7*a^2*tan(e/2 + (f*x)/2)^4 + 5*a^2*tan(e/2 + (f*x)/2)^5 + 3*a^2*tan(e/2 + (f*x)/2)^6 + a^2*tan(e/2 + (f*x)/2)^7 + a^2 + 3*a^2*tan(e/2 + (f*x)/2))) + (5*c^3*atan((5*c^3*tan(e/2 + (f*x)/2)*(2*A - 5*B))/(10*A*c^3 - 25*B*c^3))*(2*A - 5*B))/(a^2*f)","B"
63,1,242,108,14.526784,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^2)/(a + a*sin(e + f*x))^2,x)","\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,c^2-30\,B\,c^2\right)+\frac{8\,A\,c^2}{3}-\frac{38\,B\,c^2}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(8\,A\,c^2-26\,B\,c^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{8\,A\,c^2}{3}-\frac{74\,B\,c^2}{3}\right)-8\,B\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}+\frac{2\,c^2\,\mathrm{atan}\left(\frac{2\,c^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A-4\,B\right)}{2\,A\,c^2-8\,B\,c^2}\right)\,\left(A-4\,B\right)}{a^2\,f}","Not used",1,"(tan(e/2 + (f*x)/2)*(8*A*c^2 - 30*B*c^2) + (8*A*c^2)/3 - (38*B*c^2)/3 + tan(e/2 + (f*x)/2)^3*(8*A*c^2 - 26*B*c^2) + tan(e/2 + (f*x)/2)^2*((8*A*c^2)/3 - (74*B*c^2)/3) - 8*B*c^2*tan(e/2 + (f*x)/2)^4)/(f*(4*a^2*tan(e/2 + (f*x)/2)^2 + 4*a^2*tan(e/2 + (f*x)/2)^3 + 3*a^2*tan(e/2 + (f*x)/2)^4 + a^2*tan(e/2 + (f*x)/2)^5 + a^2 + 3*a^2*tan(e/2 + (f*x)/2))) + (2*c^2*atan((2*c^2*tan(e/2 + (f*x)/2)*(A - 4*B))/(2*A*c^2 - 8*B*c^2))*(A - 4*B))/(a^2*f)","B"
64,1,133,72,12.825584,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x)))/(a + a*sin(e + f*x))^2,x)","-\frac{B\,c\,x}{a^2}-\frac{\left(\frac{c\,\left(6\,A+6\,B+9\,B\,\left(e+f\,x\right)\right)}{3}-3\,B\,c\,\left(e+f\,x\right)\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(\frac{c\,\left(24\,B+9\,B\,\left(e+f\,x\right)\right)}{3}-3\,B\,c\,\left(e+f\,x\right)\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{c\,\left(2\,A+10\,B+3\,B\,\left(e+f\,x\right)\right)}{3}-B\,c\,\left(e+f\,x\right)}{a^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"- (B*c*x)/a^2 - (tan(e/2 + (f*x)/2)^2*((c*(6*A + 6*B + 9*B*(e + f*x)))/3 - 3*B*c*(e + f*x)) + tan(e/2 + (f*x)/2)*((c*(24*B + 9*B*(e + f*x)))/3 - 3*B*c*(e + f*x)) + (c*(2*A + 10*B + 3*B*(e + f*x)))/3 - B*c*(e + f*x))/(a^2*f*(tan(e/2 + (f*x)/2) + 1)^3)","B"
65,1,117,62,12.285641,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))),x)","\frac{2\,\left(\frac{3\,B}{2}-A\,\cos\left(e+f\,x\right)+B\,\cos\left(e+f\,x\right)+2\,A\,\sin\left(e+f\,x\right)+B\,\sin\left(e+f\,x\right)-A\,\cos\left(2\,e+2\,f\,x\right)-\frac{B\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{A\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{B\,\sin\left(2\,e+2\,f\,x\right)}{2}\right)}{3\,a^2\,c\,f\,\left(2\,\cos\left(e+f\,x\right)+\sin\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"(2*((3*B)/2 - A*cos(e + f*x) + B*cos(e + f*x) + 2*A*sin(e + f*x) + B*sin(e + f*x) - A*cos(2*e + 2*f*x) - (B*cos(2*e + 2*f*x))/2 - (A*sin(2*e + 2*f*x))/2 + (B*sin(2*e + 2*f*x))/2))/(3*a^2*c*f*(2*cos(e + f*x) + sin(2*e + 2*f*x)))","B"
66,1,82,62,12.383304,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^2),x)","-\frac{2\,\left(3\,A\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,B\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-2\,A\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,A\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+B\right)}{3\,a^2\,c^2\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}^3}","Not used",1,"-(2*(B + 3*A*tan(e/2 + (f*x)/2) - 2*A*tan(e/2 + (f*x)/2)^3 + 3*A*tan(e/2 + (f*x)/2)^5 + 3*B*tan(e/2 + (f*x)/2)^4))/(3*a^2*c^2*f*(tan(e/2 + (f*x)/2)^2 - 1)^3)","B"
67,1,183,93,12.450181,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^3),x)","\frac{\left(\frac{8\,A}{15}-\frac{2\,B}{15}-\frac{16\,A\,\sin\left(e+f\,x\right)}{15}+\frac{4\,B\,\sin\left(e+f\,x\right)}{15}\right)\,{\cos\left(e+f\,x\right)}^2+\frac{2\,A}{15}-\frac{8\,B}{15}-\frac{8\,A\,\sin\left(e+f\,x\right)}{15}+\frac{2\,B\,\sin\left(e+f\,x\right)}{15}}{a^2\,c^3\,f\,\left(2\,{\cos\left(e+f\,x\right)}^3\,\sin\left(e+f\,x\right)-2\,{\cos\left(e+f\,x\right)}^3\right)}-\frac{\frac{2\,A}{5}+\frac{2\,B}{5}-\frac{2\,A\,\sin\left(e+f\,x\right)}{5}-\frac{2\,B\,\sin\left(e+f\,x\right)}{5}}{a^2\,c^3\,f\,\left(2\,\sin\left(e+f\,x\right)-2\right)}-\frac{\cos\left(e+f\,x\right)\,\left(\frac{16\,A}{15}-\frac{4\,B}{15}\right)}{a^2\,c^3\,f\,\left(2\,\sin\left(e+f\,x\right)-2\right)}","Not used",1,"((2*A)/15 - (8*B)/15 - (8*A*sin(e + f*x))/15 + (2*B*sin(e + f*x))/15 + cos(e + f*x)^2*((8*A)/15 - (2*B)/15 - (16*A*sin(e + f*x))/15 + (4*B*sin(e + f*x))/15))/(a^2*c^3*f*(2*cos(e + f*x)^3*sin(e + f*x) - 2*cos(e + f*x)^3)) - ((2*A)/5 + (2*B)/5 - (2*A*sin(e + f*x))/5 - (2*B*sin(e + f*x))/5)/(a^2*c^3*f*(2*sin(e + f*x) - 2)) - (cos(e + f*x)*((16*A)/15 - (4*B)/15))/(a^2*c^3*f*(2*sin(e + f*x) - 2))","B"
68,1,197,135,12.749207,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^4),x)","-\frac{\left(\frac{32\,A}{21}-\frac{64\,B}{105}-\frac{16\,A\,\sin\left(e+f\,x\right)}{21}+\frac{32\,B\,\sin\left(e+f\,x\right)}{105}\right)\,{\cos\left(e+f\,x\right)}^4+\left(\frac{8\,A}{7}+\frac{12\,B}{35}-\frac{8\,A\,\sin\left(e+f\,x\right)}{7}-\frac{12\,B\,\sin\left(e+f\,x\right)}{35}+\frac{\left(4\,\sin\left(e+f\,x\right)-4\right)\,\left(\frac{4\,A}{7}+\frac{6\,B}{35}\right)}{2}\right)\,{\cos\left(e+f\,x\right)}^3+\left(\frac{32\,B}{105}-\frac{16\,A}{21}+\frac{8\,A\,\sin\left(e+f\,x\right)}{7}-\frac{16\,B\,\sin\left(e+f\,x\right)}{35}\right)\,{\cos\left(e+f\,x\right)}^2-\frac{4\,A}{21}+\frac{10\,B}{21}+\frac{10\,A\,\sin\left(e+f\,x\right)}{21}-\frac{4\,B\,\sin\left(e+f\,x\right)}{21}}{a^2\,c^4\,f\,\left(4\,{\cos\left(e+f\,x\right)}^3\,\sin\left(e+f\,x\right)-4\,{\cos\left(e+f\,x\right)}^3+2\,{\cos\left(e+f\,x\right)}^5\right)}","Not used",1,"-((10*B)/21 - (4*A)/21 + (10*A*sin(e + f*x))/21 - (4*B*sin(e + f*x))/21 + cos(e + f*x)^3*((8*A)/7 + (12*B)/35 - (8*A*sin(e + f*x))/7 - (12*B*sin(e + f*x))/35 + ((4*sin(e + f*x) - 4)*((4*A)/7 + (6*B)/35))/2) - cos(e + f*x)^2*((16*A)/21 - (32*B)/105 - (8*A*sin(e + f*x))/7 + (16*B*sin(e + f*x))/35) + cos(e + f*x)^4*((32*A)/21 - (64*B)/105 - (16*A*sin(e + f*x))/21 + (32*B*sin(e + f*x))/105))/(a^2*c^4*f*(4*cos(e + f*x)^3*sin(e + f*x) - 4*cos(e + f*x)^3 + 2*cos(e + f*x)^5))","B"
69,1,337,175,12.882814,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^5),x)","\frac{2\,\left(7\,A-14\,B-14\,A\,\sin\left(e+f\,x\right)+7\,B\,\sin\left(e+f\,x\right)+30\,A\,{\cos\left(e+f\,x\right)}^2-76\,A\,{\cos\left(e+f\,x\right)}^3-72\,A\,{\cos\left(e+f\,x\right)}^4+57\,A\,{\cos\left(e+f\,x\right)}^5+16\,A\,{\cos\left(e+f\,x\right)}^6-15\,B\,{\cos\left(e+f\,x\right)}^2-4\,B\,{\cos\left(e+f\,x\right)}^3+36\,B\,{\cos\left(e+f\,x\right)}^4+3\,B\,{\cos\left(e+f\,x\right)}^5-8\,B\,{\cos\left(e+f\,x\right)}^6-40\,A\,{\cos\left(e+f\,x\right)}^2\,\sin\left(e+f\,x\right)+76\,A\,{\cos\left(e+f\,x\right)}^3\,\sin\left(e+f\,x\right)+48\,A\,{\cos\left(e+f\,x\right)}^4\,\sin\left(e+f\,x\right)-19\,A\,{\cos\left(e+f\,x\right)}^5\,\sin\left(e+f\,x\right)+20\,B\,{\cos\left(e+f\,x\right)}^2\,\sin\left(e+f\,x\right)+4\,B\,{\cos\left(e+f\,x\right)}^3\,\sin\left(e+f\,x\right)-24\,B\,{\cos\left(e+f\,x\right)}^4\,\sin\left(e+f\,x\right)-B\,{\cos\left(e+f\,x\right)}^5\,\sin\left(e+f\,x\right)\right)}{63\,a^2\,c^5\,f\,\left(8\,{\cos\left(e+f\,x\right)}^3\,\sin\left(e+f\,x\right)-2\,{\cos\left(e+f\,x\right)}^5\,\sin\left(e+f\,x\right)-8\,{\cos\left(e+f\,x\right)}^3+6\,{\cos\left(e+f\,x\right)}^5\right)}","Not used",1,"(2*(7*A - 14*B - 14*A*sin(e + f*x) + 7*B*sin(e + f*x) + 30*A*cos(e + f*x)^2 - 76*A*cos(e + f*x)^3 - 72*A*cos(e + f*x)^4 + 57*A*cos(e + f*x)^5 + 16*A*cos(e + f*x)^6 - 15*B*cos(e + f*x)^2 - 4*B*cos(e + f*x)^3 + 36*B*cos(e + f*x)^4 + 3*B*cos(e + f*x)^5 - 8*B*cos(e + f*x)^6 - 40*A*cos(e + f*x)^2*sin(e + f*x) + 76*A*cos(e + f*x)^3*sin(e + f*x) + 48*A*cos(e + f*x)^4*sin(e + f*x) - 19*A*cos(e + f*x)^5*sin(e + f*x) + 20*B*cos(e + f*x)^2*sin(e + f*x) + 4*B*cos(e + f*x)^3*sin(e + f*x) - 24*B*cos(e + f*x)^4*sin(e + f*x) - B*cos(e + f*x)^5*sin(e + f*x)))/(63*a^2*c^5*f*(8*cos(e + f*x)^3*sin(e + f*x) - 2*cos(e + f*x)^5*sin(e + f*x) - 8*cos(e + f*x)^3 + 6*cos(e + f*x)^5))","B"
70,1,501,243,14.754075,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^5)/(a + a*sin(e + f*x))^3,x)","-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(431\,A\,c^5-\frac{3454\,B\,c^5}{3}\right)+\frac{496\,A\,c^5}{5}-\frac{3958\,B\,c^5}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(65\,A\,c^5-168\,B\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(309\,A\,c^5-838\,B\,c^5\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(826\,A\,c^5-\frac{6418\,B\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(1418\,A\,c^5-\frac{11636\,B\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(1654\,A\,c^5-\frac{13372\,B\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2332\,A\,c^5-\frac{19072\,B\,c^5}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{4903\,A\,c^5}{5}-\frac{38884\,B\,c^5}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{11156\,A\,c^5}{5}-\frac{86708\,B\,c^5}{15}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{11758\,A\,c^5}{5}-\frac{92224\,B\,c^5}{15}\right)}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+13\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+25\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+38\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+46\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+46\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+38\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+25\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+13\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}-\frac{21\,c^5\,\mathrm{atan}\left(\frac{21\,c^5\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A-8\,B\right)}{63\,A\,c^5-168\,B\,c^5}\right)\,\left(3\,A-8\,B\right)}{a^3\,f}","Not used",1,"- (tan(e/2 + (f*x)/2)*(431*A*c^5 - (3454*B*c^5)/3) + (496*A*c^5)/5 - (3958*B*c^5)/15 + tan(e/2 + (f*x)/2)^10*(65*A*c^5 - 168*B*c^5) + tan(e/2 + (f*x)/2)^9*(309*A*c^5 - 838*B*c^5) + tan(e/2 + (f*x)/2)^8*(826*A*c^5 - (6418*B*c^5)/3) + tan(e/2 + (f*x)/2)^7*(1418*A*c^5 - (11636*B*c^5)/3) + tan(e/2 + (f*x)/2)^3*(1654*A*c^5 - (13372*B*c^5)/3) + tan(e/2 + (f*x)/2)^5*(2332*A*c^5 - (19072*B*c^5)/3) + tan(e/2 + (f*x)/2)^2*((4903*A*c^5)/5 - (38884*B*c^5)/15) + tan(e/2 + (f*x)/2)^6*((11156*A*c^5)/5 - (86708*B*c^5)/15) + tan(e/2 + (f*x)/2)^4*((11758*A*c^5)/5 - (92224*B*c^5)/15))/(f*(13*a^3*tan(e/2 + (f*x)/2)^2 + 25*a^3*tan(e/2 + (f*x)/2)^3 + 38*a^3*tan(e/2 + (f*x)/2)^4 + 46*a^3*tan(e/2 + (f*x)/2)^5 + 46*a^3*tan(e/2 + (f*x)/2)^6 + 38*a^3*tan(e/2 + (f*x)/2)^7 + 25*a^3*tan(e/2 + (f*x)/2)^8 + 13*a^3*tan(e/2 + (f*x)/2)^9 + 5*a^3*tan(e/2 + (f*x)/2)^10 + a^3*tan(e/2 + (f*x)/2)^11 + a^3 + 5*a^3*tan(e/2 + (f*x)/2))) - (21*c^5*atan((21*c^5*tan(e/2 + (f*x)/2)*(3*A - 8*B))/(63*A*c^5 - 168*B*c^5))*(3*A - 8*B))/(a^3*f)","B"
71,1,419,201,14.711354,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^4)/(a + a*sin(e + f*x))^3,x)","-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{286\,A\,c^4}{3}-\frac{1007\,B\,c^4}{3}\right)+\frac{334\,A\,c^4}{15}-\frac{1154\,B\,c^4}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(16\,A\,c^4-49\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(66\,A\,c^4-243\,B\,c^4\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{542\,A\,c^4}{3}-\frac{1741\,B\,c^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(\frac{706\,A\,c^4}{3}-\frac{2621\,B\,c^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{794\,A\,c^4}{3}-\frac{2875\,B\,c^4}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{1006\,A\,c^4}{5}-\frac{3401\,B\,c^4}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{1718\,A\,c^4}{5}-\frac{5633\,B\,c^4}{5}\right)}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+12\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+20\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+26\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+26\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+20\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+12\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}-\frac{7\,c^4\,\mathrm{atan}\left(\frac{7\,c^4\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A-7\,B\right)}{14\,A\,c^4-49\,B\,c^4}\right)\,\left(2\,A-7\,B\right)}{a^3\,f}","Not used",1,"- (tan(e/2 + (f*x)/2)*((286*A*c^4)/3 - (1007*B*c^4)/3) + (334*A*c^4)/15 - (1154*B*c^4)/15 + tan(e/2 + (f*x)/2)^8*(16*A*c^4 - 49*B*c^4) + tan(e/2 + (f*x)/2)^7*(66*A*c^4 - 243*B*c^4) + tan(e/2 + (f*x)/2)^6*((542*A*c^4)/3 - (1741*B*c^4)/3) + tan(e/2 + (f*x)/2)^5*((706*A*c^4)/3 - (2621*B*c^4)/3) + tan(e/2 + (f*x)/2)^3*((794*A*c^4)/3 - (2875*B*c^4)/3) + tan(e/2 + (f*x)/2)^2*((1006*A*c^4)/5 - (3401*B*c^4)/5) + tan(e/2 + (f*x)/2)^4*((1718*A*c^4)/5 - (5633*B*c^4)/5))/(f*(12*a^3*tan(e/2 + (f*x)/2)^2 + 20*a^3*tan(e/2 + (f*x)/2)^3 + 26*a^3*tan(e/2 + (f*x)/2)^4 + 26*a^3*tan(e/2 + (f*x)/2)^5 + 20*a^3*tan(e/2 + (f*x)/2)^6 + 12*a^3*tan(e/2 + (f*x)/2)^7 + 5*a^3*tan(e/2 + (f*x)/2)^8 + a^3*tan(e/2 + (f*x)/2)^9 + a^3 + 5*a^3*tan(e/2 + (f*x)/2))) - (7*c^4*atan((7*c^4*tan(e/2 + (f*x)/2)*(2*A - 7*B))/(14*A*c^4 - 49*B*c^4))*(2*A - 7*B))/(a^3*f)","B"
72,1,333,153,14.364627,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^3)/(a + a*sin(e + f*x))^3,x)","-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{40\,A\,c^3}{3}-82\,B\,c^3\right)+\frac{52\,A\,c^3}{15}-\frac{94\,B\,c^3}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,A\,c^3-12\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(8\,A\,c^3-58\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{64\,A\,c^3}{3}-148\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{92\,A\,c^3}{3}-134\,B\,c^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{452\,A\,c^3}{15}-\frac{744\,B\,c^3}{5}\right)}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+11\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+15\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+15\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+11\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}-\frac{2\,c^3\,\mathrm{atan}\left(\frac{2\,c^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A-6\,B\right)}{2\,A\,c^3-12\,B\,c^3}\right)\,\left(A-6\,B\right)}{a^3\,f}","Not used",1,"- (tan(e/2 + (f*x)/2)*((40*A*c^3)/3 - 82*B*c^3) + (52*A*c^3)/15 - (94*B*c^3)/5 + tan(e/2 + (f*x)/2)^6*(4*A*c^3 - 12*B*c^3) + tan(e/2 + (f*x)/2)^5*(8*A*c^3 - 58*B*c^3) + tan(e/2 + (f*x)/2)^3*((64*A*c^3)/3 - 148*B*c^3) + tan(e/2 + (f*x)/2)^4*((92*A*c^3)/3 - 134*B*c^3) + tan(e/2 + (f*x)/2)^2*((452*A*c^3)/15 - (744*B*c^3)/5))/(f*(11*a^3*tan(e/2 + (f*x)/2)^2 + 15*a^3*tan(e/2 + (f*x)/2)^3 + 15*a^3*tan(e/2 + (f*x)/2)^4 + 11*a^3*tan(e/2 + (f*x)/2)^5 + 5*a^3*tan(e/2 + (f*x)/2)^6 + a^3*tan(e/2 + (f*x)/2)^7 + a^3 + 5*a^3*tan(e/2 + (f*x)/2))) - (2*c^3*atan((2*c^3*tan(e/2 + (f*x)/2)*(A - 6*B))/(2*A*c^3 - 12*B*c^3))*(A - 6*B))/(a^3*f)","B"
73,1,230,110,15.081228,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^2)/(a + a*sin(e + f*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{c^2\,\left(120\,B+150\,B\,\left(e+f\,x\right)\right)}{15}-10\,B\,c^2\,\left(e+f\,x\right)\right)+\frac{c^2\,\left(46\,B-6\,A+15\,B\,\left(e+f\,x\right)\right)}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{c^2\,\left(30\,B-30\,A+75\,B\,\left(e+f\,x\right)\right)}{15}-5\,B\,c^2\,\left(e+f\,x\right)\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{c^2\,\left(340\,B-60\,A+150\,B\,\left(e+f\,x\right)\right)}{15}-10\,B\,c^2\,\left(e+f\,x\right)\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{c^2\,\left(200\,B+75\,B\,\left(e+f\,x\right)\right)}{15}-5\,B\,c^2\,\left(e+f\,x\right)\right)-B\,c^2\,\left(e+f\,x\right)}{a^3\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^5}+\frac{B\,c^2\,x}{a^3}","Not used",1,"(tan(e/2 + (f*x)/2)^3*((c^2*(120*B + 150*B*(e + f*x)))/15 - 10*B*c^2*(e + f*x)) + (c^2*(46*B - 6*A + 15*B*(e + f*x)))/15 + tan(e/2 + (f*x)/2)^4*((c^2*(30*B - 30*A + 75*B*(e + f*x)))/15 - 5*B*c^2*(e + f*x)) + tan(e/2 + (f*x)/2)^2*((c^2*(340*B - 60*A + 150*B*(e + f*x)))/15 - 10*B*c^2*(e + f*x)) + tan(e/2 + (f*x)/2)*((c^2*(200*B + 75*B*(e + f*x)))/15 - 5*B*c^2*(e + f*x)) - B*c^2*(e + f*x))/(a^3*f*(tan(e/2 + (f*x)/2) + 1)^5) + (B*c^2*x)/a^3","B"
74,1,172,103,13.026128,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x)))/(a + a*sin(e + f*x))^3,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{41\,A\,c}{4}-\frac{B\,c}{4}-\frac{11\,A\,c\,\cos\left(e+f\,x\right)}{2}+\frac{B\,c\,\cos\left(e+f\,x\right)}{2}+5\,A\,c\,\sin\left(e+f\,x\right)+5\,B\,c\,\sin\left(e+f\,x\right)-\frac{3\,A\,c\,\cos\left(2\,e+2\,f\,x\right)}{4}+\frac{3\,B\,c\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{5\,A\,c\,\sin\left(2\,e+2\,f\,x\right)}{4}-\frac{5\,B\,c\,\sin\left(2\,e+2\,f\,x\right)}{4}\right)}{15\,a^3\,f\,\left(\frac{5\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{5\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}+\frac{\sqrt{2}\,\cos\left(\frac{5\,e}{2}-\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((41*A*c)/4 - (B*c)/4 - (11*A*c*cos(e + f*x))/2 + (B*c*cos(e + f*x))/2 + 5*A*c*sin(e + f*x) + 5*B*c*sin(e + f*x) - (3*A*c*cos(2*e + 2*f*x))/4 + (3*B*c*cos(2*e + 2*f*x))/4 - (5*A*c*sin(2*e + 2*f*x))/4 - (5*B*c*sin(2*e + 2*f*x))/4))/(15*a^3*f*((5*2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/4 - (5*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 + (2^(1/2)*cos((5*e)/2 - pi/4 + (5*f*x)/2))/4))","B"
75,1,178,102,12.429307,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))),x)","-\frac{2\,\left(\frac{15\,A\,\cos\left(e+f\,x\right)}{4}-\frac{5\,B}{2}-\frac{5\,B\,\cos\left(e+f\,x\right)}{8}-\frac{15\,A\,\sin\left(e+f\,x\right)}{4}-\frac{5\,B\,\sin\left(e+f\,x\right)}{2}+3\,A\,\cos\left(2\,e+2\,f\,x\right)-\frac{3\,A\,\cos\left(3\,e+3\,f\,x\right)}{4}+2\,B\,\cos\left(2\,e+2\,f\,x\right)+\frac{B\,\cos\left(3\,e+3\,f\,x\right)}{8}+3\,A\,\sin\left(2\,e+2\,f\,x\right)+\frac{3\,A\,\sin\left(3\,e+3\,f\,x\right)}{4}-\frac{B\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{B\,\sin\left(3\,e+3\,f\,x\right)}{2}\right)}{15\,a^3\,c\,f\,\left(\frac{5\,\cos\left(e+f\,x\right)}{4}-\frac{\cos\left(3\,e+3\,f\,x\right)}{4}+\sin\left(2\,e+2\,f\,x\right)\right)}","Not used",1,"-(2*((15*A*cos(e + f*x))/4 - (5*B)/2 - (5*B*cos(e + f*x))/8 - (15*A*sin(e + f*x))/4 - (5*B*sin(e + f*x))/2 + 3*A*cos(2*e + 2*f*x) - (3*A*cos(3*e + 3*f*x))/4 + 2*B*cos(2*e + 2*f*x) + (B*cos(3*e + 3*f*x))/8 + 3*A*sin(2*e + 2*f*x) + (3*A*sin(3*e + 3*f*x))/4 - (B*sin(2*e + 2*f*x))/2 + (B*sin(3*e + 3*f*x))/2))/(15*a^3*c*f*((5*cos(e + f*x))/4 - cos(3*e + 3*f*x)/4 + sin(2*e + 2*f*x)))","B"
76,1,183,90,12.469136,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^2),x)","\frac{\left(\frac{8\,A}{15}+\frac{2\,B}{15}+\frac{16\,A\,\sin\left(e+f\,x\right)}{15}+\frac{4\,B\,\sin\left(e+f\,x\right)}{15}\right)\,{\cos\left(e+f\,x\right)}^2+\frac{2\,A}{15}+\frac{8\,B}{15}+\frac{8\,A\,\sin\left(e+f\,x\right)}{15}+\frac{2\,B\,\sin\left(e+f\,x\right)}{15}}{a^3\,c^2\,f\,\left(2\,{\cos\left(e+f\,x\right)}^3\,\sin\left(e+f\,x\right)+2\,{\cos\left(e+f\,x\right)}^3\right)}-\frac{\frac{2\,A}{5}-\frac{2\,B}{5}+\frac{2\,A\,\sin\left(e+f\,x\right)}{5}-\frac{2\,B\,\sin\left(e+f\,x\right)}{5}}{a^3\,c^2\,f\,\left(2\,\sin\left(e+f\,x\right)+2\right)}-\frac{\cos\left(e+f\,x\right)\,\left(\frac{16\,A}{15}+\frac{4\,B}{15}\right)}{a^3\,c^2\,f\,\left(2\,\sin\left(e+f\,x\right)+2\right)}","Not used",1,"((2*A)/15 + (8*B)/15 + (8*A*sin(e + f*x))/15 + (2*B*sin(e + f*x))/15 + cos(e + f*x)^2*((8*A)/15 + (2*B)/15 + (16*A*sin(e + f*x))/15 + (4*B*sin(e + f*x))/15))/(a^3*c^2*f*(2*cos(e + f*x)^3*sin(e + f*x) + 2*cos(e + f*x)^3)) - ((2*A)/5 - (2*B)/5 + (2*A*sin(e + f*x))/5 - (2*B*sin(e + f*x))/5)/(a^3*c^2*f*(2*sin(e + f*x) + 2)) - (cos(e + f*x)*((16*A)/15 + (4*B)/15))/(a^3*c^2*f*(2*sin(e + f*x) + 2))","B"
77,1,126,84,14.421307,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^3),x)","-\frac{2\,\left(15\,A\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9+15\,B\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8-20\,A\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+58\,A\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+30\,B\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4-20\,A\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+15\,A\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+3\,B\right)}{15\,a^3\,c^3\,f\,{\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)}^5}","Not used",1,"-(2*(3*B + 15*A*tan(e/2 + (f*x)/2) - 20*A*tan(e/2 + (f*x)/2)^3 + 58*A*tan(e/2 + (f*x)/2)^5 - 20*A*tan(e/2 + (f*x)/2)^7 + 15*A*tan(e/2 + (f*x)/2)^9 + 30*B*tan(e/2 + (f*x)/2)^4 + 15*B*tan(e/2 + (f*x)/2)^8))/(15*a^3*c^3*f*(tan(e/2 + (f*x)/2)^2 - 1)^5)","B"
78,1,217,121,13.158252,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^4),x)","\frac{\left(\frac{16\,A}{35}-\frac{8\,B}{105}-\frac{32\,A\,\sin\left(e+f\,x\right)}{35}+\frac{16\,B\,\sin\left(e+f\,x\right)}{105}\right)\,{\cos\left(e+f\,x\right)}^4+\left(\frac{4\,A}{35}-\frac{2\,B}{105}-\frac{16\,A\,\sin\left(e+f\,x\right)}{35}+\frac{8\,B\,\sin\left(e+f\,x\right)}{105}\right)\,{\cos\left(e+f\,x\right)}^2+\frac{2\,A}{35}-\frac{12\,B}{35}-\frac{12\,A\,\sin\left(e+f\,x\right)}{35}+\frac{2\,B\,\sin\left(e+f\,x\right)}{35}}{a^3\,c^4\,f\,\left(2\,{\cos\left(e+f\,x\right)}^5\,\sin\left(e+f\,x\right)-2\,{\cos\left(e+f\,x\right)}^5\right)}-\frac{\frac{2\,A}{7}+\frac{2\,B}{7}-\frac{2\,A\,\sin\left(e+f\,x\right)}{7}-\frac{2\,B\,\sin\left(e+f\,x\right)}{7}}{a^3\,c^4\,f\,\left(2\,\sin\left(e+f\,x\right)-2\right)}-\frac{\cos\left(e+f\,x\right)\,\left(\frac{32\,A}{35}-\frac{16\,B}{105}\right)}{a^3\,c^4\,f\,\left(2\,\sin\left(e+f\,x\right)-2\right)}","Not used",1,"((2*A)/35 - (12*B)/35 - (12*A*sin(e + f*x))/35 + (2*B*sin(e + f*x))/35 + cos(e + f*x)^2*((4*A)/35 - (2*B)/105 - (16*A*sin(e + f*x))/35 + (8*B*sin(e + f*x))/105) + cos(e + f*x)^4*((16*A)/35 - (8*B)/105 - (32*A*sin(e + f*x))/35 + (16*B*sin(e + f*x))/105))/(a^3*c^4*f*(2*cos(e + f*x)^5*sin(e + f*x) - 2*cos(e + f*x)^5)) - ((2*A)/7 + (2*B)/7 - (2*A*sin(e + f*x))/7 - (2*B*sin(e + f*x))/7)/(a^3*c^4*f*(2*sin(e + f*x) - 2)) - (cos(e + f*x)*((32*A)/35 - (16*B)/105))/(a^3*c^4*f*(2*sin(e + f*x) - 2))","B"
79,1,231,162,13.139206,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^5),x)","\frac{\left(\frac{128\,B}{315}-\frac{64\,A}{45}+\frac{32\,A\,\sin\left(e+f\,x\right)}{45}-\frac{64\,B\,\sin\left(e+f\,x\right)}{315}\right)\,{\cos\left(e+f\,x\right)}^6+\left(\frac{8\,A\,\sin\left(e+f\,x\right)}{9}-\frac{20\,B}{63}-\frac{8\,A}{9}+\frac{20\,B\,\sin\left(e+f\,x\right)}{63}-\frac{\left(4\,\sin\left(e+f\,x\right)-4\right)\,\left(\frac{4\,A}{9}+\frac{10\,B}{63}\right)}{2}\right)\,{\cos\left(e+f\,x\right)}^5+\left(\frac{32\,A}{45}-\frac{64\,B}{315}-\frac{16\,A\,\sin\left(e+f\,x\right)}{15}+\frac{32\,B\,\sin\left(e+f\,x\right)}{105}\right)\,{\cos\left(e+f\,x\right)}^4+\left(\frac{8\,A}{45}-\frac{16\,B}{315}-\frac{4\,A\,\sin\left(e+f\,x\right)}{9}+\frac{8\,B\,\sin\left(e+f\,x\right)}{63}\right)\,{\cos\left(e+f\,x\right)}^2+\frac{4\,A}{45}-\frac{14\,B}{45}-\frac{14\,A\,\sin\left(e+f\,x\right)}{45}+\frac{4\,B\,\sin\left(e+f\,x\right)}{45}}{a^3\,c^5\,f\,\left(4\,{\cos\left(e+f\,x\right)}^5\,\sin\left(e+f\,x\right)-4\,{\cos\left(e+f\,x\right)}^5+2\,{\cos\left(e+f\,x\right)}^7\right)}","Not used",1,"((4*A)/45 - (14*B)/45 - (14*A*sin(e + f*x))/45 + (4*B*sin(e + f*x))/45 - cos(e + f*x)^5*((8*A)/9 + (20*B)/63 - (8*A*sin(e + f*x))/9 - (20*B*sin(e + f*x))/63 + ((4*sin(e + f*x) - 4)*((4*A)/9 + (10*B)/63))/2) + cos(e + f*x)^2*((8*A)/45 - (16*B)/315 - (4*A*sin(e + f*x))/9 + (8*B*sin(e + f*x))/63) + cos(e + f*x)^4*((32*A)/45 - (64*B)/315 - (16*A*sin(e + f*x))/15 + (32*B*sin(e + f*x))/105) - cos(e + f*x)^6*((64*A)/45 - (128*B)/315 - (32*A*sin(e + f*x))/45 + (64*B*sin(e + f*x))/315))/(a^3*c^5*f*(4*cos(e + f*x)^5*sin(e + f*x) - 4*cos(e + f*x)^5 + 2*cos(e + f*x)^7))","B"
80,1,474,205,14.521950,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^6),x)","\frac{2\,\left(\frac{165\,B\,\sin\left(e+f\,x\right)}{4}-\frac{6875\,A\,\cos\left(e+f\,x\right)}{64}-\frac{825\,B\,\cos\left(e+f\,x\right)}{64}-110\,A\,\sin\left(e+f\,x\right)-\frac{495\,B}{8}-66\,A\,\cos\left(2\,e+2\,f\,x\right)-\frac{2125\,A\,\cos\left(3\,e+3\,f\,x\right)}{64}-50\,A\,\cos\left(4\,e+4\,f\,x\right)+\frac{625\,A\,\cos\left(5\,e+5\,f\,x\right)}{64}-10\,A\,\cos\left(6\,e+6\,f\,x\right)+\frac{375\,A\,\cos\left(7\,e+7\,f\,x\right)}{64}+A\,\cos\left(8\,e+8\,f\,x\right)+\frac{99\,B\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{255\,B\,\cos\left(3\,e+3\,f\,x\right)}{64}+\frac{75\,B\,\cos\left(4\,e+4\,f\,x\right)}{4}+\frac{75\,B\,\cos\left(5\,e+5\,f\,x\right)}{64}+\frac{15\,B\,\cos\left(6\,e+6\,f\,x\right)}{4}+\frac{45\,B\,\cos\left(7\,e+7\,f\,x\right)}{64}-\frac{3\,B\,\cos\left(8\,e+8\,f\,x\right)}{8}+\frac{4125\,A\,\sin\left(2\,e+2\,f\,x\right)}{64}-34\,A\,\sin\left(3\,e+3\,f\,x\right)+\frac{3125\,A\,\sin\left(4\,e+4\,f\,x\right)}{64}+10\,A\,\sin\left(5\,e+5\,f\,x\right)+\frac{625\,A\,\sin\left(6\,e+6\,f\,x\right)}{64}+6\,A\,\sin\left(7\,e+7\,f\,x\right)-\frac{125\,A\,\sin\left(8\,e+8\,f\,x\right)}{128}+\frac{495\,B\,\sin\left(2\,e+2\,f\,x\right)}{64}+\frac{51\,B\,\sin\left(3\,e+3\,f\,x\right)}{4}+\frac{375\,B\,\sin\left(4\,e+4\,f\,x\right)}{64}-\frac{15\,B\,\sin\left(5\,e+5\,f\,x\right)}{4}+\frac{75\,B\,\sin\left(6\,e+6\,f\,x\right)}{64}-\frac{9\,B\,\sin\left(7\,e+7\,f\,x\right)}{4}-\frac{15\,B\,\sin\left(8\,e+8\,f\,x\right)}{128}\right)}{495\,a^3\,c^6\,f\,\left(\frac{5\,\cos\left(5\,e+5\,f\,x\right)}{32}-\frac{17\,\cos\left(3\,e+3\,f\,x\right)}{32}-\frac{55\,\cos\left(e+f\,x\right)}{32}+\frac{3\,\cos\left(7\,e+7\,f\,x\right)}{32}+\frac{33\,\sin\left(2\,e+2\,f\,x\right)}{32}+\frac{25\,\sin\left(4\,e+4\,f\,x\right)}{32}+\frac{5\,\sin\left(6\,e+6\,f\,x\right)}{32}-\frac{\sin\left(8\,e+8\,f\,x\right)}{64}\right)}","Not used",1,"(2*((165*B*sin(e + f*x))/4 - (6875*A*cos(e + f*x))/64 - (825*B*cos(e + f*x))/64 - 110*A*sin(e + f*x) - (495*B)/8 - 66*A*cos(2*e + 2*f*x) - (2125*A*cos(3*e + 3*f*x))/64 - 50*A*cos(4*e + 4*f*x) + (625*A*cos(5*e + 5*f*x))/64 - 10*A*cos(6*e + 6*f*x) + (375*A*cos(7*e + 7*f*x))/64 + A*cos(8*e + 8*f*x) + (99*B*cos(2*e + 2*f*x))/4 - (255*B*cos(3*e + 3*f*x))/64 + (75*B*cos(4*e + 4*f*x))/4 + (75*B*cos(5*e + 5*f*x))/64 + (15*B*cos(6*e + 6*f*x))/4 + (45*B*cos(7*e + 7*f*x))/64 - (3*B*cos(8*e + 8*f*x))/8 + (4125*A*sin(2*e + 2*f*x))/64 - 34*A*sin(3*e + 3*f*x) + (3125*A*sin(4*e + 4*f*x))/64 + 10*A*sin(5*e + 5*f*x) + (625*A*sin(6*e + 6*f*x))/64 + 6*A*sin(7*e + 7*f*x) - (125*A*sin(8*e + 8*f*x))/128 + (495*B*sin(2*e + 2*f*x))/64 + (51*B*sin(3*e + 3*f*x))/4 + (375*B*sin(4*e + 4*f*x))/64 - (15*B*sin(5*e + 5*f*x))/4 + (75*B*sin(6*e + 6*f*x))/64 - (9*B*sin(7*e + 7*f*x))/4 - (15*B*sin(8*e + 8*f*x))/128))/(495*a^3*c^6*f*((5*cos(5*e + 5*f*x))/32 - (17*cos(3*e + 3*f*x))/32 - (55*cos(e + f*x))/32 + (3*cos(7*e + 7*f*x))/32 + (33*sin(2*e + 2*f*x))/32 + (25*sin(4*e + 4*f*x))/32 + (5*sin(6*e + 6*f*x))/32 - sin(8*e + 8*f*x)/64))","B"
81,0,-1,198,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2), x)","F"
82,0,-1,157,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2), x)","F"
83,0,-1,116,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2), x)","F"
84,0,-1,73,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2), x)","F"
85,0,-1,122,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(1/2), x)","F"
86,0,-1,115,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(3/2), x)","F"
87,0,-1,126,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(5/2), x)","F"
88,0,-1,163,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c - c*sin(e + f*x))^(7/2), x)","F"
89,0,-1,210,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(7/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(7/2), x)","F"
90,0,-1,167,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2), x)","F"
91,0,-1,120,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2), x)","F"
92,0,-1,81,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2), x)","F"
93,0,-1,161,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(1/2), x)","F"
94,0,-1,176,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(3/2), x)","F"
95,0,-1,175,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(5/2), x)","F"
96,0,-1,175,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(7/2), x)","F"
97,0,-1,222,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c - c*sin(e + f*x))^(9/2), x)","F"
98,0,-1,210,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(7/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(7/2), x)","F"
99,0,-1,161,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2), x)","F"
100,0,-1,124,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2), x)","F"
101,0,-1,81,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2), x)","F"
102,0,-1,200,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(1/2), x)","F"
103,0,-1,218,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(3/2), x)","F"
104,0,-1,225,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(5/2), x)","F"
105,0,-1,217,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(7/2), x)","F"
106,0,-1,217,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(9/2), x)","F"
107,0,-1,266,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c - c*sin(e + f*x))^(11/2), x)","F"
108,0,-1,200,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x)), x)","F"
109,0,-1,159,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x)), x)","F"
110,0,-1,118,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x)), x)","F"
111,1,128,73,13.150073,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x)),x)","\frac{2\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(2\,B\,\sin\left(2\,e+2\,f\,x\right)-2\,A\,\sin\left(2\,e+2\,f\,x\right)-4\,A\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)+7\,B\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)+B\,\left(2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2-1\right)\right)}{a\,f\,\left(4\,{\sin\left(e+f\,x\right)}^2+\sin\left(e+f\,x\right)+\sin\left(3\,e+3\,f\,x\right)-4\right)}","Not used",1,"(2*(-c*(sin(e + f*x) - 1))^(1/2)*(2*B*sin(2*e + 2*f*x) - 2*A*sin(2*e + 2*f*x) - 4*A*(2*sin(e/2 + (f*x)/2)^2 - 1) + 7*B*(2*sin(e/2 + (f*x)/2)^2 - 1) + B*(2*sin((3*e)/2 + (3*f*x)/2)^2 - 1)))/(a*f*(sin(e + f*x) + sin(3*e + 3*f*x) + 4*sin(e + f*x)^2 - 4))","B"
112,0,-1,91,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2)), x)","F"
113,0,-1,136,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2)), x)","F"
114,0,-1,180,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2)), x)","F"
115,0,-1,242,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^2, x)","F"
116,0,-1,201,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^2, x)","F"
117,0,-1,154,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^2, x)","F"
118,1,492,115,17.178125,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^2,x)","-\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,B\,c}{a^2\,f}-\frac{B\,c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{a^2\,f}\right)}{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,B\,c}{3\,a^2\,f}-\frac{c\,\left(2\,A-3\,B\right)}{3\,a^2\,f}-\frac{2\,c\,\left(3\,A-2\,B\right)}{3\,a^2\,f}+\frac{c\,\left(A\,2{}\mathrm{i}-B\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{3\,a^2\,f}+\frac{c\,\left(A\,3{}\mathrm{i}-B\,2{}\mathrm{i}\right)\,2{}\mathrm{i}}{3\,a^2\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{c\,\left(A-B\right)\,4{}\mathrm{i}}{a^2\,f}+\frac{c\,\left(A\,1{}\mathrm{i}-B\,2{}\mathrm{i}\right)}{a^2\,f}+\frac{c\,\left(A\,1{}\mathrm{i}+B\,2{}\mathrm{i}\right)}{3\,a^2\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{4\,B\,c}{a^2\,f}+\frac{c\,\left(A\,1{}\mathrm{i}-B\,2{}\mathrm{i}\right)\,4{}\mathrm{i}}{a^2\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}","Not used",1,"(exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((2*B*c)/(3*a^2*f) - (c*(2*A - 3*B))/(3*a^2*f) - (2*c*(3*A - 2*B))/(3*a^2*f) + (c*(A*2i - B*3i)*1i)/(3*a^2*f) + (c*(A*3i - B*2i)*2i)/(3*a^2*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) - ((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((2*B*c)/(a^2*f) - (B*c*exp(e*1i + f*x*1i)*2i)/(a^2*f)))/(exp(e*1i + f*x*1i) - 1i) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c*(A - B)*4i)/(a^2*f) + (c*(A*1i - B*2i))/(a^2*f) + (c*(A*1i + B*2i))/(3*a^2*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((4*B*c)/(a^2*f) + (c*(A*1i - B*2i)*4i)/(a^2*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i))","B"
119,1,137,78,17.508380,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^2,x)","\frac{4\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(B\,3{}\mathrm{i}+2\,A\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+4\,B\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-B\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,3{}\mathrm{i}\right)}{3\,a^2\,f\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3\,\left(1+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}\right)}","Not used",1,"(4*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(B*3i + 2*A*exp(e*1i + f*x*1i) + 4*B*exp(e*1i + f*x*1i) - B*exp(e*2i + f*x*2i)*3i))/(3*a^2*f*(exp(e*1i + f*x*1i) + 1i)^3*(exp(e*1i + f*x*1i)*1i + 1))","B"
120,0,-1,135,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(1/2)), x)","F"
121,0,-1,175,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(3/2)), x)","F"
122,0,-1,225,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c - c*sin(e + f*x))^(5/2)), x)","F"
123,0,-1,242,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^3, x)","F"
124,0,-1,209,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^3, x)","F"
125,1,904,160,22.785472,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^3,x)","\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,B\,c^2}{a^3\,f}-\frac{B\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{a^3\,f}\right)}{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,B\,c^2}{3\,a^3\,f}-\frac{c^2\,\left(42\,A-67\,B\right)}{15\,a^3\,f}-\frac{2\,c^2\,\left(7\,A-12\,B\right)}{3\,a^3\,f}+\frac{c^2\,\left(A\,2{}\mathrm{i}-B\,7{}\mathrm{i}\right)\,1{}\mathrm{i}}{3\,a^3\,f}+\frac{c^2\,\left(A\,23{}\mathrm{i}-B\,28{}\mathrm{i}\right)\,2{}\mathrm{i}}{3\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{4\,B\,c^2}{a^3\,f}+\frac{c^2\,\left(A\,1{}\mathrm{i}-B\,4{}\mathrm{i}\right)\,4{}\mathrm{i}}{a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{8\,c^2\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)}{a^3\,f}+\frac{c^2\,\left(A\,1{}\mathrm{i}-B\,3{}\mathrm{i}\right)}{2\,a^3\,f}+\frac{c^2\,\left(A\,11{}\mathrm{i}-B\,1{}\mathrm{i}\right)}{10\,a^3\,f}+\frac{c^2\,\left(12\,A-17\,B\right)\,1{}\mathrm{i}}{4\,a^3\,f}+\frac{c^2\,\left(52\,A-47\,B\right)\,1{}\mathrm{i}}{4\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^4}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{c^2\,\left(A\,1{}\mathrm{i}-B\,4{}\mathrm{i}\right)}{a^3\,f}+\frac{c^2\,\left(A\,5{}\mathrm{i}-B\,4{}\mathrm{i}\right)}{3\,a^3\,f}+\frac{c^2\,\left(A-2\,B\right)\,8{}\mathrm{i}}{a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,B\,c^2}{5\,a^3\,f}-\frac{c^2\,\left(4\,A-3\,B\right)}{a^3\,f}-\frac{c^2\,\left(10\,A-11\,B\right)}{5\,a^3\,f}-\frac{c^2\,\left(2\,A-5\,B\right)}{5\,a^3\,f}+\frac{c^2\,\left(A\,2{}\mathrm{i}-B\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{5\,a^3\,f}+\frac{c^2\,\left(A\,4{}\mathrm{i}-B\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^3\,f}+\frac{c^2\,\left(A\,10{}\mathrm{i}-B\,11{}\mathrm{i}\right)\,1{}\mathrm{i}}{5\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5}","Not used",1,"((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((2*B*c^2)/(a^3*f) - (B*c^2*exp(e*1i + f*x*1i)*2i)/(a^3*f)))/(exp(e*1i + f*x*1i) - 1i) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c^2*(A*2i - B*7i)*1i)/(3*a^3*f) - (2*c^2*(7*A - 12*B))/(3*a^3*f) + (c^2*(A*23i - B*28i)*2i)/(3*a^3*f) - (c^2*(42*A - 67*B))/(15*a^3*f) + (2*B*c^2)/(3*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) + (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c^2*(A*1i - B*4i)*4i)/(a^3*f) + (4*B*c^2)/(a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((8*c^2*(A*1i - B*1i))/(a^3*f) + (c^2*(A*1i - B*3i))/(2*a^3*f) + (c^2*(A*11i - B*1i))/(10*a^3*f) + (c^2*(12*A - 17*B)*1i)/(4*a^3*f) + (c^2*(52*A - 47*B)*1i)/(4*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^4) + (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c^2*(A*1i - B*4i))/(a^3*f) + (c^2*(A*5i - B*4i))/(3*a^3*f) + (c^2*(A - 2*B)*8i)/(a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) + (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c^2*(A*2i - B*5i)*1i)/(5*a^3*f) - (c^2*(4*A - 3*B))/(a^3*f) - (c^2*(2*A - 5*B))/(5*a^3*f) + (c^2*(A*4i - B*3i)*1i)/(a^3*f) - (c^2*(10*A - 11*B))/(5*a^3*f) + (c^2*(A*10i - B*11i)*1i)/(5*a^3*f) + (2*B*c^2)/(5*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^5)","B"
126,1,683,121,19.156621,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^3,x)","\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{4\,B\,c}{5\,a^3\,f}-\frac{2\,c\,\left(2\,A-3\,B\right)}{5\,a^3\,f}-\frac{4\,c\,\left(3\,A-2\,B\right)}{5\,a^3\,f}+\frac{c\,\left(A\,2{}\mathrm{i}-B\,3{}\mathrm{i}\right)\,2{}\mathrm{i}}{5\,a^3\,f}+\frac{c\,\left(A\,3{}\mathrm{i}-B\,2{}\mathrm{i}\right)\,4{}\mathrm{i}}{5\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{2\,B\,c}{3\,a^3\,f}+\frac{c\,\left(A\,2{}\mathrm{i}-B\,5{}\mathrm{i}\right)\,2{}\mathrm{i}}{3\,a^3\,f}-\frac{2\,c\,\left(10\,A-13\,B\right)}{3\,a^3\,f}+\frac{c\,\left(A\,8{}\mathrm{i}-B\,13{}\mathrm{i}\right)\,2{}\mathrm{i}}{15\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(-\frac{B\,c\,1{}\mathrm{i}}{a^3\,f}+\frac{c\,\left(2\,A-3\,B\right)\,1{}\mathrm{i}}{3\,a^3\,f}+\frac{2\,c\,\left(A\,1{}\mathrm{i}-B\,3{}\mathrm{i}\right)}{a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{c\,\left(A-B\right)\,4{}\mathrm{i}}{a^3\,f}-\frac{B\,c\,1{}\mathrm{i}}{2\,a^3\,f}+\frac{c\,\left(8\,A-3\,B\right)\,1{}\mathrm{i}}{10\,a^3\,f}+\frac{c\,\left(A\,1{}\mathrm{i}-B\,2{}\mathrm{i}\right)}{a^3\,f}+\frac{c\,\left(A\,7{}\mathrm{i}-B\,6{}\mathrm{i}\right)}{a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^4}+\frac{4\,B\,c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}","Not used",1,"(exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((4*B*c)/(5*a^3*f) - (2*c*(2*A - 3*B))/(5*a^3*f) - (4*c*(3*A - 2*B))/(5*a^3*f) + (c*(A*2i - B*3i)*2i)/(5*a^3*f) + (c*(A*3i - B*2i)*4i)/(5*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^5) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((2*B*c)/(3*a^3*f) + (c*(A*2i - B*5i)*2i)/(3*a^3*f) - (2*c*(10*A - 13*B))/(3*a^3*f) + (c*(A*8i - B*13i)*2i)/(15*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) + (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c*(2*A - 3*B)*1i)/(3*a^3*f) - (B*c*1i)/(a^3*f) + (2*c*(A*1i - B*3i))/(a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((c*(A - B)*4i)/(a^3*f) - (B*c*1i)/(2*a^3*f) + (c*(8*A - 3*B)*1i)/(10*a^3*f) + (c*(A*1i - B*2i))/(a^3*f) + (c*(A*7i - B*6i))/(a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^4) + (4*B*c*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i))","B"
127,1,479,85,17.535144,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^3,x)","\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{8\,B}{5\,a^3\,f}-\frac{16\,A-8\,B}{10\,a^3\,f}+\frac{\left(A\,16{}\mathrm{i}-B\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{10\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^5}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{4\,B}{3\,a^3\,f}-\frac{16\,A-16\,B}{30\,a^3\,f}+\frac{\left(A\,80{}\mathrm{i}-B\,120{}\mathrm{i}\right)\,1{}\mathrm{i}}{30\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^3}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(-\frac{B\,1{}\mathrm{i}}{a^3\,f}+\frac{A\,16{}\mathrm{i}-B\,16{}\mathrm{i}}{40\,a^3\,f}+\frac{A\,80{}\mathrm{i}-B\,80{}\mathrm{i}}{40\,a^3\,f}+\frac{\left(160\,A-120\,B\right)\,1{}\mathrm{i}}{40\,a^3\,f}\right)}{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^4}-\frac{B\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,8{}\mathrm{i}}{3\,a^3\,f\,\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}-\mathrm{i}\right)\,{\left({\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}+1{}\mathrm{i}\right)}^2}","Not used",1,"(exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((8*B)/(5*a^3*f) - (16*A - 8*B)/(10*a^3*f) + ((A*16i - B*8i)*1i)/(10*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^5) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((4*B)/(3*a^3*f) - (16*A - 16*B)/(30*a^3*f) + ((A*80i - B*120i)*1i)/(30*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^3) - (exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((A*16i - B*16i)/(40*a^3*f) - (B*1i)/(a^3*f) + (A*80i - B*80i)/(40*a^3*f) + ((160*A - 120*B)*1i)/(40*a^3*f)))/((exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^4) - (B*exp(e*1i + f*x*1i)*(c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*8i)/(3*a^3*f*(exp(e*1i + f*x*1i) - 1i)*(exp(e*1i + f*x*1i) + 1i)^2)","B"
128,0,-1,174,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(1/2)), x)","F"
129,0,-1,224,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(3/2)), x)","F"
130,0,-1,258,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^(5/2)), x)","F"
131,1,173,94,16.165922,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(7/2),x)","-\frac{c^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(100\,B\,\cos\left(e+f\,x\right)-140\,A\,\cos\left(e+f\,x\right)-135\,A\,\cos\left(3\,e+3\,f\,x\right)+5\,A\,\cos\left(5\,e+5\,f\,x\right)+85\,B\,\cos\left(3\,e+3\,f\,x\right)-15\,B\,\cos\left(5\,e+5\,f\,x\right)-240\,A\,\sin\left(2\,e+2\,f\,x\right)+40\,A\,\sin\left(4\,e+4\,f\,x\right)+90\,B\,\sin\left(2\,e+2\,f\,x\right)-48\,B\,\sin\left(4\,e+4\,f\,x\right)+2\,B\,\sin\left(6\,e+6\,f\,x\right)\right)}{160\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(c^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(100*B*cos(e + f*x) - 140*A*cos(e + f*x) - 135*A*cos(3*e + 3*f*x) + 5*A*cos(5*e + 5*f*x) + 85*B*cos(3*e + 3*f*x) - 15*B*cos(5*e + 5*f*x) - 240*A*sin(2*e + 2*f*x) + 40*A*sin(4*e + 4*f*x) + 90*B*sin(2*e + 2*f*x) - 48*B*sin(4*e + 4*f*x) + 2*B*sin(6*e + 6*f*x)))/(160*f*(cos(2*e + 2*f*x) + 1))","B"
132,1,149,94,14.959416,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(48\,A\,\cos\left(e+f\,x\right)-36\,B\,\cos\left(e+f\,x\right)+48\,A\,\cos\left(3\,e+3\,f\,x\right)-33\,B\,\cos\left(3\,e+3\,f\,x\right)+3\,B\,\cos\left(5\,e+5\,f\,x\right)+112\,A\,\sin\left(2\,e+2\,f\,x\right)-8\,A\,\sin\left(4\,e+4\,f\,x\right)-32\,B\,\sin\left(2\,e+2\,f\,x\right)+16\,B\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(48*A*cos(e + f*x) - 36*B*cos(e + f*x) + 48*A*cos(3*e + 3*f*x) - 33*B*cos(3*e + 3*f*x) + 3*B*cos(5*e + 5*f*x) + 112*A*sin(2*e + 2*f*x) - 8*A*sin(4*e + 4*f*x) - 32*B*sin(2*e + 2*f*x) + 16*B*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
133,1,122,94,1.787105,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2),x)","\frac{c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(3\,A\,\cos\left(e+f\,x\right)-3\,B\,\cos\left(e+f\,x\right)+3\,A\,\cos\left(3\,e+3\,f\,x\right)-3\,B\,\cos\left(3\,e+3\,f\,x\right)+12\,A\,\sin\left(2\,e+2\,f\,x\right)-2\,B\,\sin\left(2\,e+2\,f\,x\right)+B\,\sin\left(4\,e+4\,f\,x\right)\right)}{12\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(3*A*cos(e + f*x) - 3*B*cos(e + f*x) + 3*A*cos(3*e + 3*f*x) - 3*B*cos(3*e + 3*f*x) + 12*A*sin(2*e + 2*f*x) - 2*B*sin(2*e + 2*f*x) + B*sin(4*e + 4*f*x)))/(12*f*(cos(2*e + 2*f*x) + 1))","B"
134,1,75,92,0.938325,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(B\,\cos\left(e+f\,x\right)+B\,\cos\left(3\,e+3\,f\,x\right)-4\,A\,\sin\left(2\,e+2\,f\,x\right)\right)}{4\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(B*cos(e + f*x) + B*cos(3*e + 3*f*x) - 4*A*sin(2*e + 2*f*x)))/(4*f*(cos(2*e + 2*f*x) + 1))","B"
135,0,-1,100,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
136,0,-1,99,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
137,0,-1,92,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
138,1,153,94,17.626075,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c - c*sin(e + f*x))^(7/2),x)","-\frac{2\,A\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}-B\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}+3\,B\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\frac{9\,c^4\,f\,\cos\left(3\,e+3\,f\,x\right)}{2}+\frac{21\,c^4\,f\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{3\,c^4\,f\,\sin\left(4\,e+4\,f\,x\right)}{4}-\frac{21\,c^4\,f\,\cos\left(e+f\,x\right)}{2}}","Not used",1,"-(2*A*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2) - B*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2) + 3*B*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2))/((9*c^4*f*cos(3*e + 3*f*x))/2 + (21*c^4*f*sin(2*e + 2*f*x))/2 - (3*c^4*f*sin(4*e + 4*f*x))/4 - (21*c^4*f*cos(e + f*x))/2)","B"
139,1,323,146,17.532457,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{{\mathrm{e}}^{-e\,6{}\mathrm{i}-f\,x\,6{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{B\,a\,c^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{96\,f}-\frac{a\,c^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(A\,7{}\mathrm{i}-B\,2{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{4\,f}+\frac{a\,c^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(2\,A-B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{16\,f}+\frac{a\,c^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(16\,A-11\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}-\frac{a\,c^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(A\,3{}\mathrm{i}+B\,2{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{24\,f}+\frac{a\,c^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,2{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{40\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*6i - f*x*6i)*(c - c*sin(e + f*x))^(1/2)*((B*a*c^3*exp(e*6i + f*x*6i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(96*f) - (a*c^3*exp(e*6i + f*x*6i)*sin(e + f*x)*(A*7i - B*2i)*(a + a*sin(e + f*x))^(1/2)*1i)/(4*f) + (a*c^3*exp(e*6i + f*x*6i)*cos(4*e + 4*f*x)*(2*A - B)*(a + a*sin(e + f*x))^(1/2))/(16*f) + (a*c^3*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(16*A - 11*B)*(a + a*sin(e + f*x))^(1/2))/(32*f) - (a*c^3*exp(e*6i + f*x*6i)*sin(3*e + 3*f*x)*(A*3i + B*2i)*(a + a*sin(e + f*x))^(1/2)*1i)/(24*f) + (a*c^3*exp(e*6i + f*x*6i)*sin(5*e + 5*f*x)*(A*1i - B*2i)*(a + a*sin(e + f*x))^(1/2)*1i)/(40*f)))/(2*cos(e + f*x))","B"
140,1,174,146,16.566703,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{a\,c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(60\,A\,\cos\left(e+f\,x\right)-60\,B\,\cos\left(e+f\,x\right)+75\,A\,\cos\left(3\,e+3\,f\,x\right)+15\,A\,\cos\left(5\,e+5\,f\,x\right)-75\,B\,\cos\left(3\,e+3\,f\,x\right)-15\,B\,\cos\left(5\,e+5\,f\,x\right)+400\,A\,\sin\left(2\,e+2\,f\,x\right)+40\,A\,\sin\left(4\,e+4\,f\,x\right)-50\,B\,\sin\left(2\,e+2\,f\,x\right)+16\,B\,\sin\left(4\,e+4\,f\,x\right)+6\,B\,\sin\left(6\,e+6\,f\,x\right)\right)}{480\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"(a*c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(60*A*cos(e + f*x) - 60*B*cos(e + f*x) + 75*A*cos(3*e + 3*f*x) + 15*A*cos(5*e + 5*f*x) - 75*B*cos(3*e + 3*f*x) - 15*B*cos(5*e + 5*f*x) + 400*A*sin(2*e + 2*f*x) + 40*A*sin(4*e + 4*f*x) - 50*B*sin(2*e + 2*f*x) + 16*B*sin(4*e + 4*f*x) + 6*B*sin(6*e + 6*f*x)))/(480*f*(cos(2*e + 2*f*x) + 1))","B"
141,1,103,134,1.841516,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{a\,c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(12\,B\,\cos\left(e+f\,x\right)+15\,B\,\cos\left(3\,e+3\,f\,x\right)+3\,B\,\cos\left(5\,e+5\,f\,x\right)-80\,A\,\sin\left(2\,e+2\,f\,x\right)-8\,A\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a*c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(12*B*cos(e + f*x) + 15*B*cos(3*e + 3*f*x) + 3*B*cos(5*e + 5*f*x) - 80*A*sin(2*e + 2*f*x) - 8*A*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
142,1,122,96,14.292200,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(3\,A\,\cos\left(e+f\,x\right)+3\,B\,\cos\left(e+f\,x\right)+3\,A\,\cos\left(3\,e+3\,f\,x\right)+3\,B\,\cos\left(3\,e+3\,f\,x\right)-12\,A\,\sin\left(2\,e+2\,f\,x\right)-2\,B\,\sin\left(2\,e+2\,f\,x\right)+B\,\sin\left(4\,e+4\,f\,x\right)\right)}{12\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(3*A*cos(e + f*x) + 3*B*cos(e + f*x) + 3*A*cos(3*e + 3*f*x) + 3*B*cos(3*e + 3*f*x) - 12*A*sin(2*e + 2*f*x) - 2*B*sin(2*e + 2*f*x) + B*sin(4*e + 4*f*x)))/(12*f*(cos(2*e + 2*f*x) + 1))","B"
143,0,-1,145,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
144,0,-1,158,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
145,0,-1,149,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
146,0,-1,96,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
147,1,245,146,18.993920,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(9/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{8\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(2\,A+3\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^5\,f}+\frac{32\,A\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^5\,f}-\frac{8\,B\,a\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^5\,f}\right)}{84\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}-54\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)+2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)-96\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)+16\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((8*a*exp(e*5i + f*x*5i)*(2*A + 3*B)*(a + a*sin(e + f*x))^(1/2))/(3*c^5*f) + (32*A*a*exp(e*5i + f*x*5i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^5*f) - (8*B*a*exp(e*5i + f*x*5i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^5*f)))/(84*cos(e + f*x)*exp(e*5i + f*x*5i) - 54*exp(e*5i + f*x*5i)*cos(3*e + 3*f*x) + 2*exp(e*5i + f*x*5i)*cos(5*e + 5*f*x) - 96*exp(e*5i + f*x*5i)*sin(2*e + 2*f*x) + 16*exp(e*5i + f*x*5i)*sin(4*e + 4*f*x))","B"
148,1,279,154,20.226517,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c - c*sin(e + f*x))^(11/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(A+B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,48{}\mathrm{i}}{5\,c^6\,f}-\frac{B\,a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,32{}\mathrm{i}}{3\,c^6\,f}+\frac{16\,a\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(A\,3{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^6\,f}\right)}{\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,264{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)\,220{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)\,20{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)\,330{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)\,88{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)\,2{}\mathrm{i}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((a*exp(e*6i + f*x*6i)*(A + B)*(a + a*sin(e + f*x))^(1/2)*48i)/(5*c^6*f) - (B*a*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2)*32i)/(3*c^6*f) + (16*a*exp(e*6i + f*x*6i)*sin(e + f*x)*(A*3i + B*1i)*(a + a*sin(e + f*x))^(1/2))/(3*c^6*f)))/(cos(e + f*x)*exp(e*6i + f*x*6i)*264i - exp(e*6i + f*x*6i)*cos(3*e + 3*f*x)*220i + exp(e*6i + f*x*6i)*cos(5*e + 5*f*x)*20i - exp(e*6i + f*x*6i)*sin(2*e + 2*f*x)*330i + exp(e*6i + f*x*6i)*sin(4*e + 4*f*x)*88i - exp(e*6i + f*x*6i)*sin(6*e + 6*f*x)*2i)","B"
149,1,383,198,18.172738,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{{\mathrm{e}}^{-e\,7{}\mathrm{i}-f\,x\,7{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(-\frac{a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,5{}\mathrm{i}}{32\,f}-\frac{a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{16\,f}-\frac{a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{96\,f}+\frac{a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(4\,A+3\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{5\,a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(8\,A-B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(20\,A+B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{96\,f}+\frac{B\,a^2\,c^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*7i - f*x*7i)*(c - c*sin(e + f*x))^(1/2)*((a^2*c^3*exp(e*7i + f*x*7i)*sin(5*e + 5*f*x)*(4*A + 3*B)*(a + a*sin(e + f*x))^(1/2))/(160*f) - (a^2*c^3*exp(e*7i + f*x*7i)*cos(4*e + 4*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*1i)/(16*f) - (a^2*c^3*exp(e*7i + f*x*7i)*cos(6*e + 6*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*1i)/(96*f) - (a^2*c^3*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*5i)/(32*f) + (5*a^2*c^3*exp(e*7i + f*x*7i)*sin(e + f*x)*(8*A - B)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (a^2*c^3*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(20*A + B)*(a + a*sin(e + f*x))^(1/2))/(96*f) + (B*a^2*c^3*exp(e*7i + f*x*7i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f)))/(2*cos(e + f*x))","B"
150,1,131,180,16.003389,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2),x)","-\frac{a^2\,c^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(75\,B\,\cos\left(e+f\,x\right)+105\,B\,\cos\left(3\,e+3\,f\,x\right)+35\,B\,\cos\left(5\,e+5\,f\,x\right)+5\,B\,\cos\left(7\,e+7\,f\,x\right)-700\,A\,\sin\left(2\,e+2\,f\,x\right)-112\,A\,\sin\left(4\,e+4\,f\,x\right)-12\,A\,\sin\left(6\,e+6\,f\,x\right)\right)}{960\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*c^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(75*B*cos(e + f*x) + 105*B*cos(3*e + 3*f*x) + 35*B*cos(5*e + 5*f*x) + 5*B*cos(7*e + 7*f*x) - 700*A*sin(2*e + 2*f*x) - 112*A*sin(4*e + 4*f*x) - 12*A*sin(6*e + 6*f*x)))/(960*f*(cos(2*e + 2*f*x) + 1))","B"
151,1,174,142,16.323550,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{a^2\,c\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(60\,A\,\cos\left(e+f\,x\right)+60\,B\,\cos\left(e+f\,x\right)+75\,A\,\cos\left(3\,e+3\,f\,x\right)+15\,A\,\cos\left(5\,e+5\,f\,x\right)+75\,B\,\cos\left(3\,e+3\,f\,x\right)+15\,B\,\cos\left(5\,e+5\,f\,x\right)-400\,A\,\sin\left(2\,e+2\,f\,x\right)-40\,A\,\sin\left(4\,e+4\,f\,x\right)-50\,B\,\sin\left(2\,e+2\,f\,x\right)+16\,B\,\sin\left(4\,e+4\,f\,x\right)+6\,B\,\sin\left(6\,e+6\,f\,x\right)\right)}{480\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*c*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(60*A*cos(e + f*x) + 60*B*cos(e + f*x) + 75*A*cos(3*e + 3*f*x) + 15*A*cos(5*e + 5*f*x) + 75*B*cos(3*e + 3*f*x) + 15*B*cos(5*e + 5*f*x) - 400*A*sin(2*e + 2*f*x) - 40*A*sin(4*e + 4*f*x) - 50*B*sin(2*e + 2*f*x) + 16*B*sin(4*e + 4*f*x) + 6*B*sin(6*e + 6*f*x)))/(480*f*(cos(2*e + 2*f*x) + 1))","B"
152,1,149,96,2.700553,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^2\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(48\,A\,\cos\left(e+f\,x\right)+36\,B\,\cos\left(e+f\,x\right)+48\,A\,\cos\left(3\,e+3\,f\,x\right)+33\,B\,\cos\left(3\,e+3\,f\,x\right)-3\,B\,\cos\left(5\,e+5\,f\,x\right)-112\,A\,\sin\left(2\,e+2\,f\,x\right)+8\,A\,\sin\left(4\,e+4\,f\,x\right)-32\,B\,\sin\left(2\,e+2\,f\,x\right)+16\,B\,\sin\left(4\,e+4\,f\,x\right)\right)}{96\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^2*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(48*A*cos(e + f*x) + 36*B*cos(e + f*x) + 48*A*cos(3*e + 3*f*x) + 33*B*cos(3*e + 3*f*x) - 3*B*cos(5*e + 5*f*x) - 112*A*sin(2*e + 2*f*x) + 8*A*sin(4*e + 4*f*x) - 32*B*sin(2*e + 2*f*x) + 16*B*sin(4*e + 4*f*x)))/(96*f*(cos(2*e + 2*f*x) + 1))","B"
153,0,-1,193,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
154,0,-1,210,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
155,0,-1,212,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
156,0,-1,196,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
157,0,-1,96,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
158,1,341,146,20.756353,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(11/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{16\,a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(A\,6{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^6\,f}-\frac{16\,a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(A\,2{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^6\,f}+\frac{a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(8\,A+13\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,8{}\mathrm{i}}{3\,c^6\,f}-\frac{B\,a^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,8{}\mathrm{i}}{c^6\,f}\right)}{\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,264{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)\,220{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)\,20{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)\,330{}\mathrm{i}+{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)\,88{}\mathrm{i}-{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)\,2{}\mathrm{i}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((16*a^2*exp(e*6i + f*x*6i)*(A*6i + B*1i)*(a + a*sin(e + f*x))^(1/2))/(5*c^6*f) - (16*a^2*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(A*2i + B*1i)*(a + a*sin(e + f*x))^(1/2))/(3*c^6*f) + (a^2*exp(e*6i + f*x*6i)*sin(e + f*x)*(8*A + 13*B)*(a + a*sin(e + f*x))^(1/2)*8i)/(3*c^6*f) - (B*a^2*exp(e*6i + f*x*6i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2)*8i)/(c^6*f)))/(cos(e + f*x)*exp(e*6i + f*x*6i)*264i - exp(e*6i + f*x*6i)*cos(3*e + 3*f*x)*220i + exp(e*6i + f*x*6i)*cos(5*e + 5*f*x)*20i - exp(e*6i + f*x*6i)*sin(2*e + 2*f*x)*330i + exp(e*6i + f*x*6i)*sin(4*e + 4*f*x)*88i - exp(e*6i + f*x*6i)*sin(6*e + 6*f*x)*2i)","B"
159,1,357,196,20.714893,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c - c*sin(e + f*x))^(13/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(A\,29{}\mathrm{i}+B\,13{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,16{}\mathrm{i}}{15\,c^7\,f}-\frac{a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(A\,1{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,16{}\mathrm{i}}{c^7\,f}-\frac{32\,a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(6\,A+7\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^7\,f}+\frac{32\,B\,a^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{3\,c^7\,f}\right)}{-858\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+858\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)-130\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)+2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(7\,e+7\,f\,x\right)+1144\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)-416\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)+24\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((a^2*exp(e*7i + f*x*7i)*(A*29i + B*13i)*(a + a*sin(e + f*x))^(1/2)*16i)/(15*c^7*f) - (a^2*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(A*1i + B*1i)*(a + a*sin(e + f*x))^(1/2)*16i)/(c^7*f) - (32*a^2*exp(e*7i + f*x*7i)*sin(e + f*x)*(6*A + 7*B)*(a + a*sin(e + f*x))^(1/2))/(5*c^7*f) + (32*B*a^2*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(3*c^7*f)))/(858*exp(e*7i + f*x*7i)*cos(3*e + 3*f*x) - 858*cos(e + f*x)*exp(e*7i + f*x*7i) - 130*exp(e*7i + f*x*7i)*cos(5*e + 5*f*x) + 2*exp(e*7i + f*x*7i)*cos(7*e + 7*f*x) + 1144*exp(e*7i + f*x*7i)*sin(2*e + 2*f*x) - 416*exp(e*7i + f*x*7i)*sin(4*e + 4*f*x) + 24*exp(e*7i + f*x*7i)*sin(6*e + 6*f*x))","B"
160,1,482,250,20.031174,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(9/2),x)","\frac{{\mathrm{e}}^{-e\,9{}\mathrm{i}-f\,x\,9{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(-\frac{a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,7{}\mathrm{i}}{64\,f}-\frac{a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,7{}\mathrm{i}}{128\,f}-\frac{a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{64\,f}-\frac{a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\left(A\,1{}\mathrm{i}-B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{512\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(7\,A+2\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\left(4\,A+5\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{896\,f}+\frac{7\,A\,a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(10\,A-B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}+\frac{B\,a^3\,c^4\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sin\left(9\,e+9\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{1152\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*9i - f*x*9i)*(c - c*sin(e + f*x))^(1/2)*((a^3*c^4*exp(e*9i + f*x*9i)*sin(5*e + 5*f*x)*(7*A + 2*B)*(a + a*sin(e + f*x))^(1/2))/(160*f) - (a^3*c^4*exp(e*9i + f*x*9i)*cos(4*e + 4*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*7i)/(128*f) - (a^3*c^4*exp(e*9i + f*x*9i)*cos(6*e + 6*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*1i)/(64*f) - (a^3*c^4*exp(e*9i + f*x*9i)*cos(8*e + 8*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*1i)/(512*f) - (a^3*c^4*exp(e*9i + f*x*9i)*cos(2*e + 2*f*x)*(A*1i - B*1i)*(a + a*sin(e + f*x))^(1/2)*7i)/(64*f) + (a^3*c^4*exp(e*9i + f*x*9i)*sin(7*e + 7*f*x)*(4*A + 5*B)*(a + a*sin(e + f*x))^(1/2))/(896*f) + (7*A*a^3*c^4*exp(e*9i + f*x*9i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*a^3*c^4*exp(e*9i + f*x*9i)*sin(e + f*x)*(10*A - B)*(a + a*sin(e + f*x))^(1/2))/(64*f) + (B*a^3*c^4*exp(e*9i + f*x*9i)*sin(9*e + 9*f*x)*(a + a*sin(e + f*x))^(1/2))/(1152*f)))/(2*cos(e + f*x))","B"
161,1,384,226,17.652954,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(7/2),x)","\frac{{\mathrm{e}}^{-e\,8{}\mathrm{i}-f\,x\,8{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{35\,A\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}-\frac{7\,B\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}-\frac{7\,B\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{128\,f}-\frac{B\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{64\,f}-\frac{B\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\cos\left(8\,e+8\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{512\,f}+\frac{7\,A\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{7\,A\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{A\,a^3\,c^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*8i - f*x*8i)*(c - c*sin(e + f*x))^(1/2)*((35*A*a^3*c^3*exp(e*8i + f*x*8i)*sin(e + f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) - (7*B*a^3*c^3*exp(e*8i + f*x*8i)*cos(2*e + 2*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) - (7*B*a^3*c^3*exp(e*8i + f*x*8i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(128*f) - (B*a^3*c^3*exp(e*8i + f*x*8i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(64*f) - (B*a^3*c^3*exp(e*8i + f*x*8i)*cos(8*e + 8*f*x)*(a + a*sin(e + f*x))^(1/2))/(512*f) + (7*A*a^3*c^3*exp(e*8i + f*x*8i)*sin(3*e + 3*f*x)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (7*A*a^3*c^3*exp(e*8i + f*x*8i)*sin(5*e + 5*f*x)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (A*a^3*c^3*exp(e*8i + f*x*8i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f)))/(2*cos(e + f*x))","B"
162,1,383,192,18.428351,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(5/2),x)","\frac{{\mathrm{e}}^{-e\,7{}\mathrm{i}-f\,x\,7{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(A\,1{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,5{}\mathrm{i}}{32\,f}+\frac{a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(A\,1{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{16\,f}+\frac{a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\left(A\,1{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{96\,f}+\frac{a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(4\,A-3\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{160\,f}+\frac{a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(20\,A-B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{96\,f}+\frac{5\,a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(8\,A+B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}-\frac{B\,a^3\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(7\,e+7\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{224\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"(exp(- e*7i - f*x*7i)*(c - c*sin(e + f*x))^(1/2)*((a^3*c^2*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(A*1i + B*1i)*(a + a*sin(e + f*x))^(1/2)*5i)/(32*f) + (a^3*c^2*exp(e*7i + f*x*7i)*cos(4*e + 4*f*x)*(A*1i + B*1i)*(a + a*sin(e + f*x))^(1/2)*1i)/(16*f) + (a^3*c^2*exp(e*7i + f*x*7i)*cos(6*e + 6*f*x)*(A*1i + B*1i)*(a + a*sin(e + f*x))^(1/2)*1i)/(96*f) + (a^3*c^2*exp(e*7i + f*x*7i)*sin(5*e + 5*f*x)*(4*A - 3*B)*(a + a*sin(e + f*x))^(1/2))/(160*f) + (a^3*c^2*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(20*A - B)*(a + a*sin(e + f*x))^(1/2))/(96*f) + (5*a^3*c^2*exp(e*7i + f*x*7i)*sin(e + f*x)*(8*A + B)*(a + a*sin(e + f*x))^(1/2))/(32*f) - (B*a^3*c^2*exp(e*7i + f*x*7i)*sin(7*e + 7*f*x)*(a + a*sin(e + f*x))^(1/2))/(224*f)))/(2*cos(e + f*x))","B"
163,1,321,142,18.169036,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(3/2),x)","-\frac{{\mathrm{e}}^{-e\,6{}\mathrm{i}-f\,x\,6{}\mathrm{i}}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{a^3\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\left(2\,A+B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{16\,f}-\frac{B\,a^3\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(6\,e+6\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{96\,f}+\frac{a^3\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(A\,7{}\mathrm{i}+B\,2{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{4\,f}+\frac{a^3\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(16\,A+11\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{32\,f}+\frac{a^3\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(A\,3{}\mathrm{i}-B\,2{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{24\,f}-\frac{a^3\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sin\left(5\,e+5\,f\,x\right)\,\left(A\,1{}\mathrm{i}+B\,2{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,1{}\mathrm{i}}{40\,f}\right)}{2\,\cos\left(e+f\,x\right)}","Not used",1,"-(exp(- e*6i - f*x*6i)*(c - c*sin(e + f*x))^(1/2)*((a^3*c*exp(e*6i + f*x*6i)*cos(4*e + 4*f*x)*(2*A + B)*(a + a*sin(e + f*x))^(1/2))/(16*f) - (B*a^3*c*exp(e*6i + f*x*6i)*cos(6*e + 6*f*x)*(a + a*sin(e + f*x))^(1/2))/(96*f) + (a^3*c*exp(e*6i + f*x*6i)*sin(e + f*x)*(A*7i + B*2i)*(a + a*sin(e + f*x))^(1/2)*1i)/(4*f) + (a^3*c*exp(e*6i + f*x*6i)*cos(2*e + 2*f*x)*(16*A + 11*B)*(a + a*sin(e + f*x))^(1/2))/(32*f) + (a^3*c*exp(e*6i + f*x*6i)*sin(3*e + 3*f*x)*(A*3i - B*2i)*(a + a*sin(e + f*x))^(1/2)*1i)/(24*f) - (a^3*c*exp(e*6i + f*x*6i)*sin(5*e + 5*f*x)*(A*1i + B*2i)*(a + a*sin(e + f*x))^(1/2)*1i)/(40*f)))/(2*cos(e + f*x))","B"
164,1,173,96,16.679449,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2)*(c - c*sin(e + f*x))^(1/2),x)","-\frac{a^3\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(140\,A\,\cos\left(e+f\,x\right)+100\,B\,\cos\left(e+f\,x\right)+135\,A\,\cos\left(3\,e+3\,f\,x\right)-5\,A\,\cos\left(5\,e+5\,f\,x\right)+85\,B\,\cos\left(3\,e+3\,f\,x\right)-15\,B\,\cos\left(5\,e+5\,f\,x\right)-240\,A\,\sin\left(2\,e+2\,f\,x\right)+40\,A\,\sin\left(4\,e+4\,f\,x\right)-90\,B\,\sin\left(2\,e+2\,f\,x\right)+48\,B\,\sin\left(4\,e+4\,f\,x\right)-2\,B\,\sin\left(6\,e+6\,f\,x\right)\right)}{160\,f\,\left(\cos\left(2\,e+2\,f\,x\right)+1\right)}","Not used",1,"-(a^3*(a*(sin(e + f*x) + 1))^(1/2)*(-c*(sin(e + f*x) - 1))^(1/2)*(140*A*cos(e + f*x) + 100*B*cos(e + f*x) + 135*A*cos(3*e + 3*f*x) - 5*A*cos(5*e + 5*f*x) + 85*B*cos(3*e + 3*f*x) - 15*B*cos(5*e + 5*f*x) - 240*A*sin(2*e + 2*f*x) + 40*A*sin(4*e + 4*f*x) - 90*B*sin(2*e + 2*f*x) + 48*B*sin(4*e + 4*f*x) - 2*B*sin(6*e + 6*f*x)))/(160*f*(cos(2*e + 2*f*x) + 1))","B"
165,0,-1,239,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(1/2), x)","F"
166,0,-1,271,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(3/2), x)","F"
167,0,-1,263,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(5/2), x)","F"
168,0,-1,264,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(7/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(7/2), x)","F"
169,0,-1,247,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(9/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(9/2), x)","F"
170,0,-1,96,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(11/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{11/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(11/2), x)","F"
171,1,406,146,22.847692,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(13/2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{56\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\left(4\,A+5\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{5\,c^7\,f}+\frac{a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(3\,e+3\,f\,x\right)\,\left(A\,1{}\mathrm{i}+B\,1{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,32{}\mathrm{i}}{3\,c^7\,f}-\frac{32\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(2\,e+2\,f\,x\right)\,\left(A+2\,B\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^7\,f}+\frac{8\,B\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(4\,e+4\,f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c^7\,f}-\frac{a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(e+f\,x\right)\,\left(A\,13{}\mathrm{i}+B\,5{}\mathrm{i}\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,32{}\mathrm{i}}{5\,c^7\,f}\right)}{-858\,\cos\left(e+f\,x\right)\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}+858\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(3\,e+3\,f\,x\right)-130\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(5\,e+5\,f\,x\right)+2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\cos\left(7\,e+7\,f\,x\right)+1144\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(2\,e+2\,f\,x\right)-416\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(4\,e+4\,f\,x\right)+24\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sin\left(6\,e+6\,f\,x\right)}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((56*a^3*exp(e*7i + f*x*7i)*(4*A + 5*B)*(a + a*sin(e + f*x))^(1/2))/(5*c^7*f) + (a^3*exp(e*7i + f*x*7i)*sin(3*e + 3*f*x)*(A*1i + B*1i)*(a + a*sin(e + f*x))^(1/2)*32i)/(3*c^7*f) - (32*a^3*exp(e*7i + f*x*7i)*cos(2*e + 2*f*x)*(A + 2*B)*(a + a*sin(e + f*x))^(1/2))/(c^7*f) + (8*B*a^3*exp(e*7i + f*x*7i)*cos(4*e + 4*f*x)*(a + a*sin(e + f*x))^(1/2))/(c^7*f) - (a^3*exp(e*7i + f*x*7i)*sin(e + f*x)*(A*13i + B*5i)*(a + a*sin(e + f*x))^(1/2)*32i)/(5*c^7*f)))/(858*exp(e*7i + f*x*7i)*cos(3*e + 3*f*x) - 858*cos(e + f*x)*exp(e*7i + f*x*7i) - 130*exp(e*7i + f*x*7i)*cos(5*e + 5*f*x) + 2*exp(e*7i + f*x*7i)*cos(7*e + 7*f*x) + 1144*exp(e*7i + f*x*7i)*sin(2*e + 2*f*x) - 416*exp(e*7i + f*x*7i)*sin(4*e + 4*f*x) + 24*exp(e*7i + f*x*7i)*sin(6*e + 6*f*x))","B"
172,1,827,202,25.255703,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(15/2),x)","-\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{B\,a^3\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,16{}\mathrm{i}}{3\,c^8\,f}+\frac{B\,a^3\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,16{}\mathrm{i}}{3\,c^8\,f}-\frac{a^3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,3{}\mathrm{i}+B\,5{}\mathrm{i}\right)\,8{}\mathrm{i}}{3\,c^8\,f}+\frac{a^3\,{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,3{}\mathrm{i}+B\,5{}\mathrm{i}\right)\,8{}\mathrm{i}}{3\,c^8\,f}-\frac{a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(27\,A+41\,B\right)\,16{}\mathrm{i}}{15\,c^8\,f}-\frac{a^3\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(27\,A+41\,B\right)\,16{}\mathrm{i}}{15\,c^8\,f}+\frac{a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,43{}\mathrm{i}+B\,29{}\mathrm{i}\right)\,8{}\mathrm{i}}{5\,c^8\,f}-\frac{a^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,43{}\mathrm{i}+B\,29{}\mathrm{i}\right)\,8{}\mathrm{i}}{5\,c^8\,f}+\frac{a^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(89\,A+82\,B\right)\,32{}\mathrm{i}}{35\,c^8\,f}\right)}{1+910\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-2002\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}+2002\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}-910\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}+90\,{\mathrm{e}}^{e\,14{}\mathrm{i}+f\,x\,14{}\mathrm{i}}-{\mathrm{e}}^{e\,16{}\mathrm{i}+f\,x\,16{}\mathrm{i}}-90\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,14{}\mathrm{i}-{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,350{}\mathrm{i}+{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,1638{}\mathrm{i}-{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,1430{}\mathrm{i}-{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,1430{}\mathrm{i}+{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,1638{}\mathrm{i}-{\mathrm{e}}^{e\,13{}\mathrm{i}+f\,x\,13{}\mathrm{i}}\,350{}\mathrm{i}+{\mathrm{e}}^{e\,15{}\mathrm{i}+f\,x\,15{}\mathrm{i}}\,14{}\mathrm{i}}","Not used",1,"-((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((B*a^3*exp(e*4i + f*x*4i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*16i)/(3*c^8*f) + (B*a^3*exp(e*12i + f*x*12i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*16i)/(3*c^8*f) - (a^3*exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*3i + B*5i)*8i)/(3*c^8*f) + (a^3*exp(e*11i + f*x*11i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*3i + B*5i)*8i)/(3*c^8*f) - (a^3*exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(27*A + 41*B)*16i)/(15*c^8*f) - (a^3*exp(e*10i + f*x*10i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(27*A + 41*B)*16i)/(15*c^8*f) + (a^3*exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*43i + B*29i)*8i)/(5*c^8*f) - (a^3*exp(e*9i + f*x*9i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*43i + B*29i)*8i)/(5*c^8*f) + (a^3*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(89*A + 82*B)*32i)/(35*c^8*f)))/(exp(e*1i + f*x*1i)*14i - 90*exp(e*2i + f*x*2i) - exp(e*3i + f*x*3i)*350i + 910*exp(e*4i + f*x*4i) + exp(e*5i + f*x*5i)*1638i - 2002*exp(e*6i + f*x*6i) - exp(e*7i + f*x*7i)*1430i - exp(e*9i + f*x*9i)*1430i + 2002*exp(e*10i + f*x*10i) + exp(e*11i + f*x*11i)*1638i - 910*exp(e*12i + f*x*12i) - exp(e*13i + f*x*13i)*350i + 90*exp(e*14i + f*x*14i) + exp(e*15i + f*x*15i)*14i - exp(e*16i + f*x*16i) + 1)","B"
173,1,841,246,28.344386,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(7/2))/(c - c*sin(e + f*x))^(17/2),x)","\frac{\sqrt{c-c\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(\frac{8\,B\,a^3\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{c^9\,f}+\frac{8\,B\,a^3\,{\mathrm{e}}^{e\,13{}\mathrm{i}+f\,x\,13{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}}{c^9\,f}-\frac{64\,a^3\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,1{}\mathrm{i}+B\,2{}\mathrm{i}\right)}{5\,c^9\,f}-\frac{32\,a^3\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(8\,A+11\,B\right)}{5\,c^9\,f}+\frac{64\,a^3\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,1{}\mathrm{i}+B\,2{}\mathrm{i}\right)}{5\,c^9\,f}-\frac{32\,a^3\,{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(8\,A+11\,B\right)}{5\,c^9\,f}+\frac{64\,a^3\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,13{}\mathrm{i}+B\,10{}\mathrm{i}\right)}{7\,c^9\,f}-\frac{64\,a^3\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(A\,13{}\mathrm{i}+B\,10{}\mathrm{i}\right)}{7\,c^9\,f}+\frac{16\,a^3\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-e\,1{}\mathrm{i}-f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}-\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}}{2}\right)}\,\left(64\,A+53\,B\right)}{7\,c^9\,f}\right)}{1+1700\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-6188\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}+4862\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}+4862\,{\mathrm{e}}^{e\,10{}\mathrm{i}+f\,x\,10{}\mathrm{i}}-6188\,{\mathrm{e}}^{e\,12{}\mathrm{i}+f\,x\,12{}\mathrm{i}}+1700\,{\mathrm{e}}^{e\,14{}\mathrm{i}+f\,x\,14{}\mathrm{i}}-119\,{\mathrm{e}}^{e\,16{}\mathrm{i}+f\,x\,16{}\mathrm{i}}+{\mathrm{e}}^{e\,18{}\mathrm{i}+f\,x\,18{}\mathrm{i}}-119\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}+{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,16{}\mathrm{i}-{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,544{}\mathrm{i}+{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,3808{}\mathrm{i}-{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,7072{}\mathrm{i}+{\mathrm{e}}^{e\,11{}\mathrm{i}+f\,x\,11{}\mathrm{i}}\,7072{}\mathrm{i}-{\mathrm{e}}^{e\,13{}\mathrm{i}+f\,x\,13{}\mathrm{i}}\,3808{}\mathrm{i}+{\mathrm{e}}^{e\,15{}\mathrm{i}+f\,x\,15{}\mathrm{i}}\,544{}\mathrm{i}-{\mathrm{e}}^{e\,17{}\mathrm{i}+f\,x\,17{}\mathrm{i}}\,16{}\mathrm{i}}","Not used",1,"((c - c*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*((8*B*a^3*exp(e*5i + f*x*5i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(c^9*f) + (8*B*a^3*exp(e*13i + f*x*13i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2))/(c^9*f) - (64*a^3*exp(e*6i + f*x*6i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*1i + B*2i))/(5*c^9*f) - (32*a^3*exp(e*7i + f*x*7i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(8*A + 11*B))/(5*c^9*f) + (64*a^3*exp(e*12i + f*x*12i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*1i + B*2i))/(5*c^9*f) - (32*a^3*exp(e*11i + f*x*11i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(8*A + 11*B))/(5*c^9*f) + (64*a^3*exp(e*8i + f*x*8i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*13i + B*10i))/(7*c^9*f) - (64*a^3*exp(e*10i + f*x*10i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(A*13i + B*10i))/(7*c^9*f) + (16*a^3*exp(e*9i + f*x*9i)*(a + a*((exp(- e*1i - f*x*1i)*1i)/2 - (exp(e*1i + f*x*1i)*1i)/2))^(1/2)*(64*A + 53*B))/(7*c^9*f)))/(exp(e*1i + f*x*1i)*16i - 119*exp(e*2i + f*x*2i) - exp(e*3i + f*x*3i)*544i + 1700*exp(e*4i + f*x*4i) + exp(e*5i + f*x*5i)*3808i - 6188*exp(e*6i + f*x*6i) - exp(e*7i + f*x*7i)*7072i + 4862*exp(e*8i + f*x*8i) + 4862*exp(e*10i + f*x*10i) + exp(e*11i + f*x*11i)*7072i - 6188*exp(e*12i + f*x*12i) - exp(e*13i + f*x*13i)*3808i + 1700*exp(e*14i + f*x*14i) + exp(e*15i + f*x*15i)*544i - 119*exp(e*16i + f*x*16i) - exp(e*17i + f*x*17i)*16i + exp(e*18i + f*x*18i) + 1)","B"
174,0,-1,197,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(1/2), x)","F"
175,0,-1,146,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(1/2), x)","F"
176,0,-1,96,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(1/2), x)","F"
177,0,-1,113,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
178,0,-1,103,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
179,0,-1,153,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
180,0,-1,271,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
181,0,-1,210,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
182,0,-1,159,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
183,0,-1,100,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{c-c\,\sin\left(e+f\,x\right)}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(3/2), x)","F"
184,0,-1,103,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
185,0,-1,150,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
186,0,-1,217,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
187,0,-1,323,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{9/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(9/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
188,0,-1,263,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{7/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(7/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
189,0,-1,211,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(5/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
190,0,-1,149,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(3/2))/(a + a*sin(e + f*x))^(5/2), x)","F"
191,1,156,94,14.860565,"\text{Not used}","int(((A + B*sin(e + f*x))*(c - c*sin(e + f*x))^(1/2))/(a + a*sin(e + f*x))^(5/2),x)","-\frac{2\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(A\,\sin\left(2\,e+2\,f\,x\right)+3\,B\,\sin\left(2\,e+2\,f\,x\right)-2\,A\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)-3\,B\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)+B\,\left(2\,{\sin\left(\frac{3\,e}{2}+\frac{3\,f\,x}{2}\right)}^2-1\right)\right)}{a^2\,f\,\sqrt{a\,\left(\sin\left(e+f\,x\right)+1\right)}\,\left(-8\,{\sin\left(e+f\,x\right)}^2+4\,\sin\left(e+f\,x\right)+2\,{\sin\left(2\,e+2\,f\,x\right)}^2+4\,\sin\left(3\,e+3\,f\,x\right)+8\right)}","Not used",1,"-(2*(-c*(sin(e + f*x) - 1))^(1/2)*(A*sin(2*e + 2*f*x) + 3*B*sin(2*e + 2*f*x) - 2*A*(2*sin(e/2 + (f*x)/2)^2 - 1) - 3*B*(2*sin(e/2 + (f*x)/2)^2 - 1) + B*(2*sin((3*e)/2 + (3*f*x)/2)^2 - 1)))/(a^2*f*(a*(sin(e + f*x) + 1))^(1/2)*(4*sin(e + f*x) + 4*sin(3*e + 3*f*x) + 2*sin(2*e + 2*f*x)^2 - 8*sin(e + f*x)^2 + 8))","B"
192,0,-1,151,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(1/2)), x)","F"
193,0,-1,208,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
194,0,-1,245,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c - c*sin(e + f*x))^(5/2)), x)","F"
195,0,-1,174,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
196,0,-1,145,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3, x)","F"
197,0,-1,145,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^2, x)","F"
198,0,-1,139,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(c-c\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x)), x)","F"
199,0,-1,117,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
200,0,-1,123,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c-c\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x)), x)","F"
201,0,-1,148,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^2, x)","F"
202,0,-1,148,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^3, x)","F"
203,0,-1,118,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2), x)","F"
204,0,-1,118,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + c*sin(e + f*x))^m)/(a - a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+c\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{a-a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + c*sin(e + f*x))^m)/(a - a*sin(e + f*x))^(1/2), x)","F"
205,1,749,275,21.059553,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{B\,c^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c^2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(2100\,A-1575\,B+1272\,A\,m-110\,B\,m+304\,A\,m^2+32\,A\,m^3-68\,B\,m^2-8\,B\,m^3\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,2100{}\mathrm{i}-B\,1575{}\mathrm{i}+A\,m\,1272{}\mathrm{i}-B\,m\,110{}\mathrm{i}+A\,m^2\,304{}\mathrm{i}+A\,m^3\,32{}\mathrm{i}-B\,m^2\,68{}\mathrm{i}-B\,m^3\,8{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(350\,A-385\,B+184\,A\,m-104\,B\,m+24\,A\,m^2-12\,B\,m^2\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c^2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,350{}\mathrm{i}-B\,385{}\mathrm{i}+A\,m\,184{}\mathrm{i}-B\,m\,104{}\mathrm{i}+A\,m^2\,24{}\mathrm{i}-B\,m^2\,12{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{B\,c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(14\,A-35\,B+4\,A\,m-6\,B\,m\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(A\,14{}\mathrm{i}-B\,35{}\mathrm{i}+A\,m\,4{}\mathrm{i}-B\,m\,6{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}\right)}{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}{16\,m^4+128\,m^3+344\,m^2+352\,m+105}}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((B*c^2*(a + a*sin(e + f*x))^m*(m*46i + m^2*36i + m^3*8i + 15i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c^2*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^m*(2100*A - 1575*B + 1272*A*m - 110*B*m + 304*A*m^2 + 32*A*m^3 - 68*B*m^2 - 8*B*m^3))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c^2*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^m*(A*2100i - B*1575i + A*m*1272i - B*m*110i + A*m^2*304i + A*m^3*32i - B*m^2*68i - B*m^3*8i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c^2*exp(e*5i + f*x*5i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(350*A - 385*B + 184*A*m - 104*B*m + 24*A*m^2 - 12*B*m^2))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c^2*exp(e*2i + f*x*2i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(A*350i - B*385i + A*m*184i - B*m*104i + A*m^2*24i - B*m^2*12i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (B*c^2*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^m*(46*m + 36*m^2 + 8*m^3 + 15))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c^2*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(14*A - 35*B + 4*A*m - 6*B*m))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c^2*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(A*14i - B*35i + A*m*4i - B*m*6i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))))/(exp(e*4i + f*x*4i) - (exp(e*3i + f*x*3i)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i))/(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))","B"
206,1,480,166,19.203199,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{c\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(45\,A-30\,B+28\,A\,m+4\,B\,m+4\,A\,m^2\right)}{f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,45{}\mathrm{i}-B\,30{}\mathrm{i}+A\,m\,28{}\mathrm{i}+B\,m\,4{}\mathrm{i}+A\,m^2\,4{}\mathrm{i}\right)}{f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{B\,c\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,4{}\mathrm{i}+m\,8{}\mathrm{i}+3{}\mathrm{i}\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{B\,c\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(10\,A-15\,B+4\,A\,m-2\,B\,m\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{c\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,10{}\mathrm{i}-B\,15{}\mathrm{i}+A\,m\,4{}\mathrm{i}-B\,m\,2{}\mathrm{i}\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}\right)}{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}+\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(8\,m^3+36\,m^2+46\,m+15\right)}{m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((c*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^m*(45*A - 30*B + 28*A*m + 4*B*m + 4*A*m^2))/(f*(m*46i + m^2*36i + m^3*8i + 15i)) + (c*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^m*(A*45i - B*30i + A*m*28i + B*m*4i + A*m^2*4i))/(f*(m*46i + m^2*36i + m^3*8i + 15i)) + (B*c*(a + a*sin(e + f*x))^m*(m*8i + m^2*4i + 3i))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i)) + (B*c*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i)) + (c*exp(e*1i + f*x*1i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(10*A - 15*B + 4*A*m - 2*B*m))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i)) + (c*exp(e*4i + f*x*4i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(A*10i - B*15i + A*m*4i - B*m*2i))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i))))/(exp(e*3i + f*x*3i) + (exp(e*2i + f*x*2i)*(46*m + 36*m^2 + 8*m^3 + 15))/(m*46i + m^2*36i + m^3*8i + 15i))","B"
207,1,105,104,1.442044,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(6\,A\,\cos\left(e+f\,x\right)-4\,B\,\cos\left(e+f\,x\right)+B\,\sin\left(2\,e+2\,f\,x\right)+4\,A\,m\,\cos\left(e+f\,x\right)+2\,B\,m\,\sin\left(2\,e+2\,f\,x\right)\right)}{f\,\left(\sin\left(e+f\,x\right)-1\right)\,\left(4\,m^2+8\,m+3\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(6*A*cos(e + f*x) - 4*B*cos(e + f*x) + B*sin(2*e + 2*f*x) + 4*A*m*cos(e + f*x) + 2*B*m*sin(2*e + 2*f*x)))/(f*(sin(e + f*x) - 1)*(8*m + 4*m^2 + 3))","B"
208,0,-1,118,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2), x)","F"
209,0,-1,134,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2), x)","F"
210,0,-1,134,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2), x)","F"
211,1,368,267,22.233354,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 4),x)","-\frac{\sin\left(4\,e+4\,f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,B-3\,A+2\,B\,m\right)\,1{}\mathrm{i}}{4\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+4}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}+\frac{\cos\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,168{}\mathrm{i}-B\,84{}\mathrm{i}+A\,m\,340{}\mathrm{i}-B\,m\,96{}\mathrm{i}+A\,m^2\,192{}\mathrm{i}+A\,m^3\,32{}\mathrm{i}-B\,m^2\,24{}\mathrm{i}\right)}{4\,f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+4}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}+\frac{\sin\left(2\,e+2\,f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(2\,m^2+8\,m+7\right)\,\left(4\,B-3\,A+2\,B\,m\right)\,1{}\mathrm{i}}{f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+4}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}+\frac{\cos\left(3\,e+3\,f\,x\right)\,\left(m+2\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(-A\,3{}\mathrm{i}+B\,4{}\mathrm{i}+B\,m\,2{}\mathrm{i}\right)}{f\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+4}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}","Not used",1,"(cos(e + f*x)*(a + a*sin(e + f*x))^m*(A*168i - B*84i + A*m*340i - B*m*96i + A*m^2*192i + A*m^3*32i - B*m^2*24i))/(4*f*(c - c*sin(e + f*x))^(m + 4)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i)) - (sin(4*e + 4*f*x)*(a + a*sin(e + f*x))^m*(4*B - 3*A + 2*B*m)*1i)/(4*f*(c - c*sin(e + f*x))^(m + 4)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i)) + (sin(2*e + 2*f*x)*(a + a*sin(e + f*x))^m*(8*m + 2*m^2 + 7)*(4*B - 3*A + 2*B*m)*1i)/(f*(c - c*sin(e + f*x))^(m + 4)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i)) + (cos(3*e + 3*f*x)*(m + 2)*(a + a*sin(e + f*x))^m*(B*4i - A*3i + B*m*2i))/(f*(c - c*sin(e + f*x))^(m + 4)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i))","B"
212,1,239,191,15.483873,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 3),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(30\,A\,\cos\left(e+f\,x\right)-15\,B\,\cos\left(e+f\,x\right)-2\,A\,\cos\left(3\,e+3\,f\,x\right)+3\,B\,\cos\left(3\,e+3\,f\,x\right)-12\,A\,\sin\left(2\,e+2\,f\,x\right)+18\,B\,\sin\left(2\,e+2\,f\,x\right)+8\,B\,m^2\,\sin\left(2\,e+2\,f\,x\right)+48\,A\,m\,\cos\left(e+f\,x\right)-10\,B\,m\,\cos\left(e+f\,x\right)+16\,A\,m^2\,\cos\left(e+f\,x\right)+2\,B\,m\,\cos\left(3\,e+3\,f\,x\right)-8\,A\,m\,\sin\left(2\,e+2\,f\,x\right)+24\,B\,m\,\sin\left(2\,e+2\,f\,x\right)\right)}{c^3\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)\,\left(15\,\sin\left(e+f\,x\right)+6\,\cos\left(2\,e+2\,f\,x\right)-\sin\left(3\,e+3\,f\,x\right)-10\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(30*A*cos(e + f*x) - 15*B*cos(e + f*x) - 2*A*cos(3*e + 3*f*x) + 3*B*cos(3*e + 3*f*x) - 12*A*sin(2*e + 2*f*x) + 18*B*sin(2*e + 2*f*x) + 8*B*m^2*sin(2*e + 2*f*x) + 48*A*m*cos(e + f*x) - 10*B*m*cos(e + f*x) + 16*A*m^2*cos(e + f*x) + 2*B*m*cos(3*e + 3*f*x) - 8*A*m*sin(2*e + 2*f*x) + 24*B*m*sin(2*e + 2*f*x)))/(c^3*f*(-c*(sin(e + f*x) - 1))^m*(46*m + 36*m^2 + 8*m^3 + 15)*(15*sin(e + f*x) + 6*cos(2*e + 2*f*x) - sin(3*e + 3*f*x) - 10))","B"
213,1,134,114,14.157719,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(4\,A\,\cos\left(e+f\,x\right)-2\,B\,\cos\left(e+f\,x\right)-A\,\sin\left(2\,e+2\,f\,x\right)+2\,B\,\sin\left(2\,e+2\,f\,x\right)+4\,A\,m\,\cos\left(e+f\,x\right)+2\,B\,m\,\sin\left(2\,e+2\,f\,x\right)\right)}{c^2\,f\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(4\,\sin\left(e+f\,x\right)+\cos\left(2\,e+2\,f\,x\right)-3\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(4*A*cos(e + f*x) - 2*B*cos(e + f*x) - A*sin(2*e + 2*f*x) + 2*B*sin(2*e + 2*f*x) + 4*A*m*cos(e + f*x) + 2*B*m*sin(2*e + 2*f*x)))/(c^2*f*(-c*(sin(e + f*x) - 1))^m*(8*m + 4*m^2 + 3)*(4*sin(e + f*x) + cos(2*e + 2*f*x) - 3))","B"
214,0,-1,163,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 1),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(m + 1), x)","F"
215,0,-1,158,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^m,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^m} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^m, x)","F"
216,0,-1,170,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{1-m} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1 - m), x)","F"
217,0,-1,173,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(2 - m),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{2-m} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(2 - m), x)","F"
218,1,64,34,14.447389,"\text{Not used}","int(-(B*(n - 3) + B*sin(e + f*x)*(n + 4))*(a + a*sin(e + f*x))^3*(c - c*sin(e + f*x))^n,x)","\frac{B\,a^3\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^n\,\left(14\,\cos\left(e+f\,x\right)-6\,\cos\left(3\,e+3\,f\,x\right)+14\,\sin\left(2\,e+2\,f\,x\right)-\sin\left(4\,e+4\,f\,x\right)\right)}{8\,f}","Not used",1,"(B*a^3*(-c*(sin(e + f*x) - 1))^n*(14*cos(e + f*x) - 6*cos(3*e + 3*f*x) + 14*sin(2*e + 2*f*x) - sin(4*e + 4*f*x)))/(8*f)","B"
219,1,61,34,14.457446,"\text{Not used}","int(-(B*(n - 3) - B*sin(e + f*x)*(n + 4))*(a - a*sin(e + f*x))^3*(c + c*sin(e + f*x))^n,x)","-\frac{B\,a^3\,{\left(c\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^n\,\left(14\,\cos\left(e+f\,x\right)-6\,\cos\left(3\,e+3\,f\,x\right)-14\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)\right)}{8\,f}","Not used",1,"-(B*a^3*(c*(sin(e + f*x) + 1))^n*(14*cos(e + f*x) - 6*cos(3*e + 3*f*x) - 14*sin(2*e + 2*f*x) + sin(4*e + 4*f*x)))/(8*f)","B"
220,1,61,33,14.378181,"\text{Not used}","int((B*(m - 3) - B*sin(e + f*x)*(m + 4))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^3,x)","\frac{B\,c^3\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(14\,\cos\left(e+f\,x\right)-6\,\cos\left(3\,e+3\,f\,x\right)-14\,\sin\left(2\,e+2\,f\,x\right)+\sin\left(4\,e+4\,f\,x\right)\right)}{8\,f}","Not used",1,"(B*c^3*(a*(sin(e + f*x) + 1))^m*(14*cos(e + f*x) - 6*cos(3*e + 3*f*x) - 14*sin(2*e + 2*f*x) + sin(4*e + 4*f*x)))/(8*f)","B"
221,1,64,35,14.363302,"\text{Not used}","int((B*(m - 3) + B*sin(e + f*x)*(m + 4))*(a - a*sin(e + f*x))^m*(c + c*sin(e + f*x))^3,x)","-\frac{B\,c^3\,{\left(-a\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(14\,\cos\left(e+f\,x\right)-6\,\cos\left(3\,e+3\,f\,x\right)+14\,\sin\left(2\,e+2\,f\,x\right)-\sin\left(4\,e+4\,f\,x\right)\right)}{8\,f}","Not used",1,"-(B*c^3*(-a*(sin(e + f*x) - 1))^m*(14*cos(e + f*x) - 6*cos(3*e + 3*f*x) + 14*sin(2*e + 2*f*x) - sin(4*e + 4*f*x)))/(8*f)","B"
222,1,36,36,13.542131,"\text{Not used}","int((B*(m - n) - B*sin(e + f*x)*(m + n + 1))*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\frac{B\,\cos\left(e+f\,x\right)\,{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,{\left(-c\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^n}{f}","Not used",1,"(B*cos(e + f*x)*(a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^n)/f","B"
223,1,37,37,13.497488,"\text{Not used}","int((B*(m - n) + B*sin(e + f*x)*(m + n + 1))*(a - a*sin(e + f*x))^m*(c + c*sin(e + f*x))^n,x)","-\frac{B\,\cos\left(e+f\,x\right)\,{\left(-a\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,{\left(c\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^n}{f}","Not used",1,"-(B*cos(e + f*x)*(-a*(sin(e + f*x) - 1))^m*(c*(sin(e + f*x) + 1))^n)/f","B"
224,1,300,140,15.303805,"\text{Not used}","int(sin(c + d*x)^3*(A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{A\,a^3\,\left(105\,c-210\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2464\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1400\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4032\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6790\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2240\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-14560\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-6790\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-3360\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+1400\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+105\,d\,x+735\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(c+d\,x\right)+2205\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(c+d\,x\right)+3675\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(c+d\,x\right)+3675\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(c+d\,x\right)+2205\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(c+d\,x\right)+735\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(c+d\,x\right)+105\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(c+d\,x\right)-352\right)}{840\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(A*a^3*(105*c - 210*tan(c/2 + (d*x)/2) - 2464*tan(c/2 + (d*x)/2)^2 - 1400*tan(c/2 + (d*x)/2)^3 - 4032*tan(c/2 + (d*x)/2)^4 + 6790*tan(c/2 + (d*x)/2)^5 + 2240*tan(c/2 + (d*x)/2)^6 - 14560*tan(c/2 + (d*x)/2)^8 - 6790*tan(c/2 + (d*x)/2)^9 - 3360*tan(c/2 + (d*x)/2)^10 + 1400*tan(c/2 + (d*x)/2)^11 + 210*tan(c/2 + (d*x)/2)^13 + 105*d*x + 735*tan(c/2 + (d*x)/2)^2*(c + d*x) + 2205*tan(c/2 + (d*x)/2)^4*(c + d*x) + 3675*tan(c/2 + (d*x)/2)^6*(c + d*x) + 3675*tan(c/2 + (d*x)/2)^8*(c + d*x) + 2205*tan(c/2 + (d*x)/2)^10*(c + d*x) + 735*tan(c/2 + (d*x)/2)^12*(c + d*x) + 105*tan(c/2 + (d*x)/2)^14*(c + d*x) - 352))/(840*d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
225,1,256,121,15.285895,"\text{Not used}","int(sin(c + d*x)^2*(A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{A\,a^3\,\left(45\,c-90\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-768\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+130\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+1500\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-1280\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-1500\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-1920\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-130\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+90\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+45\,d\,x+270\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(c+d\,x\right)+675\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(c+d\,x\right)+900\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(c+d\,x\right)+675\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(c+d\,x\right)+270\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(c+d\,x\right)+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(c+d\,x\right)-128\right)}{240\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(A*a^3*(45*c - 90*tan(c/2 + (d*x)/2) - 768*tan(c/2 + (d*x)/2)^2 + 130*tan(c/2 + (d*x)/2)^3 + 1500*tan(c/2 + (d*x)/2)^5 - 1280*tan(c/2 + (d*x)/2)^6 - 1500*tan(c/2 + (d*x)/2)^7 - 1920*tan(c/2 + (d*x)/2)^8 - 130*tan(c/2 + (d*x)/2)^9 + 90*tan(c/2 + (d*x)/2)^11 + 45*d*x + 270*tan(c/2 + (d*x)/2)^2*(c + d*x) + 675*tan(c/2 + (d*x)/2)^4*(c + d*x) + 900*tan(c/2 + (d*x)/2)^6*(c + d*x) + 675*tan(c/2 + (d*x)/2)^8*(c + d*x) + 270*tan(c/2 + (d*x)/2)^10*(c + d*x) + 45*tan(c/2 + (d*x)/2)^12*(c + d*x) - 128))/(240*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
226,1,292,96,15.029984,"\text{Not used}","int(sin(c + d*x)*(A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{A\,a^3\,x}{4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{12}-\frac{A\,a^3\,\left(75\,c+75\,d\,x-120\right)}{60}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{12}-\frac{A\,a^3\,\left(75\,c+75\,d\,x-160\right)}{60}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{6}-\frac{A\,a^3\,\left(150\,c+150\,d\,x-80\right)}{60}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{6}-\frac{A\,a^3\,\left(150\,c+150\,d\,x-480\right)}{60}\right)+\frac{A\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-3\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{60}-\frac{A\,a^3\,\left(15\,c+15\,d\,x-56\right)}{60}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(A*a^3*x)/4 - (tan(c/2 + (d*x)/2)^8*((A*a^3*(15*c + 15*d*x))/12 - (A*a^3*(75*c + 75*d*x - 120))/60) + tan(c/2 + (d*x)/2)^2*((A*a^3*(15*c + 15*d*x))/12 - (A*a^3*(75*c + 75*d*x - 160))/60) + tan(c/2 + (d*x)/2)^4*((A*a^3*(15*c + 15*d*x))/6 - (A*a^3*(150*c + 150*d*x - 80))/60) + tan(c/2 + (d*x)/2)^6*((A*a^3*(15*c + 15*d*x))/6 - (A*a^3*(150*c + 150*d*x - 480))/60) + (A*a^3*tan(c/2 + (d*x)/2))/2 - 3*A*a^3*tan(c/2 + (d*x)/2)^3 + 3*A*a^3*tan(c/2 + (d*x)/2)^7 - (A*a^3*tan(c/2 + (d*x)/2)^9)/2 + (A*a^3*(15*c + 15*d*x))/60 - (A*a^3*(15*c + 15*d*x - 56))/60)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
227,1,250,82,15.187874,"\text{Not used}","int((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3,x)","\frac{5\,A\,a^3\,x}{8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{6}-\frac{A\,a^3\,\left(60\,c+60\,d\,x-32\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{6}-\frac{A\,a^3\,\left(60\,c+60\,d\,x-96\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{4}-\frac{A\,a^3\,\left(90\,c+90\,d\,x-96\right)}{24}\right)-\frac{3\,A\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{11\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{11\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{3\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{A\,a^3\,\left(15\,c+15\,d\,x\right)}{24}-\frac{A\,a^3\,\left(15\,c+15\,d\,x-32\right)}{24}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(5*A*a^3*x)/8 - (tan(c/2 + (d*x)/2)^2*((A*a^3*(15*c + 15*d*x))/6 - (A*a^3*(60*c + 60*d*x - 32))/24) + tan(c/2 + (d*x)/2)^6*((A*a^3*(15*c + 15*d*x))/6 - (A*a^3*(60*c + 60*d*x - 96))/24) + tan(c/2 + (d*x)/2)^4*((A*a^3*(15*c + 15*d*x))/4 - (A*a^3*(90*c + 90*d*x - 96))/24) - (3*A*a^3*tan(c/2 + (d*x)/2))/4 - (11*A*a^3*tan(c/2 + (d*x)/2)^3)/4 + (11*A*a^3*tan(c/2 + (d*x)/2)^5)/4 + (3*A*a^3*tan(c/2 + (d*x)/2)^7)/4 + (A*a^3*(15*c + 15*d*x))/24 - (A*a^3*(15*c + 15*d*x - 32))/24)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
228,1,212,76,13.226845,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x),x)","\frac{-2\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,A\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4\,A\,a^3}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,A\,a^3\,\mathrm{atan}\left(\frac{4\,A^2\,a^6}{4\,A^2\,a^6-4\,A^2\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{4\,A^2\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,A^2\,a^6-4\,A^2\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"((4*A*a^3)/3 + 2*A*a^3*tan(c/2 + (d*x)/2) + 4*A*a^3*tan(c/2 + (d*x)/2)^2 - 2*A*a^3*tan(c/2 + (d*x)/2)^5)/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) + (2*A*a^3*atan((4*A^2*a^6)/(4*A^2*a^6 - 4*A^2*a^6*tan(c/2 + (d*x)/2)) + (4*A^2*a^6*tan(c/2 + (d*x)/2))/(4*A^2*a^6 - 4*A^2*a^6*tan(c/2 + (d*x)/2))))/d + (A*a^3*log(tan(c/2 + (d*x)/2)))/d","B"
229,1,226,79,13.193639,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x)^2,x)","\frac{A\,a^3\,\mathrm{atan}\left(\frac{A^2\,a^6}{4\,A^2\,a^6+A^2\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{4\,A^2\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,A^2\,a^6+A^2\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{3\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,A\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,A\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+A\,a^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{2\,A\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{A\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(A*a^3*atan((A^2*a^6)/(4*A^2*a^6 + A^2*a^6*tan(c/2 + (d*x)/2)) - (4*A^2*a^6*tan(c/2 + (d*x)/2))/(4*A^2*a^6 + A^2*a^6*tan(c/2 + (d*x)/2))))/d - (A*a^3 - 8*A*a^3*tan(c/2 + (d*x)/2) - 8*A*a^3*tan(c/2 + (d*x)/2)^3 + 3*A*a^3*tan(c/2 + (d*x)/2)^4)/(d*(2*tan(c/2 + (d*x)/2) + 4*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^5)) + (2*A*a^3*log(tan(c/2 + (d*x)/2)))/d + (A*a^3*tan(c/2 + (d*x)/2))/(2*d)","B"
230,1,220,78,13.500292,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x)^3,x)","\frac{A\,a^3\,\left(\frac{\cos\left(c+d\,x\right)}{2}-4\,\mathrm{atan}\left(\frac{\sqrt{17}\,\left(4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{17\,\cos\left(\frac{c}{2}-\mathrm{atan}\left(4\right)+\frac{d\,x}{2}\right)}\right)-\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\cos\left(2\,c+2\,d\,x\right)+\frac{\cos\left(3\,c+3\,d\,x\right)}{2}+2\,\sin\left(2\,c+2\,d\,x\right)+4\,\mathrm{atan}\left(\frac{\sqrt{17}\,\left(4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{17\,\cos\left(\frac{c}{2}-\mathrm{atan}\left(4\right)+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}-1\right)}{2\,d\,\left({\cos\left(c+d\,x\right)}^2-1\right)}","Not used",1,"(A*a^3*(cos(c + d*x)/2 - 4*atan((17^(1/2)*(4*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)))/(17*cos(c/2 - atan(4) + (d*x)/2))) - log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/2 + cos(2*c + 2*d*x) + cos(3*c + 3*d*x)/2 + 2*sin(2*c + 2*d*x) + 4*atan((17^(1/2)*(4*cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)))/(17*cos(c/2 - atan(4) + (d*x)/2)))*cos(2*c + 2*d*x) + (log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 - 1))/(2*d*(cos(c + d*x)^2 - 1))","B"
231,1,245,78,13.315565,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x)^4,x)","-\frac{\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}-\frac{A\,a^3\,\cos\left(3\,c+3\,d\,x\right)}{6}+\frac{A\,a^3\,\cos\left(c+d\,x\right)}{2}-\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,\cos\left(\frac{c}{2}+\frac{\pi }{4}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{A\,a^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{4}}{\frac{3\,d\,\sin\left(c+d\,x\right)}{4}-\frac{d\,\sin\left(3\,c+3\,d\,x\right)}{4}}","Not used",1,"-((A*a^3*sin(2*c + 2*d*x))/2 - (A*a^3*cos(3*c + 3*d*x))/6 + (A*a^3*cos(c + d*x))/2 - (A*a^3*sin(3*c + 3*d*x)*atan((2^(1/2)*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)))/(2*cos(c/2 + pi/4 + (d*x)/2))))/2 + (3*A*a^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (3*A*a^3*sin(c + d*x)*atan((2^(1/2)*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)))/(2*cos(c/2 + pi/4 + (d*x)/2))))/2 - (A*a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/4)/((3*d*sin(c + d*x))/4 - (d*sin(3*c + 3*d*x))/4)","B"
232,1,244,86,13.115925,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x)^5,x)","-\frac{A\,a^3\,\left(3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-16\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{192\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}","Not used",1,"-(A*a^3*(3*cos(c/2 + (d*x)/2)^8 - 3*sin(c/2 + (d*x)/2)^8 - 16*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^7 + 16*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2) - 24*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 48*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5 - 48*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3 + 24*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4))/(192*d*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4)","B"
233,1,244,105,13.155349,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x)^6,x)","-\frac{A\,a^3\,\left(3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-25\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+90\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-90\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+25\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+120\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}{480\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(A*a^3*(3*cos(c/2 + (d*x)/2)^10 - 3*sin(c/2 + (d*x)/2)^10 - 15*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - 25*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 90*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 90*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 25*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 120*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5))/(480*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)","B"
234,1,340,130,13.365456,"\text{Not used}","int(((A - A*sin(c + d*x))*(a + a*sin(c + d*x))^3)/sin(c + d*x)^7,x)","-\frac{A\,a^3\,\left(5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-24\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+360\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}{1920\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}","Not used",1,"-(A*a^3*(5*cos(c/2 + (d*x)/2)^12 - 5*sin(c/2 + (d*x)/2)^12 - 24*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^11 + 24*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2) - 45*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 - 40*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9 + 15*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 240*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7 - 240*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5 - 15*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 40*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3 + 45*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 360*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6))/(1920*d*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)","B"
235,1,326,129,17.076138,"\text{Not used}","int((sin(c + d*x)^4*(A - A*sin(c + d*x)))/(a + a*sin(c + d*x))^3,x)","\frac{\left(\frac{95\,A\,\left(c+d\,x\right)}{2}-\frac{A\,\left(1425\,c+1425\,d\,x+570\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(114\,A\,\left(c+d\,x\right)-\frac{A\,\left(3420\,c+3420\,d\,x+2850\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(190\,A\,\left(c+d\,x\right)-\frac{A\,\left(5700\,c+5700\,d\,x+6650\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(247\,A\,\left(c+d\,x\right)-\frac{A\,\left(7410\,c+7410\,d\,x+10450\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(247\,A\,\left(c+d\,x\right)-\frac{A\,\left(7410\,c+7410\,d\,x+12846\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(190\,A\,\left(c+d\,x\right)-\frac{A\,\left(5700\,c+5700\,d\,x+11270\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(114\,A\,\left(c+d\,x\right)-\frac{A\,\left(3420\,c+3420\,d\,x+7902\right)}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{95\,A\,\left(c+d\,x\right)}{2}-\frac{A\,\left(1425\,c+1425\,d\,x+3910\right)}{30}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{19\,A\,\left(c+d\,x\right)}{2}-\frac{A\,\left(285\,c+285\,d\,x+896\right)}{30}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}-\frac{19\,A\,x}{2\,a^3}","Not used",1,"(tan(c/2 + (d*x)/2)*((95*A*(c + d*x))/2 - (A*(1425*c + 1425*d*x + 3910))/30) + tan(c/2 + (d*x)/2)^8*((95*A*(c + d*x))/2 - (A*(1425*c + 1425*d*x + 570))/30) + tan(c/2 + (d*x)/2)^7*(114*A*(c + d*x) - (A*(3420*c + 3420*d*x + 2850))/30) + tan(c/2 + (d*x)/2)^2*(114*A*(c + d*x) - (A*(3420*c + 3420*d*x + 7902))/30) + tan(c/2 + (d*x)/2)^6*(190*A*(c + d*x) - (A*(5700*c + 5700*d*x + 6650))/30) + tan(c/2 + (d*x)/2)^3*(190*A*(c + d*x) - (A*(5700*c + 5700*d*x + 11270))/30) + tan(c/2 + (d*x)/2)^5*(247*A*(c + d*x) - (A*(7410*c + 7410*d*x + 10450))/30) + tan(c/2 + (d*x)/2)^4*(247*A*(c + d*x) - (A*(7410*c + 7410*d*x + 12846))/30) + (19*A*(c + d*x))/2 - (A*(285*c + 285*d*x + 896))/30)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^5*(tan(c/2 + (d*x)/2)^2 + 1)^2) - (19*A*x)/(2*a^3)","B"
236,1,261,103,16.929360,"\text{Not used}","int((sin(c + d*x)^3*(A - A*sin(c + d*x)))/(a + a*sin(c + d*x))^3,x)","\frac{4\,A\,x}{a^3}-\frac{\left(20\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(75\,c+75\,d\,x+30\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(44\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(165\,c+165\,d\,x+150\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(60\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(225\,c+225\,d\,x+320\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(60\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(225\,c+225\,d\,x+385\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(44\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(165\,c+165\,d\,x+367\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(20\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(75\,c+75\,d\,x+205\right)}{15}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,A\,\left(c+d\,x\right)-\frac{4\,A\,\left(15\,c+15\,d\,x+47\right)}{15}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(4*A*x)/a^3 - (tan(c/2 + (d*x)/2)*(20*A*(c + d*x) - (4*A*(75*c + 75*d*x + 205))/15) + tan(c/2 + (d*x)/2)^6*(20*A*(c + d*x) - (4*A*(75*c + 75*d*x + 30))/15) + tan(c/2 + (d*x)/2)^5*(44*A*(c + d*x) - (4*A*(165*c + 165*d*x + 150))/15) + tan(c/2 + (d*x)/2)^2*(44*A*(c + d*x) - (4*A*(165*c + 165*d*x + 367))/15) + tan(c/2 + (d*x)/2)^4*(60*A*(c + d*x) - (4*A*(225*c + 225*d*x + 320))/15) + tan(c/2 + (d*x)/2)^3*(60*A*(c + d*x) - (4*A*(225*c + 225*d*x + 385))/15) + 4*A*(c + d*x) - (4*A*(15*c + 15*d*x + 47))/15)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^5*(tan(c/2 + (d*x)/2)^2 + 1))","B"
237,1,178,89,14.924330,"\text{Not used}","int((sin(c + d*x)^2*(A - A*sin(c + d*x)))/(a + a*sin(c + d*x))^3,x)","\frac{\left(5\,A\,\left(c+d\,x\right)-\frac{A\,\left(25\,c+25\,d\,x+10\right)}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(10\,A\,\left(c+d\,x\right)-\frac{A\,\left(50\,c+50\,d\,x+50\right)}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(10\,A\,\left(c+d\,x\right)-\frac{A\,\left(50\,c+50\,d\,x+110\right)}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(5\,A\,\left(c+d\,x\right)-\frac{A\,\left(25\,c+25\,d\,x+70\right)}{5}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+A\,\left(c+d\,x\right)-\frac{A\,\left(5\,c+5\,d\,x+16\right)}{5}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}-\frac{A\,x}{a^3}","Not used",1,"(tan(c/2 + (d*x)/2)*(5*A*(c + d*x) - (A*(25*c + 25*d*x + 70))/5) + tan(c/2 + (d*x)/2)^4*(5*A*(c + d*x) - (A*(25*c + 25*d*x + 10))/5) + tan(c/2 + (d*x)/2)^3*(10*A*(c + d*x) - (A*(50*c + 50*d*x + 50))/5) + tan(c/2 + (d*x)/2)^2*(10*A*(c + d*x) - (A*(50*c + 50*d*x + 110))/5) + A*(c + d*x) - (A*(5*c + 5*d*x + 16))/5)/(a^3*d*(tan(c/2 + (d*x)/2) + 1)^5) - (A*x)/a^3","B"
238,1,110,82,13.447762,"\text{Not used}","int((sin(c + d*x)*(A - A*sin(c + d*x)))/(a + a*sin(c + d*x))^3,x)","-\frac{2\,A\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}{15\,a^3\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^5}","Not used",1,"-(2*A*cos(c/2 + (d*x)/2)^2*(cos(c/2 + (d*x)/2)^3 + 15*sin(c/2 + (d*x)/2)^3 - 5*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^2 + 5*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)))/(15*a^3*d*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^5)","B"
239,1,134,58,13.308878,"\text{Not used}","int((A - A*sin(c + d*x))/(a + a*sin(c + d*x))^3,x)","-\frac{2\,A\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+25\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{15\,a^3\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^5}","Not used",1,"-(2*A*cos(c/2 + (d*x)/2)*(4*cos(c/2 + (d*x)/2)^4 + 15*sin(c/2 + (d*x)/2)^4 + 15*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^3 + 5*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2) + 25*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2))/(15*a^3*d*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^5)","B"
240,1,199,98,14.770728,"\text{Not used}","int((A - A*sin(c + d*x))/(sin(c + d*x)*(a + a*sin(c + d*x))^3),x)","\frac{A\,\left(5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+90\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+150\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+110\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+25\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+50\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+50\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+25\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+26\right)}{5\,a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}","Not used",1,"(A*(5*log(tan(c/2 + (d*x)/2)) + 90*tan(c/2 + (d*x)/2) + 150*tan(c/2 + (d*x)/2)^2 + 110*tan(c/2 + (d*x)/2)^3 + 40*tan(c/2 + (d*x)/2)^4 + 25*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2) + 50*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^2 + 50*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^3 + 25*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^4 + 5*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^5 + 26))/(5*a^3*d*(tan(c/2 + (d*x)/2) + 1)^5)","B"
241,1,210,113,15.774073,"\text{Not used}","int((A - A*sin(c + d*x))/(sin(c + d*x)^2*(a + a*sin(c + d*x))^3),x)","\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{4\,A\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{37\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+121\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{514\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{338\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{491\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+A}{d\,\left(2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(A*tan(c/2 + (d*x)/2))/(2*a^3*d) - (4*A*log(tan(c/2 + (d*x)/2)))/(a^3*d) - (A + (491*A*tan(c/2 + (d*x)/2))/15 + (338*A*tan(c/2 + (d*x)/2)^2)/3 + (514*A*tan(c/2 + (d*x)/2)^3)/3 + 121*A*tan(c/2 + (d*x)/2)^4 + 37*A*tan(c/2 + (d*x)/2)^5)/(d*(10*a^3*tan(c/2 + (d*x)/2)^2 + 20*a^3*tan(c/2 + (d*x)/2)^3 + 20*a^3*tan(c/2 + (d*x)/2)^4 + 10*a^3*tan(c/2 + (d*x)/2)^5 + 2*a^3*tan(c/2 + (d*x)/2)^6 + 2*a^3*tan(c/2 + (d*x)/2)))","B"
242,1,288,138,15.741132,"\text{Not used}","int((A - A*sin(c + d*x))/(sin(c + d*x)^3*(a + a*sin(c + d*x))^3),x)","\frac{A\,\left(165\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4234\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+14090\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+19780\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+12060\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+1830\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-1050\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-165\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+1140\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+5700\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+11400\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+11400\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+5700\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1140\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-15\right)}{120\,a^3\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}","Not used",1,"(A*(165*tan(c/2 + (d*x)/2) + 4234*tan(c/2 + (d*x)/2)^2 + 14090*tan(c/2 + (d*x)/2)^3 + 19780*tan(c/2 + (d*x)/2)^4 + 12060*tan(c/2 + (d*x)/2)^5 + 1830*tan(c/2 + (d*x)/2)^6 - 1050*tan(c/2 + (d*x)/2)^7 - 165*tan(c/2 + (d*x)/2)^8 + 15*tan(c/2 + (d*x)/2)^9 + 1140*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^2 + 5700*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^3 + 11400*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^4 + 11400*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^5 + 5700*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^6 + 1140*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^7 - 15))/(120*a^3*d*tan(c/2 + (d*x)/2)^2*(tan(c/2 + (d*x)/2) + 1)^5)","B"
243,1,314,153,15.280173,"\text{Not used}","int((A - A*sin(c + d*x))/(sin(c + d*x)^4*(a + a*sin(c + d*x))^3),x)","-\frac{A\,\left(335\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-35\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7559\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24610\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+33170\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+18670\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1310\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-2375\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-335\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+2160\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10800\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+21600\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+21600\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10800\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2160\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+5\right)}{120\,a^3\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}","Not used",1,"-(A*(335*tan(c/2 + (d*x)/2)^2 - 35*tan(c/2 + (d*x)/2) + 7559*tan(c/2 + (d*x)/2)^3 + 24610*tan(c/2 + (d*x)/2)^4 + 33170*tan(c/2 + (d*x)/2)^5 + 18670*tan(c/2 + (d*x)/2)^6 + 1310*tan(c/2 + (d*x)/2)^7 - 2375*tan(c/2 + (d*x)/2)^8 - 335*tan(c/2 + (d*x)/2)^9 + 35*tan(c/2 + (d*x)/2)^10 - 5*tan(c/2 + (d*x)/2)^11 + 2160*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^3 + 10800*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^4 + 21600*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^5 + 21600*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^6 + 10800*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^7 + 2160*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^8 + 5))/(120*a^3*d*tan(c/2 + (d*x)/2)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
244,1,830,327,15.575597,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,c^3+3\,A\,d^3+4\,B\,c^3+3\,B\,d^3+12\,A\,c\,d^2+12\,A\,c^2\,d+9\,B\,c\,d^2+12\,B\,c^2\,d\right)}{4\,\left(2\,A\,a\,c^3+\frac{3\,A\,a\,d^3}{4}+B\,a\,c^3+\frac{3\,B\,a\,d^3}{4}+3\,A\,a\,c\,d^2+3\,A\,a\,c^2\,d+\frac{9\,B\,a\,c\,d^2}{4}+3\,B\,a\,c^2\,d\right)}\right)\,\left(8\,A\,c^3+3\,A\,d^3+4\,B\,c^3+3\,B\,d^3+12\,A\,c\,d^2+12\,A\,c^2\,d+9\,B\,c\,d^2+12\,B\,c^2\,d\right)}{4\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{3\,A\,a\,d^3}{4}+B\,a\,c^3+\frac{3\,B\,a\,d^3}{4}+3\,A\,a\,c\,d^2+3\,A\,a\,c^2\,d+\frac{9\,B\,a\,c\,d^2}{4}+3\,B\,a\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,A\,a\,c^3+2\,B\,a\,c^3+6\,A\,a\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(8\,A\,a\,c^3+\frac{20\,A\,a\,d^3}{3}+8\,B\,a\,c^3+\frac{16\,B\,a\,d^3}{3}+20\,A\,a\,c\,d^2+24\,A\,a\,c^2\,d+20\,B\,a\,c\,d^2+20\,B\,a\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(12\,A\,a\,c^3+\frac{28\,A\,a\,d^3}{3}+12\,B\,a\,c^3+\frac{32\,B\,a\,d^3}{3}+28\,A\,a\,c\,d^2+36\,A\,a\,c^2\,d+28\,B\,a\,c\,d^2+28\,B\,a\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(8\,A\,a\,c^3+4\,A\,a\,d^3+8\,B\,a\,c^3+12\,A\,a\,c\,d^2+24\,A\,a\,c^2\,d+12\,B\,a\,c\,d^2+12\,B\,a\,c^2\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(\frac{3\,A\,a\,d^3}{4}+B\,a\,c^3+\frac{3\,B\,a\,d^3}{4}+3\,A\,a\,c\,d^2+3\,A\,a\,c^2\,d+\frac{9\,B\,a\,c\,d^2}{4}+3\,B\,a\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{7\,A\,a\,d^3}{2}+2\,B\,a\,c^3+\frac{7\,B\,a\,d^3}{2}+6\,A\,a\,c\,d^2+6\,A\,a\,c^2\,d+\frac{21\,B\,a\,c\,d^2}{2}+6\,B\,a\,c^2\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(\frac{7\,A\,a\,d^3}{2}+2\,B\,a\,c^3+\frac{7\,B\,a\,d^3}{2}+6\,A\,a\,c\,d^2+6\,A\,a\,c^2\,d+\frac{21\,B\,a\,c\,d^2}{2}+6\,B\,a\,c^2\,d\right)+2\,A\,a\,c^3+\frac{4\,A\,a\,d^3}{3}+2\,B\,a\,c^3+\frac{16\,B\,a\,d^3}{15}+4\,A\,a\,c\,d^2+6\,A\,a\,c^2\,d+4\,B\,a\,c\,d^2+4\,B\,a\,c^2\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(e/2 + (f*x)/2)*(8*A*c^3 + 3*A*d^3 + 4*B*c^3 + 3*B*d^3 + 12*A*c*d^2 + 12*A*c^2*d + 9*B*c*d^2 + 12*B*c^2*d))/(4*(2*A*a*c^3 + (3*A*a*d^3)/4 + B*a*c^3 + (3*B*a*d^3)/4 + 3*A*a*c*d^2 + 3*A*a*c^2*d + (9*B*a*c*d^2)/4 + 3*B*a*c^2*d)))*(8*A*c^3 + 3*A*d^3 + 4*B*c^3 + 3*B*d^3 + 12*A*c*d^2 + 12*A*c^2*d + 9*B*c*d^2 + 12*B*c^2*d))/(4*f) - (tan(e/2 + (f*x)/2)*((3*A*a*d^3)/4 + B*a*c^3 + (3*B*a*d^3)/4 + 3*A*a*c*d^2 + 3*A*a*c^2*d + (9*B*a*c*d^2)/4 + 3*B*a*c^2*d) + tan(e/2 + (f*x)/2)^8*(2*A*a*c^3 + 2*B*a*c^3 + 6*A*a*c^2*d) + tan(e/2 + (f*x)/2)^2*(8*A*a*c^3 + (20*A*a*d^3)/3 + 8*B*a*c^3 + (16*B*a*d^3)/3 + 20*A*a*c*d^2 + 24*A*a*c^2*d + 20*B*a*c*d^2 + 20*B*a*c^2*d) + tan(e/2 + (f*x)/2)^4*(12*A*a*c^3 + (28*A*a*d^3)/3 + 12*B*a*c^3 + (32*B*a*d^3)/3 + 28*A*a*c*d^2 + 36*A*a*c^2*d + 28*B*a*c*d^2 + 28*B*a*c^2*d) + tan(e/2 + (f*x)/2)^6*(8*A*a*c^3 + 4*A*a*d^3 + 8*B*a*c^3 + 12*A*a*c*d^2 + 24*A*a*c^2*d + 12*B*a*c*d^2 + 12*B*a*c^2*d) - tan(e/2 + (f*x)/2)^9*((3*A*a*d^3)/4 + B*a*c^3 + (3*B*a*d^3)/4 + 3*A*a*c*d^2 + 3*A*a*c^2*d + (9*B*a*c*d^2)/4 + 3*B*a*c^2*d) + tan(e/2 + (f*x)/2)^3*((7*A*a*d^3)/2 + 2*B*a*c^3 + (7*B*a*d^3)/2 + 6*A*a*c*d^2 + 6*A*a*c^2*d + (21*B*a*c*d^2)/2 + 6*B*a*c^2*d) - tan(e/2 + (f*x)/2)^7*((7*A*a*d^3)/2 + 2*B*a*c^3 + (7*B*a*d^3)/2 + 6*A*a*c*d^2 + 6*A*a*c^2*d + (21*B*a*c*d^2)/2 + 6*B*a*c^2*d) + 2*A*a*c^3 + (4*A*a*d^3)/3 + 2*B*a*c^3 + (16*B*a*d^3)/15 + 4*A*a*c*d^2 + 6*A*a*c^2*d + 4*B*a*c*d^2 + 4*B*a*c^2*d)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1))","B"
245,1,547,213,15.413389,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^2,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,c^2+4\,A\,d^2+4\,B\,c^2+3\,B\,d^2+8\,A\,c\,d+8\,B\,c\,d\right)}{4\,\left(2\,A\,a\,c^2+A\,a\,d^2+B\,a\,c^2+\frac{3\,B\,a\,d^2}{4}+2\,A\,a\,c\,d+2\,B\,a\,c\,d\right)}\right)\,\left(8\,A\,c^2+4\,A\,d^2+4\,B\,c^2+3\,B\,d^2+8\,A\,c\,d+8\,B\,c\,d\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,A\,a\,c^2+2\,B\,a\,c^2+4\,A\,a\,c\,d\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a\,d^2+B\,a\,c^2+\frac{3\,B\,a\,d^2}{4}+2\,A\,a\,c\,d+2\,B\,a\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(6\,A\,a\,c^2+4\,A\,a\,d^2+6\,B\,a\,c^2+4\,B\,a\,d^2+12\,A\,a\,c\,d+8\,B\,a\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(6\,A\,a\,c^2+\frac{16\,A\,a\,d^2}{3}+6\,B\,a\,c^2+\frac{16\,B\,a\,d^2}{3}+12\,A\,a\,c\,d+\frac{32\,B\,a\,c\,d}{3}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(A\,a\,d^2+B\,a\,c^2+\frac{3\,B\,a\,d^2}{4}+2\,A\,a\,c\,d+2\,B\,a\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a\,d^2+B\,a\,c^2+\frac{11\,B\,a\,d^2}{4}+2\,A\,a\,c\,d+2\,B\,a\,c\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(A\,a\,d^2+B\,a\,c^2+\frac{11\,B\,a\,d^2}{4}+2\,A\,a\,c\,d+2\,B\,a\,c\,d\right)+2\,A\,a\,c^2+\frac{4\,A\,a\,d^2}{3}+2\,B\,a\,c^2+\frac{4\,B\,a\,d^2}{3}+4\,A\,a\,c\,d+\frac{8\,B\,a\,c\,d}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atan((a*tan(e/2 + (f*x)/2)*(8*A*c^2 + 4*A*d^2 + 4*B*c^2 + 3*B*d^2 + 8*A*c*d + 8*B*c*d))/(4*(2*A*a*c^2 + A*a*d^2 + B*a*c^2 + (3*B*a*d^2)/4 + 2*A*a*c*d + 2*B*a*c*d)))*(8*A*c^2 + 4*A*d^2 + 4*B*c^2 + 3*B*d^2 + 8*A*c*d + 8*B*c*d))/(4*f) - (tan(e/2 + (f*x)/2)^6*(2*A*a*c^2 + 2*B*a*c^2 + 4*A*a*c*d) + tan(e/2 + (f*x)/2)*(A*a*d^2 + B*a*c^2 + (3*B*a*d^2)/4 + 2*A*a*c*d + 2*B*a*c*d) + tan(e/2 + (f*x)/2)^4*(6*A*a*c^2 + 4*A*a*d^2 + 6*B*a*c^2 + 4*B*a*d^2 + 12*A*a*c*d + 8*B*a*c*d) + tan(e/2 + (f*x)/2)^2*(6*A*a*c^2 + (16*A*a*d^2)/3 + 6*B*a*c^2 + (16*B*a*d^2)/3 + 12*A*a*c*d + (32*B*a*c*d)/3) - tan(e/2 + (f*x)/2)^7*(A*a*d^2 + B*a*c^2 + (3*B*a*d^2)/4 + 2*A*a*c*d + 2*B*a*c*d) + tan(e/2 + (f*x)/2)^3*(A*a*d^2 + B*a*c^2 + (11*B*a*d^2)/4 + 2*A*a*c*d + 2*B*a*c*d) - tan(e/2 + (f*x)/2)^5*(A*a*d^2 + B*a*c^2 + (11*B*a*d^2)/4 + 2*A*a*c*d + 2*B*a*c*d) + 2*A*a*c^2 + (4*A*a*d^2)/3 + 2*B*a*c^2 + (4*B*a*d^2)/3 + 4*A*a*c*d + (8*B*a*c*d)/3)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1))","B"
246,1,134,111,13.314296,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c + d*sin(e + f*x)),x)","-\frac{\frac{3\,A\,a\,d\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{B\,a\,d\,\cos\left(3\,e+3\,f\,x\right)}{2}+\frac{3\,B\,a\,c\,\sin\left(2\,e+2\,f\,x\right)}{2}+\frac{3\,B\,a\,d\,\sin\left(2\,e+2\,f\,x\right)}{2}+6\,A\,a\,c\,\cos\left(e+f\,x\right)+6\,A\,a\,d\,\cos\left(e+f\,x\right)+6\,B\,a\,c\,\cos\left(e+f\,x\right)+\frac{9\,B\,a\,d\,\cos\left(e+f\,x\right)}{2}-6\,A\,a\,c\,f\,x-3\,A\,a\,d\,f\,x-3\,B\,a\,c\,f\,x-3\,B\,a\,d\,f\,x}{6\,f}","Not used",1,"-((3*A*a*d*sin(2*e + 2*f*x))/2 - (B*a*d*cos(3*e + 3*f*x))/2 + (3*B*a*c*sin(2*e + 2*f*x))/2 + (3*B*a*d*sin(2*e + 2*f*x))/2 + 6*A*a*c*cos(e + f*x) + 6*A*a*d*cos(e + f*x) + 6*B*a*c*cos(e + f*x) + (9*B*a*d*cos(e + f*x))/2 - 6*A*a*c*f*x - 3*A*a*d*f*x - 3*B*a*c*f*x - 3*B*a*d*f*x)/(6*f)","B"
247,1,100,48,13.262693,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x)),x)","A\,a\,x-\frac{-B\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\left(2\,A\,a+2\,B\,a\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+B\,a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A\,a+2\,B\,a}{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{B\,a\,x}{2}","Not used",1,"A*a*x - (2*A*a + 2*B*a + tan(e/2 + (f*x)/2)^2*(2*A*a + 2*B*a) - B*a*tan(e/2 + (f*x)/2)^3 + B*a*tan(e/2 + (f*x)/2))/(f*(2*tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^4 + 1)) + (B*a*x)/2","B"
248,1,3074,98,16.580326,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c + d*sin(e + f*x)),x)","\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f\,\left(c+d\right)}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{f\,\left(c+d\right)}-\frac{B\,a\,\cos\left(e+f\,x\right)}{f\,\left(c+d\right)}+\frac{2\,A\,a\,c\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{d\,f\,\left(c+d\right)}-\frac{A\,a\,\mathrm{atan}\left(\frac{A^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}+A^2\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-B^2\,c^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-B^2\,c^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+B^2\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+A\,B\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+A^2\,c\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+A^2\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+B^2\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+B^2\,c^3\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+B^2\,c^5\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+A^2\,c\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+A^2\,c^2\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+A^2\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-B^2\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A^2\,c^2\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,3{}\mathrm{i}-A^2\,c^3\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A^2\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+B^2\,c^2\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}-B^2\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+B^2\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+A\,B\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,6{}\mathrm{i}+A\,B\,c\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+A\,B\,c^3\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+A\,B\,c^5\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}-A\,B\,c^2\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+A\,B\,c^2\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c^4\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}-A\,B\,c^3\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,10{}\mathrm{i}+A\,B\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{4\,A^2\,d^7\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,B^2\,d^7\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A^2\,c^2\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,A^2\,c^3\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,A^2\,c^4\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,B^2\,c^3\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+B^2\,c^5\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,A^2\,c^2\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,A^2\,c^3\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,B^2\,c^2\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,B^2\,c^4\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A\,B\,d^7\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A^2\,c\,d^6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+B^2\,c\,d^6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A^2\,c\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,A\,B\,c^3\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A\,B\,c^5\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-8\,A\,B\,c^2\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A\,B\,c^4\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A\,B\,c\,d^6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{d\,f\,\left(c+d\right)}-\frac{2\,B\,a\,c^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)}{d^2\,f\,\left(c+d\right)}-\frac{B\,a\,c\,\cos\left(e+f\,x\right)}{d\,f\,\left(c+d\right)}+\frac{B\,a\,c\,\mathrm{atan}\left(\frac{A^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}+A^2\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-B^2\,c^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}-B^2\,c^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+B^2\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+A\,B\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+A^2\,c\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+A^2\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+B^2\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+B^2\,c^3\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,1{}\mathrm{i}+B^2\,c^5\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}+A^2\,c\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}+A^2\,c^2\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+A^2\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,1{}\mathrm{i}-B^2\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A^2\,c^2\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+A^2\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,3{}\mathrm{i}-A^2\,c^3\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A^2\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}+B^2\,c^2\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,3{}\mathrm{i}-B^2\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+B^2\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+A\,B\,c\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,6{}\mathrm{i}+A\,B\,c\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}+A\,B\,c^3\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,4{}\mathrm{i}+A\,B\,c^5\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,4{}\mathrm{i}-A\,B\,c^2\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,{\left(d^2-c^2\right)}^{3/2}\,2{}\mathrm{i}+A\,B\,c^2\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c^3\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c^4\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}-A\,B\,c^2\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,6{}\mathrm{i}-A\,B\,c^3\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,10{}\mathrm{i}+A\,B\,c^4\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{4\,A^2\,d^7\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,B^2\,d^7\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A^2\,c^2\,d^5\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,A^2\,c^3\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,A^2\,c^4\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-2\,B^2\,c^3\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+B^2\,c^5\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,A^2\,c^2\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,A^2\,c^3\,d^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,B^2\,c^2\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,B^2\,c^4\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A\,B\,d^7\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A^2\,c\,d^6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+B^2\,c\,d^6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A^2\,c\,d^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-4\,A\,B\,c^3\,d^4\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A\,B\,c^5\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-8\,A\,B\,c^2\,d^5\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+4\,A\,B\,c^4\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A\,B\,c\,d^6\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}\right)\,\sqrt{d^2-c^2}\,2{}\mathrm{i}}{d^2\,f\,\left(c+d\right)}","Not used",1,"(2*A*a*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(f*(c + d)) + (2*B*a*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(f*(c + d)) - (B*a*cos(e + f*x))/(f*(c + d)) + (2*A*a*c*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(d*f*(c + d)) - (A*a*atan((A^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i + A^2*d^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - B^2*c^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i - B^2*c^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + B^2*d^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + A*B*d^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i + A^2*c*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*1i + A^2*c*d^5*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + B^2*c*d^5*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + B^2*c^3*d*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*1i + B^2*c^5*d*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + A^2*c*d^5*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i + A^2*c^2*d^4*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + A^2*c^3*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - B^2*c^3*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A^2*c^2*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i + A^2*c^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*3i - A^2*c^3*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A^2*c^4*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + B^2*c^2*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i - B^2*c^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + B^2*c^4*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + A*B*c*d^5*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*6i + A*B*c*d^5*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + A*B*c^3*d*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*4i + A*B*c^5*d*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i - A*B*c^2*d^2*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i + A*B*c^2*d^4*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c^3*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c^4*d^2*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i - A*B*c^3*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*10i + A*B*c^4*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i)/(4*A^2*d^7*sin(e/2 + (f*x)/2) + 2*B^2*d^7*sin(e/2 + (f*x)/2) + 2*A^2*c^2*d^5*cos(e/2 + (f*x)/2) - 2*A^2*c^3*d^4*cos(e/2 + (f*x)/2) - 2*A^2*c^4*d^3*cos(e/2 + (f*x)/2) - 2*B^2*c^3*d^4*cos(e/2 + (f*x)/2) + B^2*c^5*d^2*cos(e/2 + (f*x)/2) - 4*A^2*c^2*d^5*sin(e/2 + (f*x)/2) - 4*A^2*c^3*d^4*sin(e/2 + (f*x)/2) - 4*B^2*c^2*d^5*sin(e/2 + (f*x)/2) + 2*B^2*c^4*d^3*sin(e/2 + (f*x)/2) + 4*A*B*d^7*sin(e/2 + (f*x)/2) + 2*A^2*c*d^6*cos(e/2 + (f*x)/2) + B^2*c*d^6*cos(e/2 + (f*x)/2) + 4*A^2*c*d^6*sin(e/2 + (f*x)/2) - 4*A*B*c^3*d^4*cos(e/2 + (f*x)/2) + 2*A*B*c^5*d^2*cos(e/2 + (f*x)/2) - 8*A*B*c^2*d^5*sin(e/2 + (f*x)/2) + 4*A*B*c^4*d^3*sin(e/2 + (f*x)/2) + 2*A*B*c*d^6*cos(e/2 + (f*x)/2)))*(d^2 - c^2)^(1/2)*2i)/(d*f*(c + d)) - (2*B*a*c^2*atan(sin(e/2 + (f*x)/2)/cos(e/2 + (f*x)/2)))/(d^2*f*(c + d)) - (B*a*c*cos(e + f*x))/(d*f*(c + d)) + (B*a*c*atan((A^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i + A^2*d^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - B^2*c^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i - B^2*c^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + B^2*d^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + A*B*d^6*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i + A^2*c*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*1i + A^2*c*d^5*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + B^2*c*d^5*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + B^2*c^3*d*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*1i + B^2*c^5*d*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i + A^2*c*d^5*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i + A^2*c^2*d^4*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + A^2*c^3*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*1i - B^2*c^3*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A^2*c^2*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i + A^2*c^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*3i - A^2*c^3*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A^2*c^4*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i + B^2*c^2*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*3i - B^2*c^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + B^2*c^4*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + A*B*c*d^5*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*6i + A*B*c*d^5*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i + A*B*c^3*d*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*4i + A*B*c^5*d*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*4i - A*B*c^2*d^2*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(3/2)*2i + A*B*c^2*d^4*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c^3*d^3*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c^4*d^2*cos(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i - A*B*c^2*d^4*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*6i - A*B*c^3*d^3*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*10i + A*B*c^4*d^2*sin(e/2 + (f*x)/2)*(d^2 - c^2)^(1/2)*2i)/(4*A^2*d^7*sin(e/2 + (f*x)/2) + 2*B^2*d^7*sin(e/2 + (f*x)/2) + 2*A^2*c^2*d^5*cos(e/2 + (f*x)/2) - 2*A^2*c^3*d^4*cos(e/2 + (f*x)/2) - 2*A^2*c^4*d^3*cos(e/2 + (f*x)/2) - 2*B^2*c^3*d^4*cos(e/2 + (f*x)/2) + B^2*c^5*d^2*cos(e/2 + (f*x)/2) - 4*A^2*c^2*d^5*sin(e/2 + (f*x)/2) - 4*A^2*c^3*d^4*sin(e/2 + (f*x)/2) - 4*B^2*c^2*d^5*sin(e/2 + (f*x)/2) + 2*B^2*c^4*d^3*sin(e/2 + (f*x)/2) + 4*A*B*d^7*sin(e/2 + (f*x)/2) + 2*A^2*c*d^6*cos(e/2 + (f*x)/2) + B^2*c*d^6*cos(e/2 + (f*x)/2) + 4*A^2*c*d^6*sin(e/2 + (f*x)/2) - 4*A*B*c^3*d^4*cos(e/2 + (f*x)/2) + 2*A*B*c^5*d^2*cos(e/2 + (f*x)/2) - 8*A*B*c^2*d^5*sin(e/2 + (f*x)/2) + 4*A*B*c^4*d^3*sin(e/2 + (f*x)/2) + 2*A*B*c*d^6*cos(e/2 + (f*x)/2)))*(d^2 - c^2)^(1/2)*2i)/(d^2*f*(c + d))","B"
249,1,5102,124,20.316493,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c + d*sin(e + f*x))^2,x)","-\frac{\frac{2\,\left(A\,a\,d-B\,a\,c\right)}{d\,\left(c+d\right)}+\frac{2\,a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d-B\,c\right)}{c\,\left(c+d\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\frac{B\,a\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{B\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{B\,a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)}{d^2}+\frac{B\,a\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{B\,a\,\left(\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{B\,a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)}{d^2}}{\frac{64\,\left(-A^2\,B\,a^3\,c\,d^2+A\,B^2\,a^3\,c^3+A\,B^2\,a^3\,c^2\,d-2\,A\,B^2\,a^3\,c\,d^2+B^3\,a^3\,c^3+B^3\,a^3\,c^2\,d-B^3\,a^3\,c\,d^2\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,B^3\,a^3\,c^4-4\,B^3\,a^3\,c^3\,d+2\,B^3\,a^3\,c\,d^3+2\,A\,B^2\,a^3\,c^2\,d^2+2\,A\,B^2\,a^3\,c\,d^3\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{B\,a\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{B\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{B\,a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}+\frac{B\,a\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{B\,a\,\left(\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{B\,a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}\right)\,1{}\mathrm{i}}{d^2}}\right)}{d^2\,f}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)\,1{}\mathrm{i}}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}+\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)\,1{}\mathrm{i}}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}}{\frac{64\,\left(-A^2\,B\,a^3\,c\,d^2+A\,B^2\,a^3\,c^3+A\,B^2\,a^3\,c^2\,d-2\,A\,B^2\,a^3\,c\,d^2+B^3\,a^3\,c^3+B^3\,a^3\,c^2\,d-B^3\,a^3\,c\,d^2\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,B^3\,a^3\,c^4-4\,B^3\,a^3\,c^3\,d+2\,B^3\,a^3\,c\,d^3+2\,A\,B^2\,a^3\,c^2\,d^2+2\,A\,B^2\,a^3\,c\,d^3\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}-\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}+\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(B^2\,a^2\,c^4\,d+2\,B^2\,a^2\,c^3\,d^2+B^2\,a^2\,c^2\,d^3\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-A^2\,a^2\,c\,d^5+2\,A\,B\,a^2\,c^3\,d^3+2\,A\,B\,a^2\,c^2\,d^4-2\,A\,B\,a^2\,c\,d^5-2\,B^2\,a^2\,c^5\,d-4\,B^2\,a^2\,c^4\,d^2+2\,B^2\,a^2\,c^3\,d^3+6\,B^2\,a^2\,c^2\,d^4+B^2\,a^2\,c\,d^5\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(B\,a\,c\,d^6-A\,a\,c^2\,d^5-A\,a\,c^3\,d^4+B\,a\,c^2\,d^5\right)}{c^2\,d^2+2\,c\,d^3+d^4}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a\,c\,d^7+2\,B\,a\,c\,d^7+2\,A\,a\,c^2\,d^6-4\,B\,a\,c^3\,d^5-2\,B\,a\,c^4\,d^4\right)}{c^2\,d^3+2\,c\,d^4+d^5}+\frac{a\,\left(\frac{32\,\left(c^4\,d^5+2\,c^3\,d^6+c^2\,d^7\right)}{c^2\,d^2+2\,c\,d^3+d^4}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^5-4\,c^4\,d^6+c^3\,d^7+6\,c^2\,d^8+3\,c\,d^9\right)}{c^2\,d^3+2\,c\,d^4+d^5}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}\right)\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)}{-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6}}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(A\,d^2-B\,c^2+B\,d^2-B\,c\,d\right)\,2{}\mathrm{i}}{f\,\left(-c^4\,d^2-2\,c^3\,d^3+2\,c\,d^5+d^6\right)}","Not used",1,"(2*B*a*atan(((B*a*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (B*a*((32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) - (32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (B*a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*1i)/d^2)*1i)/d^2))/d^2 + (B*a*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (B*a*((32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) + (B*a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*1i)/d^2)*1i)/d^2))/d^2)/((64*(B^3*a^3*c^3 + A*B^2*a^3*c^3 - B^3*a^3*c*d^2 + B^3*a^3*c^2*d - 2*A*B^2*a^3*c*d^2 + A*B^2*a^3*c^2*d - A^2*B*a^3*c*d^2))/(2*c*d^3 + d^4 + c^2*d^2) - (64*tan(e/2 + (f*x)/2)*(2*B^3*a^3*c*d^3 - 2*B^3*a^3*c^4 - 4*B^3*a^3*c^3*d + 2*A*B^2*a^3*c*d^3 + 2*A*B^2*a^3*c^2*d^2))/(2*c*d^4 + d^5 + c^2*d^3) - (B*a*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (B*a*((32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) - (32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (B*a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*1i)/d^2)*1i)/d^2)*1i)/d^2 + (B*a*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (B*a*((32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) + (B*a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*1i)/d^2)*1i)/d^2)*1i)/d^2)))/(d^2*f) - ((2*(A*a*d - B*a*c))/(d*(c + d)) + (2*a*tan(e/2 + (f*x)/2)*(A*d - B*c))/(c*(c + d)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + c*tan(e/2 + (f*x)/2)^2)) + (a*atan(((a*(-(c + d)^3*(c - d))^(1/2)*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (a*(-(c + d)^3*(c - d))^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) - (32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d)*1i)/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2) + (a*(-(c + d)^3*(c - d))^(1/2)*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (a*(-(c + d)^3*(c - d))^(1/2)*((32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) + (a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d)*1i)/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))/((64*(B^3*a^3*c^3 + A*B^2*a^3*c^3 - B^3*a^3*c*d^2 + B^3*a^3*c^2*d - 2*A*B^2*a^3*c*d^2 + A*B^2*a^3*c^2*d - A^2*B*a^3*c*d^2))/(2*c*d^3 + d^4 + c^2*d^2) - (64*tan(e/2 + (f*x)/2)*(2*B^3*a^3*c*d^3 - 2*B^3*a^3*c^4 - 4*B^3*a^3*c^3*d + 2*A*B^2*a^3*c*d^3 + 2*A*B^2*a^3*c^2*d^2))/(2*c*d^4 + d^5 + c^2*d^3) - (a*(-(c + d)^3*(c - d))^(1/2)*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (a*(-(c + d)^3*(c - d))^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) - (32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2) + (a*(-(c + d)^3*(c - d))^(1/2)*((32*(B^2*a^2*c^2*d^3 + 2*B^2*a^2*c^3*d^2 + B^2*a^2*c^4*d))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(6*B^2*a^2*c^2*d^4 + 2*B^2*a^2*c^3*d^3 - 4*B^2*a^2*c^4*d^2 - A^2*a^2*c*d^5 + B^2*a^2*c*d^5 - 2*B^2*a^2*c^5*d + 2*A*B*a^2*c^2*d^4 + 2*A*B*a^2*c^3*d^3 - 2*A*B*a^2*c*d^5))/(2*c*d^4 + d^5 + c^2*d^3) + (a*(-(c + d)^3*(c - d))^(1/2)*((32*(B*a*c*d^6 - A*a*c^2*d^5 - A*a*c^3*d^4 + B*a*c^2*d^5))/(2*c*d^3 + d^4 + c^2*d^2) - (32*tan(e/2 + (f*x)/2)*(2*A*a*c*d^7 + 2*B*a*c*d^7 + 2*A*a*c^2*d^6 - 4*B*a*c^3*d^5 - 2*B*a*c^4*d^4))/(2*c*d^4 + d^5 + c^2*d^3) + (a*((32*(c^2*d^7 + 2*c^3*d^6 + c^4*d^5))/(2*c*d^3 + d^4 + c^2*d^2) + (32*tan(e/2 + (f*x)/2)*(3*c*d^9 + 6*c^2*d^8 + c^3*d^7 - 4*c^4*d^6 - 2*c^5*d^5))/(2*c*d^4 + d^5 + c^2*d^3))*(-(c + d)^3*(c - d))^(1/2)*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))*(A*d^2 - B*c^2 + B*d^2 - B*c*d))/(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2)))*(-(c + d)^3*(c - d))^(1/2)*(A*d^2 - B*c^2 + B*d^2 - B*c*d)*2i)/(f*(2*c*d^5 + d^6 - 2*c^3*d^3 - c^4*d^2))","B"
250,1,554,176,15.588932,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x)))/(c + d*sin(e + f*x))^3,x)","-\frac{\frac{A\,a\,d^2-2\,A\,a\,c^2-2\,B\,a\,c^2+2\,A\,a\,c\,d+B\,a\,c\,d}{-c^3-c^2\,d+c\,d^2+d^3}+\frac{a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,d^3-B\,c^3+6\,A\,c\,d^2-5\,A\,c^2\,d+4\,B\,c\,d^2-6\,B\,c^2\,d\right)}{c\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,d^3+B\,c^3+2\,A\,c\,d^2-3\,A\,c^2\,d-2\,B\,c^2\,d\right)}{c\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(A\,d^2-2\,A\,c^2-2\,B\,c^2+2\,A\,c\,d+B\,c\,d\right)}{c^2\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{a\,\mathrm{atan}\left(\frac{\left(\frac{a\,\left(2\,A\,c-A\,d+B\,c-2\,B\,d\right)\,\left(-2\,c^3\,d-2\,c^2\,d^2+2\,c\,d^3+2\,d^4\right)}{2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{3/2}\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{a\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,c-A\,d+B\,c-2\,B\,d\right)}{{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{3/2}}\right)\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}{2\,A\,a\,c-A\,a\,d+B\,a\,c-2\,B\,a\,d}\right)\,\left(2\,A\,c-A\,d+B\,c-2\,B\,d\right)}{f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{3/2}}","Not used",1,"- ((A*a*d^2 - 2*A*a*c^2 - 2*B*a*c^2 + 2*A*a*c*d + B*a*c*d)/(c*d^2 - c^2*d - c^3 + d^3) + (a*tan(e/2 + (f*x)/2)*(2*A*d^3 - B*c^3 + 6*A*c*d^2 - 5*A*c^2*d + 4*B*c*d^2 - 6*B*c^2*d))/(c*(c*d^2 - c^2*d - c^3 + d^3)) + (a*tan(e/2 + (f*x)/2)^3*(2*A*d^3 + B*c^3 + 2*A*c*d^2 - 3*A*c^2*d - 2*B*c^2*d))/(c*(c*d^2 - c^2*d - c^3 + d^3)) + (a*tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(A*d^2 - 2*A*c^2 - 2*B*c^2 + 2*A*c*d + B*c*d))/(c^2*(c*d^2 - c^2*d - c^3 + d^3)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) - (a*atan((((a*(2*A*c - A*d + B*c - 2*B*d)*(2*c*d^3 - 2*c^3*d + 2*d^4 - 2*c^2*d^2))/(2*(c + d)^(5/2)*(c - d)^(3/2)*(c*d^2 - c^2*d - c^3 + d^3)) + (a*c*tan(e/2 + (f*x)/2)*(2*A*c - A*d + B*c - 2*B*d))/((c + d)^(5/2)*(c - d)^(3/2)))*(c*d^2 - c^2*d - c^3 + d^3))/(2*A*a*c - A*a*d + B*a*c - 2*B*a*d))*(2*A*c - A*d + B*c - 2*B*d))/(f*(c + d)^(5/2)*(c - d)^(3/2))","B"
251,1,1291,464,15.986751,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^3,x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,c^3+12\,A\,d^3+16\,B\,c^3+11\,B\,d^3+42\,A\,c\,d^2+48\,A\,c^2\,d+36\,B\,c\,d^2+42\,B\,c^2\,d\right)}{8\,\left(3\,A\,a^2\,c^3+\frac{3\,A\,a^2\,d^3}{2}+2\,B\,a^2\,c^3+\frac{11\,B\,a^2\,d^3}{8}+\frac{21\,A\,a^2\,c\,d^2}{4}+6\,A\,a^2\,c^2\,d+\frac{9\,B\,a^2\,c\,d^2}{2}+\frac{21\,B\,a^2\,c^2\,d}{4}\right)}\right)\,\left(24\,A\,c^3+12\,A\,d^3+16\,B\,c^3+11\,B\,d^3+42\,A\,c\,d^2+48\,A\,c^2\,d+36\,B\,c\,d^2+42\,B\,c^2\,d\right)}{8\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a^2\,c^3+\frac{3\,A\,a^2\,d^3}{2}+2\,B\,a^2\,c^3+\frac{11\,B\,a^2\,d^3}{8}+\frac{21\,A\,a^2\,c\,d^2}{4}+6\,A\,a^2\,c^2\,d+\frac{9\,B\,a^2\,c\,d^2}{2}+\frac{21\,B\,a^2\,c^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(20\,A\,a^2\,c^3+4\,A\,a^2\,d^3+14\,B\,a^2\,c^3+24\,A\,a^2\,c\,d^2+42\,A\,a^2\,c^2\,d+12\,B\,a^2\,c\,d^2+24\,B\,a^2\,c^2\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(A\,a^2\,c^3+\frac{3\,A\,a^2\,d^3}{2}+2\,B\,a^2\,c^3+\frac{11\,B\,a^2\,d^3}{8}+\frac{21\,A\,a^2\,c\,d^2}{4}+6\,A\,a^2\,c^2\,d+\frac{9\,B\,a^2\,c\,d^2}{2}+\frac{21\,B\,a^2\,c^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,A\,a^2\,c^3+7\,A\,a^2\,d^3+4\,B\,a^2\,c^3+\frac{47\,B\,a^2\,d^3}{4}+\frac{33\,A\,a^2\,c\,d^2}{2}+12\,A\,a^2\,c^2\,d+21\,B\,a^2\,c\,d^2+\frac{33\,B\,a^2\,c^2\,d}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,A\,a^2\,c^3+7\,A\,a^2\,d^3+4\,B\,a^2\,c^3+\frac{47\,B\,a^2\,d^3}{4}+\frac{33\,A\,a^2\,c\,d^2}{2}+12\,A\,a^2\,c^2\,d+21\,B\,a^2\,c\,d^2+\frac{33\,B\,a^2\,c^2\,d}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,A\,a^2\,c^3+\frac{17\,A\,a^2\,d^3}{2}+6\,B\,a^2\,c^3+\frac{187\,B\,a^2\,d^3}{24}+\frac{87\,A\,a^2\,c\,d^2}{4}+18\,A\,a^2\,c^2\,d+\frac{51\,B\,a^2\,c\,d^2}{2}+\frac{87\,B\,a^2\,c^2\,d}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(3\,A\,a^2\,c^3+\frac{17\,A\,a^2\,d^3}{2}+6\,B\,a^2\,c^3+\frac{187\,B\,a^2\,d^3}{24}+\frac{87\,A\,a^2\,c\,d^2}{4}+18\,A\,a^2\,c^2\,d+\frac{51\,B\,a^2\,c\,d^2}{2}+\frac{87\,B\,a^2\,c^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(40\,A\,a^2\,c^3+32\,A\,a^2\,d^3+36\,B\,a^2\,c^3+32\,B\,a^2\,d^3+96\,A\,a^2\,c\,d^2+108\,A\,a^2\,c^2\,d+96\,B\,a^2\,c\,d^2+96\,B\,a^2\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(20\,A\,a^2\,c^3+\frac{72\,A\,a^2\,d^3}{5}+18\,B\,a^2\,c^3+\frac{64\,B\,a^2\,d^3}{5}+48\,A\,a^2\,c\,d^2+54\,A\,a^2\,c^2\,d+\frac{216\,B\,a^2\,c\,d^2}{5}+48\,B\,a^2\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(40\,A\,a^2\,c^3+24\,A\,a^2\,d^3+\frac{100\,B\,a^2\,c^3}{3}+\frac{64\,B\,a^2\,d^3}{3}+80\,A\,a^2\,c\,d^2+100\,A\,a^2\,c^2\,d+72\,B\,a^2\,c\,d^2+80\,B\,a^2\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(4\,A\,a^2\,c^3+2\,B\,a^2\,c^3+6\,A\,a^2\,c^2\,d\right)+4\,A\,a^2\,c^3+\frac{12\,A\,a^2\,d^3}{5}+\frac{10\,B\,a^2\,c^3}{3}+\frac{32\,B\,a^2\,d^3}{15}+8\,A\,a^2\,c\,d^2+10\,A\,a^2\,c^2\,d+\frac{36\,B\,a^2\,c\,d^2}{5}+8\,B\,a^2\,c^2\,d}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^2*atan((a^2*tan(e/2 + (f*x)/2)*(24*A*c^3 + 12*A*d^3 + 16*B*c^3 + 11*B*d^3 + 42*A*c*d^2 + 48*A*c^2*d + 36*B*c*d^2 + 42*B*c^2*d))/(8*(3*A*a^2*c^3 + (3*A*a^2*d^3)/2 + 2*B*a^2*c^3 + (11*B*a^2*d^3)/8 + (21*A*a^2*c*d^2)/4 + 6*A*a^2*c^2*d + (9*B*a^2*c*d^2)/2 + (21*B*a^2*c^2*d)/4)))*(24*A*c^3 + 12*A*d^3 + 16*B*c^3 + 11*B*d^3 + 42*A*c*d^2 + 48*A*c^2*d + 36*B*c*d^2 + 42*B*c^2*d))/(8*f) - (tan(e/2 + (f*x)/2)*(A*a^2*c^3 + (3*A*a^2*d^3)/2 + 2*B*a^2*c^3 + (11*B*a^2*d^3)/8 + (21*A*a^2*c*d^2)/4 + 6*A*a^2*c^2*d + (9*B*a^2*c*d^2)/2 + (21*B*a^2*c^2*d)/4) + tan(e/2 + (f*x)/2)^8*(20*A*a^2*c^3 + 4*A*a^2*d^3 + 14*B*a^2*c^3 + 24*A*a^2*c*d^2 + 42*A*a^2*c^2*d + 12*B*a^2*c*d^2 + 24*B*a^2*c^2*d) - tan(e/2 + (f*x)/2)^11*(A*a^2*c^3 + (3*A*a^2*d^3)/2 + 2*B*a^2*c^3 + (11*B*a^2*d^3)/8 + (21*A*a^2*c*d^2)/4 + 6*A*a^2*c^2*d + (9*B*a^2*c*d^2)/2 + (21*B*a^2*c^2*d)/4) + tan(e/2 + (f*x)/2)^5*(2*A*a^2*c^3 + 7*A*a^2*d^3 + 4*B*a^2*c^3 + (47*B*a^2*d^3)/4 + (33*A*a^2*c*d^2)/2 + 12*A*a^2*c^2*d + 21*B*a^2*c*d^2 + (33*B*a^2*c^2*d)/2) - tan(e/2 + (f*x)/2)^7*(2*A*a^2*c^3 + 7*A*a^2*d^3 + 4*B*a^2*c^3 + (47*B*a^2*d^3)/4 + (33*A*a^2*c*d^2)/2 + 12*A*a^2*c^2*d + 21*B*a^2*c*d^2 + (33*B*a^2*c^2*d)/2) + tan(e/2 + (f*x)/2)^3*(3*A*a^2*c^3 + (17*A*a^2*d^3)/2 + 6*B*a^2*c^3 + (187*B*a^2*d^3)/24 + (87*A*a^2*c*d^2)/4 + 18*A*a^2*c^2*d + (51*B*a^2*c*d^2)/2 + (87*B*a^2*c^2*d)/4) - tan(e/2 + (f*x)/2)^9*(3*A*a^2*c^3 + (17*A*a^2*d^3)/2 + 6*B*a^2*c^3 + (187*B*a^2*d^3)/24 + (87*A*a^2*c*d^2)/4 + 18*A*a^2*c^2*d + (51*B*a^2*c*d^2)/2 + (87*B*a^2*c^2*d)/4) + tan(e/2 + (f*x)/2)^4*(40*A*a^2*c^3 + 32*A*a^2*d^3 + 36*B*a^2*c^3 + 32*B*a^2*d^3 + 96*A*a^2*c*d^2 + 108*A*a^2*c^2*d + 96*B*a^2*c*d^2 + 96*B*a^2*c^2*d) + tan(e/2 + (f*x)/2)^2*(20*A*a^2*c^3 + (72*A*a^2*d^3)/5 + 18*B*a^2*c^3 + (64*B*a^2*d^3)/5 + 48*A*a^2*c*d^2 + 54*A*a^2*c^2*d + (216*B*a^2*c*d^2)/5 + 48*B*a^2*c^2*d) + tan(e/2 + (f*x)/2)^6*(40*A*a^2*c^3 + 24*A*a^2*d^3 + (100*B*a^2*c^3)/3 + (64*B*a^2*d^3)/3 + 80*A*a^2*c*d^2 + 100*A*a^2*c^2*d + 72*B*a^2*c*d^2 + 80*B*a^2*c^2*d) + tan(e/2 + (f*x)/2)^10*(4*A*a^2*c^3 + 2*B*a^2*c^3 + 6*A*a^2*c^2*d) + 4*A*a^2*c^3 + (12*A*a^2*d^3)/5 + (10*B*a^2*c^3)/3 + (32*B*a^2*d^3)/15 + 8*A*a^2*c*d^2 + 10*A*a^2*c^2*d + (36*B*a^2*c*d^2)/5 + 8*B*a^2*c^2*d)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1))","B"
252,1,765,336,15.705242,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^2,x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,c^2+7\,A\,d^2+8\,B\,c^2+6\,B\,d^2+16\,A\,c\,d+14\,B\,c\,d\right)}{4\,\left(3\,A\,a^2\,c^2+\frac{7\,A\,a^2\,d^2}{4}+2\,B\,a^2\,c^2+\frac{3\,B\,a^2\,d^2}{2}+4\,A\,a^2\,c\,d+\frac{7\,B\,a^2\,c\,d}{2}\right)}\right)\,\left(12\,A\,c^2+7\,A\,d^2+8\,B\,c^2+6\,B\,d^2+16\,A\,c\,d+14\,B\,c\,d\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(4\,A\,a^2\,c^2+2\,B\,a^2\,c^2+4\,A\,a^2\,c\,d\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a^2\,c^2+\frac{7\,A\,a^2\,d^2}{4}+2\,B\,a^2\,c^2+\frac{3\,B\,a^2\,d^2}{2}+4\,A\,a^2\,c\,d+\frac{7\,B\,a^2\,c\,d}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(A\,a^2\,c^2+\frac{7\,A\,a^2\,d^2}{4}+2\,B\,a^2\,c^2+\frac{3\,B\,a^2\,d^2}{2}+4\,A\,a^2\,c\,d+\frac{7\,B\,a^2\,c\,d}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,a^2\,c^2+\frac{11\,A\,a^2\,d^2}{2}+4\,B\,a^2\,c^2+7\,B\,a^2\,d^2+8\,A\,a^2\,c\,d+11\,B\,a^2\,c\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,A\,a^2\,c^2+\frac{11\,A\,a^2\,d^2}{2}+4\,B\,a^2\,c^2+7\,B\,a^2\,d^2+8\,A\,a^2\,c\,d+11\,B\,a^2\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(16\,A\,a^2\,c^2+8\,A\,a^2\,d^2+12\,B\,a^2\,c^2+4\,B\,a^2\,d^2+24\,A\,a^2\,c\,d+16\,B\,a^2\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(16\,A\,a^2\,c^2+\frac{40\,A\,a^2\,d^2}{3}+\frac{44\,B\,a^2\,c^2}{3}+12\,B\,a^2\,d^2+\frac{88\,A\,a^2\,c\,d}{3}+\frac{80\,B\,a^2\,c\,d}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(24\,A\,a^2\,c^2+\frac{56\,A\,a^2\,d^2}{3}+\frac{64\,B\,a^2\,c^2}{3}+20\,B\,a^2\,d^2+\frac{128\,A\,a^2\,c\,d}{3}+\frac{112\,B\,a^2\,c\,d}{3}\right)+4\,A\,a^2\,c^2+\frac{8\,A\,a^2\,d^2}{3}+\frac{10\,B\,a^2\,c^2}{3}+\frac{12\,B\,a^2\,d^2}{5}+\frac{20\,A\,a^2\,c\,d}{3}+\frac{16\,B\,a^2\,c\,d}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^2*atan((a^2*tan(e/2 + (f*x)/2)*(12*A*c^2 + 7*A*d^2 + 8*B*c^2 + 6*B*d^2 + 16*A*c*d + 14*B*c*d))/(4*(3*A*a^2*c^2 + (7*A*a^2*d^2)/4 + 2*B*a^2*c^2 + (3*B*a^2*d^2)/2 + 4*A*a^2*c*d + (7*B*a^2*c*d)/2)))*(12*A*c^2 + 7*A*d^2 + 8*B*c^2 + 6*B*d^2 + 16*A*c*d + 14*B*c*d))/(4*f) - (tan(e/2 + (f*x)/2)^8*(4*A*a^2*c^2 + 2*B*a^2*c^2 + 4*A*a^2*c*d) + tan(e/2 + (f*x)/2)*(A*a^2*c^2 + (7*A*a^2*d^2)/4 + 2*B*a^2*c^2 + (3*B*a^2*d^2)/2 + 4*A*a^2*c*d + (7*B*a^2*c*d)/2) - tan(e/2 + (f*x)/2)^9*(A*a^2*c^2 + (7*A*a^2*d^2)/4 + 2*B*a^2*c^2 + (3*B*a^2*d^2)/2 + 4*A*a^2*c*d + (7*B*a^2*c*d)/2) + tan(e/2 + (f*x)/2)^3*(2*A*a^2*c^2 + (11*A*a^2*d^2)/2 + 4*B*a^2*c^2 + 7*B*a^2*d^2 + 8*A*a^2*c*d + 11*B*a^2*c*d) - tan(e/2 + (f*x)/2)^7*(2*A*a^2*c^2 + (11*A*a^2*d^2)/2 + 4*B*a^2*c^2 + 7*B*a^2*d^2 + 8*A*a^2*c*d + 11*B*a^2*c*d) + tan(e/2 + (f*x)/2)^6*(16*A*a^2*c^2 + 8*A*a^2*d^2 + 12*B*a^2*c^2 + 4*B*a^2*d^2 + 24*A*a^2*c*d + 16*B*a^2*c*d) + tan(e/2 + (f*x)/2)^2*(16*A*a^2*c^2 + (40*A*a^2*d^2)/3 + (44*B*a^2*c^2)/3 + 12*B*a^2*d^2 + (88*A*a^2*c*d)/3 + (80*B*a^2*c*d)/3) + tan(e/2 + (f*x)/2)^4*(24*A*a^2*c^2 + (56*A*a^2*d^2)/3 + (64*B*a^2*c^2)/3 + 20*B*a^2*d^2 + (128*A*a^2*c*d)/3 + (112*B*a^2*c*d)/3) + 4*A*a^2*c^2 + (8*A*a^2*d^2)/3 + (10*B*a^2*c^2)/3 + (12*B*a^2*d^2)/5 + (20*A*a^2*c*d)/3 + (16*B*a^2*c*d)/3)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1))","B"
253,1,492,166,14.602539,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x)),x)","\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,c+8\,A\,d+8\,B\,c+7\,B\,d\right)}{4\,\left(3\,A\,a^2\,c+2\,A\,a^2\,d+2\,B\,a^2\,c+\frac{7\,B\,a^2\,d}{4}\right)}\right)\,\left(12\,A\,c+8\,A\,d+8\,B\,c+7\,B\,d\right)}{4\,f}-\frac{a^2\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(12\,A\,c+8\,A\,d+8\,B\,c+7\,B\,d\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a^2\,c+2\,A\,a^2\,d+2\,B\,a^2\,c+\frac{15\,B\,a^2\,d}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(A\,a^2\,c+2\,A\,a^2\,d+2\,B\,a^2\,c+\frac{7\,B\,a^2\,d}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(A\,a^2\,c+2\,A\,a^2\,d+2\,B\,a^2\,c+\frac{15\,B\,a^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(12\,A\,a^2\,c+10\,A\,a^2\,d+10\,B\,a^2\,c+8\,B\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(12\,A\,a^2\,c+\frac{34\,A\,a^2\,d}{3}+\frac{34\,B\,a^2\,c}{3}+\frac{32\,B\,a^2\,d}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(4\,A\,a^2\,c+2\,A\,a^2\,d+2\,B\,a^2\,c\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a^2\,c+2\,A\,a^2\,d+2\,B\,a^2\,c+\frac{7\,B\,a^2\,d}{4}\right)+4\,A\,a^2\,c+\frac{10\,A\,a^2\,d}{3}+\frac{10\,B\,a^2\,c}{3}+\frac{8\,B\,a^2\,d}{3}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^2*atan((a^2*tan(e/2 + (f*x)/2)*(12*A*c + 8*A*d + 8*B*c + 7*B*d))/(4*(3*A*a^2*c + 2*A*a^2*d + 2*B*a^2*c + (7*B*a^2*d)/4)))*(12*A*c + 8*A*d + 8*B*c + 7*B*d))/(4*f) - (a^2*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(12*A*c + 8*A*d + 8*B*c + 7*B*d))/(4*f) - (tan(e/2 + (f*x)/2)^3*(A*a^2*c + 2*A*a^2*d + 2*B*a^2*c + (15*B*a^2*d)/4) - tan(e/2 + (f*x)/2)^7*(A*a^2*c + 2*A*a^2*d + 2*B*a^2*c + (7*B*a^2*d)/4) - tan(e/2 + (f*x)/2)^5*(A*a^2*c + 2*A*a^2*d + 2*B*a^2*c + (15*B*a^2*d)/4) + tan(e/2 + (f*x)/2)^4*(12*A*a^2*c + 10*A*a^2*d + 10*B*a^2*c + 8*B*a^2*d) + tan(e/2 + (f*x)/2)^2*(12*A*a^2*c + (34*A*a^2*d)/3 + (34*B*a^2*c)/3 + (32*B*a^2*d)/3) + tan(e/2 + (f*x)/2)^6*(4*A*a^2*c + 2*A*a^2*d + 2*B*a^2*c) + tan(e/2 + (f*x)/2)*(A*a^2*c + 2*A*a^2*d + 2*B*a^2*c + (7*B*a^2*d)/4) + 4*A*a^2*c + (10*A*a^2*d)/3 + (10*B*a^2*c)/3 + (8*B*a^2*d)/3)/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1))","B"
254,1,91,94,13.160815,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2,x)","-\frac{\frac{3\,A\,a^2\,\sin\left(2\,e+2\,f\,x\right)}{2}-\frac{B\,a^2\,\cos\left(3\,e+3\,f\,x\right)}{2}+3\,B\,a^2\,\sin\left(2\,e+2\,f\,x\right)+12\,A\,a^2\,\cos\left(e+f\,x\right)+\frac{21\,B\,a^2\,\cos\left(e+f\,x\right)}{2}-9\,A\,a^2\,f\,x-6\,B\,a^2\,f\,x}{6\,f}","Not used",1,"-((3*A*a^2*sin(2*e + 2*f*x))/2 - (B*a^2*cos(3*e + 3*f*x))/2 + 3*B*a^2*sin(2*e + 2*f*x) + 12*A*a^2*cos(e + f*x) + (21*B*a^2*cos(e + f*x))/2 - 9*A*a^2*f*x - 6*B*a^2*f*x)/(6*f)","B"
255,1,7371,171,20.068845,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c + d*sin(e + f*x)),x)","-\frac{\frac{2\,\left(A\,a^2\,d-B\,a^2\,c+2\,B\,a^2\,d\right)}{d^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(A\,a^2\,d-B\,a^2\,c+2\,B\,a^2\,d\right)}{d^2}-\frac{B\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3}{d}+\frac{B\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{d}}{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\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}-\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{d^3}+\frac{\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{\left(\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{d^3}}{\frac{16\,\left(4\,A^3\,a^6\,c^4\,d^3-16\,A^3\,a^6\,c^3\,d^4+20\,A^3\,a^6\,c^2\,d^5-8\,A^3\,a^6\,c\,d^6-6\,A^2\,B\,a^6\,c^5\,d^2+24\,A^2\,B\,a^6\,c^4\,d^3-36\,A^2\,B\,a^6\,c^3\,d^4+24\,A^2\,B\,a^6\,c^2\,d^5-6\,A^2\,B\,a^6\,c\,d^6+3\,A\,B^2\,a^6\,c^4\,d^3-6\,A\,B^2\,a^6\,c^3\,d^4+3\,A\,B^2\,a^6\,c^2\,d^5+2\,B^3\,a^6\,c^7-8\,B^3\,a^6\,c^6\,d+13\,B^3\,a^6\,c^5\,d^2-10\,B^3\,a^6\,c^4\,d^3+3\,B^3\,a^6\,c^3\,d^4\right)}{d^5}-\frac{\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}-\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}+\frac{\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{\left(\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^3}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A^3\,a^6\,c^5\,d^3-48\,A^3\,a^6\,c^4\,d^4+104\,A^3\,a^6\,c^3\,d^5-96\,A^3\,a^6\,c^2\,d^6+32\,A^3\,a^6\,c\,d^7-24\,A^2\,B\,a^6\,c^6\,d^2+144\,A^2\,B\,a^6\,c^5\,d^3-336\,A^2\,B\,a^6\,c^4\,d^4+384\,A^2\,B\,a^6\,c^3\,d^5-216\,A^2\,B\,a^6\,c^2\,d^6+48\,A^2\,B\,a^6\,c\,d^7+24\,A\,B^2\,a^6\,c^7\,d-144\,A\,B^2\,a^6\,c^6\,d^2+360\,A\,B^2\,a^6\,c^5\,d^3-480\,A\,B^2\,a^6\,c^4\,d^4+354\,A\,B^2\,a^6\,c^3\,d^5-132\,A\,B^2\,a^6\,c^2\,d^6+18\,A\,B^2\,a^6\,c\,d^7-8\,B^3\,a^6\,c^8+48\,B^3\,a^6\,c^7\,d-128\,B^3\,a^6\,c^6\,d^2+192\,B^3\,a^6\,c^5\,d^3-170\,B^3\,a^6\,c^4\,d^4+84\,B^3\,a^6\,c^3\,d^5-18\,B^3\,a^6\,c^2\,d^6\right)}{d^6}}\right)\,\left(B\,a^2\,c^2\,1{}\mathrm{i}+\frac{a^2\,d^2\,\left(4\,A+3\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^2\,d\,\left(2\,A\,c+4\,B\,c\right)\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{d^3\,f}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}+\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}-\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}+\frac{a^2\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}}{d^4+c\,d^3}\right)}{d^4+c\,d^3}\right)\,1{}\mathrm{i}}{d^4+c\,d^3}+\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}+\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}+\frac{a^2\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}}{d^4+c\,d^3}\right)}{d^4+c\,d^3}\right)\,1{}\mathrm{i}}{d^4+c\,d^3}}{\frac{16\,\left(4\,A^3\,a^6\,c^4\,d^3-16\,A^3\,a^6\,c^3\,d^4+20\,A^3\,a^6\,c^2\,d^5-8\,A^3\,a^6\,c\,d^6-6\,A^2\,B\,a^6\,c^5\,d^2+24\,A^2\,B\,a^6\,c^4\,d^3-36\,A^2\,B\,a^6\,c^3\,d^4+24\,A^2\,B\,a^6\,c^2\,d^5-6\,A^2\,B\,a^6\,c\,d^6+3\,A\,B^2\,a^6\,c^4\,d^3-6\,A\,B^2\,a^6\,c^3\,d^4+3\,A\,B^2\,a^6\,c^2\,d^5+2\,B^3\,a^6\,c^7-8\,B^3\,a^6\,c^6\,d+13\,B^3\,a^6\,c^5\,d^2-10\,B^3\,a^6\,c^4\,d^3+3\,B^3\,a^6\,c^3\,d^4\right)}{d^5}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A^3\,a^6\,c^5\,d^3-48\,A^3\,a^6\,c^4\,d^4+104\,A^3\,a^6\,c^3\,d^5-96\,A^3\,a^6\,c^2\,d^6+32\,A^3\,a^6\,c\,d^7-24\,A^2\,B\,a^6\,c^6\,d^2+144\,A^2\,B\,a^6\,c^5\,d^3-336\,A^2\,B\,a^6\,c^4\,d^4+384\,A^2\,B\,a^6\,c^3\,d^5-216\,A^2\,B\,a^6\,c^2\,d^6+48\,A^2\,B\,a^6\,c\,d^7+24\,A\,B^2\,a^6\,c^7\,d-144\,A\,B^2\,a^6\,c^6\,d^2+360\,A\,B^2\,a^6\,c^5\,d^3-480\,A\,B^2\,a^6\,c^4\,d^4+354\,A\,B^2\,a^6\,c^3\,d^5-132\,A\,B^2\,a^6\,c^2\,d^6+18\,A\,B^2\,a^6\,c\,d^7-8\,B^3\,a^6\,c^8+48\,B^3\,a^6\,c^7\,d-128\,B^3\,a^6\,c^6\,d^2+192\,B^3\,a^6\,c^5\,d^3-170\,B^3\,a^6\,c^4\,d^4+84\,B^3\,a^6\,c^3\,d^5-18\,B^3\,a^6\,c^2\,d^6\right)}{d^6}-\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}+\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}-\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}+\frac{a^2\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}}{d^4+c\,d^3}\right)}{d^4+c\,d^3}\right)}{d^4+c\,d^3}+\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(4\,A^2\,a^4\,c^4\,d^4-16\,A^2\,a^4\,c^3\,d^5+16\,A^2\,a^4\,c^2\,d^6-8\,A\,B\,a^4\,c^5\,d^3+32\,A\,B\,a^4\,c^4\,d^4-44\,A\,B\,a^4\,c^3\,d^5+24\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-16\,B^2\,a^4\,c^5\,d^3+28\,B^2\,a^4\,c^4\,d^4-24\,B^2\,a^4\,c^3\,d^5+9\,B^2\,a^4\,c^2\,d^6\right)}{d^5}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^4\,c^5\,d^4+32\,A^2\,a^4\,c^4\,d^5-32\,A^2\,a^4\,c^3\,d^6-16\,A^2\,a^4\,c^2\,d^7+28\,A^2\,a^4\,c\,d^8+16\,A\,B\,a^4\,c^6\,d^3-64\,A\,B\,a^4\,c^5\,d^4+76\,A\,B\,a^4\,c^4\,d^5+8\,A\,B\,a^4\,c^3\,d^6-80\,A\,B\,a^4\,c^2\,d^7+48\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+32\,B^2\,a^4\,c^6\,d^3-44\,B^2\,a^4\,c^5\,d^4+8\,B^2\,a^4\,c^4\,d^5+43\,B^2\,a^4\,c^3\,d^6-48\,B^2\,a^4\,c^2\,d^7+18\,B^2\,a^4\,c\,d^8\right)}{d^6}+\frac{a^2\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(8\,A\,a^2\,c\,d^8+6\,B\,a^2\,c\,d^8-8\,A\,a^2\,c^2\,d^7-8\,B\,a^2\,c^2\,d^7+2\,B\,a^2\,c^3\,d^6\right)}{d^5}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^2\,c\,d^9-16\,A\,a^2\,c^2\,d^8+8\,A\,a^2\,c^3\,d^7-8\,B\,a^2\,c^2\,d^8+16\,B\,a^2\,c^3\,d^7-8\,B\,a^2\,c^4\,d^6\right)}{d^6}+\frac{a^2\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{10}-8\,c^3\,d^8\right)}{d^6}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}}{d^4+c\,d^3}\right)}{d^4+c\,d^3}\right)}{d^4+c\,d^3}}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^3}\,2{}\mathrm{i}}{f\,\left(d^4+c\,d^3\right)}","Not used",1,"(atan(((((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + ((((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 - (8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2)*1i)/d^3 + (((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + (((8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 - (8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2)*1i)/d^3)/((16*(2*B^3*a^6*c^7 + 20*A^3*a^6*c^2*d^5 - 16*A^3*a^6*c^3*d^4 + 4*A^3*a^6*c^4*d^3 + 3*B^3*a^6*c^3*d^4 - 10*B^3*a^6*c^4*d^3 + 13*B^3*a^6*c^5*d^2 - 8*A^3*a^6*c*d^6 - 8*B^3*a^6*c^6*d - 6*A^2*B*a^6*c*d^6 + 3*A*B^2*a^6*c^2*d^5 - 6*A*B^2*a^6*c^3*d^4 + 3*A*B^2*a^6*c^4*d^3 + 24*A^2*B*a^6*c^2*d^5 - 36*A^2*B*a^6*c^3*d^4 + 24*A^2*B*a^6*c^4*d^3 - 6*A^2*B*a^6*c^5*d^2))/d^5 - (((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + ((((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 - (8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 + (8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 + (((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + (((8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 - (8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6)*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2))/d^3 - (16*tan(e/2 + (f*x)/2)*(104*A^3*a^6*c^3*d^5 - 96*A^3*a^6*c^2*d^6 - 8*B^3*a^6*c^8 - 48*A^3*a^6*c^4*d^4 + 8*A^3*a^6*c^5*d^3 - 18*B^3*a^6*c^2*d^6 + 84*B^3*a^6*c^3*d^5 - 170*B^3*a^6*c^4*d^4 + 192*B^3*a^6*c^5*d^3 - 128*B^3*a^6*c^6*d^2 + 32*A^3*a^6*c*d^7 + 48*B^3*a^6*c^7*d + 18*A*B^2*a^6*c*d^7 + 24*A*B^2*a^6*c^7*d + 48*A^2*B*a^6*c*d^7 - 132*A*B^2*a^6*c^2*d^6 + 354*A*B^2*a^6*c^3*d^5 - 480*A*B^2*a^6*c^4*d^4 + 360*A*B^2*a^6*c^5*d^3 - 144*A*B^2*a^6*c^6*d^2 - 216*A^2*B*a^6*c^2*d^6 + 384*A^2*B*a^6*c^3*d^5 - 336*A^2*B*a^6*c^4*d^4 + 144*A^2*B*a^6*c^5*d^3 - 24*A^2*B*a^6*c^6*d^2))/d^6))*(B*a^2*c^2*1i + (a^2*d^2*(4*A + 3*B)*1i)/2 - (a^2*d*(2*A*c + 4*B*c)*1i)/2)*2i)/(d^3*f) - ((2*(A*a^2*d - B*a^2*c + 2*B*a^2*d))/d^2 + (2*tan(e/2 + (f*x)/2)^2*(A*a^2*d - B*a^2*c + 2*B*a^2*d))/d^2 - (B*a^2*tan(e/2 + (f*x)/2)^3)/d + (B*a^2*tan(e/2 + (f*x)/2))/d)/(f*(2*tan(e/2 + (f*x)/2)^2 + tan(e/2 + (f*x)/2)^4 + 1)) + (a^2*atan(((a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6 + (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6 - (8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 + (a^2*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2))/(c*d^3 + d^4)))/(c*d^3 + d^4))*1i)/(c*d^3 + d^4) + (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6 + (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6 + (a^2*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2))/(c*d^3 + d^4)))/(c*d^3 + d^4))*1i)/(c*d^3 + d^4))/((16*(2*B^3*a^6*c^7 + 20*A^3*a^6*c^2*d^5 - 16*A^3*a^6*c^3*d^4 + 4*A^3*a^6*c^4*d^3 + 3*B^3*a^6*c^3*d^4 - 10*B^3*a^6*c^4*d^3 + 13*B^3*a^6*c^5*d^2 - 8*A^3*a^6*c*d^6 - 8*B^3*a^6*c^6*d - 6*A^2*B*a^6*c*d^6 + 3*A*B^2*a^6*c^2*d^5 - 6*A*B^2*a^6*c^3*d^4 + 3*A*B^2*a^6*c^4*d^3 + 24*A^2*B*a^6*c^2*d^5 - 36*A^2*B*a^6*c^3*d^4 + 24*A^2*B*a^6*c^4*d^3 - 6*A^2*B*a^6*c^5*d^2))/d^5 - (16*tan(e/2 + (f*x)/2)*(104*A^3*a^6*c^3*d^5 - 96*A^3*a^6*c^2*d^6 - 8*B^3*a^6*c^8 - 48*A^3*a^6*c^4*d^4 + 8*A^3*a^6*c^5*d^3 - 18*B^3*a^6*c^2*d^6 + 84*B^3*a^6*c^3*d^5 - 170*B^3*a^6*c^4*d^4 + 192*B^3*a^6*c^5*d^3 - 128*B^3*a^6*c^6*d^2 + 32*A^3*a^6*c*d^7 + 48*B^3*a^6*c^7*d + 18*A*B^2*a^6*c*d^7 + 24*A*B^2*a^6*c^7*d + 48*A^2*B*a^6*c*d^7 - 132*A*B^2*a^6*c^2*d^6 + 354*A*B^2*a^6*c^3*d^5 - 480*A*B^2*a^6*c^4*d^4 + 360*A*B^2*a^6*c^5*d^3 - 144*A*B^2*a^6*c^6*d^2 - 216*A^2*B*a^6*c^2*d^6 + 384*A^2*B*a^6*c^3*d^5 - 336*A^2*B*a^6*c^4*d^4 + 144*A^2*B*a^6*c^5*d^3 - 24*A^2*B*a^6*c^6*d^2))/d^6 - (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6 + (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6 - (8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 + (a^2*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2))/(c*d^3 + d^4)))/(c*d^3 + d^4)))/(c*d^3 + d^4) + (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*(16*A^2*a^4*c^2*d^6 - 16*A^2*a^4*c^3*d^5 + 4*A^2*a^4*c^4*d^4 + 9*B^2*a^4*c^2*d^6 - 24*B^2*a^4*c^3*d^5 + 28*B^2*a^4*c^4*d^4 - 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2 + 24*A*B*a^4*c^2*d^6 - 44*A*B*a^4*c^3*d^5 + 32*A*B*a^4*c^4*d^4 - 8*A*B*a^4*c^5*d^3))/d^5 + (8*tan(e/2 + (f*x)/2)*(32*A^2*a^4*c^4*d^5 - 32*A^2*a^4*c^3*d^6 - 16*A^2*a^4*c^2*d^7 - 8*A^2*a^4*c^5*d^4 - 48*B^2*a^4*c^2*d^7 + 43*B^2*a^4*c^3*d^6 + 8*B^2*a^4*c^4*d^5 - 44*B^2*a^4*c^5*d^4 + 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 + 28*A^2*a^4*c*d^8 + 18*B^2*a^4*c*d^8 - 80*A*B*a^4*c^2*d^7 + 8*A*B*a^4*c^3*d^6 + 76*A*B*a^4*c^4*d^5 - 64*A*B*a^4*c^5*d^4 + 16*A*B*a^4*c^6*d^3 + 48*A*B*a^4*c*d^8))/d^6 + (a^2*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*((8*(8*A*a^2*c*d^8 + 6*B*a^2*c*d^8 - 8*A*a^2*c^2*d^7 - 8*B*a^2*c^2*d^7 + 2*B*a^2*c^3*d^6))/d^5 - (8*tan(e/2 + (f*x)/2)*(8*A*a^2*c*d^9 - 16*A*a^2*c^2*d^8 + 8*A*a^2*c^3*d^7 - 8*B*a^2*c^2*d^8 + 16*B*a^2*c^3*d^7 - 8*B*a^2*c^4*d^6))/d^6 + (a^2*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^10 - 8*c^3*d^8))/d^6)*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2))/(c*d^3 + d^4)))/(c*d^3 + d^4)))/(c*d^3 + d^4)))*(A*d - B*c)*(-(c + d)*(c - d)^3)^(1/2)*2i)/(f*(c*d^3 + d^4))","B"
256,1,8706,198,21.577972,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c + d*sin(e + f*x))^2,x)","-\frac{\frac{2\,\left(2\,B\,a^2\,c^2-A\,a^2\,c\,d+A\,a^2\,d^2\right)}{d^2\,\left(c+d\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,B\,a^2\,c^2-A\,a^2\,c\,d+A\,a^2\,d^2\right)}{d^2\,\left(c+d\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a^2\,d^2+3\,B\,a^2\,c^2-A\,a^2\,c\,d+B\,a^2\,c\,d\right)}{c\,d\,\left(c+d\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a^2\,d^2+B\,a^2\,c^2-A\,a^2\,c\,d-B\,a^2\,c\,d\right)}{c\,d\,\left(c+d\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)}{d^3}-\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}\right)}{d^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,1{}\mathrm{i}}{d^3}+\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)}{d^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,1{}\mathrm{i}}{d^3}}{\frac{64\,\left(-2\,A^3\,a^6\,c^3\,d^3-2\,A^3\,a^6\,c^2\,d^4+4\,A^3\,a^6\,c\,d^5+9\,A^2\,B\,a^6\,c^4\,d^2-21\,A^2\,B\,a^6\,c^2\,d^4+12\,A^2\,B\,a^6\,c\,d^5-12\,A\,B^2\,a^6\,c^5\,d+12\,A\,B^2\,a^6\,c^4\,d^2+21\,A\,B^2\,a^6\,c^3\,d^3-30\,A\,B^2\,a^6\,c^2\,d^4+9\,A\,B^2\,a^6\,c\,d^5+4\,B^3\,a^6\,c^6-8\,B^3\,a^6\,c^5\,d-2\,B^3\,a^6\,c^4\,d^2+14\,B^3\,a^6\,c^3\,d^3-10\,B^3\,a^6\,c^2\,d^4+2\,B^3\,a^6\,c\,d^5\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)}{d^3}-\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}\right)}{d^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)}{d^3}-\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)}{d^3}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)}{d^3}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^3\,a^6\,c^4\,d^3-4\,A^3\,a^6\,c^3\,d^4+2\,A^3\,a^6\,c^2\,d^5+4\,A^3\,a^6\,c\,d^6+12\,A^2\,B\,a^6\,c^5\,d^2+12\,A^2\,B\,a^6\,c^4\,d^3-30\,A^2\,B\,a^6\,c^3\,d^4-12\,A^2\,B\,a^6\,c^2\,d^5+18\,A^2\,B\,a^6\,c\,d^6-24\,A\,B^2\,a^6\,c^6\,d+72\,A\,B^2\,a^6\,c^4\,d^3-24\,A\,B^2\,a^6\,c^3\,d^4-48\,A\,B^2\,a^6\,c^2\,d^5+24\,A\,B^2\,a^6\,c\,d^6+16\,B^3\,a^6\,c^7-16\,B^3\,a^6\,c^6\,d-40\,B^3\,a^6\,c^5\,d^2+48\,B^3\,a^6\,c^4\,d^3+16\,B^3\,a^6\,c^3\,d^4-32\,B^3\,a^6\,c^2\,d^5+8\,B^3\,a^6\,c\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}}\right)\,\left(B\,a^2\,c\,2{}\mathrm{i}-a^2\,d\,\left(A+2\,B\right)\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{d^3\,f}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}-\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)\,1{}\mathrm{i}}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)\,1{}\mathrm{i}}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}}{\frac{64\,\left(-2\,A^3\,a^6\,c^3\,d^3-2\,A^3\,a^6\,c^2\,d^4+4\,A^3\,a^6\,c\,d^5+9\,A^2\,B\,a^6\,c^4\,d^2-21\,A^2\,B\,a^6\,c^2\,d^4+12\,A^2\,B\,a^6\,c\,d^5-12\,A\,B^2\,a^6\,c^5\,d+12\,A\,B^2\,a^6\,c^4\,d^2+21\,A\,B^2\,a^6\,c^3\,d^3-30\,A\,B^2\,a^6\,c^2\,d^4+9\,A\,B^2\,a^6\,c\,d^5+4\,B^3\,a^6\,c^6-8\,B^3\,a^6\,c^5\,d-2\,B^3\,a^6\,c^4\,d^2+14\,B^3\,a^6\,c^3\,d^3-10\,B^3\,a^6\,c^2\,d^4+2\,B^3\,a^6\,c\,d^5\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^3\,a^6\,c^4\,d^3-4\,A^3\,a^6\,c^3\,d^4+2\,A^3\,a^6\,c^2\,d^5+4\,A^3\,a^6\,c\,d^6+12\,A^2\,B\,a^6\,c^5\,d^2+12\,A^2\,B\,a^6\,c^4\,d^3-30\,A^2\,B\,a^6\,c^3\,d^4-12\,A^2\,B\,a^6\,c^2\,d^5+18\,A^2\,B\,a^6\,c\,d^6-24\,A\,B^2\,a^6\,c^6\,d+72\,A\,B^2\,a^6\,c^4\,d^3-24\,A\,B^2\,a^6\,c^3\,d^4-48\,A\,B^2\,a^6\,c^2\,d^5+24\,A\,B^2\,a^6\,c\,d^6+16\,B^3\,a^6\,c^7-16\,B^3\,a^6\,c^6\,d-40\,B^3\,a^6\,c^5\,d^2+48\,B^3\,a^6\,c^4\,d^3+16\,B^3\,a^6\,c^3\,d^4-32\,B^3\,a^6\,c^2\,d^5+8\,B^3\,a^6\,c\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}-\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}-\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(A^2\,a^4\,c^4\,d^4+2\,A^2\,a^4\,c^3\,d^5+A^2\,a^4\,c^2\,d^6-4\,A\,B\,a^4\,c^5\,d^3-4\,A\,B\,a^4\,c^4\,d^4+4\,A\,B\,a^4\,c^3\,d^5+4\,A\,B\,a^4\,c^2\,d^6+4\,B^2\,a^4\,c^6\,d^2-8\,B^2\,a^4\,c^4\,d^4+4\,B^2\,a^4\,c^2\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^2\,a^4\,c^5\,d^4-4\,A^2\,a^4\,c^4\,d^5+4\,A^2\,a^4\,c^3\,d^6+8\,A^2\,a^4\,c^2\,d^7-2\,A^2\,a^4\,c\,d^8+8\,A\,B\,a^4\,c^6\,d^3+8\,A\,B\,a^4\,c^5\,d^4-26\,A\,B\,a^4\,c^4\,d^5-16\,A\,B\,a^4\,c^3\,d^6+22\,A\,B\,a^4\,c^2\,d^7+4\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2+28\,B^2\,a^4\,c^5\,d^4-4\,B^2\,a^4\,c^4\,d^5-29\,B^2\,a^4\,c^3\,d^6+6\,B^2\,a^4\,c^2\,d^7+7\,B^2\,a^4\,c\,d^8\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(\frac{32\,\left(A\,a^2\,c\,d^9+2\,B\,a^2\,c\,d^9-A\,a^2\,c^3\,d^7+B\,a^2\,c^2\,d^8-2\,B\,a^2\,c^3\,d^7-B\,a^2\,c^4\,d^6\right)}{c^2\,d^5+2\,c\,d^6+d^7}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,a^2\,c\,d^{10}+2\,B\,a^2\,c\,d^{10}+2\,A\,a^2\,c^2\,d^9-4\,A\,a^2\,c^3\,d^8-2\,A\,a^2\,c^4\,d^7-4\,B\,a^2\,c^2\,d^9-6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+4\,B\,a^2\,c^5\,d^6\right)}{c^2\,d^6+2\,c\,d^7+d^8}+\frac{a^2\,\left(\frac{32\,\left(c^4\,d^8+2\,c^3\,d^9+c^2\,d^{10}\right)}{c^2\,d^5+2\,c\,d^6+d^7}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^5\,d^8-4\,c^4\,d^9+c^3\,d^{10}+6\,c^2\,d^{11}+3\,c\,d^{12}\right)}{c^2\,d^6+2\,c\,d^7+d^8}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}\right)\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)}{c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6}}\right)\,\sqrt{-{\left(c+d\right)}^3\,\left(c-d\right)}\,\left(2\,A\,d^2-2\,B\,c^2+B\,d^2+A\,c\,d-2\,B\,c\,d\right)\,2{}\mathrm{i}}{f\,\left(c^3\,d^3+3\,c^2\,d^4+3\,c\,d^5+d^6\right)}","Not used",1,"- ((2*(A*a^2*d^2 + 2*B*a^2*c^2 - A*a^2*c*d))/(d^2*(c + d)) + (2*tan(e/2 + (f*x)/2)^2*(A*a^2*d^2 + 2*B*a^2*c^2 - A*a^2*c*d))/(d^2*(c + d)) + (2*tan(e/2 + (f*x)/2)*(A*a^2*d^2 + 3*B*a^2*c^2 - A*a^2*c*d + B*a^2*c*d))/(c*d*(c + d)) + (2*tan(e/2 + (f*x)/2)^3*(A*a^2*d^2 + B*a^2*c^2 - A*a^2*c*d - B*a^2*c*d))/(c*d*(c + d)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + 2*c*tan(e/2 + (f*x)/2)^2 + c*tan(e/2 + (f*x)/2)^4 + 2*d*tan(e/2 + (f*x)/2)^3)) - (atan((((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(B*a^2*c*2i - a^2*d*(A + 2*B)*1i))/d^3 - (32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6)))/d^3 + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*1i)/d^3 + ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(B*a^2*c*2i - a^2*d*(A + 2*B)*1i))/d^3 - (32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6)))/d^3 + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*1i)/d^3)/((64*(4*B^3*a^6*c^6 - 2*A^3*a^6*c^2*d^4 - 2*A^3*a^6*c^3*d^3 - 10*B^3*a^6*c^2*d^4 + 14*B^3*a^6*c^3*d^3 - 2*B^3*a^6*c^4*d^2 + 4*A^3*a^6*c*d^5 + 2*B^3*a^6*c*d^5 - 8*B^3*a^6*c^5*d + 9*A*B^2*a^6*c*d^5 - 12*A*B^2*a^6*c^5*d + 12*A^2*B*a^6*c*d^5 - 30*A*B^2*a^6*c^2*d^4 + 21*A*B^2*a^6*c^3*d^3 + 12*A*B^2*a^6*c^4*d^2 - 21*A^2*B*a^6*c^2*d^4 + 9*A^2*B*a^6*c^4*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(B*a^2*c*2i - a^2*d*(A + 2*B)*1i))/d^3 - (32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6)))/d^3 + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6)))/d^3 - ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + ((B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*((32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(B*a^2*c*2i - a^2*d*(A + 2*B)*1i))/d^3 - (32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6)))/d^3 + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6)))/d^3 + (64*tan(e/2 + (f*x)/2)*(16*B^3*a^6*c^7 + 2*A^3*a^6*c^2*d^5 - 4*A^3*a^6*c^3*d^4 - 2*A^3*a^6*c^4*d^3 - 32*B^3*a^6*c^2*d^5 + 16*B^3*a^6*c^3*d^4 + 48*B^3*a^6*c^4*d^3 - 40*B^3*a^6*c^5*d^2 + 4*A^3*a^6*c*d^6 + 8*B^3*a^6*c*d^6 - 16*B^3*a^6*c^6*d + 24*A*B^2*a^6*c*d^6 - 24*A*B^2*a^6*c^6*d + 18*A^2*B*a^6*c*d^6 - 48*A*B^2*a^6*c^2*d^5 - 24*A*B^2*a^6*c^3*d^4 + 72*A*B^2*a^6*c^4*d^3 - 12*A^2*B*a^6*c^2*d^5 - 30*A^2*B*a^6*c^3*d^4 + 12*A^2*B*a^6*c^4*d^3 + 12*A^2*B*a^6*c^5*d^2))/(2*c*d^7 + d^8 + c^2*d^6)))*(B*a^2*c*2i - a^2*d*(A + 2*B)*1i)*2i)/(d^3*f) - (a^2*atan(((a^2*(-(c + d)^3*(c - d))^(1/2)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) - (32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (a^2*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d))^(1/2)*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d)*1i)/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3) + (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) - (32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d))^(1/2)*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d)*1i)/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))/((64*(4*B^3*a^6*c^6 - 2*A^3*a^6*c^2*d^4 - 2*A^3*a^6*c^3*d^3 - 10*B^3*a^6*c^2*d^4 + 14*B^3*a^6*c^3*d^3 - 2*B^3*a^6*c^4*d^2 + 4*A^3*a^6*c*d^5 + 2*B^3*a^6*c*d^5 - 8*B^3*a^6*c^5*d + 9*A*B^2*a^6*c*d^5 - 12*A*B^2*a^6*c^5*d + 12*A^2*B*a^6*c*d^5 - 30*A*B^2*a^6*c^2*d^4 + 21*A*B^2*a^6*c^3*d^3 + 12*A*B^2*a^6*c^4*d^2 - 21*A^2*B*a^6*c^2*d^4 + 9*A^2*B*a^6*c^4*d^2))/(2*c*d^6 + d^7 + c^2*d^5) + (64*tan(e/2 + (f*x)/2)*(16*B^3*a^6*c^7 + 2*A^3*a^6*c^2*d^5 - 4*A^3*a^6*c^3*d^4 - 2*A^3*a^6*c^4*d^3 - 32*B^3*a^6*c^2*d^5 + 16*B^3*a^6*c^3*d^4 + 48*B^3*a^6*c^4*d^3 - 40*B^3*a^6*c^5*d^2 + 4*A^3*a^6*c*d^6 + 8*B^3*a^6*c*d^6 - 16*B^3*a^6*c^6*d + 24*A*B^2*a^6*c*d^6 - 24*A*B^2*a^6*c^6*d + 18*A^2*B*a^6*c*d^6 - 48*A*B^2*a^6*c^2*d^5 - 24*A*B^2*a^6*c^3*d^4 + 72*A*B^2*a^6*c^4*d^3 - 12*A^2*B*a^6*c^2*d^5 - 30*A^2*B*a^6*c^3*d^4 + 12*A^2*B*a^6*c^4*d^3 + 12*A^2*B*a^6*c^5*d^2))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) - (32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) + (a^2*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d))^(1/2)*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3) - (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*(A^2*a^4*c^2*d^6 + 2*A^2*a^4*c^3*d^5 + A^2*a^4*c^4*d^4 + 4*B^2*a^4*c^2*d^6 - 8*B^2*a^4*c^4*d^4 + 4*B^2*a^4*c^6*d^2 + 4*A*B*a^4*c^2*d^6 + 4*A*B*a^4*c^3*d^5 - 4*A*B*a^4*c^4*d^4 - 4*A*B*a^4*c^5*d^3))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(8*A^2*a^4*c^2*d^7 + 4*A^2*a^4*c^3*d^6 - 4*A^2*a^4*c^4*d^5 - 2*A^2*a^4*c^5*d^4 + 6*B^2*a^4*c^2*d^7 - 29*B^2*a^4*c^3*d^6 - 4*B^2*a^4*c^4*d^5 + 28*B^2*a^4*c^5*d^4 - 8*B^2*a^4*c^7*d^2 - 2*A^2*a^4*c*d^8 + 7*B^2*a^4*c*d^8 + 22*A*B*a^4*c^2*d^7 - 16*A*B*a^4*c^3*d^6 - 26*A*B*a^4*c^4*d^5 + 8*A*B*a^4*c^5*d^4 + 8*A*B*a^4*c^6*d^3 + 4*A*B*a^4*c*d^8))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*(-(c + d)^3*(c - d))^(1/2)*((32*(A*a^2*c*d^9 + 2*B*a^2*c*d^9 - A*a^2*c^3*d^7 + B*a^2*c^2*d^8 - 2*B*a^2*c^3*d^7 - B*a^2*c^4*d^6))/(2*c*d^6 + d^7 + c^2*d^5) - (32*tan(e/2 + (f*x)/2)*(4*A*a^2*c*d^10 + 2*B*a^2*c*d^10 + 2*A*a^2*c^2*d^9 - 4*A*a^2*c^3*d^8 - 2*A*a^2*c^4*d^7 - 4*B*a^2*c^2*d^9 - 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 4*B*a^2*c^5*d^6))/(2*c*d^7 + d^8 + c^2*d^6) + (a^2*((32*(c^2*d^10 + 2*c^3*d^9 + c^4*d^8))/(2*c*d^6 + d^7 + c^2*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^12 + 6*c^2*d^11 + c^3*d^10 - 4*c^4*d^9 - 2*c^5*d^8))/(2*c*d^7 + d^8 + c^2*d^6))*(-(c + d)^3*(c - d))^(1/2)*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d))/(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3)))*(-(c + d)^3*(c - d))^(1/2)*(2*A*d^2 - 2*B*c^2 + B*d^2 + A*c*d - 2*B*c*d)*2i)/(f*(3*c*d^5 + d^6 + 3*c^2*d^4 + c^3*d^3))","B"
257,1,8632,215,22.497149,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2)/(c + d*sin(e + f*x))^3,x)","-\frac{\frac{A\,a^2\,d^3-2\,B\,a^2\,c^3+4\,A\,a^2\,c\,d^2+B\,a^2\,c\,d^2-4\,B\,a^2\,c^2\,d}{d^2\,\left(c^2+2\,c\,d+d^2\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(B\,a^2\,c^3-2\,A\,a^2\,d^3-4\,A\,a^2\,c\,d^2+A\,a^2\,c^2\,d+4\,B\,a^2\,c^2\,d\right)}{c\,d\,\left(c^2+2\,c\,d+d^2\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a^2\,d^3-7\,B\,a^2\,c^3+12\,A\,a^2\,c\,d^2+A\,a^2\,c^2\,d+4\,B\,a^2\,c\,d^2-12\,B\,a^2\,c^2\,d\right)}{c\,d\,\left(c^2+2\,c\,d+d^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(c^2+2\,d^2\right)\,\left(A\,a^2\,d^3-2\,B\,a^2\,c^3+4\,A\,a^2\,c\,d^2+B\,a^2\,c\,d^2-4\,B\,a^2\,c^2\,d\right)}{c^2\,d^2\,\left(c^2+2\,c\,d+d^2\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+c^2+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}+\frac{2\,B\,a^2\,\mathrm{atan}\left(\frac{\frac{B\,a^2\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{B\,a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)}{d^3}}{\frac{16\,\left(-9\,A^2\,B\,a^6\,c\,d^4+6\,A\,B^2\,a^6\,c^4\,d+12\,A\,B^2\,a^6\,c^3\,d^2-24\,A\,B^2\,a^6\,c\,d^4+2\,B^3\,a^6\,c^5+12\,B^3\,a^6\,c^4\,d+17\,B^3\,a^6\,c^3\,d^2-16\,B^3\,a^6\,c\,d^4\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,B^3\,a^6\,c^6-32\,B^3\,a^6\,c^5\,d-44\,B^3\,a^6\,c^4\,d^2-8\,B^3\,a^6\,c^3\,d^3+28\,B^3\,a^6\,c^2\,d^4+16\,B^3\,a^6\,c\,d^5+12\,A\,B^2\,a^6\,c^3\,d^3+24\,A\,B^2\,a^6\,c^2\,d^4+12\,A\,B^2\,a^6\,c\,d^5\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{B\,a^2\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{B\,a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{B\,a^2\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}\right)\,1{}\mathrm{i}}{d^3}}\right)}{d^3\,f}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)\,1{}\mathrm{i}}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)\,1{}\mathrm{i}}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}}{\frac{16\,\left(-9\,A^2\,B\,a^6\,c\,d^4+6\,A\,B^2\,a^6\,c^4\,d+12\,A\,B^2\,a^6\,c^3\,d^2-24\,A\,B^2\,a^6\,c\,d^4+2\,B^3\,a^6\,c^5+12\,B^3\,a^6\,c^4\,d+17\,B^3\,a^6\,c^3\,d^2-16\,B^3\,a^6\,c\,d^4\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,B^3\,a^6\,c^6-32\,B^3\,a^6\,c^5\,d-44\,B^3\,a^6\,c^4\,d^2-8\,B^3\,a^6\,c^3\,d^3+28\,B^3\,a^6\,c^2\,d^4+16\,B^3\,a^6\,c\,d^5+12\,A\,B^2\,a^6\,c^3\,d^3+24\,A\,B^2\,a^6\,c^2\,d^4+12\,A\,B^2\,a^6\,c\,d^5\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}-\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,B^2\,a^4\,c^6\,d^2+16\,B^2\,a^4\,c^5\,d^3+24\,B^2\,a^4\,c^4\,d^4+16\,B^2\,a^4\,c^3\,d^5+4\,B^2\,a^4\,c^2\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-9\,A^2\,a^4\,c\,d^8+12\,A\,B\,a^4\,c^4\,d^5+24\,A\,B\,a^4\,c^3\,d^6+6\,A\,B\,a^4\,c^2\,d^7-24\,A\,B\,a^4\,c\,d^8-8\,B^2\,a^4\,c^7\,d^2-32\,B^2\,a^4\,c^6\,d^3-36\,B^2\,a^4\,c^5\,d^4+24\,B^2\,a^4\,c^4\,d^5+75\,B^2\,a^4\,c^3\,d^6+40\,B^2\,a^4\,c^2\,d^7-8\,B^2\,a^4\,c\,d^8\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,B\,a^2\,c\,d^{10}-6\,A\,a^2\,c^2\,d^9-12\,A\,a^2\,c^3\,d^8-6\,A\,a^2\,c^4\,d^7+8\,B\,a^2\,c^2\,d^9+6\,B\,a^2\,c^3\,d^8+4\,B\,a^2\,c^4\,d^7+2\,B\,a^2\,c^5\,d^6\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,A\,a^2\,c\,d^{11}+16\,B\,a^2\,c\,d^{11}+24\,A\,a^2\,c^2\,d^{10}+12\,A\,a^2\,c^3\,d^9+28\,B\,a^2\,c^2\,d^{10}-8\,B\,a^2\,c^3\,d^9-44\,B\,a^2\,c^4\,d^8-32\,B\,a^2\,c^5\,d^7-8\,B\,a^2\,c^6\,d^6\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}+\frac{a^2\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^8+16\,c^5\,d^9+24\,c^4\,d^{10}+16\,c^3\,d^{11}+4\,c^2\,d^{12}\right)}{c^4\,d^5+4\,c^3\,d^6+6\,c^2\,d^7+4\,c\,d^8+d^9}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^8-32\,c^6\,d^9-36\,c^5\,d^{10}+16\,c^4\,d^{11}+64\,c^3\,d^{12}+48\,c^2\,d^{13}+12\,c\,d^{14}\right)}{c^4\,d^6+4\,c^3\,d^7+6\,c^2\,d^8+4\,c\,d^9+d^{10}}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}\right)\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}}\right)\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(2\,B\,c^3-3\,A\,d^3-4\,B\,d^3+B\,c\,d^2+4\,B\,c^2\,d\right)\,1{}\mathrm{i}}{f\,\left(-c^6\,d^3-4\,c^5\,d^4-5\,c^4\,d^5+5\,c^2\,d^7+4\,c\,d^8+d^9\right)}","Not used",1,"(2*B*a^2*atan(((B*a^2*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (B*a^2*((8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (B*a^2*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3)*1i)/d^3))/d^3 + (B*a^2*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (B*a^2*((8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (B*a^2*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3)*1i)/d^3))/d^3)/((16*(2*B^3*a^6*c^5 + 17*B^3*a^6*c^3*d^2 - 16*B^3*a^6*c*d^4 + 12*B^3*a^6*c^4*d - 24*A*B^2*a^6*c*d^4 + 6*A*B^2*a^6*c^4*d - 9*A^2*B*a^6*c*d^4 + 12*A*B^2*a^6*c^3*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (16*tan(e/2 + (f*x)/2)*(28*B^3*a^6*c^2*d^4 - 8*B^3*a^6*c^6 - 8*B^3*a^6*c^3*d^3 - 44*B^3*a^6*c^4*d^2 + 16*B^3*a^6*c*d^5 - 32*B^3*a^6*c^5*d + 12*A*B^2*a^6*c*d^5 + 24*A*B^2*a^6*c^2*d^4 + 12*A*B^2*a^6*c^3*d^3))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (B*a^2*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (B*a^2*((8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (B*a^2*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3)*1i)/d^3)*1i)/d^3 + (B*a^2*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (B*a^2*((8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (B*a^2*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*1i)/d^3)*1i)/d^3)*1i)/d^3)))/(d^3*f) - ((A*a^2*d^3 - 2*B*a^2*c^3 + 4*A*a^2*c*d^2 + B*a^2*c*d^2 - 4*B*a^2*c^2*d)/(d^2*(2*c*d + c^2 + d^2)) - (tan(e/2 + (f*x)/2)^3*(B*a^2*c^3 - 2*A*a^2*d^3 - 4*A*a^2*c*d^2 + A*a^2*c^2*d + 4*B*a^2*c^2*d))/(c*d*(2*c*d + c^2 + d^2)) + (tan(e/2 + (f*x)/2)*(2*A*a^2*d^3 - 7*B*a^2*c^3 + 12*A*a^2*c*d^2 + A*a^2*c^2*d + 4*B*a^2*c*d^2 - 12*B*a^2*c^2*d))/(c*d*(2*c*d + c^2 + d^2)) + (tan(e/2 + (f*x)/2)^2*(c^2 + 2*d^2)*(A*a^2*d^3 - 2*B*a^2*c^3 + 4*A*a^2*c*d^2 + B*a^2*c*d^2 - 4*B*a^2*c^2*d))/(c^2*d^2*(2*c*d + c^2 + d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^4 + c^2 + 4*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2))) + (a^2*atan(((a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d)*1i)/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d)*1i)/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))/((16*(2*B^3*a^6*c^5 + 17*B^3*a^6*c^3*d^2 - 16*B^3*a^6*c*d^4 + 12*B^3*a^6*c^4*d - 24*A*B^2*a^6*c*d^4 + 6*A*B^2*a^6*c^4*d - 9*A^2*B*a^6*c*d^4 + 12*A*B^2*a^6*c^3*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (16*tan(e/2 + (f*x)/2)*(28*B^3*a^6*c^2*d^4 - 8*B^3*a^6*c^6 - 8*B^3*a^6*c^3*d^3 - 44*B^3*a^6*c^4*d^2 + 16*B^3*a^6*c*d^5 - 32*B^3*a^6*c^5*d + 12*A*B^2*a^6*c*d^5 + 24*A*B^2*a^6*c^2*d^4 + 12*A*B^2*a^6*c^3*d^3))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) - (8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*B^2*a^4*c^2*d^6 + 16*B^2*a^4*c^3*d^5 + 24*B^2*a^4*c^4*d^4 + 16*B^2*a^4*c^5*d^3 + 4*B^2*a^4*c^6*d^2))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(40*B^2*a^4*c^2*d^7 + 75*B^2*a^4*c^3*d^6 + 24*B^2*a^4*c^4*d^5 - 36*B^2*a^4*c^5*d^4 - 32*B^2*a^4*c^6*d^3 - 8*B^2*a^4*c^7*d^2 - 9*A^2*a^4*c*d^8 - 8*B^2*a^4*c*d^8 + 6*A*B*a^4*c^2*d^7 + 24*A*B*a^4*c^3*d^6 + 12*A*B*a^4*c^4*d^5 - 24*A*B*a^4*c*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*B*a^2*c*d^10 - 6*A*a^2*c^2*d^9 - 12*A*a^2*c^3*d^8 - 6*A*a^2*c^4*d^7 + 8*B*a^2*c^2*d^9 + 6*B*a^2*c^3*d^8 + 4*B*a^2*c^4*d^7 + 2*B*a^2*c^5*d^6))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) - (8*tan(e/2 + (f*x)/2)*(12*A*a^2*c*d^11 + 16*B*a^2*c*d^11 + 24*A*a^2*c^2*d^10 + 12*A*a^2*c^3*d^9 + 28*B*a^2*c^2*d^10 - 8*B*a^2*c^3*d^9 - 44*B*a^2*c^4*d^8 - 32*B*a^2*c^5*d^7 - 8*B*a^2*c^6*d^6))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6) + (a^2*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^12 + 16*c^3*d^11 + 24*c^4*d^10 + 16*c^5*d^9 + 4*c^6*d^8))/(4*c*d^8 + d^9 + 6*c^2*d^7 + 4*c^3*d^6 + c^4*d^5) + (8*tan(e/2 + (f*x)/2)*(12*c*d^14 + 48*c^2*d^13 + 64*c^3*d^12 + 16*c^4*d^11 - 36*c^5*d^10 - 32*c^6*d^9 - 8*c^7*d^8))/(4*c*d^9 + d^10 + 6*c^2*d^8 + 4*c^3*d^7 + c^4*d^6))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3)))*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d))/(2*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3))))*(-(c + d)^5*(c - d))^(1/2)*(2*B*c^3 - 3*A*d^3 - 4*B*d^3 + B*c*d^2 + 4*B*c^2*d)*1i)/(f*(4*c*d^8 + d^9 + 5*c^2*d^7 - 5*c^4*d^5 - 4*c^5*d^4 - c^6*d^3))","B"
258,1,1395,604,16.175559,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^3,x)","\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(40\,A\,c^3+23\,A\,d^3+30\,B\,c^3+21\,B\,d^3+78\,A\,c\,d^2+90\,A\,c^2\,d+69\,B\,c\,d^2+78\,B\,c^2\,d\right)}{8\,\left(5\,A\,a^3\,c^3+\frac{23\,A\,a^3\,d^3}{8}+\frac{15\,B\,a^3\,c^3}{4}+\frac{21\,B\,a^3\,d^3}{8}+\frac{39\,A\,a^3\,c\,d^2}{4}+\frac{45\,A\,a^3\,c^2\,d}{4}+\frac{69\,B\,a^3\,c\,d^2}{8}+\frac{39\,B\,a^3\,c^2\,d}{4}\right)}\right)\,\left(40\,A\,c^3+23\,A\,d^3+30\,B\,c^3+21\,B\,d^3+78\,A\,c\,d^2+90\,A\,c^2\,d+69\,B\,c\,d^2+78\,B\,c^2\,d\right)}{8\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A\,a^3\,c^3+\frac{23\,A\,a^3\,d^3}{8}+\frac{15\,B\,a^3\,c^3}{4}+\frac{21\,B\,a^3\,d^3}{8}+\frac{39\,A\,a^3\,c\,d^2}{4}+\frac{45\,A\,a^3\,c^2\,d}{4}+\frac{69\,B\,a^3\,c\,d^2}{8}+\frac{39\,B\,a^3\,c^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(40\,A\,a^3\,c^3+4\,A\,a^3\,d^3+24\,B\,a^3\,c^3+36\,A\,a^3\,c\,d^2+72\,A\,a^3\,c^2\,d+12\,B\,a^3\,c\,d^2+36\,B\,a^3\,c^2\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{13}\,\left(3\,A\,a^3\,c^3+\frac{23\,A\,a^3\,d^3}{8}+\frac{15\,B\,a^3\,c^3}{4}+\frac{21\,B\,a^3\,d^3}{8}+\frac{39\,A\,a^3\,c\,d^2}{4}+\frac{45\,A\,a^3\,c^2\,d}{4}+\frac{69\,B\,a^3\,c\,d^2}{8}+\frac{39\,B\,a^3\,c^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(12\,A\,a^3\,c^3+\frac{115\,A\,a^3\,d^3}{6}+17\,B\,a^3\,c^3+\frac{35\,B\,a^3\,d^3}{2}+57\,A\,a^3\,c\,d^2+51\,A\,a^3\,c^2\,d+\frac{115\,B\,a^3\,c\,d^2}{2}+57\,B\,a^3\,c^2\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(12\,A\,a^3\,c^3+\frac{115\,A\,a^3\,d^3}{6}+17\,B\,a^3\,c^3+\frac{35\,B\,a^3\,d^3}{2}+57\,A\,a^3\,c\,d^2+51\,A\,a^3\,c^2\,d+\frac{115\,B\,a^3\,c\,d^2}{2}+57\,B\,a^3\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(\frac{322\,A\,a^3\,c^3}{3}+\frac{148\,A\,a^3\,d^3}{3}+82\,B\,a^3\,c^3+32\,B\,a^3\,d^3+188\,A\,a^3\,c\,d^2+246\,A\,a^3\,c^2\,d+148\,B\,a^3\,c\,d^2+188\,B\,a^3\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{448\,A\,a^3\,c^3}{3}+\frac{328\,A\,a^3\,d^3}{3}+128\,B\,a^3\,c^3+112\,B\,a^3\,d^3+344\,A\,a^3\,c\,d^2+384\,A\,a^3\,c^2\,d+328\,B\,a^3\,c\,d^2+344\,B\,a^3\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{136\,A\,a^3\,c^3}{3}+\frac{476\,A\,a^3\,d^3}{15}+40\,B\,a^3\,c^3+\frac{144\,B\,a^3\,d^3}{5}+\frac{532\,A\,a^3\,c\,d^2}{5}+120\,A\,a^3\,c^2\,d+\frac{476\,B\,a^3\,c\,d^2}{5}+\frac{532\,B\,a^3\,c^2\,d}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(15\,A\,a^3\,c^3+\frac{841\,A\,a^3\,d^3}{24}+\frac{91\,B\,a^3\,c^3}{4}+\frac{345\,B\,a^3\,d^3}{8}+\frac{339\,A\,a^3\,c\,d^2}{4}+\frac{273\,A\,a^3\,c^2\,d}{4}+\frac{841\,B\,a^3\,c\,d^2}{8}+\frac{339\,B\,a^3\,c^2\,d}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(15\,A\,a^3\,c^3+\frac{841\,A\,a^3\,d^3}{24}+\frac{91\,B\,a^3\,c^3}{4}+\frac{345\,B\,a^3\,d^3}{8}+\frac{339\,A\,a^3\,c\,d^2}{4}+\frac{273\,A\,a^3\,c^2\,d}{4}+\frac{841\,B\,a^3\,c\,d^2}{8}+\frac{339\,B\,a^3\,c^2\,d}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(114\,A\,a^3\,c^3+\frac{456\,A\,a^3\,d^3}{5}+102\,B\,a^3\,c^3+\frac{432\,B\,a^3\,d^3}{5}+\frac{1416\,A\,a^3\,c\,d^2}{5}+306\,A\,a^3\,c^2\,d+\frac{1368\,B\,a^3\,c\,d^2}{5}+\frac{1416\,B\,a^3\,c^2\,d}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}\,\left(6\,A\,a^3\,c^3+2\,B\,a^3\,c^3+6\,A\,a^3\,c^2\,d\right)+\frac{22\,A\,a^3\,c^3}{3}+\frac{68\,A\,a^3\,d^3}{15}+6\,B\,a^3\,c^3+\frac{144\,B\,a^3\,d^3}{35}+\frac{76\,A\,a^3\,c\,d^2}{5}+18\,A\,a^3\,c^2\,d+\frac{68\,B\,a^3\,c\,d^2}{5}+\frac{76\,B\,a^3\,c^2\,d}{5}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*atan((a^3*tan(e/2 + (f*x)/2)*(40*A*c^3 + 23*A*d^3 + 30*B*c^3 + 21*B*d^3 + 78*A*c*d^2 + 90*A*c^2*d + 69*B*c*d^2 + 78*B*c^2*d))/(8*(5*A*a^3*c^3 + (23*A*a^3*d^3)/8 + (15*B*a^3*c^3)/4 + (21*B*a^3*d^3)/8 + (39*A*a^3*c*d^2)/4 + (45*A*a^3*c^2*d)/4 + (69*B*a^3*c*d^2)/8 + (39*B*a^3*c^2*d)/4)))*(40*A*c^3 + 23*A*d^3 + 30*B*c^3 + 21*B*d^3 + 78*A*c*d^2 + 90*A*c^2*d + 69*B*c*d^2 + 78*B*c^2*d))/(8*f) - (tan(e/2 + (f*x)/2)*(3*A*a^3*c^3 + (23*A*a^3*d^3)/8 + (15*B*a^3*c^3)/4 + (21*B*a^3*d^3)/8 + (39*A*a^3*c*d^2)/4 + (45*A*a^3*c^2*d)/4 + (69*B*a^3*c*d^2)/8 + (39*B*a^3*c^2*d)/4) + tan(e/2 + (f*x)/2)^10*(40*A*a^3*c^3 + 4*A*a^3*d^3 + 24*B*a^3*c^3 + 36*A*a^3*c*d^2 + 72*A*a^3*c^2*d + 12*B*a^3*c*d^2 + 36*B*a^3*c^2*d) - tan(e/2 + (f*x)/2)^13*(3*A*a^3*c^3 + (23*A*a^3*d^3)/8 + (15*B*a^3*c^3)/4 + (21*B*a^3*d^3)/8 + (39*A*a^3*c*d^2)/4 + (45*A*a^3*c^2*d)/4 + (69*B*a^3*c*d^2)/8 + (39*B*a^3*c^2*d)/4) + tan(e/2 + (f*x)/2)^3*(12*A*a^3*c^3 + (115*A*a^3*d^3)/6 + 17*B*a^3*c^3 + (35*B*a^3*d^3)/2 + 57*A*a^3*c*d^2 + 51*A*a^3*c^2*d + (115*B*a^3*c*d^2)/2 + 57*B*a^3*c^2*d) - tan(e/2 + (f*x)/2)^11*(12*A*a^3*c^3 + (115*A*a^3*d^3)/6 + 17*B*a^3*c^3 + (35*B*a^3*d^3)/2 + 57*A*a^3*c*d^2 + 51*A*a^3*c^2*d + (115*B*a^3*c*d^2)/2 + 57*B*a^3*c^2*d) + tan(e/2 + (f*x)/2)^8*((322*A*a^3*c^3)/3 + (148*A*a^3*d^3)/3 + 82*B*a^3*c^3 + 32*B*a^3*d^3 + 188*A*a^3*c*d^2 + 246*A*a^3*c^2*d + 148*B*a^3*c*d^2 + 188*B*a^3*c^2*d) + tan(e/2 + (f*x)/2)^6*((448*A*a^3*c^3)/3 + (328*A*a^3*d^3)/3 + 128*B*a^3*c^3 + 112*B*a^3*d^3 + 344*A*a^3*c*d^2 + 384*A*a^3*c^2*d + 328*B*a^3*c*d^2 + 344*B*a^3*c^2*d) + tan(e/2 + (f*x)/2)^2*((136*A*a^3*c^3)/3 + (476*A*a^3*d^3)/15 + 40*B*a^3*c^3 + (144*B*a^3*d^3)/5 + (532*A*a^3*c*d^2)/5 + 120*A*a^3*c^2*d + (476*B*a^3*c*d^2)/5 + (532*B*a^3*c^2*d)/5) + tan(e/2 + (f*x)/2)^5*(15*A*a^3*c^3 + (841*A*a^3*d^3)/24 + (91*B*a^3*c^3)/4 + (345*B*a^3*d^3)/8 + (339*A*a^3*c*d^2)/4 + (273*A*a^3*c^2*d)/4 + (841*B*a^3*c*d^2)/8 + (339*B*a^3*c^2*d)/4) - tan(e/2 + (f*x)/2)^9*(15*A*a^3*c^3 + (841*A*a^3*d^3)/24 + (91*B*a^3*c^3)/4 + (345*B*a^3*d^3)/8 + (339*A*a^3*c*d^2)/4 + (273*A*a^3*c^2*d)/4 + (841*B*a^3*c*d^2)/8 + (339*B*a^3*c^2*d)/4) + tan(e/2 + (f*x)/2)^4*(114*A*a^3*c^3 + (456*A*a^3*d^3)/5 + 102*B*a^3*c^3 + (432*B*a^3*d^3)/5 + (1416*A*a^3*c*d^2)/5 + 306*A*a^3*c^2*d + (1368*B*a^3*c*d^2)/5 + (1416*B*a^3*c^2*d)/5) + tan(e/2 + (f*x)/2)^12*(6*A*a^3*c^3 + 2*B*a^3*c^3 + 6*A*a^3*c^2*d) + (22*A*a^3*c^3)/3 + (68*A*a^3*d^3)/15 + 6*B*a^3*c^3 + (144*B*a^3*d^3)/35 + (76*A*a^3*c*d^2)/5 + 18*A*a^3*c^2*d + (68*B*a^3*c*d^2)/5 + (76*B*a^3*c^2*d)/5)/(f*(7*tan(e/2 + (f*x)/2)^2 + 21*tan(e/2 + (f*x)/2)^4 + 35*tan(e/2 + (f*x)/2)^6 + 35*tan(e/2 + (f*x)/2)^8 + 21*tan(e/2 + (f*x)/2)^10 + 7*tan(e/2 + (f*x)/2)^12 + tan(e/2 + (f*x)/2)^14 + 1))","B"
259,1,976,463,15.626257,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^2,x)","\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(40\,A\,c^2+26\,A\,d^2+30\,B\,c^2+23\,B\,d^2+60\,A\,c\,d+52\,B\,c\,d\right)}{8\,\left(5\,A\,a^3\,c^2+\frac{13\,A\,a^3\,d^2}{4}+\frac{15\,B\,a^3\,c^2}{4}+\frac{23\,B\,a^3\,d^2}{8}+\frac{15\,A\,a^3\,c\,d}{2}+\frac{13\,B\,a^3\,c\,d}{2}\right)}\right)\,\left(40\,A\,c^2+26\,A\,d^2+30\,B\,c^2+23\,B\,d^2+60\,A\,c\,d+52\,B\,c\,d\right)}{8\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}\,\left(6\,A\,a^3\,c^2+2\,B\,a^3\,c^2+4\,A\,a^3\,c\,d\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A\,a^3\,c^2+\frac{13\,A\,a^3\,d^2}{4}+\frac{15\,B\,a^3\,c^2}{4}+\frac{23\,B\,a^3\,d^2}{8}+\frac{15\,A\,a^3\,c\,d}{2}+\frac{13\,B\,a^3\,c\,d}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{11}\,\left(3\,A\,a^3\,c^2+\frac{13\,A\,a^3\,d^2}{4}+\frac{15\,B\,a^3\,c^2}{4}+\frac{23\,B\,a^3\,d^2}{8}+\frac{15\,A\,a^3\,c\,d}{2}+\frac{13\,B\,a^3\,c\,d}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(34\,A\,a^3\,c^2+12\,A\,a^3\,d^2+22\,B\,a^3\,c^2+4\,B\,a^3\,d^2+44\,A\,a^3\,c\,d+24\,B\,a^3\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(6\,A\,a^3\,c^2+\frac{25\,A\,a^3\,d^2}{2}+\frac{19\,B\,a^3\,c^2}{2}+\frac{75\,B\,a^3\,d^2}{4}+19\,A\,a^3\,c\,d+25\,B\,a^3\,c\,d\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(6\,A\,a^3\,c^2+\frac{25\,A\,a^3\,d^2}{2}+\frac{19\,B\,a^3\,c^2}{2}+\frac{75\,B\,a^3\,d^2}{4}+19\,A\,a^3\,c\,d+25\,B\,a^3\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(76\,A\,a^3\,c^2+64\,A\,a^3\,d^2+68\,B\,a^3\,c^2+64\,B\,a^3\,d^2+136\,A\,a^3\,c\,d+128\,B\,a^3\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(9\,A\,a^3\,c^2+\frac{63\,A\,a^3\,d^2}{4}+\frac{53\,B\,a^3\,c^2}{4}+\frac{391\,B\,a^3\,d^2}{24}+\frac{53\,A\,a^3\,c\,d}{2}+\frac{63\,B\,a^3\,c\,d}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(9\,A\,a^3\,c^2+\frac{63\,A\,a^3\,d^2}{4}+\frac{53\,B\,a^3\,c^2}{4}+\frac{391\,B\,a^3\,d^2}{24}+\frac{53\,A\,a^3\,c\,d}{2}+\frac{63\,B\,a^3\,c\,d}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(38\,A\,a^3\,c^2+\frac{152\,A\,a^3\,d^2}{5}+34\,B\,a^3\,c^2+\frac{136\,B\,a^3\,d^2}{5}+68\,A\,a^3\,c\,d+\frac{304\,B\,a^3\,c\,d}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(\frac{220\,A\,a^3\,c^2}{3}+\frac{152\,A\,a^3\,d^2}{3}+60\,B\,a^3\,c^2+\frac{136\,B\,a^3\,d^2}{3}+120\,A\,a^3\,c\,d+\frac{304\,B\,a^3\,c\,d}{3}\right)+\frac{22\,A\,a^3\,c^2}{3}+\frac{76\,A\,a^3\,d^2}{15}+6\,B\,a^3\,c^2+\frac{68\,B\,a^3\,d^2}{15}+12\,A\,a^3\,c\,d+\frac{152\,B\,a^3\,c\,d}{15}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*atan((a^3*tan(e/2 + (f*x)/2)*(40*A*c^2 + 26*A*d^2 + 30*B*c^2 + 23*B*d^2 + 60*A*c*d + 52*B*c*d))/(8*(5*A*a^3*c^2 + (13*A*a^3*d^2)/4 + (15*B*a^3*c^2)/4 + (23*B*a^3*d^2)/8 + (15*A*a^3*c*d)/2 + (13*B*a^3*c*d)/2)))*(40*A*c^2 + 26*A*d^2 + 30*B*c^2 + 23*B*d^2 + 60*A*c*d + 52*B*c*d))/(8*f) - (tan(e/2 + (f*x)/2)^10*(6*A*a^3*c^2 + 2*B*a^3*c^2 + 4*A*a^3*c*d) + tan(e/2 + (f*x)/2)*(3*A*a^3*c^2 + (13*A*a^3*d^2)/4 + (15*B*a^3*c^2)/4 + (23*B*a^3*d^2)/8 + (15*A*a^3*c*d)/2 + (13*B*a^3*c*d)/2) - tan(e/2 + (f*x)/2)^11*(3*A*a^3*c^2 + (13*A*a^3*d^2)/4 + (15*B*a^3*c^2)/4 + (23*B*a^3*d^2)/8 + (15*A*a^3*c*d)/2 + (13*B*a^3*c*d)/2) + tan(e/2 + (f*x)/2)^8*(34*A*a^3*c^2 + 12*A*a^3*d^2 + 22*B*a^3*c^2 + 4*B*a^3*d^2 + 44*A*a^3*c*d + 24*B*a^3*c*d) + tan(e/2 + (f*x)/2)^5*(6*A*a^3*c^2 + (25*A*a^3*d^2)/2 + (19*B*a^3*c^2)/2 + (75*B*a^3*d^2)/4 + 19*A*a^3*c*d + 25*B*a^3*c*d) - tan(e/2 + (f*x)/2)^7*(6*A*a^3*c^2 + (25*A*a^3*d^2)/2 + (19*B*a^3*c^2)/2 + (75*B*a^3*d^2)/4 + 19*A*a^3*c*d + 25*B*a^3*c*d) + tan(e/2 + (f*x)/2)^4*(76*A*a^3*c^2 + 64*A*a^3*d^2 + 68*B*a^3*c^2 + 64*B*a^3*d^2 + 136*A*a^3*c*d + 128*B*a^3*c*d) + tan(e/2 + (f*x)/2)^3*(9*A*a^3*c^2 + (63*A*a^3*d^2)/4 + (53*B*a^3*c^2)/4 + (391*B*a^3*d^2)/24 + (53*A*a^3*c*d)/2 + (63*B*a^3*c*d)/2) - tan(e/2 + (f*x)/2)^9*(9*A*a^3*c^2 + (63*A*a^3*d^2)/4 + (53*B*a^3*c^2)/4 + (391*B*a^3*d^2)/24 + (53*A*a^3*c*d)/2 + (63*B*a^3*c*d)/2) + tan(e/2 + (f*x)/2)^2*(38*A*a^3*c^2 + (152*A*a^3*d^2)/5 + 34*B*a^3*c^2 + (136*B*a^3*d^2)/5 + 68*A*a^3*c*d + (304*B*a^3*c*d)/5) + tan(e/2 + (f*x)/2)^6*((220*A*a^3*c^2)/3 + (152*A*a^3*d^2)/3 + 60*B*a^3*c^2 + (136*B*a^3*d^2)/3 + 120*A*a^3*c*d + (304*B*a^3*c*d)/3) + (22*A*a^3*c^2)/3 + (76*A*a^3*d^2)/15 + 6*B*a^3*c^2 + (68*B*a^3*d^2)/15 + 12*A*a^3*c*d + (152*B*a^3*c*d)/15)/(f*(6*tan(e/2 + (f*x)/2)^2 + 15*tan(e/2 + (f*x)/2)^4 + 20*tan(e/2 + (f*x)/2)^6 + 15*tan(e/2 + (f*x)/2)^8 + 6*tan(e/2 + (f*x)/2)^10 + tan(e/2 + (f*x)/2)^12 + 1))","B"
260,1,550,201,14.623126,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3*(c + d*sin(e + f*x)),x)","\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(20\,A\,c+15\,A\,d+15\,B\,c+13\,B\,d\right)}{4\,\left(5\,A\,a^3\,c+\frac{15\,A\,a^3\,d}{4}+\frac{15\,B\,a^3\,c}{4}+\frac{13\,B\,a^3\,d}{4}\right)}\right)\,\left(20\,A\,c+15\,A\,d+15\,B\,c+13\,B\,d\right)}{4\,f}-\frac{a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)\,\left(20\,A\,c+15\,A\,d+15\,B\,c+13\,B\,d\right)}{4\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(6\,A\,a^3\,c+\frac{19\,A\,a^3\,d}{2}+\frac{19\,B\,a^3\,c}{2}+\frac{25\,B\,a^3\,d}{2}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\,\left(3\,A\,a^3\,c+\frac{15\,A\,a^3\,d}{4}+\frac{15\,B\,a^3\,c}{4}+\frac{13\,B\,a^3\,d}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(6\,A\,a^3\,c+\frac{19\,A\,a^3\,d}{2}+\frac{19\,B\,a^3\,c}{2}+\frac{25\,B\,a^3\,d}{2}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(28\,A\,a^3\,c+20\,A\,a^3\,d+20\,B\,a^3\,c+12\,B\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{92\,A\,a^3\,c}{3}+28\,A\,a^3\,d+28\,B\,a^3\,c+\frac{76\,B\,a^3\,d}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{136\,A\,a^3\,c}{3}+40\,A\,a^3\,d+40\,B\,a^3\,c+\frac{116\,B\,a^3\,d}{3}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(6\,A\,a^3\,c+2\,A\,a^3\,d+2\,B\,a^3\,c\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A\,a^3\,c+\frac{15\,A\,a^3\,d}{4}+\frac{15\,B\,a^3\,c}{4}+\frac{13\,B\,a^3\,d}{4}\right)+\frac{22\,A\,a^3\,c}{3}+6\,A\,a^3\,d+6\,B\,a^3\,c+\frac{76\,B\,a^3\,d}{15}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*atan((a^3*tan(e/2 + (f*x)/2)*(20*A*c + 15*A*d + 15*B*c + 13*B*d))/(4*(5*A*a^3*c + (15*A*a^3*d)/4 + (15*B*a^3*c)/4 + (13*B*a^3*d)/4)))*(20*A*c + 15*A*d + 15*B*c + 13*B*d))/(4*f) - (a^3*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2)*(20*A*c + 15*A*d + 15*B*c + 13*B*d))/(4*f) - (tan(e/2 + (f*x)/2)^3*(6*A*a^3*c + (19*A*a^3*d)/2 + (19*B*a^3*c)/2 + (25*B*a^3*d)/2) - tan(e/2 + (f*x)/2)^9*(3*A*a^3*c + (15*A*a^3*d)/4 + (15*B*a^3*c)/4 + (13*B*a^3*d)/4) - tan(e/2 + (f*x)/2)^7*(6*A*a^3*c + (19*A*a^3*d)/2 + (19*B*a^3*c)/2 + (25*B*a^3*d)/2) + tan(e/2 + (f*x)/2)^6*(28*A*a^3*c + 20*A*a^3*d + 20*B*a^3*c + 12*B*a^3*d) + tan(e/2 + (f*x)/2)^2*((92*A*a^3*c)/3 + 28*A*a^3*d + 28*B*a^3*c + (76*B*a^3*d)/3) + tan(e/2 + (f*x)/2)^4*((136*A*a^3*c)/3 + 40*A*a^3*d + 40*B*a^3*c + (116*B*a^3*d)/3) + tan(e/2 + (f*x)/2)^8*(6*A*a^3*c + 2*A*a^3*d + 2*B*a^3*c) + tan(e/2 + (f*x)/2)*(3*A*a^3*c + (15*A*a^3*d)/4 + (15*B*a^3*c)/4 + (13*B*a^3*d)/4) + (22*A*a^3*c)/3 + 6*A*a^3*d + 6*B*a^3*c + (76*B*a^3*d)/15)/(f*(5*tan(e/2 + (f*x)/2)^2 + 10*tan(e/2 + (f*x)/2)^4 + 10*tan(e/2 + (f*x)/2)^6 + 5*tan(e/2 + (f*x)/2)^8 + tan(e/2 + (f*x)/2)^10 + 1))","B"
261,1,330,127,14.256309,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3,x)","\frac{5\,a^3\,\mathrm{atan}\left(\frac{5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A+3\,B\right)}{4\,\left(5\,A\,a^3+\frac{15\,B\,a^3}{4}\right)}\right)\,\left(4\,A+3\,B\right)}{4\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A\,a^3+\frac{15\,B\,a^3}{4}\right)+\frac{22\,A\,a^3}{3}+6\,B\,a^3+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(6\,A\,a^3+2\,B\,a^3\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(3\,A\,a^3+\frac{15\,B\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(3\,A\,a^3+\frac{23\,B\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(3\,A\,a^3+\frac{23\,B\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(22\,A\,a^3+18\,B\,a^3\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{70\,A\,a^3}{3}+22\,B\,a^3\right)}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+1\right)}-\frac{5\,a^3\,\left(4\,A+3\,B\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)-\frac{f\,x}{2}\right)}{4\,f}","Not used",1,"(5*a^3*atan((5*a^3*tan(e/2 + (f*x)/2)*(4*A + 3*B))/(4*(5*A*a^3 + (15*B*a^3)/4)))*(4*A + 3*B))/(4*f) - (tan(e/2 + (f*x)/2)*(3*A*a^3 + (15*B*a^3)/4) + (22*A*a^3)/3 + 6*B*a^3 + tan(e/2 + (f*x)/2)^6*(6*A*a^3 + 2*B*a^3) - tan(e/2 + (f*x)/2)^7*(3*A*a^3 + (15*B*a^3)/4) + tan(e/2 + (f*x)/2)^3*(3*A*a^3 + (23*B*a^3)/4) - tan(e/2 + (f*x)/2)^5*(3*A*a^3 + (23*B*a^3)/4) + tan(e/2 + (f*x)/2)^4*(22*A*a^3 + 18*B*a^3) + tan(e/2 + (f*x)/2)^2*((70*A*a^3)/3 + 22*B*a^3))/(f*(4*tan(e/2 + (f*x)/2)^2 + 6*tan(e/2 + (f*x)/2)^4 + 4*tan(e/2 + (f*x)/2)^6 + tan(e/2 + (f*x)/2)^8 + 1)) - (5*a^3*(4*A + 3*B)*(atan(tan(e/2 + (f*x)/2)) - (f*x)/2))/(4*f)","B"
262,1,10256,246,21.761251,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c + d*sin(e + f*x)),x)","-\frac{\frac{2\,\left(9\,A\,a^3\,d^2+3\,B\,a^3\,c^2+11\,B\,a^3\,d^2-3\,A\,a^3\,c\,d-9\,B\,a^3\,c\,d\right)}{3\,d^3}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(A\,a^3\,d-B\,a^3\,c+3\,B\,a^3\,d\right)}{d^2}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,A\,a^3\,d^2+B\,a^3\,c^2+4\,B\,a^3\,d^2-A\,a^3\,c\,d-3\,B\,a^3\,c\,d\right)}{d^3}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,A\,a^3\,d^2+B\,a^3\,c^2+3\,B\,a^3\,d^2-A\,a^3\,c\,d-3\,B\,a^3\,c\,d\right)}{d^3}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,a^3\,d-B\,a^3\,c+3\,B\,a^3\,d\right)}{d^2}}{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{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{d^4}+\frac{\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{\left(\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{d^4}}{\frac{16\,\left(-2\,A^3\,a^9\,c^7\,d^3+8\,A^3\,a^9\,c^6\,d^4-7\,A^3\,a^9\,c^5\,d^5-21\,A^3\,a^9\,c^4\,d^6+55\,A^3\,a^9\,c^3\,d^7-47\,A^3\,a^9\,c^2\,d^8+14\,A^3\,a^9\,c\,d^9+6\,A^2\,B\,a^9\,c^8\,d^2-34\,A^2\,B\,a^9\,c^7\,d^3+81\,A^2\,B\,a^9\,c^6\,d^4-97\,A^2\,B\,a^9\,c^5\,d^5+45\,A^2\,B\,a^9\,c^4\,d^6+21\,A^2\,B\,a^9\,c^3\,d^7-32\,A^2\,B\,a^9\,c^2\,d^8+10\,A^2\,B\,a^9\,c\,d^9-6\,A\,B^2\,a^9\,c^9\,d+44\,A\,B^2\,a^9\,c^8\,d^2-141\,A\,B^2\,a^9\,c^7\,d^3+257\,A\,B^2\,a^9\,c^6\,d^4-280\,A\,B^2\,a^9\,c^5\,d^5+174\,A\,B^2\,a^9\,c^4\,d^6-53\,A\,B^2\,a^9\,c^3\,d^7+5\,A\,B^2\,a^9\,c^2\,d^8+2\,B^3\,a^9\,c^{10}-18\,B^3\,a^9\,c^9\,d+67\,B^3\,a^9\,c^8\,d^2-139\,B^3\,a^9\,c^7\,d^3+180\,B^3\,a^9\,c^6\,d^4-148\,B^3\,a^9\,c^5\,d^5+71\,B^3\,a^9\,c^4\,d^6-15\,B^3\,a^9\,c^3\,d^7\right)}{d^8}+\frac{\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{\left(\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}+\frac{\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)}{d^4}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^3\,a^9\,c^8\,d^3+72\,A^3\,a^9\,c^7\,d^4-296\,A^3\,a^9\,c^6\,d^5+704\,A^3\,a^9\,c^5\,d^6-1034\,A^3\,a^9\,c^4\,d^7+926\,A^3\,a^9\,c^3\,d^8-462\,A^3\,a^9\,c^2\,d^9+98\,A^3\,a^9\,c\,d^{10}+24\,A^2\,B\,a^9\,c^9\,d^2-216\,A^2\,B\,a^9\,c^8\,d^3+888\,A^2\,B\,a^9\,c^7\,d^4-2152\,A^2\,B\,a^9\,c^6\,d^5+3342\,A^2\,B\,a^9\,c^5\,d^6-3398\,A^2\,B\,a^9\,c^4\,d^7+2206\,A^2\,B\,a^9\,c^3\,d^8-834\,A^2\,B\,a^9\,c^2\,d^9+140\,A^2\,B\,a^9\,c\,d^{10}-24\,A\,B^2\,a^9\,c^{10}\,d+216\,A\,B^2\,a^9\,c^9\,d^2-888\,A\,B^2\,a^9\,c^8\,d^3+2192\,A\,B^2\,a^9\,c^7\,d^4-3582\,A\,B^2\,a^9\,c^6\,d^5+4018\,A\,B^2\,a^9\,c^5\,d^6-3076\,A\,B^2\,a^9\,c^4\,d^7+1524\,A\,B^2\,a^9\,c^3\,d^8-430\,A\,B^2\,a^9\,c^2\,d^9+50\,A\,B^2\,a^9\,c\,d^{10}+8\,B^3\,a^9\,c^{11}-72\,B^3\,a^9\,c^{10}\,d+296\,B^3\,a^9\,c^9\,d^2-744\,B^3\,a^9\,c^8\,d^3+1274\,B^3\,a^9\,c^7\,d^4-1546\,B^3\,a^9\,c^6\,d^5+1332\,B^3\,a^9\,c^5\,d^6-788\,B^3\,a^9\,c^4\,d^7+290\,B^3\,a^9\,c^3\,d^8-50\,B^3\,a^9\,c^2\,d^9\right)}{d^9}}\right)\,\left(B\,a^3\,c^3\,1{}\mathrm{i}+\frac{a^3\,d^2\,\left(6\,A\,c+7\,B\,c\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d^3\,\left(7\,A+5\,B\right)\,1{}\mathrm{i}}{2}-\frac{a^3\,d\,\left(2\,A\,c^2+6\,B\,c^2\right)\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{d^4\,f}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}-\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^5+c\,d^4}\right)}{d^5+c\,d^4}\right)\,1{}\mathrm{i}}{d^5+c\,d^4}+\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^5+c\,d^4}\right)}{d^5+c\,d^4}\right)\,1{}\mathrm{i}}{d^5+c\,d^4}}{\frac{16\,\left(-2\,A^3\,a^9\,c^7\,d^3+8\,A^3\,a^9\,c^6\,d^4-7\,A^3\,a^9\,c^5\,d^5-21\,A^3\,a^9\,c^4\,d^6+55\,A^3\,a^9\,c^3\,d^7-47\,A^3\,a^9\,c^2\,d^8+14\,A^3\,a^9\,c\,d^9+6\,A^2\,B\,a^9\,c^8\,d^2-34\,A^2\,B\,a^9\,c^7\,d^3+81\,A^2\,B\,a^9\,c^6\,d^4-97\,A^2\,B\,a^9\,c^5\,d^5+45\,A^2\,B\,a^9\,c^4\,d^6+21\,A^2\,B\,a^9\,c^3\,d^7-32\,A^2\,B\,a^9\,c^2\,d^8+10\,A^2\,B\,a^9\,c\,d^9-6\,A\,B^2\,a^9\,c^9\,d+44\,A\,B^2\,a^9\,c^8\,d^2-141\,A\,B^2\,a^9\,c^7\,d^3+257\,A\,B^2\,a^9\,c^6\,d^4-280\,A\,B^2\,a^9\,c^5\,d^5+174\,A\,B^2\,a^9\,c^4\,d^6-53\,A\,B^2\,a^9\,c^3\,d^7+5\,A\,B^2\,a^9\,c^2\,d^8+2\,B^3\,a^9\,c^{10}-18\,B^3\,a^9\,c^9\,d+67\,B^3\,a^9\,c^8\,d^2-139\,B^3\,a^9\,c^7\,d^3+180\,B^3\,a^9\,c^6\,d^4-148\,B^3\,a^9\,c^5\,d^5+71\,B^3\,a^9\,c^4\,d^6-15\,B^3\,a^9\,c^3\,d^7\right)}{d^8}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^3\,a^9\,c^8\,d^3+72\,A^3\,a^9\,c^7\,d^4-296\,A^3\,a^9\,c^6\,d^5+704\,A^3\,a^9\,c^5\,d^6-1034\,A^3\,a^9\,c^4\,d^7+926\,A^3\,a^9\,c^3\,d^8-462\,A^3\,a^9\,c^2\,d^9+98\,A^3\,a^9\,c\,d^{10}+24\,A^2\,B\,a^9\,c^9\,d^2-216\,A^2\,B\,a^9\,c^8\,d^3+888\,A^2\,B\,a^9\,c^7\,d^4-2152\,A^2\,B\,a^9\,c^6\,d^5+3342\,A^2\,B\,a^9\,c^5\,d^6-3398\,A^2\,B\,a^9\,c^4\,d^7+2206\,A^2\,B\,a^9\,c^3\,d^8-834\,A^2\,B\,a^9\,c^2\,d^9+140\,A^2\,B\,a^9\,c\,d^{10}-24\,A\,B^2\,a^9\,c^{10}\,d+216\,A\,B^2\,a^9\,c^9\,d^2-888\,A\,B^2\,a^9\,c^8\,d^3+2192\,A\,B^2\,a^9\,c^7\,d^4-3582\,A\,B^2\,a^9\,c^6\,d^5+4018\,A\,B^2\,a^9\,c^5\,d^6-3076\,A\,B^2\,a^9\,c^4\,d^7+1524\,A\,B^2\,a^9\,c^3\,d^8-430\,A\,B^2\,a^9\,c^2\,d^9+50\,A\,B^2\,a^9\,c\,d^{10}+8\,B^3\,a^9\,c^{11}-72\,B^3\,a^9\,c^{10}\,d+296\,B^3\,a^9\,c^9\,d^2-744\,B^3\,a^9\,c^8\,d^3+1274\,B^3\,a^9\,c^7\,d^4-1546\,B^3\,a^9\,c^6\,d^5+1332\,B^3\,a^9\,c^5\,d^6-788\,B^3\,a^9\,c^4\,d^7+290\,B^3\,a^9\,c^3\,d^8-50\,B^3\,a^9\,c^2\,d^9\right)}{d^9}+\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}-\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^5+c\,d^4}\right)}{d^5+c\,d^4}\right)}{d^5+c\,d^4}-\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5-24\,A^2\,a^6\,c^5\,d^6+64\,A^2\,a^6\,c^4\,d^7-84\,A^2\,a^6\,c^3\,d^8+49\,A^2\,a^6\,c^2\,d^9-8\,A\,B\,a^6\,c^7\,d^4+48\,A\,B\,a^6\,c^6\,d^5-128\,A\,B\,a^6\,c^5\,d^6+188\,A\,B\,a^6\,c^4\,d^7-158\,A\,B\,a^6\,c^3\,d^8+70\,A\,B\,a^6\,c^2\,d^9+4\,B^2\,a^6\,c^8\,d^3-24\,B^2\,a^6\,c^7\,d^4+64\,B^2\,a^6\,c^6\,d^5-104\,B^2\,a^6\,c^5\,d^6+109\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+25\,B^2\,a^6\,c^2\,d^9\right)}{d^8}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5+48\,A^2\,a^6\,c^6\,d^6-116\,A^2\,a^6\,c^5\,d^7+116\,A^2\,a^6\,c^4\,d^8+19\,A^2\,a^6\,c^3\,d^9-144\,A^2\,a^6\,c^2\,d^{10}+94\,A^2\,a^6\,c\,d^{11}+16\,A\,B\,a^6\,c^8\,d^4-96\,A\,B\,a^6\,c^7\,d^5+232\,A\,B\,a^6\,c^6\,d^6-252\,A\,B\,a^6\,c^5\,d^7+22\,A\,B\,a^6\,c^4\,d^8+258\,A\,B\,a^6\,c^3\,d^9-308\,A\,B\,a^6\,c^2\,d^{10}+140\,A\,B\,a^6\,c\,d^{11}-8\,B^2\,a^6\,c^9\,d^3+48\,B^2\,a^6\,c^8\,d^4-116\,B^2\,a^6\,c^7\,d^5+136\,B^2\,a^6\,c^6\,d^6-41\,B^2\,a^6\,c^5\,d^7-114\,B^2\,a^6\,c^4\,d^8+189\,B^2\,a^6\,c^3\,d^9-140\,B^2\,a^6\,c^2\,d^{10}+50\,B^2\,a^6\,c\,d^{11}\right)}{d^9}+\frac{a^3\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,\left(\frac{8\,\left(14\,A\,a^3\,c\,d^{11}+10\,B\,a^3\,c\,d^{11}-16\,A\,a^3\,c^2\,d^{10}+2\,A\,a^3\,c^3\,d^9-14\,B\,a^3\,c^2\,d^{10}+6\,B\,a^3\,c^3\,d^9-2\,B\,a^3\,c^4\,d^8\right)}{d^8}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(8\,A\,a^3\,c\,d^{12}-24\,A\,a^3\,c^2\,d^{11}+24\,A\,a^3\,c^3\,d^{10}-8\,A\,a^3\,c^4\,d^9-8\,B\,a^3\,c^2\,d^{11}+24\,B\,a^3\,c^3\,d^{10}-24\,B\,a^3\,c^4\,d^9+8\,B\,a^3\,c^5\,d^8\right)}{d^9}+\frac{a^3\,\left(32\,c^2\,d^3+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,c\,d^{13}-8\,c^3\,d^{11}\right)}{d^9}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}}{d^5+c\,d^4}\right)}{d^5+c\,d^4}\right)}{d^5+c\,d^4}}\right)\,\left(A\,d-B\,c\right)\,\sqrt{-\left(c+d\right)\,{\left(c-d\right)}^5}\,2{}\mathrm{i}}{f\,\left(d^5+c\,d^4\right)}","Not used",1,"- ((2*(9*A*a^3*d^2 + 3*B*a^3*c^2 + 11*B*a^3*d^2 - 3*A*a^3*c*d - 9*B*a^3*c*d))/(3*d^3) - (tan(e/2 + (f*x)/2)^5*(A*a^3*d - B*a^3*c + 3*B*a^3*d))/d^2 + (4*tan(e/2 + (f*x)/2)^2*(3*A*a^3*d^2 + B*a^3*c^2 + 4*B*a^3*d^2 - A*a^3*c*d - 3*B*a^3*c*d))/d^3 + (2*tan(e/2 + (f*x)/2)^4*(3*A*a^3*d^2 + B*a^3*c^2 + 3*B*a^3*d^2 - A*a^3*c*d - 3*B*a^3*c*d))/d^3 + (tan(e/2 + (f*x)/2)*(A*a^3*d - B*a^3*c + 3*B*a^3*d))/d^2)/(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(((((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + ((((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4 - (8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 + (8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2)*1i)/d^4 + (((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + (((8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4 - (8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2)*1i)/d^4)/((16*(2*B^3*a^9*c^10 - 47*A^3*a^9*c^2*d^8 + 55*A^3*a^9*c^3*d^7 - 21*A^3*a^9*c^4*d^6 - 7*A^3*a^9*c^5*d^5 + 8*A^3*a^9*c^6*d^4 - 2*A^3*a^9*c^7*d^3 - 15*B^3*a^9*c^3*d^7 + 71*B^3*a^9*c^4*d^6 - 148*B^3*a^9*c^5*d^5 + 180*B^3*a^9*c^6*d^4 - 139*B^3*a^9*c^7*d^3 + 67*B^3*a^9*c^8*d^2 + 14*A^3*a^9*c*d^9 - 18*B^3*a^9*c^9*d - 6*A*B^2*a^9*c^9*d + 10*A^2*B*a^9*c*d^9 + 5*A*B^2*a^9*c^2*d^8 - 53*A*B^2*a^9*c^3*d^7 + 174*A*B^2*a^9*c^4*d^6 - 280*A*B^2*a^9*c^5*d^5 + 257*A*B^2*a^9*c^6*d^4 - 141*A*B^2*a^9*c^7*d^3 + 44*A*B^2*a^9*c^8*d^2 - 32*A^2*B*a^9*c^2*d^8 + 21*A^2*B*a^9*c^3*d^7 + 45*A^2*B*a^9*c^4*d^6 - 97*A^2*B*a^9*c^5*d^5 + 81*A^2*B*a^9*c^6*d^4 - 34*A^2*B*a^9*c^7*d^3 + 6*A^2*B*a^9*c^8*d^2))/d^8 + (((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + ((((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4 - (8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 + (8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4 - (((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + (((8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 + ((32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4 - (8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4)*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2))/d^4 + (16*tan(e/2 + (f*x)/2)*(8*B^3*a^9*c^11 - 462*A^3*a^9*c^2*d^9 + 926*A^3*a^9*c^3*d^8 - 1034*A^3*a^9*c^4*d^7 + 704*A^3*a^9*c^5*d^6 - 296*A^3*a^9*c^6*d^5 + 72*A^3*a^9*c^7*d^4 - 8*A^3*a^9*c^8*d^3 - 50*B^3*a^9*c^2*d^9 + 290*B^3*a^9*c^3*d^8 - 788*B^3*a^9*c^4*d^7 + 1332*B^3*a^9*c^5*d^6 - 1546*B^3*a^9*c^6*d^5 + 1274*B^3*a^9*c^7*d^4 - 744*B^3*a^9*c^8*d^3 + 296*B^3*a^9*c^9*d^2 + 98*A^3*a^9*c*d^10 - 72*B^3*a^9*c^10*d + 50*A*B^2*a^9*c*d^10 - 24*A*B^2*a^9*c^10*d + 140*A^2*B*a^9*c*d^10 - 430*A*B^2*a^9*c^2*d^9 + 1524*A*B^2*a^9*c^3*d^8 - 3076*A*B^2*a^9*c^4*d^7 + 4018*A*B^2*a^9*c^5*d^6 - 3582*A*B^2*a^9*c^6*d^5 + 2192*A*B^2*a^9*c^7*d^4 - 888*A*B^2*a^9*c^8*d^3 + 216*A*B^2*a^9*c^9*d^2 - 834*A^2*B*a^9*c^2*d^9 + 2206*A^2*B*a^9*c^3*d^8 - 3398*A^2*B*a^9*c^4*d^7 + 3342*A^2*B*a^9*c^5*d^6 - 2152*A^2*B*a^9*c^6*d^5 + 888*A^2*B*a^9*c^7*d^4 - 216*A^2*B*a^9*c^8*d^3 + 24*A^2*B*a^9*c^9*d^2))/d^9))*(B*a^3*c^3*1i + (a^3*d^2*(6*A*c + 7*B*c)*1i)/2 - (a^3*d^3*(7*A + 5*B)*1i)/2 - (a^3*d*(2*A*c^2 + 6*B*c^2)*1i)/2)*2i)/(d^4*f) - (a^3*atan(((a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9 - (8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2))/(c*d^4 + d^5)))/(c*d^4 + d^5))*1i)/(c*d^4 + d^5) + (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 - (8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2))/(c*d^4 + d^5)))/(c*d^4 + d^5))*1i)/(c*d^4 + d^5))/((16*(2*B^3*a^9*c^10 - 47*A^3*a^9*c^2*d^8 + 55*A^3*a^9*c^3*d^7 - 21*A^3*a^9*c^4*d^6 - 7*A^3*a^9*c^5*d^5 + 8*A^3*a^9*c^6*d^4 - 2*A^3*a^9*c^7*d^3 - 15*B^3*a^9*c^3*d^7 + 71*B^3*a^9*c^4*d^6 - 148*B^3*a^9*c^5*d^5 + 180*B^3*a^9*c^6*d^4 - 139*B^3*a^9*c^7*d^3 + 67*B^3*a^9*c^8*d^2 + 14*A^3*a^9*c*d^9 - 18*B^3*a^9*c^9*d - 6*A*B^2*a^9*c^9*d + 10*A^2*B*a^9*c*d^9 + 5*A*B^2*a^9*c^2*d^8 - 53*A*B^2*a^9*c^3*d^7 + 174*A*B^2*a^9*c^4*d^6 - 280*A*B^2*a^9*c^5*d^5 + 257*A*B^2*a^9*c^6*d^4 - 141*A*B^2*a^9*c^7*d^3 + 44*A*B^2*a^9*c^8*d^2 - 32*A^2*B*a^9*c^2*d^8 + 21*A^2*B*a^9*c^3*d^7 + 45*A^2*B*a^9*c^4*d^6 - 97*A^2*B*a^9*c^5*d^5 + 81*A^2*B*a^9*c^6*d^4 - 34*A^2*B*a^9*c^7*d^3 + 6*A^2*B*a^9*c^8*d^2))/d^8 + (16*tan(e/2 + (f*x)/2)*(8*B^3*a^9*c^11 - 462*A^3*a^9*c^2*d^9 + 926*A^3*a^9*c^3*d^8 - 1034*A^3*a^9*c^4*d^7 + 704*A^3*a^9*c^5*d^6 - 296*A^3*a^9*c^6*d^5 + 72*A^3*a^9*c^7*d^4 - 8*A^3*a^9*c^8*d^3 - 50*B^3*a^9*c^2*d^9 + 290*B^3*a^9*c^3*d^8 - 788*B^3*a^9*c^4*d^7 + 1332*B^3*a^9*c^5*d^6 - 1546*B^3*a^9*c^6*d^5 + 1274*B^3*a^9*c^7*d^4 - 744*B^3*a^9*c^8*d^3 + 296*B^3*a^9*c^9*d^2 + 98*A^3*a^9*c*d^10 - 72*B^3*a^9*c^10*d + 50*A*B^2*a^9*c*d^10 - 24*A*B^2*a^9*c^10*d + 140*A^2*B*a^9*c*d^10 - 430*A*B^2*a^9*c^2*d^9 + 1524*A*B^2*a^9*c^3*d^8 - 3076*A*B^2*a^9*c^4*d^7 + 4018*A*B^2*a^9*c^5*d^6 - 3582*A*B^2*a^9*c^6*d^5 + 2192*A*B^2*a^9*c^7*d^4 - 888*A*B^2*a^9*c^8*d^3 + 216*A*B^2*a^9*c^9*d^2 - 834*A^2*B*a^9*c^2*d^9 + 2206*A^2*B*a^9*c^3*d^8 - 3398*A^2*B*a^9*c^4*d^7 + 3342*A^2*B*a^9*c^5*d^6 - 2152*A^2*B*a^9*c^6*d^5 + 888*A^2*B*a^9*c^7*d^4 - 216*A^2*B*a^9*c^8*d^3 + 24*A^2*B*a^9*c^9*d^2))/d^9 + (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9 - (8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2))/(c*d^4 + d^5)))/(c*d^4 + d^5)))/(c*d^4 + d^5) - (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*(49*A^2*a^6*c^2*d^9 - 84*A^2*a^6*c^3*d^8 + 64*A^2*a^6*c^4*d^7 - 24*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 25*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 + 109*B^2*a^6*c^4*d^7 - 104*B^2*a^6*c^5*d^6 + 64*B^2*a^6*c^6*d^5 - 24*B^2*a^6*c^7*d^4 + 4*B^2*a^6*c^8*d^3 + 70*A*B*a^6*c^2*d^9 - 158*A*B*a^6*c^3*d^8 + 188*A*B*a^6*c^4*d^7 - 128*A*B*a^6*c^5*d^6 + 48*A*B*a^6*c^6*d^5 - 8*A*B*a^6*c^7*d^4))/d^8 + (8*tan(e/2 + (f*x)/2)*(19*A^2*a^6*c^3*d^9 - 144*A^2*a^6*c^2*d^10 + 116*A^2*a^6*c^4*d^8 - 116*A^2*a^6*c^5*d^7 + 48*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 - 140*B^2*a^6*c^2*d^10 + 189*B^2*a^6*c^3*d^9 - 114*B^2*a^6*c^4*d^8 - 41*B^2*a^6*c^5*d^7 + 136*B^2*a^6*c^6*d^6 - 116*B^2*a^6*c^7*d^5 + 48*B^2*a^6*c^8*d^4 - 8*B^2*a^6*c^9*d^3 + 94*A^2*a^6*c*d^11 + 50*B^2*a^6*c*d^11 - 308*A*B*a^6*c^2*d^10 + 258*A*B*a^6*c^3*d^9 + 22*A*B*a^6*c^4*d^8 - 252*A*B*a^6*c^5*d^7 + 232*A*B*a^6*c^6*d^6 - 96*A*B*a^6*c^7*d^5 + 16*A*B*a^6*c^8*d^4 + 140*A*B*a^6*c*d^11))/d^9 + (a^3*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*((8*(14*A*a^3*c*d^11 + 10*B*a^3*c*d^11 - 16*A*a^3*c^2*d^10 + 2*A*a^3*c^3*d^9 - 14*B*a^3*c^2*d^10 + 6*B*a^3*c^3*d^9 - 2*B*a^3*c^4*d^8))/d^8 - (8*tan(e/2 + (f*x)/2)*(8*A*a^3*c*d^12 - 24*A*a^3*c^2*d^11 + 24*A*a^3*c^3*d^10 - 8*A*a^3*c^4*d^9 - 8*B*a^3*c^2*d^11 + 24*B*a^3*c^3*d^10 - 24*B*a^3*c^4*d^9 + 8*B*a^3*c^5*d^8))/d^9 + (a^3*(32*c^2*d^3 + (8*tan(e/2 + (f*x)/2)*(12*c*d^13 - 8*c^3*d^11))/d^9)*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2))/(c*d^4 + d^5)))/(c*d^4 + d^5)))/(c*d^4 + d^5)))*(A*d - B*c)*(-(c + d)*(c - d)^5)^(1/2)*2i)/(f*(c*d^4 + d^5))","B"
263,1,11993,283,23.882560,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c + d*sin(e + f*x))^2,x)","-\frac{\frac{2\,\left(A\,a^3\,d^3-3\,B\,a^3\,c^3-A\,a^3\,c\,d^2+2\,A\,a^3\,c^2\,d+2\,B\,a^3\,c\,d^2+3\,B\,a^3\,c^2\,d\right)}{d^3\,\left(c+d\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(A\,a^3\,d^3-3\,B\,a^3\,c^3-B\,a^3\,d^3-A\,a^3\,c\,d^2+2\,A\,a^3\,c^2\,d+B\,a^3\,c\,d^2+3\,B\,a^3\,c^2\,d\right)}{d^3\,\left(c+d\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,A\,a^3\,d^3-6\,B\,a^3\,c^3+B\,a^3\,d^3-2\,A\,a^3\,c\,d^2+4\,A\,a^3\,c^2\,d+5\,B\,a^3\,c\,d^2+6\,B\,a^3\,c^2\,d\right)}{d^3\,\left(c+d\right)}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a^3\,d^3-3\,B\,a^3\,c^3-A\,a^3\,c\,d^2+2\,A\,a^3\,c^2\,d+2\,B\,a^3\,c\,d^2+3\,B\,a^3\,c^2\,d\right)}{c\,d^2\,\left(c+d\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,A\,a^3\,d^3-3\,B\,a^3\,c^3-4\,A\,a^3\,c\,d^2+2\,A\,a^3\,c^2\,d-2\,B\,a^3\,c\,d^2+3\,B\,a^3\,c^2\,d\right)}{c\,d^2\,\left(c+d\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a^3\,d^3-9\,B\,a^3\,c^3+6\,A\,a^3\,c^2\,d+10\,B\,a^3\,c\,d^2+9\,B\,a^3\,c^2\,d\right)}{c\,d^2\,\left(c+d\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{d^4}+\frac{\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{d^4}}{\frac{16\,\left(16\,A^3\,a^9\,c^6\,d^3-80\,A^3\,a^9\,c^5\,d^4+76\,A^3\,a^9\,c^4\,d^5+132\,A^3\,a^9\,c^3\,d^6-252\,A^3\,a^9\,c^2\,d^7+108\,A^3\,a^9\,c\,d^8-72\,A^2\,B\,a^9\,c^7\,d^2+336\,A^2\,B\,a^9\,c^6\,d^3-402\,A^2\,B\,a^9\,c^5\,d^4-288\,A^2\,B\,a^9\,c^4\,d^5+996\,A^2\,B\,a^9\,c^3\,d^6-768\,A^2\,B\,a^9\,c^2\,d^7+198\,A^2\,B\,a^9\,c\,d^8+108\,A\,B^2\,a^9\,c^8\,d-468\,A\,B^2\,a^9\,c^7\,d^2+630\,A\,B^2\,a^9\,c^6\,d^3+93\,A\,B^2\,a^9\,c^5\,d^4-1125\,A\,B^2\,a^9\,c^4\,d^5+1239\,A\,B^2\,a^9\,c^3\,d^6-573\,A\,B^2\,a^9\,c^2\,d^7+96\,A\,B^2\,a^9\,c\,d^8-54\,B^3\,a^9\,c^9+216\,B^3\,a^9\,c^8\,d-297\,B^3\,a^9\,c^7\,d^2+36\,B^3\,a^9\,c^6\,d^3+387\,B^3\,a^9\,c^5\,d^4-537\,B^3\,a^9\,c^4\,d^5+350\,B^3\,a^9\,c^3\,d^6-115\,B^3\,a^9\,c^2\,d^7+14\,B^3\,a^9\,c\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(64\,A^3\,a^9\,c^7\,d^3-160\,A^3\,a^9\,c^6\,d^4-112\,A^3\,a^9\,c^5\,d^5+520\,A^3\,a^9\,c^4\,d^6-168\,A^3\,a^9\,c^3\,d^7-360\,A^3\,a^9\,c^2\,d^8+216\,A^3\,a^9\,c\,d^9-288\,A^2\,B\,a^9\,c^8\,d^2+864\,A^2\,B\,a^9\,c^7\,d^3+24\,A^2\,B\,a^9\,c^6\,d^4-2352\,A^2\,B\,a^9\,c^5\,d^5+2016\,A^2\,B\,a^9\,c^4\,d^6+912\,A^2\,B\,a^9\,c^3\,d^7-1752\,A^2\,B\,a^9\,c^2\,d^8+576\,A^2\,B\,a^9\,c\,d^9+432\,A\,B^2\,a^9\,c^9\,d-1512\,A\,B^2\,a^9\,c^8\,d^2+792\,A\,B^2\,a^9\,c^7\,d^3+3096\,A\,B^2\,a^9\,c^6\,d^4-4668\,A\,B^2\,a^9\,c^5\,d^5+594\,A\,B^2\,a^9\,c^4\,d^6+2982\,A\,B^2\,a^9\,c^3\,d^7-2178\,A\,B^2\,a^9\,c^2\,d^8+462\,A\,B^2\,a^9\,c\,d^9-216\,B^3\,a^9\,c^{10}+864\,B^3\,a^9\,c^9\,d-864\,B^3\,a^9\,c^8\,d^2-1080\,B^3\,a^9\,c^7\,d^3+2898\,B^3\,a^9\,c^6\,d^4-1584\,B^3\,a^9\,c^5\,d^5-1090\,B^3\,a^9\,c^4\,d^6+1702\,B^3\,a^9\,c^3\,d^7-728\,B^3\,a^9\,c^2\,d^8+98\,B^3\,a^9\,c\,d^9\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{\left(\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)}{d^4}}\right)\,\left(B\,a^3\,c^2\,3{}\mathrm{i}+a^3\,d^2\,\left(3\,A+\frac{7\,B}{2}\right)\,1{}\mathrm{i}-\frac{a^3\,d\,\left(4\,A\,c+12\,B\,c\right)\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{d^4\,f}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}-\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{a^3\,\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)\,1{}\mathrm{i}}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)\,1{}\mathrm{i}}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}}{\frac{16\,\left(16\,A^3\,a^9\,c^6\,d^3-80\,A^3\,a^9\,c^5\,d^4+76\,A^3\,a^9\,c^4\,d^5+132\,A^3\,a^9\,c^3\,d^6-252\,A^3\,a^9\,c^2\,d^7+108\,A^3\,a^9\,c\,d^8-72\,A^2\,B\,a^9\,c^7\,d^2+336\,A^2\,B\,a^9\,c^6\,d^3-402\,A^2\,B\,a^9\,c^5\,d^4-288\,A^2\,B\,a^9\,c^4\,d^5+996\,A^2\,B\,a^9\,c^3\,d^6-768\,A^2\,B\,a^9\,c^2\,d^7+198\,A^2\,B\,a^9\,c\,d^8+108\,A\,B^2\,a^9\,c^8\,d-468\,A\,B^2\,a^9\,c^7\,d^2+630\,A\,B^2\,a^9\,c^6\,d^3+93\,A\,B^2\,a^9\,c^5\,d^4-1125\,A\,B^2\,a^9\,c^4\,d^5+1239\,A\,B^2\,a^9\,c^3\,d^6-573\,A\,B^2\,a^9\,c^2\,d^7+96\,A\,B^2\,a^9\,c\,d^8-54\,B^3\,a^9\,c^9+216\,B^3\,a^9\,c^8\,d-297\,B^3\,a^9\,c^7\,d^2+36\,B^3\,a^9\,c^6\,d^3+387\,B^3\,a^9\,c^5\,d^4-537\,B^3\,a^9\,c^4\,d^5+350\,B^3\,a^9\,c^3\,d^6-115\,B^3\,a^9\,c^2\,d^7+14\,B^3\,a^9\,c\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(64\,A^3\,a^9\,c^7\,d^3-160\,A^3\,a^9\,c^6\,d^4-112\,A^3\,a^9\,c^5\,d^5+520\,A^3\,a^9\,c^4\,d^6-168\,A^3\,a^9\,c^3\,d^7-360\,A^3\,a^9\,c^2\,d^8+216\,A^3\,a^9\,c\,d^9-288\,A^2\,B\,a^9\,c^8\,d^2+864\,A^2\,B\,a^9\,c^7\,d^3+24\,A^2\,B\,a^9\,c^6\,d^4-2352\,A^2\,B\,a^9\,c^5\,d^5+2016\,A^2\,B\,a^9\,c^4\,d^6+912\,A^2\,B\,a^9\,c^3\,d^7-1752\,A^2\,B\,a^9\,c^2\,d^8+576\,A^2\,B\,a^9\,c\,d^9+432\,A\,B^2\,a^9\,c^9\,d-1512\,A\,B^2\,a^9\,c^8\,d^2+792\,A\,B^2\,a^9\,c^7\,d^3+3096\,A\,B^2\,a^9\,c^6\,d^4-4668\,A\,B^2\,a^9\,c^5\,d^5+594\,A\,B^2\,a^9\,c^4\,d^6+2982\,A\,B^2\,a^9\,c^3\,d^7-2178\,A\,B^2\,a^9\,c^2\,d^8+462\,A\,B^2\,a^9\,c\,d^9-216\,B^3\,a^9\,c^{10}+864\,B^3\,a^9\,c^9\,d-864\,B^3\,a^9\,c^8\,d^2-1080\,B^3\,a^9\,c^7\,d^3+2898\,B^3\,a^9\,c^6\,d^4-1584\,B^3\,a^9\,c^5\,d^5-1090\,B^3\,a^9\,c^4\,d^6+1702\,B^3\,a^9\,c^3\,d^7-728\,B^3\,a^9\,c^2\,d^8+98\,B^3\,a^9\,c\,d^9\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}-\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{a^3\,\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}-\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(16\,A^2\,a^6\,c^6\,d^5-16\,A^2\,a^6\,c^5\,d^6-44\,A^2\,a^6\,c^4\,d^7+24\,A^2\,a^6\,c^3\,d^8+36\,A^2\,a^6\,c^2\,d^9-48\,A\,B\,a^6\,c^7\,d^4+72\,A\,B\,a^6\,c^6\,d^5+88\,A\,B\,a^6\,c^5\,d^6-148\,A\,B\,a^6\,c^4\,d^7-32\,A\,B\,a^6\,c^3\,d^8+84\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3-72\,B^2\,a^6\,c^7\,d^4-24\,B^2\,a^6\,c^6\,d^5+144\,B^2\,a^6\,c^5\,d^6-59\,B^2\,a^6\,c^4\,d^7-70\,B^2\,a^6\,c^3\,d^8+49\,B^2\,a^6\,c^2\,d^9\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-32\,A^2\,a^6\,c^7\,d^5+32\,A^2\,a^6\,c^6\,d^6+136\,A^2\,a^6\,c^5\,d^7-136\,A^2\,a^6\,c^4\,d^8-164\,A^2\,a^6\,c^3\,d^9+144\,A^2\,a^6\,c^2\,d^{10}+36\,A^2\,a^6\,c\,d^{11}+96\,A\,B\,a^6\,c^8\,d^4-144\,A\,B\,a^6\,c^7\,d^5-320\,A\,B\,a^6\,c^6\,d^6+572\,A\,B\,a^6\,c^5\,d^7+208\,A\,B\,a^6\,c^4\,d^8-628\,A\,B\,a^6\,c^3\,d^9+88\,A\,B\,a^6\,c^2\,d^{10}+144\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3+144\,B^2\,a^6\,c^8\,d^4+156\,B^2\,a^6\,c^7\,d^5-504\,B^2\,a^6\,c^6\,d^6+91\,B^2\,a^6\,c^5\,d^7+494\,B^2\,a^6\,c^4\,d^8-299\,B^2\,a^6\,c^3\,d^9-100\,B^2\,a^6\,c^2\,d^{10}+94\,B^2\,a^6\,c\,d^{11}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{8\,\left(12\,A\,a^3\,c\,d^{12}+14\,B\,a^3\,c\,d^{12}+4\,A\,a^3\,c^2\,d^{11}-12\,A\,a^3\,c^3\,d^{10}-4\,A\,a^3\,c^4\,d^9-20\,B\,a^3\,c^3\,d^{10}+6\,B\,a^3\,c^5\,d^8\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(24\,A\,a^3\,c\,d^{13}+8\,B\,a^3\,c\,d^{13}-8\,A\,a^3\,c^2\,d^{12}-40\,A\,a^3\,c^3\,d^{11}+8\,A\,a^3\,c^4\,d^{10}+16\,A\,a^3\,c^5\,d^9-32\,B\,a^3\,c^2\,d^{12}-8\,B\,a^3\,c^3\,d^{11}+56\,B\,a^3\,c^4\,d^{10}-24\,B\,a^3\,c^6\,d^8\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}+\frac{a^3\,\left(\frac{8\,\left(4\,c^4\,d^{11}+8\,c^3\,d^{12}+4\,c^2\,d^{13}\right)}{c^2\,d^8+2\,c\,d^9+d^{10}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^5\,d^{11}-16\,c^4\,d^{12}+4\,c^3\,d^{13}+24\,c^2\,d^{14}+12\,c\,d^{15}\right)}{c^2\,d^9+2\,c\,d^{10}+d^{11}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}\right)\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7}}\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(3\,A\,d^2-3\,B\,c^2+B\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)\,2{}\mathrm{i}}{f\,\left(c^3\,d^4+3\,c^2\,d^5+3\,c\,d^6+d^7\right)}","Not used",1,"- ((2*(A*a^3*d^3 - 3*B*a^3*c^3 - A*a^3*c*d^2 + 2*A*a^3*c^2*d + 2*B*a^3*c*d^2 + 3*B*a^3*c^2*d))/(d^3*(c + d)) + (2*tan(e/2 + (f*x)/2)^4*(A*a^3*d^3 - 3*B*a^3*c^3 - B*a^3*d^3 - A*a^3*c*d^2 + 2*A*a^3*c^2*d + B*a^3*c*d^2 + 3*B*a^3*c^2*d))/(d^3*(c + d)) + (2*tan(e/2 + (f*x)/2)^2*(2*A*a^3*d^3 - 6*B*a^3*c^3 + B*a^3*d^3 - 2*A*a^3*c*d^2 + 4*A*a^3*c^2*d + 5*B*a^3*c*d^2 + 6*B*a^3*c^2*d))/(d^3*(c + d)) + (4*tan(e/2 + (f*x)/2)^3*(A*a^3*d^3 - 3*B*a^3*c^3 - A*a^3*c*d^2 + 2*A*a^3*c^2*d + 2*B*a^3*c*d^2 + 3*B*a^3*c^2*d))/(c*d^2*(c + d)) + (tan(e/2 + (f*x)/2)^5*(2*A*a^3*d^3 - 3*B*a^3*c^3 - 4*A*a^3*c*d^2 + 2*A*a^3*c^2*d - 2*B*a^3*c*d^2 + 3*B*a^3*c^2*d))/(c*d^2*(c + d)) + (tan(e/2 + (f*x)/2)*(2*A*a^3*d^3 - 9*B*a^3*c^3 + 6*A*a^3*c^2*d + 10*B*a^3*c*d^2 + 9*B*a^3*c^2*d))/(c*d^2*(c + d)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + 3*c*tan(e/2 + (f*x)/2)^2 + 3*c*tan(e/2 + (f*x)/2)^4 + c*tan(e/2 + (f*x)/2)^6 + 4*d*tan(e/2 + (f*x)/2)^3 + 2*d*tan(e/2 + (f*x)/2)^5)) - (atan(((((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (((((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4 - (8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4)*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2)*1i)/d^4 + (((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (((8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) + (((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4 - (8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4)*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2)*1i)/d^4)/((16*(132*A^3*a^9*c^3*d^6 - 252*A^3*a^9*c^2*d^7 - 54*B^3*a^9*c^9 + 76*A^3*a^9*c^4*d^5 - 80*A^3*a^9*c^5*d^4 + 16*A^3*a^9*c^6*d^3 - 115*B^3*a^9*c^2*d^7 + 350*B^3*a^9*c^3*d^6 - 537*B^3*a^9*c^4*d^5 + 387*B^3*a^9*c^5*d^4 + 36*B^3*a^9*c^6*d^3 - 297*B^3*a^9*c^7*d^2 + 108*A^3*a^9*c*d^8 + 14*B^3*a^9*c*d^8 + 216*B^3*a^9*c^8*d + 96*A*B^2*a^9*c*d^8 + 108*A*B^2*a^9*c^8*d + 198*A^2*B*a^9*c*d^8 - 573*A*B^2*a^9*c^2*d^7 + 1239*A*B^2*a^9*c^3*d^6 - 1125*A*B^2*a^9*c^4*d^5 + 93*A*B^2*a^9*c^5*d^4 + 630*A*B^2*a^9*c^6*d^3 - 468*A*B^2*a^9*c^7*d^2 - 768*A^2*B*a^9*c^2*d^7 + 996*A^2*B*a^9*c^3*d^6 - 288*A^2*B*a^9*c^4*d^5 - 402*A^2*B*a^9*c^5*d^4 + 336*A^2*B*a^9*c^6*d^3 - 72*A^2*B*a^9*c^7*d^2))/(2*c*d^9 + d^10 + c^2*d^8) + (16*tan(e/2 + (f*x)/2)*(520*A^3*a^9*c^4*d^6 - 360*A^3*a^9*c^2*d^8 - 168*A^3*a^9*c^3*d^7 - 216*B^3*a^9*c^10 - 112*A^3*a^9*c^5*d^5 - 160*A^3*a^9*c^6*d^4 + 64*A^3*a^9*c^7*d^3 - 728*B^3*a^9*c^2*d^8 + 1702*B^3*a^9*c^3*d^7 - 1090*B^3*a^9*c^4*d^6 - 1584*B^3*a^9*c^5*d^5 + 2898*B^3*a^9*c^6*d^4 - 1080*B^3*a^9*c^7*d^3 - 864*B^3*a^9*c^8*d^2 + 216*A^3*a^9*c*d^9 + 98*B^3*a^9*c*d^9 + 864*B^3*a^9*c^9*d + 462*A*B^2*a^9*c*d^9 + 432*A*B^2*a^9*c^9*d + 576*A^2*B*a^9*c*d^9 - 2178*A*B^2*a^9*c^2*d^8 + 2982*A*B^2*a^9*c^3*d^7 + 594*A*B^2*a^9*c^4*d^6 - 4668*A*B^2*a^9*c^5*d^5 + 3096*A*B^2*a^9*c^6*d^4 + 792*A*B^2*a^9*c^7*d^3 - 1512*A*B^2*a^9*c^8*d^2 - 1752*A^2*B*a^9*c^2*d^8 + 912*A^2*B*a^9*c^3*d^7 + 2016*A^2*B*a^9*c^4*d^6 - 2352*A^2*B*a^9*c^5*d^5 + 24*A^2*B*a^9*c^6*d^4 + 864*A^2*B*a^9*c^7*d^3 - 288*A^2*B*a^9*c^8*d^2))/(2*c*d^10 + d^11 + c^2*d^9) + (((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (((((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4 - (8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4)*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4 - (((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (((8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) + (((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4 - (8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4)*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2))/d^4))*(B*a^3*c^2*3i + a^3*d^2*(3*A + (7*B)/2)*1i - (a^3*d*(4*A*c + 12*B*c)*1i)/2)*2i)/(d^4*f) - (a^3*atan(((a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9) - (8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) + (a^3*((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d)*1i)/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) - (8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d)*1i)/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))/((16*(132*A^3*a^9*c^3*d^6 - 252*A^3*a^9*c^2*d^7 - 54*B^3*a^9*c^9 + 76*A^3*a^9*c^4*d^5 - 80*A^3*a^9*c^5*d^4 + 16*A^3*a^9*c^6*d^3 - 115*B^3*a^9*c^2*d^7 + 350*B^3*a^9*c^3*d^6 - 537*B^3*a^9*c^4*d^5 + 387*B^3*a^9*c^5*d^4 + 36*B^3*a^9*c^6*d^3 - 297*B^3*a^9*c^7*d^2 + 108*A^3*a^9*c*d^8 + 14*B^3*a^9*c*d^8 + 216*B^3*a^9*c^8*d + 96*A*B^2*a^9*c*d^8 + 108*A*B^2*a^9*c^8*d + 198*A^2*B*a^9*c*d^8 - 573*A*B^2*a^9*c^2*d^7 + 1239*A*B^2*a^9*c^3*d^6 - 1125*A*B^2*a^9*c^4*d^5 + 93*A*B^2*a^9*c^5*d^4 + 630*A*B^2*a^9*c^6*d^3 - 468*A*B^2*a^9*c^7*d^2 - 768*A^2*B*a^9*c^2*d^7 + 996*A^2*B*a^9*c^3*d^6 - 288*A^2*B*a^9*c^4*d^5 - 402*A^2*B*a^9*c^5*d^4 + 336*A^2*B*a^9*c^6*d^3 - 72*A^2*B*a^9*c^7*d^2))/(2*c*d^9 + d^10 + c^2*d^8) + (16*tan(e/2 + (f*x)/2)*(520*A^3*a^9*c^4*d^6 - 360*A^3*a^9*c^2*d^8 - 168*A^3*a^9*c^3*d^7 - 216*B^3*a^9*c^10 - 112*A^3*a^9*c^5*d^5 - 160*A^3*a^9*c^6*d^4 + 64*A^3*a^9*c^7*d^3 - 728*B^3*a^9*c^2*d^8 + 1702*B^3*a^9*c^3*d^7 - 1090*B^3*a^9*c^4*d^6 - 1584*B^3*a^9*c^5*d^5 + 2898*B^3*a^9*c^6*d^4 - 1080*B^3*a^9*c^7*d^3 - 864*B^3*a^9*c^8*d^2 + 216*A^3*a^9*c*d^9 + 98*B^3*a^9*c*d^9 + 864*B^3*a^9*c^9*d + 462*A*B^2*a^9*c*d^9 + 432*A*B^2*a^9*c^9*d + 576*A^2*B*a^9*c*d^9 - 2178*A*B^2*a^9*c^2*d^8 + 2982*A*B^2*a^9*c^3*d^7 + 594*A*B^2*a^9*c^4*d^6 - 4668*A*B^2*a^9*c^5*d^5 + 3096*A*B^2*a^9*c^6*d^4 + 792*A*B^2*a^9*c^7*d^3 - 1512*A*B^2*a^9*c^8*d^2 - 1752*A^2*B*a^9*c^2*d^8 + 912*A^2*B*a^9*c^3*d^7 + 2016*A^2*B*a^9*c^4*d^6 - 2352*A^2*B*a^9*c^5*d^5 + 24*A^2*B*a^9*c^6*d^4 + 864*A^2*B*a^9*c^7*d^3 - 288*A^2*B*a^9*c^8*d^2))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9) - (8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) + (a^3*((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4) - (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(36*A^2*a^6*c^2*d^9 + 24*A^2*a^6*c^3*d^8 - 44*A^2*a^6*c^4*d^7 - 16*A^2*a^6*c^5*d^6 + 16*A^2*a^6*c^6*d^5 + 49*B^2*a^6*c^2*d^9 - 70*B^2*a^6*c^3*d^8 - 59*B^2*a^6*c^4*d^7 + 144*B^2*a^6*c^5*d^6 - 24*B^2*a^6*c^6*d^5 - 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 84*A*B*a^6*c^2*d^9 - 32*A*B*a^6*c^3*d^8 - 148*A*B*a^6*c^4*d^7 + 88*A*B*a^6*c^5*d^6 + 72*A*B*a^6*c^6*d^5 - 48*A*B*a^6*c^7*d^4))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(144*A^2*a^6*c^2*d^10 - 164*A^2*a^6*c^3*d^9 - 136*A^2*a^6*c^4*d^8 + 136*A^2*a^6*c^5*d^7 + 32*A^2*a^6*c^6*d^6 - 32*A^2*a^6*c^7*d^5 - 100*B^2*a^6*c^2*d^10 - 299*B^2*a^6*c^3*d^9 + 494*B^2*a^6*c^4*d^8 + 91*B^2*a^6*c^5*d^7 - 504*B^2*a^6*c^6*d^6 + 156*B^2*a^6*c^7*d^5 + 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 + 36*A^2*a^6*c*d^11 + 94*B^2*a^6*c*d^11 + 88*A*B*a^6*c^2*d^10 - 628*A*B*a^6*c^3*d^9 + 208*A*B*a^6*c^4*d^8 + 572*A*B*a^6*c^5*d^7 - 320*A*B*a^6*c^6*d^6 - 144*A*B*a^6*c^7*d^5 + 96*A*B*a^6*c^8*d^4 + 144*A*B*a^6*c*d^11))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*(-(c + d)^3*(c - d)^3)^(1/2)*((8*(12*A*a^3*c*d^12 + 14*B*a^3*c*d^12 + 4*A*a^3*c^2*d^11 - 12*A*a^3*c^3*d^10 - 4*A*a^3*c^4*d^9 - 20*B*a^3*c^3*d^10 + 6*B*a^3*c^5*d^8))/(2*c*d^9 + d^10 + c^2*d^8) - (8*tan(e/2 + (f*x)/2)*(24*A*a^3*c*d^13 + 8*B*a^3*c*d^13 - 8*A*a^3*c^2*d^12 - 40*A*a^3*c^3*d^11 + 8*A*a^3*c^4*d^10 + 16*A*a^3*c^5*d^9 - 32*B*a^3*c^2*d^12 - 8*B*a^3*c^3*d^11 + 56*B*a^3*c^4*d^10 - 24*B*a^3*c^6*d^8))/(2*c*d^10 + d^11 + c^2*d^9) + (a^3*((8*(4*c^2*d^13 + 8*c^3*d^12 + 4*c^4*d^11))/(2*c*d^9 + d^10 + c^2*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^15 + 24*c^2*d^14 + 4*c^3*d^13 - 16*c^4*d^12 - 8*c^5*d^11))/(2*c*d^10 + d^11 + c^2*d^9))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d))/(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4)))*(-(c + d)^3*(c - d)^3)^(1/2)*(3*A*d^2 - 3*B*c^2 + B*d^2 + 2*A*c*d - 3*B*c*d)*2i)/(f*(3*c*d^6 + d^7 + 3*c^2*d^5 + c^3*d^4))","B"
264,1,13891,305,25.413204,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^3)/(c + d*sin(e + f*x))^3,x)","-\frac{\frac{A\,a^3\,d^4+6\,B\,a^3\,c^4+5\,A\,a^3\,c\,d^3-2\,A\,a^3\,c^3\,d+B\,a^3\,c\,d^3+6\,B\,a^3\,c^3\,d-4\,A\,a^3\,c^2\,d^2-5\,B\,a^3\,c^2\,d^2}{d^3\,{\left(c+d\right)}^2}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,a^3\,d^4+6\,B\,a^3\,c^4+5\,A\,a^3\,c\,d^3-2\,A\,a^3\,c^3\,d+B\,a^3\,c\,d^3+6\,B\,a^3\,c^3\,d-4\,A\,a^3\,c^2\,d^2-5\,B\,a^3\,c^2\,d^2\right)}{c\,d^2\,{\left(c+d\right)}^2}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,A\,a^3\,d^4+3\,B\,a^3\,c^4+4\,A\,a^3\,c\,d^3-A\,a^3\,c^3\,d+3\,B\,a^3\,c^3\,d-5\,A\,a^3\,c^2\,d^2-6\,B\,a^3\,c^2\,d^2\right)}{c\,d^2\,{\left(c+d\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(A\,a^3\,d^6+6\,B\,a^3\,c^6+5\,A\,a^3\,c\,d^5-2\,A\,a^3\,c^5\,d+B\,a^3\,c\,d^5+6\,B\,a^3\,c^5\,d-3\,A\,a^3\,c^2\,d^4+3\,A\,a^3\,c^3\,d^3-4\,A\,a^3\,c^4\,d^2-3\,B\,a^3\,c^2\,d^4+11\,B\,a^3\,c^3\,d^3+3\,B\,a^3\,c^4\,d^2\right)}{c^2\,d^3\,{\left(c+d\right)}^2}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,a^3\,d^6+6\,B\,a^3\,c^6+10\,A\,a^3\,c\,d^5-2\,A\,a^3\,c^5\,d+2\,B\,a^3\,c\,d^5+6\,B\,a^3\,c^5\,d-7\,A\,a^3\,c^2\,d^4+A\,a^3\,c^3\,d^3-4\,A\,a^3\,c^4\,d^2-14\,B\,a^3\,c^2\,d^4+5\,B\,a^3\,c^3\,d^3+3\,B\,a^3\,c^4\,d^2\right)}{c^2\,d^3\,{\left(c+d\right)}^2}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,a^3\,d^4+21\,B\,a^3\,c^4+16\,A\,a^3\,c\,d^3-7\,A\,a^3\,c^3\,d+4\,B\,a^3\,c\,d^3+21\,B\,a^3\,c^3\,d-11\,A\,a^3\,c^2\,d^2-14\,B\,a^3\,c^2\,d^2\right)}{c\,d^2\,{\left(c+d\right)}^2}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(3\,c^2+4\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,c^2+4\,d^2\right)+c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+c^2+8\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,c\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+4\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}-\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)}{d^4}\right)}{d^4}\right)\,1{}\mathrm{i}}{d^4}+\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)}{d^4}\right)}{d^4}\right)\,1{}\mathrm{i}}{d^4}}{\frac{16\,\left(-2\,A^3\,a^9\,c^5\,d^3-18\,A^3\,a^9\,c^4\,d^4-29\,A^3\,a^9\,c^3\,d^5+49\,A^3\,a^9\,c\,d^7+18\,A^2\,B\,a^9\,c^6\,d^2+114\,A^2\,B\,a^9\,c^5\,d^3+69\,A^2\,B\,a^9\,c^4\,d^4-201\,A^2\,B\,a^9\,c^3\,d^5-231\,A^2\,B\,a^9\,c^2\,d^6+231\,A^2\,B\,a^9\,c\,d^7-54\,A\,B^2\,a^9\,c^7\,d-198\,A\,B^2\,a^9\,c^6\,d^2+135\,A\,B^2\,a^9\,c^5\,d^3+540\,A\,B^2\,a^9\,c^4\,d^4-135\,A\,B^2\,a^9\,c^3\,d^5-576\,A\,B^2\,a^9\,c^2\,d^6+288\,A\,B^2\,a^9\,c\,d^7+54\,B^3\,a^9\,c^8+54\,B^3\,a^9\,c^7\,d-243\,B^3\,a^9\,c^6\,d^2-135\,B^3\,a^9\,c^5\,d^3+405\,B^3\,a^9\,c^4\,d^4+81\,B^3\,a^9\,c^3\,d^5-324\,B^3\,a^9\,c^2\,d^6+108\,B^3\,a^9\,c\,d^7\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^3\,a^9\,c^6\,d^3-32\,A^3\,a^9\,c^5\,d^4-44\,A^3\,a^9\,c^4\,d^5+4\,A^3\,a^9\,c^3\,d^6+52\,A^3\,a^9\,c^2\,d^7+28\,A^3\,a^9\,c\,d^8+72\,A^2\,B\,a^9\,c^7\,d^2+216\,A^2\,B\,a^9\,c^6\,d^3+108\,A^2\,B\,a^9\,c^5\,d^4-372\,A^2\,B\,a^9\,c^4\,d^5-372\,A^2\,B\,a^9\,c^3\,d^6+156\,A^2\,B\,a^9\,c^2\,d^7+192\,A^2\,B\,a^9\,c\,d^8-216\,A\,B^2\,a^9\,c^8\,d-432\,A\,B^2\,a^9\,c^7\,d^2+324\,A\,B^2\,a^9\,c^6\,d^3+1260\,A\,B^2\,a^9\,c^5\,d^4-1224\,A\,B^2\,a^9\,c^3\,d^6-108\,A\,B^2\,a^9\,c^2\,d^7+396\,A\,B^2\,a^9\,c\,d^8+216\,B^3\,a^9\,c^9+216\,B^3\,a^9\,c^8\,d-756\,B^3\,a^9\,c^7\,d^2-756\,B^3\,a^9\,c^6\,d^3+1080\,B^3\,a^9\,c^5\,d^4+864\,B^3\,a^9\,c^4\,d^5-756\,B^3\,a^9\,c^3\,d^6-324\,B^3\,a^9\,c^2\,d^7+216\,B^3\,a^9\,c\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}-\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)}{d^4}\right)}{d^4}\right)}{d^4}-\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)}{d^4}\right)}{d^4}\right)}{d^4}}\right)\,\left(B\,a^3\,c\,3{}\mathrm{i}-a^3\,d\,\left(A+3\,B\right)\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{d^4\,f}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}-\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)\,1{}\mathrm{i}}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)\,1{}\mathrm{i}}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}}{\frac{16\,\left(-2\,A^3\,a^9\,c^5\,d^3-18\,A^3\,a^9\,c^4\,d^4-29\,A^3\,a^9\,c^3\,d^5+49\,A^3\,a^9\,c\,d^7+18\,A^2\,B\,a^9\,c^6\,d^2+114\,A^2\,B\,a^9\,c^5\,d^3+69\,A^2\,B\,a^9\,c^4\,d^4-201\,A^2\,B\,a^9\,c^3\,d^5-231\,A^2\,B\,a^9\,c^2\,d^6+231\,A^2\,B\,a^9\,c\,d^7-54\,A\,B^2\,a^9\,c^7\,d-198\,A\,B^2\,a^9\,c^6\,d^2+135\,A\,B^2\,a^9\,c^5\,d^3+540\,A\,B^2\,a^9\,c^4\,d^4-135\,A\,B^2\,a^9\,c^3\,d^5-576\,A\,B^2\,a^9\,c^2\,d^6+288\,A\,B^2\,a^9\,c\,d^7+54\,B^3\,a^9\,c^8+54\,B^3\,a^9\,c^7\,d-243\,B^3\,a^9\,c^6\,d^2-135\,B^3\,a^9\,c^5\,d^3+405\,B^3\,a^9\,c^4\,d^4+81\,B^3\,a^9\,c^3\,d^5-324\,B^3\,a^9\,c^2\,d^6+108\,B^3\,a^9\,c\,d^7\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{16\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^3\,a^9\,c^6\,d^3-32\,A^3\,a^9\,c^5\,d^4-44\,A^3\,a^9\,c^4\,d^5+4\,A^3\,a^9\,c^3\,d^6+52\,A^3\,a^9\,c^2\,d^7+28\,A^3\,a^9\,c\,d^8+72\,A^2\,B\,a^9\,c^7\,d^2+216\,A^2\,B\,a^9\,c^6\,d^3+108\,A^2\,B\,a^9\,c^5\,d^4-372\,A^2\,B\,a^9\,c^4\,d^5-372\,A^2\,B\,a^9\,c^3\,d^6+156\,A^2\,B\,a^9\,c^2\,d^7+192\,A^2\,B\,a^9\,c\,d^8-216\,A\,B^2\,a^9\,c^8\,d-432\,A\,B^2\,a^9\,c^7\,d^2+324\,A\,B^2\,a^9\,c^6\,d^3+1260\,A\,B^2\,a^9\,c^5\,d^4-1224\,A\,B^2\,a^9\,c^3\,d^6-108\,A\,B^2\,a^9\,c^2\,d^7+396\,A\,B^2\,a^9\,c\,d^8+216\,B^3\,a^9\,c^9+216\,B^3\,a^9\,c^8\,d-756\,B^3\,a^9\,c^7\,d^2-756\,B^3\,a^9\,c^6\,d^3+1080\,B^3\,a^9\,c^5\,d^4+864\,B^3\,a^9\,c^4\,d^5-756\,B^3\,a^9\,c^3\,d^6-324\,B^3\,a^9\,c^2\,d^7+216\,B^3\,a^9\,c\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}-\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}-\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,A^2\,a^6\,c^6\,d^5+16\,A^2\,a^6\,c^5\,d^6+24\,A^2\,a^6\,c^4\,d^7+16\,A^2\,a^6\,c^3\,d^8+4\,A^2\,a^6\,c^2\,d^9-24\,A\,B\,a^6\,c^7\,d^4-72\,A\,B\,a^6\,c^6\,d^5-48\,A\,B\,a^6\,c^5\,d^6+48\,A\,B\,a^6\,c^4\,d^7+72\,A\,B\,a^6\,c^3\,d^8+24\,A\,B\,a^6\,c^2\,d^9+36\,B^2\,a^6\,c^8\,d^3+72\,B^2\,a^6\,c^7\,d^4-36\,B^2\,a^6\,c^6\,d^5-144\,B^2\,a^6\,c^5\,d^6-36\,B^2\,a^6\,c^4\,d^7+72\,B^2\,a^6\,c^3\,d^8+36\,B^2\,a^6\,c^2\,d^9\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,A^2\,a^6\,c^7\,d^5-32\,A^2\,a^6\,c^6\,d^6-36\,A^2\,a^6\,c^5\,d^7+36\,A^2\,a^6\,c^4\,d^8+99\,A^2\,a^6\,c^3\,d^9+46\,A^2\,a^6\,c^2\,d^{10}-41\,A^2\,a^6\,c\,d^{11}+48\,A\,B\,a^6\,c^8\,d^4+144\,A\,B\,a^6\,c^7\,d^5+24\,A\,B\,a^6\,c^6\,d^6-372\,A\,B\,a^6\,c^5\,d^7-318\,A\,B\,a^6\,c^4\,d^8+228\,A\,B\,a^6\,c^3\,d^9+282\,A\,B\,a^6\,c^2\,d^{10}-36\,A\,B\,a^6\,c\,d^{11}-72\,B^2\,a^6\,c^9\,d^3-144\,B^2\,a^6\,c^8\,d^4+180\,B^2\,a^6\,c^7\,d^5+504\,B^2\,a^6\,c^6\,d^6-81\,B^2\,a^6\,c^5\,d^7-594\,B^2\,a^6\,c^4\,d^8-81\,B^2\,a^6\,c^3\,d^9+252\,B^2\,a^6\,c^2\,d^{10}+36\,B^2\,a^6\,c\,d^{11}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,c\,d^{13}+12\,B\,a^3\,c\,d^{13}+2\,A\,a^3\,c^2\,d^{12}-6\,A\,a^3\,c^3\,d^{11}-2\,A\,a^3\,c^4\,d^{10}+2\,A\,a^3\,c^5\,d^9+24\,B\,a^3\,c^2\,d^{12}+6\,B\,a^3\,c^3\,d^{11}-18\,B\,a^3\,c^4\,d^{10}-18\,B\,a^3\,c^5\,d^9-6\,B\,a^3\,c^6\,d^8\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}-\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(28\,A\,a^3\,c\,d^{14}+24\,B\,a^3\,c\,d^{14}+52\,A\,a^3\,c^2\,d^{13}+4\,A\,a^3\,c^3\,d^{12}-44\,A\,a^3\,c^4\,d^{11}-32\,A\,a^3\,c^5\,d^{10}-8\,A\,a^3\,c^6\,d^9+12\,B\,a^3\,c^2\,d^{13}-84\,B\,a^3\,c^3\,d^{12}-84\,B\,a^3\,c^4\,d^{11}+36\,B\,a^3\,c^5\,d^{10}+72\,B\,a^3\,c^6\,d^9+24\,B\,a^3\,c^7\,d^8\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}+\frac{a^3\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(\frac{8\,\left(4\,c^6\,d^{11}+16\,c^5\,d^{12}+24\,c^4\,d^{13}+16\,c^3\,d^{14}+4\,c^2\,d^{15}\right)}{c^4\,d^8+4\,c^3\,d^9+6\,c^2\,d^{10}+4\,c\,d^{11}+d^{12}}+\frac{8\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-8\,c^7\,d^{11}-32\,c^6\,d^{12}-36\,c^5\,d^{13}+16\,c^4\,d^{14}+64\,c^3\,d^{15}+48\,c^2\,d^{16}+12\,c\,d^{17}\right)}{c^4\,d^9+4\,c^3\,d^{10}+6\,c^2\,d^{11}+4\,c\,d^{12}+d^{13}}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}\right)\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)}{2\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}}\right)\,\sqrt{-{\left(c+d\right)}^5\,\left(c-d\right)}\,\left(7\,A\,d^3-6\,B\,c^3+6\,B\,d^3+6\,A\,c\,d^2+2\,A\,c^2\,d-3\,B\,c\,d^2-12\,B\,c^2\,d\right)\,1{}\mathrm{i}}{f\,\left(c^5\,d^4+5\,c^4\,d^5+10\,c^3\,d^6+10\,c^2\,d^7+5\,c\,d^8+d^9\right)}","Not used",1,"- ((A*a^3*d^4 + 6*B*a^3*c^4 + 5*A*a^3*c*d^3 - 2*A*a^3*c^3*d + B*a^3*c*d^3 + 6*B*a^3*c^3*d - 4*A*a^3*c^2*d^2 - 5*B*a^3*c^2*d^2)/(d^3*(c + d)^2) + (4*tan(e/2 + (f*x)/2)^3*(A*a^3*d^4 + 6*B*a^3*c^4 + 5*A*a^3*c*d^3 - 2*A*a^3*c^3*d + B*a^3*c*d^3 + 6*B*a^3*c^3*d - 4*A*a^3*c^2*d^2 - 5*B*a^3*c^2*d^2))/(c*d^2*(c + d)^2) + (tan(e/2 + (f*x)/2)^5*(2*A*a^3*d^4 + 3*B*a^3*c^4 + 4*A*a^3*c*d^3 - A*a^3*c^3*d + 3*B*a^3*c^3*d - 5*A*a^3*c^2*d^2 - 6*B*a^3*c^2*d^2))/(c*d^2*(c + d)^2) + (2*tan(e/2 + (f*x)/2)^2*(A*a^3*d^6 + 6*B*a^3*c^6 + 5*A*a^3*c*d^5 - 2*A*a^3*c^5*d + B*a^3*c*d^5 + 6*B*a^3*c^5*d - 3*A*a^3*c^2*d^4 + 3*A*a^3*c^3*d^3 - 4*A*a^3*c^4*d^2 - 3*B*a^3*c^2*d^4 + 11*B*a^3*c^3*d^3 + 3*B*a^3*c^4*d^2))/(c^2*d^3*(c + d)^2) + (tan(e/2 + (f*x)/2)^4*(2*A*a^3*d^6 + 6*B*a^3*c^6 + 10*A*a^3*c*d^5 - 2*A*a^3*c^5*d + 2*B*a^3*c*d^5 + 6*B*a^3*c^5*d - 7*A*a^3*c^2*d^4 + A*a^3*c^3*d^3 - 4*A*a^3*c^4*d^2 - 14*B*a^3*c^2*d^4 + 5*B*a^3*c^3*d^3 + 3*B*a^3*c^4*d^2))/(c^2*d^3*(c + d)^2) + (tan(e/2 + (f*x)/2)*(2*A*a^3*d^4 + 21*B*a^3*c^4 + 16*A*a^3*c*d^3 - 7*A*a^3*c^3*d + 4*B*a^3*c*d^3 + 21*B*a^3*c^3*d - 11*A*a^3*c^2*d^2 - 14*B*a^3*c^2*d^2))/(c*d^2*(c + d)^2))/(f*(tan(e/2 + (f*x)/2)^2*(3*c^2 + 4*d^2) + tan(e/2 + (f*x)/2)^4*(3*c^2 + 4*d^2) + c^2*tan(e/2 + (f*x)/2)^6 + c^2 + 8*c*d*tan(e/2 + (f*x)/2)^3 + 4*c*d*tan(e/2 + (f*x)/2)^5 + 4*c*d*tan(e/2 + (f*x)/2))) - (atan((((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) - (8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(B*a^3*c*3i - a^3*d*(A + 3*B)*1i))/d^4))/d^4)*1i)/d^4 + ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) - (8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(B*a^3*c*3i - a^3*d*(A + 3*B)*1i))/d^4))/d^4)*1i)/d^4)/((16*(54*B^3*a^9*c^8 - 29*A^3*a^9*c^3*d^5 - 18*A^3*a^9*c^4*d^4 - 2*A^3*a^9*c^5*d^3 - 324*B^3*a^9*c^2*d^6 + 81*B^3*a^9*c^3*d^5 + 405*B^3*a^9*c^4*d^4 - 135*B^3*a^9*c^5*d^3 - 243*B^3*a^9*c^6*d^2 + 49*A^3*a^9*c*d^7 + 108*B^3*a^9*c*d^7 + 54*B^3*a^9*c^7*d + 288*A*B^2*a^9*c*d^7 - 54*A*B^2*a^9*c^7*d + 231*A^2*B*a^9*c*d^7 - 576*A*B^2*a^9*c^2*d^6 - 135*A*B^2*a^9*c^3*d^5 + 540*A*B^2*a^9*c^4*d^4 + 135*A*B^2*a^9*c^5*d^3 - 198*A*B^2*a^9*c^6*d^2 - 231*A^2*B*a^9*c^2*d^6 - 201*A^2*B*a^9*c^3*d^5 + 69*A^2*B*a^9*c^4*d^4 + 114*A^2*B*a^9*c^5*d^3 + 18*A^2*B*a^9*c^6*d^2))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (16*tan(e/2 + (f*x)/2)*(216*B^3*a^9*c^9 + 52*A^3*a^9*c^2*d^7 + 4*A^3*a^9*c^3*d^6 - 44*A^3*a^9*c^4*d^5 - 32*A^3*a^9*c^5*d^4 - 8*A^3*a^9*c^6*d^3 - 324*B^3*a^9*c^2*d^7 - 756*B^3*a^9*c^3*d^6 + 864*B^3*a^9*c^4*d^5 + 1080*B^3*a^9*c^5*d^4 - 756*B^3*a^9*c^6*d^3 - 756*B^3*a^9*c^7*d^2 + 28*A^3*a^9*c*d^8 + 216*B^3*a^9*c*d^8 + 216*B^3*a^9*c^8*d + 396*A*B^2*a^9*c*d^8 - 216*A*B^2*a^9*c^8*d + 192*A^2*B*a^9*c*d^8 - 108*A*B^2*a^9*c^2*d^7 - 1224*A*B^2*a^9*c^3*d^6 + 1260*A*B^2*a^9*c^5*d^4 + 324*A*B^2*a^9*c^6*d^3 - 432*A*B^2*a^9*c^7*d^2 + 156*A^2*B*a^9*c^2*d^7 - 372*A^2*B*a^9*c^3*d^6 - 372*A^2*B*a^9*c^4*d^5 + 108*A^2*B*a^9*c^5*d^4 + 216*A^2*B*a^9*c^6*d^3 + 72*A^2*B*a^9*c^7*d^2))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) - (8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(B*a^3*c*3i - a^3*d*(A + 3*B)*1i))/d^4))/d^4))/d^4 - ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + ((B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*((8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) - (8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(B*a^3*c*3i - a^3*d*(A + 3*B)*1i))/d^4))/d^4))/d^4))*(B*a^3*c*3i - a^3*d*(A + 3*B)*1i)*2i)/(d^4*f) - (a^3*atan(((a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) - (8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d)*1i)/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) - (8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d)*1i)/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))/((16*(54*B^3*a^9*c^8 - 29*A^3*a^9*c^3*d^5 - 18*A^3*a^9*c^4*d^4 - 2*A^3*a^9*c^5*d^3 - 324*B^3*a^9*c^2*d^6 + 81*B^3*a^9*c^3*d^5 + 405*B^3*a^9*c^4*d^4 - 135*B^3*a^9*c^5*d^3 - 243*B^3*a^9*c^6*d^2 + 49*A^3*a^9*c*d^7 + 108*B^3*a^9*c*d^7 + 54*B^3*a^9*c^7*d + 288*A*B^2*a^9*c*d^7 - 54*A*B^2*a^9*c^7*d + 231*A^2*B*a^9*c*d^7 - 576*A*B^2*a^9*c^2*d^6 - 135*A*B^2*a^9*c^3*d^5 + 540*A*B^2*a^9*c^4*d^4 + 135*A*B^2*a^9*c^5*d^3 - 198*A*B^2*a^9*c^6*d^2 - 231*A^2*B*a^9*c^2*d^6 - 201*A^2*B*a^9*c^3*d^5 + 69*A^2*B*a^9*c^4*d^4 + 114*A^2*B*a^9*c^5*d^3 + 18*A^2*B*a^9*c^6*d^2))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (16*tan(e/2 + (f*x)/2)*(216*B^3*a^9*c^9 + 52*A^3*a^9*c^2*d^7 + 4*A^3*a^9*c^3*d^6 - 44*A^3*a^9*c^4*d^5 - 32*A^3*a^9*c^5*d^4 - 8*A^3*a^9*c^6*d^3 - 324*B^3*a^9*c^2*d^7 - 756*B^3*a^9*c^3*d^6 + 864*B^3*a^9*c^4*d^5 + 1080*B^3*a^9*c^5*d^4 - 756*B^3*a^9*c^6*d^3 - 756*B^3*a^9*c^7*d^2 + 28*A^3*a^9*c*d^8 + 216*B^3*a^9*c*d^8 + 216*B^3*a^9*c^8*d + 396*A*B^2*a^9*c*d^8 - 216*A*B^2*a^9*c^8*d + 192*A^2*B*a^9*c*d^8 - 108*A*B^2*a^9*c^2*d^7 - 1224*A*B^2*a^9*c^3*d^6 + 1260*A*B^2*a^9*c^5*d^4 + 324*A*B^2*a^9*c^6*d^3 - 432*A*B^2*a^9*c^7*d^2 + 156*A^2*B*a^9*c^2*d^7 - 372*A^2*B*a^9*c^3*d^6 - 372*A^2*B*a^9*c^4*d^5 + 108*A^2*B*a^9*c^5*d^4 + 216*A^2*B*a^9*c^6*d^3 + 72*A^2*B*a^9*c^7*d^2))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) - (8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)) - (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*A^2*a^6*c^2*d^9 + 16*A^2*a^6*c^3*d^8 + 24*A^2*a^6*c^4*d^7 + 16*A^2*a^6*c^5*d^6 + 4*A^2*a^6*c^6*d^5 + 36*B^2*a^6*c^2*d^9 + 72*B^2*a^6*c^3*d^8 - 36*B^2*a^6*c^4*d^7 - 144*B^2*a^6*c^5*d^6 - 36*B^2*a^6*c^6*d^5 + 72*B^2*a^6*c^7*d^4 + 36*B^2*a^6*c^8*d^3 + 24*A*B*a^6*c^2*d^9 + 72*A*B*a^6*c^3*d^8 + 48*A*B*a^6*c^4*d^7 - 48*A*B*a^6*c^5*d^6 - 72*A*B*a^6*c^6*d^5 - 24*A*B*a^6*c^7*d^4))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(46*A^2*a^6*c^2*d^10 + 99*A^2*a^6*c^3*d^9 + 36*A^2*a^6*c^4*d^8 - 36*A^2*a^6*c^5*d^7 - 32*A^2*a^6*c^6*d^6 - 8*A^2*a^6*c^7*d^5 + 252*B^2*a^6*c^2*d^10 - 81*B^2*a^6*c^3*d^9 - 594*B^2*a^6*c^4*d^8 - 81*B^2*a^6*c^5*d^7 + 504*B^2*a^6*c^6*d^6 + 180*B^2*a^6*c^7*d^5 - 144*B^2*a^6*c^8*d^4 - 72*B^2*a^6*c^9*d^3 - 41*A^2*a^6*c*d^11 + 36*B^2*a^6*c*d^11 + 282*A*B*a^6*c^2*d^10 + 228*A*B*a^6*c^3*d^9 - 318*A*B*a^6*c^4*d^8 - 372*A*B*a^6*c^5*d^7 + 24*A*B*a^6*c^6*d^6 + 144*A*B*a^6*c^7*d^5 + 48*A*B*a^6*c^8*d^4 - 36*A*B*a^6*c*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*A*a^3*c*d^13 + 12*B*a^3*c*d^13 + 2*A*a^3*c^2*d^12 - 6*A*a^3*c^3*d^11 - 2*A*a^3*c^4*d^10 + 2*A*a^3*c^5*d^9 + 24*B*a^3*c^2*d^12 + 6*B*a^3*c^3*d^11 - 18*B*a^3*c^4*d^10 - 18*B*a^3*c^5*d^9 - 6*B*a^3*c^6*d^8))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) - (8*tan(e/2 + (f*x)/2)*(28*A*a^3*c*d^14 + 24*B*a^3*c*d^14 + 52*A*a^3*c^2*d^13 + 4*A*a^3*c^3*d^12 - 44*A*a^3*c^4*d^11 - 32*A*a^3*c^5*d^10 - 8*A*a^3*c^6*d^9 + 12*B*a^3*c^2*d^13 - 84*B*a^3*c^3*d^12 - 84*B*a^3*c^4*d^11 + 36*B*a^3*c^5*d^10 + 72*B*a^3*c^6*d^9 + 24*B*a^3*c^7*d^8))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9) + (a^3*(-(c + d)^5*(c - d))^(1/2)*((8*(4*c^2*d^15 + 16*c^3*d^14 + 24*c^4*d^13 + 16*c^5*d^12 + 4*c^6*d^11))/(4*c*d^11 + d^12 + 6*c^2*d^10 + 4*c^3*d^9 + c^4*d^8) + (8*tan(e/2 + (f*x)/2)*(12*c*d^17 + 48*c^2*d^16 + 64*c^3*d^15 + 16*c^4*d^14 - 36*c^5*d^13 - 32*c^6*d^12 - 8*c^7*d^11))/(4*c*d^12 + d^13 + 6*c^2*d^11 + 4*c^3*d^10 + c^4*d^9))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4)))*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d))/(2*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4))))*(-(c + d)^5*(c - d))^(1/2)*(7*A*d^3 - 6*B*c^3 + 6*B*d^3 + 6*A*c*d^2 + 2*A*c^2*d - 3*B*c*d^2 - 12*B*c^2*d)*1i)/(f*(5*c*d^8 + d^9 + 10*c^2*d^7 + 10*c^3*d^6 + 5*c^4*d^5 + c^5*d^4))","B"
265,1,839,220,14.053574,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x)),x)","-\frac{12\,A\,c^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-18\,A\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-12\,B\,c^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+18\,B\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,A\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-12\,A\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-6\,B\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+36\,B\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5-16\,B\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7-9\,A\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-6\,B\,c^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)+9\,B\,d^3\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-9\,A\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-6\,B\,c^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)+9\,B\,d^3\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-18\,A\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+12\,A\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+18\,B\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+12\,B\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-16\,B\,d^3\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+36\,A\,c\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-36\,A\,c^2\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)-54\,B\,c\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+36\,B\,c^2\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+36\,A\,c\,d^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+18\,B\,c\,d^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+36\,B\,c^2\,d\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3-36\,B\,c\,d^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+18\,A\,c\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-18\,A\,c^2\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-27\,B\,c\,d^2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)+18\,B\,c^2\,d\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)+18\,A\,c\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-18\,A\,c^2\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)-27\,B\,c\,d^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)+18\,B\,c^2\,d\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(e+f\,x\right)+36\,A\,c\,d^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)-54\,B\,c\,d^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+36\,B\,c^2\,d\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)+36\,B\,c\,d^2\,{\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}{6\,a\,f\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)+6\,a\,f\,\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}","Not used",1,"-(12*A*c^3*cos(e/2 + (f*x)/2) - 18*A*d^3*cos(e/2 + (f*x)/2) - 12*B*c^3*cos(e/2 + (f*x)/2) + 18*B*d^3*cos(e/2 + (f*x)/2) + 6*A*d^3*cos(e/2 + (f*x)/2)^3 - 12*A*d^3*cos(e/2 + (f*x)/2)^5 - 6*B*d^3*cos(e/2 + (f*x)/2)^3 + 36*B*d^3*cos(e/2 + (f*x)/2)^5 - 16*B*d^3*cos(e/2 + (f*x)/2)^7 - 9*A*d^3*cos(e/2 + (f*x)/2)*(e + f*x) - 6*B*c^3*cos(e/2 + (f*x)/2)*(e + f*x) + 9*B*d^3*cos(e/2 + (f*x)/2)*(e + f*x) - 9*A*d^3*sin(e/2 + (f*x)/2)*(e + f*x) - 6*B*c^3*sin(e/2 + (f*x)/2)*(e + f*x) + 9*B*d^3*sin(e/2 + (f*x)/2)*(e + f*x) - 18*A*d^3*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2) + 12*A*d^3*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2) + 18*B*d^3*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2) + 12*B*d^3*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2) - 16*B*d^3*cos(e/2 + (f*x)/2)^6*sin(e/2 + (f*x)/2) + 36*A*c*d^2*cos(e/2 + (f*x)/2) - 36*A*c^2*d*cos(e/2 + (f*x)/2) - 54*B*c*d^2*cos(e/2 + (f*x)/2) + 36*B*c^2*d*cos(e/2 + (f*x)/2) + 36*A*c*d^2*cos(e/2 + (f*x)/2)^3 + 18*B*c*d^2*cos(e/2 + (f*x)/2)^3 + 36*B*c^2*d*cos(e/2 + (f*x)/2)^3 - 36*B*c*d^2*cos(e/2 + (f*x)/2)^5 + 18*A*c*d^2*cos(e/2 + (f*x)/2)*(e + f*x) - 18*A*c^2*d*cos(e/2 + (f*x)/2)*(e + f*x) - 27*B*c*d^2*cos(e/2 + (f*x)/2)*(e + f*x) + 18*B*c^2*d*cos(e/2 + (f*x)/2)*(e + f*x) + 18*A*c*d^2*sin(e/2 + (f*x)/2)*(e + f*x) - 18*A*c^2*d*sin(e/2 + (f*x)/2)*(e + f*x) - 27*B*c*d^2*sin(e/2 + (f*x)/2)*(e + f*x) + 18*B*c^2*d*sin(e/2 + (f*x)/2)*(e + f*x) + 36*A*c*d^2*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2) - 54*B*c*d^2*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2) + 36*B*c^2*d*cos(e/2 + (f*x)/2)^2*sin(e/2 + (f*x)/2) + 36*B*c*d^2*cos(e/2 + (f*x)/2)^4*sin(e/2 + (f*x)/2))/(6*a*f*cos(e/2 + (f*x)/2) + 6*a*f*sin(e/2 + (f*x)/2))","B"
266,1,297,143,16.666054,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x)),x)","\frac{x\,\left(2\,B\,c^2-2\,A\,d^2+3\,B\,d^2+4\,A\,c\,d-4\,B\,c\,d\right)}{2\,a}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,d^2-3\,B\,d^2+4\,B\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,c^2+2\,A\,d^2-2\,B\,c^2-3\,B\,d^2-4\,A\,c\,d+4\,B\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,A\,c^2+6\,A\,d^2-4\,B\,c^2-5\,B\,d^2-8\,A\,c\,d+12\,B\,c\,d\right)+2\,A\,c^2+4\,A\,d^2-2\,B\,c^2-4\,B\,d^2+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,d^2-B\,d^2+4\,B\,c\,d\right)-4\,A\,c\,d+8\,B\,c\,d}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}","Not used",1,"(x*(2*B*c^2 - 2*A*d^2 + 3*B*d^2 + 4*A*c*d - 4*B*c*d))/(2*a) - (tan(e/2 + (f*x)/2)^3*(2*A*d^2 - 3*B*d^2 + 4*B*c*d) + tan(e/2 + (f*x)/2)^4*(2*A*c^2 + 2*A*d^2 - 2*B*c^2 - 3*B*d^2 - 4*A*c*d + 4*B*c*d) + tan(e/2 + (f*x)/2)^2*(4*A*c^2 + 6*A*d^2 - 4*B*c^2 - 5*B*d^2 - 8*A*c*d + 12*B*c*d) + 2*A*c^2 + 4*A*d^2 - 2*B*c^2 - 4*B*d^2 + tan(e/2 + (f*x)/2)*(2*A*d^2 - B*d^2 + 4*B*c*d) - 4*A*c*d + 8*B*c*d)/(f*(a + a*tan(e/2 + (f*x)/2) + 2*a*tan(e/2 + (f*x)/2)^2 + 2*a*tan(e/2 + (f*x)/2)^3 + a*tan(e/2 + (f*x)/2)^4 + a*tan(e/2 + (f*x)/2)^5))","B"
267,1,122,67,13.680660,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x)),x)","\frac{x\,\left(A\,d+B\,c-B\,d\right)}{a}-\frac{\left(2\,A\,c-2\,A\,d-2\,B\,c+2\,B\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,B\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+2\,A\,c-2\,A\,d-2\,B\,c+4\,B\,d}{f\,\left(a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\right)}","Not used",1,"(x*(A*d + B*c - B*d))/a - (2*A*c - 2*A*d - 2*B*c + 4*B*d + tan(e/2 + (f*x)/2)^2*(2*A*c - 2*A*d - 2*B*c + 2*B*d) + 2*B*d*tan(e/2 + (f*x)/2))/(f*(a + a*tan(e/2 + (f*x)/2) + a*tan(e/2 + (f*x)/2)^2 + a*tan(e/2 + (f*x)/2)^3))","B"
268,1,35,35,12.919800,"\text{Not used}","int((A + B*sin(e + f*x))/(a + a*sin(e + f*x)),x)","\frac{B\,x}{a}-\frac{2\,A-2\,B}{a\,f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}","Not used",1,"(B*x)/a - (2*A - 2*B)/(a*f*(tan(e/2 + (f*x)/2) + 1))","B"
269,1,154,101,13.321654,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))),x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\left(A\,d-B\,c\right)\,\left(2\,a\,d^2-2\,a\,c\,d\right)}{a\,\sqrt{c+d}\,{\left(c-d\right)}^{3/2}}-\frac{2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d-B\,c\right)\,\left(a\,c-a\,d\right)}{a\,\sqrt{c+d}\,{\left(c-d\right)}^{3/2}}}{2\,A\,d-2\,B\,c}\right)\,\left(A\,d-B\,c\right)}{a\,f\,\sqrt{c+d}\,{\left(c-d\right)}^{3/2}}-\frac{2\,\left(A-B\right)}{f\,\left(a+a\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\right)\,\left(c-d\right)}","Not used",1,"(2*atan((((A*d - B*c)*(2*a*d^2 - 2*a*c*d))/(a*(c + d)^(1/2)*(c - d)^(3/2)) - (2*c*tan(e/2 + (f*x)/2)*(A*d - B*c)*(a*c - a*d))/(a*(c + d)^(1/2)*(c - d)^(3/2)))/(2*A*d - 2*B*c))*(A*d - B*c))/(a*f*(c + d)^(1/2)*(c - d)^(3/2)) - (2*(A - B))/(f*(a + a*tan(e/2 + (f*x)/2))*(c - d))","B"
270,1,437,181,15.530528,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^2),x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\left(2\,a\,c^3\,d-2\,a\,c^2\,d^2-2\,a\,c\,d^3+2\,a\,d^4\right)\,\left(B\,c^2-A\,d^2+B\,d^2-2\,A\,c\,d+B\,c\,d\right)}{a\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{5/2}}+\frac{2\,c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c^3-a\,c^2\,d-a\,c\,d^2+a\,d^3\right)\,\left(B\,c^2-A\,d^2+B\,d^2-2\,A\,c\,d+B\,c\,d\right)}{a\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{5/2}}}{2\,B\,c^2-2\,A\,d^2+2\,B\,d^2-4\,A\,c\,d+2\,B\,c\,d}\right)\,\left(B\,c^2-A\,d^2+B\,d^2-2\,A\,c\,d+B\,c\,d\right)}{a\,f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{2\,\left(A\,c^2+A\,d^2-B\,c^2+A\,c\,d-2\,B\,c\,d\right)}{\left(c+d\right)\,{\left(c-d\right)}^2}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d^2+2\,A\,c\,d-3\,B\,c\,d\right)}{c\,{\left(c-d\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(A\,c^3+A\,d^3-B\,c^3+A\,c^2\,d-B\,c\,d^2-B\,c^2\,d\right)}{c\,\left(c+d\right)\,{\left(c-d\right)}^2}}{f\,\left(a\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+\left(a\,c+2\,a\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(a\,c+2\,a\,d\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a\,c\right)}","Not used",1,"(2*atan((((2*a*d^4 - 2*a*c^2*d^2 - 2*a*c*d^3 + 2*a*c^3*d)*(B*c^2 - A*d^2 + B*d^2 - 2*A*c*d + B*c*d))/(a*(c + d)^(3/2)*(c - d)^(5/2)) + (2*c*tan(e/2 + (f*x)/2)*(a*c^3 + a*d^3 - a*c*d^2 - a*c^2*d)*(B*c^2 - A*d^2 + B*d^2 - 2*A*c*d + B*c*d))/(a*(c + d)^(3/2)*(c - d)^(5/2)))/(2*B*c^2 - 2*A*d^2 + 2*B*d^2 - 4*A*c*d + 2*B*c*d))*(B*c^2 - A*d^2 + B*d^2 - 2*A*c*d + B*c*d))/(a*f*(c + d)^(3/2)*(c - d)^(5/2)) - ((2*(A*c^2 + A*d^2 - B*c^2 + A*c*d - 2*B*c*d))/((c + d)*(c - d)^2) + (2*tan(e/2 + (f*x)/2)*(A*d^2 + 2*A*c*d - 3*B*c*d))/(c*(c - d)^2) + (2*tan(e/2 + (f*x)/2)^2*(A*c^3 + A*d^3 - B*c^3 + A*c^2*d - B*c*d^2 - B*c^2*d))/(c*(c + d)*(c - d)^2))/(f*(a*c + tan(e/2 + (f*x)/2)^2*(a*c + 2*a*d) + tan(e/2 + (f*x)/2)*(a*c + 2*a*d) + a*c*tan(e/2 + (f*x)/2)^3))","B"
271,1,1076,283,17.439346,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))*(c + d*sin(e + f*x))^3),x)","\frac{\frac{A\,d^4-2\,A\,c^4+2\,B\,c^4-8\,A\,c^2\,d^2+4\,B\,c^2\,d^2-2\,A\,c\,d^3-4\,A\,c^3\,d+B\,c\,d^3+8\,B\,c^3\,d}{\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^2-2\,c\,d+d^2\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,d^6-13\,A\,c^2\,d^4-17\,A\,c^3\,d^3-22\,A\,c^4\,d^2+4\,B\,c^2\,d^4+19\,B\,c^3\,d^3+23\,B\,c^4\,d^2-2\,A\,c\,d^5-8\,A\,c^5\,d+2\,B\,c\,d^5+12\,B\,c^5\,d\right)}{c^2\,\left(c^2-2\,c\,d+d^2\right)\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,A\,d^5-4\,A\,c^5+4\,B\,c^5-21\,A\,c^2\,d^3-14\,A\,c^3\,d^2+14\,B\,c^2\,d^3+17\,B\,c^3\,d^2-4\,A\,c\,d^4-4\,A\,c^4\,d+2\,B\,c\,d^4+8\,B\,c^4\,d\right)}{c^2\,\left(c^2-d^2\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,c^5-2\,A\,d^5-2\,B\,c^5+7\,A\,c^2\,d^3+2\,A\,c^3\,d^2-2\,B\,c^2\,d^3-7\,B\,c^3\,d^2+2\,A\,c\,d^4+4\,A\,c^4\,d-4\,B\,c^4\,d\right)}{c\,\left(c^2-2\,c\,d+d^2\right)\,\left(-c^3-c^2\,d+c\,d^2+d^3\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,d^5-27\,A\,c^2\,d^3-22\,A\,c^3\,d^2+15\,B\,c^2\,d^3+29\,B\,c^3\,d^2-5\,A\,c\,d^4-8\,A\,c^4\,d+4\,B\,c\,d^4+12\,B\,c^4\,d\right)}{c\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^2-2\,c\,d+d^2\right)}}{f\,\left({\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(2\,a\,c^2+4\,a\,c\,d+4\,a\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,a\,c^2+4\,a\,c\,d+4\,a\,d^2\right)+a\,c^2+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c^2+4\,a\,d\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(a\,c^2+4\,a\,d\,c\right)+a\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-2\,a\,c^5\,d+2\,a\,c^4\,d^2+4\,a\,c^3\,d^3-4\,a\,c^2\,d^4-2\,a\,c\,d^5+2\,a\,d^6\right)\,\left(2\,B\,c^3-3\,A\,d^3+2\,B\,d^3-6\,A\,c\,d^2-6\,A\,c^2\,d+7\,B\,c\,d^2+4\,B\,c^2\,d\right)}{2\,a\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{7/2}}-\frac{c\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a\,c^5-a\,c^4\,d-2\,a\,c^3\,d^2+2\,a\,c^2\,d^3+a\,c\,d^4-a\,d^5\right)\,\left(2\,B\,c^3-3\,A\,d^3+2\,B\,d^3-6\,A\,c\,d^2-6\,A\,c^2\,d+7\,B\,c\,d^2+4\,B\,c^2\,d\right)}{a\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{7/2}}}{2\,B\,c^3-3\,A\,d^3+2\,B\,d^3-6\,A\,c\,d^2-6\,A\,c^2\,d+7\,B\,c\,d^2+4\,B\,c^2\,d}\right)\,\left(2\,B\,c^3-3\,A\,d^3+2\,B\,d^3-6\,A\,c\,d^2-6\,A\,c^2\,d+7\,B\,c\,d^2+4\,B\,c^2\,d\right)}{a\,f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{7/2}}","Not used",1,"((A*d^4 - 2*A*c^4 + 2*B*c^4 - 8*A*c^2*d^2 + 4*B*c^2*d^2 - 2*A*c*d^3 - 4*A*c^3*d + B*c*d^3 + 8*B*c^3*d)/((c + d)*(c^2 - d^2)*(c^2 - 2*c*d + d^2)) - (tan(e/2 + (f*x)/2)^3*(2*A*d^6 - 13*A*c^2*d^4 - 17*A*c^3*d^3 - 22*A*c^4*d^2 + 4*B*c^2*d^4 + 19*B*c^3*d^3 + 23*B*c^4*d^2 - 2*A*c*d^5 - 8*A*c^5*d + 2*B*c*d^5 + 12*B*c^5*d))/(c^2*(c^2 - 2*c*d + d^2)*(c*d^2 - c^2*d - c^3 + d^3)) + (tan(e/2 + (f*x)/2)^2*(2*A*d^5 - 4*A*c^5 + 4*B*c^5 - 21*A*c^2*d^3 - 14*A*c^3*d^2 + 14*B*c^2*d^3 + 17*B*c^3*d^2 - 4*A*c*d^4 - 4*A*c^4*d + 2*B*c*d^4 + 8*B*c^4*d))/(c^2*(c^2 - d^2)*(c^2 - 2*c*d + d^2)) + (tan(e/2 + (f*x)/2)^4*(2*A*c^5 - 2*A*d^5 - 2*B*c^5 + 7*A*c^2*d^3 + 2*A*c^3*d^2 - 2*B*c^2*d^3 - 7*B*c^3*d^2 + 2*A*c*d^4 + 4*A*c^4*d - 4*B*c^4*d))/(c*(c^2 - 2*c*d + d^2)*(c*d^2 - c^2*d - c^3 + d^3)) + (tan(e/2 + (f*x)/2)*(2*A*d^5 - 27*A*c^2*d^3 - 22*A*c^3*d^2 + 15*B*c^2*d^3 + 29*B*c^3*d^2 - 5*A*c*d^4 - 8*A*c^4*d + 4*B*c*d^4 + 12*B*c^4*d))/(c*(c + d)*(c^2 - d^2)*(c^2 - 2*c*d + d^2)))/(f*(tan(e/2 + (f*x)/2)^2*(2*a*c^2 + 4*a*d^2 + 4*a*c*d) + tan(e/2 + (f*x)/2)^3*(2*a*c^2 + 4*a*d^2 + 4*a*c*d) + a*c^2 + tan(e/2 + (f*x)/2)*(a*c^2 + 4*a*c*d) + tan(e/2 + (f*x)/2)^4*(a*c^2 + 4*a*c*d) + a*c^2*tan(e/2 + (f*x)/2)^5)) - (atan((((2*a*d^6 - 4*a*c^2*d^4 + 4*a*c^3*d^3 + 2*a*c^4*d^2 - 2*a*c*d^5 - 2*a*c^5*d)*(2*B*c^3 - 3*A*d^3 + 2*B*d^3 - 6*A*c*d^2 - 6*A*c^2*d + 7*B*c*d^2 + 4*B*c^2*d))/(2*a*(c + d)^(5/2)*(c - d)^(7/2)) - (c*tan(e/2 + (f*x)/2)*(a*c^5 - a*d^5 + 2*a*c^2*d^3 - 2*a*c^3*d^2 + a*c*d^4 - a*c^4*d)*(2*B*c^3 - 3*A*d^3 + 2*B*d^3 - 6*A*c*d^2 - 6*A*c^2*d + 7*B*c*d^2 + 4*B*c^2*d))/(a*(c + d)^(5/2)*(c - d)^(7/2)))/(2*B*c^3 - 3*A*d^3 + 2*B*d^3 - 6*A*c*d^2 - 6*A*c^2*d + 7*B*c*d^2 + 4*B*c^2*d))*(2*B*c^3 - 3*A*d^3 + 2*B*d^3 - 6*A*c*d^2 - 6*A*c^2*d + 7*B*c*d^2 + 4*B*c^2*d))/(a*f*(c + d)^(5/2)*(c - d)^(7/2))","B"
272,1,663,228,16.345815,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^2,x)","\frac{d\,\mathrm{atan}\left(\frac{d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,B\,c^2-4\,A\,d^2+7\,B\,d^2+6\,A\,c\,d-12\,B\,c\,d\right)}{7\,B\,d^3-4\,A\,d^3+6\,A\,c\,d^2-12\,B\,c\,d^2+6\,B\,c^2\,d}\right)\,\left(6\,B\,c^2-4\,A\,d^2+7\,B\,d^2+6\,A\,c\,d-12\,B\,c\,d\right)}{a^2\,f}-\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,c^3+16\,A\,d^3+2\,B\,c^3-25\,B\,d^3-18\,A\,c\,d^2+6\,A\,c^2\,d+48\,B\,c\,d^2-18\,B\,c^2\,d\right)+\frac{4\,A\,c^3}{3}+\frac{20\,A\,d^3}{3}+\frac{2\,B\,c^3}{3}-\frac{32\,B\,d^3}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,A\,c^3+4\,A\,d^3-7\,B\,d^3-6\,A\,c\,d^2+12\,B\,c\,d^2-6\,B\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,A\,c^3+12\,A\,d^3+2\,B\,c^3-21\,B\,d^3-18\,A\,c\,d^2+6\,A\,c^2\,d+36\,B\,c\,d^2-18\,B\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,A\,c^3+28\,A\,d^3+4\,B\,c^3-42\,B\,d^3-36\,A\,c\,d^2+12\,A\,c^2\,d+84\,B\,c\,d^2-36\,B\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{16\,A\,c^3}{3}+\frac{56\,A\,d^3}{3}+\frac{2\,B\,c^3}{3}-\frac{98\,B\,d^3}{3}-20\,A\,c\,d^2+2\,A\,c^2\,d+56\,B\,c\,d^2-20\,B\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{14\,A\,c^3}{3}+\frac{64\,A\,d^3}{3}+\frac{4\,B\,c^3}{3}-\frac{97\,B\,d^3}{3}-22\,A\,c\,d^2+4\,A\,c^2\,d+64\,B\,c\,d^2-22\,B\,c^2\,d\right)-8\,A\,c\,d^2+2\,A\,c^2\,d+20\,B\,c\,d^2-8\,B\,c^2\,d}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+5\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+7\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+5\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(d*atan((d*tan(e/2 + (f*x)/2)*(6*B*c^2 - 4*A*d^2 + 7*B*d^2 + 6*A*c*d - 12*B*c*d))/(7*B*d^3 - 4*A*d^3 + 6*A*c*d^2 - 12*B*c*d^2 + 6*B*c^2*d))*(6*B*c^2 - 4*A*d^2 + 7*B*d^2 + 6*A*c*d - 12*B*c*d))/(a^2*f) - (tan(e/2 + (f*x)/2)*(2*A*c^3 + 16*A*d^3 + 2*B*c^3 - 25*B*d^3 - 18*A*c*d^2 + 6*A*c^2*d + 48*B*c*d^2 - 18*B*c^2*d) + (4*A*c^3)/3 + (20*A*d^3)/3 + (2*B*c^3)/3 - (32*B*d^3)/3 + tan(e/2 + (f*x)/2)^6*(2*A*c^3 + 4*A*d^3 - 7*B*d^3 - 6*A*c*d^2 + 12*B*c*d^2 - 6*B*c^2*d) + tan(e/2 + (f*x)/2)^5*(2*A*c^3 + 12*A*d^3 + 2*B*c^3 - 21*B*d^3 - 18*A*c*d^2 + 6*A*c^2*d + 36*B*c*d^2 - 18*B*c^2*d) + tan(e/2 + (f*x)/2)^3*(4*A*c^3 + 28*A*d^3 + 4*B*c^3 - 42*B*d^3 - 36*A*c*d^2 + 12*A*c^2*d + 84*B*c*d^2 - 36*B*c^2*d) + tan(e/2 + (f*x)/2)^4*((16*A*c^3)/3 + (56*A*d^3)/3 + (2*B*c^3)/3 - (98*B*d^3)/3 - 20*A*c*d^2 + 2*A*c^2*d + 56*B*c*d^2 - 20*B*c^2*d) + tan(e/2 + (f*x)/2)^2*((14*A*c^3)/3 + (64*A*d^3)/3 + (4*B*c^3)/3 - (97*B*d^3)/3 - 22*A*c*d^2 + 4*A*c^2*d + 64*B*c*d^2 - 22*B*c^2*d) - 8*A*c*d^2 + 2*A*c^2*d + 20*B*c*d^2 - 8*B*c^2*d)/(f*(5*a^2*tan(e/2 + (f*x)/2)^2 + 7*a^2*tan(e/2 + (f*x)/2)^3 + 7*a^2*tan(e/2 + (f*x)/2)^4 + 5*a^2*tan(e/2 + (f*x)/2)^5 + 3*a^2*tan(e/2 + (f*x)/2)^6 + a^2*tan(e/2 + (f*x)/2)^7 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
273,1,365,132,16.037993,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^2,x)","\frac{2\,d\,\mathrm{atan}\left(\frac{2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d+2\,B\,c-2\,B\,d\right)}{2\,A\,d^2-4\,B\,d^2+4\,B\,c\,d}\right)\,\left(A\,d+2\,B\,c-2\,B\,d\right)}{a^2\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,c^2-6\,A\,d^2+2\,B\,c^2+12\,B\,d^2+4\,A\,c\,d-12\,B\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{10\,A\,c^2}{3}-\frac{14\,A\,d^2}{3}+\frac{2\,B\,c^2}{3}+\frac{44\,B\,d^2}{3}+\frac{4\,A\,c\,d}{3}-\frac{28\,B\,c\,d}{3}\right)+\frac{4\,A\,c^2}{3}-\frac{8\,A\,d^2}{3}+\frac{2\,B\,c^2}{3}+\frac{20\,B\,d^2}{3}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,c^2-2\,A\,d^2+4\,B\,d^2-4\,B\,c\,d\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(2\,A\,c^2-6\,A\,d^2+2\,B\,c^2+16\,B\,d^2+4\,A\,c\,d-12\,B\,c\,d\right)+\frac{4\,A\,c\,d}{3}-\frac{16\,B\,c\,d}{3}}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(2*d*atan((2*d*tan(e/2 + (f*x)/2)*(A*d + 2*B*c - 2*B*d))/(2*A*d^2 - 4*B*d^2 + 4*B*c*d))*(A*d + 2*B*c - 2*B*d))/(a^2*f) - (tan(e/2 + (f*x)/2)^3*(2*A*c^2 - 6*A*d^2 + 2*B*c^2 + 12*B*d^2 + 4*A*c*d - 12*B*c*d) + tan(e/2 + (f*x)/2)^2*((10*A*c^2)/3 - (14*A*d^2)/3 + (2*B*c^2)/3 + (44*B*d^2)/3 + (4*A*c*d)/3 - (28*B*c*d)/3) + (4*A*c^2)/3 - (8*A*d^2)/3 + (2*B*c^2)/3 + (20*B*d^2)/3 + tan(e/2 + (f*x)/2)^4*(2*A*c^2 - 2*A*d^2 + 4*B*d^2 - 4*B*c*d) + tan(e/2 + (f*x)/2)*(2*A*c^2 - 6*A*d^2 + 2*B*c^2 + 16*B*d^2 + 4*A*c*d - 12*B*c*d) + (4*A*c*d)/3 - (16*B*c*d)/3)/(f*(4*a^2*tan(e/2 + (f*x)/2)^2 + 4*a^2*tan(e/2 + (f*x)/2)^3 + 3*a^2*tan(e/2 + (f*x)/2)^4 + a^2*tan(e/2 + (f*x)/2)^5 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
274,1,94,85,13.738388,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^2,x)","\frac{B\,d\,x}{a^2}-\frac{\left(2\,A\,c-2\,B\,d\right)\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+\left(2\,A\,c+2\,A\,d+2\,B\,c-6\,B\,d\right)\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+\frac{4\,A\,c}{3}+\frac{2\,A\,d}{3}+\frac{2\,B\,c}{3}-\frac{8\,B\,d}{3}}{a^2\,f\,{\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+1\right)}^3}","Not used",1,"(B*d*x)/a^2 - ((4*A*c)/3 + (2*A*d)/3 + (2*B*c)/3 - (8*B*d)/3 + tan(e/2 + (f*x)/2)*(2*A*c + 2*A*d + 2*B*c - 6*B*d) + tan(e/2 + (f*x)/2)^2*(2*A*c - 2*B*d))/(a^2*f*(tan(e/2 + (f*x)/2) + 1)^3)","B"
275,1,97,65,13.387677,"\text{Not used}","int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^2,x)","-\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{5\,A}{2}+\frac{B}{2}-\frac{A\,\cos\left(e+f\,x\right)}{2}+\frac{B\,\cos\left(e+f\,x\right)}{2}+\frac{3\,A\,\sin\left(e+f\,x\right)}{2}+\frac{3\,B\,\sin\left(e+f\,x\right)}{2}\right)}{3\,a^2\,f\,\left(\frac{3\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}-\frac{\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{2}\right)}","Not used",1,"-(2*cos(e/2 + (f*x)/2)*((5*A)/2 + B/2 - (A*cos(e + f*x))/2 + (B*cos(e + f*x))/2 + (3*A*sin(e + f*x))/2 + (3*B*sin(e + f*x))/2))/(3*a^2*f*((3*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 - (2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/2))","B"
276,1,302,152,14.783093,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))),x)","\frac{2\,d\,\mathrm{atan}\left(\frac{\frac{d\,\left(A\,d-B\,c\right)\,\left(2\,a^2\,c^2\,d-4\,a^2\,c\,d^2+2\,a^2\,d^3\right)}{a^2\,\sqrt{c+d}\,{\left(c-d\right)}^{5/2}}+\frac{2\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d-B\,c\right)\,\left(a^2\,c^2-2\,a^2\,c\,d+a^2\,d^2\right)}{a^2\,\sqrt{c+d}\,{\left(c-d\right)}^{5/2}}}{2\,A\,d^2-2\,B\,c\,d}\right)\,\left(A\,d-B\,c\right)}{a^2\,f\,\sqrt{c+d}\,{\left(c-d\right)}^{5/2}}-\frac{\frac{2\,\left(2\,A\,c-5\,A\,d+B\,c+2\,B\,d\right)}{3\,{\left(c-d\right)}^2}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,c-3\,A\,d+B\,c+B\,d\right)}{{\left(c-d\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(A\,c-2\,A\,d+B\,d\right)}{{\left(c-d\right)}^2}}{f\,\left(a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+3\,a^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+3\,a^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^2\right)}","Not used",1,"(2*d*atan(((d*(A*d - B*c)*(2*a^2*d^3 - 4*a^2*c*d^2 + 2*a^2*c^2*d))/(a^2*(c + d)^(1/2)*(c - d)^(5/2)) + (2*c*d*tan(e/2 + (f*x)/2)*(A*d - B*c)*(a^2*c^2 + a^2*d^2 - 2*a^2*c*d))/(a^2*(c + d)^(1/2)*(c - d)^(5/2)))/(2*A*d^2 - 2*B*c*d))*(A*d - B*c))/(a^2*f*(c + d)^(1/2)*(c - d)^(5/2)) - ((2*(2*A*c - 5*A*d + B*c + 2*B*d))/(3*(c - d)^2) + (2*tan(e/2 + (f*x)/2)*(A*c - 3*A*d + B*c + B*d))/(c - d)^2 + (2*tan(e/2 + (f*x)/2)^2*(A*c - 2*A*d + B*d))/(c - d)^2)/(f*(3*a^2*tan(e/2 + (f*x)/2)^2 + a^2*tan(e/2 + (f*x)/2)^3 + a^2 + 3*a^2*tan(e/2 + (f*x)/2)))","B"
277,1,844,275,16.762963,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^2),x)","\frac{2\,d\,\mathrm{atan}\left(\frac{\frac{d\,\left(-2\,a^2\,c^4\,d+4\,a^2\,c^3\,d^2-4\,a^2\,c\,d^4+2\,a^2\,d^5\right)\,\left(2\,B\,c^2-2\,A\,d^2+B\,d^2-3\,A\,c\,d+2\,B\,c\,d\right)}{a^2\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{7/2}}-\frac{2\,c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(a^2\,c^4-2\,a^2\,c^3\,d+2\,a^2\,c\,d^3-a^2\,d^4\right)\,\left(2\,B\,c^2-2\,A\,d^2+B\,d^2-3\,A\,c\,d+2\,B\,c\,d\right)}{a^2\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{7/2}}}{2\,B\,d^3-4\,A\,d^3-6\,A\,c\,d^2+4\,B\,c\,d^2+4\,B\,c^2\,d}\right)\,\left(2\,B\,c^2-2\,A\,d^2+B\,d^2-3\,A\,c\,d+2\,B\,c\,d\right)}{a^2\,f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{7/2}}-\frac{\frac{2\,\left(2\,A\,c^3-3\,A\,d^3+B\,c^3-8\,A\,c\,d^2-6\,A\,c^2\,d+8\,B\,c\,d^2+6\,B\,c^2\,d\right)}{3\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(5\,A\,c^3-9\,A\,d^3+B\,c^3-30\,A\,c\,d^2-11\,A\,c^2\,d+27\,B\,c\,d^2+17\,B\,c^2\,d\right)}{3\,c\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(A\,c^4-3\,A\,d^4+B\,c^4-9\,A\,c^2\,d^2+8\,B\,c^2\,d^2-7\,A\,c\,d^3-2\,A\,c^3\,d+7\,B\,c\,d^3+4\,B\,c^3\,d\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,A\,c^4-3\,A\,d^4+3\,B\,c^4-27\,A\,c^2\,d^2+30\,B\,c^2\,d^2-25\,A\,c\,d^3-8\,A\,c^3\,d+13\,B\,c\,d^3+14\,B\,c^3\,d\right)}{3\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(A\,c^4-A\,d^4-3\,A\,c^2\,d^2+2\,B\,c^2\,d^2-2\,A\,c^3\,d+B\,c\,d^3+2\,B\,c^3\,d\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}}{f\,\left(a^2\,c+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^2\,c+2\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(3\,a^2\,c+2\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(4\,a^2\,c+6\,a^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,a^2\,c+6\,a^2\,d\right)+a^2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\right)}","Not used",1,"(2*d*atan(((d*(2*a^2*d^5 - 4*a^2*c*d^4 - 2*a^2*c^4*d + 4*a^2*c^3*d^2)*(2*B*c^2 - 2*A*d^2 + B*d^2 - 3*A*c*d + 2*B*c*d))/(a^2*(c + d)^(3/2)*(c - d)^(7/2)) - (2*c*d*tan(e/2 + (f*x)/2)*(a^2*c^4 - a^2*d^4 + 2*a^2*c*d^3 - 2*a^2*c^3*d)*(2*B*c^2 - 2*A*d^2 + B*d^2 - 3*A*c*d + 2*B*c*d))/(a^2*(c + d)^(3/2)*(c - d)^(7/2)))/(2*B*d^3 - 4*A*d^3 - 6*A*c*d^2 + 4*B*c*d^2 + 4*B*c^2*d))*(2*B*c^2 - 2*A*d^2 + B*d^2 - 3*A*c*d + 2*B*c*d))/(a^2*f*(c + d)^(3/2)*(c - d)^(7/2)) - ((2*(2*A*c^3 - 3*A*d^3 + B*c^3 - 8*A*c*d^2 - 6*A*c^2*d + 8*B*c*d^2 + 6*B*c^2*d))/(3*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^2*(5*A*c^3 - 9*A*d^3 + B*c^3 - 30*A*c*d^2 - 11*A*c^2*d + 27*B*c*d^2 + 17*B*c^2*d))/(3*c*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^3*(A*c^4 - 3*A*d^4 + B*c^4 - 9*A*c^2*d^2 + 8*B*c^2*d^2 - 7*A*c*d^3 - 2*A*c^3*d + 7*B*c*d^3 + 4*B*c^3*d))/(c*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)*(3*A*c^4 - 3*A*d^4 + 3*B*c^4 - 27*A*c^2*d^2 + 30*B*c^2*d^2 - 25*A*c*d^3 - 8*A*c^3*d + 13*B*c*d^3 + 14*B*c^3*d))/(3*c*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^4*(A*c^4 - A*d^4 - 3*A*c^2*d^2 + 2*B*c^2*d^2 - 2*A*c^3*d + B*c*d^3 + 2*B*c^3*d))/(c*(c + d)*(c - d)*(c^2 - 2*c*d + d^2)))/(f*(a^2*c + tan(e/2 + (f*x)/2)*(3*a^2*c + 2*a^2*d) + tan(e/2 + (f*x)/2)^4*(3*a^2*c + 2*a^2*d) + tan(e/2 + (f*x)/2)^2*(4*a^2*c + 6*a^2*d) + tan(e/2 + (f*x)/2)^3*(4*a^2*c + 6*a^2*d) + a^2*c*tan(e/2 + (f*x)/2)^5))","B"
278,1,1686,386,17.692522,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^3),x)","\frac{d\,\mathrm{atan}\left(\frac{\frac{d\,\left(-2\,a^2\,c^6\,d+4\,a^2\,c^5\,d^2+2\,a^2\,c^4\,d^3-8\,a^2\,c^3\,d^4+2\,a^2\,c^2\,d^5+4\,a^2\,c\,d^6-2\,a^2\,d^7\right)\,\left(6\,B\,c^3-7\,A\,d^3+4\,B\,d^3-16\,A\,c\,d^2-12\,A\,c^2\,d+13\,B\,c\,d^2+12\,B\,c^2\,d\right)}{2\,a^2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{9/2}}+\frac{c\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-a^2\,c^6+2\,a^2\,c^5\,d+a^2\,c^4\,d^2-4\,a^2\,c^3\,d^3+a^2\,c^2\,d^4+2\,a^2\,c\,d^5-a^2\,d^6\right)\,\left(6\,B\,c^3-7\,A\,d^3+4\,B\,d^3-16\,A\,c\,d^2-12\,A\,c^2\,d+13\,B\,c\,d^2+12\,B\,c^2\,d\right)}{a^2\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{9/2}}}{4\,B\,d^4-7\,A\,d^4-12\,A\,c^2\,d^2+12\,B\,c^2\,d^2-16\,A\,c\,d^3+13\,B\,c\,d^3+6\,B\,c^3\,d}\right)\,\left(6\,B\,c^3-7\,A\,d^3+4\,B\,d^3-16\,A\,c\,d^2-12\,A\,c^2\,d+13\,B\,c\,d^2+12\,B\,c^2\,d\right)}{a^2\,f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{9/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,A\,c^6+2\,A\,d^6+2\,B\,c^6-23\,A\,c^2\,d^4-40\,A\,c^3\,d^3-38\,A\,c^4\,d^2+6\,B\,c^2\,d^4+43\,B\,c^3\,d^3+40\,B\,c^4\,d^2-4\,A\,c\,d^5-4\,A\,c^5\,d+2\,B\,c\,d^5+12\,B\,c^5\,d\right)}{c^2\,\left(c^5-3\,c^4\,d+2\,c^3\,d^2+2\,c^2\,d^3-3\,c\,d^4+d^5\right)}+\frac{4\,A\,c^5+3\,A\,d^5+2\,B\,c^5-46\,A\,c^2\,d^3-40\,A\,c^3\,d^2+28\,B\,c^2\,d^3+52\,B\,c^3\,d^2-12\,A\,c\,d^4-14\,A\,c^4\,d+3\,B\,c\,d^4+20\,B\,c^4\,d}{3\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(6\,A\,c^6+9\,A\,d^6+6\,B\,c^6-177\,A\,c^2\,d^4-212\,A\,c^3\,d^3-102\,A\,c^4\,d^2+105\,B\,c^2\,d^4+215\,B\,c^3\,d^3+150\,B\,c^4\,d^2-33\,A\,c\,d^5-16\,A\,c^5\,d+9\,B\,c\,d^5+40\,B\,c^5\,d\right)}{3\,c^2\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(6\,A\,c^5+6\,A\,d^5+6\,B\,c^5-160\,A\,c^2\,d^3-114\,A\,c^3\,d^2+97\,B\,c^2\,d^3+156\,B\,c^3\,d^2-33\,A\,c\,d^4-20\,A\,c^4\,d+12\,B\,c\,d^4+44\,B\,c^4\,d\right)}{3\,c\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(14\,A\,c^7+6\,A\,d^7+4\,B\,c^7-232\,A\,c^2\,d^5-583\,A\,c^3\,d^4-532\,A\,c^4\,d^3-226\,A\,c^5\,d^2+124\,B\,c^2\,d^5+412\,B\,c^3\,d^4+595\,B\,c^4\,d^3+352\,B\,c^5\,d^2-6\,A\,c\,d^6-16\,A\,c^6\,d+6\,B\,c\,d^6+82\,B\,c^6\,d\right)}{3\,c^2\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(16\,A\,c^7+18\,A\,d^7+2\,B\,c^7-303\,A\,c^2\,d^5-522\,A\,c^3\,d^4-502\,A\,c^4\,d^3-220\,A\,c^5\,d^2+156\,B\,c^2\,d^5+453\,B\,c^3\,d^4+538\,B\,c^4\,d^3+328\,B\,c^5\,d^2-48\,A\,c\,d^6-14\,A\,c^6\,d+18\,B\,c\,d^6+80\,B\,c^6\,d\right)}{3\,c^2\,\left(c+d\right)\,\left(c^2-d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,A\,c^6+2\,A\,d^6-9\,A\,c^2\,d^4-8\,A\,c^3\,d^3-14\,A\,c^4\,d^2+4\,B\,c^2\,d^4+13\,B\,c^3\,d^3+12\,B\,c^4\,d^2-4\,A\,c\,d^5-4\,A\,c^5\,d+6\,B\,c^5\,d\right)}{c\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}}{f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,a^2\,c^2+4\,d\,a^2\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(5\,a^2\,c^2+12\,a^2\,c\,d+4\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(5\,a^2\,c^2+12\,a^2\,c\,d+4\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(7\,a^2\,c^2+16\,a^2\,c\,d+12\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(7\,a^2\,c^2+16\,a^2\,c\,d+12\,a^2\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(3\,a^2\,c^2+4\,d\,a^2\,c\right)+a^2\,c^2+a^2\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}","Not used",1,"(d*atan(((d*(4*a^2*c*d^6 - 2*a^2*d^7 - 2*a^2*c^6*d + 2*a^2*c^2*d^5 - 8*a^2*c^3*d^4 + 2*a^2*c^4*d^3 + 4*a^2*c^5*d^2)*(6*B*c^3 - 7*A*d^3 + 4*B*d^3 - 16*A*c*d^2 - 12*A*c^2*d + 13*B*c*d^2 + 12*B*c^2*d))/(2*a^2*(c + d)^(5/2)*(c - d)^(9/2)) + (c*d*tan(e/2 + (f*x)/2)*(2*a^2*c*d^5 - a^2*d^6 - a^2*c^6 + 2*a^2*c^5*d + a^2*c^2*d^4 - 4*a^2*c^3*d^3 + a^2*c^4*d^2)*(6*B*c^3 - 7*A*d^3 + 4*B*d^3 - 16*A*c*d^2 - 12*A*c^2*d + 13*B*c*d^2 + 12*B*c^2*d))/(a^2*(c + d)^(5/2)*(c - d)^(9/2)))/(4*B*d^4 - 7*A*d^4 - 12*A*c^2*d^2 + 12*B*c^2*d^2 - 16*A*c*d^3 + 13*B*c*d^3 + 6*B*c^3*d))*(6*B*c^3 - 7*A*d^3 + 4*B*d^3 - 16*A*c*d^2 - 12*A*c^2*d + 13*B*c*d^2 + 12*B*c^2*d))/(a^2*f*(c + d)^(5/2)*(c - d)^(9/2)) - ((tan(e/2 + (f*x)/2)^5*(2*A*c^6 + 2*A*d^6 + 2*B*c^6 - 23*A*c^2*d^4 - 40*A*c^3*d^3 - 38*A*c^4*d^2 + 6*B*c^2*d^4 + 43*B*c^3*d^3 + 40*B*c^4*d^2 - 4*A*c*d^5 - 4*A*c^5*d + 2*B*c*d^5 + 12*B*c^5*d))/(c^2*(c^5 - 3*c^4*d - 3*c*d^4 + d^5 + 2*c^2*d^3 + 2*c^3*d^2)) + (4*A*c^5 + 3*A*d^5 + 2*B*c^5 - 46*A*c^2*d^3 - 40*A*c^3*d^2 + 28*B*c^2*d^3 + 52*B*c^3*d^2 - 12*A*c*d^4 - 14*A*c^4*d + 3*B*c*d^4 + 20*B*c^4*d)/(3*(c + d)*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^3*(6*A*c^6 + 9*A*d^6 + 6*B*c^6 - 177*A*c^2*d^4 - 212*A*c^3*d^3 - 102*A*c^4*d^2 + 105*B*c^2*d^4 + 215*B*c^3*d^3 + 150*B*c^4*d^2 - 33*A*c*d^5 - 16*A*c^5*d + 9*B*c*d^5 + 40*B*c^5*d))/(3*c^2*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)*(6*A*c^5 + 6*A*d^5 + 6*B*c^5 - 160*A*c^2*d^3 - 114*A*c^3*d^2 + 97*B*c^2*d^3 + 156*B*c^3*d^2 - 33*A*c*d^4 - 20*A*c^4*d + 12*B*c*d^4 + 44*B*c^4*d))/(3*c*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^2*(14*A*c^7 + 6*A*d^7 + 4*B*c^7 - 232*A*c^2*d^5 - 583*A*c^3*d^4 - 532*A*c^4*d^3 - 226*A*c^5*d^2 + 124*B*c^2*d^5 + 412*B*c^3*d^4 + 595*B*c^4*d^3 + 352*B*c^5*d^2 - 6*A*c*d^6 - 16*A*c^6*d + 6*B*c*d^6 + 82*B*c^6*d))/(3*c^2*(c + d)*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^4*(16*A*c^7 + 18*A*d^7 + 2*B*c^7 - 303*A*c^2*d^5 - 522*A*c^3*d^4 - 502*A*c^4*d^3 - 220*A*c^5*d^2 + 156*B*c^2*d^5 + 453*B*c^3*d^4 + 538*B*c^4*d^3 + 328*B*c^5*d^2 - 48*A*c*d^6 - 14*A*c^6*d + 18*B*c*d^6 + 80*B*c^6*d))/(3*c^2*(c + d)*(c^2 - d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (tan(e/2 + (f*x)/2)^6*(2*A*c^6 + 2*A*d^6 - 9*A*c^2*d^4 - 8*A*c^3*d^3 - 14*A*c^4*d^2 + 4*B*c^2*d^4 + 13*B*c^3*d^3 + 12*B*c^4*d^2 - 4*A*c*d^5 - 4*A*c^5*d + 6*B*c^5*d))/(c*(c - d)*(2*c*d + c^2 + d^2)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)))/(f*(tan(e/2 + (f*x)/2)*(3*a^2*c^2 + 4*a^2*c*d) + tan(e/2 + (f*x)/2)^2*(5*a^2*c^2 + 4*a^2*d^2 + 12*a^2*c*d) + tan(e/2 + (f*x)/2)^5*(5*a^2*c^2 + 4*a^2*d^2 + 12*a^2*c*d) + tan(e/2 + (f*x)/2)^3*(7*a^2*c^2 + 12*a^2*d^2 + 16*a^2*c*d) + tan(e/2 + (f*x)/2)^4*(7*a^2*c^2 + 12*a^2*d^2 + 16*a^2*c*d) + tan(e/2 + (f*x)/2)^6*(3*a^2*c^2 + 4*a^2*c*d) + a^2*c^2 + a^2*c^2*tan(e/2 + (f*x)/2)^7))","B"
279,1,593,225,15.695480,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^3,x)","\frac{2\,d^2\,\mathrm{atan}\left(\frac{2\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d+3\,B\,c-3\,B\,d\right)}{2\,A\,d^3-6\,B\,d^3+6\,B\,c\,d^2}\right)\,\left(A\,d+3\,B\,c-3\,B\,d\right)}{a^3\,f}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(4\,A\,c^3-10\,A\,d^3+2\,B\,c^3+30\,B\,d^3+6\,A\,c^2\,d-30\,B\,c\,d^2\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8\,A\,c^3}{3}-\frac{38\,A\,d^3}{3}+2\,B\,c^3+42\,B\,d^3+4\,A\,c\,d^2+6\,A\,c^2\,d-38\,B\,c\,d^2+4\,B\,c^2\,d\right)+\frac{14\,A\,c^3}{15}-\frac{44\,A\,d^3}{15}+\frac{2\,B\,c^3}{5}+\frac{48\,B\,d^3}{5}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(\frac{22\,A\,c^3}{3}-\frac{64\,A\,d^3}{3}+2\,B\,c^3+64\,B\,d^3+8\,A\,c\,d^2+6\,A\,c^2\,d-64\,B\,c\,d^2+8\,B\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(\frac{20\,A\,c^3}{3}-\frac{68\,A\,d^3}{3}+4\,B\,c^3+80\,B\,d^3+4\,A\,c\,d^2+12\,A\,c^2\,d-68\,B\,c\,d^2+4\,B\,c^2\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{94\,A\,c^3}{15}-\frac{334\,A\,d^3}{15}+\frac{12\,B\,c^3}{5}+\frac{378\,B\,d^3}{5}+\frac{44\,A\,c\,d^2}{5}+\frac{36\,A\,c^2\,d}{5}-\frac{334\,B\,c\,d^2}{5}+\frac{44\,B\,c^2\,d}{5}\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(2\,A\,c^3-2\,A\,d^3+6\,B\,d^3-6\,B\,c\,d^2\right)+\frac{4\,A\,c\,d^2}{5}+\frac{6\,A\,c^2\,d}{5}-\frac{44\,B\,c\,d^2}{5}+\frac{4\,B\,c^2\,d}{5}}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6+11\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+15\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+15\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+11\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(2*d^2*atan((2*d^2*tan(e/2 + (f*x)/2)*(A*d + 3*B*c - 3*B*d))/(2*A*d^3 - 6*B*d^3 + 6*B*c*d^2))*(A*d + 3*B*c - 3*B*d))/(a^3*f) - (tan(e/2 + (f*x)/2)^5*(4*A*c^3 - 10*A*d^3 + 2*B*c^3 + 30*B*d^3 + 6*A*c^2*d - 30*B*c*d^2) + tan(e/2 + (f*x)/2)*((8*A*c^3)/3 - (38*A*d^3)/3 + 2*B*c^3 + 42*B*d^3 + 4*A*c*d^2 + 6*A*c^2*d - 38*B*c*d^2 + 4*B*c^2*d) + (14*A*c^3)/15 - (44*A*d^3)/15 + (2*B*c^3)/5 + (48*B*d^3)/5 + tan(e/2 + (f*x)/2)^4*((22*A*c^3)/3 - (64*A*d^3)/3 + 2*B*c^3 + 64*B*d^3 + 8*A*c*d^2 + 6*A*c^2*d - 64*B*c*d^2 + 8*B*c^2*d) + tan(e/2 + (f*x)/2)^3*((20*A*c^3)/3 - (68*A*d^3)/3 + 4*B*c^3 + 80*B*d^3 + 4*A*c*d^2 + 12*A*c^2*d - 68*B*c*d^2 + 4*B*c^2*d) + tan(e/2 + (f*x)/2)^2*((94*A*c^3)/15 - (334*A*d^3)/15 + (12*B*c^3)/5 + (378*B*d^3)/5 + (44*A*c*d^2)/5 + (36*A*c^2*d)/5 - (334*B*c*d^2)/5 + (44*B*c^2*d)/5) + tan(e/2 + (f*x)/2)^6*(2*A*c^3 - 2*A*d^3 + 6*B*d^3 - 6*B*c*d^2) + (4*A*c*d^2)/5 + (6*A*c^2*d)/5 - (44*B*c*d^2)/5 + (4*B*c^2*d)/5)/(f*(11*a^3*tan(e/2 + (f*x)/2)^2 + 15*a^3*tan(e/2 + (f*x)/2)^3 + 15*a^3*tan(e/2 + (f*x)/2)^4 + 11*a^3*tan(e/2 + (f*x)/2)^5 + 5*a^3*tan(e/2 + (f*x)/2)^6 + a^3*tan(e/2 + (f*x)/2)^7 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
280,1,286,164,16.544294,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^3,x)","\frac{B\,d^2\,x}{a^3}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(\frac{16\,A\,c^2}{3}+\frac{8\,A\,d^2}{3}+2\,B\,c^2-\frac{58\,B\,d^2}{3}+4\,A\,c\,d+\frac{16\,B\,c\,d}{3}\right)+\frac{14\,A\,c^2}{15}+\frac{4\,A\,d^2}{15}+\frac{2\,B\,c^2}{5}-\frac{44\,B\,d^2}{15}+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(4\,A\,c^2+2\,B\,c^2-10\,B\,d^2+4\,A\,c\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(2\,A\,c^2-2\,B\,d^2\right)+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{8\,A\,c^2}{3}+\frac{4\,A\,d^2}{3}+2\,B\,c^2-\frac{38\,B\,d^2}{3}+4\,A\,c\,d+\frac{8\,B\,c\,d}{3}\right)+\frac{4\,A\,c\,d}{5}+\frac{8\,B\,c\,d}{15}}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(B*d^2*x)/a^3 - (tan(e/2 + (f*x)/2)^2*((16*A*c^2)/3 + (8*A*d^2)/3 + 2*B*c^2 - (58*B*d^2)/3 + 4*A*c*d + (16*B*c*d)/3) + (14*A*c^2)/15 + (4*A*d^2)/15 + (2*B*c^2)/5 - (44*B*d^2)/15 + tan(e/2 + (f*x)/2)^3*(4*A*c^2 + 2*B*c^2 - 10*B*d^2 + 4*A*c*d) + tan(e/2 + (f*x)/2)^4*(2*A*c^2 - 2*B*d^2) + tan(e/2 + (f*x)/2)*((8*A*c^2)/3 + (4*A*d^2)/3 + 2*B*c^2 - (38*B*d^2)/3 + 4*A*c*d + (8*B*c*d)/3) + (4*A*c*d)/5 + (8*B*c*d)/15)/(f*(10*a^3*tan(e/2 + (f*x)/2)^2 + 10*a^3*tan(e/2 + (f*x)/2)^3 + 5*a^3*tan(e/2 + (f*x)/2)^4 + a^3*tan(e/2 + (f*x)/2)^5 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
281,1,245,127,14.259110,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^3,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{53\,A\,c}{4}+3\,A\,d+3\,B\,c+\frac{13\,B\,d}{4}-4\,A\,c\,\cos\left(e+f\,x\right)+\frac{3\,A\,d\,\cos\left(e+f\,x\right)}{2}+\frac{3\,B\,c\,\cos\left(e+f\,x\right)}{2}+B\,d\,\cos\left(e+f\,x\right)+\frac{25\,A\,c\,\sin\left(e+f\,x\right)}{2}+\frac{15\,A\,d\,\sin\left(e+f\,x\right)}{2}+\frac{15\,B\,c\,\sin\left(e+f\,x\right)}{2}+\frac{5\,B\,d\,\sin\left(e+f\,x\right)}{2}-\frac{9\,A\,c\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{3\,A\,d\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{3\,B\,c\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{9\,B\,d\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{5\,A\,c\,\sin\left(2\,e+2\,f\,x\right)}{4}+\frac{5\,B\,d\,\sin\left(2\,e+2\,f\,x\right)}{4}\right)}{15\,a^3\,f\,\left(\frac{5\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{5\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}+\frac{\sqrt{2}\,\cos\left(\frac{5\,e}{2}-\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((53*A*c)/4 + 3*A*d + 3*B*c + (13*B*d)/4 - 4*A*c*cos(e + f*x) + (3*A*d*cos(e + f*x))/2 + (3*B*c*cos(e + f*x))/2 + B*d*cos(e + f*x) + (25*A*c*sin(e + f*x))/2 + (15*A*d*sin(e + f*x))/2 + (15*B*c*sin(e + f*x))/2 + (5*B*d*sin(e + f*x))/2 - (9*A*c*cos(2*e + 2*f*x))/4 - (3*A*d*cos(2*e + 2*f*x))/2 - (3*B*c*cos(2*e + 2*f*x))/2 - (9*B*d*cos(2*e + 2*f*x))/4 - (5*A*c*sin(2*e + 2*f*x))/4 + (5*B*d*sin(2*e + 2*f*x))/4))/(15*a^3*f*((5*2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/4 - (5*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 + (2^(1/2)*cos((5*e)/2 - pi/4 + (5*f*x)/2))/4))","B"
282,1,150,102,13.803517,"\text{Not used}","int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^3,x)","\frac{2\,\cos\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(\frac{53\,A}{4}+3\,B-4\,A\,\cos\left(e+f\,x\right)+\frac{3\,B\,\cos\left(e+f\,x\right)}{2}+\frac{25\,A\,\sin\left(e+f\,x\right)}{2}+\frac{15\,B\,\sin\left(e+f\,x\right)}{2}-\frac{9\,A\,\cos\left(2\,e+2\,f\,x\right)}{4}-\frac{3\,B\,\cos\left(2\,e+2\,f\,x\right)}{2}-\frac{5\,A\,\sin\left(2\,e+2\,f\,x\right)}{4}\right)}{15\,a^3\,f\,\left(\frac{5\,\sqrt{2}\,\cos\left(\frac{3\,e}{2}+\frac{\pi }{4}+\frac{3\,f\,x}{2}\right)}{4}-\frac{5\,\sqrt{2}\,\cos\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\right)}{2}+\frac{\sqrt{2}\,\cos\left(\frac{5\,e}{2}-\frac{\pi }{4}+\frac{5\,f\,x}{2}\right)}{4}\right)}","Not used",1,"(2*cos(e/2 + (f*x)/2)*((53*A)/4 + 3*B - 4*A*cos(e + f*x) + (3*B*cos(e + f*x))/2 + (25*A*sin(e + f*x))/2 + (15*B*sin(e + f*x))/2 - (9*A*cos(2*e + 2*f*x))/4 - (3*B*cos(2*e + 2*f*x))/2 - (5*A*sin(2*e + 2*f*x))/4))/(15*a^3*f*((5*2^(1/2)*cos((3*e)/2 + pi/4 + (3*f*x)/2))/4 - (5*2^(1/2)*cos(e/2 - pi/4 + (f*x)/2))/2 + (2^(1/2)*cos((5*e)/2 - pi/4 + (5*f*x)/2))/4))","B"
283,1,591,229,17.184176,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))),x)","\frac{2\,d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(A\,d-B\,c\right)\,\left(-2\,a^3\,c^3\,d+6\,a^3\,c^2\,d^2-6\,a^3\,c\,d^3+2\,a^3\,d^4\right)}{a^3\,\sqrt{c+d}\,{\left(c-d\right)}^{7/2}}-\frac{2\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A\,d-B\,c\right)\,\left(a^3\,c^3-3\,a^3\,c^2\,d+3\,a^3\,c\,d^2-a^3\,d^3\right)}{a^3\,\sqrt{c+d}\,{\left(c-d\right)}^{7/2}}}{2\,A\,d^3-2\,B\,c\,d^2}\right)\,\left(A\,d-B\,c\right)}{a^3\,f\,\sqrt{c+d}\,{\left(c-d\right)}^{7/2}}-\frac{\frac{2\,\left(7\,A\,c^2+32\,A\,d^2+3\,B\,c^2-7\,B\,d^2-24\,A\,c\,d-11\,B\,c\,d\right)}{15\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(4\,A\,c^2+23\,A\,d^2+3\,B\,c^2-4\,B\,d^2-15\,A\,c\,d-11\,B\,c\,d\right)}{3\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(2\,A\,c^2+9\,A\,d^2+B\,c^2-2\,B\,d^2-7\,A\,c\,d-3\,B\,c\,d\right)}{\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(8\,A\,c^2+37\,A\,d^2+3\,B\,c^2-8\,B\,d^2-27\,A\,c\,d-13\,B\,c\,d\right)}{3\,\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(A\,c^2+3\,A\,d^2-B\,d^2-3\,A\,c\,d\right)}{\left(c-d\right)\,\left(c^2-2\,c\,d+d^2\right)}}{f\,\left(a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5+5\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+10\,a^3\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+5\,a^3\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+a^3\right)}","Not used",1,"(2*d^2*atan(((d^2*(A*d - B*c)*(2*a^3*d^4 - 6*a^3*c*d^3 - 2*a^3*c^3*d + 6*a^3*c^2*d^2))/(a^3*(c + d)^(1/2)*(c - d)^(7/2)) - (2*c*d^2*tan(e/2 + (f*x)/2)*(A*d - B*c)*(a^3*c^3 - a^3*d^3 + 3*a^3*c*d^2 - 3*a^3*c^2*d))/(a^3*(c + d)^(1/2)*(c - d)^(7/2)))/(2*A*d^3 - 2*B*c*d^2))*(A*d - B*c))/(a^3*f*(c + d)^(1/2)*(c - d)^(7/2)) - ((2*(7*A*c^2 + 32*A*d^2 + 3*B*c^2 - 7*B*d^2 - 24*A*c*d - 11*B*c*d))/(15*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)*(4*A*c^2 + 23*A*d^2 + 3*B*c^2 - 4*B*d^2 - 15*A*c*d - 11*B*c*d))/(3*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^3*(2*A*c^2 + 9*A*d^2 + B*c^2 - 2*B*d^2 - 7*A*c*d - 3*B*c*d))/((c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^2*(8*A*c^2 + 37*A*d^2 + 3*B*c^2 - 8*B*d^2 - 27*A*c*d - 13*B*c*d))/(3*(c - d)*(c^2 - 2*c*d + d^2)) + (2*tan(e/2 + (f*x)/2)^4*(A*c^2 + 3*A*d^2 - B*d^2 - 3*A*c*d))/((c - d)*(c^2 - 2*c*d + d^2)))/(f*(10*a^3*tan(e/2 + (f*x)/2)^2 + 10*a^3*tan(e/2 + (f*x)/2)^3 + 5*a^3*tan(e/2 + (f*x)/2)^4 + a^3*tan(e/2 + (f*x)/2)^5 + a^3 + 5*a^3*tan(e/2 + (f*x)/2)))","B"
284,1,1349,381,17.668552,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^2),x)","\frac{2\,d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(3\,B\,c^2-3\,A\,d^2+B\,d^2-4\,A\,c\,d+3\,B\,c\,d\right)\,\left(2\,a^3\,c^5\,d-6\,a^3\,c^4\,d^2+4\,a^3\,c^3\,d^3+4\,a^3\,c^2\,d^4-6\,a^3\,c\,d^5+2\,a^3\,d^6\right)}{a^3\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{9/2}}+\frac{2\,c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(3\,B\,c^2-3\,A\,d^2+B\,d^2-4\,A\,c\,d+3\,B\,c\,d\right)\,\left(a^3\,c^5-3\,a^3\,c^4\,d+2\,a^3\,c^3\,d^2+2\,a^3\,c^2\,d^3-3\,a^3\,c\,d^4+a^3\,d^5\right)}{a^3\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{9/2}}}{2\,B\,d^4-6\,A\,d^4+6\,B\,c^2\,d^2-8\,A\,c\,d^3+6\,B\,c\,d^3}\right)\,\left(3\,B\,c^2-3\,A\,d^2+B\,d^2-4\,A\,c\,d+3\,B\,c\,d\right)}{a^3\,f\,{\left(c+d\right)}^{3/2}\,{\left(c-d\right)}^{9/2}}-\frac{\frac{2\,\left(7\,A\,c^4+15\,A\,d^4+3\,B\,c^4+38\,A\,c^2\,d^2-48\,B\,c^2\,d^2+72\,A\,c\,d^3-27\,A\,c^3\,d-47\,B\,c\,d^3-13\,B\,c^3\,d\right)}{15\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(5\,A\,c^4+15\,A\,d^4+3\,B\,c^4+19\,A\,c^2\,d^2-45\,B\,c^2\,d^2+84\,A\,c\,d^3-18\,A\,c^3\,d-52\,B\,c\,d^3-11\,B\,c^3\,d\right)}{3\,c\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(20\,A\,c^5+15\,A\,d^5+15\,B\,c^5+346\,A\,c^2\,d^3+106\,A\,c^3\,d^2-286\,B\,c^2\,d^3-221\,B\,c^3\,d^2+219\,A\,c\,d^4-76\,A\,c^4\,d-79\,B\,c\,d^4-59\,B\,c^4\,d\right)}{15\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(2\,A\,c^5+5\,A\,d^5+B\,c^5+24\,A\,c^2\,d^3+4\,A\,c^3\,d^2-16\,B\,c^2\,d^3-13\,B\,c^3\,d^2+13\,A\,c\,d^4-6\,A\,c^4\,d-11\,B\,c\,d^4-3\,B\,c^4\,d\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(11\,A\,c^5+30\,A\,d^5+3\,B\,c^5+162\,A\,c^2\,d^3+4\,A\,c^3\,d^2-139\,B\,c^2\,d^3-84\,B\,c^3\,d^2+135\,A\,c\,d^4-27\,A\,c^4\,d-84\,B\,c\,d^4-11\,B\,c^4\,d\right)}{3\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(47\,A\,c^5+75\,A\,d^5+18\,B\,c^5+812\,A\,c^2\,d^3+88\,A\,c^3\,d^2-757\,B\,c^2\,d^3-463\,B\,c^3\,d^2+690\,A\,c\,d^4-137\,A\,c^4\,d-305\,B\,c\,d^4-68\,B\,c^4\,d\right)}{15\,c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(A\,c^5+A\,d^5+6\,A\,c^2\,d^3+2\,A\,c^3\,d^2-3\,B\,c^2\,d^3-3\,B\,c^3\,d^2-3\,A\,c^4\,d-B\,c\,d^4\right)}{c\,\left(c+d\right)\,\left(c-d\right)\,\left(c^3-3\,c^2\,d+3\,c\,d^2-d^3\right)}}{f\,\left(a^3\,c+\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,a^3\,c+2\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(5\,a^3\,c+2\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(11\,a^3\,c+10\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(11\,a^3\,c+10\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(15\,a^3\,c+20\,a^3\,d\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(15\,a^3\,c+20\,a^3\,d\right)+a^3\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\right)}","Not used",1,"(2*d^2*atan(((d^2*(3*B*c^2 - 3*A*d^2 + B*d^2 - 4*A*c*d + 3*B*c*d)*(2*a^3*d^6 - 6*a^3*c*d^5 + 2*a^3*c^5*d + 4*a^3*c^2*d^4 + 4*a^3*c^3*d^3 - 6*a^3*c^4*d^2))/(a^3*(c + d)^(3/2)*(c - d)^(9/2)) + (2*c*d^2*tan(e/2 + (f*x)/2)*(3*B*c^2 - 3*A*d^2 + B*d^2 - 4*A*c*d + 3*B*c*d)*(a^3*c^5 + a^3*d^5 - 3*a^3*c*d^4 - 3*a^3*c^4*d + 2*a^3*c^2*d^3 + 2*a^3*c^3*d^2))/(a^3*(c + d)^(3/2)*(c - d)^(9/2)))/(2*B*d^4 - 6*A*d^4 + 6*B*c^2*d^2 - 8*A*c*d^3 + 6*B*c*d^3))*(3*B*c^2 - 3*A*d^2 + B*d^2 - 4*A*c*d + 3*B*c*d))/(a^3*f*(c + d)^(3/2)*(c - d)^(9/2)) - ((2*(7*A*c^4 + 15*A*d^4 + 3*B*c^4 + 38*A*c^2*d^2 - 48*B*c^2*d^2 + 72*A*c*d^3 - 27*A*c^3*d - 47*B*c*d^3 - 13*B*c^3*d))/(15*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (4*tan(e/2 + (f*x)/2)^3*(5*A*c^4 + 15*A*d^4 + 3*B*c^4 + 19*A*c^2*d^2 - 45*B*c^2*d^2 + 84*A*c*d^3 - 18*A*c^3*d - 52*B*c*d^3 - 11*B*c^3*d))/(3*c*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)*(20*A*c^5 + 15*A*d^5 + 15*B*c^5 + 346*A*c^2*d^3 + 106*A*c^3*d^2 - 286*B*c^2*d^3 - 221*B*c^3*d^2 + 219*A*c*d^4 - 76*A*c^4*d - 79*B*c*d^4 - 59*B*c^4*d))/(15*c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^5*(2*A*c^5 + 5*A*d^5 + B*c^5 + 24*A*c^2*d^3 + 4*A*c^3*d^2 - 16*B*c^2*d^3 - 13*B*c^3*d^2 + 13*A*c*d^4 - 6*A*c^4*d - 11*B*c*d^4 - 3*B*c^4*d))/(c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^4*(11*A*c^5 + 30*A*d^5 + 3*B*c^5 + 162*A*c^2*d^3 + 4*A*c^3*d^2 - 139*B*c^2*d^3 - 84*B*c^3*d^2 + 135*A*c*d^4 - 27*A*c^4*d - 84*B*c*d^4 - 11*B*c^4*d))/(3*c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^2*(47*A*c^5 + 75*A*d^5 + 18*B*c^5 + 812*A*c^2*d^3 + 88*A*c^3*d^2 - 757*B*c^2*d^3 - 463*B*c^3*d^2 + 690*A*c*d^4 - 137*A*c^4*d - 305*B*c*d^4 - 68*B*c^4*d))/(15*c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)) + (2*tan(e/2 + (f*x)/2)^6*(A*c^5 + A*d^5 + 6*A*c^2*d^3 + 2*A*c^3*d^2 - 3*B*c^2*d^3 - 3*B*c^3*d^2 - 3*A*c^4*d - B*c*d^4))/(c*(c + d)*(c - d)*(3*c*d^2 - 3*c^2*d + c^3 - d^3)))/(f*(a^3*c + tan(e/2 + (f*x)/2)*(5*a^3*c + 2*a^3*d) + tan(e/2 + (f*x)/2)^6*(5*a^3*c + 2*a^3*d) + tan(e/2 + (f*x)/2)^2*(11*a^3*c + 10*a^3*d) + tan(e/2 + (f*x)/2)^5*(11*a^3*c + 10*a^3*d) + tan(e/2 + (f*x)/2)^3*(15*a^3*c + 20*a^3*d) + tan(e/2 + (f*x)/2)^4*(15*a^3*c + 20*a^3*d) + a^3*c*tan(e/2 + (f*x)/2)^7))","B"
285,1,2387,508,19.881830,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^3*(c + d*sin(e + f*x))^3),x)","\frac{\frac{15\,A\,d^6-14\,A\,c^6-6\,B\,c^6-404\,A\,c^2\,d^4-420\,A\,c^3\,d^3-92\,A\,c^4\,d^2+234\,B\,c^2\,d^4+450\,B\,c^3\,d^3+222\,B\,c^4\,d^2-90\,A\,c\,d^5+60\,A\,c^5\,d+15\,B\,c\,d^5+30\,B\,c^5\,d}{15\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(2\,A\,d^8-4\,A\,c^8-2\,B\,c^8-49\,A\,c^2\,d^6-141\,A\,c^3\,d^5-200\,A\,c^4\,d^4-122\,A\,c^5\,d^3+2\,A\,c^6\,d^2+12\,B\,c^2\,d^6+95\,B\,c^3\,d^5+187\,B\,c^4\,d^4+146\,B\,c^5\,d^3+58\,B\,c^6\,d^2-2\,A\,c\,d^7+10\,A\,c^7\,d+2\,B\,c\,d^7+6\,B\,c^7\,d\right)}{c^2\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(30\,A\,d^8-28\,A\,c^8-6\,B\,c^8-759\,A\,c^2\,d^6-1707\,A\,c^3\,d^5-1960\,A\,c^4\,d^4-870\,A\,c^5\,d^3+62\,A\,c^6\,d^2+336\,B\,c^2\,d^6+1257\,B\,c^3\,d^5+1893\,B\,c^4\,d^4+1350\,B\,c^5\,d^3+414\,B\,c^6\,d^2-114\,A\,c\,d^7+54\,A\,c^7\,d+30\,B\,c\,d^7+18\,B\,c^7\,d\right)}{3\,c^2\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(60\,A\,d^8-32\,A\,c^8-18\,B\,c^8-1857\,A\,c^2\,d^6-3763\,A\,c^3\,d^5-3560\,A\,c^4\,d^4-1294\,A\,c^5\,d^3+70\,A\,c^6\,d^2+900\,B\,c^2\,d^6+2859\,B\,c^3\,d^5+3705\,B\,c^4\,d^4+2358\,B\,c^5\,d^3+678\,B\,c^6\,d^2-270\,A\,c\,d^7+62\,A\,c^7\,d+60\,B\,c\,d^7+42\,B\,c^7\,d\right)}{3\,c^2\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(30\,A\,d^8-108\,A\,c^8-42\,B\,c^8-2501\,A\,c^2\,d^6-8725\,A\,c^3\,d^5-10616\,A\,c^4\,d^4-4810\,A\,c^5\,d^3+10\,A\,c^6\,d^2+1056\,B\,c^2\,d^6+5235\,B\,c^3\,d^5+9891\,B\,c^4\,d^4+7770\,B\,c^5\,d^3+2370\,B\,c^6\,d^2-30\,A\,c\,d^7+290\,A\,c^7\,d+30\,B\,c\,d^7+150\,B\,c^7\,d\right)}{15\,c^2\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(150\,A\,d^8-140\,A\,c^8-90\,B\,c^8-7945\,A\,c^2\,d^6-19441\,A\,c^3\,d^5-18600\,A\,c^4\,d^4-6898\,A\,c^5\,d^3+210\,A\,c^6\,d^2+3660\,B\,c^2\,d^6+13311\,B\,c^3\,d^5+19455\,B\,c^4\,d^4+12618\,B\,c^5\,d^3+3570\,B\,c^6\,d^2-570\,A\,c\,d^7+314\,A\,c^7\,d+150\,B\,c\,d^7+246\,B\,c^7\,d\right)}{15\,c^2\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(30\,A\,d^7-40\,A\,c^7-30\,B\,c^7-1901\,A\,c^2\,d^5-3400\,A\,c^3\,d^4-2018\,A\,c^4\,d^3-190\,A\,c^5\,d^2+921\,B\,c^2\,d^5+2655\,B\,c^3\,d^4+2778\,B\,c^4\,d^3+1050\,B\,c^5\,d^2-195\,A\,c\,d^6+154\,A\,c^6\,d+60\,B\,c\,d^6+126\,B\,c^6\,d\right)}{15\,c\,{\left(c+d\right)}^2\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}-\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(2\,A\,c^7-2\,A\,d^7+11\,A\,c^2\,d^5+20\,A\,c^3\,d^4+30\,A\,c^4\,d^3+2\,A\,c^5\,d^2-6\,B\,c^2\,d^5-21\,B\,c^3\,d^4-24\,B\,c^4\,d^3-12\,B\,c^5\,d^2+6\,A\,c\,d^6-6\,A\,c^6\,d\right)}{c\,\left(c-d\right)\,\left(c^2+2\,c\,d+d^2\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}+\frac{{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(300\,A\,d^7-204\,A\,c^7-66\,B\,c^7-10235\,A\,c^2\,d^5-14330\,A\,c^3\,d^4-7254\,A\,c^4\,d^3-316\,A\,c^5\,d^2+5460\,B\,c^2\,d^5+12675\,B\,c^3\,d^4+10764\,B\,c^4\,d^3+3666\,B\,c^5\,d^2-1650\,A\,c\,d^6+614\,A\,c^6\,d+300\,B\,c\,d^6+276\,B\,c^6\,d\right)}{15\,c^2\,\left(c+d\right)\,\left(c-d\right)\,\left(c^4-4\,c^3\,d+6\,c^2\,d^2-4\,c\,d^3+d^4\right)}}{f\,\left(\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(5\,a^3\,c^2+4\,d\,a^3\,c\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(12\,a^3\,c^2+20\,a^3\,c\,d+4\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^7\,\left(12\,a^3\,c^2+20\,a^3\,c\,d+4\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(20\,a^3\,c^2+44\,a^3\,c\,d+20\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^6\,\left(20\,a^3\,c^2+44\,a^3\,c\,d+20\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4\,\left(26\,a^3\,c^2+60\,a^3\,c\,d+40\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^5\,\left(26\,a^3\,c^2+60\,a^3\,c\,d+40\,a^3\,d^2\right)+{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^8\,\left(5\,a^3\,c^2+4\,d\,a^3\,c\right)+a^3\,c^2+a^3\,c^2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^9\right)}-\frac{d^2\,\mathrm{atan}\left(\frac{\frac{d^2\,\left(12\,B\,c^3-13\,A\,d^3+6\,B\,d^3-30\,A\,c\,d^2-20\,A\,c^2\,d+21\,B\,c\,d^2+24\,B\,c^2\,d\right)\,\left(-2\,a^3\,c^7\,d+6\,a^3\,c^6\,d^2-2\,a^3\,c^5\,d^3-10\,a^3\,c^4\,d^4+10\,a^3\,c^3\,d^5+2\,a^3\,c^2\,d^6-6\,a^3\,c\,d^7+2\,a^3\,d^8\right)}{2\,a^3\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{11/2}}-\frac{c\,d^2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(12\,B\,c^3-13\,A\,d^3+6\,B\,d^3-30\,A\,c\,d^2-20\,A\,c^2\,d+21\,B\,c\,d^2+24\,B\,c^2\,d\right)\,\left(a^3\,c^7-3\,a^3\,c^6\,d+a^3\,c^5\,d^2+5\,a^3\,c^4\,d^3-5\,a^3\,c^3\,d^4-a^3\,c^2\,d^5+3\,a^3\,c\,d^6-a^3\,d^7\right)}{a^3\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{11/2}}}{6\,B\,d^5-13\,A\,d^5-20\,A\,c^2\,d^3+24\,B\,c^2\,d^3+12\,B\,c^3\,d^2-30\,A\,c\,d^4+21\,B\,c\,d^4}\right)\,\left(12\,B\,c^3-13\,A\,d^3+6\,B\,d^3-30\,A\,c\,d^2-20\,A\,c^2\,d+21\,B\,c\,d^2+24\,B\,c^2\,d\right)}{a^3\,f\,{\left(c+d\right)}^{5/2}\,{\left(c-d\right)}^{11/2}}","Not used",1,"((15*A*d^6 - 14*A*c^6 - 6*B*c^6 - 404*A*c^2*d^4 - 420*A*c^3*d^3 - 92*A*c^4*d^2 + 234*B*c^2*d^4 + 450*B*c^3*d^3 + 222*B*c^4*d^2 - 90*A*c*d^5 + 60*A*c^5*d + 15*B*c*d^5 + 30*B*c^5*d)/(15*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^7*(2*A*d^8 - 4*A*c^8 - 2*B*c^8 - 49*A*c^2*d^6 - 141*A*c^3*d^5 - 200*A*c^4*d^4 - 122*A*c^5*d^3 + 2*A*c^6*d^2 + 12*B*c^2*d^6 + 95*B*c^3*d^5 + 187*B*c^4*d^4 + 146*B*c^5*d^3 + 58*B*c^6*d^2 - 2*A*c*d^7 + 10*A*c^7*d + 2*B*c*d^7 + 6*B*c^7*d))/(c^2*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^6*(30*A*d^8 - 28*A*c^8 - 6*B*c^8 - 759*A*c^2*d^6 - 1707*A*c^3*d^5 - 1960*A*c^4*d^4 - 870*A*c^5*d^3 + 62*A*c^6*d^2 + 336*B*c^2*d^6 + 1257*B*c^3*d^5 + 1893*B*c^4*d^4 + 1350*B*c^5*d^3 + 414*B*c^6*d^2 - 114*A*c*d^7 + 54*A*c^7*d + 30*B*c*d^7 + 18*B*c^7*d))/(3*c^2*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^5*(60*A*d^8 - 32*A*c^8 - 18*B*c^8 - 1857*A*c^2*d^6 - 3763*A*c^3*d^5 - 3560*A*c^4*d^4 - 1294*A*c^5*d^3 + 70*A*c^6*d^2 + 900*B*c^2*d^6 + 2859*B*c^3*d^5 + 3705*B*c^4*d^4 + 2358*B*c^5*d^3 + 678*B*c^6*d^2 - 270*A*c*d^7 + 62*A*c^7*d + 60*B*c*d^7 + 42*B*c^7*d))/(3*c^2*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^2*(30*A*d^8 - 108*A*c^8 - 42*B*c^8 - 2501*A*c^2*d^6 - 8725*A*c^3*d^5 - 10616*A*c^4*d^4 - 4810*A*c^5*d^3 + 10*A*c^6*d^2 + 1056*B*c^2*d^6 + 5235*B*c^3*d^5 + 9891*B*c^4*d^4 + 7770*B*c^5*d^3 + 2370*B*c^6*d^2 - 30*A*c*d^7 + 290*A*c^7*d + 30*B*c*d^7 + 150*B*c^7*d))/(15*c^2*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^3*(150*A*d^8 - 140*A*c^8 - 90*B*c^8 - 7945*A*c^2*d^6 - 19441*A*c^3*d^5 - 18600*A*c^4*d^4 - 6898*A*c^5*d^3 + 210*A*c^6*d^2 + 3660*B*c^2*d^6 + 13311*B*c^3*d^5 + 19455*B*c^4*d^4 + 12618*B*c^5*d^3 + 3570*B*c^6*d^2 - 570*A*c*d^7 + 314*A*c^7*d + 150*B*c*d^7 + 246*B*c^7*d))/(15*c^2*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)*(30*A*d^7 - 40*A*c^7 - 30*B*c^7 - 1901*A*c^2*d^5 - 3400*A*c^3*d^4 - 2018*A*c^4*d^3 - 190*A*c^5*d^2 + 921*B*c^2*d^5 + 2655*B*c^3*d^4 + 2778*B*c^4*d^3 + 1050*B*c^5*d^2 - 195*A*c*d^6 + 154*A*c^6*d + 60*B*c*d^6 + 126*B*c^6*d))/(15*c*(c + d)^2*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) - (tan(e/2 + (f*x)/2)^8*(2*A*c^7 - 2*A*d^7 + 11*A*c^2*d^5 + 20*A*c^3*d^4 + 30*A*c^4*d^3 + 2*A*c^5*d^2 - 6*B*c^2*d^5 - 21*B*c^3*d^4 - 24*B*c^4*d^3 - 12*B*c^5*d^2 + 6*A*c*d^6 - 6*A*c^6*d))/(c*(c - d)*(2*c*d + c^2 + d^2)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)) + (tan(e/2 + (f*x)/2)^4*(300*A*d^7 - 204*A*c^7 - 66*B*c^7 - 10235*A*c^2*d^5 - 14330*A*c^3*d^4 - 7254*A*c^4*d^3 - 316*A*c^5*d^2 + 5460*B*c^2*d^5 + 12675*B*c^3*d^4 + 10764*B*c^4*d^3 + 3666*B*c^5*d^2 - 1650*A*c*d^6 + 614*A*c^6*d + 300*B*c*d^6 + 276*B*c^6*d))/(15*c^2*(c + d)*(c - d)*(c^4 - 4*c^3*d - 4*c*d^3 + d^4 + 6*c^2*d^2)))/(f*(tan(e/2 + (f*x)/2)*(5*a^3*c^2 + 4*a^3*c*d) + tan(e/2 + (f*x)/2)^2*(12*a^3*c^2 + 4*a^3*d^2 + 20*a^3*c*d) + tan(e/2 + (f*x)/2)^7*(12*a^3*c^2 + 4*a^3*d^2 + 20*a^3*c*d) + tan(e/2 + (f*x)/2)^3*(20*a^3*c^2 + 20*a^3*d^2 + 44*a^3*c*d) + tan(e/2 + (f*x)/2)^6*(20*a^3*c^2 + 20*a^3*d^2 + 44*a^3*c*d) + tan(e/2 + (f*x)/2)^4*(26*a^3*c^2 + 40*a^3*d^2 + 60*a^3*c*d) + tan(e/2 + (f*x)/2)^5*(26*a^3*c^2 + 40*a^3*d^2 + 60*a^3*c*d) + tan(e/2 + (f*x)/2)^8*(5*a^3*c^2 + 4*a^3*c*d) + a^3*c^2 + a^3*c^2*tan(e/2 + (f*x)/2)^9)) - (d^2*atan(((d^2*(12*B*c^3 - 13*A*d^3 + 6*B*d^3 - 30*A*c*d^2 - 20*A*c^2*d + 21*B*c*d^2 + 24*B*c^2*d)*(2*a^3*d^8 - 6*a^3*c*d^7 - 2*a^3*c^7*d + 2*a^3*c^2*d^6 + 10*a^3*c^3*d^5 - 10*a^3*c^4*d^4 - 2*a^3*c^5*d^3 + 6*a^3*c^6*d^2))/(2*a^3*(c + d)^(5/2)*(c - d)^(11/2)) - (c*d^2*tan(e/2 + (f*x)/2)*(12*B*c^3 - 13*A*d^3 + 6*B*d^3 - 30*A*c*d^2 - 20*A*c^2*d + 21*B*c*d^2 + 24*B*c^2*d)*(a^3*c^7 - a^3*d^7 + 3*a^3*c*d^6 - 3*a^3*c^6*d - a^3*c^2*d^5 - 5*a^3*c^3*d^4 + 5*a^3*c^4*d^3 + a^3*c^5*d^2))/(a^3*(c + d)^(5/2)*(c - d)^(11/2)))/(6*B*d^5 - 13*A*d^5 - 20*A*c^2*d^3 + 24*B*c^2*d^3 + 12*B*c^3*d^2 - 30*A*c*d^4 + 21*B*c*d^4))*(12*B*c^3 - 13*A*d^3 + 6*B*d^3 - 30*A*c*d^2 - 20*A*c^2*d + 21*B*c*d^2 + 24*B*c^2*d))/(a^3*f*(c + d)^(5/2)*(c - d)^(11/2))","B"
286,0,-1,256,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3, x)","F"
287,0,-1,192,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2, x)","F"
288,0,-1,118,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x)),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x)), x)","F"
289,0,-1,62,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2), x)","F"
290,0,-1,100,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x)), x)","F"
291,0,-1,126,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x))^2, x)","F"
292,0,-1,192,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2))/(c + d*sin(e + f*x))^3, x)","F"
293,0,-1,374,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3, x)","F"
294,0,-1,294,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2, x)","F"
295,0,-1,165,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x)),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x)), x)","F"
296,0,-1,101,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2), x)","F"
297,0,-1,153,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c + d*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c + d*sin(e + f*x)), x)","F"
298,0,-1,191,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c + d*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c + d*sin(e + f*x))^2, x)","F"
299,0,-1,221,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c + d*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2))/(c + d*sin(e + f*x))^3, x)","F"
300,0,-1,534,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3, x)","F"
301,0,-1,429,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2, x)","F"
302,0,-1,212,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x)),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x)), x)","F"
303,0,-1,138,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2), x)","F"
304,0,-1,218,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c + d*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c + d*sin(e + f*x)), x)","F"
305,0,-1,265,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c + d*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c + d*sin(e + f*x))^2, x)","F"
306,0,-1,308,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c + d*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(5/2))/(c + d*sin(e + f*x))^3, x)","F"
307,0,-1,284,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^(1/2), x)","F"
308,0,-1,200,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^(1/2), x)","F"
309,0,-1,130,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(c+d\,\sin\left(e+f\,x\right)\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^(1/2), x)","F"
310,1,151,79,1.055813,"\text{Not used}","int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^(1/2),x)","-\frac{A\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|1\right)\,\sqrt{\frac{2\,\left(a+a\,\sin\left(e+f\,x\right)\right)}{a}}}{f\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}-\frac{B\,\left(4\,\mathrm{E}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|1\right)-2\,\mathrm{F}\left(\mathrm{asin}\left(\frac{\sqrt{2}\,\sqrt{1-\sin\left(e+f\,x\right)}}{2}\right)\middle|1\right)\right)\,\sqrt{{\cos\left(e+f\,x\right)}^2}\,\sqrt{\frac{a+a\,\sin\left(e+f\,x\right)}{2\,a}}}{f\,\cos\left(e+f\,x\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}}","Not used",1,"- (A*ellipticF(pi/4 - e/2 - (f*x)/2, 1)*((2*(a + a*sin(e + f*x)))/a)^(1/2))/(f*(a + a*sin(e + f*x))^(1/2)) - (B*(4*ellipticE(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), 1) - 2*ellipticF(asin((2^(1/2)*(1 - sin(e + f*x))^(1/2))/2), 1))*(cos(e + f*x)^2)^(1/2)*((a + a*sin(e + f*x))/(2*a))^(1/2))/(f*cos(e + f*x)*(a + a*sin(e + f*x))^(1/2))","B"
311,0,-1,136,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))), x)","F"
312,0,-1,207,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^2), x)","F"
313,0,-1,309,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^3), x)","F"
314,0,-1,283,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^(3/2), x)","F"
315,0,-1,203,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^(3/2), x)","F"
316,0,-1,133,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(c+d\,\sin\left(e+f\,x\right)\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^(3/2), x)","F"
317,0,-1,87,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^(3/2), x)","F"
318,0,-1,187,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))), x)","F"
319,0,-1,292,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^2), x)","F"
320,0,-1,402,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^3), x)","F"
321,0,-1,308,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^3)/(a + a*sin(e + f*x))^(5/2), x)","F"
322,0,-1,219,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^2)/(a + a*sin(e + f*x))^(5/2), x)","F"
323,0,-1,151,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(c+d\,\sin\left(e+f\,x\right)\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x)))/(a + a*sin(e + f*x))^(5/2), x)","F"
324,0,-1,126,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/(a + a*sin(e + f*x))^(5/2), x)","F"
325,0,-1,261,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,\left(c+d\,\sin\left(e+f\,x\right)\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))), x)","F"
326,0,-1,395,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^2), x)","F"
327,0,-1,519,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + a*sin(e + f*x))^(5/2)*(c + d*sin(e + f*x))^3), x)","F"
328,0,-1,221,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^2*(c + d*sin(e + f*x))^n, x)","F"
329,0,-1,217,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\left(a+a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
330,0,-1,221,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x)), x)","F"
331,0,-1,223,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^2, x)","F"
332,0,-1,427,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^n, x)","F"
333,0,-1,167,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^(1/2)*(c + d*sin(e + f*x))^n, x)","F"
334,0,-1,220,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^(1/2), x)","F"
335,0,-1,269,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^n)/(a + a*sin(e + f*x))^(3/2), x)","F"
336,0,-1,351,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^2,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^2, x)","F"
337,0,-1,199,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x)),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(c+d\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x)), x)","F"
338,0,-1,117,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m, x)","F"
339,0,-1,191,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x)),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x)), x)","F"
340,0,-1,293,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^2,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^2, x)","F"
341,0,-1,467,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^3,x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^3, x)","F"
342,0,-1,284,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2), x)","F"
343,0,-1,274,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2),x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2), x)","F"
344,0,-1,274,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(1/2), x)","F"
345,0,-1,288,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(3/2), x)","F"
346,0,-1,270,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
347,0,-1,277,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(m + 1),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(m + 1), x)","F"
348,0,-1,132,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(a - a*sin(e + f*x))*(c + d*sin(e + f*x))^n,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(a-a\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(a - a*sin(e + f*x))*(c + d*sin(e + f*x))^n, x)","F"
349,0,-1,139,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(a - a*sin(e + f*x)))/(c + d*sin(e + f*x))^(m + 1),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(a-a\,\sin\left(e+f\,x\right)\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{m+1}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(a - a*sin(e + f*x)))/(c + d*sin(e + f*x))^(m + 1), x)","F"
350,1,98,39,14.774453,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(d - m*(c - d) + sin(e + f*x)*(c + m*(c - d))))/(c + d*sin(e + f*x))^(m + 2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\left(d\,\sin\left(2\,e+2\,f\,x\right)-2\,c\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)\right)}{f\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^m\,\left(d^2\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)+2\,c^2+d^2+4\,c\,d\,\sin\left(e+f\,x\right)\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(d*sin(2*e + 2*f*x) - 2*c*(2*sin(e/2 + (f*x)/2)^2 - 1)))/(f*(c + d*sin(e + f*x))^m*(d^2*(2*sin(e + f*x)^2 - 1) + 2*c^2 + d^2 + 4*c*d*sin(e + f*x)))","B"
351,1,99,40,14.621305,"\text{Not used}","int(((a - a*sin(e + f*x))^m*(d + sin(e + f*x)*(c + m*(c + d)) + m*(c + d)))/(c + d*sin(e + f*x))^(m + 2),x)","-\frac{{\left(-a\,\left(\sin\left(e+f\,x\right)-1\right)\right)}^m\,\left(d\,\sin\left(2\,e+2\,f\,x\right)-2\,c\,\left(2\,{\sin\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2-1\right)\right)}{f\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^m\,\left(d^2\,\left(2\,{\sin\left(e+f\,x\right)}^2-1\right)+2\,c^2+d^2+4\,c\,d\,\sin\left(e+f\,x\right)\right)}","Not used",1,"-((-a*(sin(e + f*x) - 1))^m*(d*sin(2*e + 2*f*x) - 2*c*(2*sin(e/2 + (f*x)/2)^2 - 1)))/(f*(c + d*sin(e + f*x))^m*(d^2*(2*sin(e + f*x)^2 - 1) + 2*c^2 + d^2 + 4*c*d*sin(e + f*x)))","B"
352,1,16312,199,27.619205,"\text{Not used}","int(((A + B*sin(e + f*x))*(a + b*sin(e + f*x))^2)/(c + d*sin(e + f*x))^2,x)","\frac{\frac{2\,\left(-B\,a^2\,c\,d^2+A\,a^2\,d^3+2\,B\,a\,b\,c^2\,d-2\,A\,a\,b\,c\,d^2-2\,B\,b^2\,c^3+A\,b^2\,c^2\,d+B\,b^2\,c\,d^2\right)}{d^2\,\left(c^2-d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2\,\left(-B\,a^2\,c\,d^2+A\,a^2\,d^3+2\,B\,a\,b\,c^2\,d-2\,A\,a\,b\,c\,d^2-2\,B\,b^2\,c^3+A\,b^2\,c^2\,d+B\,b^2\,c\,d^2\right)}{d^2\,\left(c^2-d^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3\,\left(-B\,a^2\,c\,d^2+A\,a^2\,d^3+2\,B\,a\,b\,c^2\,d-2\,A\,a\,b\,c\,d^2-B\,b^2\,c^3+A\,b^2\,c^2\,d\right)}{c\,d\,\left(c^2-d^2\right)}+\frac{2\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-B\,a^2\,c\,d^2+A\,a^2\,d^3+2\,B\,a\,b\,c^2\,d-2\,A\,a\,b\,c\,d^2-3\,B\,b^2\,c^3+A\,b^2\,c^2\,d+2\,B\,b^2\,c\,d^2\right)}{c\,d\,\left(c^2-d^2\right)}}{f\,\left(c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^4+2\,d\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^3+2\,c\,{\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)}^2+2\,d\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)+c\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)}{d^3}-\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,1{}\mathrm{i}}{d^3}+\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,1{}\mathrm{i}}{d^3}}{\frac{64\,\left(-A^3\,a^4\,b^2\,c^3\,d^5+4\,A^3\,a^3\,b^3\,c^2\,d^6+A^3\,a^2\,b^4\,c^5\,d^3-3\,A^3\,a^2\,b^4\,c^3\,d^5-4\,A^3\,a^2\,b^4\,c\,d^7-2\,A^3\,a\,b^5\,c^4\,d^4+6\,A^3\,a\,b^5\,c^2\,d^6+A^3\,b^6\,c^5\,d^3-2\,A^3\,b^6\,c^3\,d^5-2\,A^2\,B\,a^5\,b\,c^3\,d^5+2\,A^2\,B\,a^4\,b^2\,c^4\,d^4+10\,A^2\,B\,a^4\,b^2\,c^2\,d^6+4\,A^2\,B\,a^3\,b^3\,c^5\,d^3-20\,A^2\,B\,a^3\,b^3\,c^3\,d^5-12\,A^2\,B\,a^3\,b^3\,c\,d^7-4\,A^2\,B\,a^2\,b^4\,c^6\,d^2+A^2\,B\,a^2\,b^4\,c^4\,d^4+35\,A^2\,B\,a^2\,b^4\,c^2\,d^6+14\,A^2\,B\,a\,b^5\,c^5\,d^3-32\,A^2\,B\,a\,b^5\,c^3\,d^5-5\,A^2\,B\,b^6\,c^6\,d^2+9\,A^2\,B\,b^6\,c^4\,d^4+4\,A\,B^2\,a^5\,b\,c^2\,d^6+4\,A\,B^2\,a^4\,b^2\,c^5\,d^3-16\,A\,B^2\,a^4\,b^2\,c^3\,d^5-9\,A\,B^2\,a^4\,b^2\,c\,d^7-8\,A\,B^2\,a^3\,b^3\,c^6\,d^2+8\,A\,B^2\,a^3\,b^3\,c^4\,d^4+44\,A\,B^2\,a^3\,b^3\,c^2\,d^6+4\,A\,B^2\,a^2\,b^4\,c^7\,d+24\,A\,B^2\,a^2\,b^4\,c^5\,d^3-74\,A\,B^2\,a^2\,b^4\,c^3\,d^5-28\,A\,B^2\,a\,b^5\,c^6\,d^2+52\,A\,B^2\,a\,b^5\,c^4\,d^4+8\,A\,B^2\,b^6\,c^7\,d-13\,A\,B^2\,b^6\,c^5\,d^3-2\,B^3\,a^5\,b\,c\,d^7-4\,B^3\,a^4\,b^2\,c^4\,d^4+14\,B^3\,a^4\,b^2\,c^2\,d^6+16\,B^3\,a^3\,b^3\,c^5\,d^3-36\,B^3\,a^3\,b^3\,c^3\,d^5-24\,B^3\,a^2\,b^4\,c^6\,d^2+44\,B^3\,a^2\,b^4\,c^4\,d^4+16\,B^3\,a\,b^5\,c^7\,d-26\,B^3\,a\,b^5\,c^5\,d^3-4\,B^3\,b^6\,c^8+6\,B^3\,b^6\,c^6\,d^2\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)}{d^3}-\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)}{d^3}-\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,\left(\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)}{d^3}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)}{d^3}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^3\,a^2\,b^4\,c^4\,d^5+2\,A^3\,a^2\,b^4\,c^2\,d^7+4\,A^3\,a\,b^5\,c^3\,d^6-4\,A^3\,a\,b^5\,c\,d^8+2\,A^3\,b^6\,c^6\,d^3-6\,A^3\,b^6\,c^4\,d^5+4\,A^3\,b^6\,c^2\,d^7-8\,A^2\,B\,a^3\,b^3\,c^4\,d^5+8\,A^2\,B\,a^3\,b^3\,c^2\,d^7+8\,A^2\,B\,a^2\,b^4\,c^5\,d^4+10\,A^2\,B\,a^2\,b^4\,c^3\,d^6-18\,A^2\,B\,a^2\,b^4\,c\,d^8+12\,A^2\,B\,a\,b^5\,c^6\,d^3-52\,A^2\,B\,a\,b^5\,c^4\,d^5+40\,A^2\,B\,a\,b^5\,c^2\,d^7-12\,A^2\,B\,b^6\,c^7\,d^2+34\,A^2\,B\,b^6\,c^5\,d^4-22\,A^2\,B\,b^6\,c^3\,d^6-8\,A\,B^2\,a^4\,b^2\,c^4\,d^5+8\,A\,B^2\,a^4\,b^2\,c^2\,d^7+16\,A\,B^2\,a^3\,b^3\,c^5\,d^4+8\,A\,B^2\,a^3\,b^3\,c^3\,d^6-24\,A\,B^2\,a^3\,b^3\,c\,d^8+16\,A\,B^2\,a^2\,b^4\,c^6\,d^3-104\,A\,B^2\,a^2\,b^4\,c^4\,d^5+88\,A\,B^2\,a^2\,b^4\,c^2\,d^7-48\,A\,B^2\,a\,b^5\,c^7\,d^2+152\,A\,B^2\,a\,b^5\,c^5\,d^4-104\,A\,B^2\,a\,b^5\,c^3\,d^6+24\,A\,B^2\,b^6\,c^8\,d-64\,A\,B^2\,b^6\,c^6\,d^3+40\,A\,B^2\,b^6\,c^4\,d^5+8\,B^3\,a^4\,b^2\,c^3\,d^6-8\,B^3\,a^4\,b^2\,c\,d^8+16\,B^3\,a^3\,b^3\,c^6\,d^3-64\,B^3\,a^3\,b^3\,c^4\,d^5+48\,B^3\,a^3\,b^3\,c^2\,d^7-48\,B^3\,a^2\,b^4\,c^7\,d^2+144\,B^3\,a^2\,b^4\,c^5\,d^4-96\,B^3\,a^2\,b^4\,c^3\,d^6+48\,B^3\,a\,b^5\,c^8\,d-128\,B^3\,a\,b^5\,c^6\,d^3+80\,B^3\,a\,b^5\,c^4\,d^5-16\,B^3\,b^6\,c^9+40\,B^3\,b^6\,c^7\,d^2-24\,B^3\,b^6\,c^5\,d^4\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}}\right)\,\left(b\,d\,\left(A\,b+2\,B\,a\right)\,1{}\mathrm{i}-B\,b^2\,c\,2{}\mathrm{i}\right)\,2{}\mathrm{i}}{d^3\,f}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}-\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)\,1{}\mathrm{i}}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)\,1{}\mathrm{i}}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}}{\frac{64\,\left(-A^3\,a^4\,b^2\,c^3\,d^5+4\,A^3\,a^3\,b^3\,c^2\,d^6+A^3\,a^2\,b^4\,c^5\,d^3-3\,A^3\,a^2\,b^4\,c^3\,d^5-4\,A^3\,a^2\,b^4\,c\,d^7-2\,A^3\,a\,b^5\,c^4\,d^4+6\,A^3\,a\,b^5\,c^2\,d^6+A^3\,b^6\,c^5\,d^3-2\,A^3\,b^6\,c^3\,d^5-2\,A^2\,B\,a^5\,b\,c^3\,d^5+2\,A^2\,B\,a^4\,b^2\,c^4\,d^4+10\,A^2\,B\,a^4\,b^2\,c^2\,d^6+4\,A^2\,B\,a^3\,b^3\,c^5\,d^3-20\,A^2\,B\,a^3\,b^3\,c^3\,d^5-12\,A^2\,B\,a^3\,b^3\,c\,d^7-4\,A^2\,B\,a^2\,b^4\,c^6\,d^2+A^2\,B\,a^2\,b^4\,c^4\,d^4+35\,A^2\,B\,a^2\,b^4\,c^2\,d^6+14\,A^2\,B\,a\,b^5\,c^5\,d^3-32\,A^2\,B\,a\,b^5\,c^3\,d^5-5\,A^2\,B\,b^6\,c^6\,d^2+9\,A^2\,B\,b^6\,c^4\,d^4+4\,A\,B^2\,a^5\,b\,c^2\,d^6+4\,A\,B^2\,a^4\,b^2\,c^5\,d^3-16\,A\,B^2\,a^4\,b^2\,c^3\,d^5-9\,A\,B^2\,a^4\,b^2\,c\,d^7-8\,A\,B^2\,a^3\,b^3\,c^6\,d^2+8\,A\,B^2\,a^3\,b^3\,c^4\,d^4+44\,A\,B^2\,a^3\,b^3\,c^2\,d^6+4\,A\,B^2\,a^2\,b^4\,c^7\,d+24\,A\,B^2\,a^2\,b^4\,c^5\,d^3-74\,A\,B^2\,a^2\,b^4\,c^3\,d^5-28\,A\,B^2\,a\,b^5\,c^6\,d^2+52\,A\,B^2\,a\,b^5\,c^4\,d^4+8\,A\,B^2\,b^6\,c^7\,d-13\,A\,B^2\,b^6\,c^5\,d^3-2\,B^3\,a^5\,b\,c\,d^7-4\,B^3\,a^4\,b^2\,c^4\,d^4+14\,B^3\,a^4\,b^2\,c^2\,d^6+16\,B^3\,a^3\,b^3\,c^5\,d^3-36\,B^3\,a^3\,b^3\,c^3\,d^5-24\,B^3\,a^2\,b^4\,c^6\,d^2+44\,B^3\,a^2\,b^4\,c^4\,d^4+16\,B^3\,a\,b^5\,c^7\,d-26\,B^3\,a\,b^5\,c^5\,d^3-4\,B^3\,b^6\,c^8+6\,B^3\,b^6\,c^6\,d^2\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{64\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A^3\,a^2\,b^4\,c^4\,d^5+2\,A^3\,a^2\,b^4\,c^2\,d^7+4\,A^3\,a\,b^5\,c^3\,d^6-4\,A^3\,a\,b^5\,c\,d^8+2\,A^3\,b^6\,c^6\,d^3-6\,A^3\,b^6\,c^4\,d^5+4\,A^3\,b^6\,c^2\,d^7-8\,A^2\,B\,a^3\,b^3\,c^4\,d^5+8\,A^2\,B\,a^3\,b^3\,c^2\,d^7+8\,A^2\,B\,a^2\,b^4\,c^5\,d^4+10\,A^2\,B\,a^2\,b^4\,c^3\,d^6-18\,A^2\,B\,a^2\,b^4\,c\,d^8+12\,A^2\,B\,a\,b^5\,c^6\,d^3-52\,A^2\,B\,a\,b^5\,c^4\,d^5+40\,A^2\,B\,a\,b^5\,c^2\,d^7-12\,A^2\,B\,b^6\,c^7\,d^2+34\,A^2\,B\,b^6\,c^5\,d^4-22\,A^2\,B\,b^6\,c^3\,d^6-8\,A\,B^2\,a^4\,b^2\,c^4\,d^5+8\,A\,B^2\,a^4\,b^2\,c^2\,d^7+16\,A\,B^2\,a^3\,b^3\,c^5\,d^4+8\,A\,B^2\,a^3\,b^3\,c^3\,d^6-24\,A\,B^2\,a^3\,b^3\,c\,d^8+16\,A\,B^2\,a^2\,b^4\,c^6\,d^3-104\,A\,B^2\,a^2\,b^4\,c^4\,d^5+88\,A\,B^2\,a^2\,b^4\,c^2\,d^7-48\,A\,B^2\,a\,b^5\,c^7\,d^2+152\,A\,B^2\,a\,b^5\,c^5\,d^4-104\,A\,B^2\,a\,b^5\,c^3\,d^6+24\,A\,B^2\,b^6\,c^8\,d-64\,A\,B^2\,b^6\,c^6\,d^3+40\,A\,B^2\,b^6\,c^4\,d^5+8\,B^3\,a^4\,b^2\,c^3\,d^6-8\,B^3\,a^4\,b^2\,c\,d^8+16\,B^3\,a^3\,b^3\,c^6\,d^3-64\,B^3\,a^3\,b^3\,c^4\,d^5+48\,B^3\,a^3\,b^3\,c^2\,d^7-48\,B^3\,a^2\,b^4\,c^7\,d^2+144\,B^3\,a^2\,b^4\,c^5\,d^4-96\,B^3\,a^2\,b^4\,c^3\,d^6+48\,B^3\,a\,b^5\,c^8\,d-128\,B^3\,a\,b^5\,c^6\,d^3+80\,B^3\,a\,b^5\,c^4\,d^5-16\,B^3\,b^6\,c^9+40\,B^3\,b^6\,c^7\,d^2-24\,B^3\,b^6\,c^5\,d^4\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}-\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}-\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(A^2\,b^4\,c^6\,d^4-2\,A^2\,b^4\,c^4\,d^6+A^2\,b^4\,c^2\,d^8+4\,A\,B\,a\,b^3\,c^6\,d^4-8\,A\,B\,a\,b^3\,c^4\,d^6+4\,A\,B\,a\,b^3\,c^2\,d^8-4\,A\,B\,b^4\,c^7\,d^3+8\,A\,B\,b^4\,c^5\,d^5-4\,A\,B\,b^4\,c^3\,d^7+4\,B^2\,a^2\,b^2\,c^6\,d^4-8\,B^2\,a^2\,b^2\,c^4\,d^6+4\,B^2\,a^2\,b^2\,c^2\,d^8-8\,B^2\,a\,b^3\,c^7\,d^3+16\,B^2\,a\,b^3\,c^5\,d^5-8\,B^2\,a\,b^3\,c^3\,d^7+4\,B^2\,b^4\,c^8\,d^2-8\,B^2\,b^4\,c^6\,d^4+4\,B^2\,b^4\,c^4\,d^6\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(A^2\,a^4\,c^3\,d^8-4\,A^2\,a^3\,b\,c^2\,d^9-2\,A^2\,a^2\,b^2\,c^5\,d^6+4\,A^2\,a^2\,b^2\,c^3\,d^8+4\,A^2\,a^2\,b^2\,c\,d^{10}+4\,A^2\,a\,b^3\,c^4\,d^7-8\,A^2\,a\,b^3\,c^2\,d^9+2\,A^2\,b^4\,c^7\,d^4-8\,A^2\,b^4\,c^5\,d^6+9\,A^2\,b^4\,c^3\,d^8-2\,A^2\,b^4\,c\,d^{10}-2\,A\,B\,a^4\,c^2\,d^9-4\,A\,B\,a^3\,b\,c^5\,d^6+8\,A\,B\,a^3\,b\,c^3\,d^8+4\,A\,B\,a^3\,b\,c\,d^{10}+4\,A\,B\,a^2\,b^2\,c^6\,d^5+4\,A\,B\,a^2\,b^2\,c^4\,d^7-20\,A\,B\,a^2\,b^2\,c^2\,d^9+8\,A\,B\,a\,b^3\,c^7\,d^4-40\,A\,B\,a\,b^3\,c^5\,d^6+48\,A\,B\,a\,b^3\,c^3\,d^8-8\,A\,B\,a\,b^3\,c\,d^{10}-8\,A\,B\,b^4\,c^8\,d^3+30\,A\,B\,b^4\,c^6\,d^5-32\,A\,B\,b^4\,c^4\,d^7+8\,A\,B\,b^4\,c^2\,d^9+B^2\,a^4\,c\,d^{10}+4\,B^2\,a^3\,b\,c^4\,d^7-8\,B^2\,a^3\,b\,c^2\,d^9+8\,B^2\,a^2\,b^2\,c^7\,d^4-36\,B^2\,a^2\,b^2\,c^5\,d^6+42\,B^2\,a^2\,b^2\,c^3\,d^8-8\,B^2\,a^2\,b^2\,c\,d^{10}-16\,B^2\,a\,b^3\,c^8\,d^3+60\,B^2\,a\,b^3\,c^6\,d^5-64\,B^2\,a\,b^3\,c^4\,d^7+16\,B^2\,a\,b^3\,c^2\,d^9+8\,B^2\,b^4\,c^9\,d^2-28\,B^2\,b^4\,c^7\,d^4+29\,B^2\,b^4\,c^5\,d^6-8\,B^2\,b^4\,c^3\,d^8\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(\frac{32\,\left(A\,a^2\,c^5\,d^7-B\,a^2\,c^4\,d^8-A\,a^2\,c^3\,d^9+B\,a^2\,c^2\,d^{10}-2\,A\,a\,b\,c^4\,d^8+2\,B\,a\,b\,c^3\,d^9+2\,A\,a\,b\,c^2\,d^{10}-2\,B\,a\,b\,c\,d^{11}+B\,b^2\,c^6\,d^6-3\,B\,b^2\,c^4\,d^8+A\,b^2\,c^3\,d^9+2\,B\,b^2\,c^2\,d^{10}-A\,b^2\,c\,d^{11}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}-\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,A\,a^2\,c^4\,d^9+2\,B\,a^2\,c^3\,d^{10}+2\,A\,a^2\,c^2\,d^{11}-2\,B\,a^2\,c\,d^{12}+4\,B\,a\,b\,c^6\,d^7-12\,B\,a\,b\,c^4\,d^9+4\,A\,a\,b\,c^3\,d^{10}+8\,B\,a\,b\,c^2\,d^{11}-4\,A\,a\,b\,c\,d^{12}-4\,B\,b^2\,c^7\,d^6+2\,A\,b^2\,c^6\,d^7+10\,B\,b^2\,c^5\,d^8-6\,A\,b^2\,c^4\,d^9-6\,B\,b^2\,c^3\,d^{10}+4\,A\,b^2\,c^2\,d^{11}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}+\frac{\left(\frac{32\,\left(c^6\,d^8-2\,c^4\,d^{10}+c^2\,d^{12}\right)}{c^4\,d^5-2\,c^2\,d^7+d^9}+\frac{32\,\mathrm{tan}\left(\frac{e}{2}+\frac{f\,x}{2}\right)\,\left(-2\,c^7\,d^8+7\,c^5\,d^{10}-8\,c^3\,d^{12}+3\,c\,d^{14}\right)}{c^4\,d^6-2\,c^2\,d^8+d^{10}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}\right)\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)}{-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9}}\right)\,\left(a\,d-b\,c\right)\,\sqrt{-{\left(c+d\right)}^3\,{\left(c-d\right)}^3}\,\left(2\,A\,b\,d^3+B\,a\,d^3+2\,B\,b\,c^3-A\,a\,c\,d^2-A\,b\,c^2\,d-3\,B\,b\,c\,d^2\right)\,2{}\mathrm{i}}{f\,\left(-c^6\,d^3+3\,c^4\,d^5-3\,c^2\,d^7+d^9\right)}","Not used",1,"((2*(A*a^2*d^3 - 2*B*b^2*c^3 + A*b^2*c^2*d - B*a^2*c*d^2 + B*b^2*c*d^2 - 2*A*a*b*c*d^2 + 2*B*a*b*c^2*d))/(d^2*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)^2*(A*a^2*d^3 - 2*B*b^2*c^3 + A*b^2*c^2*d - B*a^2*c*d^2 + B*b^2*c*d^2 - 2*A*a*b*c*d^2 + 2*B*a*b*c^2*d))/(d^2*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)^3*(A*a^2*d^3 - B*b^2*c^3 + A*b^2*c^2*d - B*a^2*c*d^2 - 2*A*a*b*c*d^2 + 2*B*a*b*c^2*d))/(c*d*(c^2 - d^2)) + (2*tan(e/2 + (f*x)/2)*(A*a^2*d^3 - 3*B*b^2*c^3 + A*b^2*c^2*d - B*a^2*c*d^2 + 2*B*b^2*c*d^2 - 2*A*a*b*c*d^2 + 2*B*a*b*c^2*d))/(c*d*(c^2 - d^2)))/(f*(c + 2*d*tan(e/2 + (f*x)/2) + 2*c*tan(e/2 + (f*x)/2)^2 + c*tan(e/2 + (f*x)/2)^4 + 2*d*tan(e/2 + (f*x)/2)^3)) + (atan((((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) + ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i))/d^3 - (32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6)))/d^3 - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6))*1i)/d^3 + ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) + ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i))/d^3 - (32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6)))/d^3 - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6))*1i)/d^3)/((64*(A^3*b^6*c^5*d^3 - 2*A^3*b^6*c^3*d^5 - 4*B^3*b^6*c^8 + 6*B^3*b^6*c^6*d^2 - 3*A^3*a^2*b^4*c^3*d^5 + A^3*a^2*b^4*c^5*d^3 + 4*A^3*a^3*b^3*c^2*d^6 - A^3*a^4*b^2*c^3*d^5 + 44*B^3*a^2*b^4*c^4*d^4 - 24*B^3*a^2*b^4*c^6*d^2 - 36*B^3*a^3*b^3*c^3*d^5 + 16*B^3*a^3*b^3*c^5*d^3 + 14*B^3*a^4*b^2*c^2*d^6 - 4*B^3*a^4*b^2*c^4*d^4 + 8*A*B^2*b^6*c^7*d + 16*B^3*a*b^5*c^7*d - 2*B^3*a^5*b*c*d^7 - 13*A*B^2*b^6*c^5*d^3 + 9*A^2*B*b^6*c^4*d^4 - 5*A^2*B*b^6*c^6*d^2 + 6*A^3*a*b^5*c^2*d^6 - 2*A^3*a*b^5*c^4*d^4 - 4*A^3*a^2*b^4*c*d^7 - 26*B^3*a*b^5*c^5*d^3 - 74*A*B^2*a^2*b^4*c^3*d^5 + 24*A*B^2*a^2*b^4*c^5*d^3 + 44*A*B^2*a^3*b^3*c^2*d^6 + 8*A*B^2*a^3*b^3*c^4*d^4 - 8*A*B^2*a^3*b^3*c^6*d^2 - 16*A*B^2*a^4*b^2*c^3*d^5 + 4*A*B^2*a^4*b^2*c^5*d^3 + 35*A^2*B*a^2*b^4*c^2*d^6 + A^2*B*a^2*b^4*c^4*d^4 - 4*A^2*B*a^2*b^4*c^6*d^2 - 20*A^2*B*a^3*b^3*c^3*d^5 + 4*A^2*B*a^3*b^3*c^5*d^3 + 10*A^2*B*a^4*b^2*c^2*d^6 + 2*A^2*B*a^4*b^2*c^4*d^4 + 52*A*B^2*a*b^5*c^4*d^4 - 28*A*B^2*a*b^5*c^6*d^2 + 4*A*B^2*a^2*b^4*c^7*d - 9*A*B^2*a^4*b^2*c*d^7 + 4*A*B^2*a^5*b*c^2*d^6 - 32*A^2*B*a*b^5*c^3*d^5 + 14*A^2*B*a*b^5*c^5*d^3 - 12*A^2*B*a^3*b^3*c*d^7 - 2*A^2*B*a^5*b*c^3*d^5))/(d^9 - 2*c^2*d^7 + c^4*d^5) + ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) + ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i))/d^3 - (32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6)))/d^3 - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6)))/d^3 - ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) + ((b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*((32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i))/d^3 - (32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6)))/d^3 - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6)))/d^3 + (64*tan(e/2 + (f*x)/2)*(4*A^3*b^6*c^2*d^7 - 16*B^3*b^6*c^9 - 6*A^3*b^6*c^4*d^5 + 2*A^3*b^6*c^6*d^3 - 24*B^3*b^6*c^5*d^4 + 40*B^3*b^6*c^7*d^2 + 2*A^3*a^2*b^4*c^2*d^7 - 2*A^3*a^2*b^4*c^4*d^5 - 96*B^3*a^2*b^4*c^3*d^6 + 144*B^3*a^2*b^4*c^5*d^4 - 48*B^3*a^2*b^4*c^7*d^2 + 48*B^3*a^3*b^3*c^2*d^7 - 64*B^3*a^3*b^3*c^4*d^5 + 16*B^3*a^3*b^3*c^6*d^3 + 8*B^3*a^4*b^2*c^3*d^6 + 24*A*B^2*b^6*c^8*d - 4*A^3*a*b^5*c*d^8 + 48*B^3*a*b^5*c^8*d + 40*A*B^2*b^6*c^4*d^5 - 64*A*B^2*b^6*c^6*d^3 - 22*A^2*B*b^6*c^3*d^6 + 34*A^2*B*b^6*c^5*d^4 - 12*A^2*B*b^6*c^7*d^2 + 4*A^3*a*b^5*c^3*d^6 + 80*B^3*a*b^5*c^4*d^5 - 128*B^3*a*b^5*c^6*d^3 - 8*B^3*a^4*b^2*c*d^8 + 88*A*B^2*a^2*b^4*c^2*d^7 - 104*A*B^2*a^2*b^4*c^4*d^5 + 16*A*B^2*a^2*b^4*c^6*d^3 + 8*A*B^2*a^3*b^3*c^3*d^6 + 16*A*B^2*a^3*b^3*c^5*d^4 + 8*A*B^2*a^4*b^2*c^2*d^7 - 8*A*B^2*a^4*b^2*c^4*d^5 + 10*A^2*B*a^2*b^4*c^3*d^6 + 8*A^2*B*a^2*b^4*c^5*d^4 + 8*A^2*B*a^3*b^3*c^2*d^7 - 8*A^2*B*a^3*b^3*c^4*d^5 - 104*A*B^2*a*b^5*c^3*d^6 + 152*A*B^2*a*b^5*c^5*d^4 - 48*A*B^2*a*b^5*c^7*d^2 - 24*A*B^2*a^3*b^3*c*d^8 + 40*A^2*B*a*b^5*c^2*d^7 - 52*A^2*B*a*b^5*c^4*d^5 + 12*A^2*B*a*b^5*c^6*d^3 - 18*A^2*B*a^2*b^4*c*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6)))*(b*d*(A*b + 2*B*a)*1i - B*b^2*c*2i)*2i)/(d^3*f) + (atan((((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6) - (32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2)*1i)/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2)*1i)/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))/((64*(A^3*b^6*c^5*d^3 - 2*A^3*b^6*c^3*d^5 - 4*B^3*b^6*c^8 + 6*B^3*b^6*c^6*d^2 - 3*A^3*a^2*b^4*c^3*d^5 + A^3*a^2*b^4*c^5*d^3 + 4*A^3*a^3*b^3*c^2*d^6 - A^3*a^4*b^2*c^3*d^5 + 44*B^3*a^2*b^4*c^4*d^4 - 24*B^3*a^2*b^4*c^6*d^2 - 36*B^3*a^3*b^3*c^3*d^5 + 16*B^3*a^3*b^3*c^5*d^3 + 14*B^3*a^4*b^2*c^2*d^6 - 4*B^3*a^4*b^2*c^4*d^4 + 8*A*B^2*b^6*c^7*d + 16*B^3*a*b^5*c^7*d - 2*B^3*a^5*b*c*d^7 - 13*A*B^2*b^6*c^5*d^3 + 9*A^2*B*b^6*c^4*d^4 - 5*A^2*B*b^6*c^6*d^2 + 6*A^3*a*b^5*c^2*d^6 - 2*A^3*a*b^5*c^4*d^4 - 4*A^3*a^2*b^4*c*d^7 - 26*B^3*a*b^5*c^5*d^3 - 74*A*B^2*a^2*b^4*c^3*d^5 + 24*A*B^2*a^2*b^4*c^5*d^3 + 44*A*B^2*a^3*b^3*c^2*d^6 + 8*A*B^2*a^3*b^3*c^4*d^4 - 8*A*B^2*a^3*b^3*c^6*d^2 - 16*A*B^2*a^4*b^2*c^3*d^5 + 4*A*B^2*a^4*b^2*c^5*d^3 + 35*A^2*B*a^2*b^4*c^2*d^6 + A^2*B*a^2*b^4*c^4*d^4 - 4*A^2*B*a^2*b^4*c^6*d^2 - 20*A^2*B*a^3*b^3*c^3*d^5 + 4*A^2*B*a^3*b^3*c^5*d^3 + 10*A^2*B*a^4*b^2*c^2*d^6 + 2*A^2*B*a^4*b^2*c^4*d^4 + 52*A*B^2*a*b^5*c^4*d^4 - 28*A*B^2*a*b^5*c^6*d^2 + 4*A*B^2*a^2*b^4*c^7*d - 9*A*B^2*a^4*b^2*c*d^7 + 4*A*B^2*a^5*b*c^2*d^6 - 32*A^2*B*a*b^5*c^3*d^5 + 14*A^2*B*a*b^5*c^5*d^3 - 12*A^2*B*a^3*b^3*c*d^7 - 2*A^2*B*a^5*b*c^3*d^5))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (64*tan(e/2 + (f*x)/2)*(4*A^3*b^6*c^2*d^7 - 16*B^3*b^6*c^9 - 6*A^3*b^6*c^4*d^5 + 2*A^3*b^6*c^6*d^3 - 24*B^3*b^6*c^5*d^4 + 40*B^3*b^6*c^7*d^2 + 2*A^3*a^2*b^4*c^2*d^7 - 2*A^3*a^2*b^4*c^4*d^5 - 96*B^3*a^2*b^4*c^3*d^6 + 144*B^3*a^2*b^4*c^5*d^4 - 48*B^3*a^2*b^4*c^7*d^2 + 48*B^3*a^3*b^3*c^2*d^7 - 64*B^3*a^3*b^3*c^4*d^5 + 16*B^3*a^3*b^3*c^6*d^3 + 8*B^3*a^4*b^2*c^3*d^6 + 24*A*B^2*b^6*c^8*d - 4*A^3*a*b^5*c*d^8 + 48*B^3*a*b^5*c^8*d + 40*A*B^2*b^6*c^4*d^5 - 64*A*B^2*b^6*c^6*d^3 - 22*A^2*B*b^6*c^3*d^6 + 34*A^2*B*b^6*c^5*d^4 - 12*A^2*B*b^6*c^7*d^2 + 4*A^3*a*b^5*c^3*d^6 + 80*B^3*a*b^5*c^4*d^5 - 128*B^3*a*b^5*c^6*d^3 - 8*B^3*a^4*b^2*c*d^8 + 88*A*B^2*a^2*b^4*c^2*d^7 - 104*A*B^2*a^2*b^4*c^4*d^5 + 16*A*B^2*a^2*b^4*c^6*d^3 + 8*A*B^2*a^3*b^3*c^3*d^6 + 16*A*B^2*a^3*b^3*c^5*d^4 + 8*A*B^2*a^4*b^2*c^2*d^7 - 8*A*B^2*a^4*b^2*c^4*d^5 + 10*A^2*B*a^2*b^4*c^3*d^6 + 8*A^2*B*a^2*b^4*c^5*d^4 + 8*A^2*B*a^3*b^3*c^2*d^7 - 8*A^2*B*a^3*b^3*c^4*d^5 - 104*A*B^2*a*b^5*c^3*d^6 + 152*A*B^2*a*b^5*c^5*d^4 - 48*A*B^2*a*b^5*c^7*d^2 - 24*A*B^2*a^3*b^3*c*d^8 + 40*A^2*B*a*b^5*c^2*d^7 - 52*A^2*B*a*b^5*c^4*d^5 + 12*A^2*B*a*b^5*c^6*d^3 - 18*A^2*B*a^2*b^4*c*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6) - (32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3) - ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(A^2*b^4*c^2*d^8 - 2*A^2*b^4*c^4*d^6 + A^2*b^4*c^6*d^4 + 4*B^2*b^4*c^4*d^6 - 8*B^2*b^4*c^6*d^4 + 4*B^2*b^4*c^8*d^2 + 4*B^2*a^2*b^2*c^2*d^8 - 8*B^2*a^2*b^2*c^4*d^6 + 4*B^2*a^2*b^2*c^6*d^4 - 4*A*B*b^4*c^3*d^7 + 8*A*B*b^4*c^5*d^5 - 4*A*B*b^4*c^7*d^3 - 8*B^2*a*b^3*c^3*d^7 + 16*B^2*a*b^3*c^5*d^5 - 8*B^2*a*b^3*c^7*d^3 + 4*A*B*a*b^3*c^2*d^8 - 8*A*B*a*b^3*c^4*d^6 + 4*A*B*a*b^3*c^6*d^4))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(A^2*a^4*c^3*d^8 + 9*A^2*b^4*c^3*d^8 - 8*A^2*b^4*c^5*d^6 + 2*A^2*b^4*c^7*d^4 - 8*B^2*b^4*c^3*d^8 + 29*B^2*b^4*c^5*d^6 - 28*B^2*b^4*c^7*d^4 + 8*B^2*b^4*c^9*d^2 - 2*A^2*b^4*c*d^10 + B^2*a^4*c*d^10 + 4*A^2*a^2*b^2*c^3*d^8 - 2*A^2*a^2*b^2*c^5*d^6 + 42*B^2*a^2*b^2*c^3*d^8 - 36*B^2*a^2*b^2*c^5*d^6 + 8*B^2*a^2*b^2*c^7*d^4 - 2*A*B*a^4*c^2*d^9 + 8*A*B*b^4*c^2*d^9 - 32*A*B*b^4*c^4*d^7 + 30*A*B*b^4*c^6*d^5 - 8*A*B*b^4*c^8*d^3 - 8*A^2*a*b^3*c^2*d^9 + 4*A^2*a*b^3*c^4*d^7 + 4*A^2*a^2*b^2*c*d^10 - 4*A^2*a^3*b*c^2*d^9 + 16*B^2*a*b^3*c^2*d^9 - 64*B^2*a*b^3*c^4*d^7 + 60*B^2*a*b^3*c^6*d^5 - 16*B^2*a*b^3*c^8*d^3 - 8*B^2*a^2*b^2*c*d^10 - 8*B^2*a^3*b*c^2*d^9 + 4*B^2*a^3*b*c^4*d^7 - 8*A*B*a*b^3*c*d^10 + 4*A*B*a^3*b*c*d^10 + 48*A*B*a*b^3*c^3*d^8 - 40*A*B*a*b^3*c^5*d^6 + 8*A*B*a*b^3*c^7*d^4 + 8*A*B*a^3*b*c^3*d^8 - 4*A*B*a^3*b*c^5*d^6 - 20*A*B*a^2*b^2*c^2*d^9 + 4*A*B*a^2*b^2*c^4*d^7 + 4*A*B*a^2*b^2*c^6*d^5))/(d^10 - 2*c^2*d^8 + c^4*d^6) + ((a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*((32*(A*a^2*c^5*d^7 - A*a^2*c^3*d^9 - A*b^2*c*d^11 + A*b^2*c^3*d^9 + B*a^2*c^2*d^10 - B*a^2*c^4*d^8 + 2*B*b^2*c^2*d^10 - 3*B*b^2*c^4*d^8 + B*b^2*c^6*d^6 - 2*B*a*b*c*d^11 + 2*A*a*b*c^2*d^10 - 2*A*a*b*c^4*d^8 + 2*B*a*b*c^3*d^9))/(d^9 - 2*c^2*d^7 + c^4*d^5) - (32*tan(e/2 + (f*x)/2)*(2*A*a^2*c^2*d^11 - 2*B*a^2*c*d^12 - 2*A*a^2*c^4*d^9 + 4*A*b^2*c^2*d^11 - 6*A*b^2*c^4*d^9 + 2*A*b^2*c^6*d^7 + 2*B*a^2*c^3*d^10 - 6*B*b^2*c^3*d^10 + 10*B*b^2*c^5*d^8 - 4*B*b^2*c^7*d^6 - 4*A*a*b*c*d^12 + 4*A*a*b*c^3*d^10 + 8*B*a*b*c^2*d^11 - 12*B*a*b*c^4*d^9 + 4*B*a*b*c^6*d^7))/(d^10 - 2*c^2*d^8 + c^4*d^6) + (((32*(c^2*d^12 - 2*c^4*d^10 + c^6*d^8))/(d^9 - 2*c^2*d^7 + c^4*d^5) + (32*tan(e/2 + (f*x)/2)*(3*c*d^14 - 8*c^3*d^12 + 7*c^5*d^10 - 2*c^7*d^8))/(d^10 - 2*c^2*d^8 + c^4*d^6))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2))/(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3)))*(a*d - b*c)*(-(c + d)^3*(c - d)^3)^(1/2)*(2*A*b*d^3 + B*a*d^3 + 2*B*b*c^3 - A*a*c*d^2 - A*b*c^2*d - 3*B*b*c*d^2)*2i)/(f*(d^9 - 3*c^2*d^7 + 3*c^4*d^5 - c^6*d^3))","B"
353,0,-1,840,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2))/(a + b*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^(3/2))/(a + b*sin(e + f*x))^(3/2), x)","F"
354,0,-1,630,0.000000,"\text{Not used}","int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x))^(3/2),x)","\int \frac{\left(A+B\,\sin\left(e+f\,x\right)\right)\,\sqrt{c+d\,\sin\left(e+f\,x\right)}}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*sin(e + f*x))*(c + d*sin(e + f*x))^(1/2))/(a + b*sin(e + f*x))^(3/2), x)","F"
355,0,-1,417,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(1/2)), x)","F"
356,0,-1,544,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(3/2)), x)","F"
357,0,-1,858,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2)),x)","\int \frac{A+B\,\sin\left(e+f\,x\right)}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^{3/2}\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x))/((a + b*sin(e + f*x))^(3/2)*(c + d*sin(e + f*x))^(5/2)), x)","F"
358,0,-1,38,0.000000,"\text{Not used}","int((A + B*sin(e + f*x))*(a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int \left(A+B\,\sin\left(e+f\,x\right)\right)\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",0,"int((A + B*sin(e + f*x))*(a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"