1,1,35,36,0.525555,"\text{Not used}","int(sin(x)^3*(a*cos(x) + b*sin(x)),x)","\frac{a\,{\cos\left(x\right)}^4}{4}+\frac{b\,\sin\left(x\right)\,{\cos\left(x\right)}^3}{4}-\frac{a\,{\cos\left(x\right)}^2}{2}-\frac{5\,b\,\sin\left(x\right)\,\cos\left(x\right)}{8}+\frac{3\,b\,x}{8}","Not used",1,"(3*b*x)/8 - (a*cos(x)^2)/2 + (a*cos(x)^4)/4 - (5*b*cos(x)*sin(x))/8 + (b*cos(x)^3*sin(x))/4","B"
2,1,32,24,0.453855,"\text{Not used}","int(sin(x)^2*(a*cos(x) + b*sin(x)),x)","-\frac{4\,\left(-2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+b\right)}{3\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}^3}","Not used",1,"-(4*(b - 2*a*tan(x/2)^3 + 3*b*tan(x/2)^2))/(3*(tan(x/2)^2 + 1)^3)","B"
3,1,19,25,0.412290,"\text{Not used}","int(sin(x)*(a*cos(x) + b*sin(x)),x)","\frac{a\,{\sin\left(x\right)}^2}{2}-\frac{b\,\cos\left(x\right)\,\sin\left(x\right)}{2}+\frac{b\,x}{2}","Not used",1,"(a*sin(x)^2)/2 + (b*x)/2 - (b*cos(x)*sin(x))/2","B"
4,1,10,10,0.399003,"\text{Not used}","int(a*cos(x) + b*sin(x),x)","a\,\sin\left(x\right)-b\,\cos\left(x\right)","Not used",1,"a*sin(x) - b*cos(x)","B"
5,1,54,9,0.540288,"\text{Not used}","int((a*cos(x) + b*sin(x))/sin(x),x)","a\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-a\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)-a\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)-b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,1{}\mathrm{i}+b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"a*log(tan(x/2)) - a*log(tan(x/2) - 1i) - a*log(tan(x/2) + 1i) - b*log(tan(x/2) - 1i)*1i + b*log(tan(x/2) + 1i)*1i","B"
6,1,24,12,0.396849,"\text{Not used}","int((a*cos(x) + b*sin(x))/sin(x)^2,x)","b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\frac{a}{2\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}","Not used",1,"b*log(tan(x/2)) - a/(2*tan(x/2)) - (a*tan(x/2))/2","B"
7,1,14,15,0.409313,"\text{Not used}","int((a*cos(x) + b*sin(x))/sin(x)^3,x)","-\frac{a+b\,\sin\left(2\,x\right)}{2\,{\sin\left(x\right)}^2}","Not used",1,"-(a + b*sin(2*x))/(2*sin(x)^2)","B"
8,1,3512,91,7.500753,"\text{Not used}","int(sin(x)^3/(a*cos(x) + b*sin(x)),x)","\frac{4\,a^3\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2+b^2}-\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^2+b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{a^3\,\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{4\,a^3\,\left(\frac{b\,\left(\frac{8\,\left(-8\,a^{10}-8\,a^8\,b^2+12\,a^6\,b^4+16\,a^4\,b^6+4\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2+b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{16\,a^3\,b\,\left(3\,a^2+b^2\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{b\,\left(3\,a^2+b^2\right)\,\left(\frac{8\,\left(21\,a^7\,b^2+32\,a^5\,b^4+13\,a^3\,b^6+2\,a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a^3\,\left(\frac{8\,\left(-8\,a^{10}-8\,a^8\,b^2+12\,a^6\,b^4+16\,a^4\,b^6+4\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{b^3\,{\left(3\,a^2+b^2\right)}^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(16\,a^8-73\,a^6\,b^2-13\,a^4\,b^4+5\,a^2\,b^6+b^8\right)}{{\left(16\,a^8+25\,a^6\,b^2+15\,a^4\,b^4+7\,a^2\,b^6+b^8\right)}^2}+\frac{2\,a\,b\,\left(-28\,a^6+17\,a^4\,b^2+10\,a^2\,b^4+b^6\right)\,\left(\frac{8\,\left(8\,a^8+9\,a^6\,b^2+2\,a^4\,b^4\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a^3\,\left(\frac{8\,\left(21\,a^7\,b^2+32\,a^5\,b^4+13\,a^3\,b^6+2\,a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a^3\,\left(\frac{8\,\left(-8\,a^{10}-8\,a^8\,b^2+12\,a^6\,b^4+16\,a^4\,b^6+4\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{b\,\left(3\,a^2+b^2\right)\,\left(\frac{b\,\left(\frac{8\,\left(-8\,a^{10}-8\,a^8\,b^2+12\,a^6\,b^4+16\,a^4\,b^6+4\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2+b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{16\,a^3\,b\,\left(3\,a^2+b^2\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{8\,a^3\,b^2\,{\left(3\,a^2+b^2\right)}^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{{\left(16\,a^8+25\,a^6\,b^2+15\,a^4\,b^4+7\,a^2\,b^6+b^8\right)}^2}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{12\,a^3\,b+4\,a\,b^3}-\frac{\left(\frac{4\,a^3\,\left(\frac{b\,\left(3\,a^2+b^2\right)\,\left(\frac{8\,\left(-10\,a^9\,b-16\,a^7\,b^3+8\,a^3\,b^7+2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a^3\,b\,\left(3\,a^2+b^2\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{b\,\left(\frac{8\,\left(a^6\,b^3+2\,a^4\,b^5+a^2\,b^7\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a^3\,\left(\frac{8\,\left(-10\,a^9\,b-16\,a^7\,b^3+8\,a^3\,b^7+2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)\,\left(3\,a^2+b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b^3\,{\left(3\,a^2+b^2\right)}^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(16\,a^8-73\,a^6\,b^2-13\,a^4\,b^4+5\,a^2\,b^6+b^8\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(12\,a^3\,b+4\,a\,b^3\right)\,{\left(16\,a^8+25\,a^6\,b^2+15\,a^4\,b^4+7\,a^2\,b^6+b^8\right)}^2}+\frac{2\,a\,b\,\left(-28\,a^6+17\,a^4\,b^2+10\,a^2\,b^4+b^6\right)\,\left(\frac{8\,\left(2\,a^7\,b+a^5\,b^3\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a^3\,\left(\frac{8\,\left(a^6\,b^3+2\,a^4\,b^5+a^2\,b^7\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a^3\,\left(\frac{8\,\left(-10\,a^9\,b-16\,a^7\,b^3+8\,a^3\,b^7+2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{b\,\left(\frac{b\,\left(3\,a^2+b^2\right)\,\left(\frac{8\,\left(-10\,a^9\,b-16\,a^7\,b^3+8\,a^3\,b^7+2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a^3\,b\,\left(3\,a^2+b^2\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2+b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{8\,a^3\,b^2\,{\left(3\,a^2+b^2\right)}^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(12\,a^3\,b+4\,a\,b^3\right)\,{\left(16\,a^8+25\,a^6\,b^2+15\,a^4\,b^4+7\,a^2\,b^6+b^8\right)}^2}\right)\,\left(3\,a^2+b^2\right)}{a^4+2\,a^2\,b^2+b^4}","Not used",1,"(4*a^3*log(1/(cos(x) + 1)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - ((b*tan(x/2))/(a^2 + b^2) + (2*a*tan(x/2)^2)/(a^2 + b^2) - (b*tan(x/2)^3)/(a^2 + b^2))/(2*tan(x/2)^2 + tan(x/2)^4 + 1) - (a^3*log(a + 2*b*tan(x/2) - a*tan(x/2)^2))/(a^4 + b^4 + 2*a^2*b^2) - (b*atan((tan(x/2)*((((4*a^3*((b*((8*(4*a^2*b^8 - 8*a^10 + 16*a^4*b^6 + 12*a^6*b^4 - 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 + b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (16*a^3*b*(3*a^2 + b^2)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (b*(3*a^2 + b^2)*((8*(2*a*b^8 + 13*a^3*b^6 + 32*a^5*b^4 + 21*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a^3*((8*(4*a^2*b^8 - 8*a^10 + 16*a^4*b^6 + 12*a^6*b^4 - 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (b^3*(3*a^2 + b^2)^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(16*a^8 + b^8 + 5*a^2*b^6 - 13*a^4*b^4 - 73*a^6*b^2))/(16*a^8 + b^8 + 7*a^2*b^6 + 15*a^4*b^4 + 25*a^6*b^2)^2 + (2*a*b*(b^6 - 28*a^6 + 10*a^2*b^4 + 17*a^4*b^2)*((8*(8*a^8 + 2*a^4*b^4 + 9*a^6*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a^3*((8*(2*a*b^8 + 13*a^3*b^6 + 32*a^5*b^4 + 21*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a^3*((8*(4*a^2*b^8 - 8*a^10 + 16*a^4*b^6 + 12*a^6*b^4 - 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (b*(3*a^2 + b^2)*((b*((8*(4*a^2*b^8 - 8*a^10 + 16*a^4*b^6 + 12*a^6*b^4 - 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 + b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (16*a^3*b*(3*a^2 + b^2)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (8*a^3*b^2*(3*a^2 + b^2)^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(16*a^8 + b^8 + 7*a^2*b^6 + 15*a^4*b^4 + 25*a^6*b^2)^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/(4*a*b^3 + 12*a^3*b) - (((4*a^3*((b*(3*a^2 + b^2)*((8*(2*a*b^9 - 10*a^9*b + 8*a^3*b^7 - 16*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a^3*b*(3*a^2 + b^2)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (b*((8*(a^2*b^7 + 2*a^4*b^5 + a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a^3*((8*(2*a*b^9 - 10*a^9*b + 8*a^3*b^7 - 16*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2))*(3*a^2 + b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (b^3*(3*a^2 + b^2)^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(16*a^8 + b^8 + 5*a^2*b^6 - 13*a^4*b^4 - 73*a^6*b^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a*b^3 + 12*a^3*b)*(16*a^8 + b^8 + 7*a^2*b^6 + 15*a^4*b^4 + 25*a^6*b^2)^2) + (2*a*b*(b^6 - 28*a^6 + 10*a^2*b^4 + 17*a^4*b^2)*((8*(2*a^7*b + a^5*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a^3*((8*(a^2*b^7 + 2*a^4*b^5 + a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a^3*((8*(2*a*b^9 - 10*a^9*b + 8*a^3*b^7 - 16*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (b*((b*(3*a^2 + b^2)*((8*(2*a*b^9 - 10*a^9*b + 8*a^3*b^7 - 16*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a^3*b*(3*a^2 + b^2)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 + b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (8*a^3*b^2*(3*a^2 + b^2)^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a*b^3 + 12*a^3*b)*(16*a^8 + b^8 + 7*a^2*b^6 + 15*a^4*b^4 + 25*a^6*b^2)^2))*(3*a^2 + b^2))/(a^4 + b^4 + 2*a^2*b^2)","B"
9,1,94,68,0.581195,"\text{Not used}","int(sin(x)^2/(a*cos(x) + b*sin(x)),x)","-\frac{\frac{2\,b}{a^2+b^2}+\frac{2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{2\,a^2\,\mathrm{atanh}\left(\frac{2\,a^2\,b+2\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+b^2\right)}{2\,{\left(a^2+b^2\right)}^{3/2}}\right)}{{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"- ((2*b)/(a^2 + b^2) + (2*a*tan(x/2))/(a^2 + b^2))/(tan(x/2)^2 + 1) - (2*a^2*atanh((2*a^2*b + 2*b^3 - 2*a*tan(x/2)*(a^2 + b^2))/(2*(a^2 + b^2)^(3/2))))/(a^2 + b^2)^(3/2)","B"
10,1,970,35,2.141135,"\text{Not used}","int(sin(x)/(a*cos(x) + b*sin(x)),x)","-\frac{a\,\ln\left(a\,\cos\left(x\right)+b\,\sin\left(x\right)\right)}{a^2+b^2}-\frac{2\,b\,\mathrm{atan}\left(\frac{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(4\,a^4-13\,a^2\,b^2+b^4\right)\,\left(\frac{b\,\left(64\,a\,b^2+\frac{a\,\left(32\,a^2\,b^2-64\,a^4+\frac{a\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}-\frac{b^3\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^3}+\frac{a\,\left(\frac{b\,\left(32\,a^2\,b^2-64\,a^4+\frac{a\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}\right)}{{\left(4\,a^4+5\,a^2\,b^2+b^4\right)}^2}-\frac{6\,a\,b\,\left(2\,a^2-b^2\right)\,\left(64\,a^2+\frac{a\,\left(64\,a\,b^2+\frac{a\,\left(32\,a^2\,b^2-64\,a^4+\frac{a\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}-\frac{b\,\left(\frac{b\,\left(32\,a^2\,b^2-64\,a^4+\frac{a\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}-\frac{a\,b^2\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^3}\right)}{{\left(4\,a^4+5\,a^2\,b^2+b^4\right)}^2}\right)-\frac{\left(4\,a^4-13\,a^2\,b^2+b^4\right)\,\left(\frac{b\,\left(32\,a^2\,b-\frac{a\,\left(64\,a^3\,b-32\,a\,b^3+\frac{a\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{b^3\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^3}-\frac{a\,\left(\frac{b\,\left(64\,a^3\,b-32\,a\,b^3+\frac{a\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}\right)}{{\left(4\,a^4+5\,a^2\,b^2+b^4\right)}^2}+\frac{6\,a\,b\,\left(2\,a^2-b^2\right)\,\left(\frac{a\,\left(32\,a^2\,b-\frac{a\,\left(64\,a^3\,b-32\,a\,b^3+\frac{a\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{b\,\left(\frac{b\,\left(64\,a^3\,b-32\,a\,b^3+\frac{a\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}+\frac{a\,b^2\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^3}\right)}{{\left(4\,a^4+5\,a^2\,b^2+b^4\right)}^2}\right)}{32\,a\,b}\right)}{a^2+b^2}","Not used",1,"- (a*log(a*cos(x) + b*sin(x)))/(a^2 + b^2) - (2*b*atan(((a^4 + b^4 + 2*a^2*b^2)*(tan(x/2)*(((4*a^4 + b^4 - 13*a^2*b^2)*((b*(64*a*b^2 + (a*(32*a^2*b^2 - 64*a^4 + (a*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) - (b^3*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^3 + (a*((b*(32*a^2*b^2 - 64*a^4 + (a*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2) + (a*b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^2))/(a^2 + b^2)))/(4*a^4 + b^4 + 5*a^2*b^2)^2 - (6*a*b*(2*a^2 - b^2)*(64*a^2 + (a*(64*a*b^2 + (a*(32*a^2*b^2 - 64*a^4 + (a*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) - (b*((b*(32*a^2*b^2 - 64*a^4 + (a*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2) + (a*b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^2))/(a^2 + b^2) - (a*b^2*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^3))/(4*a^4 + b^4 + 5*a^2*b^2)^2) - ((4*a^4 + b^4 - 13*a^2*b^2)*((b*(32*a^2*b - (a*(64*a^3*b - 32*a*b^3 + (a*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) + (b^3*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^3 - (a*((b*(64*a^3*b - 32*a*b^3 + (a*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2) + (a*b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^2))/(a^2 + b^2)))/(4*a^4 + b^4 + 5*a^2*b^2)^2 + (6*a*b*(2*a^2 - b^2)*((a*(32*a^2*b - (a*(64*a^3*b - 32*a*b^3 + (a*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) + (b*((b*(64*a^3*b - 32*a*b^3 + (a*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2) + (a*b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^2))/(a^2 + b^2) + (a*b^2*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^3))/(4*a^4 + b^4 + 5*a^2*b^2)^2))/(32*a*b)))/(a^2 + b^2)","B"
11,1,31,36,1.052497,"\text{Not used}","int(1/(a*cos(x) + b*sin(x)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{b-a\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}","Not used",1,"-(2*atanh((b - a*tan(x/2))/(a^2 + b^2)^(1/2)))/(a^2 + b^2)^(1/2)","B"
12,1,32,23,0.575319,"\text{Not used}","int(1/(sin(x)*(a*cos(x) + b*sin(x))),x)","-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"-(log(a + 2*b*tan(x/2) - a*tan(x/2)^2) - log(tan(x/2)))/a","B"
13,1,170,55,0.678298,"\text{Not used}","int(1/(sin(x)^2*(a*cos(x) + b*sin(x))),x)","\frac{2\,\mathrm{atanh}\left(\frac{a^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}+4\,b^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}+3\,a^2\,b\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}+2\,a\,b^2\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}}{\sin\left(\frac{x}{2}\right)\,a^4+2\,\cos\left(\frac{x}{2}\right)\,a^3\,b+5\,\sin\left(\frac{x}{2}\right)\,a^2\,b^2+2\,\cos\left(\frac{x}{2}\right)\,a\,b^3+4\,\sin\left(\frac{x}{2}\right)\,b^4}\right)\,\sqrt{a^2+b^2}}{a^2}-\frac{1}{a\,\sin\left(x\right)}-\frac{b\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{a^2}","Not used",1,"(2*atanh((a^3*cos(x/2)*(a^2 + b^2)^(1/2) + 4*b^3*sin(x/2)*(a^2 + b^2)^(1/2) + 3*a^2*b*sin(x/2)*(a^2 + b^2)^(1/2) + 2*a*b^2*cos(x/2)*(a^2 + b^2)^(1/2))/(a^4*sin(x/2) + 4*b^4*sin(x/2) + 5*a^2*b^2*sin(x/2) + 2*a*b^3*cos(x/2) + 2*a^3*b*cos(x/2)))*(a^2 + b^2)^(1/2))/a^2 - 1/(a*sin(x)) - (b*log(sin(x/2)/cos(x/2)))/a^2","B"
14,1,91,55,0.571066,"\text{Not used}","int(1/(sin(x)^3*(a*cos(x) + b*sin(x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^2+b^2\right)}{a^3}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(a^2+b^2\right)}{a^3}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}-\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^2}-\frac{\frac{a}{2}-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{4\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}","Not used",1,"(log(tan(x/2))*(a^2 + b^2))/a^3 - (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(a^2 + b^2))/a^3 - tan(x/2)^2/(8*a) - (b*tan(x/2))/(2*a^2) - (a/2 - 2*b*tan(x/2))/(4*a^2*tan(x/2)^2)","B"
15,1,224,107,0.835915,"\text{Not used}","int(sin(x)^3/(a*cos(x) + b*sin(x))^2,x)","-\frac{\frac{2\,\left(a\,b^2-2\,a^3\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2\,b-2\,b^3\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{6\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}-\frac{6\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^4+2\,a^2\,b^2+b^4}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{6\,a^2\,b\,\mathrm{atanh}\left(\frac{2\,a^4\,b+2\,b^5+4\,a^2\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{2\,{\left(a^2+b^2\right)}^{5/2}}\right)}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"- ((2*(a*b^2 - 2*a^3))/(a^4 + b^4 + 2*a^2*b^2) - (2*tan(x/2)*(a^2*b - 2*b^3))/(a^4 + b^4 + 2*a^2*b^2) + (6*a*b^2*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2) - (6*a^2*b*tan(x/2)^3)/(a^4 + b^4 + 2*a^2*b^2))/(a + 2*b*tan(x/2) - a*tan(x/2)^4 + 2*b*tan(x/2)^3) - (6*a^2*b*atanh((2*a^4*b + 2*b^5 + 4*a^2*b^3 - 2*a*tan(x/2)*(a^4 + b^4 + 2*a^2*b^2))/(2*(a^2 + b^2)^(5/2))))/(a^2 + b^2)^(5/2)","B"
16,1,626,64,7.063674,"\text{Not used}","int(sin(x)^2/(a*cos(x) + b*sin(x))^2,x)","\frac{a^3\,\sin\left(x\right)+a\,b^2\,\sin\left(x\right)-2\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\cos\left(x\right)+2\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)+2\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\cos\left(x\right)-2\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)+2\,a^2\,b\,\cos\left(x\right)\,\ln\left(\frac{1024\,a^{14}+26624\,a^{12}\,b^2+146432\,a^{10}\,b^4-348160\,a^8\,b^6+146432\,a^6\,b^8+26624\,a^4\,b^{10}+1024\,a^2\,b^{12}}{\frac{a^{16}}{2}+\frac{b^{16}}{2}+4\,a^2\,b^{14}+14\,a^4\,b^{12}+28\,a^6\,b^{10}+35\,a^8\,b^8+28\,a^{10}\,b^6+14\,a^{12}\,b^4+4\,a^{14}\,b^2+\frac{a^{16}\,\cos\left(x\right)}{2}+\frac{b^{16}\,\cos\left(x\right)}{2}+4\,a^2\,b^{14}\,\cos\left(x\right)+14\,a^4\,b^{12}\,\cos\left(x\right)+28\,a^6\,b^{10}\,\cos\left(x\right)+35\,a^8\,b^8\,\cos\left(x\right)+28\,a^{10}\,b^6\,\cos\left(x\right)+14\,a^{12}\,b^4\,\cos\left(x\right)+4\,a^{14}\,b^2\,\cos\left(x\right)}\right)+2\,a\,b^2\,\ln\left(\frac{1024\,a^{14}+26624\,a^{12}\,b^2+146432\,a^{10}\,b^4-348160\,a^8\,b^6+146432\,a^6\,b^8+26624\,a^4\,b^{10}+1024\,a^2\,b^{12}}{\frac{a^{16}}{2}+\frac{b^{16}}{2}+4\,a^2\,b^{14}+14\,a^4\,b^{12}+28\,a^6\,b^{10}+35\,a^8\,b^8+28\,a^{10}\,b^6+14\,a^{12}\,b^4+4\,a^{14}\,b^2+\frac{a^{16}\,\cos\left(x\right)}{2}+\frac{b^{16}\,\cos\left(x\right)}{2}+4\,a^2\,b^{14}\,\cos\left(x\right)+14\,a^4\,b^{12}\,\cos\left(x\right)+28\,a^6\,b^{10}\,\cos\left(x\right)+35\,a^8\,b^8\,\cos\left(x\right)+28\,a^{10}\,b^6\,\cos\left(x\right)+14\,a^{12}\,b^4\,\cos\left(x\right)+4\,a^{14}\,b^2\,\cos\left(x\right)}\right)\,\sin\left(x\right)-2\,a^2\,b\,\ln\left(\frac{a\,\cos\left(x\right)+b\,\sin\left(x\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)\,\cos\left(x\right)-2\,a\,b^2\,\ln\left(\frac{a\,\cos\left(x\right)+b\,\sin\left(x\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)\,\sin\left(x\right)}{\cos\left(x\right)\,a^5+\sin\left(x\right)\,a^4\,b+2\,\cos\left(x\right)\,a^3\,b^2+2\,\sin\left(x\right)\,a^2\,b^3+\cos\left(x\right)\,a\,b^4+\sin\left(x\right)\,b^5}","Not used",1,"(a^3*sin(x) + a*b^2*sin(x) - 2*a^3*atan(sin(x/2)/cos(x/2))*cos(x) + 2*b^3*atan(sin(x/2)/cos(x/2))*sin(x) + 2*a*b^2*atan(sin(x/2)/cos(x/2))*cos(x) - 2*a^2*b*atan(sin(x/2)/cos(x/2))*sin(x) + 2*a^2*b*cos(x)*log((1024*a^14 + 1024*a^2*b^12 + 26624*a^4*b^10 + 146432*a^6*b^8 - 348160*a^8*b^6 + 146432*a^10*b^4 + 26624*a^12*b^2)/(a^16/2 + b^16/2 + 4*a^2*b^14 + 14*a^4*b^12 + 28*a^6*b^10 + 35*a^8*b^8 + 28*a^10*b^6 + 14*a^12*b^4 + 4*a^14*b^2 + (a^16*cos(x))/2 + (b^16*cos(x))/2 + 4*a^2*b^14*cos(x) + 14*a^4*b^12*cos(x) + 28*a^6*b^10*cos(x) + 35*a^8*b^8*cos(x) + 28*a^10*b^6*cos(x) + 14*a^12*b^4*cos(x) + 4*a^14*b^2*cos(x))) + 2*a*b^2*log((1024*a^14 + 1024*a^2*b^12 + 26624*a^4*b^10 + 146432*a^6*b^8 - 348160*a^8*b^6 + 146432*a^10*b^4 + 26624*a^12*b^2)/(a^16/2 + b^16/2 + 4*a^2*b^14 + 14*a^4*b^12 + 28*a^6*b^10 + 35*a^8*b^8 + 28*a^10*b^6 + 14*a^12*b^4 + 4*a^14*b^2 + (a^16*cos(x))/2 + (b^16*cos(x))/2 + 4*a^2*b^14*cos(x) + 14*a^4*b^12*cos(x) + 28*a^6*b^10*cos(x) + 35*a^8*b^8*cos(x) + 28*a^10*b^6*cos(x) + 14*a^12*b^4*cos(x) + 4*a^14*b^2*cos(x)))*sin(x) - 2*a^2*b*log((a*cos(x) + b*sin(x))/cos(x/2)^2)*cos(x) - 2*a*b^2*log((a*cos(x) + b*sin(x))/cos(x/2)^2)*sin(x))/(b^5*sin(x) + a^5*cos(x) + a*b^4*cos(x) + a^4*b*sin(x) + 2*a^3*b^2*cos(x) + 2*a^2*b^3*sin(x))","B"
17,1,86,60,0.611796,"\text{Not used}","int(sin(x)/(a*cos(x) + b*sin(x))^2,x)","\frac{\frac{2\,a}{a^2+b^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{2\,b\,\mathrm{atanh}\left(\frac{2\,b-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,\sqrt{a^2+b^2}}\right)}{{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"((2*a)/(a^2 + b^2) + (2*b*tan(x/2))/(a^2 + b^2))/(a + 2*b*tan(x/2) - a*tan(x/2)^2) - (2*b*atanh((2*b - 2*a*tan(x/2))/(2*(a^2 + b^2)^(1/2))))/(a^2 + b^2)^(3/2)","B"
18,1,29,17,0.431354,"\text{Not used}","int(1/(a*cos(x) + b*sin(x))^2,x)","\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{a\,\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}","Not used",1,"(2*tan(x/2))/(a*(a + 2*b*tan(x/2) - a*tan(x/2)^2))","B"
19,1,492,63,0.812426,"\text{Not used}","int(1/(sin(x)*(a*cos(x) + b*sin(x))^2),x)","\frac{\frac{2}{a}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^2}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{a^2+b^2}\,\left(4\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+4\,b^2\right)}{a}+\frac{b\,\left(2\,a^2\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^4+4\,a^2\,b^2\right)}{a}\right)\,\sqrt{a^2+b^2}}{a^4+a^2\,b^2}\right)\,1{}\mathrm{i}}{a^4+a^2\,b^2}+\frac{b\,\sqrt{a^2+b^2}\,\left(4\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+4\,b^2\right)}{a}-\frac{b\,\left(2\,a^2\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^4+4\,a^2\,b^2\right)}{a}\right)\,\sqrt{a^2+b^2}}{a^4+a^2\,b^2}\right)\,1{}\mathrm{i}}{a^4+a^2\,b^2}}{\frac{4\,b}{a^2}+\frac{b\,\sqrt{a^2+b^2}\,\left(4\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+4\,b^2\right)}{a}+\frac{b\,\left(2\,a^2\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^4+4\,a^2\,b^2\right)}{a}\right)\,\sqrt{a^2+b^2}}{a^4+a^2\,b^2}\right)}{a^4+a^2\,b^2}-\frac{b\,\sqrt{a^2+b^2}\,\left(4\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+4\,b^2\right)}{a}-\frac{b\,\left(2\,a^2\,b+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^4+4\,a^2\,b^2\right)}{a}\right)\,\sqrt{a^2+b^2}}{a^4+a^2\,b^2}\right)}{a^4+a^2\,b^2}}\right)\,\sqrt{a^2+b^2}\,2{}\mathrm{i}}{a^4+a^2\,b^2}","Not used",1,"(2/a + (2*b*tan(x/2))/a^2)/(a + 2*b*tan(x/2) - a*tan(x/2)^2) + log(tan(x/2))/a^2 + (b*atan(((b*(a^2 + b^2)^(1/2)*(4*b + (2*tan(x/2)*(a^2 + 4*b^2))/a + (b*(2*a^2*b + (2*tan(x/2)*(3*a^4 + 4*a^2*b^2))/a)*(a^2 + b^2)^(1/2))/(a^4 + a^2*b^2))*1i)/(a^4 + a^2*b^2) + (b*(a^2 + b^2)^(1/2)*(4*b + (2*tan(x/2)*(a^2 + 4*b^2))/a - (b*(2*a^2*b + (2*tan(x/2)*(3*a^4 + 4*a^2*b^2))/a)*(a^2 + b^2)^(1/2))/(a^4 + a^2*b^2))*1i)/(a^4 + a^2*b^2))/((4*b)/a^2 + (b*(a^2 + b^2)^(1/2)*(4*b + (2*tan(x/2)*(a^2 + 4*b^2))/a + (b*(2*a^2*b + (2*tan(x/2)*(3*a^4 + 4*a^2*b^2))/a)*(a^2 + b^2)^(1/2))/(a^4 + a^2*b^2)))/(a^4 + a^2*b^2) - (b*(a^2 + b^2)^(1/2)*(4*b + (2*tan(x/2)*(a^2 + 4*b^2))/a - (b*(2*a^2*b + (2*tan(x/2)*(3*a^4 + 4*a^2*b^2))/a)*(a^2 + b^2)^(1/2))/(a^4 + a^2*b^2)))/(a^4 + a^2*b^2)))*(a^2 + b^2)^(1/2)*2i)/(a^4 + a^2*b^2)","B"
20,1,114,49,0.620893,"\text{Not used}","int(1/(sin(x)^2*(a*cos(x) + b*sin(x))^2),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^2}-\frac{a+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(5\,a^2+4\,b^2\right)}{a}}{-2\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)+4\,b\,a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}+\frac{2\,b\,\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^3}-\frac{2\,b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}","Not used",1,"tan(x/2)/(2*a^2) - (a + 2*b*tan(x/2) - (tan(x/2)^2*(5*a^2 + 4*b^2))/a)/(2*a^3*tan(x/2) - 2*a^3*tan(x/2)^3 + 4*a^2*b*tan(x/2)^2) + (2*b*log(a + 2*b*tan(x/2) - a*tan(x/2)^2))/a^3 - (2*b*log(tan(x/2)))/a^3","B"
21,1,511,118,0.743600,"\text{Not used}","int(1/(sin(x)^3*(a*cos(x) + b*sin(x))^2),x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(\frac{17\,a^2}{2}+16\,b^2\right)-\frac{a^2}{2}+3\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2\,b+2\,b^3\right)}{a}}{-4\,a^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^2}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(3\,a^2+6\,b^2\right)}{2\,a^4}+\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^3}-\frac{6\,b\,\mathrm{atanh}\left(\frac{54\,b^2\,\sqrt{a^2+b^2}}{18\,a^2\,b+90\,b^3+\frac{72\,b^5}{a^2}+\frac{216\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+\frac{144\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^3}+72\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}+\frac{72\,b^4\,\sqrt{a^2+b^2}}{18\,a^4\,b+72\,b^5+90\,a^2\,b^3+72\,a^3\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{144\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a}+216\,a\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}+\frac{144\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}}{216\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)+90\,a\,b^3+18\,a^3\,b+\frac{72\,b^5}{a}+72\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{144\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}}+\frac{144\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}}{18\,a^5\,b+72\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^4\,b^2+90\,a^3\,b^3+216\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^4+72\,a\,b^5+144\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^6}+\frac{18\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}}{18\,a\,b+72\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{90\,b^3}{a}+\frac{72\,b^5}{a^3}+\frac{216\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}+\frac{144\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4}}\right)\,\sqrt{a^2+b^2}}{a^4}","Not used",1,"(tan(x/2)^2*((17*a^2)/2 + 16*b^2) - a^2/2 + 3*a*b*tan(x/2) + (4*tan(x/2)^3*(a^2*b + 2*b^3))/a)/(4*a^4*tan(x/2)^2 - 4*a^4*tan(x/2)^4 + 8*a^3*b*tan(x/2)^3) + tan(x/2)^2/(8*a^2) + (log(tan(x/2))*(3*a^2 + 6*b^2))/(2*a^4) + (b*tan(x/2))/a^3 - (6*b*atanh((54*b^2*(a^2 + b^2)^(1/2))/(18*a^2*b + 90*b^3 + (72*b^5)/a^2 + (216*b^4*tan(x/2))/a + (144*b^6*tan(x/2))/a^3 + 72*a*b^2*tan(x/2)) + (72*b^4*(a^2 + b^2)^(1/2))/(18*a^4*b + 72*b^5 + 90*a^2*b^3 + 72*a^3*b^2*tan(x/2) + (144*b^6*tan(x/2))/a + 216*a*b^4*tan(x/2)) + (144*b^3*tan(x/2)*(a^2 + b^2)^(1/2))/(216*b^4*tan(x/2) + 90*a*b^3 + 18*a^3*b + (72*b^5)/a + 72*a^2*b^2*tan(x/2) + (144*b^6*tan(x/2))/a^2) + (144*b^5*tan(x/2)*(a^2 + b^2)^(1/2))/(144*b^6*tan(x/2) + 72*a*b^5 + 18*a^5*b + 90*a^3*b^3 + 216*a^2*b^4*tan(x/2) + 72*a^4*b^2*tan(x/2)) + (18*b*tan(x/2)*(a^2 + b^2)^(1/2))/(18*a*b + 72*b^2*tan(x/2) + (90*b^3)/a + (72*b^5)/a^3 + (216*b^4*tan(x/2))/a^2 + (144*b^6*tan(x/2))/a^4))*(a^2 + b^2)^(1/2))/a^4","B"
22,1,5324,98,8.599099,"\text{Not used}","int(sin(x)^3/(a*cos(x) + b*sin(x))^3,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^3+5\,a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^4+2\,a^2\,b^2+b^4}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4+2\,a^2\,b^2+b^4}}{a^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(3\,a\,b^2-a^3\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(6\,a\,b^2-2\,a^3\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{2\,b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{b\,\left(\frac{32\,\left(-2\,a^{14}+3\,a^{12}\,b^2+33\,a^{10}\,b^4+62\,a^8\,b^6+48\,a^6\,b^8+15\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,b\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{b\,\left(\frac{32\,\left(18\,a^9\,b^2+8\,a^7\,b^4-36\,a^5\,b^6-24\,a^3\,b^8+2\,a\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{32\,\left(-2\,a^{14}+3\,a^{12}\,b^2+33\,a^{10}\,b^4+62\,a^8\,b^6+48\,a^6\,b^8+15\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,b^3\,{\left(3\,a^2-b^2\right)}^3\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(4\,a^8-61\,a^6\,b^2+155\,a^4\,b^4-67\,a^2\,b^6+b^8\right)}{{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}+\frac{2\,a\,b\,\left(10\,a^6-59\,a^4\,b^2+68\,a^2\,b^4-7\,b^6\right)\,\left(\frac{32\,\left(2\,a^8-6\,a^6\,b^2+2\,a^4\,b^4-6\,a^2\,b^6\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{32\,\left(18\,a^9\,b^2+8\,a^7\,b^4-36\,a^5\,b^6-24\,a^3\,b^8+2\,a\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{32\,\left(-2\,a^{14}+3\,a^{12}\,b^2+33\,a^{10}\,b^4+62\,a^8\,b^6+48\,a^6\,b^8+15\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{b\,\left(\frac{b\,\left(\frac{32\,\left(-2\,a^{14}+3\,a^{12}\,b^2+33\,a^{10}\,b^4+62\,a^8\,b^6+48\,a^6\,b^8+15\,a^4\,b^{10}+a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,b\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,b^2\,\left(6\,a\,b^2-2\,a^3\right)\,{\left(3\,a^2-b^2\right)}^2\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{32\,a\,b^3-96\,a^3\,b}+\frac{\left(\frac{b\,\left(\frac{32\,\left(-3\,a^{10}\,b-4\,a^8\,b^3+6\,a^6\,b^5+12\,a^4\,b^7+5\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{32\,\left(-4\,a^{13}\,b-9\,a^{11}\,b^3+3\,a^9\,b^5+22\,a^7\,b^7+18\,a^5\,b^9+3\,a^3\,b^{11}-a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{b\,\left(\frac{32\,\left(-4\,a^{13}\,b-9\,a^{11}\,b^3+3\,a^9\,b^5+22\,a^7\,b^7+18\,a^5\,b^9+3\,a^3\,b^{11}-a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,b\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{32\,b^3\,{\left(3\,a^2-b^2\right)}^3\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(4\,a^8-61\,a^6\,b^2+155\,a^4\,b^4-67\,a^2\,b^6+b^8\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(32\,a\,b^3-96\,a^3\,b\right)\,{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}+\frac{2\,a\,b\,\left(\frac{32\,\left(2\,a^7\,b-8\,a^5\,b^3+6\,a^3\,b^5\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{32\,\left(-3\,a^{10}\,b-4\,a^8\,b^3+6\,a^6\,b^5+12\,a^4\,b^7+5\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a\,b^2-2\,a^3\right)\,\left(\frac{32\,\left(-4\,a^{13}\,b-9\,a^{11}\,b^3+3\,a^9\,b^5+22\,a^7\,b^7+18\,a^5\,b^9+3\,a^3\,b^{11}-a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{b\,\left(\frac{b\,\left(\frac{32\,\left(-4\,a^{13}\,b-9\,a^{11}\,b^3+3\,a^9\,b^5+22\,a^7\,b^7+18\,a^5\,b^9+3\,a^3\,b^{11}-a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,b\,\left(6\,a\,b^2-2\,a^3\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,b^2\,\left(6\,a\,b^2-2\,a^3\right)\,{\left(3\,a^2-b^2\right)}^2\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(10\,a^6-59\,a^4\,b^2+68\,a^2\,b^4-7\,b^6\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(32\,a\,b^3-96\,a^3\,b\right)\,{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}","Not used",1,"((2*tan(x/2)^2*(5*a*b^2 + a^3))/(a^4 + b^4 + 2*a^2*b^2) - (4*a^2*b*tan(x/2)^3)/(a^4 + b^4 + 2*a^2*b^2) + (4*a^2*b*tan(x/2))/(a^4 + b^4 + 2*a^2*b^2))/(a^2 - tan(x/2)^2*(2*a^2 - 4*b^2) + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) - 4*a*b*tan(x/2)^3) - (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(3*a*b^2 - a^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (log(1/(cos(x) + 1))*(6*a*b^2 - 2*a^3))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (2*b*atan((tan(x/2)*(((((6*a*b^2 - 2*a^3)*((b*((32*(a^2*b^12 - 2*a^14 + 15*a^4*b^10 + 48*a^6*b^8 + 62*a^8*b^6 + 33*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(6*a*b^2 - 2*a^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*b*(6*a*b^2 - 2*a^3)*(3*a^2 - b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (b*((32*(2*a*b^10 - 24*a^3*b^8 - 36*a^5*b^6 + 8*a^7*b^4 + 18*a^9*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a*b^2 - 2*a^3)*((32*(a^2*b^12 - 2*a^14 + 15*a^4*b^10 + 48*a^6*b^8 + 62*a^8*b^6 + 33*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(6*a*b^2 - 2*a^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*b^3*(3*a^2 - b^2)^3*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(4*a^8 + b^8 - 67*a^2*b^6 + 155*a^4*b^4 - 61*a^6*b^2))/(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2 + (2*a*b*(10*a^6 - 7*b^6 + 68*a^2*b^4 - 59*a^4*b^2)*((32*(2*a^8 - 6*a^2*b^6 + 2*a^4*b^4 - 6*a^6*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a*b^2 - 2*a^3)*((32*(2*a*b^10 - 24*a^3*b^8 - 36*a^5*b^6 + 8*a^7*b^4 + 18*a^9*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a*b^2 - 2*a^3)*((32*(a^2*b^12 - 2*a^14 + 15*a^4*b^10 + 48*a^6*b^8 + 62*a^8*b^6 + 33*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(6*a*b^2 - 2*a^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (b*((b*((32*(a^2*b^12 - 2*a^14 + 15*a^4*b^10 + 48*a^6*b^8 + 62*a^8*b^6 + 33*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(6*a*b^2 - 2*a^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*b*(6*a*b^2 - 2*a^3)*(3*a^2 - b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*b^2*(6*a*b^2 - 2*a^3)*(3*a^2 - b^2)^2*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/(32*a*b^3 - 96*a^3*b) + (((b*((32*(5*a^2*b^9 - 3*a^10*b + 12*a^4*b^7 + 6*a^6*b^5 - 4*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a*b^2 - 2*a^3)*((32*(3*a^3*b^11 - 4*a^13*b - a*b^13 + 18*a^5*b^9 + 22*a^7*b^7 + 3*a^9*b^5 - 9*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a*b^2 - 2*a^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - ((6*a*b^2 - 2*a^3)*((b*((32*(3*a^3*b^11 - 4*a^13*b - a*b^13 + 18*a^5*b^9 + 22*a^7*b^7 + 3*a^9*b^5 - 9*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a*b^2 - 2*a^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*b*(6*a*b^2 - 2*a^3)*(3*a^2 - b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (32*b^3*(3*a^2 - b^2)^3*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(4*a^8 + b^8 - 67*a^2*b^6 + 155*a^4*b^4 - 61*a^6*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((32*a*b^3 - 96*a^3*b)*(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2) + (2*a*b*((32*(2*a^7*b + 6*a^3*b^5 - 8*a^5*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((6*a*b^2 - 2*a^3)*((32*(5*a^2*b^9 - 3*a^10*b + 12*a^4*b^7 + 6*a^6*b^5 - 4*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a*b^2 - 2*a^3)*((32*(3*a^3*b^11 - 4*a^13*b - a*b^13 + 18*a^5*b^9 + 22*a^7*b^7 + 3*a^9*b^5 - 9*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a*b^2 - 2*a^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (b*((b*((32*(3*a^3*b^11 - 4*a^13*b - a*b^13 + 18*a^5*b^9 + 22*a^7*b^7 + 3*a^9*b^5 - 9*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a*b^2 - 2*a^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*b*(6*a*b^2 - 2*a^3)*(3*a^2 - b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*b^2*(6*a*b^2 - 2*a^3)*(3*a^2 - b^2)^2*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(10*a^6 - 7*b^6 + 68*a^2*b^4 - 59*a^4*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((32*a*b^3 - 96*a^3*b)*(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)","B"
23,1,263,92,0.797130,"\text{Not used}","int(sin(x)^2/(a*cos(x) + b*sin(x))^3,x)","\frac{\frac{3\,a^2\,b}{a^4+2\,a^2\,b^2+b^4}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+10\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2-2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2-2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}}{a^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{\mathrm{atanh}\left(\frac{2\,a^4\,b+4\,a^2\,b^3+2\,b^5}{2\,{\left(a^2+b^2\right)}^{5/2}}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^{5/2}}\right)\,\left(a^2-2\,b^2\right)}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"((3*a^2*b)/(a^4 + b^4 + 2*a^2*b^2) + (a*tan(x/2)*(a^2 + 10*b^2))/(a^4 + b^4 + 2*a^2*b^2) + (a*tan(x/2)^3*(a^2 - 2*b^2))/(a^4 + b^4 + 2*a^2*b^2) - (3*b*tan(x/2)^2*(a^2 - 2*b^2))/(a^4 + b^4 + 2*a^2*b^2))/(a^2 - tan(x/2)^2*(2*a^2 - 4*b^2) + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) - 4*a*b*tan(x/2)^3) + (atanh((2*a^4*b + 2*b^5 + 4*a^2*b^3)/(2*(a^2 + b^2)^(5/2)) - (a*tan(x/2)*(a^4 + b^4 + 2*a^2*b^2))/(a^2 + b^2)^(5/2))*(a^2 - 2*b^2))/(a^2 + b^2)^(5/2)","B"
24,1,48,15,0.493188,"\text{Not used}","int(sin(x)/(a*cos(x) + b*sin(x))^3,x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a-\frac{2\,a^2-4\,b^2}{2\,a}\right)}{b^2\,{\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}^2}","Not used",1,"(tan(x/2)^2*(a - (2*a^2 - 4*b^2)/(2*a)))/(b^2*(a + 2*b*tan(x/2) - a*tan(x/2)^2)^2)","B"
25,1,216,73,0.755367,"\text{Not used}","int(1/(a*cos(x) + b*sin(x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{a\,\left(a^2+b^2\right)}-\frac{b}{a^2+b^2}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-2\,b^2\right)}{a\,\left(a^2+b^2\right)}+\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2-2\,b^2\right)}{a^2\,\left(a^2+b^2\right)}}{a^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}-\frac{\mathrm{atanh}\left(-\frac{\left(2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{2\,a^2\,b+2\,b^3}{a^2+b^2}\right)\,\left(\frac{a^2}{2}+\frac{b^2}{2}\right)}{{\left(a^2+b^2\right)}^{3/2}}\right)}{{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"((tan(x/2)^3*(a^2 + 2*b^2))/(a*(a^2 + b^2)) - b/(a^2 + b^2) + (tan(x/2)*(a^2 - 2*b^2))/(a*(a^2 + b^2)) + (b*tan(x/2)^2*(a^2 - 2*b^2))/(a^2*(a^2 + b^2)))/(a^2 - tan(x/2)^2*(2*a^2 - 4*b^2) + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) - 4*a*b*tan(x/2)^3) - atanh(-((2*a*tan(x/2) - (2*a^2*b + 2*b^3)/(a^2 + b^2))*(a^2/2 + b^2/2))/(a^2 + b^2)^(3/2))/(a^2 + b^2)^(3/2)","B"
26,1,131,59,0.711413,"\text{Not used}","int(1/(sin(x)*(a*cos(x) + b*sin(x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^3}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^3}+\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2-3\,b^2\right)}{a^3}+\frac{4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^2}-\frac{4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2}}{a^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}","Not used",1,"log(tan(x/2))/a^3 - log(a + 2*b*tan(x/2) - a*tan(x/2)^2)/a^3 + ((2*tan(x/2)^2*(a^2 - 3*b^2))/a^3 + (4*b*tan(x/2)^3)/a^2 - (4*b*tan(x/2))/a^2)/(a^2 - tan(x/2)^2*(2*a^2 - 4*b^2) + a^2*tan(x/2)^4 + 4*a*b*tan(x/2) - 4*a*b*tan(x/2)^3)","B"
27,1,813,184,1.005462,"\text{Not used}","int(1/(sin(x)^2*(a*cos(x) + b*sin(x))^3),x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^2+12\,b^2\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(4\,a^2-32\,b^2\right)-a^2-14\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(7\,a^2\,b-10\,b^3\right)}{a}}{2\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a^5-8\,a^3\,b^2\right)+2\,a^5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+8\,a^4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-8\,a^4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^3}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a^4}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2+2\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{3\,a^6+12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^4\,b+24\,a^2\,b^3\right)}{a^5}-\frac{3\,\left(a^2+2\,b^2\right)\,\left(2\,a^2\,b+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^8+8\,a^6\,b^2\right)}{a^5}\right)\,\sqrt{a^2+b^2}}{2\,\left(a^6+a^4\,b^2\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^6+a^4\,b^2\right)}+\frac{\left(a^2+2\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{3\,a^6+12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^4\,b+24\,a^2\,b^3\right)}{a^5}+\frac{3\,\left(a^2+2\,b^2\right)\,\left(2\,a^2\,b+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^8+8\,a^6\,b^2\right)}{a^5}\right)\,\sqrt{a^2+b^2}}{2\,\left(a^6+a^4\,b^2\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^6+a^4\,b^2\right)}}{\frac{2\,\left(9\,a^2\,b+18\,b^3\right)}{a^6}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(9\,a^2+18\,b^2\right)}{a^5}-\frac{3\,\left(a^2+2\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{3\,a^6+12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^4\,b+24\,a^2\,b^3\right)}{a^5}-\frac{3\,\left(a^2+2\,b^2\right)\,\left(2\,a^2\,b+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^8+8\,a^6\,b^2\right)}{a^5}\right)\,\sqrt{a^2+b^2}}{2\,\left(a^6+a^4\,b^2\right)}\right)}{2\,\left(a^6+a^4\,b^2\right)}+\frac{3\,\left(a^2+2\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{3\,a^6+12\,a^4\,b^2}{a^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(12\,a^4\,b+24\,a^2\,b^3\right)}{a^5}+\frac{3\,\left(a^2+2\,b^2\right)\,\left(2\,a^2\,b+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(6\,a^8+8\,a^6\,b^2\right)}{a^5}\right)\,\sqrt{a^2+b^2}}{2\,\left(a^6+a^4\,b^2\right)}\right)}{2\,\left(a^6+a^4\,b^2\right)}}\right)\,\left(a^2+2\,b^2\right)\,\sqrt{a^2+b^2}\,3{}\mathrm{i}}{a^6+a^4\,b^2}","Not used",1,"(tan(x/2)^4*(a^2 + 12*b^2) + tan(x/2)^2*(4*a^2 - 32*b^2) - a^2 - 14*a*b*tan(x/2) + (2*tan(x/2)^3*(7*a^2*b - 10*b^3))/a)/(2*a^5*tan(x/2) - tan(x/2)^3*(4*a^5 - 8*a^3*b^2) + 2*a^5*tan(x/2)^5 + 8*a^4*b*tan(x/2)^2 - 8*a^4*b*tan(x/2)^4) - tan(x/2)/(2*a^3) - (3*b*log(tan(x/2)))/a^4 - (atan((((a^2 + 2*b^2)*(a^2 + b^2)^(1/2)*((3*a^6 + 12*a^4*b^2)/a^6 + (tan(x/2)*(12*a^4*b + 24*a^2*b^3))/a^5 - (3*(a^2 + 2*b^2)*(2*a^2*b + (tan(x/2)*(6*a^8 + 8*a^6*b^2))/a^5)*(a^2 + b^2)^(1/2))/(2*(a^6 + a^4*b^2)))*3i)/(2*(a^6 + a^4*b^2)) + ((a^2 + 2*b^2)*(a^2 + b^2)^(1/2)*((3*a^6 + 12*a^4*b^2)/a^6 + (tan(x/2)*(12*a^4*b + 24*a^2*b^3))/a^5 + (3*(a^2 + 2*b^2)*(2*a^2*b + (tan(x/2)*(6*a^8 + 8*a^6*b^2))/a^5)*(a^2 + b^2)^(1/2))/(2*(a^6 + a^4*b^2)))*3i)/(2*(a^6 + a^4*b^2)))/((2*(9*a^2*b + 18*b^3))/a^6 - (2*tan(x/2)*(9*a^2 + 18*b^2))/a^5 - (3*(a^2 + 2*b^2)*(a^2 + b^2)^(1/2)*((3*a^6 + 12*a^4*b^2)/a^6 + (tan(x/2)*(12*a^4*b + 24*a^2*b^3))/a^5 - (3*(a^2 + 2*b^2)*(2*a^2*b + (tan(x/2)*(6*a^8 + 8*a^6*b^2))/a^5)*(a^2 + b^2)^(1/2))/(2*(a^6 + a^4*b^2))))/(2*(a^6 + a^4*b^2)) + (3*(a^2 + 2*b^2)*(a^2 + b^2)^(1/2)*((3*a^6 + 12*a^4*b^2)/a^6 + (tan(x/2)*(12*a^4*b + 24*a^2*b^3))/a^5 + (3*(a^2 + 2*b^2)*(2*a^2*b + (tan(x/2)*(6*a^8 + 8*a^6*b^2))/a^5)*(a^2 + b^2)^(1/2))/(2*(a^6 + a^4*b^2))))/(2*(a^6 + a^4*b^2))))*(a^2 + 2*b^2)*(a^2 + b^2)^(1/2)*3i)/(a^6 + a^4*b^2)","B"
28,1,253,117,0.855508,"\text{Not used}","int(1/(sin(x)^3*(a*cos(x) + b*sin(x))^3),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(2\,a^2+6\,b^2\right)}{a^5}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(42\,a^2\,b+8\,b^3\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(38\,a^2\,b+32\,b^3\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^3+22\,a\,b^2\right)+\frac{a^3}{2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(-15\,a^4+144\,a^2\,b^2+112\,b^4\right)}{2\,a}-4\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{4\,a^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(8\,a^6-16\,a^4\,b^2\right)+4\,a^6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+16\,a^5\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3-16\,a^5\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(2\,a^2+6\,b^2\right)}{a^5}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a^3}-\frac{3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a^4}","Not used",1,"(log(tan(x/2))*(2*a^2 + 6*b^2))/a^5 - (tan(x/2)^3*(42*a^2*b + 8*b^3) - tan(x/2)^5*(38*a^2*b + 32*b^3) - tan(x/2)^2*(22*a*b^2 + a^3) + a^3/2 + (tan(x/2)^4*(112*b^4 - 15*a^4 + 144*a^2*b^2))/(2*a) - 4*a^2*b*tan(x/2))/(4*a^6*tan(x/2)^2 - tan(x/2)^4*(8*a^6 - 16*a^4*b^2) + 4*a^6*tan(x/2)^6 + 16*a^5*b*tan(x/2)^3 - 16*a^5*b*tan(x/2)^5) - (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(2*a^2 + 6*b^2))/a^5 - tan(x/2)^2/(8*a^3) - (3*b*tan(x/2))/(2*a^4)","B"
29,0,-1,66,0.000000,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^n/sin(c + d*x)^n,x)","\int \frac{{\left(a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)}^n}{{\sin\left(c+d\,x\right)}^n} \,d x","Not used",1,"int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^n/sin(c + d*x)^n, x)","F"
30,1,149,87,4.204961,"\text{Not used}","int(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{5\,a\,x}{16}+\frac{-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{20\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(5*a*x)/16 + ((11*a*tan(c/2 + (d*x)/2))/8 - (5*a*tan(c/2 + (d*x)/2)^3)/24 + (15*a*tan(c/2 + (d*x)/2)^5)/4 - (15*a*tan(c/2 + (d*x)/2)^7)/4 + (5*a*tan(c/2 + (d*x)/2)^9)/24 - (11*a*tan(c/2 + (d*x)/2)^11)/8 + 2*b*tan(c/2 + (d*x)/2)^2 + (20*b*tan(c/2 + (d*x)/2)^6)/3 + 2*b*tan(c/2 + (d*x)/2)^10)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
31,1,67,60,0.464361,"\text{Not used}","int(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{8\,a\,\sin\left(c+d\,x\right)}{15\,d}-\frac{b\,{\cos\left(c+d\,x\right)}^5}{5\,d}+\frac{4\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{15\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,d}","Not used",1,"(8*a*sin(c + d*x))/(15*d) - (b*cos(c + d*x)^5)/(5*d) + (4*a*cos(c + d*x)^2*sin(c + d*x))/(15*d) + (a*cos(c + d*x)^4*sin(c + d*x))/(5*d)","B"
32,1,107,65,4.105554,"\text{Not used}","int(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(3*a*x)/8 + ((5*a*tan(c/2 + (d*x)/2))/4 - (3*a*tan(c/2 + (d*x)/2)^3)/4 + (3*a*tan(c/2 + (d*x)/2)^5)/4 - (5*a*tan(c/2 + (d*x)/2)^7)/4 + 2*b*tan(c/2 + (d*x)/2)^2 + 2*b*tan(c/2 + (d*x)/2)^6)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
33,1,47,44,0.436967,"\text{Not used}","int(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{2\,a\,\sin\left(c+d\,x\right)}{3\,d}-\frac{b\,{\cos\left(c+d\,x\right)}^3}{3\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*a*sin(c + d*x))/(3*d) - (b*cos(c + d*x)^3)/(3*d) + (a*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
34,1,35,43,0.428395,"\text{Not used}","int(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{a\,x}{2}-\frac{b\,\cos\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(a*x)/2 - (b*cos(2*c + 2*d*x))/(4*d) + (a*sin(2*c + 2*d*x))/(4*d)","B"
35,1,38,24,0.357263,"\text{Not used}","int(a*cos(c + d*x) + b*sin(c + d*x),x)","-\frac{2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"-(2*cos(c/2 + (d*x)/2)*(b*cos(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2)))/d","B"
36,1,70,17,0.571999,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x),x)","\frac{b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{b\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)}{d}","Not used",1,"(b*log(1/cos(c/2 + (d*x)/2)^2))/d + (2*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (b*log(cos(c + d*x)/(cos(c + d*x) + 1)))/d","B"
37,1,38,24,0.413244,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x)^2,x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,b}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (2*b)/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
38,1,23,28,0.398978,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x)^3,x)","\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(2\,a+b\,\mathrm{tan}\left(c+d\,x\right)\right)}{2\,d}","Not used",1,"(tan(c + d*x)*(2*a + b*tan(c + d*x)))/(2*d)","B"
39,1,105,52,2.207135,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x)^4,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{2\,b}{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)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2)))/d - ((2*b)/3 + a*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^5 + 2*b*tan(c/2 + (d*x)/2)^4)/(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))","B"
40,1,40,44,0.523299,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x)^5,x)","\frac{\frac{b}{4}+\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{3}+\frac{a\,\sin\left(4\,c+4\,d\,x\right)}{12}}{d\,{\cos\left(c+d\,x\right)}^4}","Not used",1,"(b/4 + (a*sin(2*c + 2*d*x))/3 + (a*sin(4*c + 4*d*x))/12)/(d*cos(c + d*x)^4)","B"
41,1,175,74,4.117648,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x)^6,x)","\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{2\,b}{5}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*a*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((2*b)/5 + (5*a*tan(c/2 + (d*x)/2))/4 - (a*tan(c/2 + (d*x)/2)^3)/2 + (a*tan(c/2 + (d*x)/2)^7)/2 - (5*a*tan(c/2 + (d*x)/2)^9)/4 + 4*b*tan(c/2 + (d*x)/2)^4 + 2*b*tan(c/2 + (d*x)/2)^8)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
42,1,65,60,0.673769,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))/cos(c + d*x)^7,x)","\frac{\frac{8\,a\,\sin\left(c+d\,x\right)\,{\cos\left(c+d\,x\right)}^5}{15}+\frac{4\,a\,\sin\left(c+d\,x\right)\,{\cos\left(c+d\,x\right)}^3}{15}+\frac{a\,\sin\left(c+d\,x\right)\,\cos\left(c+d\,x\right)}{5}+\frac{b}{6}}{d\,{\cos\left(c+d\,x\right)}^6}","Not used",1,"(b/6 + (a*cos(c + d*x)*sin(c + d*x))/5 + (4*a*cos(c + d*x)^3*sin(c + d*x))/15 + (8*a*cos(c + d*x)^5*sin(c + d*x))/15)/(d*cos(c + d*x)^6)","B"
43,1,176,137,0.694812,"\text{Not used}","int(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{16\,a^2\,\sin\left(c+d\,x\right)}{35\,d}+\frac{8\,b^2\,\sin\left(c+d\,x\right)}{105\,d}+\frac{8\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{35\,d}+\frac{6\,a^2\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{35\,d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^6\,\sin\left(c+d\,x\right)}{7\,d}+\frac{4\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{105\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{35\,d}-\frac{b^2\,{\cos\left(c+d\,x\right)}^6\,\sin\left(c+d\,x\right)}{7\,d}-\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^7}{7\,d}","Not used",1,"(16*a^2*sin(c + d*x))/(35*d) + (8*b^2*sin(c + d*x))/(105*d) + (8*a^2*cos(c + d*x)^2*sin(c + d*x))/(35*d) + (6*a^2*cos(c + d*x)^4*sin(c + d*x))/(35*d) + (a^2*cos(c + d*x)^6*sin(c + d*x))/(7*d) + (4*b^2*cos(c + d*x)^2*sin(c + d*x))/(105*d) + (b^2*cos(c + d*x)^4*sin(c + d*x))/(35*d) - (b^2*cos(c + d*x)^6*sin(c + d*x))/(7*d) - (2*a*b*cos(c + d*x)^7)/(7*d)","B"
44,1,156,174,0.609766,"\text{Not used}","int(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{5\,a^2\,x}{16}+\frac{b^2\,x}{16}+\frac{5\,a^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{24\,d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{6\,d}+\frac{b^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{24\,d}-\frac{b^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{6\,d}-\frac{a\,b\,{\cos\left(c+d\,x\right)}^6}{3\,d}+\frac{5\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{16\,d}+\frac{b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{16\,d}","Not used",1,"(5*a^2*x)/16 + (b^2*x)/16 + (5*a^2*cos(c + d*x)^3*sin(c + d*x))/(24*d) + (a^2*cos(c + d*x)^5*sin(c + d*x))/(6*d) + (b^2*cos(c + d*x)^3*sin(c + d*x))/(24*d) - (b^2*cos(c + d*x)^5*sin(c + d*x))/(6*d) - (a*b*cos(c + d*x)^6)/(3*d) + (5*a^2*cos(c + d*x)*sin(c + d*x))/(16*d) + (b^2*cos(c + d*x)*sin(c + d*x))/(16*d)","B"
45,1,115,103,0.614963,"\text{Not used}","int(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{2\,\left(\frac{3\,\sin\left(c+d\,x\right)\,a^2\,{\cos\left(c+d\,x\right)}^4}{2}+2\,\sin\left(c+d\,x\right)\,a^2\,{\cos\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)\,a^2-3\,a\,b\,{\cos\left(c+d\,x\right)}^5-\frac{3\,\sin\left(c+d\,x\right)\,b^2\,{\cos\left(c+d\,x\right)}^4}{2}+\frac{\sin\left(c+d\,x\right)\,b^2\,{\cos\left(c+d\,x\right)}^2}{2}+\sin\left(c+d\,x\right)\,b^2\right)}{15\,d}","Not used",1,"(2*(4*a^2*sin(c + d*x) + b^2*sin(c + d*x) + 2*a^2*cos(c + d*x)^2*sin(c + d*x) + (3*a^2*cos(c + d*x)^4*sin(c + d*x))/2 + (b^2*cos(c + d*x)^2*sin(c + d*x))/2 - (3*b^2*cos(c + d*x)^4*sin(c + d*x))/2 - 3*a*b*cos(c + d*x)^5))/(15*d)","B"
46,1,89,126,0.584075,"\text{Not used}","int(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{4\,a^2\,\sin\left(2\,c+2\,d\,x\right)+\frac{a^2\,\sin\left(4\,c+4\,d\,x\right)}{2}-\frac{b^2\,\sin\left(4\,c+4\,d\,x\right)}{2}+2\,a\,b\,{\sin\left(2\,c+2\,d\,x\right)}^2+8\,a\,b\,{\sin\left(c+d\,x\right)}^2+6\,a^2\,d\,x+2\,b^2\,d\,x}{16\,d}","Not used",1,"(4*a^2*sin(2*c + 2*d*x) + (a^2*sin(4*c + 4*d*x))/2 - (b^2*sin(4*c + 4*d*x))/2 + 2*a*b*sin(2*c + 2*d*x)^2 + 8*a*b*sin(c + d*x)^2 + 6*a^2*d*x + 2*b^2*d*x)/(16*d)","B"
47,1,77,67,0.513911,"\text{Not used}","int(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{2\,\left(\frac{\sin\left(c+d\,x\right)\,a^2\,{\cos\left(c+d\,x\right)}^2}{2}+\sin\left(c+d\,x\right)\,a^2-a\,b\,{\cos\left(c+d\,x\right)}^3-\frac{\sin\left(c+d\,x\right)\,b^2\,{\cos\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)\,b^2}{2}\right)}{3\,d}","Not used",1,"(2*(a^2*sin(c + d*x) + (b^2*sin(c + d*x))/2 + (a^2*cos(c + d*x)^2*sin(c + d*x))/2 - (b^2*cos(c + d*x)^2*sin(c + d*x))/2 - a*b*cos(c + d*x)^3))/(3*d)","B"
48,1,63,55,0.482095,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{a^2\,x}{2}+\frac{b^2\,x}{2}+\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{a\,b\,\cos\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(a^2*x)/2 + (b^2*x)/2 + (a^2*sin(2*c + 2*d*x))/(4*d) - (b^2*sin(2*c + 2*d*x))/(4*d) - (a*b*cos(2*c + 2*d*x))/(2*d)","B"
49,1,66,55,0.489165,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x),x)","\frac{2\,b^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{4\,a\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-2\,b^2\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(2*b^2*atanh(tan(c/2 + (d*x)/2)))/d - (4*a*b - tan(c/2 + (d*x)/2)*(2*a^2 - 2*b^2))/(d*(tan(c/2 + (d*x)/2)^2 + 1))","B"
50,1,118,39,0.679245,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^2,x)","\frac{b^2\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,a\,b\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)}{d}+\frac{2\,a\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}","Not used",1,"(b^2*tan(c + d*x))/d + (2*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*a*b*log(cos(c + d*x)/(cos(c + d*x) + 1)))/d + (2*a*b*log(1/cos(c/2 + (d*x)/2)^2))/d","B"
51,1,106,67,0.901003,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^3,x)","\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a\,b}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-b^2\right)}{d}","Not used",1,"(4*a*b + b^2*tan(c/2 + (d*x)/2)^3 + b^2*tan(c/2 + (d*x)/2) - 4*a*b*tan(c/2 + (d*x)/2)^2)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (atanh(tan(c/2 + (d*x)/2))*(2*a^2 - b^2))/d","B"
52,1,68,30,0.490779,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^4,x)","\frac{\frac{b^2\,\sin\left(c+d\,x\right)}{3}+\frac{{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,\left(3\,a^2-b^2\right)}{3}+a\,b\,\cos\left(c+d\,x\right)\,{\sin\left(c+d\,x\right)}^2}{d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"((b^2*sin(c + d*x))/3 + (cos(c + d*x)^2*sin(c + d*x)*(3*a^2 - b^2))/3 + a*b*cos(c + d*x)*sin(c + d*x)^2)/(d*cos(c + d*x)^3)","B"
53,1,216,120,3.160876,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^5,x)","\frac{\left(a^2+\frac{b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{7\,b^2}{4}-a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{7\,b^2}{4}-a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\left(a^2+\frac{b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4\,a\,b}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-\frac{b^2}{4}\right)}{d}","Not used",1,"((4*a*b)/3 + tan(c/2 + (d*x)/2)*(a^2 + b^2/4) + tan(c/2 + (d*x)/2)^7*(a^2 + b^2/4) - tan(c/2 + (d*x)/2)^3*(a^2 - (7*b^2)/4) - tan(c/2 + (d*x)/2)^5*(a^2 - (7*b^2)/4) - (4*a*b*tan(c/2 + (d*x)/2)^2)/3 + 4*a*b*tan(c/2 + (d*x)/2)^4 - 4*a*b*tan(c/2 + (d*x)/2)^6)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh(tan(c/2 + (d*x)/2))*(a^2 - b^2/4))/d","B"
54,1,98,85,0.621048,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^6,x)","\frac{\frac{b^2\,\sin\left(c+d\,x\right)}{5}+{\cos\left(c+d\,x\right)}^2\,\left(\frac{a^2\,\sin\left(c+d\,x\right)}{3}-\frac{b^2\,\sin\left(c+d\,x\right)}{15}\right)+{\cos\left(c+d\,x\right)}^4\,\left(\frac{2\,a^2\,\sin\left(c+d\,x\right)}{3}-\frac{2\,b^2\,\sin\left(c+d\,x\right)}{15}\right)+\frac{a\,b\,\cos\left(c+d\,x\right)}{2}}{d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"((b^2*sin(c + d*x))/5 + cos(c + d*x)^2*((a^2*sin(c + d*x))/3 - (b^2*sin(c + d*x))/15) + cos(c + d*x)^4*((2*a^2*sin(c + d*x))/3 - (2*b^2*sin(c + d*x))/15) + (a*b*cos(c + d*x))/2)/(d*cos(c + d*x)^5)","B"
55,1,328,168,3.258757,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^7,x)","\frac{\left(\frac{5\,a^2}{4}+\frac{b^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(\frac{47\,b^2}{24}-\frac{7\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(\frac{a^2}{2}+\frac{13\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{a^2}{2}+\frac{13\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{47\,b^2}{24}-\frac{7\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\left(\frac{5\,a^2}{4}+\frac{b^2}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{4\,a\,b}{5}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2}{4}-\frac{b^2}{8}\right)}{d}","Not used",1,"((4*a*b)/5 + tan(c/2 + (d*x)/2)^5*(a^2/2 + (13*b^2)/4) + tan(c/2 + (d*x)/2)^7*(a^2/2 + (13*b^2)/4) + tan(c/2 + (d*x)/2)^11*((5*a^2)/4 + b^2/8) - tan(c/2 + (d*x)/2)^3*((7*a^2)/4 - (47*b^2)/24) - tan(c/2 + (d*x)/2)^9*((7*a^2)/4 - (47*b^2)/24) + tan(c/2 + (d*x)/2)*((5*a^2)/4 + b^2/8) - (4*a*b*tan(c/2 + (d*x)/2)^2)/5 + 8*a*b*tan(c/2 + (d*x)/2)^4 - 8*a*b*tan(c/2 + (d*x)/2)^6 + 4*a*b*tan(c/2 + (d*x)/2)^8 - 4*a*b*tan(c/2 + (d*x)/2)^10)/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (atanh(tan(c/2 + (d*x)/2))*((3*a^2)/4 - b^2/8))/d","B"
56,1,130,125,0.827301,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^2/cos(c + d*x)^8,x)","\frac{\frac{b^2\,\sin\left(c+d\,x\right)}{7}+{\cos\left(c+d\,x\right)}^2\,\left(\frac{a^2\,\sin\left(c+d\,x\right)}{5}-\frac{b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^4\,\left(\frac{4\,a^2\,\sin\left(c+d\,x\right)}{15}-\frac{4\,b^2\,\sin\left(c+d\,x\right)}{105}\right)+{\cos\left(c+d\,x\right)}^6\,\left(\frac{8\,a^2\,\sin\left(c+d\,x\right)}{15}-\frac{8\,b^2\,\sin\left(c+d\,x\right)}{105}\right)+\frac{a\,b\,\cos\left(c+d\,x\right)}{3}}{d\,{\cos\left(c+d\,x\right)}^7}","Not used",1,"((b^2*sin(c + d*x))/7 + cos(c + d*x)^2*((a^2*sin(c + d*x))/5 - (b^2*sin(c + d*x))/35) + cos(c + d*x)^4*((4*a^2*sin(c + d*x))/15 - (4*b^2*sin(c + d*x))/105) + cos(c + d*x)^6*((8*a^2*sin(c + d*x))/15 - (8*b^2*sin(c + d*x))/105) + (a*b*cos(c + d*x))/3)/(d*cos(c + d*x)^7)","B"
57,1,523,265,2.289194,"\text{Not used}","int(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{15\,a\,b^2}{64}-\frac{93\,a^3}{64}\right)+\frac{40\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{15\,a\,b^2}{64}-\frac{93\,a^3}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{91\,a^3}{192}+\frac{397\,a\,b^2}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{91\,a^3}{192}+\frac{397\,a\,b^2}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{895\,a\,b^2}{64}-\frac{1799\,a^3}{192}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{895\,a\,b^2}{64}-\frac{1799\,a^3}{192}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{1765\,a\,b^2}{64}-\frac{1085\,a^3}{192}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1765\,a\,b^2}{64}-\frac{1085\,a^3}{192}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(42\,a^2\,b-\frac{16\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(42\,a^2\,b-\frac{16\,b^3}{3}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{5\,a\,\mathrm{atan}\left(\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2+3\,b^2\right)}{64\,\left(\frac{35\,a^3}{64}+\frac{15\,a\,b^2}{64}\right)}\right)\,\left(7\,a^2+3\,b^2\right)}{64\,d}-\frac{5\,a\,\left(7\,a^2+3\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{64\,d}","Not used",1,"(4*b^3*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)*((15*a*b^2)/64 - (93*a^3)/64) + (40*b^3*tan(c/2 + (d*x)/2)^8)/3 + 4*b^3*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^15*((15*a*b^2)/64 - (93*a^3)/64) + tan(c/2 + (d*x)/2)^3*((397*a*b^2)/64 + (91*a^3)/192) - tan(c/2 + (d*x)/2)^13*((397*a*b^2)/64 + (91*a^3)/192) - tan(c/2 + (d*x)/2)^5*((895*a*b^2)/64 - (1799*a^3)/192) + tan(c/2 + (d*x)/2)^11*((895*a*b^2)/64 - (1799*a^3)/192) + tan(c/2 + (d*x)/2)^7*((1765*a*b^2)/64 - (1085*a^3)/192) - tan(c/2 + (d*x)/2)^9*((1765*a*b^2)/64 - (1085*a^3)/192) + tan(c/2 + (d*x)/2)^6*(42*a^2*b - (16*b^3)/3) + tan(c/2 + (d*x)/2)^10*(42*a^2*b - (16*b^3)/3) + 6*a^2*b*tan(c/2 + (d*x)/2)^2 + 6*a^2*b*tan(c/2 + (d*x)/2)^14)/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) + (5*a*atan((5*a*tan(c/2 + (d*x)/2)*(7*a^2 + 3*b^2))/(64*((15*a*b^2)/64 + (35*a^3)/64)))*(7*a^2 + 3*b^2))/(64*d) - (5*a*(7*a^2 + 3*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d)","B"
58,1,214,175,0.784343,"\text{Not used}","int(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{16\,a^3\,\sin\left(c+d\,x\right)}{35\,d}-\frac{b^3\,{\cos\left(c+d\,x\right)}^5}{5\,d}+\frac{b^3\,{\cos\left(c+d\,x\right)}^7}{7\,d}-\frac{3\,a^2\,b\,{\cos\left(c+d\,x\right)}^7}{7\,d}+\frac{8\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{35\,d}+\frac{6\,a^3\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{35\,d}+\frac{a^3\,{\cos\left(c+d\,x\right)}^6\,\sin\left(c+d\,x\right)}{7\,d}+\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)}{35\,d}+\frac{4\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{35\,d}+\frac{3\,a\,b^2\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{35\,d}-\frac{3\,a\,b^2\,{\cos\left(c+d\,x\right)}^6\,\sin\left(c+d\,x\right)}{7\,d}","Not used",1,"(16*a^3*sin(c + d*x))/(35*d) - (b^3*cos(c + d*x)^5)/(5*d) + (b^3*cos(c + d*x)^7)/(7*d) - (3*a^2*b*cos(c + d*x)^7)/(7*d) + (8*a^3*cos(c + d*x)^2*sin(c + d*x))/(35*d) + (6*a^3*cos(c + d*x)^4*sin(c + d*x))/(35*d) + (a^3*cos(c + d*x)^6*sin(c + d*x))/(7*d) + (8*a*b^2*sin(c + d*x))/(35*d) + (4*a*b^2*cos(c + d*x)^2*sin(c + d*x))/(35*d) + (3*a*b^2*cos(c + d*x)^4*sin(c + d*x))/(35*d) - (3*a*b^2*cos(c + d*x)^6*sin(c + d*x))/(7*d)","B"
59,1,407,216,2.030457,"\text{Not used}","int(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b^2}{8}-\frac{11\,a^3}{8}\right)+4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{3\,a\,b^2}{8}-\frac{11\,a^3}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{39\,a\,b^2}{4}-\frac{15\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{39\,a\,b^2}{4}-\frac{15\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{47\,a\,b^2}{8}-\frac{5\,a^3}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{47\,a\,b^2}{8}-\frac{5\,a^3}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(20\,a^2\,b-\frac{8\,b^3}{3}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2+3\,b^2\right)}{8\,\left(\frac{5\,a^3}{8}+\frac{3\,a\,b^2}{8}\right)}\right)\,\left(5\,a^2+3\,b^2\right)}{8\,d}-\frac{a\,\left(5\,a^2+3\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(4*b^3*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)*((3*a*b^2)/8 - (11*a^3)/8) + 4*b^3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^11*((3*a*b^2)/8 - (11*a^3)/8) - tan(c/2 + (d*x)/2)^5*((39*a*b^2)/4 - (15*a^3)/4) + tan(c/2 + (d*x)/2)^7*((39*a*b^2)/4 - (15*a^3)/4) + tan(c/2 + (d*x)/2)^3*((47*a*b^2)/8 - (5*a^3)/24) - tan(c/2 + (d*x)/2)^9*((47*a*b^2)/8 - (5*a^3)/24) + tan(c/2 + (d*x)/2)^6*(20*a^2*b - (8*b^3)/3) + 6*a^2*b*tan(c/2 + (d*x)/2)^2 + 6*a^2*b*tan(c/2 + (d*x)/2)^10)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(5*a^2 + 3*b^2))/(8*((3*a*b^2)/8 + (5*a^3)/8)))*(5*a^2 + 3*b^2))/(8*d) - (a*(5*a^2 + 3*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
60,1,147,140,0.697660,"\text{Not used}","int(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{2\,\left(\frac{3\,\sin\left(c+d\,x\right)\,a^3\,{\cos\left(c+d\,x\right)}^4}{2}+2\,\sin\left(c+d\,x\right)\,a^3\,{\cos\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)\,a^3-\frac{9\,a^2\,b\,{\cos\left(c+d\,x\right)}^5}{2}-\frac{9\,\sin\left(c+d\,x\right)\,a\,b^2\,{\cos\left(c+d\,x\right)}^4}{2}+\frac{3\,\sin\left(c+d\,x\right)\,a\,b^2\,{\cos\left(c+d\,x\right)}^2}{2}+3\,\sin\left(c+d\,x\right)\,a\,b^2+\frac{3\,b^3\,{\cos\left(c+d\,x\right)}^5}{2}-\frac{5\,b^3\,{\cos\left(c+d\,x\right)}^3}{2}\right)}{15\,d}","Not used",1,"(2*(4*a^3*sin(c + d*x) - (5*b^3*cos(c + d*x)^3)/2 + (3*b^3*cos(c + d*x)^5)/2 - (9*a^2*b*cos(c + d*x)^5)/2 + 2*a^3*cos(c + d*x)^2*sin(c + d*x) + (3*a^3*cos(c + d*x)^4*sin(c + d*x))/2 + 3*a*b^2*sin(c + d*x) + (3*a*b^2*cos(c + d*x)^2*sin(c + d*x))/2 - (9*a*b^2*cos(c + d*x)^4*sin(c + d*x))/2))/(15*d)","B"
61,1,281,78,1.626826,"\text{Not used}","int(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b^2}{4}-\frac{5\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{3\,a\,b^2}{4}-\frac{5\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{21\,a\,b^2}{4}-\frac{3\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{21\,a\,b^2}{4}-\frac{3\,a^3}{4}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{3\,a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(a^2+b^2\right)}{4\,d}+\frac{3\,a\,\mathrm{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+b^2\right)}{4\,\left(\frac{3\,a^3}{4}+\frac{3\,a\,b^2}{4}\right)}\right)\,\left(a^2+b^2\right)}{4\,d}","Not used",1,"(4*b^3*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)*((3*a*b^2)/4 - (5*a^3)/4) + tan(c/2 + (d*x)/2)^7*((3*a*b^2)/4 - (5*a^3)/4) + tan(c/2 + (d*x)/2)^3*((21*a*b^2)/4 - (3*a^3)/4) - tan(c/2 + (d*x)/2)^5*((21*a*b^2)/4 - (3*a^3)/4) + 6*a^2*b*tan(c/2 + (d*x)/2)^2 + 6*a^2*b*tan(c/2 + (d*x)/2)^6)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (3*a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(a^2 + b^2))/(4*d) + (3*a*atan((3*a*tan(c/2 + (d*x)/2)*(a^2 + b^2))/(4*((3*a*b^2)/4 + (3*a^3)/4)))*(a^2 + b^2))/(4*d)","B"
62,1,104,58,0.571746,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{\frac{\sin\left(c+d\,x\right)\,a^3\,{\cos\left(c+d\,x\right)}^2}{3}+\frac{2\,\sin\left(c+d\,x\right)\,a^3}{3}-a^2\,b\,{\cos\left(c+d\,x\right)}^3-\sin\left(c+d\,x\right)\,a\,b^2\,{\cos\left(c+d\,x\right)}^2+\sin\left(c+d\,x\right)\,a\,b^2+\frac{b^3\,{\cos\left(c+d\,x\right)}^3}{3}-b^3\,\cos\left(c+d\,x\right)}{d}","Not used",1,"((2*a^3*sin(c + d*x))/3 - b^3*cos(c + d*x) + (b^3*cos(c + d*x)^3)/3 - a^2*b*cos(c + d*x)^3 + (a^3*cos(c + d*x)^2*sin(c + d*x))/3 + a*b^2*sin(c + d*x) - a*b^2*cos(c + d*x)^2*sin(c + d*x))/d","B"
63,1,156,91,1.242333,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x),x)","\frac{b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)-b^3\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)+a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{b^3\,\cos\left(2\,c+2\,d\,x\right)}{4}+\frac{a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+3\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{3\,a^2\,b\,\cos\left(2\,c+2\,d\,x\right)}{4}-\frac{3\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}}{d}","Not used",1,"(b^3*log(1/cos(c/2 + (d*x)/2)^2) - b^3*log(cos(c + d*x)/(cos(c + d*x) + 1)) + a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (b^3*cos(2*c + 2*d*x))/4 + (a^3*sin(2*c + 2*d*x))/4 + 3*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (3*a^2*b*cos(2*c + 2*d*x))/4 - (3*a*b^2*sin(2*c + 2*d*x))/4)/d","B"
64,1,116,86,1.051198,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^2,x)","\frac{6\,a\,b^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a\,b^2-2\,a^3\right)-6\,a^2\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a\,b^2-2\,a^3\right)+4\,b^3+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}","Not used",1,"(6*a*b^2*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 2*a^3) - 6*a^2*b - tan(c/2 + (d*x)/2)*(6*a*b^2 - 2*a^3) + 4*b^3 + 6*a^2*b*tan(c/2 + (d*x)/2)^2)/(d*(tan(c/2 + (d*x)/2)^4 - 1))","B"
65,1,183,72,1.863948,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^3,x)","\frac{2\,\left(\frac{b^3\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)}{2}-\frac{b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{2}+a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{3\,a^2\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{2}-3\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{3\,a^2\,b\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)}{2}\right)}{d}+\frac{\frac{b^3}{2}+\frac{3\,a\,\sin\left(2\,c+2\,d\,x\right)\,b^2}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((b^3*log(cos(c + d*x)/(cos(c + d*x) + 1)))/2 - (b^3*log(1/cos(c/2 + (d*x)/2)^2))/2 + a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (3*a^2*b*log(1/cos(c/2 + (d*x)/2)^2))/2 - 3*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (3*a^2*b*log(cos(c + d*x)/(cos(c + d*x) + 1)))/2))/d + (b^3/2 + (3*a*b^2*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
66,1,160,103,2.377845,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^4,x)","-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a\,b^2-2\,a^3\right)}{d}-\frac{6\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^2\,b-4\,b^3\right)-\frac{4\,b^3}{3}+3\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{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)}","Not used",1,"- (atanh(tan(c/2 + (d*x)/2))*(3*a*b^2 - 2*a^3))/d - (6*a^2*b - tan(c/2 + (d*x)/2)^2*(12*a^2*b - 4*b^3) - (4*b^3)/3 + 3*a*b^2*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^4 - 3*a*b^2*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))","B"
67,1,88,30,0.635509,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^5,x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(a^3\,\sin\left(c+d\,x\right)-a\,b^2\,\sin\left(c+d\,x\right)\right)+{\cos\left(c+d\,x\right)}^2\,\left(\frac{3\,a^2\,b}{2}-\frac{b^3}{2}\right)+\frac{b^3}{4}+a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^4}","Not used",1,"(cos(c + d*x)^3*(a^3*sin(c + d*x) - a*b^2*sin(c + d*x)) + cos(c + d*x)^2*((3*a^2*b)/2 - b^3/2) + b^3/4 + a*b^2*cos(c + d*x)*sin(c + d*x))/(d*cos(c + d*x)^4)","B"
68,1,293,158,4.277728,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^6,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(a^3+\frac{3\,a\,b^2}{4}\right)-2\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{9\,a\,b^2}{2}-2\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{9\,a\,b^2}{2}-2\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2\,b-\frac{4\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^2\,b+\frac{4\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a^2\,b-4\,b^3\right)+\frac{4\,b^3}{15}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^3+\frac{3\,a\,b^2}{4}\right)-6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a\,b^2}{4}-a^3\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*((3*a*b^2)/4 + a^3) - 2*a^2*b - tan(c/2 + (d*x)/2)^3*((9*a*b^2)/2 - 2*a^3) + tan(c/2 + (d*x)/2)^7*((9*a*b^2)/2 - 2*a^3) + tan(c/2 + (d*x)/2)^2*(4*a^2*b - (4*b^3)/3) - tan(c/2 + (d*x)/2)^4*(8*a^2*b + (4*b^3)/3) + tan(c/2 + (d*x)/2)^6*(12*a^2*b - 4*b^3) + (4*b^3)/15 - tan(c/2 + (d*x)/2)*((3*a*b^2)/4 + a^3) - 6*a^2*b*tan(c/2 + (d*x)/2)^8)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - (atanh(tan(c/2 + (d*x)/2))*((3*a*b^2)/4 - a^3))/d","B"
69,1,123,120,0.841111,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^7,x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{a^3\,\sin\left(c+d\,x\right)}{3}-\frac{a\,b^2\,\sin\left(c+d\,x\right)}{5}\right)+{\cos\left(c+d\,x\right)}^5\,\left(\frac{2\,a^3\,\sin\left(c+d\,x\right)}{3}-\frac{2\,a\,b^2\,\sin\left(c+d\,x\right)}{5}\right)+{\cos\left(c+d\,x\right)}^2\,\left(\frac{3\,a^2\,b}{4}-\frac{b^3}{4}\right)+\frac{b^3}{6}+\frac{3\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^6}","Not used",1,"(cos(c + d*x)^3*((a^3*sin(c + d*x))/3 - (a*b^2*sin(c + d*x))/5) + cos(c + d*x)^5*((2*a^3*sin(c + d*x))/3 - (2*a*b^2*sin(c + d*x))/5) + cos(c + d*x)^2*((3*a^2*b)/4 - b^3/4) + b^3/6 + (3*a*b^2*cos(c + d*x)*sin(c + d*x))/5)/(d*cos(c + d*x)^6)","B"
70,1,423,210,4.282024,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^8,x)","\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-b^2\right)}{8\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a^3}{4}+\frac{3\,a\,b^2}{8}\right)+\frac{6\,a^2\,b}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{11\,a\,b^2}{2}-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{11\,a\,b^2}{2}-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{5\,a^3}{4}+\frac{3\,a\,b^2}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{9\,a^3}{4}+\frac{31\,a\,b^2}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{9\,a^3}{4}+\frac{31\,a\,b^2}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(12\,a^2\,b-4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{12\,a^2\,b}{5}-\frac{4\,b^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(18\,a^2\,b+4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(24\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{66\,a^2\,b}{5}+\frac{8\,b^3}{5}\right)-\frac{4\,b^3}{35}+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*a*atanh(tan(c/2 + (d*x)/2))*(2*a^2 - b^2))/(8*d) - (tan(c/2 + (d*x)/2)*((3*a*b^2)/8 + (5*a^3)/4) + (6*a^2*b)/5 + tan(c/2 + (d*x)/2)^3*((11*a*b^2)/2 - 3*a^3) - tan(c/2 + (d*x)/2)^11*((11*a*b^2)/2 - 3*a^3) - tan(c/2 + (d*x)/2)^13*((3*a*b^2)/8 + (5*a^3)/4) + tan(c/2 + (d*x)/2)^5*((31*a*b^2)/8 + (9*a^3)/4) - tan(c/2 + (d*x)/2)^9*((31*a*b^2)/8 + (9*a^3)/4) - tan(c/2 + (d*x)/2)^10*(12*a^2*b - 4*b^3) - tan(c/2 + (d*x)/2)^2*((12*a^2*b)/5 - (4*b^3)/5) + tan(c/2 + (d*x)/2)^8*(18*a^2*b + 4*b^3) - tan(c/2 + (d*x)/2)^6*(24*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^4*((66*a^2*b)/5 + (8*b^3)/5) - (4*b^3)/35 + 6*a^2*b*tan(c/2 + (d*x)/2)^12)/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
71,1,156,174,1.154013,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^9,x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{a^3\,\sin\left(c+d\,x\right)}{5}-\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^5\,\left(\frac{4\,a^3\,\sin\left(c+d\,x\right)}{15}-\frac{4\,a\,b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^7\,\left(\frac{8\,a^3\,\sin\left(c+d\,x\right)}{15}-\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^2\,\left(\frac{a^2\,b}{2}-\frac{b^3}{6}\right)+\frac{b^3}{8}+\frac{3\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{7}}{d\,{\cos\left(c+d\,x\right)}^8}","Not used",1,"(cos(c + d*x)^3*((a^3*sin(c + d*x))/5 - (3*a*b^2*sin(c + d*x))/35) + cos(c + d*x)^5*((4*a^3*sin(c + d*x))/15 - (4*a*b^2*sin(c + d*x))/35) + cos(c + d*x)^7*((8*a^3*sin(c + d*x))/15 - (8*a*b^2*sin(c + d*x))/35) + cos(c + d*x)^2*((a^2*b)/2 - b^3/6) + b^3/8 + (3*a*b^2*cos(c + d*x)*sin(c + d*x))/7)/(d*cos(c + d*x)^8)","B"
72,1,547,259,4.556669,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^10,x)","-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{15\,a\,b^2}{64}-\frac{5\,a^3}{8}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{11\,a^3}{8}+\frac{15\,a\,b^2}{64}\right)+\frac{6\,a^2\,b}{7}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{11\,a^3}{8}+\frac{15\,a\,b^2}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{191\,a\,b^2}{32}-\frac{47\,a^3}{12}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{191\,a\,b^2}{32}-\frac{47\,a^3}{12}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{29\,a^3}{4}+\frac{249\,a\,b^2}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{29\,a^3}{4}+\frac{249\,a\,b^2}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{435\,a\,b^2}{32}-\frac{33\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{435\,a\,b^2}{32}-\frac{33\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(12\,a^2\,b-4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{12\,a^2\,b}{7}-\frac{4\,b^3}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(36\,a^2\,b-12\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(48\,a^2\,b+12\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(36\,a^2\,b+\frac{20\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(60\,a^2\,b-20\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{132\,a^2\,b}{7}+\frac{12\,b^3}{7}\right)-\frac{4\,b^3}{63}+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- (atanh(tan(c/2 + (d*x)/2))*((15*a*b^2)/64 - (5*a^3)/8))/d - (tan(c/2 + (d*x)/2)*((15*a*b^2)/64 + (11*a^3)/8) + (6*a^2*b)/7 - tan(c/2 + (d*x)/2)^17*((15*a*b^2)/64 + (11*a^3)/8) + tan(c/2 + (d*x)/2)^3*((191*a*b^2)/32 - (47*a^3)/12) - tan(c/2 + (d*x)/2)^15*((191*a*b^2)/32 - (47*a^3)/12) + tan(c/2 + (d*x)/2)^5*((249*a*b^2)/32 + (29*a^3)/4) - tan(c/2 + (d*x)/2)^13*((249*a*b^2)/32 + (29*a^3)/4) + tan(c/2 + (d*x)/2)^7*((435*a*b^2)/32 - (33*a^3)/4) - tan(c/2 + (d*x)/2)^11*((435*a*b^2)/32 - (33*a^3)/4) - tan(c/2 + (d*x)/2)^14*(12*a^2*b - 4*b^3) - tan(c/2 + (d*x)/2)^2*((12*a^2*b)/7 - (4*b^3)/7) - tan(c/2 + (d*x)/2)^6*(36*a^2*b - 12*b^3) + tan(c/2 + (d*x)/2)^8*(48*a^2*b + 12*b^3) + tan(c/2 + (d*x)/2)^12*(36*a^2*b + (20*b^3)/3) - tan(c/2 + (d*x)/2)^10*(60*a^2*b - 20*b^3) + tan(c/2 + (d*x)/2)^4*((132*a^2*b)/7 + (12*b^3)/7) - (4*b^3)/63 + 6*a^2*b*tan(c/2 + (d*x)/2)^16)/(d*(9*tan(c/2 + (d*x)/2)^2 - 36*tan(c/2 + (d*x)/2)^4 + 84*tan(c/2 + (d*x)/2)^6 - 126*tan(c/2 + (d*x)/2)^8 + 126*tan(c/2 + (d*x)/2)^10 - 84*tan(c/2 + (d*x)/2)^12 + 36*tan(c/2 + (d*x)/2)^14 - 9*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^18 - 1))","B"
73,1,189,213,1.579764,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^3/cos(c + d*x)^11,x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{a^3\,\sin\left(c+d\,x\right)}{7}-\frac{a\,b^2\,\sin\left(c+d\,x\right)}{21}\right)+{\cos\left(c+d\,x\right)}^5\,\left(\frac{6\,a^3\,\sin\left(c+d\,x\right)}{35}-\frac{2\,a\,b^2\,\sin\left(c+d\,x\right)}{35}\right)+{\cos\left(c+d\,x\right)}^7\,\left(\frac{8\,a^3\,\sin\left(c+d\,x\right)}{35}-\frac{8\,a\,b^2\,\sin\left(c+d\,x\right)}{105}\right)+{\cos\left(c+d\,x\right)}^9\,\left(\frac{16\,a^3\,\sin\left(c+d\,x\right)}{35}-\frac{16\,a\,b^2\,\sin\left(c+d\,x\right)}{105}\right)+{\cos\left(c+d\,x\right)}^2\,\left(\frac{3\,a^2\,b}{8}-\frac{b^3}{8}\right)+\frac{b^3}{10}+\frac{a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{3}}{d\,{\cos\left(c+d\,x\right)}^{10}}","Not used",1,"(cos(c + d*x)^3*((a^3*sin(c + d*x))/7 - (a*b^2*sin(c + d*x))/21) + cos(c + d*x)^5*((6*a^3*sin(c + d*x))/35 - (2*a*b^2*sin(c + d*x))/35) + cos(c + d*x)^7*((8*a^3*sin(c + d*x))/35 - (8*a*b^2*sin(c + d*x))/105) + cos(c + d*x)^9*((16*a^3*sin(c + d*x))/35 - (16*a*b^2*sin(c + d*x))/105) + cos(c + d*x)^2*((3*a^2*b)/8 - b^3/8) + b^3/10 + (a*b^2*cos(c + d*x)*sin(c + d*x))/3)/(d*cos(c + d*x)^10)","B"
74,1,334,279,2.001138,"\text{Not used}","int(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","-\frac{\frac{b^4\,\sin\left(3\,c+3\,d\,x\right)}{192}-\frac{3\,b^4\,\sin\left(c+d\,x\right)}{128}-\frac{7\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{64}-\frac{9\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{320}-\frac{9\,a^4\,\sin\left(7\,c+7\,d\,x\right)}{1792}-\frac{a^4\,\sin\left(9\,c+9\,d\,x\right)}{2304}-\frac{63\,a^4\,\sin\left(c+d\,x\right)}{128}+\frac{b^4\,\sin\left(5\,c+5\,d\,x\right)}{320}-\frac{b^4\,\sin\left(7\,c+7\,d\,x\right)}{1792}-\frac{b^4\,\sin\left(9\,c+9\,d\,x\right)}{2304}+\frac{a\,b^3\,\cos\left(3\,c+3\,d\,x\right)}{24}+\frac{7\,a^3\,b\,\cos\left(3\,c+3\,d\,x\right)}{48}+\frac{a^3\,b\,\cos\left(5\,c+5\,d\,x\right)}{16}-\frac{3\,a\,b^3\,\cos\left(7\,c+7\,d\,x\right)}{448}+\frac{a^3\,b\,\cos\left(7\,c+7\,d\,x\right)}{64}-\frac{a\,b^3\,\cos\left(9\,c+9\,d\,x\right)}{576}+\frac{a^3\,b\,\cos\left(9\,c+9\,d\,x\right)}{576}-\frac{21\,a^2\,b^2\,\sin\left(c+d\,x\right)}{64}+\frac{3\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{80}+\frac{15\,a^2\,b^2\,\sin\left(7\,c+7\,d\,x\right)}{896}+\frac{a^2\,b^2\,\sin\left(9\,c+9\,d\,x\right)}{384}+\frac{3\,a\,b^3\,\cos\left(c+d\,x\right)}{32}+\frac{7\,a^3\,b\,\cos\left(c+d\,x\right)}{32}}{d}","Not used",1,"-((b^4*sin(3*c + 3*d*x))/192 - (3*b^4*sin(c + d*x))/128 - (7*a^4*sin(3*c + 3*d*x))/64 - (9*a^4*sin(5*c + 5*d*x))/320 - (9*a^4*sin(7*c + 7*d*x))/1792 - (a^4*sin(9*c + 9*d*x))/2304 - (63*a^4*sin(c + d*x))/128 + (b^4*sin(5*c + 5*d*x))/320 - (b^4*sin(7*c + 7*d*x))/1792 - (b^4*sin(9*c + 9*d*x))/2304 + (a*b^3*cos(3*c + 3*d*x))/24 + (7*a^3*b*cos(3*c + 3*d*x))/48 + (a^3*b*cos(5*c + 5*d*x))/16 - (3*a*b^3*cos(7*c + 7*d*x))/448 + (a^3*b*cos(7*c + 7*d*x))/64 - (a*b^3*cos(9*c + 9*d*x))/576 + (a^3*b*cos(9*c + 9*d*x))/576 - (21*a^2*b^2*sin(c + d*x))/64 + (3*a^2*b^2*sin(5*c + 5*d*x))/80 + (15*a^2*b^2*sin(7*c + 7*d*x))/896 + (a^2*b^2*sin(9*c + 9*d*x))/384 + (3*a*b^3*cos(c + d*x))/32 + (7*a^3*b*cos(c + d*x))/32)/d","B"
75,1,343,381,1.688076,"\text{Not used}","int(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{35\,a^4\,x}{128}+\frac{3\,b^4\,x}{128}+\frac{15\,a^2\,b^2\,x}{64}-\frac{2\,a\,b^3\,{\cos\left(c+d\,x\right)}^6}{3\,d}+\frac{a\,b^3\,{\cos\left(c+d\,x\right)}^8}{2\,d}-\frac{a^3\,b\,{\cos\left(c+d\,x\right)}^8}{2\,d}+\frac{35\,a^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{192\,d}+\frac{7\,a^4\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{48\,d}+\frac{a^4\,{\cos\left(c+d\,x\right)}^7\,\sin\left(c+d\,x\right)}{8\,d}+\frac{b^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{64\,d}-\frac{3\,b^4\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{16\,d}+\frac{b^4\,{\cos\left(c+d\,x\right)}^7\,\sin\left(c+d\,x\right)}{8\,d}+\frac{35\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{128\,d}+\frac{3\,b^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{128\,d}+\frac{15\,a^2\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{64\,d}+\frac{5\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{32\,d}+\frac{a^2\,b^2\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{8\,d}-\frac{3\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^7\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(35*a^4*x)/128 + (3*b^4*x)/128 + (15*a^2*b^2*x)/64 - (2*a*b^3*cos(c + d*x)^6)/(3*d) + (a*b^3*cos(c + d*x)^8)/(2*d) - (a^3*b*cos(c + d*x)^8)/(2*d) + (35*a^4*cos(c + d*x)^3*sin(c + d*x))/(192*d) + (7*a^4*cos(c + d*x)^5*sin(c + d*x))/(48*d) + (a^4*cos(c + d*x)^7*sin(c + d*x))/(8*d) + (b^4*cos(c + d*x)^3*sin(c + d*x))/(64*d) - (3*b^4*cos(c + d*x)^5*sin(c + d*x))/(16*d) + (b^4*cos(c + d*x)^7*sin(c + d*x))/(8*d) + (35*a^4*cos(c + d*x)*sin(c + d*x))/(128*d) + (3*b^4*cos(c + d*x)*sin(c + d*x))/(128*d) + (15*a^2*b^2*cos(c + d*x)*sin(c + d*x))/(64*d) + (5*a^2*b^2*cos(c + d*x)^3*sin(c + d*x))/(32*d) + (a^2*b^2*cos(c + d*x)^5*sin(c + d*x))/(8*d) - (3*a^2*b^2*cos(c + d*x)^7*sin(c + d*x))/(4*d)","B"
76,1,291,220,1.277487,"\text{Not used}","int(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","-\frac{\frac{b^4\,\sin\left(3\,c+3\,d\,x\right)}{64}-\frac{3\,b^4\,\sin\left(c+d\,x\right)}{64}-\frac{7\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{64}-\frac{7\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{320}-\frac{a^4\,\sin\left(7\,c+7\,d\,x\right)}{448}-\frac{35\,a^4\,\sin\left(c+d\,x\right)}{64}+\frac{b^4\,\sin\left(5\,c+5\,d\,x\right)}{320}-\frac{b^4\,\sin\left(7\,c+7\,d\,x\right)}{448}+\frac{a\,b^3\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{3\,a^3\,b\,\cos\left(3\,c+3\,d\,x\right)}{16}-\frac{a\,b^3\,\cos\left(5\,c+5\,d\,x\right)}{80}+\frac{a^3\,b\,\cos\left(5\,c+5\,d\,x\right)}{16}-\frac{a\,b^3\,\cos\left(7\,c+7\,d\,x\right)}{112}+\frac{a^3\,b\,\cos\left(7\,c+7\,d\,x\right)}{112}-\frac{15\,a^2\,b^2\,\sin\left(c+d\,x\right)}{32}+\frac{a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{9\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{160}+\frac{3\,a^2\,b^2\,\sin\left(7\,c+7\,d\,x\right)}{224}+\frac{3\,a\,b^3\,\cos\left(c+d\,x\right)}{16}+\frac{5\,a^3\,b\,\cos\left(c+d\,x\right)}{16}}{d}","Not used",1,"-((b^4*sin(3*c + 3*d*x))/64 - (3*b^4*sin(c + d*x))/64 - (7*a^4*sin(3*c + 3*d*x))/64 - (7*a^4*sin(5*c + 5*d*x))/320 - (a^4*sin(7*c + 7*d*x))/448 - (35*a^4*sin(c + d*x))/64 + (b^4*sin(5*c + 5*d*x))/320 - (b^4*sin(7*c + 7*d*x))/448 + (a*b^3*cos(3*c + 3*d*x))/16 + (3*a^3*b*cos(3*c + 3*d*x))/16 - (a*b^3*cos(5*c + 5*d*x))/80 + (a^3*b*cos(5*c + 5*d*x))/16 - (a*b^3*cos(7*c + 7*d*x))/112 + (a^3*b*cos(7*c + 7*d*x))/112 - (15*a^2*b^2*sin(c + d*x))/32 + (a^2*b^2*sin(3*c + 3*d*x))/32 + (9*a^2*b^2*sin(5*c + 5*d*x))/160 + (3*a^2*b^2*sin(7*c + 7*d*x))/224 + (3*a*b^3*cos(c + d*x))/16 + (5*a^3*b*cos(c + d*x))/16)/d","B"
77,1,471,301,2.305745,"\text{Not used}","int(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-\frac{11\,a^4}{8}+\frac{3\,a^2\,b^2}{4}+\frac{b^4}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{15\,a^4}{4}-\frac{39\,a^2\,b^2}{2}+\frac{19\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{15\,a^4}{4}-\frac{39\,a^2\,b^2}{2}+\frac{19\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,a^4}{24}-\frac{47\,a^2\,b^2}{4}+\frac{17\,b^4}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{5\,a^4}{24}-\frac{47\,a^2\,b^2}{4}+\frac{17\,b^4}{24}\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{11\,a^4}{8}+\frac{3\,a^2\,b^2}{4}+\frac{b^4}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{32\,a\,b^3}{3}-\frac{80\,a^3\,b}{3}\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+16\,a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(5\,a^4+6\,a^2\,b^2+b^4\right)}{8\,d}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)}{8\,\left(\frac{5\,a^4}{8}+\frac{3\,a^2\,b^2}{4}+\frac{b^4}{8}\right)}\right)\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*(b^4/8 - (11*a^4)/8 + (3*a^2*b^2)/4) + tan(c/2 + (d*x)/2)^5*((15*a^4)/4 + (19*b^4)/4 - (39*a^2*b^2)/2) - tan(c/2 + (d*x)/2)^7*((15*a^4)/4 + (19*b^4)/4 - (39*a^2*b^2)/2) - tan(c/2 + (d*x)/2)^3*((5*a^4)/24 + (17*b^4)/24 - (47*a^2*b^2)/4) + tan(c/2 + (d*x)/2)^9*((5*a^4)/24 + (17*b^4)/24 - (47*a^2*b^2)/4) - tan(c/2 + (d*x)/2)*(b^4/8 - (11*a^4)/8 + (3*a^2*b^2)/4) - tan(c/2 + (d*x)/2)^6*((32*a*b^3)/3 - (80*a^3*b)/3) + 8*a^3*b*tan(c/2 + (d*x)/2)^2 + 16*a*b^3*tan(c/2 + (d*x)/2)^4 + 16*a*b^3*tan(c/2 + (d*x)/2)^8 + 8*a^3*b*tan(c/2 + (d*x)/2)^10)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - ((atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(5*a^4 + b^4 + 6*a^2*b^2))/(8*d) + (atan((tan(c/2 + (d*x)/2)*(5*a^2 + b^2)*(a^2 + b^2))/(8*((5*a^4)/8 + b^4/8 + (3*a^2*b^2)/4)))*(5*a^2 + b^2)*(a^2 + b^2))/(8*d)","B"
78,1,204,165,0.827807,"\text{Not used}","int(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{2\,\left(\frac{3\,\sin\left(c+d\,x\right)\,a^4\,{\cos\left(c+d\,x\right)}^4}{2}+2\,\sin\left(c+d\,x\right)\,a^4\,{\cos\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)\,a^4-6\,a^3\,b\,{\cos\left(c+d\,x\right)}^5-9\,\sin\left(c+d\,x\right)\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^4+3\,\sin\left(c+d\,x\right)\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^2+6\,\sin\left(c+d\,x\right)\,a^2\,b^2+6\,a\,b^3\,{\cos\left(c+d\,x\right)}^5-10\,a\,b^3\,{\cos\left(c+d\,x\right)}^3+\frac{3\,\sin\left(c+d\,x\right)\,b^4\,{\cos\left(c+d\,x\right)}^4}{2}-3\,\sin\left(c+d\,x\right)\,b^4\,{\cos\left(c+d\,x\right)}^2+\frac{3\,\sin\left(c+d\,x\right)\,b^4}{2}\right)}{15\,d}","Not used",1,"(2*(4*a^4*sin(c + d*x) + (3*b^4*sin(c + d*x))/2 - 10*a*b^3*cos(c + d*x)^3 + 6*a*b^3*cos(c + d*x)^5 - 6*a^3*b*cos(c + d*x)^5 + 2*a^4*cos(c + d*x)^2*sin(c + d*x) + (3*a^4*cos(c + d*x)^4*sin(c + d*x))/2 + 6*a^2*b^2*sin(c + d*x) - 3*b^4*cos(c + d*x)^2*sin(c + d*x) + (3*b^4*cos(c + d*x)^4*sin(c + d*x))/2 + 3*a^2*b^2*cos(c + d*x)^2*sin(c + d*x) - 9*a^2*b^2*cos(c + d*x)^4*sin(c + d*x)))/(15*d)","B"
79,1,320,108,1.959185,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{3\,\mathrm{atan}\left(\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^2}{4\,\left(\frac{3\,a^4}{4}+\frac{3\,a^2\,b^2}{2}+\frac{3\,b^4}{4}\right)}\right)\,{\left(a^2+b^2\right)}^2}{4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{5\,a^4}{4}+\frac{3\,a^2\,b^2}{2}+\frac{3\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{3\,a^4}{4}-\frac{21\,a^2\,b^2}{2}+\frac{11\,b^4}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,a^4}{4}-\frac{21\,a^2\,b^2}{2}+\frac{11\,b^4}{4}\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{5\,a^4}{4}+\frac{3\,a^2\,b^2}{2}+\frac{3\,b^4}{4}\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+16\,a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^2}{4\,d}","Not used",1,"(3*atan((3*tan(c/2 + (d*x)/2)*(a^2 + b^2)^2)/(4*((3*a^4)/4 + (3*b^4)/4 + (3*a^2*b^2)/2)))*(a^2 + b^2)^2)/(4*d) + (tan(c/2 + (d*x)/2)^7*((3*b^4)/4 - (5*a^4)/4 + (3*a^2*b^2)/2) - tan(c/2 + (d*x)/2)^3*((3*a^4)/4 + (11*b^4)/4 - (21*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^5*((3*a^4)/4 + (11*b^4)/4 - (21*a^2*b^2)/2) - tan(c/2 + (d*x)/2)*((3*b^4)/4 - (5*a^4)/4 + (3*a^2*b^2)/2) + 8*a^3*b*tan(c/2 + (d*x)/2)^2 + 16*a*b^3*tan(c/2 + (d*x)/2)^4 + 8*a^3*b*tan(c/2 + (d*x)/2)^6)/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (3*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(a^2 + b^2)^2)/(4*d)","B"
80,1,190,150,2.749639,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x),x)","\frac{2\,b^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\frac{16\,a\,b^3}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4-2\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{4\,a^4}{3}+16\,a^2\,b^2-\frac{20\,b^4}{3}\right)+\frac{8\,a^3\,b}{3}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4-2\,b^4\right)+16\,a\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{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)}","Not used",1,"(2*b^4*atanh(tan(c/2 + (d*x)/2)))/d - ((16*a*b^3)/3 - tan(c/2 + (d*x)/2)^5*(2*a^4 - 2*b^4) - tan(c/2 + (d*x)/2)^3*((4*a^4)/3 - (20*b^4)/3 + 16*a^2*b^2) + (8*a^3*b)/3 - tan(c/2 + (d*x)/2)*(2*a^4 - 2*b^4) + 16*a*b^3*tan(c/2 + (d*x)/2)^2 + 8*a^3*b*tan(c/2 + (d*x)/2)^4)/(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))","B"
81,1,255,119,1.231155,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^2,x)","\frac{a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-3\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+4\,a\,b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)+6\,a^2\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-4\,a\,b^3\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)}{d}+\frac{\frac{a^4\,\sin\left(c+d\,x\right)}{8}+\frac{9\,b^4\,\sin\left(c+d\,x\right)}{8}+\frac{a^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{b^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{a\,b^3\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{a^3\,b\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{3\,a^2\,b^2\,\sin\left(c+d\,x\right)}{4}-\frac{3\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 3*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 4*a*b^3*log(1/cos(c/2 + (d*x)/2)^2) + 6*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 4*a*b^3*log(cos(c + d*x)/(cos(c + d*x) + 1)))/d + ((a^4*sin(c + d*x))/8 + (9*b^4*sin(c + d*x))/8 + (a^4*sin(3*c + 3*d*x))/8 + (b^4*sin(3*c + 3*d*x))/8 + (a*b^3*cos(3*c + 3*d*x))/2 - (a^3*b*cos(3*c + 3*d*x))/2 - (3*a^2*b^2*sin(c + d*x))/4 - (3*a^2*b^2*sin(3*c + 3*d*x))/4)/(d*cos(c + d*x))","B"
82,1,221,151,2.962383,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^4-24\,a^2\,b^2+2\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4-12\,a^2\,b^2+3\,b^4\right)-16\,a\,b^3+8\,a^3\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4-12\,a^2\,b^2+3\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(16\,a\,b^3-16\,a^3\,b\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,b^4-12\,a^2\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(4*a^4 + 2*b^4 - 24*a^2*b^2) - tan(c/2 + (d*x)/2)^5*(2*a^4 + 3*b^4 - 12*a^2*b^2) - 16*a*b^3 + 8*a^3*b - tan(c/2 + (d*x)/2)*(2*a^4 + 3*b^4 - 12*a^2*b^2) + tan(c/2 + (d*x)/2)^2*(16*a*b^3 - 16*a^3*b) + 8*a^3*b*tan(c/2 + (d*x)/2)^4)/(d*(tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 - 1)) - (atanh(tan(c/2 + (d*x)/2))*(3*b^4 - 12*a^2*b^2))/d","B"
83,1,546,103,1.794176,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^4,x)","\frac{\frac{3\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{b^4\,\sin\left(3\,c+3\,d\,x\right)}{3}+\frac{3\,b^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{a\,b^3\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2}+\frac{a^4\,\mathrm{atan}\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(3\,c+3\,d\,x\right)}{2}+\frac{b^4\,\mathrm{atan}\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(3\,c+3\,d\,x\right)}{2}+\frac{3\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{a\,b^3\,\cos\left(c+d\,x\right)}{2}+3\,a\,b^3\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(c+d\,x\right)-3\,a^3\,b\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(c+d\,x\right)-3\,a^2\,b^2\,\mathrm{atan}\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(3\,c+3\,d\,x\right)-3\,a\,b^3\,\cos\left(c+d\,x\right)\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)+3\,a^3\,b\,\cos\left(c+d\,x\right)\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)+a\,b^3\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(3\,c+3\,d\,x\right)-a^3\,b\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(3\,c+3\,d\,x\right)-a\,b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(3\,c+3\,d\,x\right)+a^3\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(3\,c+3\,d\,x\right)-9\,a^2\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((3*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (b^4*sin(3*c + 3*d*x))/3 + (3*b^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (a*b^3*cos(3*c + 3*d*x))/2 + (3*a^2*b^2*sin(c + d*x))/2 + (a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (3*a^2*b^2*sin(3*c + 3*d*x))/2 + (a*b^3*cos(c + d*x))/2 + 3*a*b^3*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(c + d*x) - 3*a^3*b*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(c + d*x) - 3*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) - 3*a*b^3*cos(c + d*x)*log(1/cos(c/2 + (d*x)/2)^2) + 3*a^3*b*cos(c + d*x)*log(1/cos(c/2 + (d*x)/2)^2) + a*b^3*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(3*c + 3*d*x) - a^3*b*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(3*c + 3*d*x) - a*b^3*log(1/cos(c/2 + (d*x)/2)^2)*cos(3*c + 3*d*x) + a^3*b*log(1/cos(c/2 + (d*x)/2)^2)*cos(3*c + 3*d*x) - 9*a^2*b^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
84,1,278,168,4.214711,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^4-6\,a^2\,b^2+\frac{3\,b^4}{4}\right)}{d}-\frac{\frac{16\,a\,b^3}{3}-8\,a^3\,b+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,b^4}{4}-6\,a^2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{3\,b^4}{4}-6\,a^2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{11\,b^4}{4}-6\,a^2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{11\,b^4}{4}-6\,a^2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a\,b^3-24\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{64\,a\,b^3}{3}-24\,a^3\,b\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(2*a^4 + (3*b^4)/4 - 6*a^2*b^2))/d - ((16*a*b^3)/3 - 8*a^3*b + tan(c/2 + (d*x)/2)*((3*b^4)/4 - 6*a^2*b^2) + tan(c/2 + (d*x)/2)^7*((3*b^4)/4 - 6*a^2*b^2) - tan(c/2 + (d*x)/2)^3*((11*b^4)/4 - 6*a^2*b^2) - tan(c/2 + (d*x)/2)^5*((11*b^4)/4 - 6*a^2*b^2) + tan(c/2 + (d*x)/2)^4*(16*a*b^3 - 24*a^3*b) - tan(c/2 + (d*x)/2)^2*((64*a*b^3)/3 - 24*a^3*b) + 8*a^3*b*tan(c/2 + (d*x)/2)^6)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
85,1,139,30,0.799637,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^6,x)","\frac{\frac{b^4\,\sin\left(c+d\,x\right)}{5}-{\cos\left(c+d\,x\right)}^3\,\left(2\,a\,b^3-2\,a^3\,b\right)-{\cos\left(c+d\,x\right)}^2\,\left(\frac{2\,b^4\,\sin\left(c+d\,x\right)}{5}-2\,a^2\,b^2\,\sin\left(c+d\,x\right)\right)+{\cos\left(c+d\,x\right)}^4\,\left(\sin\left(c+d\,x\right)\,a^4-2\,\sin\left(c+d\,x\right)\,a^2\,b^2+\frac{\sin\left(c+d\,x\right)\,b^4}{5}\right)+a\,b^3\,\cos\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"((b^4*sin(c + d*x))/5 - cos(c + d*x)^3*(2*a*b^3 - 2*a^3*b) - cos(c + d*x)^2*((2*b^4*sin(c + d*x))/5 - 2*a^2*b^2*sin(c + d*x)) + cos(c + d*x)^4*(a^4*sin(c + d*x) + (b^4*sin(c + d*x))/5 - 2*a^2*b^2*sin(c + d*x)) + a*b^3*cos(c + d*x))/(d*cos(c + d*x)^5)","B"
86,1,419,258,4.266197,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^7,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4-\frac{3\,a^2\,b^2}{2}+\frac{b^4}{8}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4-9\,a^2\,b^2+\frac{19\,b^4}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^4-9\,a^2\,b^2+\frac{19\,b^4}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-3\,a^4+\frac{15\,a^2\,b^2}{2}+\frac{17\,b^4}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-3\,a^4+\frac{15\,a^2\,b^2}{2}+\frac{17\,b^4}{24}\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+\frac{3\,a^2\,b^2}{2}-\frac{b^4}{8}\right)-\frac{16\,a\,b^3}{15}+\frac{8\,a^3\,b}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(a^4+\frac{3\,a^2\,b^2}{2}-\frac{b^4}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{32\,a\,b^3}{5}-8\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(16\,a\,b^3-24\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{32\,a\,b^3}{3}-\frac{80\,a^3\,b}{3}\right)+16\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(a^4 + b^4/8 - (3*a^2*b^2)/2))/d + (tan(c/2 + (d*x)/2)^5*(2*a^4 + (19*b^4)/4 - 9*a^2*b^2) + tan(c/2 + (d*x)/2)^7*(2*a^4 + (19*b^4)/4 - 9*a^2*b^2) + tan(c/2 + (d*x)/2)^3*((17*b^4)/24 - 3*a^4 + (15*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^9*((17*b^4)/24 - 3*a^4 + (15*a^2*b^2)/2) + tan(c/2 + (d*x)/2)*(a^4 - b^4/8 + (3*a^2*b^2)/2) - (16*a*b^3)/15 + (8*a^3*b)/3 + tan(c/2 + (d*x)/2)^11*(a^4 - b^4/8 + (3*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^2*((32*a*b^3)/5 - 8*a^3*b) - tan(c/2 + (d*x)/2)^8*(16*a*b^3 - 24*a^3*b) + tan(c/2 + (d*x)/2)^6*((32*a*b^3)/3 - (80*a^3*b)/3) + 16*a^3*b*tan(c/2 + (d*x)/2)^4 - 8*a^3*b*tan(c/2 + (d*x)/2)^10)/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
87,1,186,143,1.098376,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^8,x)","\frac{\frac{b^4\,\sin\left(c+d\,x\right)}{7}-{\cos\left(c+d\,x\right)}^3\,\left(a\,b^3-a^3\,b\right)-{\cos\left(c+d\,x\right)}^2\,\left(\frac{8\,b^4\,\sin\left(c+d\,x\right)}{35}-\frac{6\,a^2\,b^2\,\sin\left(c+d\,x\right)}{5}\right)+{\cos\left(c+d\,x\right)}^4\,\left(\frac{\sin\left(c+d\,x\right)\,a^4}{3}-\frac{2\,\sin\left(c+d\,x\right)\,a^2\,b^2}{5}+\frac{\sin\left(c+d\,x\right)\,b^4}{35}\right)+{\cos\left(c+d\,x\right)}^6\,\left(\frac{2\,\sin\left(c+d\,x\right)\,a^4}{3}-\frac{4\,\sin\left(c+d\,x\right)\,a^2\,b^2}{5}+\frac{2\,\sin\left(c+d\,x\right)\,b^4}{35}\right)+\frac{2\,a\,b^3\,\cos\left(c+d\,x\right)}{3}}{d\,{\cos\left(c+d\,x\right)}^7}","Not used",1,"((b^4*sin(c + d*x))/7 - cos(c + d*x)^3*(a*b^3 - a^3*b) - cos(c + d*x)^2*((8*b^4*sin(c + d*x))/35 - (6*a^2*b^2*sin(c + d*x))/5) + cos(c + d*x)^4*((a^4*sin(c + d*x))/3 + (b^4*sin(c + d*x))/35 - (2*a^2*b^2*sin(c + d*x))/5) + cos(c + d*x)^6*((2*a^4*sin(c + d*x))/3 + (2*b^4*sin(c + d*x))/35 - (4*a^2*b^2*sin(c + d*x))/5) + (2*a*b^3*cos(c + d*x))/3)/(d*cos(c + d*x)^7)","B"
88,1,566,330,4.400425,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^9,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{5\,a^4}{4}+\frac{3\,a^2\,b^2}{4}-\frac{3\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-\frac{17\,a^4}{4}+\frac{41\,a^2\,b^2}{4}+\frac{23\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(-\frac{17\,a^4}{4}+\frac{41\,a^2\,b^2}{4}+\frac{23\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{21\,a^4}{4}-\frac{13\,a^2\,b^2}{4}+\frac{333\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{21\,a^4}{4}-\frac{13\,a^2\,b^2}{4}+\frac{333\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{9\,a^4}{4}+\frac{31\,a^2\,b^2}{4}-\frac{671\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{9\,a^4}{4}+\frac{31\,a^2\,b^2}{4}-\frac{671\,b^4}{64}\right)-\frac{16\,a\,b^3}{35}+\frac{8\,a^3\,b}{5}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a^4}{4}+\frac{3\,a^2\,b^2}{4}-\frac{3\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(16\,a\,b^3-24\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(16\,a\,b^3-56\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{104\,a^3\,b}{5}+\frac{16\,a\,b^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{128\,a\,b^3}{35}-\frac{24\,a^3\,b}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{128\,a\,b^3}{5}-\frac{248\,a^3\,b}{5}\right)-40\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^4}{4}-\frac{3\,a^2\,b^2}{4}+\frac{3\,b^4}{64}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^15*((5*a^4)/4 - (3*b^4)/64 + (3*a^2*b^2)/4) + tan(c/2 + (d*x)/2)^3*((23*b^4)/64 - (17*a^4)/4 + (41*a^2*b^2)/4) + tan(c/2 + (d*x)/2)^13*((23*b^4)/64 - (17*a^4)/4 + (41*a^2*b^2)/4) + tan(c/2 + (d*x)/2)^5*((21*a^4)/4 + (333*b^4)/64 - (13*a^2*b^2)/4) + tan(c/2 + (d*x)/2)^11*((21*a^4)/4 + (333*b^4)/64 - (13*a^2*b^2)/4) - tan(c/2 + (d*x)/2)^7*((9*a^4)/4 - (671*b^4)/64 + (31*a^2*b^2)/4) - tan(c/2 + (d*x)/2)^9*((9*a^4)/4 - (671*b^4)/64 + (31*a^2*b^2)/4) - (16*a*b^3)/35 + (8*a^3*b)/5 + tan(c/2 + (d*x)/2)*((5*a^4)/4 - (3*b^4)/64 + (3*a^2*b^2)/4) - tan(c/2 + (d*x)/2)^12*(16*a*b^3 - 24*a^3*b) - tan(c/2 + (d*x)/2)^8*(16*a*b^3 - 56*a^3*b) + tan(c/2 + (d*x)/2)^4*((16*a*b^3)/5 + (104*a^3*b)/5) + tan(c/2 + (d*x)/2)^2*((128*a*b^3)/35 - (24*a^3*b)/5) + tan(c/2 + (d*x)/2)^6*((128*a*b^3)/5 - (248*a^3*b)/5) - 40*a^3*b*tan(c/2 + (d*x)/2)^10 - 8*a^3*b*tan(c/2 + (d*x)/2)^14)/(d*(28*tan(c/2 + (d*x)/2)^4 - 8*tan(c/2 + (d*x)/2)^2 - 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 - 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 - 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) + (atanh(tan(c/2 + (d*x)/2))*((3*a^4)/4 + (3*b^4)/64 - (3*a^2*b^2)/4))/d","B"
89,1,447,201,4.284390,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^10,x)","-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{152\,a^4}{5}-\frac{96\,a^2\,b^2}{5}+\frac{32\,b^4}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{152\,a^4}{5}-\frac{96\,a^2\,b^2}{5}+\frac{32\,b^4}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{288\,a^4}{5}+\frac{1488\,a^2\,b^2}{35}+\frac{384\,b^4}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-\frac{288\,a^4}{5}+\frac{1488\,a^2\,b^2}{35}+\frac{384\,b^4}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1076\,a^4}{15}-\frac{2752\,a^2\,b^2}{35}+\frac{6976\,b^4}{315}\right)+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{32\,a^4}{3}-16\,a^2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{32\,a^4}{3}-16\,a^2\,b^2\right)+2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a\,b^3-24\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(16\,a\,b^3-24\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(32\,a\,b^3-88\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(32\,a\,b^3-88\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{152\,a^3\,b}{3}+\frac{16\,a\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{152\,a^3\,b}{3}+\frac{16\,a\,b^3}{3}\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^9}","Not used",1,"-(tan(c/2 + (d*x)/2)^5*((152*a^4)/5 + (32*b^4)/5 - (96*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^13*((152*a^4)/5 + (32*b^4)/5 - (96*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^7*((384*b^4)/35 - (288*a^4)/5 + (1488*a^2*b^2)/35) + tan(c/2 + (d*x)/2)^11*((384*b^4)/35 - (288*a^4)/5 + (1488*a^2*b^2)/35) + tan(c/2 + (d*x)/2)^9*((1076*a^4)/15 + (6976*b^4)/315 - (2752*a^2*b^2)/35) + 2*a^4*tan(c/2 + (d*x)/2)^17 - tan(c/2 + (d*x)/2)^3*((32*a^4)/3 - 16*a^2*b^2) - tan(c/2 + (d*x)/2)^15*((32*a^4)/3 - 16*a^2*b^2) + 2*a^4*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^4*(16*a*b^3 - 24*a^3*b) - tan(c/2 + (d*x)/2)^14*(16*a*b^3 - 24*a^3*b) + tan(c/2 + (d*x)/2)^8*(32*a*b^3 - 88*a^3*b) - tan(c/2 + (d*x)/2)^10*(32*a*b^3 - 88*a^3*b) + tan(c/2 + (d*x)/2)^6*((16*a*b^3)/3 + (152*a^3*b)/3) - tan(c/2 + (d*x)/2)^12*((16*a*b^3)/3 + (152*a^3*b)/3) + 8*a^3*b*tan(c/2 + (d*x)/2)^2 - 8*a^3*b*tan(c/2 + (d*x)/2)^16)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^9)","B"
90,1,703,408,5.147181,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^11,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{5\,a^4}{8}-\frac{15\,a^2\,b^2}{32}+\frac{3\,b^4}{128}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\left(\frac{11\,a^4}{8}+\frac{15\,a^2\,b^2}{32}-\frac{3\,b^4}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{31\,a^4}{2}+\frac{93\,a^2\,b^2}{8}+\frac{519\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(-\frac{31\,a^4}{2}+\frac{93\,a^2\,b^2}{8}+\frac{519\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-\frac{127\,a^4}{24}+\frac{367\,a^2\,b^2}{32}+\frac{29\,b^4}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(-\frac{127\,a^4}{24}+\frac{367\,a^2\,b^2}{32}+\frac{29\,b^4}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{67\,a^4}{6}+\frac{29\,a^2\,b^2}{8}+\frac{867\,b^4}{160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{67\,a^4}{6}+\frac{29\,a^2\,b^2}{8}+\frac{867\,b^4}{160}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{33\,a^4}{4}-\frac{435\,a^2\,b^2}{16}+\frac{1879\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{33\,a^4}{4}-\frac{435\,a^2\,b^2}{16}+\frac{1879\,b^4}{64}\right)-\frac{16\,a\,b^3}{63}+\frac{8\,a^3\,b}{7}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{11\,a^4}{8}+\frac{15\,a^2\,b^2}{32}-\frac{3\,b^4}{128}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(16\,a\,b^3-24\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(64\,a^3\,b+\frac{32\,a\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(32\,a\,b^3-144\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{192\,a^3\,b}{7}+\frac{32\,a\,b^3}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{160\,a\,b^3}{63}-\frac{24\,a^3\,b}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{160\,a\,b^3}{3}-128\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{288\,a\,b^3}{7}-\frac{512\,a^3\,b}{7}\right)+112\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-252\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((5*a^4)/8 + (3*b^4)/128 - (15*a^2*b^2)/32))/d + (tan(c/2 + (d*x)/2)^19*((11*a^4)/8 - (3*b^4)/128 + (15*a^2*b^2)/32) + tan(c/2 + (d*x)/2)^7*((519*b^4)/32 - (31*a^4)/2 + (93*a^2*b^2)/8) + tan(c/2 + (d*x)/2)^13*((519*b^4)/32 - (31*a^4)/2 + (93*a^2*b^2)/8) + tan(c/2 + (d*x)/2)^3*((29*b^4)/128 - (127*a^4)/24 + (367*a^2*b^2)/32) + tan(c/2 + (d*x)/2)^17*((29*b^4)/128 - (127*a^4)/24 + (367*a^2*b^2)/32) + tan(c/2 + (d*x)/2)^5*((67*a^4)/6 + (867*b^4)/160 + (29*a^2*b^2)/8) + tan(c/2 + (d*x)/2)^15*((67*a^4)/6 + (867*b^4)/160 + (29*a^2*b^2)/8) + tan(c/2 + (d*x)/2)^9*((33*a^4)/4 + (1879*b^4)/64 - (435*a^2*b^2)/16) + tan(c/2 + (d*x)/2)^11*((33*a^4)/4 + (1879*b^4)/64 - (435*a^2*b^2)/16) - (16*a*b^3)/63 + (8*a^3*b)/7 + tan(c/2 + (d*x)/2)*((11*a^4)/8 - (3*b^4)/128 + (15*a^2*b^2)/32) - tan(c/2 + (d*x)/2)^16*(16*a*b^3 - 24*a^3*b) - tan(c/2 + (d*x)/2)^14*((32*a*b^3)/3 + 64*a^3*b) + tan(c/2 + (d*x)/2)^10*(32*a*b^3 - 144*a^3*b) + tan(c/2 + (d*x)/2)^4*((32*a*b^3)/7 + (192*a^3*b)/7) + tan(c/2 + (d*x)/2)^2*((160*a*b^3)/63 - (24*a^3*b)/7) - tan(c/2 + (d*x)/2)^12*((160*a*b^3)/3 - 128*a^3*b) + tan(c/2 + (d*x)/2)^6*((288*a*b^3)/7 - (512*a^3*b)/7) + 112*a^3*b*tan(c/2 + (d*x)/2)^8 - 8*a^3*b*tan(c/2 + (d*x)/2)^18)/(d*(45*tan(c/2 + (d*x)/2)^4 - 10*tan(c/2 + (d*x)/2)^2 - 120*tan(c/2 + (d*x)/2)^6 + 210*tan(c/2 + (d*x)/2)^8 - 252*tan(c/2 + (d*x)/2)^10 + 210*tan(c/2 + (d*x)/2)^12 - 120*tan(c/2 + (d*x)/2)^14 + 45*tan(c/2 + (d*x)/2)^16 - 10*tan(c/2 + (d*x)/2)^18 + tan(c/2 + (d*x)/2)^20 + 1))","B"
91,1,560,254,4.817947,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^4/cos(c + d*x)^12,x)","-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{226\,a^4}{5}-\frac{64\,a^2\,b^2}{5}+\frac{32\,b^4}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{226\,a^4}{5}-\frac{64\,a^2\,b^2}{5}+\frac{32\,b^4}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1308\,a^4}{7}-\frac{3008\,a^2\,b^2}{21}+\frac{992\,b^4}{21}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{1308\,a^4}{7}-\frac{3008\,a^2\,b^2}{21}+\frac{992\,b^4}{21}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{3952\,a^4}{35}+\frac{3008\,a^2\,b^2}{35}+\frac{576\,b^4}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(-\frac{3952\,a^4}{35}+\frac{3008\,a^2\,b^2}{35}+\frac{576\,b^4}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-\frac{1528\,a^4}{7}+\frac{2272\,a^2\,b^2}{21}+\frac{10624\,b^4}{231}\right)+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^4-16\,a^2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\left(12\,a^4-16\,a^2\,b^2\right)+2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a\,b^3-24\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(16\,a\,b^3-24\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(80\,a^3\,b+16\,a\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(80\,a^3\,b+16\,a\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(80\,a\,b^3-176\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(80\,a\,b^3-176\,a^3\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{112\,a\,b^3}{5}-224\,a^3\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{112\,a\,b^3}{5}-224\,a^3\,b\right)+8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-8\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^{11}}","Not used",1,"-(tan(c/2 + (d*x)/2)^5*((226*a^4)/5 + (32*b^4)/5 - (64*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^17*((226*a^4)/5 + (32*b^4)/5 - (64*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^9*((1308*a^4)/7 + (992*b^4)/21 - (3008*a^2*b^2)/21) + tan(c/2 + (d*x)/2)^13*((1308*a^4)/7 + (992*b^4)/21 - (3008*a^2*b^2)/21) + tan(c/2 + (d*x)/2)^7*((576*b^4)/35 - (3952*a^4)/35 + (3008*a^2*b^2)/35) + tan(c/2 + (d*x)/2)^15*((576*b^4)/35 - (3952*a^4)/35 + (3008*a^2*b^2)/35) + tan(c/2 + (d*x)/2)^11*((10624*b^4)/231 - (1528*a^4)/7 + (2272*a^2*b^2)/21) + 2*a^4*tan(c/2 + (d*x)/2)^21 - tan(c/2 + (d*x)/2)^3*(12*a^4 - 16*a^2*b^2) - tan(c/2 + (d*x)/2)^19*(12*a^4 - 16*a^2*b^2) + 2*a^4*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^4*(16*a*b^3 - 24*a^3*b) - tan(c/2 + (d*x)/2)^18*(16*a*b^3 - 24*a^3*b) + tan(c/2 + (d*x)/2)^6*(16*a*b^3 + 80*a^3*b) - tan(c/2 + (d*x)/2)^16*(16*a*b^3 + 80*a^3*b) + tan(c/2 + (d*x)/2)^8*(80*a*b^3 - 176*a^3*b) - tan(c/2 + (d*x)/2)^14*(80*a*b^3 - 176*a^3*b) - tan(c/2 + (d*x)/2)^10*((112*a*b^3)/5 - 224*a^3*b) + tan(c/2 + (d*x)/2)^12*((112*a*b^3)/5 - 224*a^3*b) + 8*a^3*b*tan(c/2 + (d*x)/2)^2 - 8*a^3*b*tan(c/2 + (d*x)/2)^20)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^11)","B"
92,1,801,515,2.513366,"\text{Not used}","int(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\left(-\frac{193\,a^5}{128}+\frac{35\,a^3\,b^2}{64}+\frac{15\,a\,b^4}{128}\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{193\,a^5}{128}+\frac{35\,a^3\,b^2}{64}+\frac{15\,a\,b^4}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{159\,a^5}{128}+\frac{4105\,a^3\,b^2}{192}-\frac{145\,a\,b^4}{128}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{159\,a^5}{128}+\frac{4105\,a^3\,b^2}{192}-\frac{145\,a\,b^4}{128}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{147\,a^5}{32}-\frac{2905\,a^3\,b^2}{16}+\frac{2595\,a\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{147\,a^5}{32}-\frac{2905\,a^3\,b^2}{16}+\frac{2595\,a\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{2847\,a^5}{160}-\frac{2891\,a^3\,b^2}{48}+\frac{867\,a\,b^4}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{2847\,a^5}{160}-\frac{2891\,a^3\,b^2}{48}+\frac{867\,a\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1827\,a^5}{64}-\frac{7945\,a^3\,b^2}{32}+\frac{9395\,a\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{1827\,a^5}{64}-\frac{7945\,a^3\,b^2}{32}+\frac{9395\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(120\,a^4\,b-80\,a^2\,b^3+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(120\,a^4\,b-80\,a^2\,b^3+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(252\,a^4\,b-224\,a^2\,b^3+\frac{192\,b^5}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{64\,b^5}{3}-280\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{64\,b^5}{3}-280\,a^2\,b^3\right)+40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+252\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(63\,a^4+70\,a^2\,b^2+15\,b^4\right)}{128\,\left(\frac{63\,a^5}{128}+\frac{35\,a^3\,b^2}{64}+\frac{15\,a\,b^4}{128}\right)}\right)\,\left(63\,a^4+70\,a^2\,b^2+15\,b^4\right)}{128\,d}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(63\,a^4+70\,a^2\,b^2+15\,b^4\right)}{128\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^19*((15*a*b^4)/128 - (193*a^5)/128 + (35*a^3*b^2)/64) - tan(c/2 + (d*x)/2)*((15*a*b^4)/128 - (193*a^5)/128 + (35*a^3*b^2)/64) + tan(c/2 + (d*x)/2)^3*((159*a^5)/128 - (145*a*b^4)/128 + (4105*a^3*b^2)/192) - tan(c/2 + (d*x)/2)^17*((159*a^5)/128 - (145*a*b^4)/128 + (4105*a^3*b^2)/192) - tan(c/2 + (d*x)/2)^7*((2595*a*b^4)/32 + (147*a^5)/32 - (2905*a^3*b^2)/16) + tan(c/2 + (d*x)/2)^13*((2595*a*b^4)/32 + (147*a^5)/32 - (2905*a^3*b^2)/16) + tan(c/2 + (d*x)/2)^5*((867*a*b^4)/32 + (2847*a^5)/160 - (2891*a^3*b^2)/48) - tan(c/2 + (d*x)/2)^15*((867*a*b^4)/32 + (2847*a^5)/160 - (2891*a^3*b^2)/48) + tan(c/2 + (d*x)/2)^9*((9395*a*b^4)/64 + (1827*a^5)/64 - (7945*a^3*b^2)/32) - tan(c/2 + (d*x)/2)^11*((9395*a*b^4)/64 + (1827*a^5)/64 - (7945*a^3*b^2)/32) + tan(c/2 + (d*x)/2)^6*(120*a^4*b + (32*b^5)/3 - 80*a^2*b^3) + tan(c/2 + (d*x)/2)^14*(120*a^4*b + (32*b^5)/3 - 80*a^2*b^3) + tan(c/2 + (d*x)/2)^10*(252*a^4*b + (192*b^5)/5 - 224*a^2*b^3) - tan(c/2 + (d*x)/2)^8*((64*b^5)/3 - 280*a^2*b^3) - tan(c/2 + (d*x)/2)^12*((64*b^5)/3 - 280*a^2*b^3) + 40*a^2*b^3*tan(c/2 + (d*x)/2)^4 + 40*a^2*b^3*tan(c/2 + (d*x)/2)^16 + 10*a^4*b*tan(c/2 + (d*x)/2)^2 + 10*a^4*b*tan(c/2 + (d*x)/2)^18)/(d*(10*tan(c/2 + (d*x)/2)^2 + 45*tan(c/2 + (d*x)/2)^4 + 120*tan(c/2 + (d*x)/2)^6 + 210*tan(c/2 + (d*x)/2)^8 + 252*tan(c/2 + (d*x)/2)^10 + 210*tan(c/2 + (d*x)/2)^12 + 120*tan(c/2 + (d*x)/2)^14 + 45*tan(c/2 + (d*x)/2)^16 + 10*tan(c/2 + (d*x)/2)^18 + tan(c/2 + (d*x)/2)^20 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(63*a^4 + 15*b^4 + 70*a^2*b^2))/(128*((15*a*b^4)/128 + (63*a^5)/128 + (35*a^3*b^2)/64)))*(63*a^4 + 15*b^4 + 70*a^2*b^2))/(128*d) - (a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(63*a^4 + 15*b^4 + 70*a^2*b^2))/(128*d)","B"
93,1,495,337,4.341846,"\text{Not used}","int(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{152\,a^5}{5}-32\,a^3\,b^2+32\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{152\,a^5}{5}-32\,a^3\,b^2+32\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{1136\,a^5}{35}+\frac{1264\,a^3\,b^2}{7}-\frac{384\,a\,b^4}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{1136\,a^5}{35}+\frac{1264\,a^3\,b^2}{7}-\frac{384\,a\,b^4}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{21316\,a^5}{315}-\frac{5696\,a^3\,b^2}{63}+\frac{6976\,a\,b^4}{63}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(40\,a^4\,b-\frac{120\,a^2\,b^3}{7}+\frac{64\,b^5}{35}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(140\,a^4\,b-120\,a^2\,b^3+\frac{112\,b^5}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(\frac{280\,a^4\,b}{3}-\frac{200\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)-\frac{10\,a^4\,b}{9}-\frac{16\,b^5}{315}-\frac{40\,a^2\,b^3}{63}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{16\,a^5}{3}+\frac{80\,a^3\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{16\,a^5}{3}+\frac{80\,a^3\,b^2}{3}\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{40\,a^2\,b^3}{7}+\frac{16\,b^5}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{32\,b^5}{5}-120\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(16\,b^5-200\,a^2\,b^3\right)-40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^9}","Not used",1,"(2*a^5*tan(c/2 + (d*x)/2)^17 + tan(c/2 + (d*x)/2)^5*(32*a*b^4 + (152*a^5)/5 - 32*a^3*b^2) + tan(c/2 + (d*x)/2)^13*(32*a*b^4 + (152*a^5)/5 - 32*a^3*b^2) + tan(c/2 + (d*x)/2)^7*((1136*a^5)/35 - (384*a*b^4)/7 + (1264*a^3*b^2)/7) + tan(c/2 + (d*x)/2)^11*((1136*a^5)/35 - (384*a*b^4)/7 + (1264*a^3*b^2)/7) + tan(c/2 + (d*x)/2)^9*((6976*a*b^4)/63 + (21316*a^5)/315 - (5696*a^3*b^2)/63) - tan(c/2 + (d*x)/2)^4*(40*a^4*b + (64*b^5)/35 - (120*a^2*b^3)/7) - tan(c/2 + (d*x)/2)^8*(140*a^4*b + (112*b^5)/5 - 120*a^2*b^3) - tan(c/2 + (d*x)/2)^12*((280*a^4*b)/3 + (32*b^5)/3 - (200*a^2*b^3)/3) - (10*a^4*b)/9 - (16*b^5)/315 - (40*a^2*b^3)/63 + tan(c/2 + (d*x)/2)^3*((16*a^5)/3 + (80*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^15*((16*a^5)/3 + (80*a^3*b^2)/3) + 2*a^5*tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2*((16*b^5)/35 + (40*a^2*b^3)/7) + tan(c/2 + (d*x)/2)^6*((32*b^5)/5 - 120*a^2*b^3) + tan(c/2 + (d*x)/2)^10*(16*b^5 - 200*a^2*b^3) - 40*a^2*b^3*tan(c/2 + (d*x)/2)^14 - 10*a^4*b*tan(c/2 + (d*x)/2)^16)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^9)","B"
94,1,650,426,2.479835,"\text{Not used}","int(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(-\frac{93\,a^5}{64}+\frac{25\,a^3\,b^2}{32}+\frac{15\,a\,b^4}{64}\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{93\,a^5}{64}+\frac{25\,a^3\,b^2}{32}+\frac{15\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{91\,a^5}{192}+\frac{1985\,a^3\,b^2}{96}-\frac{115\,a\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{91\,a^5}{192}+\frac{1985\,a^3\,b^2}{96}-\frac{115\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{1799\,a^5}{192}-\frac{4475\,a^3\,b^2}{96}+\frac{1665\,a\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{1799\,a^5}{192}-\frac{4475\,a^3\,b^2}{96}+\frac{1665\,a\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{1085\,a^5}{192}-\frac{8825\,a^3\,b^2}{96}+\frac{3355\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1085\,a^5}{192}-\frac{8825\,a^3\,b^2}{96}+\frac{3355\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(70\,a^4\,b-\frac{160\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(70\,a^4\,b-\frac{160\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{32\,b^5}{3}-\frac{400\,a^2\,b^3}{3}\right)+40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{5\,a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(7\,a^4+10\,a^2\,b^2+3\,b^4\right)}{64\,d}+\frac{5\,a\,\mathrm{atan}\left(\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2+3\,b^2\right)\,\left(a^2+b^2\right)}{64\,\left(\frac{35\,a^5}{64}+\frac{25\,a^3\,b^2}{32}+\frac{15\,a\,b^4}{64}\right)}\right)\,\left(7\,a^2+3\,b^2\right)\,\left(a^2+b^2\right)}{64\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^15*((15*a*b^4)/64 - (93*a^5)/64 + (25*a^3*b^2)/32) - tan(c/2 + (d*x)/2)*((15*a*b^4)/64 - (93*a^5)/64 + (25*a^3*b^2)/32) + tan(c/2 + (d*x)/2)^3*((91*a^5)/192 - (115*a*b^4)/64 + (1985*a^3*b^2)/96) - tan(c/2 + (d*x)/2)^13*((91*a^5)/192 - (115*a*b^4)/64 + (1985*a^3*b^2)/96) + tan(c/2 + (d*x)/2)^5*((1665*a*b^4)/64 + (1799*a^5)/192 - (4475*a^3*b^2)/96) - tan(c/2 + (d*x)/2)^11*((1665*a*b^4)/64 + (1799*a^5)/192 - (4475*a^3*b^2)/96) - tan(c/2 + (d*x)/2)^7*((3355*a*b^4)/64 + (1085*a^5)/192 - (8825*a^3*b^2)/96) + tan(c/2 + (d*x)/2)^9*((3355*a*b^4)/64 + (1085*a^5)/192 - (8825*a^3*b^2)/96) + tan(c/2 + (d*x)/2)^6*(70*a^4*b + (32*b^5)/3 - (160*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^10*(70*a^4*b + (32*b^5)/3 - (160*a^2*b^3)/3) - tan(c/2 + (d*x)/2)^8*((32*b^5)/3 - (400*a^2*b^3)/3) + 40*a^2*b^3*tan(c/2 + (d*x)/2)^4 + 40*a^2*b^3*tan(c/2 + (d*x)/2)^12 + 10*a^4*b*tan(c/2 + (d*x)/2)^2 + 10*a^4*b*tan(c/2 + (d*x)/2)^14)/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) - (5*a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(7*a^4 + 3*b^4 + 10*a^2*b^2))/(64*d) + (5*a*atan((5*a*tan(c/2 + (d*x)/2)*(7*a^2 + 3*b^2)*(a^2 + b^2))/(64*((15*a*b^4)/64 + (35*a^5)/64 + (25*a^3*b^2)/32)))*(7*a^2 + 3*b^2)*(a^2 + b^2))/(64*d)","B"
95,1,372,275,4.421471,"\text{Not used}","int(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{86\,a^5}{5}-\frac{64\,a^3\,b^2}{3}+32\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{86\,a^5}{5}-\frac{64\,a^3\,b^2}{3}+32\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{424\,a^5}{35}+\frac{608\,a^3\,b^2}{7}-\frac{192\,a\,b^4}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(30\,a^4\,b-16\,a^2\,b^3+\frac{16\,b^5}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(50\,a^4\,b-40\,a^2\,b^3+\frac{32\,b^5}{3}\right)-\frac{10\,a^4\,b}{7}-\frac{16\,b^5}{105}-\frac{8\,a^2\,b^3}{7}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^5+\frac{80\,a^3\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(4\,a^5+\frac{80\,a^3\,b^2}{3}\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^2\,b^3+\frac{16\,b^5}{15}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{16\,b^5}{3}-80\,a^2\,b^3\right)-40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^7}","Not used",1,"(2*a^5*tan(c/2 + (d*x)/2)^13 + tan(c/2 + (d*x)/2)^5*(32*a*b^4 + (86*a^5)/5 - (64*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^9*(32*a*b^4 + (86*a^5)/5 - (64*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^7*((424*a^5)/35 - (192*a*b^4)/7 + (608*a^3*b^2)/7) - tan(c/2 + (d*x)/2)^4*(30*a^4*b + (16*b^5)/5 - 16*a^2*b^3) - tan(c/2 + (d*x)/2)^8*(50*a^4*b + (32*b^5)/3 - 40*a^2*b^3) - (10*a^4*b)/7 - (16*b^5)/105 - (8*a^2*b^3)/7 + tan(c/2 + (d*x)/2)^3*(4*a^5 + (80*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^11*(4*a^5 + (80*a^3*b^2)/3) + 2*a^5*tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2*((16*b^5)/15 + 8*a^2*b^3) + tan(c/2 + (d*x)/2)^6*((16*b^5)/3 - 80*a^2*b^3) - 40*a^2*b^3*tan(c/2 + (d*x)/2)^10 - 10*a^4*b*tan(c/2 + (d*x)/2)^12)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
96,1,472,126,2.318608,"\text{Not used}","int(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-\frac{11\,a^5}{8}+\frac{5\,a^3\,b^2}{4}+\frac{5\,a\,b^4}{8}\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-\frac{11\,a^5}{8}+\frac{5\,a^3\,b^2}{4}+\frac{5\,a\,b^4}{8}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{15\,a^5}{4}-\frac{65\,a^3\,b^2}{2}+\frac{95\,a\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{15\,a^5}{4}-\frac{65\,a^3\,b^2}{2}+\frac{95\,a\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,a^5}{24}-\frac{235\,a^3\,b^2}{12}+\frac{85\,a\,b^4}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{5\,a^5}{24}-\frac{235\,a^3\,b^2}{12}+\frac{85\,a\,b^4}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{100\,a^4\,b}{3}-\frac{80\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+40\,a^2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{5\,a\,\mathrm{atan}\left(\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^2}{8\,\left(\frac{5\,a^5}{8}+\frac{5\,a^3\,b^2}{4}+\frac{5\,a\,b^4}{8}\right)}\right)\,{\left(a^2+b^2\right)}^2}{8\,d}-\frac{5\,a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,{\left(a^2+b^2\right)}^2}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((5*a*b^4)/8 - (11*a^5)/8 + (5*a^3*b^2)/4) - tan(c/2 + (d*x)/2)*((5*a*b^4)/8 - (11*a^5)/8 + (5*a^3*b^2)/4) + tan(c/2 + (d*x)/2)^5*((95*a*b^4)/4 + (15*a^5)/4 - (65*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^7*((95*a*b^4)/4 + (15*a^5)/4 - (65*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^3*((85*a*b^4)/24 + (5*a^5)/24 - (235*a^3*b^2)/12) + tan(c/2 + (d*x)/2)^9*((85*a*b^4)/24 + (5*a^5)/24 - (235*a^3*b^2)/12) + tan(c/2 + (d*x)/2)^6*((100*a^4*b)/3 + (32*b^5)/3 - (80*a^2*b^3)/3) + 40*a^2*b^3*tan(c/2 + (d*x)/2)^4 + 40*a^2*b^3*tan(c/2 + (d*x)/2)^8 + 10*a^4*b*tan(c/2 + (d*x)/2)^2 + 10*a^4*b*tan(c/2 + (d*x)/2)^10)/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (5*a*atan((5*a*tan(c/2 + (d*x)/2)*(a^2 + b^2)^2)/(8*((5*a*b^4)/8 + (5*a^5)/8 + (5*a^3*b^2)/4)))*(a^2 + b^2)^2)/(8*d) - (5*a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(a^2 + b^2)^2)/(8*d)","B"
97,1,248,94,0.937585,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5,x)","\frac{2\,\left(\frac{3\,\sin\left(c+d\,x\right)\,a^5\,{\cos\left(c+d\,x\right)}^4}{2}+2\,\sin\left(c+d\,x\right)\,a^5\,{\cos\left(c+d\,x\right)}^2+4\,\sin\left(c+d\,x\right)\,a^5-\frac{15\,a^4\,b\,{\cos\left(c+d\,x\right)}^5}{2}-15\,\sin\left(c+d\,x\right)\,a^3\,b^2\,{\cos\left(c+d\,x\right)}^4+5\,\sin\left(c+d\,x\right)\,a^3\,b^2\,{\cos\left(c+d\,x\right)}^2+10\,\sin\left(c+d\,x\right)\,a^3\,b^2+15\,a^2\,b^3\,{\cos\left(c+d\,x\right)}^5-25\,a^2\,b^3\,{\cos\left(c+d\,x\right)}^3+\frac{15\,\sin\left(c+d\,x\right)\,a\,b^4\,{\cos\left(c+d\,x\right)}^4}{2}-15\,\sin\left(c+d\,x\right)\,a\,b^4\,{\cos\left(c+d\,x\right)}^2+\frac{15\,\sin\left(c+d\,x\right)\,a\,b^4}{2}-\frac{3\,b^5\,{\cos\left(c+d\,x\right)}^5}{2}+5\,b^5\,{\cos\left(c+d\,x\right)}^3-\frac{15\,b^5\,\cos\left(c+d\,x\right)}{2}\right)}{15\,d}","Not used",1,"(2*(4*a^5*sin(c + d*x) - (15*b^5*cos(c + d*x))/2 + 5*b^5*cos(c + d*x)^3 - (3*b^5*cos(c + d*x)^5)/2 - (15*a^4*b*cos(c + d*x)^5)/2 + 2*a^5*cos(c + d*x)^2*sin(c + d*x) + (3*a^5*cos(c + d*x)^4*sin(c + d*x))/2 + 10*a^3*b^2*sin(c + d*x) - 25*a^2*b^3*cos(c + d*x)^3 + 15*a^2*b^3*cos(c + d*x)^5 + (15*a*b^4*sin(c + d*x))/2 + 5*a^3*b^2*cos(c + d*x)^2*sin(c + d*x) - 15*a^3*b^2*cos(c + d*x)^4*sin(c + d*x) - 15*a*b^4*cos(c + d*x)^2*sin(c + d*x) + (15*a*b^4*cos(c + d*x)^4*sin(c + d*x))/2))/(15*d)","B"
98,1,297,170,2.647504,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x),x)","\frac{4\,b^5\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)-4\,b^5\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)+3\,a^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{3\,b^5\,\cos\left(2\,c+2\,d\,x\right)}{2}-\frac{b^5\,\cos\left(4\,c+4\,d\,x\right)}{8}+a^5\,\sin\left(2\,c+2\,d\,x\right)+\frac{a^5\,\sin\left(4\,c+4\,d\,x\right)}{8}+15\,a\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{5\,a^4\,b\,\cos\left(2\,c+2\,d\,x\right)}{2}-\frac{5\,a^4\,b\,\cos\left(4\,c+4\,d\,x\right)}{8}-5\,a\,b^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{5\,a\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+10\,a^3\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-5\,a^2\,b^3\,\cos\left(2\,c+2\,d\,x\right)+\frac{5\,a^2\,b^3\,\cos\left(4\,c+4\,d\,x\right)}{4}-\frac{5\,a^3\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{4}}{4\,d}","Not used",1,"(4*b^5*log(1/cos(c/2 + (d*x)/2)^2) - 4*b^5*log(cos(c + d*x)/(cos(c + d*x) + 1)) + 3*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (3*b^5*cos(2*c + 2*d*x))/2 - (b^5*cos(4*c + 4*d*x))/8 + a^5*sin(2*c + 2*d*x) + (a^5*sin(4*c + 4*d*x))/8 + 15*a*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (5*a^4*b*cos(2*c + 2*d*x))/2 - (5*a^4*b*cos(4*c + 4*d*x))/8 - 5*a*b^4*sin(2*c + 2*d*x) + (5*a*b^4*sin(4*c + 4*d*x))/8 + 10*a^3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 5*a^2*b^3*cos(2*c + 2*d*x) + (5*a^2*b^3*cos(4*c + 4*d*x))/4 - (5*a^3*b^2*sin(4*c + 4*d*x))/4)/(4*d)","B"
99,1,277,205,3.977616,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^2,x)","\frac{10\,a\,b^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a\,b^4-2\,a^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^4\,b-40\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,a^5}{3}-\frac{80\,a^3\,b^2}{3}+\frac{70\,a\,b^4}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{2\,a^5}{3}-\frac{80\,a^3\,b^2}{3}+\frac{70\,a\,b^4}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{10\,a^4\,b}{3}-\frac{80\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+\frac{10\,a^4\,b}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(10\,a\,b^4-2\,a^5\right)-\frac{16\,b^5}{3}+\frac{40\,a^2\,b^3}{3}-10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(10*a*b^4*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)*(10*a*b^4 - 2*a^5) + tan(c/2 + (d*x)/2)^4*(10*a^4*b - 40*a^2*b^3) + tan(c/2 + (d*x)/2)^3*((70*a*b^4)/3 + (2*a^5)/3 - (80*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^5*((70*a*b^4)/3 + (2*a^5)/3 - (80*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^2*((10*a^4*b)/3 + (32*b^5)/3 - (80*a^2*b^3)/3) + (10*a^4*b)/3 - tan(c/2 + (d*x)/2)^7*(10*a*b^4 - 2*a^5) - (16*b^5)/3 + (40*a^2*b^3)/3 - 10*a^4*b*tan(c/2 + (d*x)/2)^6)/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + 1))","B"
100,1,354,169,2.533067,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^3,x)","\frac{2\,\left(b^5\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)-b^5\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)+\frac{a^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-5\,a^2\,b^3\,\ln\left(\frac{\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)+1}\right)-\frac{15\,a\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+5\,a^2\,b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)+5\,a^3\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{5\,a^4\,b}{16}+\frac{9\,b^5}{16}-\frac{5\,a^2\,b^3}{8}-\frac{b^5\,\cos\left(4\,c+4\,d\,x\right)}{16}+\frac{a^5\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{a^5\,\sin\left(4\,c+4\,d\,x\right)}{16}-\frac{5\,a^4\,b\,\cos\left(4\,c+4\,d\,x\right)}{16}+\frac{25\,a\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{5\,a\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{5\,a^2\,b^3\,\cos\left(4\,c+4\,d\,x\right)}{8}-\frac{5\,a^3\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}-\frac{5\,a^3\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{8}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(b^5*log(cos(c + d*x)/(cos(c + d*x) + 1)) - b^5*log(1/cos(c/2 + (d*x)/2)^2) + (a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - 5*a^2*b^3*log(cos(c + d*x)/(cos(c + d*x) + 1)) - (15*a*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 5*a^2*b^3*log(1/cos(c/2 + (d*x)/2)^2) + 5*a^3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((5*a^4*b)/16 + (9*b^5)/16 - (5*a^2*b^3)/8 - (b^5*cos(4*c + 4*d*x))/16 + (a^5*sin(2*c + 2*d*x))/8 + (a^5*sin(4*c + 4*d*x))/16 - (5*a^4*b*cos(4*c + 4*d*x))/16 + (25*a*b^4*sin(2*c + 2*d*x))/8 + (5*a*b^4*sin(4*c + 4*d*x))/16 + (5*a^2*b^3*cos(4*c + 4*d*x))/8 - (5*a^3*b^2*sin(2*c + 2*d*x))/4 - (5*a^3*b^2*sin(4*c + 4*d*x))/8)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
101,1,302,204,4.047024,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^4,x)","-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,a\,b^4-20\,a^3\,b^2\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^5-20\,a^3\,b^2+15\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(30\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^5-20\,a^3\,b^2+15\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^5-60\,a^3\,b^2+25\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^5-60\,a^3\,b^2+25\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(30\,a^4\,b-80\,a^2\,b^3+\frac{32\,b^5}{3}\right)-10\,a^4\,b-\frac{16\,b^5}{3}+40\,a^2\,b^3+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- (atanh(tan(c/2 + (d*x)/2))*(15*a*b^4 - 20*a^3*b^2))/d - (tan(c/2 + (d*x)/2)*(15*a*b^4 + 2*a^5 - 20*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(30*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^7*(15*a*b^4 + 2*a^5 - 20*a^3*b^2) - tan(c/2 + (d*x)/2)^3*(25*a*b^4 + 6*a^5 - 60*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(25*a*b^4 + 6*a^5 - 60*a^3*b^2) + tan(c/2 + (d*x)/2)^2*(30*a^4*b + (32*b^5)/3 - 80*a^2*b^3) - 10*a^4*b - (16*b^5)/3 + 40*a^2*b^3 + 10*a^4*b*tan(c/2 + (d*x)/2)^6)/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 - 1))","B"
102,1,971,147,3.447469,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^5,x)","\frac{\frac{3\,b^5\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{8}-\frac{3\,b^5\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{8}+\frac{b^5}{32}+\frac{3\,a^5\,\mathrm{atan}\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{5\,a^2\,b^3}{8}-\frac{b^5\,\cos\left(2\,c+2\,d\,x\right)}{8}+\frac{3\,b^5\,\cos\left(4\,c+4\,d\,x\right)}{32}+\frac{15\,a^4\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{8}+\frac{15\,a^2\,b^3\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{4}-\frac{b^5\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}-\frac{b^5\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{15\,a\,b^4\,\mathrm{atan}\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{5\,a\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{6}-\frac{5\,a\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{6}-\frac{15\,a^2\,b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{4}+\frac{b^5\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{b^5\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+a^5\,\mathrm{atan}\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)+\frac{a^5\,\mathrm{atan}\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(4\,c+4\,d\,x\right)}{4}-\frac{15\,a^3\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{5\,a^2\,b^3\,\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{5\,a^3\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,a^3\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{4}-\frac{15\,a^4\,b\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{8}-5\,a^2\,b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(2\,c+2\,d\,x\right)-\frac{5\,a^2\,b^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}-10\,a^3\,b^2\,\mathrm{atan}\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)-\frac{5\,a^3\,b^2\,\mathrm{atan}\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(4\,c+4\,d\,x\right)}{2}-\frac{5\,a^4\,b\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}-\frac{5\,a^4\,b\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{5\,a^4\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,a^4\,b\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+5\,a^2\,b^3\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{5\,a^2\,b^3\,\ln\left(-\frac{\cos\left(c+d\,x\right)}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}+5\,a\,b^4\,\mathrm{atan}\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)+\frac{5\,a\,b^4\,\mathrm{atan}\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(4\,c+4\,d\,x\right)}{4}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((3*b^5*log(1/cos(c/2 + (d*x)/2)^2))/8 - (3*b^5*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2))/8 + b^5/32 + (3*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (5*a^2*b^3)/8 - (b^5*cos(2*c + 2*d*x))/8 + (3*b^5*cos(4*c + 4*d*x))/32 + (15*a^4*b*log(1/cos(c/2 + (d*x)/2)^2))/8 + (15*a^2*b^3*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2))/4 - (b^5*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(2*c + 2*d*x))/2 - (b^5*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(4*c + 4*d*x))/8 + (15*a*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (5*a*b^4*sin(2*c + 2*d*x))/6 - (5*a*b^4*sin(4*c + 4*d*x))/6 - (15*a^2*b^3*log(1/cos(c/2 + (d*x)/2)^2))/4 + (b^5*log(1/cos(c/2 + (d*x)/2)^2)*cos(2*c + 2*d*x))/2 + (b^5*log(1/cos(c/2 + (d*x)/2)^2)*cos(4*c + 4*d*x))/8 + a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/4 - (15*a^3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (5*a^2*b^3*cos(4*c + 4*d*x))/8 + (5*a^3*b^2*sin(2*c + 2*d*x))/2 + (5*a^3*b^2*sin(4*c + 4*d*x))/4 - (15*a^4*b*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2))/8 - 5*a^2*b^3*log(1/cos(c/2 + (d*x)/2)^2)*cos(2*c + 2*d*x) - (5*a^2*b^3*log(1/cos(c/2 + (d*x)/2)^2)*cos(4*c + 4*d*x))/4 - 10*a^3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) - (5*a^3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 - (5*a^4*b*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(2*c + 2*d*x))/2 - (5*a^4*b*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(4*c + 4*d*x))/8 + (5*a^4*b*log(1/cos(c/2 + (d*x)/2)^2)*cos(2*c + 2*d*x))/2 + (5*a^4*b*log(1/cos(c/2 + (d*x)/2)^2)*cos(4*c + 4*d*x))/8 + 5*a^2*b^3*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(2*c + 2*d*x) + (5*a^2*b^3*log(-cos(c + d*x)/cos(c/2 + (d*x)/2)^2)*cos(4*c + 4*d*x))/4 + 5*a*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (5*a*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/4)/(d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
103,1,345,224,4.256002,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^5-10\,a^3\,b^2+\frac{15\,a\,b^4}{4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{15\,a\,b^4}{4}-10\,a^3\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{35\,a\,b^4}{2}-20\,a^3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{35\,a\,b^4}{2}-20\,a^3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(40\,a^4\,b-\frac{200\,a^2\,b^3}{3}+\frac{16\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(60\,a^4\,b-\frac{280\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+10\,a^4\,b+\frac{16\,b^5}{15}-\frac{40\,a^2\,b^3}{3}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{15\,a\,b^4}{4}-10\,a^3\,b^2\right)+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((15*a*b^4)/4 + 2*a^5 - 10*a^3*b^2))/d - (tan(c/2 + (d*x)/2)^9*((15*a*b^4)/4 - 10*a^3*b^2) + tan(c/2 + (d*x)/2)^3*((35*a*b^4)/2 - 20*a^3*b^2) - tan(c/2 + (d*x)/2)^7*((35*a*b^4)/2 - 20*a^3*b^2) - tan(c/2 + (d*x)/2)^6*(40*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^2*(40*a^4*b + (16*b^5)/3 - (200*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^4*(60*a^4*b + (32*b^5)/3 - (280*a^2*b^3)/3) + 10*a^4*b + (16*b^5)/15 - (40*a^2*b^3)/3 - tan(c/2 + (d*x)/2)*((15*a*b^4)/4 - 10*a^3*b^2) + 10*a^4*b*tan(c/2 + (d*x)/2)^8)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
104,1,169,30,0.976022,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^7,x)","\frac{{\cos\left(c+d\,x\right)}^4\,\left(\frac{5\,a^4\,b}{2}-5\,a^2\,b^3+\frac{b^5}{2}\right)+{\cos\left(c+d\,x\right)}^5\,\left(\sin\left(c+d\,x\right)\,a^5-\frac{10\,\sin\left(c+d\,x\right)\,a^3\,b^2}{3}+\sin\left(c+d\,x\right)\,a\,b^4\right)-{\cos\left(c+d\,x\right)}^2\,\left(\frac{b^5}{2}-\frac{5\,a^2\,b^3}{2}\right)+\frac{b^5}{6}+{\cos\left(c+d\,x\right)}^3\,\left(\frac{10\,a^3\,b^2\,\sin\left(c+d\,x\right)}{3}-2\,a\,b^4\,\sin\left(c+d\,x\right)\right)+a\,b^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^6}","Not used",1,"(cos(c + d*x)^4*((5*a^4*b)/2 + b^5/2 - 5*a^2*b^3) + cos(c + d*x)^5*(a^5*sin(c + d*x) - (10*a^3*b^2*sin(c + d*x))/3 + a*b^4*sin(c + d*x)) - cos(c + d*x)^2*(b^5/2 - (5*a^2*b^3)/2) + b^5/6 + cos(c + d*x)^3*((10*a^3*b^2*sin(c + d*x))/3 - 2*a*b^4*sin(c + d*x)) + a*b^4*cos(c + d*x)*sin(c + d*x))/(d*cos(c + d*x)^6)","B"
105,1,514,318,4.205184,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^8,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^5-\frac{5\,a^3\,b^2}{2}+\frac{5\,a\,b^4}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-4\,a^5+10\,a^3\,b^2+\frac{25\,a\,b^4}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(a^5+\frac{5\,a^3\,b^2}{2}-\frac{5\,a\,b^4}{8}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(-4\,a^5+10\,a^3\,b^2+\frac{25\,a\,b^4}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(5\,a^5-\frac{55\,a^3\,b^2}{2}+\frac{485\,a\,b^4}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(5\,a^5-\frac{55\,a^3\,b^2}{2}+\frac{485\,a\,b^4}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(30\,a^4\,b-16\,a^2\,b^3+\frac{16\,b^5}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{40\,a^4\,b}{3}-\frac{56\,a^2\,b^3}{3}+\frac{16\,b^5}{15}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-\frac{160\,a^4\,b}{3}+\frac{80\,a^2\,b^3}{3}+\frac{16\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{190\,a^4\,b}{3}-\frac{200\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+\frac{10\,a^4\,b}{3}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^5+\frac{5\,a^3\,b^2}{2}-\frac{5\,a\,b^4}{8}\right)+\frac{16\,b^5}{105}-\frac{8\,a^2\,b^3}{3}+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((5*a*b^4)/8 + a^5 - (5*a^3*b^2)/2))/d - (tan(c/2 + (d*x)/2)^3*((25*a*b^4)/6 - 4*a^5 + 10*a^3*b^2) - tan(c/2 + (d*x)/2)^10*(40*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^13*(a^5 - (5*a*b^4)/8 + (5*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^11*((25*a*b^4)/6 - 4*a^5 + 10*a^3*b^2) + tan(c/2 + (d*x)/2)^5*((485*a*b^4)/24 + 5*a^5 - (55*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^9*((485*a*b^4)/24 + 5*a^5 - (55*a^3*b^2)/2) + tan(c/2 + (d*x)/2)^4*(30*a^4*b + (16*b^5)/5 - 16*a^2*b^3) - tan(c/2 + (d*x)/2)^2*((40*a^4*b)/3 + (16*b^5)/15 - (56*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^6*((16*b^5)/3 - (160*a^4*b)/3 + (80*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^8*((190*a^4*b)/3 + (32*b^5)/3 - (200*a^2*b^3)/3) + (10*a^4*b)/3 + tan(c/2 + (d*x)/2)*(a^5 - (5*a*b^4)/8 + (5*a^3*b^2)/2) + (16*b^5)/105 - (8*a^2*b^3)/3 + 10*a^4*b*tan(c/2 + (d*x)/2)^12)/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
106,1,419,177,4.271918,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^9,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{86\,a^5}{3}-\frac{208\,a^3\,b^2}{3}+32\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{86\,a^5}{3}-\frac{208\,a^3\,b^2}{3}+32\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{130\,a^5}{3}-\frac{224\,a^3\,b^2}{3}+\frac{32\,a\,b^4}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{130\,a^5}{3}-\frac{224\,a^3\,b^2}{3}+\frac{32\,a\,b^4}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-80\,a^4\,b+\frac{80\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(70\,a^4\,b-\frac{160\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(70\,a^4\,b-\frac{160\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{34\,a^5}{3}-\frac{80\,a^3\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{34\,a^5}{3}-\frac{80\,a^3\,b^2}{3}\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^8}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(32*a*b^4 + (86*a^5)/3 - (208*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^4*(40*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^12*(40*a^4*b - 40*a^2*b^3) - 2*a^5*tan(c/2 + (d*x)/2)^15 - tan(c/2 + (d*x)/2)^11*(32*a*b^4 + (86*a^5)/3 - (208*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^7*((32*a*b^4)/7 + (130*a^5)/3 - (224*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^9*((32*a*b^4)/7 + (130*a^5)/3 - (224*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^8*((32*b^5)/3 - 80*a^4*b + (80*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^6*(70*a^4*b + (32*b^5)/3 - (160*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^10*(70*a^4*b + (32*b^5)/3 - (160*a^2*b^3)/3) - tan(c/2 + (d*x)/2)^3*((34*a^5)/3 - (80*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^13*((34*a^5)/3 - (80*a^3*b^2)/3) + 2*a^5*tan(c/2 + (d*x)/2) + 10*a^4*b*tan(c/2 + (d*x)/2)^2 + 10*a^4*b*tan(c/2 + (d*x)/2)^14)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^8)","B"
107,1,675,391,4.709231,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^10,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^5}{4}-\frac{5\,a^3\,b^2}{4}+\frac{15\,a\,b^4}{64}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a^5}{4}+\frac{5\,a^3\,b^2}{4}-\frac{15\,a\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{5\,a^5}{4}+\frac{5\,a^3\,b^2}{4}-\frac{15\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-\frac{11\,a^5}{2}+\frac{95\,a^3\,b^2}{6}+\frac{65\,a\,b^4}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(-\frac{11\,a^5}{2}+\frac{95\,a^3\,b^2}{6}+\frac{65\,a\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{19\,a^5}{2}-\frac{45\,a^3\,b^2}{2}+\frac{775\,a\,b^4}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{19\,a^5}{2}-\frac{45\,a^3\,b^2}{2}+\frac{775\,a\,b^4}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{15\,a^5}{2}+\frac{15\,a^3\,b^2}{2}-\frac{845\,a\,b^4}{32}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{15\,a^5}{2}+\frac{15\,a^3\,b^2}{2}-\frac{845\,a\,b^4}{32}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^4\,b-\frac{72\,a^2\,b^3}{7}+\frac{16\,b^5}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(32\,a^4\,b-\frac{8\,a^2\,b^3}{7}+\frac{64\,b^5}{35}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(80\,a^4\,b-40\,a^2\,b^3+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-120\,a^4\,b+40\,a^2\,b^3+16\,b^5\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-88\,a^4\,b+56\,a^2\,b^3+\frac{32\,b^5}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(132\,a^4\,b-104\,a^2\,b^3+\frac{112\,b^5}{5}\right)+2\,a^4\,b+\frac{16\,b^5}{315}-\frac{8\,a^2\,b^3}{7}+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((15*a*b^4)/64 + (3*a^5)/4 - (5*a^3*b^2)/4))/d - (tan(c/2 + (d*x)/2)*((5*a^5)/4 - (15*a*b^4)/64 + (5*a^3*b^2)/4) - tan(c/2 + (d*x)/2)^14*(40*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^17*((5*a^5)/4 - (15*a*b^4)/64 + (5*a^3*b^2)/4) + tan(c/2 + (d*x)/2)^3*((65*a*b^4)/32 - (11*a^5)/2 + (95*a^3*b^2)/6) - tan(c/2 + (d*x)/2)^15*((65*a*b^4)/32 - (11*a^5)/2 + (95*a^3*b^2)/6) + tan(c/2 + (d*x)/2)^5*((775*a*b^4)/32 + (19*a^5)/2 - (45*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^13*((775*a*b^4)/32 + (19*a^5)/2 - (45*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^7*((15*a^5)/2 - (845*a*b^4)/32 + (15*a^3*b^2)/2) + tan(c/2 + (d*x)/2)^11*((15*a^5)/2 - (845*a*b^4)/32 + (15*a^3*b^2)/2) - tan(c/2 + (d*x)/2)^2*(8*a^4*b + (16*b^5)/35 - (72*a^2*b^3)/7) + tan(c/2 + (d*x)/2)^4*(32*a^4*b + (64*b^5)/35 - (8*a^2*b^3)/7) + tan(c/2 + (d*x)/2)^12*(80*a^4*b + (32*b^5)/3 - 40*a^2*b^3) + tan(c/2 + (d*x)/2)^10*(16*b^5 - 120*a^4*b + 40*a^2*b^3) + tan(c/2 + (d*x)/2)^6*((32*b^5)/5 - 88*a^4*b + 56*a^2*b^3) + tan(c/2 + (d*x)/2)^8*(132*a^4*b + (112*b^5)/5 - 104*a^2*b^3) + 2*a^4*b + (16*b^5)/315 - (8*a^2*b^3)/7 + 10*a^4*b*tan(c/2 + (d*x)/2)^16)/(d*(9*tan(c/2 + (d*x)/2)^2 - 36*tan(c/2 + (d*x)/2)^4 + 84*tan(c/2 + (d*x)/2)^6 - 126*tan(c/2 + (d*x)/2)^8 + 126*tan(c/2 + (d*x)/2)^10 - 84*tan(c/2 + (d*x)/2)^12 + 36*tan(c/2 + (d*x)/2)^14 - 9*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^18 - 1))","B"
108,1,548,242,4.442367,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^11,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{616\,a^5}{15}-\frac{176\,a^3\,b^2}{3}+32\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(40\,a^4\,b-40\,a^2\,b^3\right)-2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(\frac{616\,a^5}{15}-\frac{176\,a^3\,b^2}{3}+32\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-88\,a^5+\frac{720\,a^3\,b^2}{7}+\frac{160\,a\,b^4}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(-88\,a^5+\frac{720\,a^3\,b^2}{7}+\frac{160\,a\,b^4}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{388\,a^5}{3}-\frac{4240\,a^3\,b^2}{21}+\frac{3520\,a\,b^4}{63}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(\frac{388\,a^5}{3}-\frac{4240\,a^3\,b^2}{21}+\frac{3520\,a\,b^4}{63}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{280\,a^4\,b}{3}-\frac{80\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(\frac{280\,a^4\,b}{3}-\frac{80\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(220\,a^4\,b-160\,a^2\,b^3+\frac{192\,b^5}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-\frac{520\,a^4\,b}{3}+\frac{200\,a^2\,b^3}{3}+\frac{64\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(-\frac{520\,a^4\,b}{3}+\frac{200\,a^2\,b^3}{3}+\frac{64\,b^5}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{38\,a^5}{3}-\frac{80\,a^3\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{38\,a^5}{3}-\frac{80\,a^3\,b^2}{3}\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^{10}}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(32*a*b^4 + (616*a^5)/15 - (176*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^4*(40*a^4*b - 40*a^2*b^3) - tan(c/2 + (d*x)/2)^16*(40*a^4*b - 40*a^2*b^3) - 2*a^5*tan(c/2 + (d*x)/2)^19 - tan(c/2 + (d*x)/2)^15*(32*a*b^4 + (616*a^5)/15 - (176*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^7*((160*a*b^4)/7 - 88*a^5 + (720*a^3*b^2)/7) - tan(c/2 + (d*x)/2)^13*((160*a*b^4)/7 - 88*a^5 + (720*a^3*b^2)/7) + tan(c/2 + (d*x)/2)^9*((3520*a*b^4)/63 + (388*a^5)/3 - (4240*a^3*b^2)/21) - tan(c/2 + (d*x)/2)^11*((3520*a*b^4)/63 + (388*a^5)/3 - (4240*a^3*b^2)/21) + tan(c/2 + (d*x)/2)^6*((280*a^4*b)/3 + (32*b^5)/3 - (80*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^14*((280*a^4*b)/3 + (32*b^5)/3 - (80*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^10*(220*a^4*b + (192*b^5)/5 - 160*a^2*b^3) + tan(c/2 + (d*x)/2)^8*((64*b^5)/3 - (520*a^4*b)/3 + (200*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^12*((64*b^5)/3 - (520*a^4*b)/3 + (200*a^2*b^3)/3) - tan(c/2 + (d*x)/2)^3*((38*a^5)/3 - (80*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^17*((38*a^5)/3 - (80*a^3*b^2)/3) + 2*a^5*tan(c/2 + (d*x)/2) + 10*a^4*b*tan(c/2 + (d*x)/2)^2 + 10*a^4*b*tan(c/2 + (d*x)/2)^18)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^10)","B"
109,1,831,472,5.923907,"\text{Not used}","int((a*cos(c + d*x) + b*sin(c + d*x))^5/cos(c + d*x)^12,x)","\frac{5\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(16\,a^4-20\,a^2\,b^2+3\,b^4\right)}{128\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{11\,a^5}{8}+\frac{25\,a^3\,b^2}{32}-\frac{15\,a\,b^4}{128}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,\left(40\,a^4\,b-40\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-\frac{20\,a^5}{3}+\frac{55\,a^3\,b^2}{3}+\frac{5\,a\,b^4}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}\,\left(-\frac{20\,a^5}{3}+\frac{55\,a^3\,b^2}{3}+\frac{5\,a\,b^4}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-\frac{80\,a^5}{3}+\frac{40\,a^3\,b^2}{3}+54\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(-\frac{80\,a^5}{3}+\frac{40\,a^3\,b^2}{3}+54\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{21}\,\left(\frac{11\,a^5}{8}+\frac{25\,a^3\,b^2}{32}-\frac{15\,a\,b^4}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{395\,a^5}{24}-\frac{1255\,a^3\,b^2}{96}+\frac{3323\,a\,b^4}{128}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}\,\left(\frac{395\,a^5}{24}-\frac{1255\,a^3\,b^2}{96}+\frac{3323\,a\,b^4}{128}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{95\,a^5}{4}-\frac{1035\,a^3\,b^2}{16}+\frac{4205\,a\,b^4}{64}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(\frac{95\,a^5}{4}-\frac{1035\,a^3\,b^2}{16}+\frac{4205\,a\,b^4}{64}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(110\,a^4\,b-\frac{40\,a^2\,b^3}{3}+\frac{32\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-320\,a^4\,b+80\,a^2\,b^3+48\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{40\,a^4\,b}{7}-\frac{440\,a^2\,b^3}{63}+\frac{16\,b^5}{63}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(-240\,a^4\,b+\frac{320\,a^2\,b^3}{3}+\frac{80\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{270\,a^4\,b}{7}+\frac{320\,a^2\,b^3}{63}+\frac{80\,b^5}{63}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(340\,a^4\,b-\frac{640\,a^2\,b^3}{3}+\frac{176\,b^5}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-\frac{880\,a^4\,b}{7}+\frac{640\,a^2\,b^3}{7}+\frac{48\,b^5}{7}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{1620\,a^4\,b}{7}-\frac{720\,a^2\,b^3}{7}+\frac{240\,b^5}{7}\right)+\frac{10\,a^4\,b}{7}+\frac{16\,b^5}{693}-\frac{40\,a^2\,b^3}{63}+10\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}-11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-165\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+330\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-462\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+462\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-330\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+165\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(5*a*atanh(tan(c/2 + (d*x)/2))*(16*a^4 + 3*b^4 - 20*a^2*b^2))/(128*d) - (tan(c/2 + (d*x)/2)*((11*a^5)/8 - (15*a*b^4)/128 + (25*a^3*b^2)/32) - tan(c/2 + (d*x)/2)^18*(40*a^4*b - 40*a^2*b^3) + tan(c/2 + (d*x)/2)^3*((5*a*b^4)/4 - (20*a^5)/3 + (55*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^19*((5*a*b^4)/4 - (20*a^5)/3 + (55*a^3*b^2)/3) + tan(c/2 + (d*x)/2)^7*(54*a*b^4 - (80*a^5)/3 + (40*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^15*(54*a*b^4 - (80*a^5)/3 + (40*a^3*b^2)/3) - tan(c/2 + (d*x)/2)^21*((11*a^5)/8 - (15*a*b^4)/128 + (25*a^3*b^2)/32) + tan(c/2 + (d*x)/2)^5*((3323*a*b^4)/128 + (395*a^5)/24 - (1255*a^3*b^2)/96) - tan(c/2 + (d*x)/2)^17*((3323*a*b^4)/128 + (395*a^5)/24 - (1255*a^3*b^2)/96) + tan(c/2 + (d*x)/2)^9*((4205*a*b^4)/64 + (95*a^5)/4 - (1035*a^3*b^2)/16) - tan(c/2 + (d*x)/2)^13*((4205*a*b^4)/64 + (95*a^5)/4 - (1035*a^3*b^2)/16) + tan(c/2 + (d*x)/2)^16*(110*a^4*b + (32*b^5)/3 - (40*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^10*(48*b^5 - 320*a^4*b + 80*a^2*b^3) - tan(c/2 + (d*x)/2)^2*((40*a^4*b)/7 + (16*b^5)/63 - (440*a^2*b^3)/63) + tan(c/2 + (d*x)/2)^14*((80*b^5)/3 - 240*a^4*b + (320*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^4*((270*a^4*b)/7 + (80*b^5)/63 + (320*a^2*b^3)/63) + tan(c/2 + (d*x)/2)^12*(340*a^4*b + (176*b^5)/3 - (640*a^2*b^3)/3) + tan(c/2 + (d*x)/2)^6*((48*b^5)/7 - (880*a^4*b)/7 + (640*a^2*b^3)/7) + tan(c/2 + (d*x)/2)^8*((1620*a^4*b)/7 + (240*b^5)/7 - (720*a^2*b^3)/7) + (10*a^4*b)/7 + (16*b^5)/693 - (40*a^2*b^3)/63 + 10*a^4*b*tan(c/2 + (d*x)/2)^20)/(d*(11*tan(c/2 + (d*x)/2)^2 - 55*tan(c/2 + (d*x)/2)^4 + 165*tan(c/2 + (d*x)/2)^6 - 330*tan(c/2 + (d*x)/2)^8 + 462*tan(c/2 + (d*x)/2)^10 - 462*tan(c/2 + (d*x)/2)^12 + 330*tan(c/2 + (d*x)/2)^14 - 165*tan(c/2 + (d*x)/2)^16 + 55*tan(c/2 + (d*x)/2)^18 - 11*tan(c/2 + (d*x)/2)^20 + tan(c/2 + (d*x)/2)^22 - 1))","B"
110,1,6099,227,11.158473,"\text{Not used}","int(cos(c + d*x)^5/(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{b^5\,\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,b^5\,\ln\left(\frac{1}{\cos\left(c+d\,x\right)+1}\right)}{d\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)}-\frac{\frac{4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4+2\,a^2\,b^2+b^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^3+9\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a\,b^2-3\,a^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a\,b^2-3\,a^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,a^3+9\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2+2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(\frac{64\,b^5\,\left(\frac{a\,\left(\frac{48\,a^{15}\,b+352\,a^{13}\,b^3+1296\,a^{11}\,b^5+2688\,a^9\,b^7+3152\,a^7\,b^9+2016\,a^5\,b^{11}+624\,a^3\,b^{13}+64\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a\,b^5\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{a\,\left(\frac{9\,a^{15}+87\,a^{13}\,b^2+388\,a^{11}\,b^4+894\,a^9\,b^6+1089\,a^7\,b^8+475\,a^5\,b^{10}-222\,a^3\,b^{12}-192\,a\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,b^5\,\left(\frac{48\,a^{15}\,b+352\,a^{13}\,b^3+1296\,a^{11}\,b^5+2688\,a^9\,b^7+3152\,a^7\,b^9+2016\,a^5\,b^{11}+624\,a^3\,b^{13}+64\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a^3\,{\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{1024\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(9\,a^{12}+51\,a^{10}\,b^2+130\,a^8\,b^4-82\,a^6\,b^6-715\,a^4\,b^8-1441\,a^2\,b^{10}+256\,b^{12}\right)}{{\left(9\,a^{12}+69\,a^{10}\,b^2+250\,a^8\,b^4+490\,a^6\,b^6+525\,a^4\,b^8+481\,a^2\,b^{10}+256\,b^{12}\right)}^2}-\frac{2\,a\,b\,\left(\frac{9\,a^9\,b^5+60\,a^7\,b^7+181\,a^5\,b^9+210\,a^3\,b^{11}+64\,a\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,b^5\,\left(\frac{9\,a^{15}+87\,a^{13}\,b^2+388\,a^{11}\,b^4+894\,a^9\,b^6+1089\,a^7\,b^8+475\,a^5\,b^{10}-222\,a^3\,b^{12}-192\,a\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,b^5\,\left(\frac{48\,a^{15}\,b+352\,a^{13}\,b^3+1296\,a^{11}\,b^5+2688\,a^9\,b^7+3152\,a^7\,b^9+2016\,a^5\,b^{11}+624\,a^3\,b^{13}+64\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}+\frac{a\,\left(\frac{a\,\left(\frac{48\,a^{15}\,b+352\,a^{13}\,b^3+1296\,a^{11}\,b^5+2688\,a^9\,b^7+3152\,a^7\,b^9+2016\,a^5\,b^{11}+624\,a^3\,b^{13}+64\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a\,b^5\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{a^2\,b^5\,{\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{2\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(9\,a^{10}+60\,a^8\,b^2+238\,a^6\,b^4+412\,a^4\,b^6+305\,a^2\,b^8-496\,b^{10}\right)}{{\left(9\,a^{12}+69\,a^{10}\,b^2+250\,a^8\,b^4+490\,a^6\,b^6+525\,a^4\,b^8+481\,a^2\,b^{10}+256\,b^{12}\right)}^2}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{3\,a^6+10\,a^4\,b^2+15\,a^2\,b^4}+\frac{\left(\frac{64\,b^5\,\left(\frac{a\,\left(\frac{24\,a^{16}+152\,a^{14}\,b^2+408\,a^{12}\,b^4+408\,a^{10}\,b^6-248\,a^8\,b^8-888\,a^6\,b^{10}-696\,a^4\,b^{12}-184\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a\,b^5\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{a\,\left(\frac{9\,a^{14}\,b+69\,a^{12}\,b^3+202\,a^{10}\,b^5+330\,a^8\,b^7+333\,a^6\,b^9+193\,a^4\,b^{11}+48\,a^2\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,b^5\,\left(\frac{24\,a^{16}+152\,a^{14}\,b^2+408\,a^{12}\,b^4+408\,a^{10}\,b^6-248\,a^8\,b^8-888\,a^6\,b^{10}-696\,a^4\,b^{12}-184\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a^3\,{\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{1024\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(9\,a^{12}+51\,a^{10}\,b^2+130\,a^8\,b^4-82\,a^6\,b^6-715\,a^4\,b^8-1441\,a^2\,b^{10}+256\,b^{12}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{\left(3\,a^6+10\,a^4\,b^2+15\,a^2\,b^4\right)\,{\left(9\,a^{12}+69\,a^{10}\,b^2+250\,a^8\,b^4+490\,a^6\,b^6+525\,a^4\,b^8+481\,a^2\,b^{10}+256\,b^{12}\right)}^2}-\frac{2\,a\,b\,\left(\frac{9\,a^8\,b^6+42\,a^6\,b^8+73\,a^4\,b^{10}+56\,a^2\,b^{12}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,b^5\,\left(\frac{9\,a^{14}\,b+69\,a^{12}\,b^3+202\,a^{10}\,b^5+330\,a^8\,b^7+333\,a^6\,b^9+193\,a^4\,b^{11}+48\,a^2\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,b^5\,\left(\frac{24\,a^{16}+152\,a^{14}\,b^2+408\,a^{12}\,b^4+408\,a^{10}\,b^6-248\,a^8\,b^8-888\,a^6\,b^{10}-696\,a^4\,b^{12}-184\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}+\frac{a\,\left(\frac{a\,\left(\frac{24\,a^{16}+152\,a^{14}\,b^2+408\,a^{12}\,b^4+408\,a^{10}\,b^6-248\,a^8\,b^8-888\,a^6\,b^{10}-696\,a^4\,b^{12}-184\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,b^5\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a\,b^5\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{a^2\,b^5\,{\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{2\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(9\,a^{10}+60\,a^8\,b^2+238\,a^6\,b^4+412\,a^4\,b^6+305\,a^2\,b^8-496\,b^{10}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{\left(3\,a^6+10\,a^4\,b^2+15\,a^2\,b^4\right)\,{\left(9\,a^{12}+69\,a^{10}\,b^2+250\,a^8\,b^4+490\,a^6\,b^6+525\,a^4\,b^8+481\,a^2\,b^{10}+256\,b^{12}\right)}^2}\right)\,\left(3\,a^4+10\,a^2\,b^2+15\,b^4\right)}{4\,d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}","Not used",1,"(b^5*log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*b^5*log(1/(cos(c + d*x) + 1)))/(d*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)) - ((4*b^3*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 + 2*a^2*b^2) - (tan(c/2 + (d*x)/2)*(9*a*b^2 + 5*a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^3*(a*b^2 - 3*a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(a*b^2 - 3*a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^7*(9*a*b^2 + 5*a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (2*b*tan(c/2 + (d*x)/2)^2*(a^2 + 2*b^2))/(a^4 + b^4 + 2*a^2*b^2) + (2*b*tan(c/2 + (d*x)/2)^6*(a^2 + 2*b^2))/(a^4 + b^4 + 2*a^2*b^2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (a*atan((tan(c/2 + (d*x)/2)*((((64*b^5*((a*((64*a*b^15 + 48*a^15*b + 624*a^3*b^13 + 2016*a^5*b^11 + 3152*a^7*b^9 + 2688*a^9*b^7 + 1296*a^11*b^5 + 352*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a*b^5*(3*a^4 + 15*b^4 + 10*a^2*b^2)*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (a*((9*a^15 - 192*a*b^14 - 222*a^3*b^12 + 475*a^5*b^10 + 1089*a^7*b^8 + 894*a^9*b^6 + 388*a^11*b^4 + 87*a^13*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*b^5*((64*a*b^15 + 48*a^15*b + 624*a^3*b^13 + 2016*a^5*b^11 + 3152*a^7*b^9 + 2688*a^9*b^7 + 1296*a^11*b^5 + 352*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a^3*(3*a^4 + 15*b^4 + 10*a^2*b^2)^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/(1024*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(9*a^12 + 256*b^12 - 1441*a^2*b^10 - 715*a^4*b^8 - 82*a^6*b^6 + 130*a^8*b^4 + 51*a^10*b^2))/(9*a^12 + 256*b^12 + 481*a^2*b^10 + 525*a^4*b^8 + 490*a^6*b^6 + 250*a^8*b^4 + 69*a^10*b^2)^2 - (2*a*b*((64*a*b^13 + 210*a^3*b^11 + 181*a^5*b^9 + 60*a^7*b^7 + 9*a^9*b^5)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*b^5*((9*a^15 - 192*a*b^14 - 222*a^3*b^12 + 475*a^5*b^10 + 1089*a^7*b^8 + 894*a^9*b^6 + 388*a^11*b^4 + 87*a^13*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*b^5*((64*a*b^15 + 48*a^15*b + 624*a^3*b^13 + 2016*a^5*b^11 + 3152*a^7*b^9 + 2688*a^9*b^7 + 1296*a^11*b^5 + 352*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) + (a*((a*((64*a*b^15 + 48*a^15*b + 624*a^3*b^13 + 2016*a^5*b^11 + 3152*a^7*b^9 + 2688*a^9*b^7 + 1296*a^11*b^5 + 352*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a*b^5*(3*a^4 + 15*b^4 + 10*a^2*b^2)*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (a^2*b^5*(3*a^4 + 15*b^4 + 10*a^2*b^2)^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/(2*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(9*a^10 - 496*b^10 + 305*a^2*b^8 + 412*a^4*b^6 + 238*a^6*b^4 + 60*a^8*b^2))/(9*a^12 + 256*b^12 + 481*a^2*b^10 + 525*a^4*b^8 + 490*a^6*b^6 + 250*a^8*b^4 + 69*a^10*b^2)^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/(3*a^6 + 15*a^2*b^4 + 10*a^4*b^2) + (((64*b^5*((a*((24*a^16 - 184*a^2*b^14 - 696*a^4*b^12 - 888*a^6*b^10 - 248*a^8*b^8 + 408*a^10*b^6 + 408*a^12*b^4 + 152*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a*b^5*(3*a^4 + 15*b^4 + 10*a^2*b^2)*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (a*((9*a^14*b + 48*a^2*b^13 + 193*a^4*b^11 + 333*a^6*b^9 + 330*a^8*b^7 + 202*a^10*b^5 + 69*a^12*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*b^5*((24*a^16 - 184*a^2*b^14 - 696*a^4*b^12 - 888*a^6*b^10 - 248*a^8*b^8 + 408*a^10*b^6 + 408*a^12*b^4 + 152*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a^3*(3*a^4 + 15*b^4 + 10*a^2*b^2)^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/(1024*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(9*a^12 + 256*b^12 - 1441*a^2*b^10 - 715*a^4*b^8 - 82*a^6*b^6 + 130*a^8*b^4 + 51*a^10*b^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/((3*a^6 + 15*a^2*b^4 + 10*a^4*b^2)*(9*a^12 + 256*b^12 + 481*a^2*b^10 + 525*a^4*b^8 + 490*a^6*b^6 + 250*a^8*b^4 + 69*a^10*b^2)^2) - (2*a*b*((56*a^2*b^12 + 73*a^4*b^10 + 42*a^6*b^8 + 9*a^8*b^6)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*b^5*((9*a^14*b + 48*a^2*b^13 + 193*a^4*b^11 + 333*a^6*b^9 + 330*a^8*b^7 + 202*a^10*b^5 + 69*a^12*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*b^5*((24*a^16 - 184*a^2*b^14 - 696*a^4*b^12 - 888*a^6*b^10 - 248*a^8*b^8 + 408*a^10*b^6 + 408*a^12*b^4 + 152*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) + (a*((a*((24*a^16 - 184*a^2*b^14 - 696*a^4*b^12 - 888*a^6*b^10 - 248*a^8*b^8 + 408*a^10*b^6 + 408*a^12*b^4 + 152*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*b^5*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a*b^5*(3*a^4 + 15*b^4 + 10*a^2*b^2)*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (a^2*b^5*(3*a^4 + 15*b^4 + 10*a^2*b^2)^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/(2*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(9*a^10 - 496*b^10 + 305*a^2*b^8 + 412*a^4*b^6 + 238*a^6*b^4 + 60*a^8*b^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/((3*a^6 + 15*a^2*b^4 + 10*a^4*b^2)*(9*a^12 + 256*b^12 + 481*a^2*b^10 + 525*a^4*b^8 + 490*a^6*b^6 + 250*a^8*b^4 + 69*a^10*b^2)^2))*(3*a^4 + 15*b^4 + 10*a^2*b^2))/(4*d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))","B"
111,1,342,166,3.316034,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{\frac{\frac{2\,a^2\,b}{3}+\frac{8\,b^3}{3}}{a^4+2\,a^2\,b^2+b^4}+\frac{4\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^3+4\,a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{4\,a^3}{3}+\frac{16\,a\,b^2}{3}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^3+2\,a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}}{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\,b^4\,\mathrm{atanh}\left(\frac{a^4\,b+b^5+2\,a^2\,b^3-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^{5/2}}\right)}{d\,{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"(((2*a^2*b)/3 + (8*b^3)/3)/(a^4 + b^4 + 2*a^2*b^2) + (4*b^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (tan(c/2 + (d*x)/2)^5*(4*a*b^2 + 2*a^3))/(a^4 + b^4 + 2*a^2*b^2) + (tan(c/2 + (d*x)/2)^3*((16*a*b^2)/3 + (4*a^3)/3))/(a^4 + b^4 + 2*a^2*b^2) + (2*tan(c/2 + (d*x)/2)*(2*a*b^2 + a^3))/(a^4 + b^4 + 2*a^2*b^2) + (2*b*tan(c/2 + (d*x)/2)^4*(a^2 + 2*b^2))/(a^4 + b^4 + 2*a^2*b^2))/(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*b^4*atanh((a^4*b + b^5 + 2*a^2*b^3 - a*tan(c/2 + (d*x)/2)*(a^4 + b^4 + 2*a^2*b^2))/(a^2 + b^2)^(5/2)))/(d*(a^2 + b^2)^(5/2))","B"
112,1,3572,119,6.162853,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{b^3\,\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{4\,b^3\,\ln\left(\frac{1}{\cos\left(c+d\,x\right)+1}\right)}{d\,\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)}-\frac{\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^2+b^2}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2+b^2}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2+b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(\frac{4\,b^3\,\left(\frac{a\,\left(\frac{8\,\left(4\,a^9\,b+28\,a^7\,b^3+48\,a^5\,b^5+28\,a^3\,b^7+4\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^2+3\,b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a\,b^3\,\left(a^2+3\,b^2\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{a\,\left(\frac{8\,\left(a^9+8\,a^7\,b^2+13\,a^5\,b^4-6\,a^3\,b^6-12\,a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,b^3\,\left(\frac{8\,\left(4\,a^9\,b+28\,a^7\,b^3+48\,a^5\,b^5+28\,a^3\,b^7+4\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)\,\left(a^2+3\,b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{a^3\,{\left(a^2+3\,b^2\right)}^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^8+5\,a^6\,b^2-13\,a^4\,b^4-73\,a^2\,b^6+16\,b^8\right)}{{\left(a^8+7\,a^6\,b^2+15\,a^4\,b^4+25\,a^2\,b^6+16\,b^8\right)}^2}-\frac{2\,a\,b\,\left(a^6+10\,a^4\,b^2+17\,a^2\,b^4-28\,b^6\right)\,\left(\frac{8\,\left(a^5\,b^3+6\,a^3\,b^5+4\,a\,b^7\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,b^3\,\left(\frac{8\,\left(a^9+8\,a^7\,b^2+13\,a^5\,b^4-6\,a^3\,b^6-12\,a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,b^3\,\left(\frac{8\,\left(4\,a^9\,b+28\,a^7\,b^3+48\,a^5\,b^5+28\,a^3\,b^7+4\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{a\,\left(a^2+3\,b^2\right)\,\left(\frac{a\,\left(\frac{8\,\left(4\,a^9\,b+28\,a^7\,b^3+48\,a^5\,b^5+28\,a^3\,b^7+4\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^2+3\,b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a\,b^3\,\left(a^2+3\,b^2\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{8\,a^2\,b^3\,{\left(a^2+3\,b^2\right)}^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{{\left(a^8+7\,a^6\,b^2+15\,a^4\,b^4+25\,a^2\,b^6+16\,b^8\right)}^2}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{4\,a^4+12\,a^2\,b^2}+\frac{\left(\frac{4\,b^3\,\left(\frac{a\,\left(a^2+3\,b^2\right)\,\left(\frac{8\,\left(2\,a^{10}+8\,a^8\,b^2-16\,a^4\,b^6-10\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a\,b^3\,\left(a^2+3\,b^2\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{a\,\left(a^2+3\,b^2\right)\,\left(\frac{8\,\left(a^8\,b+2\,a^6\,b^3+a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,b^3\,\left(\frac{8\,\left(2\,a^{10}+8\,a^8\,b^2-16\,a^4\,b^6-10\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{a^3\,{\left(a^2+3\,b^2\right)}^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^8+5\,a^6\,b^2-13\,a^4\,b^4-73\,a^2\,b^6+16\,b^8\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(4\,a^4+12\,a^2\,b^2\right)\,{\left(a^8+7\,a^6\,b^2+15\,a^4\,b^4+25\,a^2\,b^6+16\,b^8\right)}^2}-\frac{2\,a\,b\,\left(a^6+10\,a^4\,b^2+17\,a^2\,b^4-28\,b^6\right)\,\left(\frac{8\,\left(a^4\,b^4+2\,a^2\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,b^3\,\left(\frac{8\,\left(a^8\,b+2\,a^6\,b^3+a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,b^3\,\left(\frac{8\,\left(2\,a^{10}+8\,a^8\,b^2-16\,a^4\,b^6-10\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{a\,\left(\frac{a\,\left(a^2+3\,b^2\right)\,\left(\frac{8\,\left(2\,a^{10}+8\,a^8\,b^2-16\,a^4\,b^6-10\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,b^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a\,b^3\,\left(a^2+3\,b^2\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^2+3\,b^2\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{8\,a^2\,b^3\,{\left(a^2+3\,b^2\right)}^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(4\,a^4+12\,a^2\,b^2\right)\,{\left(a^8+7\,a^6\,b^2+15\,a^4\,b^4+25\,a^2\,b^6+16\,b^8\right)}^2}\right)\,\left(a^2+3\,b^2\right)}{d\,\left(a^4+2\,a^2\,b^2+b^4\right)}","Not used",1,"(b^3*log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(d*(a^4 + b^4 + 2*a^2*b^2)) - (4*b^3*log(1/(cos(c + d*x) + 1)))/(d*(4*a^4 + 4*b^4 + 8*a^2*b^2)) - ((a*tan(c/2 + (d*x)/2)^3)/(a^2 + b^2) + (2*b*tan(c/2 + (d*x)/2)^2)/(a^2 + b^2) - (a*tan(c/2 + (d*x)/2))/(a^2 + b^2))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (a*atan((tan(c/2 + (d*x)/2)*((((4*b^3*((a*((8*(4*a*b^9 + 4*a^9*b + 28*a^3*b^7 + 48*a^5*b^5 + 28*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^2 + 3*b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a*b^3*(a^2 + 3*b^2)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (a*((8*(a^9 - 12*a*b^8 - 6*a^3*b^6 + 13*a^5*b^4 + 8*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*b^3*((8*(4*a*b^9 + 4*a^9*b + 28*a^3*b^7 + 48*a^5*b^5 + 28*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2))*(a^2 + 3*b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (a^3*(a^2 + 3*b^2)^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^8 + 16*b^8 - 73*a^2*b^6 - 13*a^4*b^4 + 5*a^6*b^2))/(a^8 + 16*b^8 + 25*a^2*b^6 + 15*a^4*b^4 + 7*a^6*b^2)^2 - (2*a*b*(a^6 - 28*b^6 + 17*a^2*b^4 + 10*a^4*b^2)*((8*(4*a*b^7 + 6*a^3*b^5 + a^5*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*b^3*((8*(a^9 - 12*a*b^8 - 6*a^3*b^6 + 13*a^5*b^4 + 8*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*b^3*((8*(4*a*b^9 + 4*a^9*b + 28*a^3*b^7 + 48*a^5*b^5 + 28*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (a*(a^2 + 3*b^2)*((a*((8*(4*a*b^9 + 4*a^9*b + 28*a^3*b^7 + 48*a^5*b^5 + 28*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^2 + 3*b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a*b^3*(a^2 + 3*b^2)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (8*a^2*b^3*(a^2 + 3*b^2)^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^8 + 16*b^8 + 25*a^2*b^6 + 15*a^4*b^4 + 7*a^6*b^2)^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/(4*a^4 + 12*a^2*b^2) + (((4*b^3*((a*(a^2 + 3*b^2)*((8*(2*a^10 - 10*a^2*b^8 - 16*a^4*b^6 + 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a*b^3*(a^2 + 3*b^2)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (a*(a^2 + 3*b^2)*((8*(a^8*b + a^4*b^5 + 2*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*b^3*((8*(2*a^10 - 10*a^2*b^8 - 16*a^4*b^6 + 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (a^3*(a^2 + 3*b^2)^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^8 + 16*b^8 - 73*a^2*b^6 - 13*a^4*b^4 + 5*a^6*b^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a^4 + 12*a^2*b^2)*(a^8 + 16*b^8 + 25*a^2*b^6 + 15*a^4*b^4 + 7*a^6*b^2)^2) - (2*a*b*(a^6 - 28*b^6 + 17*a^2*b^4 + 10*a^4*b^2)*((8*(2*a^2*b^6 + a^4*b^4))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*b^3*((8*(a^8*b + a^4*b^5 + 2*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*b^3*((8*(2*a^10 - 10*a^2*b^8 - 16*a^4*b^6 + 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (a*((a*(a^2 + 3*b^2)*((8*(2*a^10 - 10*a^2*b^8 - 16*a^4*b^6 + 8*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*b^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a*b^3*(a^2 + 3*b^2)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^2 + 3*b^2))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (8*a^2*b^3*(a^2 + 3*b^2)^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a^4 + 12*a^2*b^2)*(a^8 + 16*b^8 + 25*a^2*b^6 + 15*a^4*b^4 + 7*a^6*b^2)^2))*(a^2 + 3*b^2))/(d*(a^4 + b^4 + 2*a^2*b^2))","B"
113,1,110,91,0.630602,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{\frac{2\,b}{a^2+b^2}+\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2+b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{2\,b^2\,\mathrm{atanh}\left(\frac{a^2\,b+b^3-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+b^2\right)}{{\left(a^2+b^2\right)}^{3/2}}\right)}{d\,{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"((2*b)/(a^2 + b^2) + (2*a*tan(c/2 + (d*x)/2))/(a^2 + b^2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)) - (2*b^2*atanh((a^2*b + b^3 - a*tan(c/2 + (d*x)/2)*(a^2 + b^2))/(a^2 + b^2)^(3/2)))/(d*(a^2 + b^2)^(3/2))","B"
114,1,1069,45,1.156314,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x)),x)","\frac{b\,\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^2+b^2\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\frac{a^3\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^3}+\frac{a\,\left(96\,a\,b^2-32\,a^3+\frac{b\,\left(32\,a\,b^3+128\,a^3\,b-\frac{b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{b\,\left(\frac{a\,\left(32\,a\,b^3+128\,a^3\,b-\frac{b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}-\frac{a\,b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}\right)}{{\left(a^4+5\,a^2\,b^2+4\,b^4\right)}^2}-\frac{6\,a\,b\,\left(a^2-2\,b^2\right)\,\left(32\,a\,b-\frac{b\,\left(96\,a\,b^2-32\,a^3+\frac{b\,\left(32\,a\,b^3+128\,a^3\,b-\frac{b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,\left(\frac{a\,\left(32\,a\,b^3+128\,a^3\,b-\frac{b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{a^2+b^2}\right)}{a^2+b^2}-\frac{a\,b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}-\frac{a^2\,b\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^3}\right)}{{\left(a^4+5\,a^2\,b^2+4\,b^4\right)}^2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{32\,a^2}+\frac{\left(a^4-13\,a^2\,b^2+4\,b^4\right)\,\left(\frac{a\,\left(32\,a^2\,b-\frac{b\,\left(64\,a^2\,b^2-32\,a^4+\frac{b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a^3\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^3}-\frac{b\,\left(\frac{a\,\left(64\,a^2\,b^2-32\,a^4+\frac{b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{32\,a^2\,{\left(a^4+5\,a^2\,b^2+4\,b^4\right)}^2}+\frac{3\,b\,\left(a^2-2\,b^2\right)\,\left(\frac{b\,\left(32\,a^2\,b-\frac{b\,\left(64\,a^2\,b^2-32\,a^4+\frac{b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,\left(\frac{a\,\left(64\,a^2\,b^2-32\,a^4+\frac{b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{a^2+b^2}\right)}{a^2+b^2}+\frac{a\,b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^2}\right)}{a^2+b^2}+\frac{a^2\,b\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^3}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{16\,a\,{\left(a^4+5\,a^2\,b^2+4\,b^4\right)}^2}\right)}{d\,\left(a^2+b^2\right)}-\frac{b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d\,\left(a^2+b^2\right)}","Not used",1,"(b*log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(d*(a^2 + b^2)) - (2*a*atan((tan(c/2 + (d*x)/2)*(((a^4 + 4*b^4 - 13*a^2*b^2)*((a^3*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^3 + (a*(96*a*b^2 - 32*a^3 + (b*(32*a*b^3 + 128*a^3*b - (b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) + (b*((a*(32*a*b^3 + 128*a^3*b - (b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2) - (a*b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^2))/(a^2 + b^2)))/(a^4 + 4*b^4 + 5*a^2*b^2)^2 - (6*a*b*(a^2 - 2*b^2)*(32*a*b - (b*(96*a*b^2 - 32*a^3 + (b*(32*a*b^3 + 128*a^3*b - (b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) + (a*((a*(32*a*b^3 + 128*a^3*b - (b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)))/(a^2 + b^2) - (a*b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^2))/(a^2 + b^2) - (a^2*b*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^3))/(a^4 + 4*b^4 + 5*a^2*b^2)^2)*(a^4 + b^4 + 2*a^2*b^2))/(32*a^2) + ((a^4 + 4*b^4 - 13*a^2*b^2)*((a*(32*a^2*b - (b*(64*a^2*b^2 - 32*a^4 + (b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) + (a^3*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^3 - (b*((a*(64*a^2*b^2 - 32*a^4 + (b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2) + (a*b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^2))/(a^2 + b^2))*(a^4 + b^4 + 2*a^2*b^2))/(32*a^2*(a^4 + 4*b^4 + 5*a^2*b^2)^2) + (3*b*(a^2 - 2*b^2)*((b*(32*a^2*b - (b*(64*a^2*b^2 - 32*a^4 + (b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2)))/(a^2 + b^2) + (a*((a*(64*a^2*b^2 - 32*a^4 + (b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)))/(a^2 + b^2) + (a*b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^2))/(a^2 + b^2) + (a^2*b*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^3)*(a^4 + b^4 + 2*a^2*b^2))/(16*a*(a^4 + 4*b^4 + 5*a^2*b^2)^2)))/(d*(a^2 + b^2)) - (b*log(tan(c/2 + (d*x)/2)^2 + 1))/(d*(a^2 + b^2))","B"
115,1,39,47,0.466536,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{b-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{d\,\sqrt{a^2+b^2}}","Not used",1,"-(2*atanh((b - a*tan(c/2 + (d*x)/2))/(a^2 + b^2)^(1/2)))/(d*(a^2 + b^2)^(1/2))","B"
116,1,62,41,0.722994,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{b\,\left(b\,\cos\left(c+d\,x\right)-a\,\sin\left(c+d\,x\right)\right)}{2\,\cos\left(c+d\,x\right)\,a^2+\sin\left(c+d\,x\right)\,a\,b+\cos\left(c+d\,x\right)\,b^2}\right)}{b\,d}","Not used",1,"-(2*atanh((b*(b*cos(c + d*x) - a*sin(c + d*x)))/(2*a^2*cos(c + d*x) + b^2*cos(c + d*x) + a*b*sin(c + d*x))))/(b*d)","B"
117,1,310,80,0.712552,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\frac{64\,a^2\,\sqrt{a^2+b^2}}{64\,a^2\,b+\frac{64\,a^4}{b}+128\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+128\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{128\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{64\,a^2+\frac{64\,a^4}{b^2}+\frac{128\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+128\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{64\,a^4+128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b+64\,a^2\,b^2+128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3}\right)\,\sqrt{a^2+b^2}}{b^2\,d}-\frac{2\,a\,\mathrm{atanh}\left(\frac{64\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^2+\frac{64\,a^4}{b^2}}+\frac{64\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^4+64\,a^2\,b^2}\right)}{b^2\,d}-\frac{2}{b\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*atanh((64*a^2*(a^2 + b^2)^(1/2))/(64*a^2*b + (64*a^4)/b + 128*a^3*tan(c/2 + (d*x)/2) + 128*a*b^2*tan(c/2 + (d*x)/2)) + (128*a*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(64*a^2 + (64*a^4)/b^2 + (128*a^3*tan(c/2 + (d*x)/2))/b + 128*a*b*tan(c/2 + (d*x)/2)) + (64*a^3*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(64*a^4 + 64*a^2*b^2 + 128*a*b^3*tan(c/2 + (d*x)/2) + 128*a^3*b*tan(c/2 + (d*x)/2)))*(a^2 + b^2)^(1/2))/(b^2*d) - (2*a*atanh((64*a^2*tan(c/2 + (d*x)/2))/(64*a^2 + (64*a^4)/b^2) + (64*a^4*tan(c/2 + (d*x)/2))/(64*a^4 + 64*a^2*b^2)))/(b^2*d) - 2/(b*d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
118,1,300,88,1.495565,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))),x)","\frac{2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^3\right)}-\frac{a^2\,\mathrm{atan}\left(\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}-b^2\,1{}\mathrm{i}+2{}\mathrm{i}\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2}\right)\,2{}\mathrm{i}+b^2\,\mathrm{atan}\left(\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}-b^2\,1{}\mathrm{i}+2{}\mathrm{i}\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2}\right)\,2{}\mathrm{i}}{b^3\,d}","Not used",1,"(2*b^2*tan(c/2 + (d*x)/2)^2 + 2*a*b*tan(c/2 + (d*x)/2)^3 - 2*a*b*tan(c/2 + (d*x)/2))/(d*(b^3*tan(c/2 + (d*x)/2)^4 - 2*b^3*tan(c/2 + (d*x)/2)^2 + b^3)) - (a^2*atan((b^2*tan(c/2 + (d*x)/2)^2*1i - b^2*1i + a*b*tan(c/2 + (d*x)/2)*2i)/(2*a^2 - b^2*tan(c/2 + (d*x)/2)^2 - 2*a^2*tan(c/2 + (d*x)/2)^2 + b^2 + 2*a*b*tan(c/2 + (d*x)/2)))*2i + b^2*atan((b^2*tan(c/2 + (d*x)/2)^2*1i - b^2*1i + a*b*tan(c/2 + (d*x)/2)*2i)/(2*a^2 - b^2*tan(c/2 + (d*x)/2)^2 - 2*a^2*tan(c/2 + (d*x)/2)^2 + b^2 + 2*a*b*tan(c/2 + (d*x)/2)))*2i)/(b^3*d)","B"
119,1,724,153,2.213268,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))),x)","\frac{b^3\,\left(\cos\left(c+d\,x\right)+\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(3\,c+3\,d\,x\right)}{3}+\frac{5}{6}\right)-b^2\,\left(\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,a\,\mathrm{atanh}\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(3\,c+3\,d\,x\right)}{4}+\frac{9\,a\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}\right)+b\,\left(\frac{3\,a^2\,\cos\left(c+d\,x\right)}{4}+\frac{a^2}{2}+\frac{a^2\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{a^2\,\cos\left(3\,c+3\,d\,x\right)}{4}\right)+\frac{\mathrm{atanh}\left(\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{{\left(a^2+b^2\right)}^3}}{2}-\frac{3\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{a^3\,\mathrm{atanh}\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(3\,c+3\,d\,x\right)}{2}+\frac{3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^4+2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^5}\right)\,\sqrt{{\left(a^2+b^2\right)}^3}}{2}}{b^4\,d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"(b^3*(cos(c + d*x) + cos(2*c + 2*d*x)/2 + cos(3*c + 3*d*x)/3 + 5/6) - b^2*((a*sin(2*c + 2*d*x))/4 + (3*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (9*a*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4) + b*((3*a^2*cos(c + d*x))/4 + a^2/2 + (a^2*cos(2*c + 2*d*x))/2 + (a^2*cos(3*c + 3*d*x))/4) + (atanh((a^2*sin(c/2 + (d*x)/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 2*b^2*sin(c/2 + (d*x)/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^5*cos(c/2 + (d*x)/2) + 2*b^5*sin(c/2 + (d*x)/2) + a*b^4*cos(c/2 + (d*x)/2) + 2*a^4*b*sin(c/2 + (d*x)/2) + 2*a^3*b^2*cos(c/2 + (d*x)/2) + 4*a^2*b^3*sin(c/2 + (d*x)/2)))*cos(3*c + 3*d*x)*((a^2 + b^2)^3)^(1/2))/2 - (3*a^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (3*cos(c + d*x)*atanh((a^2*sin(c/2 + (d*x)/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 2*b^2*sin(c/2 + (d*x)/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + a*b*cos(c/2 + (d*x)/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^5*cos(c/2 + (d*x)/2) + 2*b^5*sin(c/2 + (d*x)/2) + a*b^4*cos(c/2 + (d*x)/2) + 2*a^4*b*sin(c/2 + (d*x)/2) + 2*a^3*b^2*cos(c/2 + (d*x)/2) + 4*a^2*b^3*sin(c/2 + (d*x)/2)))*((a^2 + b^2)^3)^(1/2))/2)/(b^4*d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
120,1,575,158,3.682140,"\text{Not used}","int(1/(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x))),x)","\frac{\left(6\,a^3\,b+12\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,a^2\,b^2+12\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-18\,a^3\,b-28\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-12\,a^2\,b^2-12\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(18\,a^3\,b+28\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,a^2\,b^2+12\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(-6\,a^3\,b-12\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(3\,b^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-12\,b^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+18\,b^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,b^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,b^5\right)}-\frac{a^4\,\mathrm{atan}\left(\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}-b^2\,1{}\mathrm{i}+2{}\mathrm{i}\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2}\right)\,2{}\mathrm{i}+b^4\,\mathrm{atan}\left(\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}-b^2\,1{}\mathrm{i}+2{}\mathrm{i}\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2}\right)\,2{}\mathrm{i}+a^2\,b^2\,\mathrm{atan}\left(\frac{b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}-b^2\,1{}\mathrm{i}+2{}\mathrm{i}\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2+2\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b^2}\right)\,4{}\mathrm{i}}{b^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(12*b^4 + 6*a^2*b^2) - tan(c/2 + (d*x)/2)*(12*a*b^3 + 6*a^3*b) + tan(c/2 + (d*x)/2)^6*(12*b^4 + 6*a^2*b^2) - tan(c/2 + (d*x)/2)^4*(12*b^4 + 12*a^2*b^2) + tan(c/2 + (d*x)/2)^7*(12*a*b^3 + 6*a^3*b) + tan(c/2 + (d*x)/2)^3*(28*a*b^3 + 18*a^3*b) - tan(c/2 + (d*x)/2)^5*(28*a*b^3 + 18*a^3*b))/(d*(18*b^5*tan(c/2 + (d*x)/2)^4 - 12*b^5*tan(c/2 + (d*x)/2)^2 - 12*b^5*tan(c/2 + (d*x)/2)^6 + 3*b^5*tan(c/2 + (d*x)/2)^8 + 3*b^5)) - (a^4*atan((b^2*tan(c/2 + (d*x)/2)^2*1i - b^2*1i + a*b*tan(c/2 + (d*x)/2)*2i)/(2*a^2 - b^2*tan(c/2 + (d*x)/2)^2 - 2*a^2*tan(c/2 + (d*x)/2)^2 + b^2 + 2*a*b*tan(c/2 + (d*x)/2)))*2i + b^4*atan((b^2*tan(c/2 + (d*x)/2)^2*1i - b^2*1i + a*b*tan(c/2 + (d*x)/2)*2i)/(2*a^2 - b^2*tan(c/2 + (d*x)/2)^2 - 2*a^2*tan(c/2 + (d*x)/2)^2 + b^2 + 2*a*b*tan(c/2 + (d*x)/2)))*2i + a^2*b^2*atan((b^2*tan(c/2 + (d*x)/2)^2*1i - b^2*1i + a*b*tan(c/2 + (d*x)/2)*2i)/(2*a^2 - b^2*tan(c/2 + (d*x)/2)^2 - 2*a^2*tan(c/2 + (d*x)/2)^2 + b^2 + 2*a*b*tan(c/2 + (d*x)/2)))*4i)/(b^5*d)","B"
121,1,2979,262,2.841404,"\text{Not used}","int(1/(cos(c + d*x)^6*(a*cos(c + d*x) + b*sin(c + d*x))),x)","-\frac{\frac{2\,\left(15\,a^4+35\,a^2\,b^2+23\,b^4\right)}{15\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^3+5\,a\,b^2\right)}{2\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^3+5\,a\,b^2\right)}{2\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(4\,a^3+9\,a\,b^2\right)}{4\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^4+3\,a^2\,b^2+3\,b^4\right)}{b^5}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^4+5\,a^2\,b^2+3\,b^4\right)}{b^5}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^4+13\,a^2\,b^2+7\,b^4\right)}{3\,b^5}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(9\,a^4+20\,a^2\,b^2+14\,b^4\right)}{3\,b^5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^3+9\,a\,b^2\right)}{4\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}+\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)}{b^6}\right)}{b^6}\right)\,1{}\mathrm{i}}{b^6}+\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}-\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)}{b^6}\right)}{b^6}\right)\,1{}\mathrm{i}}{b^6}}{\frac{32\,a^{16}+248\,a^{14}\,b^2+856\,a^{12}\,b^4+1695\,a^{10}\,b^6+2069\,a^8\,b^8+1549\,a^6\,b^{10}+655\,a^4\,b^{12}+120\,a^2\,b^{14}}{b^{14}}+\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}+\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)}{b^6}\right)}{b^6}\right)}{b^6}-\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}-\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\sqrt{{\left(a^2+b^2\right)}^5}\,\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)}{b^6}\right)}{b^6}\right)}{b^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{17}+1024\,a^{15}\,b^2+3584\,a^{13}\,b^4+7088\,a^{11}\,b^6+8530\,a^9\,b^8+6230\,a^7\,b^{10}+2550\,a^5\,b^{12}+450\,a^3\,b^{14}\right)}{b^{15}}}\right)\,\sqrt{{\left(a^2+b^2\right)}^5}\,2{}\mathrm{i}}{b^6\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)\,\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)}{b^6}\right)}{b^6}\right)\,1{}\mathrm{i}}{b^6}+\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}-\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)\,\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)}{b^6}\right)}{b^6}\right)\,1{}\mathrm{i}}{b^6}}{\frac{32\,a^{16}+248\,a^{14}\,b^2+856\,a^{12}\,b^4+1695\,a^{10}\,b^6+2069\,a^8\,b^8+1549\,a^6\,b^{10}+655\,a^4\,b^{12}+120\,a^2\,b^{14}}{b^{14}}+\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)\,\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)}{b^6}\right)}{b^6}\right)}{b^6}-\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{32\,a^{12}\,b^5+160\,a^{10}\,b^7+320\,a^8\,b^9+300\,a^6\,b^{11}+\frac{225\,a^4\,b^{13}}{2}}{b^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{13}\,b^5+832\,a^{11}\,b^7+2240\,a^9\,b^9+3160\,a^7\,b^{11}+2385\,a^5\,b^{13}+834\,a^3\,b^{15}+64\,a\,b^{17}\right)}{2\,b^{15}}-\frac{\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^7\,b^{12}+384\,a^5\,b^{14}+384\,a^3\,b^{16}+128\,a\,b^{18}\right)}{2\,b^{15}}-\frac{16\,a^6\,b^{12}+44\,a^4\,b^{14}+28\,a^2\,b^{16}}{b^{14}}+\frac{\left(32\,a^2\,b^3+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{17}+192\,a\,b^{19}\right)}{2\,b^{15}}\right)\,\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)}{b^6}\right)}{b^6}\right)}{b^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{17}+1024\,a^{15}\,b^2+3584\,a^{13}\,b^4+7088\,a^{11}\,b^6+8530\,a^9\,b^8+6230\,a^7\,b^{10}+2550\,a^5\,b^{12}+450\,a^3\,b^{14}\right)}{b^{15}}}\right)\,\left(a^5+\frac{5\,a^3\,b^2}{2}+\frac{15\,a\,b^4}{8}\right)\,2{}\mathrm{i}}{b^6\,d}","Not used",1,"(atan(((((a^2 + b^2)^5)^(1/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((a^2 + b^2)^5)^(1/2)*((28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 - (tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) + (((a^2 + b^2)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15)))/b^6))/b^6)*1i)/b^6 + (((a^2 + b^2)^5)^(1/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((a^2 + b^2)^5)^(1/2)*((tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) - (28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 + (((a^2 + b^2)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15)))/b^6))/b^6)*1i)/b^6)/((32*a^16 + 120*a^2*b^14 + 655*a^4*b^12 + 1549*a^6*b^10 + 2069*a^8*b^8 + 1695*a^10*b^6 + 856*a^12*b^4 + 248*a^14*b^2)/b^14 + (((a^2 + b^2)^5)^(1/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((a^2 + b^2)^5)^(1/2)*((28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 - (tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) + (((a^2 + b^2)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15)))/b^6))/b^6))/b^6 - (((a^2 + b^2)^5)^(1/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((a^2 + b^2)^5)^(1/2)*((tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) - (28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 + (((a^2 + b^2)^5)^(1/2)*(32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15)))/b^6))/b^6))/b^6 - (tan(c/2 + (d*x)/2)*(128*a^17 + 450*a^3*b^14 + 2550*a^5*b^12 + 6230*a^7*b^10 + 8530*a^9*b^8 + 7088*a^11*b^6 + 3584*a^13*b^4 + 1024*a^15*b^2))/b^15))*((a^2 + b^2)^5)^(1/2)*2i)/(b^6*d) - ((2*(15*a^4 + 23*b^4 + 35*a^2*b^2))/(15*b^5) + (tan(c/2 + (d*x)/2)^3*(5*a*b^2 + 4*a^3))/(2*b^4) - (tan(c/2 + (d*x)/2)^7*(5*a*b^2 + 4*a^3))/(2*b^4) + (tan(c/2 + (d*x)/2)^9*(9*a*b^2 + 4*a^3))/(4*b^4) + (2*tan(c/2 + (d*x)/2)^8*(a^4 + 3*b^4 + 3*a^2*b^2))/b^5 - (4*tan(c/2 + (d*x)/2)^6*(2*a^4 + 3*b^4 + 5*a^2*b^2))/b^5 - (4*tan(c/2 + (d*x)/2)^2*(6*a^4 + 7*b^4 + 13*a^2*b^2))/(3*b^5) + (4*tan(c/2 + (d*x)/2)^4*(9*a^4 + 14*b^4 + 20*a^2*b^2))/(3*b^5) - (tan(c/2 + (d*x)/2)*(9*a*b^2 + 4*a^3))/(4*b^4))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) + (atan(((((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*((28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 - (tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15))*((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2))/b^6))/b^6)*1i)/b^6 + (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*((tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) - (28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15))*((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2))/b^6))/b^6)*1i)/b^6)/((32*a^16 + 120*a^2*b^14 + 655*a^4*b^12 + 1549*a^6*b^10 + 2069*a^8*b^8 + 1695*a^10*b^6 + 856*a^12*b^4 + 248*a^14*b^2)/b^14 + (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*((28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 - (tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15))*((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2))/b^6))/b^6))/b^6 - (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*(((225*a^4*b^13)/2 + 300*a^6*b^11 + 320*a^8*b^9 + 160*a^10*b^7 + 32*a^12*b^5)/b^14 + (tan(c/2 + (d*x)/2)*(64*a*b^17 + 834*a^3*b^15 + 2385*a^5*b^13 + 3160*a^7*b^11 + 2240*a^9*b^9 + 832*a^11*b^7 + 128*a^13*b^5))/(2*b^15) - (((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*((tan(c/2 + (d*x)/2)*(128*a*b^18 + 384*a^3*b^16 + 384*a^5*b^14 + 128*a^7*b^12))/(2*b^15) - (28*a^2*b^16 + 44*a^4*b^14 + 16*a^6*b^12)/b^14 + ((32*a^2*b^3 + (tan(c/2 + (d*x)/2)*(192*a*b^19 + 128*a^3*b^17))/(2*b^15))*((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2))/b^6))/b^6))/b^6 - (tan(c/2 + (d*x)/2)*(128*a^17 + 450*a^3*b^14 + 2550*a^5*b^12 + 6230*a^7*b^10 + 8530*a^9*b^8 + 7088*a^11*b^6 + 3584*a^13*b^4 + 1024*a^15*b^2))/b^15))*((15*a*b^4)/8 + a^5 + (5*a^3*b^2)/2)*2i)/(b^6*d)","B"
122,1,6604,145,11.457075,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^2+b^2}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2+b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-a^2\,b^2+2\,b^4\right)}{a\,{\left(a^2+b^2\right)}^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^4-a^2\,b^2+2\,b^4\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^4+3\,a^2\,b^2-2\,b^4\right)}{a\,{\left(a^2+b^2\right)}^2}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^3\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{\left(\frac{8\,\left(a^{13}+15\,a^{11}\,b^2+36\,a^9\,b^4-146\,a^7\,b^6-327\,a^5\,b^8-141\,a^3\,b^{10}+18\,a\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,a\,b^3\,\left(\frac{8\,\left(4\,a^{14}\,b+72\,a^{12}\,b^3+252\,a^{10}\,b^5+368\,a^8\,b^7+252\,a^6\,b^9+72\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{16\,a\,b^3\,\left(\frac{\left(\frac{8\,\left(4\,a^{14}\,b+72\,a^{12}\,b^3+252\,a^{10}\,b^5+368\,a^8\,b^7+252\,a^6\,b^9+72\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,a\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}\right)\,\left(a^{10}+11\,a^8\,b^2-46\,a^6\,b^4-706\,a^4\,b^6+493\,a^2\,b^8-9\,b^{10}\right)}{{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}-\frac{2\,a\,b\,\left(\frac{8\,\left(4\,a^8\,b^3+48\,a^6\,b^5+52\,a^4\,b^7+72\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{\left(\frac{8\,\left(4\,a^{14}\,b+72\,a^{12}\,b^3+252\,a^{10}\,b^5+368\,a^8\,b^7+252\,a^6\,b^9+72\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,a\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{16\,a\,b^3\,\left(\frac{8\,\left(a^{13}+15\,a^{11}\,b^2+36\,a^9\,b^4-146\,a^7\,b^6-327\,a^5\,b^8-141\,a^3\,b^{10}+18\,a\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,a\,b^3\,\left(\frac{8\,\left(4\,a^{14}\,b+72\,a^{12}\,b^3+252\,a^{10}\,b^5+368\,a^8\,b^7+252\,a^6\,b^9+72\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}-\frac{32\,a\,b^3\,{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8+28\,a^6\,b^2+110\,a^4\,b^4-436\,a^2\,b^6+57\,b^8\right)}{{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{4\,a^5+24\,a^3\,b^2-12\,a\,b^4}+\frac{\left(\frac{\left(\frac{8\,\left(-a^{12}\,b+3\,a^{10}\,b^3+54\,a^8\,b^5+134\,a^6\,b^7+123\,a^4\,b^9+39\,a^2\,b^{11}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,a\,b^3\,\left(\frac{8\,\left(2\,a^{15}+18\,a^{13}\,b^2+18\,a^{11}\,b^4-62\,a^9\,b^6-138\,a^7\,b^8-90\,a^5\,b^{10}-10\,a^3\,b^{12}+6\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^3\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{16\,a\,b^3\,\left(\frac{\left(\frac{8\,\left(2\,a^{15}+18\,a^{13}\,b^2+18\,a^{11}\,b^4-62\,a^9\,b^6-138\,a^7\,b^8-90\,a^5\,b^{10}-10\,a^3\,b^{12}+6\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,a\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}\right)\,\left(a^{10}+11\,a^8\,b^2-46\,a^6\,b^4-706\,a^4\,b^6+493\,a^2\,b^8-9\,b^{10}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(4\,a^5+24\,a^3\,b^2-12\,a\,b^4\right)\,{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}-\frac{2\,a\,b\,\left(\frac{8\,\left(4\,a^7\,b^4+8\,a^5\,b^6-60\,a^3\,b^8\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{\left(\frac{8\,\left(2\,a^{15}+18\,a^{13}\,b^2+18\,a^{11}\,b^4-62\,a^9\,b^6-138\,a^7\,b^8-90\,a^5\,b^{10}-10\,a^3\,b^{12}+6\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,a\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{16\,a\,b^3\,\left(\frac{8\,\left(-a^{12}\,b+3\,a^{10}\,b^3+54\,a^8\,b^5+134\,a^6\,b^7+123\,a^4\,b^9+39\,a^2\,b^{11}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,a\,b^3\,\left(\frac{8\,\left(2\,a^{15}+18\,a^{13}\,b^2+18\,a^{11}\,b^4-62\,a^9\,b^6-138\,a^7\,b^8-90\,a^5\,b^{10}-10\,a^3\,b^{12}+6\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{128\,a\,b^3\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}\right)}{4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6}-\frac{32\,a\,b^3\,{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8+28\,a^6\,b^2+110\,a^4\,b^4-436\,a^2\,b^6+57\,b^8\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(4\,a^5+24\,a^3\,b^2-12\,a\,b^4\right)\,{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{16\,a\,b^3\,\ln\left(\left(\frac{32\,a^3\,b^4\,\left(a^4+2\,a^2\,b^2-15\,b^4\right)}{{\left(a^2+b^2\right)}^6}-\left(\frac{\sqrt{-\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2}{{\left(a^2+b^2\right)}^6}}}{2}-\frac{4\,a\,b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\left(\frac{\sqrt{-\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2}{{\left(a^2+b^2\right)}^6}}}{2}-\frac{4\,a\,b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\frac{16\,a\,\left(a^6+5\,a^4\,b^2-17\,a^2\,b^4+3\,b^6\right)}{{\left(a^2+b^2\right)}^2}+\frac{32\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+14\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^2}+96\,a\,b\,\left(\frac{\sqrt{-\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2}{{\left(a^2+b^2\right)}^6}}}{2}-\frac{4\,a\,b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(a+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+b^2\right)\right)-\frac{8\,a^2\,b\,\left(-a^4+6\,a^2\,b^2+39\,b^4\right)}{{\left(a^2+b^2\right)}^3}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8+13\,a^6\,b^2+9\,a^4\,b^4-177\,a^2\,b^6+18\,b^8\right)}{{\left(a^2+b^2\right)}^4}\right)+\frac{32\,a^2\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6+12\,a^4\,b^2+13\,a^2\,b^4+18\,b^6\right)}{{\left(a^2+b^2\right)}^6}\right)\,\left(\frac{32\,a^3\,b^4\,\left(a^4+2\,a^2\,b^2-15\,b^4\right)}{{\left(a^2+b^2\right)}^6}-\left(\frac{\sqrt{-\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2}{{\left(a^2+b^2\right)}^6}}}{2}+\frac{4\,a\,b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\left(\frac{\sqrt{-\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2}{{\left(a^2+b^2\right)}^6}}}{2}+\frac{4\,a\,b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\frac{16\,a\,\left(a^6+5\,a^4\,b^2-17\,a^2\,b^4+3\,b^6\right)}{{\left(a^2+b^2\right)}^2}+\frac{32\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+14\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^2}-96\,a\,b\,\left(\frac{\sqrt{-\frac{{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2}{{\left(a^2+b^2\right)}^6}}}{2}+\frac{4\,a\,b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(a+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+b^2\right)\right)+\frac{8\,a^2\,b\,\left(-a^4+6\,a^2\,b^2+39\,b^4\right)}{{\left(a^2+b^2\right)}^3}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8+13\,a^6\,b^2+9\,a^4\,b^4-177\,a^2\,b^6+18\,b^8\right)}{{\left(a^2+b^2\right)}^4}\right)+\frac{32\,a^2\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6+12\,a^4\,b^2+13\,a^2\,b^4+18\,b^6\right)}{{\left(a^2+b^2\right)}^6}\right)\right)}{d\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}+\frac{4\,a\,b^3\,\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}","Not used",1,"((2*b*tan(c/2 + (d*x)/2)^4)/(a^2 + b^2) - (2*b*tan(c/2 + (d*x)/2)^2)/(a^2 + b^2) + (tan(c/2 + (d*x)/2)*(a^4 + 2*b^4 - a^2*b^2))/(a*(a^2 + b^2)^2) + (tan(c/2 + (d*x)/2)^5*(a^4 + 2*b^4 - a^2*b^2))/(a*(a^4 + b^4 + 2*a^2*b^2)) - (2*tan(c/2 + (d*x)/2)^3*(a^4 - 2*b^4 + 3*a^2*b^2))/(a*(a^2 + b^2)^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2 - a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6 + 4*b*tan(c/2 + (d*x)/2)^3 + 2*b*tan(c/2 + (d*x)/2)^5)) - (atan((tan(c/2 + (d*x)/2)*(((((a^4 - 3*b^4 + 6*a^2*b^2)^3*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (((8*(18*a*b^12 + a^13 - 141*a^3*b^10 - 327*a^5*b^8 - 146*a^7*b^6 + 36*a^9*b^4 + 15*a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*a*b^3*((8*(4*a^14*b + 4*a^2*b^13 + 72*a^4*b^11 + 252*a^6*b^9 + 368*a^8*b^7 + 252*a^10*b^5 + 72*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (16*a*b^3*((((8*(4*a^14*b + 4*a^2*b^13 + 72*a^4*b^11 + 252*a^6*b^9 + 368*a^8*b^7 + 252*a^10*b^5 + 72*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*a*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2))*(a^10 - 9*b^10 + 493*a^2*b^8 - 706*a^4*b^6 - 46*a^6*b^4 + 11*a^8*b^2))/(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2 - (2*a*b*((8*(72*a^2*b^9 + 52*a^4*b^7 + 48*a^6*b^5 + 4*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((((8*(4*a^14*b + 4*a^2*b^13 + 72*a^4*b^11 + 252*a^6*b^9 + 368*a^8*b^7 + 252*a^10*b^5 + 72*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*a*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (16*a*b^3*((8*(18*a*b^12 + a^13 - 141*a^3*b^10 - 327*a^5*b^8 - 146*a^7*b^6 + 36*a^9*b^4 + 15*a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*a*b^3*((8*(4*a^14*b + 4*a^2*b^13 + 72*a^4*b^11 + 252*a^6*b^9 + 368*a^8*b^7 + 252*a^10*b^5 + 72*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2) - (32*a*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)^2*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 57*b^8 - 436*a^2*b^6 + 110*a^4*b^4 + 28*a^6*b^2))/(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/(4*a^5 - 12*a*b^4 + 24*a^3*b^2) + (((((8*(39*a^2*b^11 - a^12*b + 123*a^4*b^9 + 134*a^6*b^7 + 54*a^8*b^5 + 3*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*a*b^3*((8*(6*a*b^14 + 2*a^15 - 10*a^3*b^12 - 90*a^5*b^10 - 138*a^7*b^8 - 62*a^9*b^6 + 18*a^11*b^4 + 18*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + ((a^4 - 3*b^4 + 6*a^2*b^2)^3*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (16*a*b^3*((((8*(6*a*b^14 + 2*a^15 - 10*a^3*b^12 - 90*a^5*b^10 - 138*a^7*b^8 - 62*a^9*b^6 + 18*a^11*b^4 + 18*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*a*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2))*(a^10 - 9*b^10 + 493*a^2*b^8 - 706*a^4*b^6 - 46*a^6*b^4 + 11*a^8*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((4*a^5 - 12*a*b^4 + 24*a^3*b^2)*(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2) - (2*a*b*((8*(8*a^5*b^6 - 60*a^3*b^8 + 4*a^7*b^4))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((((8*(6*a*b^14 + 2*a^15 - 10*a^3*b^12 - 90*a^5*b^10 - 138*a^7*b^8 - 62*a^9*b^6 + 18*a^11*b^4 + 18*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*a*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (16*a*b^3*((8*(39*a^2*b^11 - a^12*b + 123*a^4*b^9 + 134*a^6*b^7 + 54*a^8*b^5 + 3*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*a*b^3*((8*(6*a*b^14 + 2*a^15 - 10*a^3*b^12 - 90*a^5*b^10 - 138*a^7*b^8 - 62*a^9*b^6 + 18*a^11*b^4 + 18*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (128*a*b^3*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)))/(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2) - (32*a*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)^2*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 57*b^8 - 436*a^2*b^6 + 110*a^4*b^4 + 28*a^6*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((4*a^5 - 12*a*b^4 + 24*a^3*b^2)*(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2))*(a^4 - 3*b^4 + 6*a^2*b^2))/(d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (16*a*b^3*log(((32*a^3*b^4*(a^4 - 15*b^4 + 2*a^2*b^2))/(a^2 + b^2)^6 - ((-(a^4 - 3*b^4 + 6*a^2*b^2)^2/(a^2 + b^2)^6)^(1/2)/2 - (4*a*b^3)/(a^2 + b^2)^3)*(((-(a^4 - 3*b^4 + 6*a^2*b^2)^2/(a^2 + b^2)^6)^(1/2)/2 - (4*a*b^3)/(a^2 + b^2)^3)*((16*a*(a^6 + 3*b^6 - 17*a^2*b^4 + 5*a^4*b^2))/(a^2 + b^2)^2 + (32*a^2*b*tan(c/2 + (d*x)/2)*(a^4 + b^4 + 14*a^2*b^2))/(a^2 + b^2)^2 + 96*a*b*((-(a^4 - 3*b^4 + 6*a^2*b^2)^2/(a^2 + b^2)^6)^(1/2)/2 - (4*a*b^3)/(a^2 + b^2)^3)*(a + b*tan(c/2 + (d*x)/2))*(a^2 + b^2)) - (8*a^2*b*(39*b^4 - a^4 + 6*a^2*b^2))/(a^2 + b^2)^3 + (8*a*tan(c/2 + (d*x)/2)*(a^8 + 18*b^8 - 177*a^2*b^6 + 9*a^4*b^4 + 13*a^6*b^2))/(a^2 + b^2)^4) + (32*a^2*b^3*tan(c/2 + (d*x)/2)*(a^6 + 18*b^6 + 13*a^2*b^4 + 12*a^4*b^2))/(a^2 + b^2)^6)*((32*a^3*b^4*(a^4 - 15*b^4 + 2*a^2*b^2))/(a^2 + b^2)^6 - ((-(a^4 - 3*b^4 + 6*a^2*b^2)^2/(a^2 + b^2)^6)^(1/2)/2 + (4*a*b^3)/(a^2 + b^2)^3)*(((-(a^4 - 3*b^4 + 6*a^2*b^2)^2/(a^2 + b^2)^6)^(1/2)/2 + (4*a*b^3)/(a^2 + b^2)^3)*((16*a*(a^6 + 3*b^6 - 17*a^2*b^4 + 5*a^4*b^2))/(a^2 + b^2)^2 + (32*a^2*b*tan(c/2 + (d*x)/2)*(a^4 + b^4 + 14*a^2*b^2))/(a^2 + b^2)^2 - 96*a*b*((-(a^4 - 3*b^4 + 6*a^2*b^2)^2/(a^2 + b^2)^6)^(1/2)/2 + (4*a*b^3)/(a^2 + b^2)^3)*(a + b*tan(c/2 + (d*x)/2))*(a^2 + b^2)) + (8*a^2*b*(39*b^4 - a^4 + 6*a^2*b^2))/(a^2 + b^2)^3 - (8*a*tan(c/2 + (d*x)/2)*(a^8 + 18*b^8 - 177*a^2*b^6 + 9*a^4*b^4 + 13*a^6*b^2))/(a^2 + b^2)^4) + (32*a^2*b^3*tan(c/2 + (d*x)/2)*(a^6 + 18*b^6 + 13*a^2*b^4 + 12*a^4*b^2))/(a^2 + b^2)^6)))/(d*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)) + (4*a*b^3*log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))","B"
123,1,286,138,2.812621,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{\frac{4\,a^2\,b-2\,b^3}{a^4+2\,a^2\,b^2+b^4}-\frac{6\,b^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+3\,a^2\,b^2-b^4\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^4-2\,a^2\,b^2+2\,b^4\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{6\,a\,b^2\,\mathrm{atanh}\left(\frac{a^4\,b+b^5+2\,a^2\,b^3-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^{5/2}}\right)}{d\,{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"((4*a^2*b - 2*b^3)/(a^4 + b^4 + 2*a^2*b^2) - (6*b^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (2*tan(c/2 + (d*x)/2)*(a^4 - b^4 + 3*a^2*b^2))/(a*(a^4 + b^4 + 2*a^2*b^2)) - (tan(c/2 + (d*x)/2)^3*(2*a^4 + 2*b^4 - 2*a^2*b^2))/(a*(a^4 + b^4 + 2*a^2*b^2)))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^4 + 2*b*tan(c/2 + (d*x)/2)^3)) - (6*a*b^2*atanh((a^4*b + b^5 + 2*a^2*b^3 - a*tan(c/2 + (d*x)/2)*(a^4 + b^4 + 2*a^2*b^2))/(a^2 + b^2)^(5/2)))/(d*(a^2 + b^2)^(5/2))","B"
124,1,3114,82,4.867198,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{2\,a\,b\,\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,a\,b\,\ln\left(\frac{1}{\cos\left(c+d\,x\right)+1}\right)}{d\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(\frac{2\,a\,b\,\left(\frac{\left(\frac{32\,\left(6\,a^8\,b+12\,a^6\,b^3+6\,a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{64\,a\,b\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{64\,a\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{\left(a+b\right)\,\left(\frac{32\,\left(a^7-8\,a^5\,b^2-7\,a^3\,b^4+2\,a\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,a\,b\,\left(\frac{32\,\left(6\,a^8\,b+12\,a^6\,b^3+6\,a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{64\,a\,b\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{32\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^6-35\,a^4\,b^2+35\,a^2\,b^4-b^6\right)}{{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}-\frac{2\,a\,b\,\left(5\,a^4-26\,a^2\,b^2+5\,b^4\right)\,\left(\frac{32\,\left(2\,a^4\,b+4\,a^2\,b^3\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{\left(a+b\right)\,\left(a-b\right)\,\left(\frac{\left(\frac{32\,\left(6\,a^8\,b+12\,a^6\,b^3+6\,a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{64\,a\,b\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{64\,a\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b\,\left(\frac{32\,\left(a^7-8\,a^5\,b^2-7\,a^3\,b^4+2\,a\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,a\,b\,\left(\frac{32\,\left(6\,a^8\,b+12\,a^6\,b^3+6\,a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{64\,a\,b\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{64\,a\,b\,{\left(a+b\right)}^2\,{\left(a-b\right)}^2\,\left(3\,a^9\,b^2+12\,a^7\,b^4+18\,a^5\,b^6+12\,a^3\,b^8+3\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{32\,a\,b^2-32\,a^3}+\frac{\left(\frac{\left(a+b\right)\,\left(a-b\right)\,\left(\frac{32\,\left(3\,a^6\,b+6\,a^4\,b^3+3\,a^2\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,a\,b\,\left(\frac{32\,\left(-a^9+2\,a^7\,b^2+6\,a^5\,b^4+2\,a^3\,b^6-a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{64\,a\,b\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{2\,a\,b\,\left(\frac{\left(\frac{32\,\left(-a^9+2\,a^7\,b^2+6\,a^5\,b^4+2\,a^3\,b^6-a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{64\,a\,b\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{64\,a\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{32\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^6-35\,a^4\,b^2+35\,a^2\,b^4-b^6\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(32\,a\,b^2-32\,a^3\right)\,{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}+\frac{2\,a\,b\,\left(5\,a^4-26\,a^2\,b^2+5\,b^4\right)\,\left(\frac{64\,a^3\,b^2}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{2\,a\,b\,\left(\frac{32\,\left(3\,a^6\,b+6\,a^4\,b^3+3\,a^2\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,a\,b\,\left(\frac{32\,\left(-a^9+2\,a^7\,b^2+6\,a^5\,b^4+2\,a^3\,b^6-a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{64\,a\,b\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{\left(a+b\right)\,\left(a-b\right)\,\left(\frac{\left(\frac{32\,\left(-a^9+2\,a^7\,b^2+6\,a^5\,b^4+2\,a^3\,b^6-a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{64\,a\,b\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{64\,a\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{64\,a\,b\,{\left(a+b\right)}^2\,{\left(a-b\right)}^2\,\left(3\,a^{10}\,b+12\,a^8\,b^3+18\,a^6\,b^5+12\,a^4\,b^7+3\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(32\,a\,b^2-32\,a^3\right)\,{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}\right)\,\left(a+b\right)\,\left(a-b\right)}{d\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\left(a^2+b^2\right)\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(2*a*b*log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))/(d*(a^4 + b^4 + 2*a^2*b^2)) - (2*a*b*log(1/(cos(c + d*x) + 1)))/(d*(a^4 + b^4 + 2*a^2*b^2)) + (2*atan((tan(c/2 + (d*x)/2)*((((2*a*b*((((32*(6*a^8*b + 6*a^4*b^5 + 12*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (64*a*b*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(a^4 + b^4 + 2*a^2*b^2) - (64*a*b*(a + b)*(a - b)*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2) - ((a + b)*((32*(2*a*b^6 + a^7 - 7*a^3*b^4 - 8*a^5*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*a*b*((32*(6*a^8*b + 6*a^4*b^5 + 12*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (64*a*b*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2))*(a - b))/(a^4 + b^4 + 2*a^2*b^2) + (32*(a + b)^3*(a - b)^3*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^6 - b^6 + 35*a^2*b^4 - 35*a^4*b^2))/(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2 - (2*a*b*(5*a^4 + 5*b^4 - 26*a^2*b^2)*((32*(2*a^4*b + 4*a^2*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + ((a + b)*(a - b)*((((32*(6*a^8*b + 6*a^4*b^5 + 12*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (64*a*b*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(a^4 + b^4 + 2*a^2*b^2) - (64*a*b*(a + b)*(a - b)*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b*((32*(2*a*b^6 + a^7 - 7*a^3*b^4 - 8*a^5*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*a*b*((32*(6*a^8*b + 6*a^4*b^5 + 12*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (64*a*b*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2)))/(a^4 + b^4 + 2*a^2*b^2) - (64*a*b*(a + b)^2*(a - b)^2*(3*a*b^10 + 12*a^3*b^8 + 18*a^5*b^6 + 12*a^7*b^4 + 3*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/(32*a*b^2 - 32*a^3) + ((((a + b)*(a - b)*((32*(3*a^6*b + 3*a^2*b^5 + 6*a^4*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*a*b*((32*(2*a^3*b^6 - a^9 - a*b^8 + 6*a^5*b^4 + 2*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (64*a*b*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2)))/(a^4 + b^4 + 2*a^2*b^2) - (2*a*b*((((32*(2*a^3*b^6 - a^9 - a*b^8 + 6*a^5*b^4 + 2*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (64*a*b*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(a^4 + b^4 + 2*a^2*b^2) + (64*a*b*(a + b)*(a - b)*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2) + (32*(a + b)^3*(a - b)^3*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^6 - b^6 + 35*a^2*b^4 - 35*a^4*b^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((32*a*b^2 - 32*a^3)*(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2) + (2*a*b*(5*a^4 + 5*b^4 - 26*a^2*b^2)*((64*a^3*b^2)/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (2*a*b*((32*(3*a^6*b + 3*a^2*b^5 + 6*a^4*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*a*b*((32*(2*a^3*b^6 - a^9 - a*b^8 + 6*a^5*b^4 + 2*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (64*a*b*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2)))/(a^4 + b^4 + 2*a^2*b^2) + ((a + b)*(a - b)*((((32*(2*a^3*b^6 - a^9 - a*b^8 + 6*a^5*b^4 + 2*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (64*a*b*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(a^4 + b^4 + 2*a^2*b^2) + (64*a*b*(a + b)*(a - b)*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^4 + b^4 + 2*a^2*b^2) + (64*a*b*(a + b)^2*(a - b)^2*(3*a^10*b + 3*a^2*b^9 + 12*a^4*b^7 + 18*a^6*b^5 + 12*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((32*a*b^2 - 32*a^3)*(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2))*(a + b)*(a - b))/(d*(a^4 + b^4 + 2*a^2*b^2)) + (2*b^2*tan(c/2 + (d*x)/2))/(a*d*(a^2 + b^2)*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))","B"
125,1,136,83,0.840208,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","-\frac{\frac{2\,b}{a^2+b^2}+\frac{2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,\left(a^2+b^2\right)}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{a\,\mathrm{atan}\left(\frac{a^2\,b\,1{}\mathrm{i}+b^3\,1{}\mathrm{i}-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+b^2\right)\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{3/2}}\right)\,2{}\mathrm{i}}{d\,{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"(a*atan((a^2*b*1i + b^3*1i - a*tan(c/2 + (d*x)/2)*(a^2 + b^2)*1i)/(a^2 + b^2)^(3/2))*2i)/(d*(a^2 + b^2)^(3/2)) - ((2*b)/(a^2 + b^2) + (2*b^2*tan(c/2 + (d*x)/2))/(a*(a^2 + b^2)))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))","B"
126,1,47,32,0.485673,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^2,x)","\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(2*tan(c/2 + (d*x)/2))/(a*d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2))","B"
127,1,383,92,1.171393,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^2),x)","-\frac{b^2\,\sin\left(c+d\,x\right)-\frac{2\,\left(a^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{a^2+b^2}+a^3\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+1{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}+2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}\right)\,\cos\left(c+d\,x\right)\,1{}\mathrm{i}\right)}{\sqrt{a^2+b^2}}+\frac{2\,b\,\left(\frac{a\,\sqrt{a^2+b^2}}{2}+\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{a^2+b^2}}{2}-a\,\sin\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{a^2+b^2}-a^2\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+1{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}+2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}\right)\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)}{\sqrt{a^2+b^2}}}{a\,b^2\,d\,\left(a\,\cos\left(c+d\,x\right)+b\,\sin\left(c+d\,x\right)\right)}","Not used",1,"-(b^2*sin(c + d*x) - (2*(a^3*atan((a^2*sin(c/2 + (d*x)/2)*1i + b^2*sin(c/2 + (d*x)/2)*2i + a*b*cos(c/2 + (d*x)/2)*1i)/(a*cos(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2) + 2*b*sin(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2)))*cos(c + d*x)*1i + a^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*(a^2 + b^2)^(1/2)))/(a^2 + b^2)^(1/2) + (2*b*((a*(a^2 + b^2)^(1/2))/2 + (a*cos(c + d*x)*(a^2 + b^2)^(1/2))/2 - a^2*atan((a^2*sin(c/2 + (d*x)/2)*1i + b^2*sin(c/2 + (d*x)/2)*2i + a*b*cos(c/2 + (d*x)/2)*1i)/(a*cos(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2) + 2*b*sin(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2)))*sin(c + d*x)*1i - a*sin(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*(a^2 + b^2)^(1/2)))/(a^2 + b^2)^(1/2))/(a*b^2*d*(a*cos(c + d*x) + b*sin(c + d*x)))","B"
128,1,382,75,2.359819,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^2),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2+b^2\right)}{a\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)}{a\,b^2}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{4\,a\,\mathrm{atanh}\left(\frac{64\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,a^3-64\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{128\,a^5}{b^2}-\frac{128\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{128\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}-\frac{64\,a^3}{64\,a^3-64\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{128\,a^5}{b^2}-\frac{128\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{128\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{128\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^3\,b+\frac{128\,a^5}{b}+128\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{128\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b}-64\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{b^3\,d}","Not used",1,"((4*tan(c/2 + (d*x)/2)^2)/b - (2*tan(c/2 + (d*x)/2)^3*(2*a^2 + b^2))/(a*b^2) + (2*tan(c/2 + (d*x)/2)*(2*a^2 + b^2))/(a*b^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4 - 2*b*tan(c/2 + (d*x)/2)^3)) - (4*a*atanh((64*a^3*tan(c/2 + (d*x)/2)^2)/(64*a^3 - 64*a^3*tan(c/2 + (d*x)/2)^2 + (128*a^5)/b^2 - (128*a^5*tan(c/2 + (d*x)/2)^2)/b^2 + (128*a^4*tan(c/2 + (d*x)/2))/b) - (64*a^3)/(64*a^3 - 64*a^3*tan(c/2 + (d*x)/2)^2 + (128*a^5)/b^2 - (128*a^5*tan(c/2 + (d*x)/2)^2)/b^2 + (128*a^4*tan(c/2 + (d*x)/2))/b) + (128*a^4*tan(c/2 + (d*x)/2))/(64*a^3*b + (128*a^5)/b + 128*a^4*tan(c/2 + (d*x)/2) - (128*a^5*tan(c/2 + (d*x)/2)^2)/b - 64*a^3*b*tan(c/2 + (d*x)/2)^2)))/(b^3*d)","B"
129,1,585,179,1.899965,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^2),x)","\frac{\mathrm{atanh}\left(\frac{648\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{216\,a\,b^2+648\,a^3+\frac{432\,a^5}{b^2}}+\frac{432\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{432\,a^5+648\,a^3\,b^2+216\,a\,b^4}+\frac{216\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{216\,a+\frac{648\,a^3}{b^2}+\frac{432\,a^5}{b^4}}\right)\,\left(6\,a^2+3\,b^2\right)}{b^4\,d}-\frac{\frac{2\,\left(3\,a^2+b^2\right)}{b^3}+\frac{6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{b^3}-\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+b^2\right)}{b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^2+2\,b^2\right)}{a\,b^2}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2+b^2\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2+2\,b^2\right)}{a\,b^2}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{6\,a\,\mathrm{atanh}\left(\frac{432\,a^3\,\sqrt{a^2+b^2}}{432\,a^3\,b+\frac{432\,a^5}{b}+864\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+864\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{864\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{432\,a^3+\frac{432\,a^5}{b^2}+864\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{864\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{432\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{432\,a^5+864\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b+432\,a^3\,b^2+864\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^3}\right)\,\sqrt{a^2+b^2}}{b^4\,d}","Not used",1,"(atanh((648*a^3*tan(c/2 + (d*x)/2))/(216*a*b^2 + 648*a^3 + (432*a^5)/b^2) + (432*a^5*tan(c/2 + (d*x)/2))/(216*a*b^4 + 432*a^5 + 648*a^3*b^2) + (216*a*tan(c/2 + (d*x)/2))/(216*a + (648*a^3)/b^2 + (432*a^5)/b^4))*(6*a^2 + 3*b^2))/(b^4*d) - ((2*(3*a^2 + b^2))/b^3 + (6*a^2*tan(c/2 + (d*x)/2)^4)/b^3 - (6*tan(c/2 + (d*x)/2)^2*(2*a^2 + b^2))/b^3 + (tan(c/2 + (d*x)/2)*(9*a^2 + 2*b^2))/(a*b^2) - (4*tan(c/2 + (d*x)/2)^3*(3*a^2 + b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^5*(3*a^2 + 2*b^2))/(a*b^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6 - 4*b*tan(c/2 + (d*x)/2)^3 + 2*b*tan(c/2 + (d*x)/2)^5)) - (6*a*atanh((432*a^3*(a^2 + b^2)^(1/2))/(432*a^3*b + (432*a^5)/b + 864*a^4*tan(c/2 + (d*x)/2) + 864*a^2*b^2*tan(c/2 + (d*x)/2)) + (864*a^2*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(432*a^3 + (432*a^5)/b^2 + 864*a^2*b*tan(c/2 + (d*x)/2) + (864*a^4*tan(c/2 + (d*x)/2))/b) + (432*a^4*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(432*a^5 + 432*a^3*b^2 + 864*a^4*b*tan(c/2 + (d*x)/2) + 864*a^2*b^3*tan(c/2 + (d*x)/2)))*(a^2 + b^2)^(1/2))/(b^4*d)","B"
130,1,1132,141,4.202635,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^2),x)","\frac{\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+b^2\right)}{b^3}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2+b^2\right)}{b^3}-\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2+2\,b^2\right)}{3\,b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^4+4\,a^2\,b^2+b^4\right)}{a\,b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^4+44\,a^2\,b^2+9\,b^4\right)}{3\,a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(36\,a^4+44\,a^2\,b^2+9\,b^4\right)}{3\,a\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^4+4\,a^2\,b^2+b^4\right)}{a\,b^4}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(a^2+b^2\right)\,\left(\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^5+4\,a^3\,b^2\right)}{b^4}-\frac{4\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}+\frac{4\,a\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}\right)\,4{}\mathrm{i}}{b^5}-\frac{a\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^5+4\,a^3\,b^2\right)}{b^4}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}+\frac{4\,a\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}\right)\,4{}\mathrm{i}}{b^5}}{\frac{8\,\left(16\,a^7+32\,a^5\,b^2+16\,a^3\,b^4\right)}{b^8}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(16\,a^7+32\,a^5\,b^2+16\,a^3\,b^4\right)}{b^8}+\frac{4\,a\,\left(a^2+b^2\right)\,\left(\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^5+4\,a^3\,b^2\right)}{b^4}-\frac{4\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}+\frac{4\,a\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}\right)}{b^5}+\frac{4\,a\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^5+4\,a^3\,b^2\right)}{b^4}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a^4\,b^5+8\,a^2\,b^7\right)}{b^8}+\frac{4\,a\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}\right)}{b^5}}\right)\,\left(a^2+b^2\right)\,8{}\mathrm{i}}{b^5\,d}","Not used",1,"((8*tan(c/2 + (d*x)/2)^2*(a^2 + b^2))/b^3 + (8*tan(c/2 + (d*x)/2)^6*(a^2 + b^2))/b^3 - (16*tan(c/2 + (d*x)/2)^4*(3*a^2 + 2*b^2))/(3*b^3) - (2*tan(c/2 + (d*x)/2)^7*(4*a^4 + b^4 + 4*a^2*b^2))/(a*b^4) - (2*tan(c/2 + (d*x)/2)^3*(36*a^4 + 9*b^4 + 44*a^2*b^2))/(3*a*b^4) + (2*tan(c/2 + (d*x)/2)^5*(36*a^4 + 9*b^4 + 44*a^2*b^2))/(3*a*b^4) + (2*tan(c/2 + (d*x)/2)*(4*a^4 + b^4 + 4*a^2*b^2))/(a*b^4))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 - 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8 - 6*b*tan(c/2 + (d*x)/2)^3 + 6*b*tan(c/2 + (d*x)/2)^5 - 2*b*tan(c/2 + (d*x)/2)^7)) + (a*atan(((a*(a^2 + b^2)*((16*tan(c/2 + (d*x)/2)*(4*a^5 + 4*a^3*b^2))/b^4 - (4*(8*a^2*b^7 + 8*a^4*b^5))/b^8 + (4*tan(c/2 + (d*x)/2)^2*(8*a^2*b^7 + 8*a^4*b^5))/b^8 + (4*a*(a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5)*4i)/b^5 - (a*(a^2 + b^2)*((4*(8*a^2*b^7 + 8*a^4*b^5))/b^8 - (16*tan(c/2 + (d*x)/2)*(4*a^5 + 4*a^3*b^2))/b^4 - (4*tan(c/2 + (d*x)/2)^2*(8*a^2*b^7 + 8*a^4*b^5))/b^8 + (4*a*(a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5)*4i)/b^5)/((8*(16*a^7 + 16*a^3*b^4 + 32*a^5*b^2))/b^8 + (8*tan(c/2 + (d*x)/2)^2*(16*a^7 + 16*a^3*b^4 + 32*a^5*b^2))/b^8 + (4*a*(a^2 + b^2)*((16*tan(c/2 + (d*x)/2)*(4*a^5 + 4*a^3*b^2))/b^4 - (4*(8*a^2*b^7 + 8*a^4*b^5))/b^8 + (4*tan(c/2 + (d*x)/2)^2*(8*a^2*b^7 + 8*a^4*b^5))/b^8 + (4*a*(a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5))/b^5 + (4*a*(a^2 + b^2)*((4*(8*a^2*b^7 + 8*a^4*b^5))/b^8 - (16*tan(c/2 + (d*x)/2)*(4*a^5 + 4*a^3*b^2))/b^4 - (4*tan(c/2 + (d*x)/2)^2*(8*a^2*b^7 + 8*a^4*b^5))/b^8 + (4*a*(a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5))/b^5))*(a^2 + b^2)*8i)/(b^5*d)","B"
131,1,610,216,4.253396,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","-\frac{\frac{-6\,a^4\,b+10\,a^2\,b^3+b^5}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^5+2\,a^3\,b^2+15\,a\,b^4\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^6\,b-30\,a^4\,b^3+15\,a^2\,b^5+2\,b^7\right)}{a^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6+18\,a^4\,b^2-31\,a^2\,b^4-2\,b^6\right)}{a\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^6-6\,a^4\,b^2+9\,a^2\,b^4+2\,b^6\right)}{a\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^6\,b-2\,a^4\,b^3+12\,a^2\,b^5+b^7\right)}{a^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+a^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-4\,b^2\right)-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{-1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7+a^6\,b\,1{}\mathrm{i}-3{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^2+a^4\,b^3\,3{}\mathrm{i}-3{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^4+a^2\,b^5\,3{}\mathrm{i}-1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^6+b^7\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{7/2}}\right)\,\left(3\,b^4-12\,a^2\,b^2\right)\,1{}\mathrm{i}}{d\,{\left(a^2+b^2\right)}^{7/2}}","Not used",1,"- ((b^5 - 6*a^4*b + 10*a^2*b^3)/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^3*(15*a*b^4 + 2*a^5 + 2*a^3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (tan(c/2 + (d*x)/2)^4*(2*a^6*b + 2*b^7 + 15*a^2*b^5 - 30*a^4*b^3))/(a^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (tan(c/2 + (d*x)/2)*(2*a^6 - 2*b^6 - 31*a^2*b^4 + 18*a^4*b^2))/(a*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (tan(c/2 + (d*x)/2)^5*(2*a^6 + 2*b^6 + 9*a^2*b^4 - 6*a^4*b^2))/(a*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^2*(2*a^6*b + b^7 + 12*a^2*b^5 - 2*a^4*b^3))/(a^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^6 + a^2 - tan(c/2 + (d*x)/2)^2*(a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^4*(a^2 - 4*b^2) - 4*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2))) - (atan((a^6*b*1i + b^7*1i + a^2*b^5*3i + a^4*b^3*3i - a^7*tan(c/2 + (d*x)/2)*1i - a*b^6*tan(c/2 + (d*x)/2)*1i - a^3*b^4*tan(c/2 + (d*x)/2)*3i - a^5*b^2*tan(c/2 + (d*x)/2)*3i)/(a^2 + b^2)^(7/2))*(3*b^4 - 12*a^2*b^2)*1i)/(d*(a^2 + b^2)^(7/2))","B"
132,1,6190,122,8.538688,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2\,b^3+b^5\right)}{a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b+b^3\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2\,b+b^3\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\ln\left(\left(\left(\sqrt{-\frac{a^2\,{\left(a^2-3\,b^2\right)}^2}{{\left(a^2+b^2\right)}^6}}+\frac{3\,a^2\,b-b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\left(\sqrt{-\frac{a^2\,{\left(a^2-3\,b^2\right)}^2}{{\left(a^2+b^2\right)}^6}}+\frac{3\,a^2\,b-b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\frac{32\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^4+5\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^2}-\frac{32\,a^2\,\left(a^4-7\,a^2\,b^2+4\,b^4\right)}{{\left(a^2+b^2\right)}^2}+96\,a\,b\,\left(a+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\sqrt{-\frac{a^2\,{\left(a^2-3\,b^2\right)}^2}{{\left(a^2+b^2\right)}^6}}+\frac{3\,a^2\,b-b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(a^2+b^2\right)\right)-\frac{32\,a^2\,b\,\left(5\,a^2-3\,b^2\right)}{{\left(a^2+b^2\right)}^3}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-17\,a^4\,b^2+27\,a^2\,b^4-3\,b^6\right)}{{\left(a^2+b^2\right)}^4}\right)-\frac{64\,a^2\,b^2\,\left(3\,a^4-4\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^6}+\frac{32\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^6+17\,a^4\,b^2-3\,a^2\,b^4-b^6\right)}{{\left(a^2+b^2\right)}^6}\right)\,\left(\left(\sqrt{-\frac{a^2\,{\left(a^2-3\,b^2\right)}^2}{{\left(a^2+b^2\right)}^6}}-\frac{3\,a^2\,b-b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\left(\sqrt{-\frac{a^2\,{\left(a^2-3\,b^2\right)}^2}{{\left(a^2+b^2\right)}^6}}-\frac{3\,a^2\,b-b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(\frac{32\,a^2\,\left(a^4-7\,a^2\,b^2+4\,b^4\right)}{{\left(a^2+b^2\right)}^2}-\frac{32\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^4+5\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^2}+96\,a\,b\,\left(a+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\sqrt{-\frac{a^2\,{\left(a^2-3\,b^2\right)}^2}{{\left(a^2+b^2\right)}^6}}-\frac{3\,a^2\,b-b^3}{{\left(a^2+b^2\right)}^3}\right)\,\left(a^2+b^2\right)\right)-\frac{32\,a^2\,b\,\left(5\,a^2-3\,b^2\right)}{{\left(a^2+b^2\right)}^3}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-17\,a^4\,b^2+27\,a^2\,b^4-3\,b^6\right)}{{\left(a^2+b^2\right)}^4}\right)+\frac{64\,a^2\,b^2\,\left(3\,a^4-4\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^6}-\frac{32\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^6+17\,a^4\,b^2-3\,a^2\,b^4-b^6\right)}{{\left(a^2+b^2\right)}^6}\right)\right)\,\left(6\,a^2\,b-2\,b^3\right)}{2\,d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(3\,a^2\,b-b^3\right)}{d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(-a^{11}+15\,a^9\,b^2+6\,a^7\,b^4-34\,a^5\,b^6-21\,a^3\,b^8+3\,a\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{32\,\left(-8\,a^{13}\,b-27\,a^{11}\,b^3-27\,a^9\,b^5+2\,a^7\,b^7+18\,a^5\,b^9+9\,a^3\,b^{11}+a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(-8\,a^{13}\,b-27\,a^{11}\,b^3-27\,a^9\,b^5+2\,a^7\,b^7+18\,a^5\,b^9+9\,a^3\,b^{11}+a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a\,\left(6\,a^2\,b-2\,b^3\right)\,\left(a^2-3\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{32\,a^3\,{\left(a^2-3\,b^2\right)}^3\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8-67\,a^6\,b^2+155\,a^4\,b^4-61\,a^2\,b^6+4\,b^8\right)}{{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}+\frac{2\,a\,b\,\left(7\,a^6-68\,a^4\,b^2+59\,a^2\,b^4-10\,b^6\right)\,\left(\frac{32\,\left(-3\,a^7\,b-17\,a^5\,b^3+3\,a^3\,b^5+a\,b^7\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{32\,\left(-a^{11}+15\,a^9\,b^2+6\,a^7\,b^4-34\,a^5\,b^6-21\,a^3\,b^8+3\,a\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{32\,\left(-8\,a^{13}\,b-27\,a^{11}\,b^3-27\,a^9\,b^5+2\,a^7\,b^7+18\,a^5\,b^9+9\,a^3\,b^{11}+a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(-8\,a^{13}\,b-27\,a^{11}\,b^3-27\,a^9\,b^5+2\,a^7\,b^7+18\,a^5\,b^9+9\,a^3\,b^{11}+a\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a\,\left(6\,a^2\,b-2\,b^3\right)\,\left(a^2-3\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a^2\,\left(6\,a^2\,b-2\,b^3\right)\,{\left(a^2-3\,b^2\right)}^2\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{32\,a^4-96\,a^2\,b^2}+\frac{\left(\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(5\,a^{10}\,b+12\,a^8\,b^3+6\,a^6\,b^5-4\,a^4\,b^7-3\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{32\,\left(-a^{14}+3\,a^{12}\,b^2+18\,a^{10}\,b^4+22\,a^8\,b^6+3\,a^6\,b^8-9\,a^4\,b^{10}-4\,a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(-a^{14}+3\,a^{12}\,b^2+18\,a^{10}\,b^4+22\,a^8\,b^6+3\,a^6\,b^8-9\,a^4\,b^{10}-4\,a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a\,\left(6\,a^2\,b-2\,b^3\right)\,\left(a^2-3\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{32\,a^3\,{\left(a^2-3\,b^2\right)}^3\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8-67\,a^6\,b^2+155\,a^4\,b^4-61\,a^2\,b^6+4\,b^8\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(32\,a^4-96\,a^2\,b^2\right)\,{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}+\frac{2\,a\,b\,\left(\frac{32\,\left(6\,a^6\,b^2-8\,a^4\,b^4+2\,a^2\,b^6\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{32\,\left(5\,a^{10}\,b+12\,a^8\,b^3+6\,a^6\,b^5-4\,a^4\,b^7-3\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(6\,a^2\,b-2\,b^3\right)\,\left(\frac{32\,\left(-a^{14}+3\,a^{12}\,b^2+18\,a^{10}\,b^4+22\,a^8\,b^6+3\,a^6\,b^8-9\,a^4\,b^{10}-4\,a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{a\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(-a^{14}+3\,a^{12}\,b^2+18\,a^{10}\,b^4+22\,a^8\,b^6+3\,a^6\,b^8-9\,a^4\,b^{10}-4\,a^2\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(6\,a^2\,b-2\,b^3\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a\,\left(6\,a^2\,b-2\,b^3\right)\,\left(a^2-3\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a^2\,\left(6\,a^2\,b-2\,b^3\right)\,{\left(a^2-3\,b^2\right)}^2\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(7\,a^6-68\,a^4\,b^2+59\,a^2\,b^4-10\,b^6\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(32\,a^4-96\,a^2\,b^2\right)\,{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}\right)\,\left(a^2-3\,b^2\right)}{d\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^2*(b^5 + 5*a^2*b^3))/(a^2*(a^4 + b^4 + 2*a^2*b^2)) + (2*b*tan(c/2 + (d*x)/2)*(3*a^2*b + b^3))/(a*(a^4 + b^4 + 2*a^2*b^2)) - (2*b*tan(c/2 + (d*x)/2)^3*(3*a^2*b + b^3))/(a*(a^4 + b^4 + 2*a^2*b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^2*(2*a^2 - 4*b^2) + a^2 - 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))) - (log((((-(a^2*(a^2 - 3*b^2)^2)/(a^2 + b^2)^6)^(1/2) + (3*a^2*b - b^3)/(a^2 + b^2)^3)*(((-(a^2*(a^2 - 3*b^2)^2)/(a^2 + b^2)^6)^(1/2) + (3*a^2*b - b^3)/(a^2 + b^2)^3)*((32*a*b*tan(c/2 + (d*x)/2)*(b^4 - 8*a^4 + 5*a^2*b^2))/(a^2 + b^2)^2 - (32*a^2*(a^4 + 4*b^4 - 7*a^2*b^2))/(a^2 + b^2)^2 + 96*a*b*(a + b*tan(c/2 + (d*x)/2))*((-(a^2*(a^2 - 3*b^2)^2)/(a^2 + b^2)^6)^(1/2) + (3*a^2*b - b^3)/(a^2 + b^2)^3)*(a^2 + b^2)) - (32*a^2*b*(5*a^2 - 3*b^2))/(a^2 + b^2)^3 + (32*a*tan(c/2 + (d*x)/2)*(a^6 - 3*b^6 + 27*a^2*b^4 - 17*a^4*b^2))/(a^2 + b^2)^4) - (64*a^2*b^2*(3*a^4 + b^4 - 4*a^2*b^2))/(a^2 + b^2)^6 + (32*a*b*tan(c/2 + (d*x)/2)*(3*a^6 - b^6 - 3*a^2*b^4 + 17*a^4*b^2))/(a^2 + b^2)^6)*(((-(a^2*(a^2 - 3*b^2)^2)/(a^2 + b^2)^6)^(1/2) - (3*a^2*b - b^3)/(a^2 + b^2)^3)*(((-(a^2*(a^2 - 3*b^2)^2)/(a^2 + b^2)^6)^(1/2) - (3*a^2*b - b^3)/(a^2 + b^2)^3)*((32*a^2*(a^4 + 4*b^4 - 7*a^2*b^2))/(a^2 + b^2)^2 - (32*a*b*tan(c/2 + (d*x)/2)*(b^4 - 8*a^4 + 5*a^2*b^2))/(a^2 + b^2)^2 + 96*a*b*(a + b*tan(c/2 + (d*x)/2))*((-(a^2*(a^2 - 3*b^2)^2)/(a^2 + b^2)^6)^(1/2) - (3*a^2*b - b^3)/(a^2 + b^2)^3)*(a^2 + b^2)) - (32*a^2*b*(5*a^2 - 3*b^2))/(a^2 + b^2)^3 + (32*a*tan(c/2 + (d*x)/2)*(a^6 - 3*b^6 + 27*a^2*b^4 - 17*a^4*b^2))/(a^2 + b^2)^4) + (64*a^2*b^2*(3*a^4 + b^4 - 4*a^2*b^2))/(a^2 + b^2)^6 - (32*a*b*tan(c/2 + (d*x)/2)*(3*a^6 - b^6 - 3*a^2*b^4 + 17*a^4*b^2))/(a^2 + b^2)^6))*(6*a^2*b - 2*b^3))/(2*d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2)*(3*a^2*b - b^3))/(d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (2*a*atan((tan(c/2 + (d*x)/2)*((((a*(a^2 - 3*b^2)*((32*(3*a*b^10 - a^11 - 21*a^3*b^8 - 34*a^5*b^6 + 6*a^7*b^4 + 15*a^9*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a^2*b - 2*b^3)*((32*(a*b^13 - 8*a^13*b + 9*a^3*b^11 + 18*a^5*b^9 + 2*a^7*b^7 - 27*a^9*b^5 - 27*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - ((6*a^2*b - 2*b^3)*((a*(a^2 - 3*b^2)*((32*(a*b^13 - 8*a^13*b + 9*a^3*b^11 + 18*a^5*b^9 + 2*a^7*b^7 - 27*a^9*b^5 - 27*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a*(6*a^2*b - 2*b^3)*(a^2 - 3*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (32*a^3*(a^2 - 3*b^2)^3*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 4*b^8 - 61*a^2*b^6 + 155*a^4*b^4 - 67*a^6*b^2))/(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2 + (2*a*b*(7*a^6 - 10*b^6 + 59*a^2*b^4 - 68*a^4*b^2)*((32*(a*b^7 - 3*a^7*b + 3*a^3*b^5 - 17*a^5*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((6*a^2*b - 2*b^3)*((32*(3*a*b^10 - a^11 - 21*a^3*b^8 - 34*a^5*b^6 + 6*a^7*b^4 + 15*a^9*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a^2*b - 2*b^3)*((32*(a*b^13 - 8*a^13*b + 9*a^3*b^11 + 18*a^5*b^9 + 2*a^7*b^7 - 27*a^9*b^5 - 27*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*(a^2 - 3*b^2)*((a*(a^2 - 3*b^2)*((32*(a*b^13 - 8*a^13*b + 9*a^3*b^11 + 18*a^5*b^9 + 2*a^7*b^7 - 27*a^9*b^5 - 27*a^11*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a*(6*a^2*b - 2*b^3)*(a^2 - 3*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a^2*(6*a^2*b - 2*b^3)*(a^2 - 3*b^2)^2*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/(32*a^4 - 96*a^2*b^2) + (((a*(a^2 - 3*b^2)*((32*(5*a^10*b - 3*a^2*b^9 - 4*a^4*b^7 + 6*a^6*b^5 + 12*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a^2*b - 2*b^3)*((32*(3*a^6*b^8 - 4*a^2*b^12 - 9*a^4*b^10 - a^14 + 22*a^8*b^6 + 18*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - ((6*a^2*b - 2*b^3)*((a*(a^2 - 3*b^2)*((32*(3*a^6*b^8 - 4*a^2*b^12 - 9*a^4*b^10 - a^14 + 22*a^8*b^6 + 18*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a*(6*a^2*b - 2*b^3)*(a^2 - 3*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (32*a^3*(a^2 - 3*b^2)^3*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 4*b^8 - 61*a^2*b^6 + 155*a^4*b^4 - 67*a^6*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((32*a^4 - 96*a^2*b^2)*(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2) + (2*a*b*((32*(2*a^2*b^6 - 8*a^4*b^4 + 6*a^6*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((6*a^2*b - 2*b^3)*((32*(5*a^10*b - 3*a^2*b^9 - 4*a^4*b^7 + 6*a^6*b^5 + 12*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((6*a^2*b - 2*b^3)*((32*(3*a^6*b^8 - 4*a^2*b^12 - 9*a^4*b^10 - a^14 + 22*a^8*b^6 + 18*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*(a^2 - 3*b^2)*((a*(a^2 - 3*b^2)*((32*(3*a^6*b^8 - 4*a^2*b^12 - 9*a^4*b^10 - a^14 + 22*a^8*b^6 + 18*a^10*b^4 + 3*a^12*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(6*a^2*b - 2*b^3)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a*(6*a^2*b - 2*b^3)*(a^2 - 3*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a^2*(6*a^2*b - 2*b^3)*(a^2 - 3*b^2)^2*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(7*a^6 - 10*b^6 + 59*a^2*b^4 - 68*a^4*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((32*a^4 - 96*a^2*b^2)*(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2))*(a^2 - 3*b^2))/(d*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))","B"
133,1,443,119,1.718440,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{\ln\left({\left(a^2+b^2\right)}^{5/2}-a^4\,b-b^5-2\,a^2\,b^3+a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-\frac{b^2}{2}\right)}{d\,{\left(a^2+b^2\right)}^{5/2}}-\frac{\ln\left({\left(a^2+b^2\right)}^{5/2}+a^4\,b+b^5+2\,a^2\,b^3-a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-b^2\right)}{2\,d\,{\left(a^2+b^2\right)}^{5/2}}-\frac{\frac{4\,a^2\,b+b^3}{a^4+2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-2\,b^2\right)\,\left(4\,a^2\,b+b^3\right)}{a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,a^2\,b+2\,b^3\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a^2\,b+2\,b^3\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(log((a^2 + b^2)^(5/2) - a^4*b - b^5 - 2*a^2*b^3 + a^5*tan(c/2 + (d*x)/2) + a*b^4*tan(c/2 + (d*x)/2) + 2*a^3*b^2*tan(c/2 + (d*x)/2))*(a^2 - b^2/2))/(d*(a^2 + b^2)^(5/2)) - (log((a^2 + b^2)^(5/2) + a^4*b + b^5 + 2*a^2*b^3 - a^5*tan(c/2 + (d*x)/2) - a*b^4*tan(c/2 + (d*x)/2) - 2*a^3*b^2*tan(c/2 + (d*x)/2))*(2*a^2 - b^2))/(2*d*(a^2 + b^2)^(5/2)) - ((4*a^2*b + b^3)/(a^4 + b^4 + 2*a^2*b^2) - (tan(c/2 + (d*x)/2)^2*(a^2 - 2*b^2)*(4*a^2*b + b^3))/(a^2*(a^4 + b^4 + 2*a^2*b^2)) + (b*tan(c/2 + (d*x)/2)*(11*a^2*b + 2*b^3))/(a*(a^4 + b^4 + 2*a^2*b^2)) - (b*tan(c/2 + (d*x)/2)^3*(5*a^2*b + 2*b^3))/(a*(a^4 + b^4 + 2*a^2*b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^2*(2*a^2 - 4*b^2) + a^2 - 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2)))","B"
134,1,85,22,0.614952,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","-\frac{b\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}-\frac{1}{2}\right)-a\,\sin\left(2\,c+2\,d\,x\right)}{a^2\,d\,\left(a^2+b^2+a^2\,\cos\left(2\,c+2\,d\,x\right)-b^2\,\cos\left(2\,c+2\,d\,x\right)+2\,a\,b\,\sin\left(2\,c+2\,d\,x\right)\right)}","Not used",1,"-(b*(cos(2*c + 2*d*x)/2 - 1/2) - a*sin(2*c + 2*d*x))/(a^2*d*(a^2 + b^2 + a^2*cos(2*c + 2*d*x) - b^2*cos(2*c + 2*d*x) + 2*a*b*sin(2*c + 2*d*x)))","B"
135,1,260,103,2.732677,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)}{a\,\left(a^2+b^2\right)}-\frac{b}{a^2+b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{a\,\left(a^2+b^2\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-2\,b^2\right)}{a^2\,\left(a^2+b^2\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{atanh}\left(\frac{\left(2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{2\,a^2\,b+2\,b^3}{a^2+b^2}\right)\,\left(\frac{a^2}{2}+\frac{b^2}{2}\right)}{{\left(a^2+b^2\right)}^{3/2}}\right)}{d\,{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"((tan(c/2 + (d*x)/2)*(a^2 - 2*b^2))/(a*(a^2 + b^2)) - b/(a^2 + b^2) + (tan(c/2 + (d*x)/2)^3*(a^2 + 2*b^2))/(a*(a^2 + b^2)) + (b*tan(c/2 + (d*x)/2)^2*(a^2 - 2*b^2))/(a^2*(a^2 + b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^2*(2*a^2 - 4*b^2) + a^2 - 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))) + atanh(((2*a*tan(c/2 + (d*x)/2) - (2*a^2*b + 2*b^3)/(a^2 + b^2))*(a^2/2 + b^2/2))/(a^2 + b^2)^(3/2))/(d*(a^2 + b^2)^(3/2))","B"
136,1,396,86,2.594939,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^3),x)","\frac{2\,\mathrm{atanh}\left(\frac{16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a+\frac{32\,a^3}{b^2}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{32\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}-\frac{16\,a}{16\,a+\frac{32\,a^3}{b^2}-16\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{32\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a\,b+\frac{32\,a^3}{b}+32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{32\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b}-16\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{b^3\,d}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2-b^2\right)}{a^2\,b}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2-b^2\right)}{a\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{a\,b^2}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(2*atanh((16*a*tan(c/2 + (d*x)/2)^2)/(16*a + (32*a^3)/b^2 - 16*a*tan(c/2 + (d*x)/2)^2 - (32*a^3*tan(c/2 + (d*x)/2)^2)/b^2 + (32*a^2*tan(c/2 + (d*x)/2))/b) - (16*a)/(16*a + (32*a^3)/b^2 - 16*a*tan(c/2 + (d*x)/2)^2 - (32*a^3*tan(c/2 + (d*x)/2)^2)/b^2 + (32*a^2*tan(c/2 + (d*x)/2))/b) + (32*a^2*tan(c/2 + (d*x)/2))/(16*a*b + (32*a^3)/b + 32*a^2*tan(c/2 + (d*x)/2) - (32*a^3*tan(c/2 + (d*x)/2)^2)/b - 16*a*b*tan(c/2 + (d*x)/2)^2)))/(b^3*d) - ((2*tan(c/2 + (d*x)/2)^2*(3*a^2 - b^2))/(a^2*b) - (2*tan(c/2 + (d*x)/2)^3*(a^2 - b^2))/(a*b^2) + (2*tan(c/2 + (d*x)/2)*(a^2 - b^2))/(a*b^2))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^2*(2*a^2 - 4*b^2) + a^2 - 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2)))","B"
137,1,1311,260,2.619585,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^3),x)","\frac{\frac{6\,a^2-b^2}{b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^4-9\,a^2\,b^2+b^4\right)}{a^2\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(21\,a^2-2\,b^2\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^4-9\,a^2\,b^2+2\,b^4\right)}{a^2\,b^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^2-b^2\right)}{a\,b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^2-2\,b^2\right)}{a\,b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2-4\,b^2\right)-a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+a^2-8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{6\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{288\,a^4}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3+108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}-\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^3\,b^8+12\,a\,b^{10}\right)}{b^9}-48\,a^2+\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{11}+12\,a\,b^{13}\right)}{b^9}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^2\,b^4+b^6\right)}+\frac{\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{288\,a^4}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3+108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}-\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(48\,a^2-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^3\,b^8+12\,a\,b^{10}\right)}{b^9}+\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{11}+12\,a\,b^{13}\right)}{b^9}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)\,3{}\mathrm{i}}{2\,\left(a^2\,b^4+b^6\right)}}{\frac{16\,\left(54\,a^4+27\,a^2\,b^2\right)}{b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(216\,a^5+108\,a^3\,b^2\right)}{b^9}-\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{288\,a^4}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3+108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}-\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^3\,b^8+12\,a\,b^{10}\right)}{b^9}-48\,a^2+\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{11}+12\,a\,b^{13}\right)}{b^9}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)}{2\,\left(a^2\,b^4+b^6\right)}+\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{288\,a^4}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^5\,b^3+108\,a^3\,b^5+9\,a\,b^7\right)}{b^9}-\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(48\,a^2-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^3\,b^8+12\,a\,b^{10}\right)}{b^9}+\frac{3\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{11}+12\,a\,b^{13}\right)}{b^9}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)}{2\,\left(a^2\,b^4+b^6\right)}\right)}{2\,\left(a^2\,b^4+b^6\right)}}\right)\,\left(2\,a^2+b^2\right)\,\sqrt{a^2+b^2}\,3{}\mathrm{i}}{d\,\left(a^2\,b^4+b^6\right)}","Not used",1,"((6*a^2 - b^2)/b^3 - (2*tan(c/2 + (d*x)/2)^2*(6*a^4 + b^4 - 9*a^2*b^2))/(a^2*b^3) + (tan(c/2 + (d*x)/2)*(21*a^2 - 2*b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^4*(6*a^4 + 2*b^4 - 9*a^2*b^2))/(a^2*b^3) - (4*tan(c/2 + (d*x)/2)^3*(6*a^2 - b^2))/(a*b^2) + (tan(c/2 + (d*x)/2)^5*(3*a^2 - 2*b^2))/(a*b^2))/(d*(tan(c/2 + (d*x)/2)^4*(3*a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^2*(3*a^2 - 4*b^2) - a^2*tan(c/2 + (d*x)/2)^6 + a^2 - 8*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2))) - (6*a*atanh(tan(c/2 + (d*x)/2)))/(b^4*d) + (atan((((2*a^2 + b^2)*(a^2 + b^2)^(1/2)*((288*a^4)/b^5 + (8*tan(c/2 + (d*x)/2)*(9*a*b^7 + 108*a^3*b^5 + 72*a^5*b^3))/b^9 - (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*((8*tan(c/2 + (d*x)/2)*(12*a*b^10 + 24*a^3*b^8))/b^9 - 48*a^2 + (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 + 8*a^3*b^11))/b^9))/(2*(b^6 + a^2*b^4))))/(2*(b^6 + a^2*b^4)))*3i)/(2*(b^6 + a^2*b^4)) + ((2*a^2 + b^2)*(a^2 + b^2)^(1/2)*((288*a^4)/b^5 + (8*tan(c/2 + (d*x)/2)*(9*a*b^7 + 108*a^3*b^5 + 72*a^5*b^3))/b^9 - (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*(48*a^2 - (8*tan(c/2 + (d*x)/2)*(12*a*b^10 + 24*a^3*b^8))/b^9 + (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 + 8*a^3*b^11))/b^9))/(2*(b^6 + a^2*b^4))))/(2*(b^6 + a^2*b^4)))*3i)/(2*(b^6 + a^2*b^4)))/((16*(54*a^4 + 27*a^2*b^2))/b^8 - (16*tan(c/2 + (d*x)/2)*(216*a^5 + 108*a^3*b^2))/b^9 - (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*((288*a^4)/b^5 + (8*tan(c/2 + (d*x)/2)*(9*a*b^7 + 108*a^3*b^5 + 72*a^5*b^3))/b^9 - (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*((8*tan(c/2 + (d*x)/2)*(12*a*b^10 + 24*a^3*b^8))/b^9 - 48*a^2 + (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 + 8*a^3*b^11))/b^9))/(2*(b^6 + a^2*b^4))))/(2*(b^6 + a^2*b^4))))/(2*(b^6 + a^2*b^4)) + (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*((288*a^4)/b^5 + (8*tan(c/2 + (d*x)/2)*(9*a*b^7 + 108*a^3*b^5 + 72*a^5*b^3))/b^9 - (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*(48*a^2 - (8*tan(c/2 + (d*x)/2)*(12*a*b^10 + 24*a^3*b^8))/b^9 + (3*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^13 + 8*a^3*b^11))/b^9))/(2*(b^6 + a^2*b^4))))/(2*(b^6 + a^2*b^4))))/(2*(b^6 + a^2*b^4))))*(2*a^2 + b^2)*(a^2 + b^2)^(1/2)*3i)/(d*(b^6 + a^2*b^4))","B"
138,1,1204,161,4.744001,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^3),x)","-\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4+2\,a^2\,b^2-b^4\right)}{a\,b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,a^4+2\,a^2\,b^2-b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-18\,a^4+2\,a^2\,b^2+3\,b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(18\,a^4+6\,a^2\,b^2-b^4\right)}{a^2\,b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-18\,a^4+2\,a^2\,b^2+3\,b^4\right)}{a\,b^4}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(18\,a^4+8\,a^2\,b^2-b^4\right)}{a^2\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(18\,a^4+6\,a^2\,b^2-b^4\right)}{a^2\,b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-8\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2-4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+a^2-12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,a^2+b^2\right)\,\left(\frac{2\,\left(3\,a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}-\frac{4\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4+2\,a^2\,b^2\right)}{b^4}\right)\,2{}\mathrm{i}}{b^5}-\frac{\left(3\,a^2+b^2\right)\,\left(\frac{4\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}+\frac{2\,\left(3\,a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4+2\,a^2\,b^2\right)}{b^4}\right)\,2{}\mathrm{i}}{b^5}}{\frac{8\,\left(36\,a^5+24\,a^3\,b^2+4\,a\,b^4\right)}{b^8}+\frac{2\,\left(3\,a^2+b^2\right)\,\left(\frac{2\,\left(3\,a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}-\frac{4\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}+\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4+2\,a^2\,b^2\right)}{b^4}\right)}{b^5}+\frac{2\,\left(3\,a^2+b^2\right)\,\left(\frac{4\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}+\frac{2\,\left(3\,a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^8+a\,b^{10}\right)}{b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^8+3\,a\,b^{10}\right)}{b^8}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^5}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^3\,b^5+4\,a\,b^7\right)}{b^8}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4+2\,a^2\,b^2\right)}{b^4}\right)}{b^5}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(36\,a^5+24\,a^3\,b^2+4\,a\,b^4\right)}{b^8}}\right)\,\left(3\,a^2+b^2\right)\,4{}\mathrm{i}}{b^5\,d}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)*(6*a^4 - b^4 + 2*a^2*b^2))/(a*b^4) - (2*tan(c/2 + (d*x)/2)^7*(6*a^4 - b^4 + 2*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^3*(3*b^4 - 18*a^4 + 2*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^2*(18*a^4 - b^4 + 6*a^2*b^2))/(a^2*b^3) - (2*tan(c/2 + (d*x)/2)^5*(3*b^4 - 18*a^4 + 2*a^2*b^2))/(a*b^4) - (4*tan(c/2 + (d*x)/2)^4*(18*a^4 - b^4 + 8*a^2*b^2))/(a^2*b^3) + (2*tan(c/2 + (d*x)/2)^6*(18*a^4 - b^4 + 6*a^2*b^2))/(a^2*b^3))/(d*(tan(c/2 + (d*x)/2)^4*(6*a^2 - 8*b^2) - tan(c/2 + (d*x)/2)^6*(4*a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^2*(4*a^2 - 4*b^2) + a^2*tan(c/2 + (d*x)/2)^8 + a^2 - 12*a*b*tan(c/2 + (d*x)/2)^3 + 12*a*b*tan(c/2 + (d*x)/2)^5 - 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2))) - (atan((((3*a^2 + b^2)*((2*(3*a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5 - (4*(4*a*b^7 + 12*a^3*b^5))/b^8 + (4*tan(c/2 + (d*x)/2)^2*(4*a*b^7 + 12*a^3*b^5))/b^8 + (16*tan(c/2 + (d*x)/2)*(6*a^4 + 2*a^2*b^2))/b^4)*2i)/b^5 - ((3*a^2 + b^2)*((4*(4*a*b^7 + 12*a^3*b^5))/b^8 + (2*(3*a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5 - (4*tan(c/2 + (d*x)/2)^2*(4*a*b^7 + 12*a^3*b^5))/b^8 - (16*tan(c/2 + (d*x)/2)*(6*a^4 + 2*a^2*b^2))/b^4)*2i)/b^5)/((8*(4*a*b^4 + 36*a^5 + 24*a^3*b^2))/b^8 + (2*(3*a^2 + b^2)*((2*(3*a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5 - (4*(4*a*b^7 + 12*a^3*b^5))/b^8 + (4*tan(c/2 + (d*x)/2)^2*(4*a*b^7 + 12*a^3*b^5))/b^8 + (16*tan(c/2 + (d*x)/2)*(6*a^4 + 2*a^2*b^2))/b^4))/b^5 + (2*(3*a^2 + b^2)*((4*(4*a*b^7 + 12*a^3*b^5))/b^8 + (2*(3*a^2 + b^2)*((4*(a*b^10 + 4*a^3*b^8))/b^8 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^10 + 4*a^3*b^8))/b^8 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^5 - (4*tan(c/2 + (d*x)/2)^2*(4*a*b^7 + 12*a^3*b^5))/b^8 - (16*tan(c/2 + (d*x)/2)*(6*a^4 + 2*a^2*b^2))/b^4))/b^5 + (8*tan(c/2 + (d*x)/2)^2*(4*a*b^4 + 36*a^5 + 24*a^3*b^2))/b^8))*(3*a^2 + b^2)*4i)/(b^5*d)","B"
139,1,1203,383,3.821950,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^3),x)","\frac{\frac{60\,a^4+35\,a^2\,b^2-3\,b^4}{3\,b^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(210\,a^4+125\,a^2\,b^2-6\,b^4\right)}{3\,a\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(20\,a^6-15\,a^4\,b^2-15\,a^2\,b^4+2\,b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(40\,a^6-30\,a^4\,b^2-35\,a^2\,b^4+3\,b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(120\,a^6-10\,a^4\,b^2-55\,a^2\,b^4+3\,b^6\right)}{3\,a^2\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(180\,a^6-95\,a^4\,b^2-120\,a^2\,b^4+9\,b^6\right)}{3\,a^2\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(10\,a^4+5\,a^2\,b^2-2\,b^4\right)}{a\,b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(50\,a^4+25\,a^2\,b^2-4\,b^4\right)}{a\,b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(60\,a^4+35\,a^2\,b^2-3\,b^4\right)}{a\,b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(330\,a^4+205\,a^2\,b^2-12\,b^4\right)}{3\,a\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^2-12\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(10\,a^2-12\,b^2\right)-a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+a^2-16\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-16\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atanh}\left(\frac{3000\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3000\,a^2+\frac{7000\,a^4}{b^2}+\frac{4000\,a^6}{b^4}}+\frac{7000\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{7000\,a^4+3000\,a^2\,b^2+\frac{4000\,a^6}{b^2}}+\frac{4000\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4000\,a^6+7000\,a^4\,b^2+3000\,a^2\,b^4}\right)\,\left(20\,a^3+15\,a\,b^2\right)}{b^6\,d}+\frac{5\,\mathrm{atanh}\left(\frac{1000\,a^2\,\sqrt{a^2+b^2}}{1000\,a^2\,b+\frac{5000\,a^4}{b}+\frac{4000\,a^6}{b^3}+10000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2000\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2}}+\frac{4000\,a^4\,\sqrt{a^2+b^2}}{5000\,a^4\,b+1000\,a^2\,b^3+\frac{4000\,a^6}{b}+8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2000\,a\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10000\,a^3\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{9000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{5000\,a^4+1000\,a^2\,b^2+\frac{4000\,a^6}{b^2}+2000\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10000\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{4000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{4000\,a^6+8000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b+5000\,a^4\,b^2+10000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^3+1000\,a^2\,b^4+2000\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^5}+\frac{2000\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2+b^2}}{1000\,a^2+\frac{5000\,a^4}{b^2}+\frac{4000\,a^6}{b^4}+\frac{10000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}+\frac{8000\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^3}+2000\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{a^2+b^2}}{b^6\,d}","Not used",1,"((60*a^4 - 3*b^4 + 35*a^2*b^2)/(3*b^5) + (tan(c/2 + (d*x)/2)*(210*a^4 - 6*b^4 + 125*a^2*b^2))/(3*a*b^4) + (tan(c/2 + (d*x)/2)^8*(20*a^6 + 2*b^6 - 15*a^2*b^4 - 15*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^6*(40*a^6 + 3*b^6 - 35*a^2*b^4 - 30*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^2*(120*a^6 + 3*b^6 - 55*a^2*b^4 - 10*a^4*b^2))/(3*a^2*b^5) + (2*tan(c/2 + (d*x)/2)^4*(180*a^6 + 9*b^6 - 120*a^2*b^4 - 95*a^4*b^2))/(3*a^2*b^5) + (tan(c/2 + (d*x)/2)^9*(10*a^4 - 2*b^4 + 5*a^2*b^2))/(a*b^4) - (2*tan(c/2 + (d*x)/2)^7*(50*a^4 - 4*b^4 + 25*a^2*b^2))/(a*b^4) + (4*tan(c/2 + (d*x)/2)^5*(60*a^4 - 3*b^4 + 35*a^2*b^2))/(a*b^4) - (2*tan(c/2 + (d*x)/2)^3*(330*a^4 - 12*b^4 + 205*a^2*b^2))/(3*a*b^4))/(d*(tan(c/2 + (d*x)/2)^8*(5*a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^2*(5*a^2 - 4*b^2) + tan(c/2 + (d*x)/2)^4*(10*a^2 - 12*b^2) - tan(c/2 + (d*x)/2)^6*(10*a^2 - 12*b^2) - a^2*tan(c/2 + (d*x)/2)^10 + a^2 - 16*a*b*tan(c/2 + (d*x)/2)^3 + 24*a*b*tan(c/2 + (d*x)/2)^5 - 16*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2)^9 + 4*a*b*tan(c/2 + (d*x)/2))) - (atanh((3000*a^2*tan(c/2 + (d*x)/2))/(3000*a^2 + (7000*a^4)/b^2 + (4000*a^6)/b^4) + (7000*a^4*tan(c/2 + (d*x)/2))/(7000*a^4 + 3000*a^2*b^2 + (4000*a^6)/b^2) + (4000*a^6*tan(c/2 + (d*x)/2))/(4000*a^6 + 3000*a^2*b^4 + 7000*a^4*b^2))*(15*a*b^2 + 20*a^3))/(b^6*d) + (5*atanh((1000*a^2*(a^2 + b^2)^(1/2))/(1000*a^2*b + (5000*a^4)/b + (4000*a^6)/b^3 + 10000*a^3*tan(c/2 + (d*x)/2) + 2000*a*b^2*tan(c/2 + (d*x)/2) + (8000*a^5*tan(c/2 + (d*x)/2))/b^2) + (4000*a^4*(a^2 + b^2)^(1/2))/(5000*a^4*b + 1000*a^2*b^3 + (4000*a^6)/b + 8000*a^5*tan(c/2 + (d*x)/2) + 2000*a*b^4*tan(c/2 + (d*x)/2) + 10000*a^3*b^2*tan(c/2 + (d*x)/2)) + (9000*a^3*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(5000*a^4 + 1000*a^2*b^2 + (4000*a^6)/b^2 + 2000*a*b^3*tan(c/2 + (d*x)/2) + 10000*a^3*b*tan(c/2 + (d*x)/2) + (8000*a^5*tan(c/2 + (d*x)/2))/b) + (4000*a^5*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(4000*a^6 + 1000*a^2*b^4 + 5000*a^4*b^2 + 2000*a*b^5*tan(c/2 + (d*x)/2) + 8000*a^5*b*tan(c/2 + (d*x)/2) + 10000*a^3*b^3*tan(c/2 + (d*x)/2)) + (2000*a*tan(c/2 + (d*x)/2)*(a^2 + b^2)^(1/2))/(1000*a^2 + (5000*a^4)/b^2 + (4000*a^6)/b^4 + (10000*a^3*tan(c/2 + (d*x)/2))/b + (8000*a^5*tan(c/2 + (d*x)/2))/b^3 + 2000*a*b*tan(c/2 + (d*x)/2)))*(4*a^2 + b^2)*(a^2 + b^2)^(1/2))/(b^6*d)","B"
140,1,1712,232,7.638432,"\text{Not used}","int(1/(cos(c + d*x)^5*(a*cos(c + d*x) + b*sin(c + d*x))^3),x)","-\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^6+18\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{a\,b^6}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(15\,a^6+18\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}{a\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(45\,a^6+54\,a^4\,b^2+9\,a^2\,b^4-b^6\right)}{a^2\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(45\,a^6+54\,a^4\,b^2+9\,a^2\,b^4-b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(75\,a^6+70\,a^4\,b^2-9\,a^2\,b^4-5\,b^6\right)}{a\,b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(75\,a^6+60\,a^4\,b^2-17\,a^2\,b^4-5\,b^6\right)}{a\,b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(75\,a^6+60\,a^4\,b^2-17\,a^2\,b^4-5\,b^6\right)}{a\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(75\,a^6+70\,a^4\,b^2-9\,a^2\,b^4-5\,b^6\right)}{a\,b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(90\,a^6+113\,a^4\,b^2+24\,a^2\,b^4-2\,b^6\right)}{a^2\,b^5}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(90\,a^6+113\,a^4\,b^2+24\,a^2\,b^4-2\,b^6\right)}{a^2\,b^5}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(135\,a^6+172\,a^4\,b^2+35\,a^2\,b^4-3\,b^6\right)}{a^2\,b^5}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(15\,a^2-16\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(6\,a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a^2-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(15\,a^2-16\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(20\,a^2-24\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+a^2-20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-40\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^6+18\,a^4\,b^2+3\,a^2\,b^4\right)}{b^6}-\frac{4\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}+\frac{3\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)\,3{}\mathrm{i}}{b^7}-\frac{\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^6+18\,a^4\,b^2+3\,a^2\,b^4\right)}{b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}+\frac{3\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)\,3{}\mathrm{i}}{b^7}}{\frac{8\,\left(225\,a^9+540\,a^7\,b^2+414\,a^5\,b^4+108\,a^3\,b^6+9\,a\,b^8\right)}{b^{12}}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(225\,a^9+540\,a^7\,b^2+414\,a^5\,b^4+108\,a^3\,b^6+9\,a\,b^8\right)}{b^{12}}+\frac{3\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^6+18\,a^4\,b^2+3\,a^2\,b^4\right)}{b^6}-\frac{4\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}+\frac{3\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)}{b^7}+\frac{3\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,a^6+18\,a^4\,b^2+3\,a^2\,b^4\right)}{b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(30\,a^5\,b^7+36\,a^3\,b^9+6\,a\,b^{11}\right)}{b^{12}}+\frac{3\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)}{b^7}}\right)\,\left(5\,a^2+b^2\right)\,\left(a^2+b^2\right)\,6{}\mathrm{i}}{b^7\,d}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)*(15*a^6 - b^6 + 3*a^2*b^4 + 18*a^4*b^2))/(a*b^6) - (2*tan(c/2 + (d*x)/2)^11*(15*a^6 - b^6 + 3*a^2*b^4 + 18*a^4*b^2))/(a*b^6) + (2*tan(c/2 + (d*x)/2)^2*(45*a^6 - b^6 + 9*a^2*b^4 + 54*a^4*b^2))/(a^2*b^5) + (2*tan(c/2 + (d*x)/2)^10*(45*a^6 - b^6 + 9*a^2*b^4 + 54*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^3*(75*a^6 - 5*b^6 - 9*a^2*b^4 + 70*a^4*b^2))/(a*b^6) + (4*tan(c/2 + (d*x)/2)^5*(75*a^6 - 5*b^6 - 17*a^2*b^4 + 60*a^4*b^2))/(a*b^6) - (4*tan(c/2 + (d*x)/2)^7*(75*a^6 - 5*b^6 - 17*a^2*b^4 + 60*a^4*b^2))/(a*b^6) + (2*tan(c/2 + (d*x)/2)^9*(75*a^6 - 5*b^6 - 9*a^2*b^4 + 70*a^4*b^2))/(a*b^6) - (4*tan(c/2 + (d*x)/2)^4*(90*a^6 - 2*b^6 + 24*a^2*b^4 + 113*a^4*b^2))/(a^2*b^5) - (4*tan(c/2 + (d*x)/2)^8*(90*a^6 - 2*b^6 + 24*a^2*b^4 + 113*a^4*b^2))/(a^2*b^5) + (4*tan(c/2 + (d*x)/2)^6*(135*a^6 - 3*b^6 + 35*a^2*b^4 + 172*a^4*b^2))/(a^2*b^5))/(d*(tan(c/2 + (d*x)/2)^4*(15*a^2 - 16*b^2) - tan(c/2 + (d*x)/2)^10*(6*a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^2*(6*a^2 - 4*b^2) + tan(c/2 + (d*x)/2)^8*(15*a^2 - 16*b^2) - tan(c/2 + (d*x)/2)^6*(20*a^2 - 24*b^2) + a^2*tan(c/2 + (d*x)/2)^12 + a^2 - 20*a*b*tan(c/2 + (d*x)/2)^3 + 40*a*b*tan(c/2 + (d*x)/2)^5 - 40*a*b*tan(c/2 + (d*x)/2)^7 + 20*a*b*tan(c/2 + (d*x)/2)^9 - 4*a*b*tan(c/2 + (d*x)/2)^11 + 4*a*b*tan(c/2 + (d*x)/2))) - (atan((((5*a^2 + b^2)*(a^2 + b^2)*((16*tan(c/2 + (d*x)/2)*(15*a^6 + 3*a^2*b^4 + 18*a^4*b^2))/b^6 - (4*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 + (4*tan(c/2 + (d*x)/2)^2*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 + (3*(5*a^2 + b^2)*(a^2 + b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7)*3i)/b^7 - ((5*a^2 + b^2)*(a^2 + b^2)*((4*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 - (16*tan(c/2 + (d*x)/2)*(15*a^6 + 3*a^2*b^4 + 18*a^4*b^2))/b^6 - (4*tan(c/2 + (d*x)/2)^2*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 + (3*(5*a^2 + b^2)*(a^2 + b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7)*3i)/b^7)/((8*(9*a*b^8 + 225*a^9 + 108*a^3*b^6 + 414*a^5*b^4 + 540*a^7*b^2))/b^12 + (8*tan(c/2 + (d*x)/2)^2*(9*a*b^8 + 225*a^9 + 108*a^3*b^6 + 414*a^5*b^4 + 540*a^7*b^2))/b^12 + (3*(5*a^2 + b^2)*(a^2 + b^2)*((16*tan(c/2 + (d*x)/2)*(15*a^6 + 3*a^2*b^4 + 18*a^4*b^2))/b^6 - (4*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 + (4*tan(c/2 + (d*x)/2)^2*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 + (3*(5*a^2 + b^2)*(a^2 + b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7))/b^7 + (3*(5*a^2 + b^2)*(a^2 + b^2)*((4*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 - (16*tan(c/2 + (d*x)/2)*(15*a^6 + 3*a^2*b^4 + 18*a^4*b^2))/b^6 - (4*tan(c/2 + (d*x)/2)^2*(6*a*b^11 + 36*a^3*b^9 + 30*a^5*b^7))/b^12 + (3*(5*a^2 + b^2)*(a^2 + b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7))/b^7))*(5*a^2 + b^2)*(a^2 + b^2)*6i)/(b^7*d)","B"
141,1,8586,165,12.554947,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(10\,a^4\,b^3+3\,a^2\,b^5+b^7\right)}{a^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^4\,b^3+3\,a^2\,b^5+b^7\right)}{a^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^4\,b+3\,a^2\,b^3+b^5\right)}{a\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-18\,a^6\,b+17\,a^4\,b^3+a^2\,b^5+2\,b^7\right)}{3\,a^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4\,b+3\,a^2\,b^3+b^5\right)}{a\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(4\,a\,b^3-4\,a^3\,b\right)}{d\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{\ln\left(\left(\left(\sqrt{-\frac{{\left(a^4-6\,a^2\,b^2+b^4\right)}^2}{{\left(a^2+b^2\right)}^8}}-\frac{4\,a\,b\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^4}\right)\,\left(\left(\sqrt{-\frac{{\left(a^4-6\,a^2\,b^2+b^4\right)}^2}{{\left(a^2+b^2\right)}^8}}-\frac{4\,a\,b\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^4}\right)\,\left(\frac{32\,a\,\left(a^6-11\,a^4\,b^2+11\,a^2\,b^4-b^6\right)}{{\left(a^2+b^2\right)}^3}+96\,a\,b\,\left(\sqrt{-\frac{{\left(a^4-6\,a^2\,b^2+b^4\right)}^2}{{\left(a^2+b^2\right)}^8}}-\frac{4\,a\,b\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^4}\right)\,\left(a+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+b^2\right)-\frac{64\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-5\,a^4+8\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^3}\right)-\frac{32\,a^2\,b\,\left(7\,a^4-18\,a^2\,b^2+7\,b^4\right)}{{\left(a^2+b^2\right)}^5}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8-27\,a^6\,b^2+105\,a^4\,b^4-57\,a^2\,b^6+2\,b^8\right)}{{\left(a^2+b^2\right)}^6}\right)+\frac{128\,a^3\,b^2\,\left(3\,a^6-13\,a^4\,b^2+13\,a^2\,b^4-3\,b^6\right)}{{\left(a^2+b^2\right)}^9}-\frac{128\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8+11\,a^6\,b^2-15\,a^4\,b^4+5\,a^2\,b^6-2\,b^8\right)}{{\left(a^2+b^2\right)}^9}\right)\,\left(\left(\sqrt{-\frac{{\left(a^4-6\,a^2\,b^2+b^4\right)}^2}{{\left(a^2+b^2\right)}^8}}+\frac{4\,a\,b\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^4}\right)\,\left(\left(\sqrt{-\frac{{\left(a^4-6\,a^2\,b^2+b^4\right)}^2}{{\left(a^2+b^2\right)}^8}}+\frac{4\,a\,b\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^4}\right)\,\left(96\,a\,b\,\left(\sqrt{-\frac{{\left(a^4-6\,a^2\,b^2+b^4\right)}^2}{{\left(a^2+b^2\right)}^8}}+\frac{4\,a\,b\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^4}\right)\,\left(a+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+b^2\right)-\frac{32\,a\,\left(a^6-11\,a^4\,b^2+11\,a^2\,b^4-b^6\right)}{{\left(a^2+b^2\right)}^3}+\frac{64\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-5\,a^4+8\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^3}\right)-\frac{32\,a^2\,b\,\left(7\,a^4-18\,a^2\,b^2+7\,b^4\right)}{{\left(a^2+b^2\right)}^5}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8-27\,a^6\,b^2+105\,a^4\,b^4-57\,a^2\,b^6+2\,b^8\right)}{{\left(a^2+b^2\right)}^6}\right)-\frac{128\,a^3\,b^2\,\left(3\,a^6-13\,a^4\,b^2+13\,a^2\,b^4-3\,b^6\right)}{{\left(a^2+b^2\right)}^9}+\frac{128\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8+11\,a^6\,b^2-15\,a^4\,b^4+5\,a^2\,b^6-2\,b^8\right)}{{\left(a^2+b^2\right)}^9}\right)\right)\,\left(8\,a\,b^3-8\,a^3\,b\right)}{2\,d\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{\left(\frac{32\,\left(4\,a^{10}\,b+44\,a^8\,b^3-60\,a^6\,b^5+20\,a^4\,b^7-8\,a^2\,b^9\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(\frac{32\,\left(a^{15}-24\,a^{13}\,b^2+27\,a^{11}\,b^4+178\,a^9\,b^6+119\,a^7\,b^8-60\,a^5\,b^{10}-51\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{32\,\left(-10\,a^{18}\,b-44\,a^{16}\,b^3-52\,a^{14}\,b^5+52\,a^{12}\,b^7+200\,a^{10}\,b^9+220\,a^8\,b^{11}+116\,a^6\,b^{13}+28\,a^4\,b^{15}+2\,a^2\,b^{17}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}\right)\,\left(8\,a\,b^3-8\,a^3\,b\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{\left(\frac{\left(\frac{32\,\left(-10\,a^{18}\,b-44\,a^{16}\,b^3-52\,a^{14}\,b^5+52\,a^{12}\,b^7+200\,a^{10}\,b^9+220\,a^8\,b^{11}+116\,a^6\,b^{13}+28\,a^4\,b^{15}+2\,a^2\,b^{17}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^2\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}+\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,{\left(-a^2+2\,a\,b+b^2\right)}^2\,{\left(a^2+2\,a\,b-b^2\right)}^2\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^3\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(18\,a^9\,b-280\,a^7\,b^3+556\,a^5\,b^5-280\,a^3\,b^7+18\,a\,b^9\right)}{{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}+\frac{\left(\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{\left(\frac{32\,\left(-10\,a^{18}\,b-44\,a^{16}\,b^3-52\,a^{14}\,b^5+52\,a^{12}\,b^7+200\,a^{10}\,b^9+220\,a^8\,b^{11}+116\,a^6\,b^{13}+28\,a^4\,b^{15}+2\,a^2\,b^{17}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^2\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{\left(\frac{32\,\left(a^{15}-24\,a^{13}\,b^2+27\,a^{11}\,b^4+178\,a^9\,b^6+119\,a^7\,b^8-60\,a^5\,b^{10}-51\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{32\,\left(-10\,a^{18}\,b-44\,a^{16}\,b^3-52\,a^{14}\,b^5+52\,a^{12}\,b^7+200\,a^{10}\,b^9+220\,a^8\,b^{11}+116\,a^6\,b^{13}+28\,a^4\,b^{15}+2\,a^2\,b^{17}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}+\frac{32\,{\left(-a^2+2\,a\,b+b^2\right)}^3\,{\left(a^2+2\,a\,b-b^2\right)}^3\,\left(3\,a^{21}\,b^2+30\,a^{19}\,b^4+135\,a^{17}\,b^6+360\,a^{15}\,b^8+630\,a^{13}\,b^{10}+756\,a^{11}\,b^{12}+630\,a^9\,b^{14}+360\,a^7\,b^{16}+135\,a^5\,b^{18}+30\,a^3\,b^{20}+3\,a\,b^{22}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^3\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(a^{10}-109\,a^8\,b^2+466\,a^6\,b^4-466\,a^4\,b^6+109\,a^2\,b^8-b^{10}\right)}{{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(a^{22}+11\,a^{20}\,b^2+55\,a^{18}\,b^4+165\,a^{16}\,b^6+330\,a^{14}\,b^8+462\,a^{12}\,b^{10}+462\,a^{10}\,b^{12}+330\,a^8\,b^{14}+165\,a^6\,b^{16}+55\,a^4\,b^{18}+11\,a^2\,b^{20}+b^{22}\right)}{32\,a^5-192\,a^3\,b^2+32\,a\,b^4}+\frac{\left(\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{\left(\frac{32\,\left(-a^{19}+5\,a^{17}\,b^2+40\,a^{15}\,b^4+80\,a^{13}\,b^6+46\,a^{11}\,b^8-46\,a^9\,b^{10}-80\,a^7\,b^{12}-40\,a^5\,b^{14}-5\,a^3\,b^{16}+a\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^2\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{\left(\frac{32\,\left(7\,a^{14}\,b+10\,a^{12}\,b^3-23\,a^{10}\,b^5-52\,a^8\,b^7-23\,a^6\,b^9+10\,a^4\,b^{11}+7\,a^2\,b^{13}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{32\,\left(-a^{19}+5\,a^{17}\,b^2+40\,a^{15}\,b^4+80\,a^{13}\,b^6+46\,a^{11}\,b^8-46\,a^9\,b^{10}-80\,a^7\,b^{12}-40\,a^5\,b^{14}-5\,a^3\,b^{16}+a\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}+\frac{32\,{\left(-a^2+2\,a\,b+b^2\right)}^3\,{\left(a^2+2\,a\,b-b^2\right)}^3\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^3\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(a^{10}-109\,a^8\,b^2+466\,a^6\,b^4-466\,a^4\,b^6+109\,a^2\,b^8-b^{10}\right)\,\left(a^{22}+11\,a^{20}\,b^2+55\,a^{18}\,b^4+165\,a^{16}\,b^6+330\,a^{14}\,b^8+462\,a^{12}\,b^{10}+462\,a^{10}\,b^{12}+330\,a^8\,b^{14}+165\,a^6\,b^{16}+55\,a^4\,b^{18}+11\,a^2\,b^{20}+b^{22}\right)}{\left(32\,a^5-192\,a^3\,b^2+32\,a\,b^4\right)\,{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}+\frac{\left(\frac{32\,\left(-12\,a^9\,b^2+52\,a^7\,b^4-52\,a^5\,b^6+12\,a^3\,b^8\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{32\,\left(7\,a^{14}\,b+10\,a^{12}\,b^3-23\,a^{10}\,b^5-52\,a^8\,b^7-23\,a^6\,b^9+10\,a^4\,b^{11}+7\,a^2\,b^{13}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(\frac{32\,\left(-a^{19}+5\,a^{17}\,b^2+40\,a^{15}\,b^4+80\,a^{13}\,b^6+46\,a^{11}\,b^8-46\,a^9\,b^{10}-80\,a^7\,b^{12}-40\,a^5\,b^{14}-5\,a^3\,b^{16}+a\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{\left(\frac{\left(\frac{32\,\left(-a^{19}+5\,a^{17}\,b^2+40\,a^{15}\,b^4+80\,a^{13}\,b^6+46\,a^{11}\,b^8-46\,a^9\,b^{10}-80\,a^7\,b^{12}-40\,a^5\,b^{14}-5\,a^3\,b^{16}+a\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}-\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^2\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}+\frac{16\,\left(8\,a\,b^3-8\,a^3\,b\right)\,{\left(-a^2+2\,a\,b+b^2\right)}^2\,{\left(a^2+2\,a\,b-b^2\right)}^2\,\left(3\,a^{22}\,b+30\,a^{20}\,b^3+135\,a^{18}\,b^5+360\,a^{16}\,b^7+630\,a^{14}\,b^9+756\,a^{12}\,b^{11}+630\,a^{10}\,b^{13}+360\,a^8\,b^{15}+135\,a^6\,b^{17}+30\,a^4\,b^{19}+3\,a^2\,b^{21}\right)}{{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^3\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(18\,a^9\,b-280\,a^7\,b^3+556\,a^5\,b^5-280\,a^3\,b^7+18\,a\,b^9\right)\,\left(a^{22}+11\,a^{20}\,b^2+55\,a^{18}\,b^4+165\,a^{16}\,b^6+330\,a^{14}\,b^8+462\,a^{12}\,b^{10}+462\,a^{10}\,b^{12}+330\,a^8\,b^{14}+165\,a^6\,b^{16}+55\,a^4\,b^{18}+11\,a^2\,b^{20}+b^{22}\right)}{\left(32\,a^5-192\,a^3\,b^2+32\,a\,b^4\right)\,{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{d\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}","Not used",1,"((4*tan(c/2 + (d*x)/2)^2*(b^7 + 3*a^2*b^5 + 10*a^4*b^3))/(a^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*tan(c/2 + (d*x)/2)^4*(b^7 + 3*a^2*b^5 + 10*a^4*b^3))/(a^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (2*b*tan(c/2 + (d*x)/2)^5*(6*a^4*b + b^5 + 3*a^2*b^3))/(a*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (4*b*tan(c/2 + (d*x)/2)^3*(2*b^7 - 18*a^6*b + a^2*b^5 + 17*a^4*b^3))/(3*a^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (2*b*tan(c/2 + (d*x)/2)*(6*a^4*b + b^5 + 3*a^2*b^3))/(a*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5)) - (log(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2)*(4*a*b^3 - 4*a^3*b))/(d*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (log((((-(a^4 + b^4 - 6*a^2*b^2)^2/(a^2 + b^2)^8)^(1/2) - (4*a*b*(a^2 - b^2))/(a^2 + b^2)^4)*(((-(a^4 + b^4 - 6*a^2*b^2)^2/(a^2 + b^2)^8)^(1/2) - (4*a*b*(a^2 - b^2))/(a^2 + b^2)^4)*((32*a*(a^6 - b^6 + 11*a^2*b^4 - 11*a^4*b^2))/(a^2 + b^2)^3 + 96*a*b*((-(a^4 + b^4 - 6*a^2*b^2)^2/(a^2 + b^2)^8)^(1/2) - (4*a*b*(a^2 - b^2))/(a^2 + b^2)^4)*(a + b*tan(c/2 + (d*x)/2))*(a^2 + b^2) - (64*a^2*b*tan(c/2 + (d*x)/2)*(b^4 - 5*a^4 + 8*a^2*b^2))/(a^2 + b^2)^3) - (32*a^2*b*(7*a^4 + 7*b^4 - 18*a^2*b^2))/(a^2 + b^2)^5 + (32*a*tan(c/2 + (d*x)/2)*(a^8 + 2*b^8 - 57*a^2*b^6 + 105*a^4*b^4 - 27*a^6*b^2))/(a^2 + b^2)^6) + (128*a^3*b^2*(3*a^6 - 3*b^6 + 13*a^2*b^4 - 13*a^4*b^2))/(a^2 + b^2)^9 - (128*a^2*b*tan(c/2 + (d*x)/2)*(a^8 - 2*b^8 + 5*a^2*b^6 - 15*a^4*b^4 + 11*a^6*b^2))/(a^2 + b^2)^9)*(((-(a^4 + b^4 - 6*a^2*b^2)^2/(a^2 + b^2)^8)^(1/2) + (4*a*b*(a^2 - b^2))/(a^2 + b^2)^4)*(((-(a^4 + b^4 - 6*a^2*b^2)^2/(a^2 + b^2)^8)^(1/2) + (4*a*b*(a^2 - b^2))/(a^2 + b^2)^4)*(96*a*b*((-(a^4 + b^4 - 6*a^2*b^2)^2/(a^2 + b^2)^8)^(1/2) + (4*a*b*(a^2 - b^2))/(a^2 + b^2)^4)*(a + b*tan(c/2 + (d*x)/2))*(a^2 + b^2) - (32*a*(a^6 - b^6 + 11*a^2*b^4 - 11*a^4*b^2))/(a^2 + b^2)^3 + (64*a^2*b*tan(c/2 + (d*x)/2)*(b^4 - 5*a^4 + 8*a^2*b^2))/(a^2 + b^2)^3) - (32*a^2*b*(7*a^4 + 7*b^4 - 18*a^2*b^2))/(a^2 + b^2)^5 + (32*a*tan(c/2 + (d*x)/2)*(a^8 + 2*b^8 - 57*a^2*b^6 + 105*a^4*b^4 - 27*a^6*b^2))/(a^2 + b^2)^6) - (128*a^3*b^2*(3*a^6 - 3*b^6 + 13*a^2*b^4 - 13*a^4*b^2))/(a^2 + b^2)^9 + (128*a^2*b*tan(c/2 + (d*x)/2)*(a^8 - 2*b^8 + 5*a^2*b^6 - 15*a^4*b^4 + 11*a^6*b^2))/(a^2 + b^2)^9))*(8*a*b^3 - 8*a^3*b))/(2*d*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - (2*atan((tan(c/2 + (d*x)/2)*((((32*(4*a^10*b - 8*a^2*b^9 + 20*a^4*b^7 - 60*a^6*b^5 + 44*a^8*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (((32*(2*a*b^14 + a^15 - 51*a^3*b^12 - 60*a^5*b^10 + 119*a^7*b^8 + 178*a^9*b^6 + 27*a^11*b^4 - 24*a^13*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - ((8*a*b^3 - 8*a^3*b)*((32*(2*a^2*b^17 - 10*a^18*b + 28*a^4*b^15 + 116*a^6*b^13 + 220*a^8*b^11 + 200*a^10*b^9 + 52*a^12*b^7 - 52*a^14*b^5 - 44*a^16*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)))*(8*a*b^3 - 8*a^3*b))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - (((((32*(2*a^2*b^17 - 10*a^18*b + 28*a^4*b^15 + 116*a^6*b^13 + 220*a^8*b^11 + 200*a^10*b^9 + 52*a^12*b^7 - 52*a^14*b^5 - 44*a^16*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^2*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) + (16*(8*a*b^3 - 8*a^3*b)*(2*a*b - a^2 + b^2)^2*(2*a*b + a^2 - b^2)^2*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^3*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(18*a*b^9 + 18*a^9*b - 280*a^3*b^7 + 556*a^5*b^5 - 280*a^7*b^3))/(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2 + ((((8*a*b^3 - 8*a^3*b)*((((32*(2*a^2*b^17 - 10*a^18*b + 28*a^4*b^15 + 116*a^6*b^13 + 220*a^8*b^11 + 200*a^10*b^9 + 52*a^12*b^7 - 52*a^14*b^5 - 44*a^16*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^2*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - (((32*(2*a*b^14 + a^15 - 51*a^3*b^12 - 60*a^5*b^10 + 119*a^7*b^8 + 178*a^9*b^6 + 27*a^11*b^4 - 24*a^13*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - ((8*a*b^3 - 8*a^3*b)*((32*(2*a^2*b^17 - 10*a^18*b + 28*a^4*b^15 + 116*a^6*b^13 + 220*a^8*b^11 + 200*a^10*b^9 + 52*a^12*b^7 - 52*a^14*b^5 - 44*a^16*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) + (32*(2*a*b - a^2 + b^2)^3*(2*a*b + a^2 - b^2)^3*(3*a*b^22 + 30*a^3*b^20 + 135*a^5*b^18 + 360*a^7*b^16 + 630*a^9*b^14 + 756*a^11*b^12 + 630*a^13*b^10 + 360*a^15*b^8 + 135*a^17*b^6 + 30*a^19*b^4 + 3*a^21*b^2))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^3*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(a^10 - b^10 + 109*a^2*b^8 - 466*a^4*b^6 + 466*a^6*b^4 - 109*a^8*b^2))/(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2)*(a^22 + b^22 + 11*a^2*b^20 + 55*a^4*b^18 + 165*a^6*b^16 + 330*a^8*b^14 + 462*a^10*b^12 + 462*a^12*b^10 + 330*a^14*b^8 + 165*a^16*b^6 + 55*a^18*b^4 + 11*a^20*b^2))/(32*a*b^4 + 32*a^5 - 192*a^3*b^2) + ((((8*a*b^3 - 8*a^3*b)*((((32*(a*b^18 - a^19 - 5*a^3*b^16 - 40*a^5*b^14 - 80*a^7*b^12 - 46*a^9*b^10 + 46*a^11*b^8 + 80*a^13*b^6 + 40*a^15*b^4 + 5*a^17*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^2*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (((32*(7*a^14*b + 7*a^2*b^13 + 10*a^4*b^11 - 23*a^6*b^9 - 52*a^8*b^7 - 23*a^10*b^5 + 10*a^12*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + ((8*a*b^3 - 8*a^3*b)*((32*(a*b^18 - a^19 - 5*a^3*b^16 - 40*a^5*b^14 - 80*a^7*b^12 - 46*a^9*b^10 + 46*a^11*b^8 + 80*a^13*b^6 + 40*a^15*b^4 + 5*a^17*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) + (32*(2*a*b - a^2 + b^2)^3*(2*a*b + a^2 - b^2)^3*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^3*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(a^10 - b^10 + 109*a^2*b^8 - 466*a^4*b^6 + 466*a^6*b^4 - 109*a^8*b^2)*(a^22 + b^22 + 11*a^2*b^20 + 55*a^4*b^18 + 165*a^6*b^16 + 330*a^8*b^14 + 462*a^10*b^12 + 462*a^12*b^10 + 330*a^14*b^8 + 165*a^16*b^6 + 55*a^18*b^4 + 11*a^20*b^2))/((32*a*b^4 + 32*a^5 - 192*a^3*b^2)*(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2) + (((32*(12*a^3*b^8 - 52*a^5*b^6 + 52*a^7*b^4 - 12*a^9*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + ((8*a*b^3 - 8*a^3*b)*((32*(7*a^14*b + 7*a^2*b^13 + 10*a^4*b^11 - 23*a^6*b^9 - 52*a^8*b^7 - 23*a^10*b^5 + 10*a^12*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + ((8*a*b^3 - 8*a^3*b)*((32*(a*b^18 - a^19 - 5*a^3*b^16 - 40*a^5*b^14 - 80*a^7*b^12 - 46*a^9*b^10 + 46*a^11*b^8 + 80*a^13*b^6 + 40*a^15*b^4 + 5*a^17*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2))))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - (((((32*(a*b^18 - a^19 - 5*a^3*b^16 - 40*a^5*b^14 - 80*a^7*b^12 - 46*a^9*b^10 + 46*a^11*b^8 + 80*a^13*b^6 + 40*a^15*b^4 + 5*a^17*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) - (16*(8*a*b^3 - 8*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^2*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) + (16*(8*a*b^3 - 8*a^3*b)*(2*a*b - a^2 + b^2)^2*(2*a*b + a^2 - b^2)^2*(3*a^22*b + 3*a^2*b^21 + 30*a^4*b^19 + 135*a^6*b^17 + 360*a^8*b^15 + 630*a^10*b^13 + 756*a^12*b^11 + 630*a^14*b^9 + 360*a^16*b^7 + 135*a^18*b^5 + 30*a^20*b^3))/((a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^3*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(18*a*b^9 + 18*a^9*b - 280*a^3*b^7 + 556*a^5*b^5 - 280*a^7*b^3)*(a^22 + b^22 + 11*a^2*b^20 + 55*a^4*b^18 + 165*a^6*b^16 + 330*a^8*b^14 + 462*a^10*b^12 + 462*a^12*b^10 + 330*a^14*b^8 + 165*a^16*b^6 + 55*a^18*b^4 + 11*a^20*b^2))/((32*a*b^4 + 32*a^5 - 192*a^3*b^2)*(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(d*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2))","B"
142,1,764,157,2.690742,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{\ln\left({\left(a^2+b^2\right)}^{7/2}+a^6\,b+b^7+3\,a^2\,b^5+3\,a^4\,b^3-a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,a^3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a\,b^2}{2}-a^3\right)}{d\,{\left(a^2+b^2\right)}^{7/2}}-\frac{\frac{18\,a^4\,b+5\,a^2\,b^3+2\,b^5}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-6\,a^6\,b+20\,a^4\,b^3+3\,a^2\,b^5+2\,b^7\right)}{a^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-6\,a^6\,b+27\,a^4\,b^3+12\,a^2\,b^5+4\,b^7\right)}{a^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(27\,a^4\,b+4\,a^2\,b^3+2\,b^5\right)}{a\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,a^4\,b+6\,a^2\,b^3+2\,b^5\right)}{a\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2-2\,b^2\right)\,\left(18\,a^4\,b+5\,a^2\,b^3+2\,b^5\right)}{3\,a^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{a\,\ln\left({\left(a^2+b^2\right)}^{7/2}-a^6\,b-b^7-3\,a^2\,b^5-3\,a^4\,b^3+a^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,a^3\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,a^5\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2-3\,b^2\right)}{2\,d\,{\left(a^2+b^2\right)}^{7/2}}","Not used",1,"(log((a^2 + b^2)^(7/2) + a^6*b + b^7 + 3*a^2*b^5 + 3*a^4*b^3 - a^7*tan(c/2 + (d*x)/2) - a*b^6*tan(c/2 + (d*x)/2) - 3*a^3*b^4*tan(c/2 + (d*x)/2) - 3*a^5*b^2*tan(c/2 + (d*x)/2))*((3*a*b^2)/2 - a^3))/(d*(a^2 + b^2)^(7/2)) - ((18*a^4*b + 2*b^5 + 5*a^2*b^3)/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^2*(2*b^7 - 6*a^6*b + 3*a^2*b^5 + 20*a^4*b^3))/(a^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (tan(c/2 + (d*x)/2)^4*(4*b^7 - 6*a^6*b + 12*a^2*b^5 + 27*a^4*b^3))/(a^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (b*tan(c/2 + (d*x)/2)*(27*a^4*b + 2*b^5 + 4*a^2*b^3))/(a*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (b*tan(c/2 + (d*x)/2)^5*(9*a^4*b + 2*b^5 + 6*a^2*b^3))/(a*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (2*b*tan(c/2 + (d*x)/2)^3*(3*a^2 - 2*b^2)*(18*a^4*b + 2*b^5 + 5*a^2*b^3))/(3*a^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5)) + (a*log((a^2 + b^2)^(7/2) - a^6*b - b^7 - 3*a^2*b^5 - 3*a^4*b^3 + a^7*tan(c/2 + (d*x)/2) + a*b^6*tan(c/2 + (d*x)/2) + 3*a^3*b^4*tan(c/2 + (d*x)/2) + 3*a^5*b^2*tan(c/2 + (d*x)/2))*(2*a^2 - 3*b^2))/(2*d*(a^2 + b^2)^(7/2))","B"
143,1,224,30,1.292476,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2}-\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^2}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2-2\,b^2\right)}{3\,a^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^5)/a + (2*tan(c/2 + (d*x)/2))/a + (4*b*tan(c/2 + (d*x)/2)^2)/a^2 - (4*b*tan(c/2 + (d*x)/2)^4)/a^2 - (4*tan(c/2 + (d*x)/2)^3*(3*a^2 - 2*b^2))/(3*a^3))/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5))","B"
144,1,505,141,3.821235,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","-\frac{\frac{\frac{5\,a^2\,b}{3}+\frac{2\,b^3}{3}}{a^4+2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^4\,b+8\,a^2\,b^3+4\,b^5\right)}{a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-4\,a^4\,b+10\,a^2\,b^3+4\,b^5\right)}{a^2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^4+6\,a^2\,b^2+2\,b^4\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^4+4\,a^2\,b^2+2\,b^4\right)}{a\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a^2\,b+2\,b^3\right)\,\left(3\,a^2-2\,b^2\right)}{3\,a^3\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{a\,\mathrm{atanh}\left(\frac{a^4\,b+2\,a^2\,b^3+b^5}{{\left(a^2+b^2\right)}^{5/2}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{{\left(a^2+b^2\right)}^{5/2}}\right)}{d\,{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"- (((5*a^2*b)/3 + (2*b^3)/3)/(a^4 + b^4 + 2*a^2*b^2) - (tan(c/2 + (d*x)/2)^4*(4*b^5 - a^4*b + 8*a^2*b^3))/(a^2*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^2*(4*b^5 - 4*a^4*b + 10*a^2*b^3))/(a^2*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)*(2*b^4 - a^4 + 6*a^2*b^2))/(a*(a^4 + b^4 + 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(a^4 + 2*b^4 + 4*a^2*b^2))/(a*(a^4 + b^4 + 2*a^2*b^2)) - (2*b*tan(c/2 + (d*x)/2)^3*(5*a^2*b + 2*b^3)*(3*a^2 - 2*b^2))/(3*a^3*(a^4 + b^4 + 2*a^2*b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5)) - (a*atanh((a^4*b + b^5 + 2*a^2*b^3)/(a^2 + b^2)^(5/2) - (a*tan(c/2 + (d*x)/2)*(a^4 + b^4 + 2*a^2*b^2))/(a^2 + b^2)^(5/2)))/(d*(a^2 + b^2)^(5/2))","B"
145,1,222,98,1.248831,"\text{Not used}","int(1/(a*cos(c + d*x) + b*sin(c + d*x))^4,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2-2\,b^2\right)}{3\,a^3}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2}-\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^5)/a + (2*tan(c/2 + (d*x)/2))/a - (4*tan(c/2 + (d*x)/2)^3*(a^2 - 2*b^2))/(3*a^3) + (4*b*tan(c/2 + (d*x)/2)^2)/a^2 - (4*b*tan(c/2 + (d*x)/2)^4)/a^2)/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5))","B"
146,1,2848,231,4.830097,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + b*sin(c + d*x))^4),x)","\frac{2\,\mathrm{atanh}\left(\frac{64\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{176\,a^3\,b^{15}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{160\,a^5\,b^{13}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{48\,a^7\,b^{11}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{64\,a\,b^{17}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}}+\frac{48\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{176\,a^3\,b^{15}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{160\,a^5\,b^{13}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{48\,a^7\,b^{11}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{64\,a\,b^{17}}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}}\right)}{b^4\,d}-\frac{\frac{6\,a^4+5\,a^2\,b^2+2\,b^4}{3\,b^3\,\left(a^2+b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,a^4+8\,a^2\,b^2+2\,b^4\right)}{a\,b^2\,\left(a^2+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^4+2\,a^2\,b^2+2\,b^4\right)}{a\,b^2\,\left(a^2+b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^6+3\,a^4\,b^2+4\,a^2\,b^4+4\,b^6\right)}{a^2\,b^3\,\left(a^2+b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^6+8\,a^4\,b^2+7\,a^2\,b^4+2\,b^6\right)}{a^2\,b^3\,\left(a^2+b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2-2\,b^2\right)\,\left(6\,a^4+5\,a^2\,b^2+2\,b^4\right)}{3\,a^3\,b^2\,\left(a^2+b^2\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-3\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a\,b^2-3\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^3+8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^3+28\,a^5\,b^5+29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^8+20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{8\,\left(2\,a^5\,b^8+6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^{11}+8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^{11}+28\,a^5\,b^{13}+32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}+\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^3+8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^3+28\,a^5\,b^5+29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(2\,a^5\,b^8+6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^8+20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}+\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^{11}+8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^{11}+28\,a^5\,b^{13}+32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}}{\frac{16\,\left(2\,a^5+3\,a^3\,b^2\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6+20\,a^4\,b^2+12\,a^2\,b^4\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^3+8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^3+28\,a^5\,b^5+29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^8+20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{8\,\left(2\,a^5\,b^8+6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^{11}+8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^{11}+28\,a^5\,b^{13}+32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}+\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^3+8\,a^4\,b^5+4\,a^2\,b^7\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^3+28\,a^5\,b^5+29\,a^3\,b^7+8\,a\,b^9\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}-\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(2\,a^5\,b^8+6\,a^3\,b^{10}+4\,a\,b^{12}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6\,b^8+20\,a^4\,b^{10}+12\,a^2\,b^{12}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}+\frac{a\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,\left(\frac{8\,\left(4\,a^6\,b^{11}+8\,a^4\,b^{13}+4\,a^2\,b^{15}\right)}{a^4\,b^8+2\,a^2\,b^{10}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^7\,b^{11}+28\,a^5\,b^{13}+32\,a^3\,b^{15}+12\,a\,b^{17}\right)}{a^4\,b^9+2\,a^2\,b^{11}+b^{13}}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}\right)}{2\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}}\right)\,\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a^2+3\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^6\,b^4+3\,a^4\,b^6+3\,a^2\,b^8+b^{10}\right)}","Not used",1,"(2*atanh((64*a*b^5*tan(c/2 + (d*x)/2))/((176*a^3*b^15)/(b^12 + 2*a^2*b^10 + a^4*b^8) + (160*a^5*b^13)/(b^12 + 2*a^2*b^10 + a^4*b^8) + (48*a^7*b^11)/(b^12 + 2*a^2*b^10 + a^4*b^8) + (64*a*b^17)/(b^12 + 2*a^2*b^10 + a^4*b^8)) + (48*a^3*b^3*tan(c/2 + (d*x)/2))/((176*a^3*b^15)/(b^12 + 2*a^2*b^10 + a^4*b^8) + (160*a^5*b^13)/(b^12 + 2*a^2*b^10 + a^4*b^8) + (48*a^7*b^11)/(b^12 + 2*a^2*b^10 + a^4*b^8) + (64*a*b^17)/(b^12 + 2*a^2*b^10 + a^4*b^8))))/(b^4*d) - ((6*a^4 + 2*b^4 + 5*a^2*b^2)/(3*b^3*(a^2 + b^2)) + (tan(c/2 + (d*x)/2)*(11*a^4 + 2*b^4 + 8*a^2*b^2))/(a*b^2*(a^2 + b^2)) + (tan(c/2 + (d*x)/2)^5*(a^4 + 2*b^4 + 2*a^2*b^2))/(a*b^2*(a^2 + b^2)) - (tan(c/2 + (d*x)/2)^4*(4*b^6 - 2*a^6 + 4*a^2*b^4 + 3*a^4*b^2))/(a^2*b^3*(a^2 + b^2)) + (2*tan(c/2 + (d*x)/2)^2*(2*b^6 - 2*a^6 + 7*a^2*b^4 + 8*a^4*b^2))/(a^2*b^3*(a^2 + b^2)) - (2*tan(c/2 + (d*x)/2)^3*(3*a^2 - 2*b^2)*(6*a^4 + 2*b^4 + 5*a^2*b^2))/(3*a^3*b^2*(a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 3*a^3) - a^3*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 3*a^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^5)) - (a*atan(((a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^7 + 8*a^4*b^5 + 4*a^6*b^3))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(8*a*b^9 + 29*a^3*b^7 + 28*a^5*b^5 + 8*a^7*b^3))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*tan(c/2 + (d*x)/2)*(12*a^2*b^12 + 20*a^4*b^10 + 8*a^6*b^8))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (8*(4*a*b^12 + 6*a^3*b^10 + 2*a^5*b^8))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^15 + 8*a^4*b^13 + 4*a^6*b^11))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 + 32*a^3*b^15 + 28*a^5*b^13 + 8*a^7*b^11))/(b^13 + 2*a^2*b^11 + a^4*b^9)))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4)))*1i)/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4)) + (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^7 + 8*a^4*b^5 + 4*a^6*b^3))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(8*a*b^9 + 29*a^3*b^7 + 28*a^5*b^5 + 8*a^7*b^3))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a*b^12 + 6*a^3*b^10 + 2*a^5*b^8))/(b^12 + 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(12*a^2*b^12 + 20*a^4*b^10 + 8*a^6*b^8))/(b^13 + 2*a^2*b^11 + a^4*b^9) + (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^15 + 8*a^4*b^13 + 4*a^6*b^11))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 + 32*a^3*b^15 + 28*a^5*b^13 + 8*a^7*b^11))/(b^13 + 2*a^2*b^11 + a^4*b^9)))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4)))*1i)/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4)))/((16*(2*a^5 + 3*a^3*b^2))/(b^12 + 2*a^2*b^10 + a^4*b^8) - (16*tan(c/2 + (d*x)/2)*(8*a^6 + 12*a^2*b^4 + 20*a^4*b^2))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^7 + 8*a^4*b^5 + 4*a^6*b^3))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(8*a*b^9 + 29*a^3*b^7 + 28*a^5*b^5 + 8*a^7*b^3))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*tan(c/2 + (d*x)/2)*(12*a^2*b^12 + 20*a^4*b^10 + 8*a^6*b^8))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (8*(4*a*b^12 + 6*a^3*b^10 + 2*a^5*b^8))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^15 + 8*a^4*b^13 + 4*a^6*b^11))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 + 32*a^3*b^15 + 28*a^5*b^13 + 8*a^7*b^11))/(b^13 + 2*a^2*b^11 + a^4*b^9)))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4)) + (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^7 + 8*a^4*b^5 + 4*a^6*b^3))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(8*a*b^9 + 29*a^3*b^7 + 28*a^5*b^5 + 8*a^7*b^3))/(b^13 + 2*a^2*b^11 + a^4*b^9) - (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a*b^12 + 6*a^3*b^10 + 2*a^5*b^8))/(b^12 + 2*a^2*b^10 + a^4*b^8) - (8*tan(c/2 + (d*x)/2)*(12*a^2*b^12 + 20*a^4*b^10 + 8*a^6*b^8))/(b^13 + 2*a^2*b^11 + a^4*b^9) + (a*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*((8*(4*a^2*b^15 + 8*a^4*b^13 + 4*a^6*b^11))/(b^12 + 2*a^2*b^10 + a^4*b^8) + (8*tan(c/2 + (d*x)/2)*(12*a*b^17 + 32*a^3*b^15 + 28*a^5*b^13 + 8*a^7*b^11))/(b^13 + 2*a^2*b^11 + a^4*b^9)))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))/(2*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))))*((a^2 + b^2)^3)^(1/2)*(2*a^2 + 3*b^2)*1i)/(d*(b^10 + 3*a^2*b^8 + 3*a^4*b^6 + a^6*b^4))","B"
147,1,666,138,4.437625,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + b*sin(c + d*x))^4),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(10\,a^4+b^4\right)}{a^2\,b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^4+b^4\right)}{a\,b^4}-\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^4-2\,a^2\,b^2+b^4\right)}{a^2\,b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(10\,a^4+b^4\right)}{a^2\,b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^6-88\,a^4\,b^2+a^2\,b^4-4\,b^6\right)}{3\,a^3\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(36\,a^6-88\,a^4\,b^2+a^2\,b^4-4\,b^6\right)}{3\,a^3\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^4+b^4\right)}{a\,b^4}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-4\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(12\,a\,b^2-4\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(24\,a\,b^2-6\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(18\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(18\,a^2\,b-8\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}-\frac{8\,a\,\mathrm{atanh}\left(\frac{256\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{256\,a^3-256\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{512\,a^5}{b^2}-\frac{512\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{512\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}-\frac{256\,a^3}{256\,a^3-256\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{512\,a^5}{b^2}-\frac{512\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b^2}+\frac{512\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b}}+\frac{512\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,a^3\,b+\frac{512\,a^5}{b}+512\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{512\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{b}-256\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{b^5\,d}","Not used",1,"((4*tan(c/2 + (d*x)/2)^2*(10*a^4 + b^4))/(a^2*b^3) - (2*tan(c/2 + (d*x)/2)^7*(4*a^4 + b^4))/(a*b^4) - (8*tan(c/2 + (d*x)/2)^4*(10*a^4 + b^4 - 2*a^2*b^2))/(a^2*b^3) + (4*tan(c/2 + (d*x)/2)^6*(10*a^4 + b^4))/(a^2*b^3) - (2*tan(c/2 + (d*x)/2)^3*(36*a^6 - 4*b^6 + a^2*b^4 - 88*a^4*b^2))/(3*a^3*b^4) + (2*tan(c/2 + (d*x)/2)^5*(36*a^6 - 4*b^6 + a^2*b^4 - 88*a^4*b^2))/(3*a^3*b^4) + (2*tan(c/2 + (d*x)/2)*(4*a^4 + b^4))/(a*b^4))/(d*(a^3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 4*a^3) + tan(c/2 + (d*x)/2)^6*(12*a*b^2 - 4*a^3) - tan(c/2 + (d*x)/2)^4*(24*a*b^2 - 6*a^3) - tan(c/2 + (d*x)/2)^3*(18*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^5*(18*a^2*b - 8*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) - 6*a^2*b*tan(c/2 + (d*x)/2)^7)) - (8*a*atanh((256*a^3*tan(c/2 + (d*x)/2)^2)/(256*a^3 - 256*a^3*tan(c/2 + (d*x)/2)^2 + (512*a^5)/b^2 - (512*a^5*tan(c/2 + (d*x)/2)^2)/b^2 + (512*a^4*tan(c/2 + (d*x)/2))/b) - (256*a^3)/(256*a^3 - 256*a^3*tan(c/2 + (d*x)/2)^2 + (512*a^5)/b^2 - (512*a^5*tan(c/2 + (d*x)/2)^2)/b^2 + (512*a^4*tan(c/2 + (d*x)/2))/b) + (512*a^4*tan(c/2 + (d*x)/2))/(256*a^3*b + (512*a^5)/b + 512*a^4*tan(c/2 + (d*x)/2) - (512*a^5*tan(c/2 + (d*x)/2)^2)/b - 256*a^3*b*tan(c/2 + (d*x)/2)^2)))/(b^5*d)","B"
148,1,1961,400,4.592842,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + b*sin(c + d*x))^4),x)","\frac{\mathrm{atanh}\left(\frac{4000\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4000\,a^3+1000\,a\,b^2}+\frac{1000\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1000\,a+\frac{4000\,a^3}{b^2}}\right)\,\left(20\,a^2+5\,b^2\right)}{b^6\,d}-\frac{\frac{60\,a^4+5\,a^2\,b^2+2\,b^4}{3\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(5\,a^4+b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-40\,a^6+140\,a^4\,b^2+5\,a^2\,b^4+6\,b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(210\,a^6-75\,a^4\,b^2+2\,a^2\,b^4-4\,b^6\right)}{3\,a^3\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-120\,a^6+280\,a^4\,b^2+25\,a^2\,b^4+6\,b^6\right)}{3\,a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(510\,a^6-105\,a^4\,b^2+2\,a^2\,b^4-4\,b^6\right)}{3\,a^3\,b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-180\,a^6+635\,a^4\,b^2+65\,a^2\,b^4+18\,b^6\right)}{3\,a^2\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-20\,a^6+45\,a^4\,b^2+4\,b^6\right)}{a^2\,b^5}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(55\,a^4+5\,a^2\,b^2+b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,a^2-4\,b^2\right)\,\left(60\,a^4+5\,a^2\,b^2+2\,b^4\right)}{3\,a^3\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-5\,a^3\right)-a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(12\,a\,b^2-5\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(36\,a\,b^2-10\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(36\,a\,b^2-10\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(24\,a^2\,b-8\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(24\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(36\,a^2\,b-16\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\left(400\,a^6\,b^5+200\,a^4\,b^7+25\,a^2\,b^9\right)}{b^{14}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^7\,b^5+1600\,a^5\,b^7+650\,a^3\,b^9+50\,a\,b^{11}\right)}{b^{15}}-\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^4\,b^{12}+60\,a^2\,b^{14}\right)}{b^{15}}-\frac{8\,\left(20\,a^3\,b^{12}+10\,a\,b^{14}\right)}{b^{14}}+\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{17}+12\,a\,b^{19}\right)}{b^{15}}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)\,5{}\mathrm{i}}{2\,\left(a^2\,b^6+b^8\right)}+\frac{a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\left(400\,a^6\,b^5+200\,a^4\,b^7+25\,a^2\,b^9\right)}{b^{14}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^7\,b^5+1600\,a^5\,b^7+650\,a^3\,b^9+50\,a\,b^{11}\right)}{b^{15}}-\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\left(20\,a^3\,b^{12}+10\,a\,b^{14}\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^4\,b^{12}+60\,a^2\,b^{14}\right)}{b^{15}}+\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{17}+12\,a\,b^{19}\right)}{b^{15}}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)\,5{}\mathrm{i}}{2\,\left(a^2\,b^6+b^8\right)}}{\frac{16\,\left(2000\,a^7+2000\,a^5\,b^2+375\,a^3\,b^4\right)}{b^{14}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8000\,a^8+10000\,a^6\,b^2+3500\,a^4\,b^4+375\,a^2\,b^6\right)}{b^{15}}-\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\left(400\,a^6\,b^5+200\,a^4\,b^7+25\,a^2\,b^9\right)}{b^{14}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^7\,b^5+1600\,a^5\,b^7+650\,a^3\,b^9+50\,a\,b^{11}\right)}{b^{15}}-\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^4\,b^{12}+60\,a^2\,b^{14}\right)}{b^{15}}-\frac{8\,\left(20\,a^3\,b^{12}+10\,a\,b^{14}\right)}{b^{14}}+\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{17}+12\,a\,b^{19}\right)}{b^{15}}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)}{2\,\left(a^2\,b^6+b^8\right)}+\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\left(400\,a^6\,b^5+200\,a^4\,b^7+25\,a^2\,b^9\right)}{b^{14}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^7\,b^5+1600\,a^5\,b^7+650\,a^3\,b^9+50\,a\,b^{11}\right)}{b^{15}}-\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(\frac{8\,\left(20\,a^3\,b^{12}+10\,a\,b^{14}\right)}{b^{14}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(80\,a^4\,b^{12}+60\,a^2\,b^{14}\right)}{b^{15}}+\frac{5\,a\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,\left(32\,a^2\,b^3+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^{17}+12\,a\,b^{19}\right)}{b^{15}}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)}{2\,\left(a^2\,b^6+b^8\right)}\right)}{2\,\left(a^2\,b^6+b^8\right)}}\right)\,\left(4\,a^2+3\,b^2\right)\,\sqrt{a^2+b^2}\,5{}\mathrm{i}}{d\,\left(a^2\,b^6+b^8\right)}","Not used",1,"(atanh((4000*a^3*tan(c/2 + (d*x)/2))/(1000*a*b^2 + 4000*a^3) + (1000*a*tan(c/2 + (d*x)/2))/(1000*a + (4000*a^3)/b^2))*(20*a^2 + 5*b^2))/(b^6*d) - ((60*a^4 + 2*b^4 + 5*a^2*b^2)/(3*b^5) + (2*tan(c/2 + (d*x)/2)^9*(5*a^4 + b^4))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^6*(6*b^6 - 40*a^6 + 5*a^2*b^4 + 140*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^7*(210*a^6 - 4*b^6 + 2*a^2*b^4 - 75*a^4*b^2))/(3*a^3*b^4) + (2*tan(c/2 + (d*x)/2)^2*(6*b^6 - 120*a^6 + 25*a^2*b^4 + 280*a^4*b^2))/(3*a^2*b^5) - (2*tan(c/2 + (d*x)/2)^3*(510*a^6 - 4*b^6 + 2*a^2*b^4 - 105*a^4*b^2))/(3*a^3*b^4) - (2*tan(c/2 + (d*x)/2)^4*(18*b^6 - 180*a^6 + 65*a^2*b^4 + 635*a^4*b^2))/(3*a^2*b^5) - (tan(c/2 + (d*x)/2)^8*(4*b^6 - 20*a^6 + 45*a^4*b^2))/(a^2*b^5) + (2*tan(c/2 + (d*x)/2)*(55*a^4 + b^4 + 5*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^5*(9*a^2 - 4*b^2)*(60*a^4 + 2*b^4 + 5*a^2*b^2))/(3*a^3*b^4))/(d*(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 5*a^3) - a^3*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^8*(12*a*b^2 - 5*a^3) - tan(c/2 + (d*x)/2)^4*(36*a*b^2 - 10*a^3) + tan(c/2 + (d*x)/2)^6*(36*a*b^2 - 10*a^3) - tan(c/2 + (d*x)/2)^3*(24*a^2*b - 8*b^3) - tan(c/2 + (d*x)/2)^7*(24*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^5*(36*a^2*b - 16*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) + 6*a^2*b*tan(c/2 + (d*x)/2)^9)) - (a*atan(((a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*(25*a^2*b^9 + 200*a^4*b^7 + 400*a^6*b^5))/b^14 + (8*tan(c/2 + (d*x)/2)*(50*a*b^11 + 650*a^3*b^9 + 1600*a^5*b^7 + 800*a^7*b^5))/b^15 - (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*tan(c/2 + (d*x)/2)*(60*a^2*b^14 + 80*a^4*b^12))/b^15 - (8*(10*a*b^14 + 20*a^3*b^12))/b^14 + (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 + 8*a^3*b^17))/b^15))/(2*(b^8 + a^2*b^6))))/(2*(b^8 + a^2*b^6)))*5i)/(2*(b^8 + a^2*b^6)) + (a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*(25*a^2*b^9 + 200*a^4*b^7 + 400*a^6*b^5))/b^14 + (8*tan(c/2 + (d*x)/2)*(50*a*b^11 + 650*a^3*b^9 + 1600*a^5*b^7 + 800*a^7*b^5))/b^15 - (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*(10*a*b^14 + 20*a^3*b^12))/b^14 - (8*tan(c/2 + (d*x)/2)*(60*a^2*b^14 + 80*a^4*b^12))/b^15 + (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 + 8*a^3*b^17))/b^15))/(2*(b^8 + a^2*b^6))))/(2*(b^8 + a^2*b^6)))*5i)/(2*(b^8 + a^2*b^6)))/((16*(2000*a^7 + 375*a^3*b^4 + 2000*a^5*b^2))/b^14 - (16*tan(c/2 + (d*x)/2)*(8000*a^8 + 375*a^2*b^6 + 3500*a^4*b^4 + 10000*a^6*b^2))/b^15 - (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*(25*a^2*b^9 + 200*a^4*b^7 + 400*a^6*b^5))/b^14 + (8*tan(c/2 + (d*x)/2)*(50*a*b^11 + 650*a^3*b^9 + 1600*a^5*b^7 + 800*a^7*b^5))/b^15 - (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*tan(c/2 + (d*x)/2)*(60*a^2*b^14 + 80*a^4*b^12))/b^15 - (8*(10*a*b^14 + 20*a^3*b^12))/b^14 + (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 + 8*a^3*b^17))/b^15))/(2*(b^8 + a^2*b^6))))/(2*(b^8 + a^2*b^6))))/(2*(b^8 + a^2*b^6)) + (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*(25*a^2*b^9 + 200*a^4*b^7 + 400*a^6*b^5))/b^14 + (8*tan(c/2 + (d*x)/2)*(50*a*b^11 + 650*a^3*b^9 + 1600*a^5*b^7 + 800*a^7*b^5))/b^15 - (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*((8*(10*a*b^14 + 20*a^3*b^12))/b^14 - (8*tan(c/2 + (d*x)/2)*(60*a^2*b^14 + 80*a^4*b^12))/b^15 + (5*a*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*(32*a^2*b^3 + (8*tan(c/2 + (d*x)/2)*(12*a*b^19 + 8*a^3*b^17))/b^15))/(2*(b^8 + a^2*b^6))))/(2*(b^8 + a^2*b^6))))/(2*(b^8 + a^2*b^6))))*(4*a^2 + 3*b^2)*(a^2 + b^2)^(1/2)*5i)/(d*(b^8 + a^2*b^6))","B"
149,1,1599,232,7.970067,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + b*sin(c + d*x))^4),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(50\,a^6+30\,a^4\,b^2+b^6\right)}{a^2\,b^5}-\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(50\,a^6+25\,a^4\,b^2-3\,a^2\,b^4+b^6\right)}{a^2\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(20\,a^6+12\,a^4\,b^2+b^6\right)}{a\,b^6}-\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(50\,a^6+25\,a^4\,b^2-3\,a^2\,b^4+b^6\right)}{a^2\,b^5}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(50\,a^6+30\,a^4\,b^2+b^6\right)}{a^2\,b^5}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-100\,a^8+160\,a^6\,b^2+140\,a^4\,b^4+a^2\,b^6+2\,b^8\right)}{a^3\,b^6}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-100\,a^8+160\,a^6\,b^2+140\,a^4\,b^4+a^2\,b^6+2\,b^8\right)}{a^3\,b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-300\,a^8+260\,a^6\,b^2+264\,a^4\,b^4-3\,a^2\,b^6+4\,b^8\right)}{3\,a^3\,b^6}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-300\,a^8+260\,a^6\,b^2+264\,a^4\,b^4-3\,a^2\,b^6+4\,b^8\right)}{3\,a^3\,b^6}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(450\,a^6+210\,a^4\,b^2-28\,a^2\,b^4+9\,b^6\right)}{3\,a^2\,b^5}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^6+12\,a^4\,b^2+b^6\right)}{a\,b^6}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-6\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(12\,a\,b^2-6\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(48\,a\,b^2-15\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(48\,a\,b^2-15\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(72\,a\,b^2-20\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(30\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(30\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(60\,a^2\,b-24\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(60\,a^2\,b-24\,b^3\right)+a^3+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^5+12\,a^3\,b^2\right)}{b^6}-\frac{4\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}+\frac{4\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)\,4{}\mathrm{i}}{b^7}-\frac{a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{4\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^5+12\,a^3\,b^2\right)}{b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}+\frac{4\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)\,4{}\mathrm{i}}{b^7}}{\frac{8\,\left(400\,a^7+480\,a^5\,b^2+144\,a^3\,b^4\right)}{b^{12}}+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(400\,a^7+480\,a^5\,b^2+144\,a^3\,b^4\right)}{b^{12}}+\frac{4\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^5+12\,a^3\,b^2\right)}{b^6}-\frac{4\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}+\frac{4\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)}{b^7}+\frac{4\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{4\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}-\frac{16\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^5+12\,a^3\,b^2\right)}{b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(40\,a^4\,b^7+24\,a^2\,b^9\right)}{b^{12}}+\frac{4\,a\,\left(5\,a^2+3\,b^2\right)\,\left(\frac{4\,\left(4\,a^3\,b^{12}+a\,b^{14}\right)}{b^{12}}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3\,b^{12}+3\,a\,b^{14}\right)}{b^{12}}+16\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{b^7}\right)}{b^7}}\right)\,\left(5\,a^2+3\,b^2\right)\,8{}\mathrm{i}}{b^7\,d}","Not used",1,"((4*tan(c/2 + (d*x)/2)^2*(50*a^6 + b^6 + 30*a^4*b^2))/(a^2*b^5) - (16*tan(c/2 + (d*x)/2)^8*(50*a^6 + b^6 - 3*a^2*b^4 + 25*a^4*b^2))/(a^2*b^5) - (2*tan(c/2 + (d*x)/2)^11*(20*a^6 + b^6 + 12*a^4*b^2))/(a*b^6) - (16*tan(c/2 + (d*x)/2)^4*(50*a^6 + b^6 - 3*a^2*b^4 + 25*a^4*b^2))/(a^2*b^5) + (4*tan(c/2 + (d*x)/2)^10*(50*a^6 + b^6 + 30*a^4*b^2))/(a^2*b^5) - (4*tan(c/2 + (d*x)/2)^5*(2*b^8 - 100*a^8 + a^2*b^6 + 140*a^4*b^4 + 160*a^6*b^2))/(a^3*b^6) + (4*tan(c/2 + (d*x)/2)^7*(2*b^8 - 100*a^8 + a^2*b^6 + 140*a^4*b^4 + 160*a^6*b^2))/(a^3*b^6) + (2*tan(c/2 + (d*x)/2)^3*(4*b^8 - 300*a^8 - 3*a^2*b^6 + 264*a^4*b^4 + 260*a^6*b^2))/(3*a^3*b^6) - (2*tan(c/2 + (d*x)/2)^9*(4*b^8 - 300*a^8 - 3*a^2*b^6 + 264*a^4*b^4 + 260*a^6*b^2))/(3*a^3*b^6) + (8*tan(c/2 + (d*x)/2)^6*(450*a^6 + 9*b^6 - 28*a^2*b^4 + 210*a^4*b^2))/(3*a^2*b^5) + (2*tan(c/2 + (d*x)/2)*(20*a^6 + b^6 + 12*a^4*b^2))/(a*b^6))/(d*(a^3*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 6*a^3) + tan(c/2 + (d*x)/2)^10*(12*a*b^2 - 6*a^3) - tan(c/2 + (d*x)/2)^4*(48*a*b^2 - 15*a^3) - tan(c/2 + (d*x)/2)^8*(48*a*b^2 - 15*a^3) + tan(c/2 + (d*x)/2)^6*(72*a*b^2 - 20*a^3) - tan(c/2 + (d*x)/2)^3*(30*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^9*(30*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^5*(60*a^2*b - 24*b^3) - tan(c/2 + (d*x)/2)^7*(60*a^2*b - 24*b^3) + a^3 + 6*a^2*b*tan(c/2 + (d*x)/2) - 6*a^2*b*tan(c/2 + (d*x)/2)^11)) + (a*atan(((a*(5*a^2 + 3*b^2)*((16*tan(c/2 + (d*x)/2)*(20*a^5 + 12*a^3*b^2))/b^6 - (4*(24*a^2*b^9 + 40*a^4*b^7))/b^12 + (4*tan(c/2 + (d*x)/2)^2*(24*a^2*b^9 + 40*a^4*b^7))/b^12 + (4*a*(5*a^2 + 3*b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7)*4i)/b^7 - (a*(5*a^2 + 3*b^2)*((4*(24*a^2*b^9 + 40*a^4*b^7))/b^12 - (16*tan(c/2 + (d*x)/2)*(20*a^5 + 12*a^3*b^2))/b^6 - (4*tan(c/2 + (d*x)/2)^2*(24*a^2*b^9 + 40*a^4*b^7))/b^12 + (4*a*(5*a^2 + 3*b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7)*4i)/b^7)/((8*(400*a^7 + 144*a^3*b^4 + 480*a^5*b^2))/b^12 + (8*tan(c/2 + (d*x)/2)^2*(400*a^7 + 144*a^3*b^4 + 480*a^5*b^2))/b^12 + (4*a*(5*a^2 + 3*b^2)*((16*tan(c/2 + (d*x)/2)*(20*a^5 + 12*a^3*b^2))/b^6 - (4*(24*a^2*b^9 + 40*a^4*b^7))/b^12 + (4*tan(c/2 + (d*x)/2)^2*(24*a^2*b^9 + 40*a^4*b^7))/b^12 + (4*a*(5*a^2 + 3*b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7))/b^7 + (4*a*(5*a^2 + 3*b^2)*((4*(24*a^2*b^9 + 40*a^4*b^7))/b^12 - (16*tan(c/2 + (d*x)/2)*(20*a^5 + 12*a^3*b^2))/b^6 - (4*tan(c/2 + (d*x)/2)^2*(24*a^2*b^9 + 40*a^4*b^7))/b^12 + (4*a*(5*a^2 + 3*b^2)*((4*(a*b^14 + 4*a^3*b^12))/b^12 - (4*tan(c/2 + (d*x)/2)^2*(3*a*b^14 + 4*a^3*b^12))/b^12 + 16*a^2*b*tan(c/2 + (d*x)/2)))/b^7))/b^7))*(5*a^2 + 3*b^2)*8i)/(b^7*d)","B"
150,1,164,99,5.137192,"\text{Not used}","int(cos(c + d*x)^5/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","\frac{5\,x}{16\,a}+\frac{\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,3{}\mathrm{i}}{4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,1{}\mathrm{i}}{12}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,1{}\mathrm{i}}{12}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,3{}\mathrm{i}}{4}+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{a\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}^4\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^6}","Not used",1,"(5*x)/(16*a) + ((11*tan(c/2 + (d*x)/2))/8 + (tan(c/2 + (d*x)/2)^2*3i)/4 - tan(c/2 + (d*x)/2)^3/3 + (tan(c/2 + (d*x)/2)^4*1i)/12 + (13*tan(c/2 + (d*x)/2)^5)/4 - (tan(c/2 + (d*x)/2)^6*1i)/12 - tan(c/2 + (d*x)/2)^7/3 - (tan(c/2 + (d*x)/2)^8*3i)/4 + (11*tan(c/2 + (d*x)/2)^9)/8)/(a*d*(tan(c/2 + (d*x)/2) + 1i)^4*(tan(c/2 + (d*x)/2)*1i + 1)^6)","B"
151,1,134,70,2.087033,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","-\frac{\left(-15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,15{}\mathrm{i}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,25{}\mathrm{i}-13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,21{}\mathrm{i}+9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3{}\mathrm{i}\right)\,2{}\mathrm{i}}{15\,a\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}^3\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^5}","Not used",1,"-((9*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2*21i - 13*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4*25i - 5*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^6*15i - 15*tan(c/2 + (d*x)/2)^7 + 3i)*2i)/(15*a*d*(tan(c/2 + (d*x)/2) + 1i)^3*(tan(c/2 + (d*x)/2)*1i + 1)^5)","B"
152,1,111,75,3.433092,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","\frac{3\,x}{8\,a}-\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,1{}\mathrm{i}}{2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}}{2}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{a\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}^2\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^4}","Not used",1,"(3*x)/(8*a) - ((5*tan(c/2 + (d*x)/2))/4 + (tan(c/2 + (d*x)/2)^2*1i)/2 - tan(c/2 + (d*x)/2)^3/2 - (tan(c/2 + (d*x)/2)^4*1i)/2 + (5*tan(c/2 + (d*x)/2)^5)/4)/(a*d*(tan(c/2 + (d*x)/2) + 1i)^2*(tan(c/2 + (d*x)/2)*1i + 1)^4)","B"
153,1,78,52,0.772163,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","\frac{\left(-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,3{}\mathrm{i}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,2{}\mathrm{i}}{3\,a\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^3}","Not used",1,"((tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2*3i - 3*tan(c/2 + (d*x)/2)^3 + 1i)*2i)/(3*a*d*(tan(c/2 + (d*x)/2) + 1i)*(tan(c/2 + (d*x)/2)*1i + 1)^3)","B"
154,1,39,46,0.712476,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","\frac{x}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^2}","Not used",1,"x/(2*a) + tan(c/2 + (d*x)/2)/(a*d*(tan(c/2 + (d*x)/2)*1i + 1)^2)","B"
155,1,25,29,0.613162,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i),x)","\frac{2{}\mathrm{i}}{a\,d\,\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}","Not used",1,"2i/(a*d*(tan(c/2 + (d*x)/2)*1i + 1))","B"
156,1,41,23,0.739440,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","-\frac{\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\right)\,1{}\mathrm{i}}{a\,d}","Not used",1,"-((2*log(tan(c/2 + (d*x)/2) - 1i) - log(tan(c/2 + (d*x)/2)^2 - 1))*1i)/(a*d)","B"
157,1,43,31,0.670087,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{2{}\mathrm{i}}{a\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)))/(a*d) + 2i/(a*d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
158,1,25,34,0.684095,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(-2+\mathrm{tan}\left(c+d\,x\right)\,1{}\mathrm{i}\right)}{2\,a\,d}","Not used",1,"-(tan(c + d*x)*(tan(c + d*x)*1i - 2))/(2*a*d)","B"
159,1,116,60,2.551921,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,2{}\mathrm{i}}{a}+\frac{2{}\mathrm{i}}{3\,a}}{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)}","Not used",1,"atanh(tan(c/2 + (d*x)/2))/(a*d) + ((tan(c/2 + (d*x)/2)^4*2i)/a + tan(c/2 + (d*x)/2)^5/a + 2i/(3*a) - tan(c/2 + (d*x)/2)/a)/(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))","B"
160,1,99,52,1.291438,"\text{Not used}","int(1/(cos(c + d*x)^5*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,3{}\mathrm{i}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3{}\mathrm{i}-3\right)}{3\,a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^4}","Not used",1,"-(2*tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)*3i + 5*tan(c/2 + (d*x)/2)^2 - 5*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^5*3i + 3*tan(c/2 + (d*x)/2)^6 - 3))/(3*a*d*(tan(c/2 + (d*x)/2)^2 - 1)^4)","B"
161,1,193,84,4.246087,"\text{Not used}","int(1/(cos(c + d*x)^6*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a\,d}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2\,a}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2\,a}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4\,a}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,4{}\mathrm{i}}{a}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,2{}\mathrm{i}}{a}+\frac{2{}\mathrm{i}}{5\,a}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(4*a*d) + (tan(c/2 + (d*x)/2)^3/(2*a) + (tan(c/2 + (d*x)/2)^4*4i)/a - tan(c/2 + (d*x)/2)^7/(2*a) + (tan(c/2 + (d*x)/2)^8*2i)/a + (5*tan(c/2 + (d*x)/2)^9)/(4*a) + 2i/(5*a) - (5*tan(c/2 + (d*x)/2))/(4*a))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
162,1,139,70,1.889452,"\text{Not used}","int(1/(cos(c + d*x)^7*(a*cos(c + d*x) + a*sin(c + d*x)*1i)),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,15{}\mathrm{i}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+78\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,50{}\mathrm{i}-78\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,15{}\mathrm{i}-15\right)}{15\,a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^6}","Not used",1,"-(2*tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)*15i + 35*tan(c/2 + (d*x)/2)^2 - 78*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^5*50i + 78*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^9*15i + 15*tan(c/2 + (d*x)/2)^10 - 15))/(15*a*d*(tan(c/2 + (d*x)/2)^2 - 1)^6)","B"
163,1,161,85,4.114438,"\text{Not used}","int(cos(c + d*x)^5/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","\frac{\left(-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,42{}\mathrm{i}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,56{}\mathrm{i}+42\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,28{}\mathrm{i}+76\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,24{}\mathrm{i}+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6{}\mathrm{i}\right)\,2{}\mathrm{i}}{21\,a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}^3\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^7}","Not used",1,"((3*tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2*24i + 76*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4*28i + 42*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^6*56i + 28*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8*42i - 21*tan(c/2 + (d*x)/2)^9 - 6i)*2i)/(21*a^2*d*(tan(c/2 + (d*x)/2) + 1i)^3*(tan(c/2 + (d*x)/2)*1i + 1)^7)","B"
164,1,138,101,4.735920,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","\frac{x}{4\,a^2}-\frac{-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,2{}\mathrm{i}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,4{}\mathrm{i}}{3}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,2{}\mathrm{i}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}^2\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^6}","Not used",1,"x/(4*a^2) - ((3*tan(c/2 + (d*x)/2))/2 + tan(c/2 + (d*x)/2)^2*2i - (7*tan(c/2 + (d*x)/2)^3)/6 + (tan(c/2 + (d*x)/2)^4*4i)/3 + (7*tan(c/2 + (d*x)/2)^5)/6 + tan(c/2 + (d*x)/2)^6*2i - (3*tan(c/2 + (d*x)/2)^7)/2)/(a^2*d*(tan(c/2 + (d*x)/2) + 1i)^2*(tan(c/2 + (d*x)/2)*1i + 1)^6)","B"
165,1,90,68,1.015323,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","-\frac{2\,\left(-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,10{}\mathrm{i}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2{}\mathrm{i}\right)}{5\,a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)}^5\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"-(2*(3*tan(c/2 + (d*x)/2) + 10*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4*10i - 5*tan(c/2 + (d*x)/2)^5 - 2i))/(5*a^2*d*(tan(c/2 + (d*x)/2) - 1i)^5*(tan(c/2 + (d*x)/2) + 1i))","B"
166,1,69,89,1.755565,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","\frac{x}{4\,a^2}+\frac{-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,2{}\mathrm{i}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{a^2\,d\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^4}","Not used",1,"x/(4*a^2) + ((3*tan(c/2 + (d*x)/2))/2 + tan(c/2 + (d*x)/2)^2*2i - (3*tan(c/2 + (d*x)/2)^3)/2)/(a^2*d*(tan(c/2 + (d*x)/2)*1i + 1)^4)","B"
167,1,79,52,0.646884,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","-\frac{2\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,3{}\mathrm{i}+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2{}\mathrm{i}\right)}{3\,a^2\,d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,1{}\mathrm{i}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3{}\mathrm{i}+1\right)}","Not used",1,"-(2*(3*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2*3i - 2i))/(3*a^2*d*(tan(c/2 + (d*x)/2)*3i - 3*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^3*1i + 1))","B"
168,1,31,31,0.610522,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2,x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)}^2}","Not used",1,"-(2*tan(c/2 + (d*x)/2))/(a^2*d*(tan(c/2 + (d*x)/2) - 1i)^2)","B"
169,1,44,46,0.671823,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2),x)","-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{4{}\mathrm{i}}{a^2\,d\,\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}","Not used",1,"4i/(a^2*d*(tan(c/2 + (d*x)/2)*1i + 1)) - (2*atanh(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
170,1,83,55,0.782032,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2),x)","\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,4{}\mathrm{i}}{a^2\,d}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,2{}\mathrm{i}}{a^2\,d}","Not used",1,"(2*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) - (log(tan(c/2 + (d*x)/2) - 1i)*4i)/(a^2*d) + (log(tan(c/2 + (d*x)/2)^2 - 1)*2i)/(a^2*d)","B"
171,1,104,56,1.181342,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,4{}\mathrm{i}}{a^2}+\frac{4{}\mathrm{i}}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)^3/a^2 - (tan(c/2 + (d*x)/2)^2*4i)/a^2 + 4i/a^2 + tan(c/2 + (d*x)/2)/a^2)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
172,1,49,34,0.725457,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2),x)","-\frac{\sin\left(c+d\,x\right)\,\left(-4\,{\cos\left(c+d\,x\right)}^2+3{}\mathrm{i}\,\sin\left(c+d\,x\right)\,\cos\left(c+d\,x\right)+1\right)}{3\,a^2\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"-(sin(c + d*x)*(cos(c + d*x)*sin(c + d*x)*3i - 4*cos(c + d*x)^2 + 1))/(3*a^2*d*cos(c + d*x)^3)","B"
173,1,136,84,3.207536,"\text{Not used}","int(1/(cos(c + d*x)^5*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2),x)","\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^2\,d}+\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,4{}\mathrm{i}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,4{}\mathrm{i}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,4{}\mathrm{i}}{3}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{4}{3}{}\mathrm{i}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^4}","Not used",1,"(5*atanh(tan(c/2 + (d*x)/2)))/(4*a^2*d) + ((3*tan(c/2 + (d*x)/2))/4 + (tan(c/2 + (d*x)/2)^2*4i)/3 - (11*tan(c/2 + (d*x)/2)^3)/4 - tan(c/2 + (d*x)/2)^4*4i - (11*tan(c/2 + (d*x)/2)^5)/4 + tan(c/2 + (d*x)/2)^6*4i + (3*tan(c/2 + (d*x)/2)^7)/4 - 4i/3)/(a^2*d*(tan(c/2 + (d*x)/2)^2 - 1)^4)","B"
174,1,76,70,0.915269,"\text{Not used}","int(1/(cos(c + d*x)^6*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^2),x)","-\frac{\sin\left(c+d\,x\right)\,\left(-4\,{\cos\left(c+d\,x\right)}^4+\frac{5{}\mathrm{i}\,\sin\left(c+d\,x\right)\,{\cos\left(c+d\,x\right)}^3}{2}-2\,{\cos\left(c+d\,x\right)}^2+\frac{5{}\mathrm{i}\,\sin\left(c+d\,x\right)\,\cos\left(c+d\,x\right)}{2}+1\right)}{5\,a^2\,d\,{\cos\left(c+d\,x\right)}^5}","Not used",1,"-(sin(c + d*x)*((cos(c + d*x)*sin(c + d*x)*5i)/2 + (cos(c + d*x)^3*sin(c + d*x)*5i)/2 - 2*cos(c + d*x)^2 - 4*cos(c + d*x)^4 + 1))/(5*a^2*d*cos(c + d*x)^5)","B"
175,1,164,125,4.785365,"\text{Not used}","int(cos(c + d*x)^5/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","\frac{5\,x}{32\,a^3}+\frac{-\frac{27\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{16}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,33{}\mathrm{i}}{8}+\frac{31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,9{}\mathrm{i}}{8}+\frac{89\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,9{}\mathrm{i}}{8}+\frac{31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,33{}\mathrm{i}}{8}-\frac{27\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}{a^3\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}^2\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^8}","Not used",1,"(5*x)/(32*a^3) + ((31*tan(c/2 + (d*x)/2)^3)/6 - (tan(c/2 + (d*x)/2)^2*33i)/8 - (27*tan(c/2 + (d*x)/2))/16 - (tan(c/2 + (d*x)/2)^4*9i)/8 + (89*tan(c/2 + (d*x)/2)^5)/24 + (tan(c/2 + (d*x)/2)^6*9i)/8 + (31*tan(c/2 + (d*x)/2)^7)/6 + (tan(c/2 + (d*x)/2)^8*33i)/8 - (27*tan(c/2 + (d*x)/2)^9)/16)/(a^3*d*(tan(c/2 + (d*x)/2) + 1i)^2*(tan(c/2 + (d*x)/2)*1i + 1)^8)","B"
176,1,134,106,3.168621,"\text{Not used}","int(cos(c + d*x)^4/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","-\frac{\left(35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,105{}\mathrm{i}-175\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,105{}\mathrm{i}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,77{}\mathrm{i}+43\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-13{}\mathrm{i}\right)\,2{}\mathrm{i}}{35\,a^3\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^7}","Not used",1,"-((43*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2*77i - 7*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4*105i - 175*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^6*105i + 35*tan(c/2 + (d*x)/2)^7 - 13i)*2i)/(35*a^3*d*(tan(c/2 + (d*x)/2) + 1i)*(tan(c/2 + (d*x)/2)*1i + 1)^7)","B"
177,1,96,131,3.486540,"\text{Not used}","int(cos(c + d*x)^3/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","\frac{x}{8\,a^3}+\frac{\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,9{}\mathrm{i}}{2}-\frac{41\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,9{}\mathrm{i}}{2}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{a^3\,d\,{\left(1+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}\right)}^6}","Not used",1,"x/(8*a^3) + ((7*tan(c/2 + (d*x)/2))/4 + (tan(c/2 + (d*x)/2)^2*9i)/2 - (41*tan(c/2 + (d*x)/2)^3)/6 - (tan(c/2 + (d*x)/2)^4*9i)/2 + (7*tan(c/2 + (d*x)/2)^5)/4)/(a^3*d*(tan(c/2 + (d*x)/2)*1i + 1)^6)","B"
178,1,133,90,0.867479,"\text{Not used}","int(cos(c + d*x)^2/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","\frac{2\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,15{}\mathrm{i}+30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,40{}\mathrm{i}-20\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+7{}\mathrm{i}\right)}{15\,a^3\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,1{}\mathrm{i}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,10{}\mathrm{i}-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,5{}\mathrm{i}+1\right)}","Not used",1,"(2*(30*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^2*40i - 20*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^4*15i + 7i))/(15*a^3*d*(tan(c/2 + (d*x)/2)*5i - 10*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^3*10i + 5*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^5*1i + 1))","B"
179,1,100,32,0.754323,"\text{Not used}","int(cos(c + d*x)/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)}{a^3\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,1{}\mathrm{i}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,6{}\mathrm{i}-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"-(2*tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2*1i - 1i))/(a^3*d*(4*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^2*6i - 4*tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^4*1i + 1i))","B"
180,1,68,31,0.632293,"\text{Not used}","int(1/(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3,x)","-\frac{2\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,3{}\mathrm{i}-\mathrm{i}\right)}{3\,a^3\,d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,1{}\mathrm{i}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,3{}\mathrm{i}+1\right)}","Not used",1,"-(2*(tan(c/2 + (d*x)/2)^2*3i - 1i))/(3*a^3*d*(tan(c/2 + (d*x)/2)*3i - 3*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^3*1i + 1))","B"
181,1,101,61,0.772558,"\text{Not used}","int(1/(cos(c + d*x)*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3),x)","-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,4{}\mathrm{i}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}+2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a^3\,1{}\mathrm{i}\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,1{}\mathrm{i}}{a^3\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2) - 1i)*2i)/(a^3*d) - (tan(c/2 + (d*x)/2)*4i)/(d*(a^3*tan(c/2 + (d*x)/2)^2*1i - a^3*1i + 2*a^3*tan(c/2 + (d*x)/2))) - (log(tan(c/2 + (d*x)/2)^2 - 1)*1i)/(a^3*d)","B"
182,1,105,62,0.992347,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3),x)","-\frac{6\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,8{}\mathrm{i}}{a^3}-\frac{10{}\mathrm{i}}{a^3}}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,1{}\mathrm{i}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}","Not used",1,"- (6*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - ((tan(c/2 + (d*x)/2)^2*8i)/a^3 - 10i/a^3 + (2*tan(c/2 + (d*x)/2))/a^3)/(d*(tan(c/2 + (d*x)/2)*1i - tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^3*1i + 1))","B"
183,1,104,75,0.923564,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,8{}\mathrm{i}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,4{}\mathrm{i}}{a^3\,d}+\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,2{}\mathrm{i}-6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^2}","Not used",1,"(tan(c/2 + (d*x)/2)^2*2i - 6*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3)/(a^3*d*(tan(c/2 + (d*x)/2)^2 - 1)^2) - (log(tan(c/2 + (d*x)/2) - 1i)*8i - log(tan(c/2 + (d*x)/2)^2 - 1)*4i)/(a^3*d)","B"
184,1,135,76,2.719896,"\text{Not used}","int(1/(cos(c + d*x)^4*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3),x)","\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}+\frac{\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,16{}\mathrm{i}}{a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,6{}\mathrm{i}}{a^3}+\frac{22{}\mathrm{i}}{3\,a^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)}","Not used",1,"(5*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) + ((tan(c/2 + (d*x)/2)^4*6i)/a^3 - (tan(c/2 + (d*x)/2)^2*16i)/a^3 - (3*tan(c/2 + (d*x)/2)^5)/a^3 + 22i/(3*a^3) + (3*tan(c/2 + (d*x)/2))/a^3)/(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))","B"
185,1,55,34,0.882718,"\text{Not used}","int(1/(cos(c + d*x)^5*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3),x)","\frac{{\sin\left(c+d\,x\right)}^2\,1{}\mathrm{i}-\frac{{\sin\left(2\,c+2\,d\,x\right)}^2\,7{}\mathrm{i}}{4}+\sin\left(4\,c+4\,d\,x\right)}{4\,a^3\,d\,{\left({\sin\left(c+d\,x\right)}^2-1\right)}^2}","Not used",1,"(sin(4*c + 4*d*x) - (sin(2*c + 2*d*x)^2*7i)/4 + sin(c + d*x)^2*1i)/(4*a^3*d*(sin(c + d*x)^2 - 1)^2)","B"
186,1,150,104,3.292516,"\text{Not used}","int(1/(cos(c + d*x)^6*(a*cos(c + d*x) + a*sin(c + d*x)*1i)^3),x)","\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^3\,d}+\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,6{}\mathrm{i}-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,16{}\mathrm{i}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,20{}\mathrm{i}}{3}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,16{}\mathrm{i}}{3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{34}{15}{}\mathrm{i}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^5}","Not used",1,"(7*atanh(tan(c/2 + (d*x)/2)))/(4*a^3*d) + ((13*tan(c/2 + (d*x)/2)^3)/2 - (tan(c/2 + (d*x)/2)^2*16i)/3 - tan(c/2 + (d*x)/2)/4 + (tan(c/2 + (d*x)/2)^4*20i)/3 - tan(c/2 + (d*x)/2)^6*16i - (13*tan(c/2 + (d*x)/2)^7)/2 + tan(c/2 + (d*x)/2)^8*6i + tan(c/2 + (d*x)/2)^9/4 + 34i/15)/(a^3*d*(tan(c/2 + (d*x)/2)^2 - 1)^5)","B"
187,0,-1,66,0.000000,"\text{Not used}","int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^n/cos(c + d*x)^n,x)","\int \frac{{\left(a\,\cos\left(c+d\,x\right)+a\,\sin\left(c+d\,x\right)\,1{}\mathrm{i}\right)}^n}{{\cos\left(c+d\,x\right)}^n} \,d x","Not used",1,"int((a*cos(c + d*x) + a*sin(c + d*x)*1i)^n/cos(c + d*x)^n, x)","F"
188,1,21,5,1.107575,"\text{Not used}","int(1/(tan(x) + 1/cos(x)),x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)","Not used",1,"2*log(tan(x/2) + 1) - log(tan(x/2)^2 + 1)","B"
189,1,21,10,0.596244,"\text{Not used}","int(sin(x)/(tan(x) + 1/cos(x)),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)+\sin\left(x\right)","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2) + 1) + sin(x)","B"
190,1,4,4,0.553602,"\text{Not used}","int(cos(x)/(tan(x) + 1/cos(x)),x)","x+\cos\left(x\right)","Not used",1,"x + cos(x)","B"
191,1,12,11,0.582906,"\text{Not used}","int(tan(x)/(tan(x) + 1/cos(x)),x)","x+\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"x + 2/(tan(x/2) + 1)","B"
192,1,23,9,0.592534,"\text{Not used}","int(cot(x)/(tan(x) + 1/cos(x)),x)","2\,\mathrm{atan}\left(\frac{8}{4\,\mathrm{tan}\left(\frac{x}{2}\right)+4}-1\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"2*atan(8/(4*tan(x/2) + 4) - 1) + log(tan(x/2))","B"
193,1,10,10,0.554845,"\text{Not used}","int(1/(cos(x)*(tan(x) + 1/cos(x))),x)","-\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"-2/(tan(x/2) + 1)","B"
194,1,15,11,0.574033,"\text{Not used}","int(1/(sin(x)*(tan(x) + 1/cos(x))),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)","Not used",1,"log(tan(x/2)) - 2*log(tan(x/2) + 1)","B"
195,1,19,9,0.956830,"\text{Not used}","int(-1/(tan(x) - 1/cos(x)),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2) - 1)","B"
196,1,23,14,0.607949,"\text{Not used}","int(-sin(x)/(tan(x) - 1/cos(x)),x)","\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)-\sin\left(x\right)","Not used",1,"log(tan(x/2)^2 + 1) - 2*log(tan(x/2) - 1) - sin(x)","B"
197,1,6,6,0.577230,"\text{Not used}","int(-cos(x)/(tan(x) - 1/cos(x)),x)","x-\cos\left(x\right)","Not used",1,"x - cos(x)","B"
198,1,14,15,0.577040,"\text{Not used}","int(-tan(x)/(tan(x) - 1/cos(x)),x)","-x-\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)-1}","Not used",1,"- x - 2/(tan(x/2) - 1)","B"
199,1,23,7,0.610035,"\text{Not used}","int(-cot(x)/(tan(x) - 1/cos(x)),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-2\,\mathrm{atan}\left(\frac{8}{4\,\mathrm{tan}\left(\frac{x}{2}\right)-4}+1\right)","Not used",1,"log(tan(x/2)) - 2*atan(8/(4*tan(x/2) - 4) + 1)","B"
200,1,10,11,0.562952,"\text{Not used}","int(-1/(cos(x)*(tan(x) - 1/cos(x))),x)","-\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)-1}","Not used",1,"-2/(tan(x/2) - 1)","B"
201,1,15,13,0.564442,"\text{Not used}","int(-1/(sin(x)*(tan(x) - 1/cos(x))),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)","Not used",1,"log(tan(x/2)) - 2*log(tan(x/2) - 1)","B"
202,1,14,23,0.589157,"\text{Not used}","int((cot(c + d*x) + 1/sin(c + d*x))/sin(c + d*x),x)","-\frac{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"-cot(c/2 + (d*x)/2)/d","B"
203,1,6,6,1.047321,"\text{Not used}","int(sin(x)/(cot(x) + 1/sin(x)),x)","x-\sin\left(x\right)","Not used",1,"x - sin(x)","B"
204,1,24,10,0.591149,"\text{Not used}","int(cos(x)/(cot(x) + 1/sin(x)),x)","-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"- log(tan(x/2)^2 + 1) - 2/(tan(x/2)^2 + 1)","B"
205,1,11,7,0.574854,"\text{Not used}","int(tan(x)/(cot(x) + 1/sin(x)),x)","2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-x","Not used",1,"2*atanh(tan(x/2)) - x","B"
206,1,8,12,0.573394,"\text{Not used}","int(cot(x)/(cot(x) + 1/sin(x)),x)","x-\mathrm{tan}\left(\frac{x}{2}\right)","Not used",1,"x - tan(x/2)","B"
207,1,11,11,0.663207,"\text{Not used}","int(1/(cos(x)*(cot(x) + 1/sin(x))),x)","-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)","Not used",1,"-log(tan(x/2)^2 - 1)","B"
208,1,4,9,0.542351,"\text{Not used}","int(1/(sin(x)*(cot(x) + 1/sin(x))),x)","\mathrm{tan}\left(\frac{x}{2}\right)","Not used",1,"tan(x/2)","B"
209,1,4,4,1.025819,"\text{Not used}","int(-sin(x)/(cot(x) - 1/sin(x)),x)","x+\sin\left(x\right)","Not used",1,"x + sin(x)","B"
210,1,31,10,0.618336,"\text{Not used}","int(-cos(x)/(cot(x) - 1/sin(x)),x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+\frac{2}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"2*log(tan(x/2)) - log(tan(x/2)^2 + 1) + 2/(tan(x/2)^2 + 1)","B"
211,1,9,5,0.569669,"\text{Not used}","int(-tan(x)/(cot(x) - 1/sin(x)),x)","x+2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"x + 2*atanh(tan(x/2))","B"
212,1,10,16,0.578288,"\text{Not used}","int(-cot(x)/(cot(x) - 1/sin(x)),x)","-x-\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"- x - cot(x/2)","B"
213,1,19,13,0.610109,"\text{Not used}","int(-1/(cos(x)*(cot(x) - 1/sin(x))),x)","2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)","Not used",1,"2*log(tan(x/2)) - log(tan(x/2)^2 - 1)","B"
214,1,6,12,0.533625,"\text{Not used}","int(-1/(sin(x)*(cot(x) - 1/sin(x))),x)","-\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"-cot(x/2)","B"
215,1,42,23,0.655902,"\text{Not used}","int(1/(sin(c + d*x) + 1/sin(c + d*x)),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{2\,\sqrt{2}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1}\right)}{2\,d}","Not used",1,"(2^(1/2)*atanh((2*2^(1/2)*sin(c/2 + (d*x)/2)^2)/(2*sin(c/2 + (d*x)/2)^2 + 1)))/(2*d)","B"
216,1,62,51,0.618889,"\text{Not used}","int(sin(c + d*x)/(sin(c + d*x) + 1/sin(c + d*x)),x)","x-\frac{\sqrt{2}\,\left(2\,\mathrm{atan}\left(\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{7\,\sqrt{2}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)+2\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)\right)}{4\,d}","Not used",1,"x - (2^(1/2)*(2*atan((7*2^(1/2)*tan(c/2 + (d*x)/2))/4 + (2^(1/2)*tan(c/2 + (d*x)/2)^3)/4) + 2*atan((2^(1/2)*tan(c/2 + (d*x)/2))/4)))/(4*d)","B"
217,1,16,18,0.058739,"\text{Not used}","int(cos(c + d*x)/(sin(c + d*x) + 1/sin(c + d*x)),x)","\frac{\ln\left({\sin\left(c+d\,x\right)}^2+1\right)}{2\,d}","Not used",1,"log(sin(c + d*x)^2 + 1)/(2*d)","B"
218,1,61,29,0.694759,"\text{Not used}","int(tan(c + d*x)/(sin(c + d*x) + 1/sin(c + d*x)),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\mathrm{atan}\left(\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)-\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{2\,d}","Not used",1,"atanh(tan(c/2 + (d*x)/2))/d - (atan((5*tan(c/2 + (d*x)/2))/2 + tan(c/2 + (d*x)/2)^3/2) - atan(tan(c/2 + (d*x)/2)/2))/(2*d)","B"
219,1,45,11,0.671262,"\text{Not used}","int(cot(c + d*x)/(sin(c + d*x) + 1/sin(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)-\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{d}","Not used",1,"(atan((5*tan(c/2 + (d*x)/2))/2 + tan(c/2 + (d*x)/2)^3/2) - atan(tan(c/2 + (d*x)/2)/2))/d","B"
220,1,14,16,0.607310,"\text{Not used}","int(1/(cos(c + d*x)*(sin(c + d*x) + 1/sin(c + d*x))),x)","\frac{\mathrm{atanh}\left({\sin\left(c+d\,x\right)}^2\right)}{2\,d}","Not used",1,"atanh(sin(c + d*x)^2)/(2*d)","B"
221,1,56,48,0.709267,"\text{Not used}","int(1/(sin(c + d*x)*(sin(c + d*x) + 1/sin(c + d*x))),x)","\frac{\sqrt{2}\,\left(\mathrm{atan}\left(\frac{\sqrt{2}\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{7\,\sqrt{2}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)+\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)\right)}{2\,d}","Not used",1,"(2^(1/2)*(atan((7*2^(1/2)*tan(c/2 + (d*x)/2))/4 + (2^(1/2)*tan(c/2 + (d*x)/2)^3)/4) + atan((2^(1/2)*tan(c/2 + (d*x)/2))/4)))/(2*d)","B"
222,1,20,10,0.662922,"\text{Not used}","int(-1/(sin(c + d*x) - 1/sin(c + d*x)),x)","-\frac{2}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"-2/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
223,1,33,14,0.619510,"\text{Not used}","int(-sin(c + d*x)/(sin(c + d*x) - 1/sin(c + d*x)),x)","-x-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- x - (2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
224,1,14,12,0.059463,"\text{Not used}","int(-cos(c + d*x)/(sin(c + d*x) - 1/sin(c + d*x)),x)","-\frac{\ln\left({\cos\left(c+d\,x\right)}^2\right)}{2\,d}","Not used",1,"-log(cos(c + d*x)^2)/(2*d)","B"
225,1,69,34,0.999572,"\text{Not used}","int(-tan(c + d*x)/(sin(c + d*x) - 1/sin(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^3)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) - atanh(tan(c/2 + (d*x)/2))/d","B"
226,1,15,11,0.639379,"\text{Not used}","int(-cot(c + d*x)/(sin(c + d*x) - 1/sin(c + d*x)),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)))/d","B"
227,1,13,15,0.043289,"\text{Not used}","int(-1/(cos(c + d*x)*(sin(c + d*x) - 1/sin(c + d*x))),x)","\frac{1}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"1/(2*d*cos(c + d*x)^2)","B"
228,1,29,10,0.580058,"\text{Not used}","int(-1/(sin(c + d*x)*(sin(c + d*x) - 1/sin(c + d*x))),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"-(2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
229,1,29,33,0.680712,"\text{Not used}","int(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x)),x)","-\frac{a\,{\cos\left(c+d\,x\right)}^4}{4\,d}-\frac{b\,{\cos\left(c+d\,x\right)}^3}{3\,d}","Not used",1,"- (a*cos(c + d*x)^4)/(4*d) - (b*cos(c + d*x)^3)/(3*d)","B"
230,1,49,33,0.644194,"\text{Not used}","int(cos(c + d*x)^2*(a*sin(c + d*x) + b*tan(c + d*x)),x)","-\frac{\left(\cos\left(c+d\,x\right)+1\right)\,\left(2\,a-3\,b-2\,a\,\cos\left(c+d\,x\right)+3\,b\,\cos\left(c+d\,x\right)+2\,a\,{\cos\left(c+d\,x\right)}^2\right)}{6\,d}","Not used",1,"-((cos(c + d*x) + 1)*(2*a - 3*b - 2*a*cos(c + d*x) + 3*b*cos(c + d*x) + 2*a*cos(c + d*x)^2))/(6*d)","B"
231,1,28,22,0.625669,"\text{Not used}","int(cos(c + d*x)*(a*sin(c + d*x) + b*tan(c + d*x)),x)","-\frac{\left(\cos\left(c+d\,x\right)+1\right)\,\left(2\,b-a+a\,\cos\left(c+d\,x\right)\right)}{2\,d}","Not used",1,"-((cos(c + d*x) + 1)*(2*b - a + a*cos(c + d*x)))/(2*d)","B"
232,1,40,26,0.654691,"\text{Not used}","int(a*sin(c + d*x) + b*tan(c + d*x),x)","\frac{2\,b\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(2*b*atanh(tan(c/2 + (d*x)/2)^2))/d - (2*a)/(d*(tan(c/2 + (d*x)/2)^2 + 1))","B"
233,1,40,25,0.663642,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))/cos(c + d*x),x)","\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,b}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)^2))/d - (2*b)/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
234,1,24,28,0.634734,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))/cos(c + d*x)^2,x)","\frac{\frac{b}{2}+a\,\cos\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(b/2 + a*cos(c + d*x))/(d*cos(c + d*x)^2)","B"
235,1,29,33,0.692767,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))/cos(c + d*x)^3,x)","\frac{a}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{b}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"a/(2*d*cos(c + d*x)^2) + b/(3*d*cos(c + d*x)^3)","B"
236,1,101,106,0.792972,"\text{Not used}","int(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{a^2\,\sin\left(c+d\,x\right)}{8\,d}+\frac{b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{a\,b\,x}{4}-\frac{a^2\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}-\frac{a^2\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}-\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}-\frac{a\,b\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}","Not used",1,"(a^2*sin(c + d*x))/(8*d) + (b^2*sin(c + d*x))/(4*d) + (a*b*x)/4 - (a^2*sin(3*c + 3*d*x))/(48*d) - (a^2*sin(5*c + 5*d*x))/(80*d) - (b^2*sin(3*c + 3*d*x))/(12*d) - (a*b*sin(4*c + 4*d*x))/(16*d)","B"
237,1,76,86,0.714734,"\text{Not used}","int(cos(c + d*x)^2*(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{a^2\,x}{8}+\frac{b^2\,x}{2}-\frac{a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}-\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a\,b\,\sin\left(c+d\,x\right)}{2\,d}-\frac{a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"(a^2*x)/8 + (b^2*x)/2 - (a^2*sin(4*c + 4*d*x))/(32*d) - (b^2*sin(2*c + 2*d*x))/(4*d) + (a*b*sin(c + d*x))/(2*d) - (a*b*sin(3*c + 3*d*x))/(6*d)","B"
238,1,121,87,0.840019,"\text{Not used}","int(cos(c + d*x)*(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{a^2\,\sin\left(c+d\,x\right)}{4\,d}-\frac{b^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{2\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(a^2*sin(c + d*x))/(4*d) - (b^2*sin(c + d*x))/d + (2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*sin(3*c + 3*d*x))/(12*d) + (2*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*b*sin(2*c + 2*d*x))/(2*d)","B"
239,1,143,77,0.796605,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{2\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{4\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^2*sin(c + d*x))/(d*cos(c + d*x)) - (2*a*b*sin(c + d*x))/d + (4*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
240,1,147,90,0.788369,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^2/cos(c + d*x),x)","\frac{2\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\sin\left(c+d\,x\right)}{d}-\frac{b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^2\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{4\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,a\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*sin(c + d*x))/d - (b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^2*sin(c + d*x))/(2*d*cos(c + d*x)^2) - (4*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*a*b*sin(c + d*x))/(d*cos(c + d*x))","B"
241,1,227,99,1.025888,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^2/cos(c + d*x)^2,x)","-\frac{\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)}{12}-\frac{b^2\,\sin\left(c+d\,x\right)}{4}-\frac{a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}-\frac{a^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{a^2\,\mathrm{atan}\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(3\,c+3\,d\,x\right)}{2}-\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{a\,b\,\mathrm{atanh}\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(3\,c+3\,d\,x\right)}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"-((b^2*sin(3*c + 3*d*x))/12 - (b^2*sin(c + d*x))/4 - (a^2*sin(3*c + 3*d*x))/4 - (a^2*sin(c + d*x))/4 + (3*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (a*b*sin(2*c + 2*d*x))/2 + (3*a*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
242,1,177,125,3.268796,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^2/cos(c + d*x)^3,x)","\frac{\left(a^2+\frac{b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-a^2-\frac{16\,a\,b}{3}+\frac{7\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-a^2+\frac{16\,a\,b}{3}+\frac{7\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(a^2+\frac{b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+\frac{b^2}{4}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((16*a*b)/3 - a^2 + (7*b^2)/4) + tan(c/2 + (d*x)/2)*(a^2 + b^2/4) + tan(c/2 + (d*x)/2)^7*(a^2 + b^2/4) - tan(c/2 + (d*x)/2)^5*((16*a*b)/3 + a^2 - (7*b^2)/4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atanh(tan(c/2 + (d*x)/2))*(a^2 + b^2/4))/d","B"
243,1,149,77,0.799636,"\text{Not used}","int(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{32\,a^3}{3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}+\frac{4\,{\left(a-b\right)}^3}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}-\frac{32\,a^2\,\left(5\,a-3\,b\right)}{5\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}-\frac{8\,{\left(a-b\right)}^2\,\left(7\,a-b\right)}{3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}+\frac{12\,a\,\left(3\,a^2-4\,a\,b+b^2\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(32*a^3)/(3*d*(tan(c/2 + (d*x)/2)^2 + 1)^6) + (4*(a - b)^3)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^2) - (32*a^2*(5*a - 3*b))/(5*d*(tan(c/2 + (d*x)/2)^2 + 1)^5) - (8*(a - b)^2*(7*a - b))/(3*d*(tan(c/2 + (d*x)/2)^2 + 1)^3) + (12*a*(3*a^2 - 4*a*b + b^2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
244,1,237,120,0.791917,"\text{Not used}","int(cos(c + d*x)^2*(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{40\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3\,d}-\frac{4\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}-\frac{16\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}+\frac{32\,a^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5\,d}-\frac{2\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d}+\frac{2\,b^3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}+\frac{2\,b^3\,\mathrm{atanh}\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}-1\right)}{d}-\frac{12\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}+\frac{12\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d}+\frac{8\,a\,b^2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d}-\frac{24\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d}+\frac{12\,a^2\,b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d}","Not used",1,"(40*a^3*cos(c/2 + (d*x)/2)^6)/(3*d) - (4*a^3*cos(c/2 + (d*x)/2)^4)/d - (16*a^3*cos(c/2 + (d*x)/2)^8)/d + (32*a^3*cos(c/2 + (d*x)/2)^10)/(5*d) - (2*b^3*cos(c/2 + (d*x)/2)^2)/d + (2*b^3*cos(c/2 + (d*x)/2)^4)/d + (2*b^3*atanh(1/cos(c/2 + (d*x)/2)^2 - 1))/d - (12*a*b^2*cos(c/2 + (d*x)/2)^4)/d + (12*a^2*b*cos(c/2 + (d*x)/2)^4)/d + (8*a*b^2*cos(c/2 + (d*x)/2)^6)/d - (24*a^2*b*cos(c/2 + (d*x)/2)^6)/d + (12*a^2*b*cos(c/2 + (d*x)/2)^8)/d","B"
245,1,225,112,4.181656,"\text{Not used}","int(cos(c + d*x)*(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^3+4\,a^2\,b-6\,a\,b^2+12\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^2\,b+6\,a\,b^2-12\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-4\,a^3+12\,a^2\,b+6\,a\,b^2+4\,b^3\right)-4\,a^2\,b+4\,b^3+6\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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{6\,a\,b^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(4*a^2*b - 6*a*b^2 + 4*a^3 + 12*b^3) - tan(c/2 + (d*x)/2)^2*(6*a*b^2 + 12*a^2*b - 12*b^3) + tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 12*a^2*b - 4*a^3 + 4*b^3) - 4*a^2*b + 4*b^3 + 6*a*b^2*tan(c/2 + (d*x)/2)^8)/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1)) + (6*a*b^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
246,1,219,116,4.524157,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-\frac{4\,a^3}{3}-6\,a^2\,b+12\,a\,b^2+2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3-6\,a^2\,b+12\,a\,b^2-6\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{20\,a^3}{3}+6\,a^2\,b-12\,a\,b^2+6\,b^3\right)+12\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,a^2\,b-2\,b^3\right)-\frac{4\,a^3}{3}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^2\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}-\frac{2\,b^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)-6\,a^2\,b\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 6*a^2*b - (4*a^3)/3 + 2*b^3) - tan(c/2 + (d*x)/2)^6*(12*a*b^2 - 6*a^2*b + 4*a^3 - 6*b^3) + tan(c/2 + (d*x)/2)^4*(6*a^2*b - 12*a*b^2 + (20*a^3)/3 + 6*b^3) + 12*a*b^2 - tan(c/2 + (d*x)/2)^8*(6*a^2*b - 2*b^3) - (4*a^3)/3)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^2*(tan(c/2 + (d*x)/2)^2 + 1)^3) - (2*b^3*atanh(tan(c/2 + (d*x)/2)^2) - 6*a^2*b*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
247,1,219,115,4.447440,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^3/cos(c + d*x),x)","\frac{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)-6\,a\,b^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^3-12\,a^2\,b+6\,a\,b^2+\frac{4\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(6\,a^3-12\,a^2\,b+6\,a\,b^2-4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^3-12\,a^2\,b+6\,a\,b^2+\frac{20\,b^3}{3}\right)+12\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(6\,a\,b^2-2\,a^3\right)-\frac{4\,b^3}{3}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^3\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(2*a^3*atanh(tan(c/2 + (d*x)/2)^2) - 6*a*b^2*atanh(tan(c/2 + (d*x)/2)^2))/d - (tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 12*a^2*b - 2*a^3 + (4*b^3)/3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 - 12*a^2*b + 6*a^3 - 4*b^3) + tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 12*a^2*b + 6*a^3 + (20*b^3)/3) + 12*a^2*b - tan(c/2 + (d*x)/2)^8*(6*a*b^2 - 2*a^3) - (4*b^3)/3)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
248,1,223,111,4.217243,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^3/cos(c + d*x)^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-12\,a^3+6\,a^2\,b+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^3-6\,a^2\,b+4\,a\,b^2+4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3+6\,a^2\,b+12\,a\,b^2-4\,b^3\right)-4\,a\,b^2+4\,a^3+6\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\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{6\,a^2\,b\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(12*a*b^2 + 6*a^2*b - 12*a^3) + tan(c/2 + (d*x)/2)^4*(4*a*b^2 - 6*a^2*b + 12*a^3 + 4*b^3) - tan(c/2 + (d*x)/2)^6*(12*a*b^2 + 6*a^2*b + 4*a^3 - 4*b^3) - 4*a*b^2 + 4*a^3 + 6*a^2*b*tan(c/2 + (d*x)/2)^8)/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (6*a^2*b*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
249,1,220,119,4.153270,"\text{Not used}","int((a*sin(c + d*x) + b*tan(c + d*x))^3/cos(c + d*x)^3,x)","-\frac{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(6\,a^3+12\,a^2\,b-12\,a\,b^2+4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-6\,a^3-28\,a^2\,b+12\,a\,b^2+\frac{4\,b^3}{3}\right)-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,a^2\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^3+20\,a^2\,b+\frac{4\,b^3}{3}\right)-\frac{4\,b^3}{15}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- (2*a^3*atanh(tan(c/2 + (d*x)/2)^2))/d - (tan(c/2 + (d*x)/2)^6*(12*a^2*b - 12*a*b^2 + 6*a^3 + 4*b^3) + tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 28*a^2*b - 6*a^3 + (4*b^3)/3) - 2*a^3*tan(c/2 + (d*x)/2)^8 - 4*a^2*b + tan(c/2 + (d*x)/2)^2*(20*a^2*b + 2*a^3 + (4*b^3)/3) - (4*b^3)/15)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
250,1,161,113,1.160065,"\text{Not used}","int(cos(c + d*x)^3/(a*sin(c + d*x) + b*tan(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}-\frac{\frac{2\,b}{a^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a+b\right)}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{b^4\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d\,\left(a^5-a^3\,b^2\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2+b^2\right)}{a^3\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) - ((2*b)/a^2 + (2*tan(c/2 + (d*x)/2)^2*(a + b))/a^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (b^4*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(d*(a^5 - a^3*b^2)) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 + b^2))/(a^3*d)","B"
251,1,117,92,0.823483,"\text{Not used}","int(cos(c + d*x)^2/(a*sin(c + d*x) + b*tan(c + d*x)),x)","\frac{2}{a\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}+\frac{b\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}+\frac{b^3\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^2\,d\,\left(a^2-b^2\right)}","Not used",1,"2/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)) + log(tan(c/2 + (d*x)/2))/(d*(a + b)) + (b*log(tan(c/2 + (d*x)/2)^2 + 1))/(a^2*d) + (b^3*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(a^2*d*(a^2 - b^2))","B"
252,1,93,80,0.867692,"\text{Not used}","int(cos(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}+\frac{b^2\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d\,\left(a\,b^2-a^3\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) + (b^2*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(d*(a*b^2 - a^3))","B"
253,1,67,74,0.899739,"\text{Not used}","int(1/(a*sin(c + d*x) + b*tan(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}+\frac{b\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d\,\left(a^2-b^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) + (b*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(d*(a^2 - b^2))","B"
254,1,68,75,0.707945,"\text{Not used}","int(1/(cos(c + d*x)*(a*sin(c + d*x) + b*tan(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}-\frac{a\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d\,\left(a^2-b^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) - (a*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(d*(a^2 - b^2))","B"
255,1,93,94,0.843005,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*sin(c + d*x) + b*tan(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{b\,d}+\frac{a^2\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d\,\left(a^2\,b-b^3\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) - log(tan(c/2 + (d*x)/2)^2 - 1)/(b*d) + (a^2*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(d*(a^2*b - b^3))","B"
256,1,118,108,0.827199,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x))),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}-\frac{2}{b\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{b^2\,d}-\frac{a^3\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{b^2\,d\,\left(a^2-b^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) - 2/(b*d*(tan(c/2 + (d*x)/2)^2 - 1)) + (a*log(tan(c/2 + (d*x)/2)^2 - 1))/(b^2*d) - (a^3*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(b^2*d*(a^2 - b^2))","B"
257,1,7329,243,5.444832,"\text{Not used}","int(cos(c + d*x)^3/(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^5+3\,a^4\,b-6\,a^3\,b^2-3\,a^2\,b^3+2\,a\,b^4+4\,b^5\right)}{a^2\,{\left(a+b\right)}^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^5-7\,a^4\,b-5\,a^3\,b^2+7\,a^2\,b^3+4\,a\,b^4-8\,b^5\right)}{a^2\,{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,a^2\,b+8\,a\,b^2-4\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{4\,b\,\mathrm{atan}\left(\frac{1920\,a^7\,b^{22}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{1920\,a^8\,b^{21}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{16640\,a^9\,b^{20}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{16640\,a^{10}\,b^{19}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{62080\,a^{11}\,b^{18}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{62080\,a^{12}\,b^{17}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{131072\,a^{13}\,b^{16}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{131072\,a^{14}\,b^{15}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{172672\,a^{15}\,b^{14}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{172672\,a^{16}\,b^{13}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{147200\,a^{17}\,b^{12}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{147200\,a^{18}\,b^{11}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{81280\,a^{19}\,b^{10}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{81280\,a^{20}\,b^9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{28160\,a^{21}\,b^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{28160\,a^{22}\,b^7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{5632\,a^{23}\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{5632\,a^{24}\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}-\frac{512\,a^{25}\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}+\frac{512\,a^{26}\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^{26}\,b^3-512\,a^{25}\,b^4-5632\,a^{24}\,b^5+5632\,a^{23}\,b^6+28160\,a^{22}\,b^7-28160\,a^{21}\,b^8-81280\,a^{20}\,b^9+81280\,a^{19}\,b^{10}+147200\,a^{18}\,b^{11}-147200\,a^{17}\,b^{12}-172672\,a^{16}\,b^{13}+172672\,a^{15}\,b^{14}+131072\,a^{14}\,b^{15}-131072\,a^{13}\,b^{16}-62080\,a^{12}\,b^{17}+62080\,a^{11}\,b^{18}+16640\,a^{10}\,b^{19}-16640\,a^9\,b^{20}-1920\,a^8\,b^{21}+1920\,a^7\,b^{22}}\right)}{a^3\,d}+\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^{29}\,b^2+384\,a^{28}\,b^3+896\,a^{27}\,b^4-3712\,a^{26}\,b^5-1920\,a^{25}\,b^6+16000\,a^{24}\,b^7-2720\,a^{23}\,b^8-39520\,a^{22}\,b^9+24640\,a^{21}\,b^{10}+59840\,a^{20}\,b^{11}-64352\,a^{19}\,b^{12}-53920\,a^{18}\,b^{13}+96256\,a^{17}\,b^{14}+22016\,a^{16}\,b^{15}-92000\,a^{15}\,b^{16}+7520\,a^{14}\,b^{17}+57280\,a^{13}\,b^{18}-15040\,a^{12}\,b^{19}-22560\,a^{11}\,b^{20}+8480\,a^{10}\,b^{21}+5120\,a^9\,b^{22}-2304\,a^8\,b^{23}-512\,a^7\,b^{24}+256\,a^6\,b^{25}\right)-\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(96\,a^{11}\,b^{22}-64\,a^{10}\,b^{23}-64\,a^{32}\,b+640\,a^{12}\,b^{21}-1120\,a^{13}\,b^{20}-2624\,a^{14}\,b^{19}+5568\,a^{15}\,b^{18}+5568\,a^{16}\,b^{17}-15744\,a^{17}\,b^{16}-5760\,a^{18}\,b^{15}+28224\,a^{19}\,b^{14}-33600\,a^{21}\,b^{12}+8064\,a^{22}\,b^{11}+26880\,a^{23}\,b^{10}-11136\,a^{24}\,b^9-14208\,a^{25}\,b^8+7872\,a^{26}\,b^7+4704\,a^{27}\,b^6-3200\,a^{28}\,b^5-864\,a^{29}\,b^4+704\,a^{30}\,b^3+64\,a^{31}\,b^2+\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{34}\,b+128\,a^{33}\,b^2+576\,a^{32}\,b^3-1280\,a^{31}\,b^4-2240\,a^{30}\,b^5+5760\,a^{29}\,b^6+4800\,a^{28}\,b^7-15360\,a^{27}\,b^8-5760\,a^{26}\,b^9+26880\,a^{25}\,b^{10}+2688\,a^{24}\,b^{11}-32256\,a^{23}\,b^{12}+2688\,a^{22}\,b^{13}+26880\,a^{21}\,b^{14}-5760\,a^{20}\,b^{15}-15360\,a^{19}\,b^{16}+4800\,a^{18}\,b^{17}+5760\,a^{17}\,b^{18}-2240\,a^{16}\,b^{19}-1280\,a^{15}\,b^{20}+576\,a^{14}\,b^{21}+128\,a^{13}\,b^{22}-64\,a^{12}\,b^{23}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}+\frac{b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^{29}\,b^2+384\,a^{28}\,b^3+896\,a^{27}\,b^4-3712\,a^{26}\,b^5-1920\,a^{25}\,b^6+16000\,a^{24}\,b^7-2720\,a^{23}\,b^8-39520\,a^{22}\,b^9+24640\,a^{21}\,b^{10}+59840\,a^{20}\,b^{11}-64352\,a^{19}\,b^{12}-53920\,a^{18}\,b^{13}+96256\,a^{17}\,b^{14}+22016\,a^{16}\,b^{15}-92000\,a^{15}\,b^{16}+7520\,a^{14}\,b^{17}+57280\,a^{13}\,b^{18}-15040\,a^{12}\,b^{19}-22560\,a^{11}\,b^{20}+8480\,a^{10}\,b^{21}+5120\,a^9\,b^{22}-2304\,a^8\,b^{23}-512\,a^7\,b^{24}+256\,a^6\,b^{25}\right)-\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(64\,a^{32}\,b+64\,a^{10}\,b^{23}-96\,a^{11}\,b^{22}-640\,a^{12}\,b^{21}+1120\,a^{13}\,b^{20}+2624\,a^{14}\,b^{19}-5568\,a^{15}\,b^{18}-5568\,a^{16}\,b^{17}+15744\,a^{17}\,b^{16}+5760\,a^{18}\,b^{15}-28224\,a^{19}\,b^{14}+33600\,a^{21}\,b^{12}-8064\,a^{22}\,b^{11}-26880\,a^{23}\,b^{10}+11136\,a^{24}\,b^9+14208\,a^{25}\,b^8-7872\,a^{26}\,b^7-4704\,a^{27}\,b^6+3200\,a^{28}\,b^5+864\,a^{29}\,b^4-704\,a^{30}\,b^3-64\,a^{31}\,b^2+\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{34}\,b+128\,a^{33}\,b^2+576\,a^{32}\,b^3-1280\,a^{31}\,b^4-2240\,a^{30}\,b^5+5760\,a^{29}\,b^6+4800\,a^{28}\,b^7-15360\,a^{27}\,b^8-5760\,a^{26}\,b^9+26880\,a^{25}\,b^{10}+2688\,a^{24}\,b^{11}-32256\,a^{23}\,b^{12}+2688\,a^{22}\,b^{13}+26880\,a^{21}\,b^{14}-5760\,a^{20}\,b^{15}-15360\,a^{19}\,b^{16}+4800\,a^{18}\,b^{17}+5760\,a^{17}\,b^{18}-2240\,a^{16}\,b^{19}-1280\,a^{15}\,b^{20}+576\,a^{14}\,b^{21}+128\,a^{13}\,b^{22}-64\,a^{12}\,b^{23}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}}{512\,a^4\,b^{25}-768\,a^5\,b^{24}-5120\,a^6\,b^{23}+7040\,a^7\,b^{22}+22912\,a^8\,b^{21}-27904\,a^9\,b^{20}-61184\,a^{10}\,b^{19}+63872\,a^{11}\,b^{18}+108160\,a^{12}\,b^{17}-94720\,a^{13}\,b^{16}-131072\,a^{14}\,b^{15}+96128\,a^{15}\,b^{14}+108160\,a^{16}\,b^{13}-67840\,a^{17}\,b^{12}-58112\,a^{18}\,b^{11}+32384\,a^{19}\,b^{10}+18304\,a^{20}\,b^9-9472\,a^{21}\,b^8-2560\,a^{22}\,b^7+1280\,a^{23}\,b^6+\frac{b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^{29}\,b^2+384\,a^{28}\,b^3+896\,a^{27}\,b^4-3712\,a^{26}\,b^5-1920\,a^{25}\,b^6+16000\,a^{24}\,b^7-2720\,a^{23}\,b^8-39520\,a^{22}\,b^9+24640\,a^{21}\,b^{10}+59840\,a^{20}\,b^{11}-64352\,a^{19}\,b^{12}-53920\,a^{18}\,b^{13}+96256\,a^{17}\,b^{14}+22016\,a^{16}\,b^{15}-92000\,a^{15}\,b^{16}+7520\,a^{14}\,b^{17}+57280\,a^{13}\,b^{18}-15040\,a^{12}\,b^{19}-22560\,a^{11}\,b^{20}+8480\,a^{10}\,b^{21}+5120\,a^9\,b^{22}-2304\,a^8\,b^{23}-512\,a^7\,b^{24}+256\,a^6\,b^{25}\right)-\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(96\,a^{11}\,b^{22}-64\,a^{10}\,b^{23}-64\,a^{32}\,b+640\,a^{12}\,b^{21}-1120\,a^{13}\,b^{20}-2624\,a^{14}\,b^{19}+5568\,a^{15}\,b^{18}+5568\,a^{16}\,b^{17}-15744\,a^{17}\,b^{16}-5760\,a^{18}\,b^{15}+28224\,a^{19}\,b^{14}-33600\,a^{21}\,b^{12}+8064\,a^{22}\,b^{11}+26880\,a^{23}\,b^{10}-11136\,a^{24}\,b^9-14208\,a^{25}\,b^8+7872\,a^{26}\,b^7+4704\,a^{27}\,b^6-3200\,a^{28}\,b^5-864\,a^{29}\,b^4+704\,a^{30}\,b^3+64\,a^{31}\,b^2+\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{34}\,b+128\,a^{33}\,b^2+576\,a^{32}\,b^3-1280\,a^{31}\,b^4-2240\,a^{30}\,b^5+5760\,a^{29}\,b^6+4800\,a^{28}\,b^7-15360\,a^{27}\,b^8-5760\,a^{26}\,b^9+26880\,a^{25}\,b^{10}+2688\,a^{24}\,b^{11}-32256\,a^{23}\,b^{12}+2688\,a^{22}\,b^{13}+26880\,a^{21}\,b^{14}-5760\,a^{20}\,b^{15}-15360\,a^{19}\,b^{16}+4800\,a^{18}\,b^{17}+5760\,a^{17}\,b^{18}-2240\,a^{16}\,b^{19}-1280\,a^{15}\,b^{20}+576\,a^{14}\,b^{21}+128\,a^{13}\,b^{22}-64\,a^{12}\,b^{23}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}-\frac{b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^{29}\,b^2+384\,a^{28}\,b^3+896\,a^{27}\,b^4-3712\,a^{26}\,b^5-1920\,a^{25}\,b^6+16000\,a^{24}\,b^7-2720\,a^{23}\,b^8-39520\,a^{22}\,b^9+24640\,a^{21}\,b^{10}+59840\,a^{20}\,b^{11}-64352\,a^{19}\,b^{12}-53920\,a^{18}\,b^{13}+96256\,a^{17}\,b^{14}+22016\,a^{16}\,b^{15}-92000\,a^{15}\,b^{16}+7520\,a^{14}\,b^{17}+57280\,a^{13}\,b^{18}-15040\,a^{12}\,b^{19}-22560\,a^{11}\,b^{20}+8480\,a^{10}\,b^{21}+5120\,a^9\,b^{22}-2304\,a^8\,b^{23}-512\,a^7\,b^{24}+256\,a^6\,b^{25}\right)-\frac{b^4\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(64\,a^{32}\,b+64\,a^{10}\,b^{23}-96\,a^{11}\,b^{22}-640\,a^{12}\,b^{21}+1120\,a^{13}\,b^{20}+2624\,a^{14}\,b^{19}-5568\,a^{15}\,b^{18}-5568\,a^{16}\,b^{17}+15744\,a^{17}\,b^{16}+5760\,a^{18}\,b^{15}-28224\,a^{19}\,b^{14}+33600\,a^{21}\,b^{12}-8064\,a^{22}\,b^{11}-26880\,a^{23}\,b^{10}+11136\,a^{24}\,b^9+14208\,a^{25}\,b^8-7872\,a^{26}\,b^7-4704\,a^{27}\,b^6+3200\,a^{28}\,b^5+864\,a^{29}\,b^4-704\,a^{30}\,b^3-64\,a^{31}\,b^2+\frac{b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{34}\,b+128\,a^{33}\,b^2+576\,a^{32}\,b^3-1280\,a^{31}\,b^4-2240\,a^{30}\,b^5+5760\,a^{29}\,b^6+4800\,a^{28}\,b^7-15360\,a^{27}\,b^8-5760\,a^{26}\,b^9+26880\,a^{25}\,b^{10}+2688\,a^{24}\,b^{11}-32256\,a^{23}\,b^{12}+2688\,a^{22}\,b^{13}+26880\,a^{21}\,b^{14}-5760\,a^{20}\,b^{15}-15360\,a^{19}\,b^{16}+4800\,a^{18}\,b^{17}+5760\,a^{17}\,b^{18}-2240\,a^{16}\,b^{19}-1280\,a^{15}\,b^{20}+576\,a^{14}\,b^{21}+128\,a^{13}\,b^{22}-64\,a^{12}\,b^{23}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}}}\right)\,\left(5\,a^2-2\,b^2\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) + (2*tan(c/2 + (d*x)/2)^2*(2*a*b^4 + 3*a^4*b + 2*a^5 + 4*b^5 - 3*a^2*b^3 - 6*a^3*b^2))/(a^2*(a + b)^2) - (tan(c/2 + (d*x)/2)^4*(4*a*b^4 - 7*a^4*b + 5*a^5 - 8*b^5 + 7*a^2*b^3 - 5*a^3*b^2))/(a^2*(a + b)^2))/(d*(tan(c/2 + (d*x)/2)^5*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) - tan(c/2 + (d*x)/2)^3*(4*a^2*b - 8*a*b^2 + 4*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (4*b*atan((1920*a^7*b^22*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (1920*a^8*b^21*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (16640*a^9*b^20*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (16640*a^10*b^19*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (62080*a^11*b^18*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (62080*a^12*b^17*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (131072*a^13*b^16*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (131072*a^14*b^15*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (172672*a^15*b^14*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (172672*a^16*b^13*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (147200*a^17*b^12*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (147200*a^18*b^11*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (81280*a^19*b^10*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (81280*a^20*b^9*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (28160*a^21*b^8*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (28160*a^22*b^7*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (5632*a^23*b^6*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (5632*a^24*b^5*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) - (512*a^25*b^4*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3) + (512*a^26*b^3*tan(c/2 + (d*x)/2))/(1920*a^7*b^22 - 1920*a^8*b^21 - 16640*a^9*b^20 + 16640*a^10*b^19 + 62080*a^11*b^18 - 62080*a^12*b^17 - 131072*a^13*b^16 + 131072*a^14*b^15 + 172672*a^15*b^14 - 172672*a^16*b^13 - 147200*a^17*b^12 + 147200*a^18*b^11 + 81280*a^19*b^10 - 81280*a^20*b^9 - 28160*a^21*b^8 + 28160*a^22*b^7 + 5632*a^23*b^6 - 5632*a^24*b^5 - 512*a^25*b^4 + 512*a^26*b^3)))/(a^3*d) + (b^4*atan(((b^4*(tan(c/2 + (d*x)/2)*(256*a^6*b^25 - 512*a^7*b^24 - 2304*a^8*b^23 + 5120*a^9*b^22 + 8480*a^10*b^21 - 22560*a^11*b^20 - 15040*a^12*b^19 + 57280*a^13*b^18 + 7520*a^14*b^17 - 92000*a^15*b^16 + 22016*a^16*b^15 + 96256*a^17*b^14 - 53920*a^18*b^13 - 64352*a^19*b^12 + 59840*a^20*b^11 + 24640*a^21*b^10 - 39520*a^22*b^9 - 2720*a^23*b^8 + 16000*a^24*b^7 - 1920*a^25*b^6 - 3712*a^26*b^5 + 896*a^27*b^4 + 384*a^28*b^3 - 128*a^29*b^2) - (b^4*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(96*a^11*b^22 - 64*a^10*b^23 - 64*a^32*b + 640*a^12*b^21 - 1120*a^13*b^20 - 2624*a^14*b^19 + 5568*a^15*b^18 + 5568*a^16*b^17 - 15744*a^17*b^16 - 5760*a^18*b^15 + 28224*a^19*b^14 - 33600*a^21*b^12 + 8064*a^22*b^11 + 26880*a^23*b^10 - 11136*a^24*b^9 - 14208*a^25*b^8 + 7872*a^26*b^7 + 4704*a^27*b^6 - 3200*a^28*b^5 - 864*a^29*b^4 + 704*a^30*b^3 + 64*a^31*b^2 + (b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^13*b^22 - 64*a^12*b^23 - 64*a^34*b + 576*a^14*b^21 - 1280*a^15*b^20 - 2240*a^16*b^19 + 5760*a^17*b^18 + 4800*a^18*b^17 - 15360*a^19*b^16 - 5760*a^20*b^15 + 26880*a^21*b^14 + 2688*a^22*b^13 - 32256*a^23*b^12 + 2688*a^24*b^11 + 26880*a^25*b^10 - 5760*a^26*b^9 - 15360*a^27*b^8 + 4800*a^28*b^7 + 5760*a^29*b^6 - 2240*a^30*b^5 - 1280*a^31*b^4 + 576*a^32*b^3 + 128*a^33*b^2))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*1i)/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2) + (b^4*(tan(c/2 + (d*x)/2)*(256*a^6*b^25 - 512*a^7*b^24 - 2304*a^8*b^23 + 5120*a^9*b^22 + 8480*a^10*b^21 - 22560*a^11*b^20 - 15040*a^12*b^19 + 57280*a^13*b^18 + 7520*a^14*b^17 - 92000*a^15*b^16 + 22016*a^16*b^15 + 96256*a^17*b^14 - 53920*a^18*b^13 - 64352*a^19*b^12 + 59840*a^20*b^11 + 24640*a^21*b^10 - 39520*a^22*b^9 - 2720*a^23*b^8 + 16000*a^24*b^7 - 1920*a^25*b^6 - 3712*a^26*b^5 + 896*a^27*b^4 + 384*a^28*b^3 - 128*a^29*b^2) - (b^4*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(64*a^32*b + 64*a^10*b^23 - 96*a^11*b^22 - 640*a^12*b^21 + 1120*a^13*b^20 + 2624*a^14*b^19 - 5568*a^15*b^18 - 5568*a^16*b^17 + 15744*a^17*b^16 + 5760*a^18*b^15 - 28224*a^19*b^14 + 33600*a^21*b^12 - 8064*a^22*b^11 - 26880*a^23*b^10 + 11136*a^24*b^9 + 14208*a^25*b^8 - 7872*a^26*b^7 - 4704*a^27*b^6 + 3200*a^28*b^5 + 864*a^29*b^4 - 704*a^30*b^3 - 64*a^31*b^2 + (b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^13*b^22 - 64*a^12*b^23 - 64*a^34*b + 576*a^14*b^21 - 1280*a^15*b^20 - 2240*a^16*b^19 + 5760*a^17*b^18 + 4800*a^18*b^17 - 15360*a^19*b^16 - 5760*a^20*b^15 + 26880*a^21*b^14 + 2688*a^22*b^13 - 32256*a^23*b^12 + 2688*a^24*b^11 + 26880*a^25*b^10 - 5760*a^26*b^9 - 15360*a^27*b^8 + 4800*a^28*b^7 + 5760*a^29*b^6 - 2240*a^30*b^5 - 1280*a^31*b^4 + 576*a^32*b^3 + 128*a^33*b^2))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*1i)/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))/(512*a^4*b^25 - 768*a^5*b^24 - 5120*a^6*b^23 + 7040*a^7*b^22 + 22912*a^8*b^21 - 27904*a^9*b^20 - 61184*a^10*b^19 + 63872*a^11*b^18 + 108160*a^12*b^17 - 94720*a^13*b^16 - 131072*a^14*b^15 + 96128*a^15*b^14 + 108160*a^16*b^13 - 67840*a^17*b^12 - 58112*a^18*b^11 + 32384*a^19*b^10 + 18304*a^20*b^9 - 9472*a^21*b^8 - 2560*a^22*b^7 + 1280*a^23*b^6 + (b^4*(tan(c/2 + (d*x)/2)*(256*a^6*b^25 - 512*a^7*b^24 - 2304*a^8*b^23 + 5120*a^9*b^22 + 8480*a^10*b^21 - 22560*a^11*b^20 - 15040*a^12*b^19 + 57280*a^13*b^18 + 7520*a^14*b^17 - 92000*a^15*b^16 + 22016*a^16*b^15 + 96256*a^17*b^14 - 53920*a^18*b^13 - 64352*a^19*b^12 + 59840*a^20*b^11 + 24640*a^21*b^10 - 39520*a^22*b^9 - 2720*a^23*b^8 + 16000*a^24*b^7 - 1920*a^25*b^6 - 3712*a^26*b^5 + 896*a^27*b^4 + 384*a^28*b^3 - 128*a^29*b^2) - (b^4*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(96*a^11*b^22 - 64*a^10*b^23 - 64*a^32*b + 640*a^12*b^21 - 1120*a^13*b^20 - 2624*a^14*b^19 + 5568*a^15*b^18 + 5568*a^16*b^17 - 15744*a^17*b^16 - 5760*a^18*b^15 + 28224*a^19*b^14 - 33600*a^21*b^12 + 8064*a^22*b^11 + 26880*a^23*b^10 - 11136*a^24*b^9 - 14208*a^25*b^8 + 7872*a^26*b^7 + 4704*a^27*b^6 - 3200*a^28*b^5 - 864*a^29*b^4 + 704*a^30*b^3 + 64*a^31*b^2 + (b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^13*b^22 - 64*a^12*b^23 - 64*a^34*b + 576*a^14*b^21 - 1280*a^15*b^20 - 2240*a^16*b^19 + 5760*a^17*b^18 + 4800*a^18*b^17 - 15360*a^19*b^16 - 5760*a^20*b^15 + 26880*a^21*b^14 + 2688*a^22*b^13 - 32256*a^23*b^12 + 2688*a^24*b^11 + 26880*a^25*b^10 - 5760*a^26*b^9 - 15360*a^27*b^8 + 4800*a^28*b^7 + 5760*a^29*b^6 - 2240*a^30*b^5 - 1280*a^31*b^4 + 576*a^32*b^3 + 128*a^33*b^2))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2) - (b^4*(tan(c/2 + (d*x)/2)*(256*a^6*b^25 - 512*a^7*b^24 - 2304*a^8*b^23 + 5120*a^9*b^22 + 8480*a^10*b^21 - 22560*a^11*b^20 - 15040*a^12*b^19 + 57280*a^13*b^18 + 7520*a^14*b^17 - 92000*a^15*b^16 + 22016*a^16*b^15 + 96256*a^17*b^14 - 53920*a^18*b^13 - 64352*a^19*b^12 + 59840*a^20*b^11 + 24640*a^21*b^10 - 39520*a^22*b^9 - 2720*a^23*b^8 + 16000*a^24*b^7 - 1920*a^25*b^6 - 3712*a^26*b^5 + 896*a^27*b^4 + 384*a^28*b^3 - 128*a^29*b^2) - (b^4*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(64*a^32*b + 64*a^10*b^23 - 96*a^11*b^22 - 640*a^12*b^21 + 1120*a^13*b^20 + 2624*a^14*b^19 - 5568*a^15*b^18 - 5568*a^16*b^17 + 15744*a^17*b^16 + 5760*a^18*b^15 - 28224*a^19*b^14 + 33600*a^21*b^12 - 8064*a^22*b^11 - 26880*a^23*b^10 + 11136*a^24*b^9 + 14208*a^25*b^8 - 7872*a^26*b^7 - 4704*a^27*b^6 + 3200*a^28*b^5 + 864*a^29*b^4 - 704*a^30*b^3 - 64*a^31*b^2 + (b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^13*b^22 - 64*a^12*b^23 - 64*a^34*b + 576*a^14*b^21 - 1280*a^15*b^20 - 2240*a^16*b^19 + 5760*a^17*b^18 + 4800*a^18*b^17 - 15360*a^19*b^16 - 5760*a^20*b^15 + 26880*a^21*b^14 + 2688*a^22*b^13 - 32256*a^23*b^12 + 2688*a^24*b^11 + 26880*a^25*b^10 - 5760*a^26*b^9 - 15360*a^27*b^8 + 4800*a^28*b^7 + 5760*a^29*b^6 - 2240*a^30*b^5 - 1280*a^31*b^4 + 576*a^32*b^3 + 128*a^33*b^2))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2))/(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(5*a^2 - 2*b^2)*((a + b)^5*(a - b)^5)^(1/2)*2i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
258,1,6093,227,5.245473,"\text{Not used}","int(cos(c + d*x)^2/(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4-3\,a^3\,b+3\,a^2\,b^2-a\,b^3+4\,b^4\right)}{a\,{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{2\,\mathrm{atan}\left(-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}}{64\,a^2\,b^{22}-192\,a^3\,b^{21}-640\,a^4\,b^{20}+1984\,a^5\,b^{19}+2624\,a^6\,b^{18}-8192\,a^7\,b^{17}-6400\,a^8\,b^{16}+18496\,a^9\,b^{15}+11072\,a^{10}\,b^{14}-25856\,a^{11}\,b^{13}-14464\,a^{12}\,b^{12}+23872\,a^{13}\,b^{11}+13760\,a^{14}\,b^{10}-15104\,a^{15}\,b^9-8704\,a^{16}\,b^8+6592\,a^{17}\,b^7+3200\,a^{18}\,b^6-1856\,a^{19}\,b^5-512\,a^{20}\,b^4+256\,a^{21}\,b^3-\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}+\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}{64\,a^2\,b^{22}-192\,a^3\,b^{21}-640\,a^4\,b^{20}+1984\,a^5\,b^{19}+2624\,a^6\,b^{18}-8192\,a^7\,b^{17}-6400\,a^8\,b^{16}+18496\,a^9\,b^{15}+11072\,a^{10}\,b^{14}-25856\,a^{11}\,b^{13}-14464\,a^{12}\,b^{12}+23872\,a^{13}\,b^{11}+13760\,a^{14}\,b^{10}-15104\,a^{15}\,b^9-8704\,a^{16}\,b^8+6592\,a^{17}\,b^7+3200\,a^{18}\,b^6-1856\,a^{19}\,b^5-512\,a^{20}\,b^4+256\,a^{21}\,b^3+\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}-\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,2{}\mathrm{i}}{d\,\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(a^4 - 3*a^3*b - a*b^3 + 4*b^4 + 3*a^2*b^2))/(a*(a + b)^2))/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - (2*atan(-((tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)/a^2 + (tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)/a^2)/(64*a^2*b^22 - 192*a^3*b^21 - 640*a^4*b^20 + 1984*a^5*b^19 + 2624*a^6*b^18 - 8192*a^7*b^17 - 6400*a^8*b^16 + 18496*a^9*b^15 + 11072*a^10*b^14 - 25856*a^11*b^13 - 14464*a^12*b^12 + 23872*a^13*b^11 + 13760*a^14*b^10 - 15104*a^15*b^9 - 8704*a^16*b^8 + 6592*a^17*b^7 + 3200*a^18*b^6 - 1856*a^19*b^5 - 512*a^20*b^4 + 256*a^21*b^3 - ((tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)*1i)/a^2 + ((tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)*1i)/a^2)))/(a^2*d) + tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (b^3*atan(((b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) + (b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))/(64*a^2*b^22 - 192*a^3*b^21 - 640*a^4*b^20 + 1984*a^5*b^19 + 2624*a^6*b^18 - 8192*a^7*b^17 - 6400*a^8*b^16 + 18496*a^9*b^15 + 11072*a^10*b^14 - 25856*a^11*b^13 - 14464*a^12*b^12 + 23872*a^13*b^11 + 13760*a^14*b^10 - 15104*a^15*b^9 - 8704*a^16*b^8 + 6592*a^17*b^7 + 3200*a^18*b^6 - 1856*a^19*b^5 - 512*a^20*b^4 + 256*a^21*b^3 + (b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) - (b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*2i)/(d*(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))","B"
259,1,213,219,1.125768,"\text{Not used}","int(cos(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^3-3\,a^2\,b+3\,a\,b^2-5\,b^3\right)}{{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{6\,a\,b^2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b + a^3 - 5*b^3))/(a + b)^2)/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (6*a*b^2*atanh((tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(3/2))))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
260,1,245,203,1.193198,"\text{Not used}","int(1/(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^3-3\,a^2\,b+7\,a\,b^2-b^3\right)}{{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-2{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)\,\left(2\,a^2+b^2\right)\,2{}\mathrm{i}}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(7*a*b^2 - 3*a^2*b + a^3 - b^3))/(a + b)^2)/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) + tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (b*atan((a^4*tan(c/2 + (d*x)/2)*1i + b^4*tan(c/2 + (d*x)/2)*1i - a^2*b^2*tan(c/2 + (d*x)/2)*2i)/((a + b)^(5/2)*(a - b)^(3/2)))*(2*a^2 + b^2)*2i)/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
261,1,245,136,1.207180,"\text{Not used}","int(1/(cos(c + d*x)*(a*sin(c + d*x) + b*tan(c + d*x))^2),x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^3-7\,a^2\,b+3\,a\,b^2-b^3\right)}{{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}-\frac{a\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-2{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)\,\left(a^2+2\,b^2\right)\,2{}\mathrm{i}}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 7*a^2*b + a^3 - b^3))/(a + b)^2)/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) - (a*atan((a^4*tan(c/2 + (d*x)/2)*1i + b^4*tan(c/2 + (d*x)/2)*1i - a^2*b^2*tan(c/2 + (d*x)/2)*2i)/((a + b)^(5/2)*(a - b)^(3/2)))*(a^2 + 2*b^2)*2i)/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
262,1,215,131,1.084123,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*sin(c + d*x) + b*tan(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{\frac{a^2-2\,a\,b+b^2}{a+b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{6\,a^2\,b\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + ((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b + 5*a^3 - b^3))/(a + b)^2)/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - (6*a^2*b*atanh((tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(3/2))))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
263,1,6056,231,5.206632,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x))^2),x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^4-a^3\,b+3\,a^2\,b^2-3\,a\,b^3+b^4\right)}{b\,{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)+\frac{32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{b^2}}{b^2}\right)\,1{}\mathrm{i}}{b^2}+\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)-\frac{32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{b^2}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}{256\,a^3\,b^{21}-512\,a^4\,b^{20}-1856\,a^5\,b^{19}+3200\,a^6\,b^{18}+6592\,a^7\,b^{17}-8704\,a^8\,b^{16}-15104\,a^9\,b^{15}+13760\,a^{10}\,b^{14}+23872\,a^{11}\,b^{13}-14464\,a^{12}\,b^{12}-25856\,a^{13}\,b^{11}+11072\,a^{14}\,b^{10}+18496\,a^{15}\,b^9-6400\,a^{16}\,b^8-8192\,a^{17}\,b^7+2624\,a^{18}\,b^6+1984\,a^{19}\,b^5-640\,a^{20}\,b^4-192\,a^{21}\,b^3+64\,a^{22}\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)+\frac{32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{b^2}}{b^2}}{b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)-\frac{32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{b^2}}{b^2}}{b^2}}\right)\,2{}\mathrm{i}}{b^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)\,1{}\mathrm{i}}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)\,1{}\mathrm{i}}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}}{256\,a^3\,b^{21}-512\,a^4\,b^{20}-1856\,a^5\,b^{19}+3200\,a^6\,b^{18}+6592\,a^7\,b^{17}-8704\,a^8\,b^{16}-15104\,a^9\,b^{15}+13760\,a^{10}\,b^{14}+23872\,a^{11}\,b^{13}-14464\,a^{12}\,b^{12}-25856\,a^{13}\,b^{11}+11072\,a^{14}\,b^{10}+18496\,a^{15}\,b^9-6400\,a^{16}\,b^8-8192\,a^{17}\,b^7+2624\,a^{18}\,b^6+1984\,a^{19}\,b^5-640\,a^{20}\,b^4-192\,a^{21}\,b^3+64\,a^{22}\,b^2-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}+\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{23}\,b^3+128\,a^{22}\,b^4+672\,a^{21}\,b^5-1376\,a^{20}\,b^6-3008\,a^{19}\,b^7+6528\,a^{18}\,b^8+7072\,a^{17}\,b^9-17632\,a^{16}\,b^{10}-8480\,a^{15}\,b^{11}+29600\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}-31744\,a^{12}\,b^{14}+8224\,a^{11}\,b^{15}+21344\,a^{10}\,b^{16}-12992\,a^9\,b^{17}-8128\,a^8\,b^{18}+9568\,a^7\,b^{19}+992\,a^6\,b^{20}-4000\,a^5\,b^{21}+480\,a^4\,b^{22}+928\,a^3\,b^{23}-224\,a^2\,b^{24}-96\,a\,b^{25}+32\,b^{26}\right)-\frac{a^3\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,b^{28}-32\,a\,b^{27}-352\,a^2\,b^{26}+480\,a^3\,b^{25}+1504\,a^4\,b^{24}-2688\,a^5\,b^{23}-3168\,a^6\,b^{22}+8064\,a^7\,b^{21}+2880\,a^8\,b^{20}-14784\,a^9\,b^{19}+1344\,a^{10}\,b^{18}+17472\,a^{11}\,b^{17}-6720\,a^{12}\,b^{16}-13440\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}+6528\,a^{15}\,b^{13}-5472\,a^{16}\,b^{12}-1824\,a^{17}\,b^{11}+2080\,a^{18}\,b^{10}+224\,a^{19}\,b^9-416\,a^{20}\,b^8+32\,a^{22}\,b^6+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-64\,a^{23}\,b^7+128\,a^{22}\,b^8+576\,a^{21}\,b^9-1280\,a^{20}\,b^{10}-2240\,a^{19}\,b^{11}+5760\,a^{18}\,b^{12}+4800\,a^{17}\,b^{13}-15360\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}+26880\,a^{14}\,b^{16}+2688\,a^{13}\,b^{17}-32256\,a^{12}\,b^{18}+2688\,a^{11}\,b^{19}+26880\,a^{10}\,b^{20}-5760\,a^9\,b^{21}-15360\,a^8\,b^{22}+4800\,a^7\,b^{23}+5760\,a^6\,b^{24}-2240\,a^5\,b^{25}-1280\,a^4\,b^{26}+576\,a^3\,b^{27}+128\,a^2\,b^{28}-64\,a\,b^{29}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}\right)}{-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}}}\right)\,\left(a-2\,b\right)\,\left(a+2\,b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{d\,\left(-a^{10}\,b^2+5\,a^8\,b^4-10\,a^6\,b^6+10\,a^4\,b^8-5\,a^2\,b^{10}+b^{12}\right)}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) + (tan(c/2 + (d*x)/2)^2*(4*a^4 - a^3*b - 3*a*b^3 + b^4 + 3*a^2*b^2))/(b*(a + b)^2))/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - (atan(-(((tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) + (32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 - (tan(c/2 + (d*x)/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/b^2)/b^2)*1i)/b^2 + ((tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) - (32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 + (tan(c/2 + (d*x)/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/b^2)/b^2)*1i)/b^2)/(256*a^3*b^21 - 512*a^4*b^20 - 1856*a^5*b^19 + 3200*a^6*b^18 + 6592*a^7*b^17 - 8704*a^8*b^16 - 15104*a^9*b^15 + 13760*a^10*b^14 + 23872*a^11*b^13 - 14464*a^12*b^12 - 25856*a^13*b^11 + 11072*a^14*b^10 + 18496*a^15*b^9 - 6400*a^16*b^8 - 8192*a^17*b^7 + 2624*a^18*b^6 + 1984*a^19*b^5 - 640*a^20*b^4 - 192*a^21*b^3 + 64*a^22*b^2 - (tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) + (32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 - (tan(c/2 + (d*x)/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/b^2)/b^2)/b^2 + (tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) - (32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 + (tan(c/2 + (d*x)/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/b^2)/b^2)/b^2))*2i)/(b^2*d) - tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (a^3*atan(((a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) + (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 - (a^3*tan(c/2 + (d*x)/2)*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))*1i)/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2) + (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) - (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 + (a^3*tan(c/2 + (d*x)/2)*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))*1i)/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))/(256*a^3*b^21 - 512*a^4*b^20 - 1856*a^5*b^19 + 3200*a^6*b^18 + 6592*a^7*b^17 - 8704*a^8*b^16 - 15104*a^9*b^15 + 13760*a^10*b^14 + 23872*a^11*b^13 - 14464*a^12*b^12 - 25856*a^13*b^11 + 11072*a^14*b^10 + 18496*a^15*b^9 - 6400*a^16*b^8 - 8192*a^17*b^7 + 2624*a^18*b^6 + 1984*a^19*b^5 - 640*a^20*b^4 - 192*a^21*b^3 + 64*a^22*b^2 - (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) + (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 - (a^3*tan(c/2 + (d*x)/2)*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2) + (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(tan(c/2 + (d*x)/2)*(32*b^26 - 96*a*b^25 - 224*a^2*b^24 + 928*a^3*b^23 + 480*a^4*b^22 - 4000*a^5*b^21 + 992*a^6*b^20 + 9568*a^7*b^19 - 8128*a^8*b^18 - 12992*a^9*b^17 + 21344*a^10*b^16 + 8224*a^11*b^15 - 31744*a^12*b^14 + 2176*a^13*b^13 + 29600*a^14*b^12 - 8480*a^15*b^11 - 17632*a^16*b^10 + 7072*a^17*b^9 + 6528*a^18*b^8 - 3008*a^19*b^7 - 1376*a^20*b^6 + 672*a^21*b^5 + 128*a^22*b^4 - 64*a^23*b^3) - (a^3*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(32*b^28 - 32*a*b^27 - 352*a^2*b^26 + 480*a^3*b^25 + 1504*a^4*b^24 - 2688*a^5*b^23 - 3168*a^6*b^22 + 8064*a^7*b^21 + 2880*a^8*b^20 - 14784*a^9*b^19 + 1344*a^10*b^18 + 17472*a^11*b^17 - 6720*a^12*b^16 - 13440*a^13*b^15 + 8256*a^14*b^14 + 6528*a^15*b^13 - 5472*a^16*b^12 - 1824*a^17*b^11 + 2080*a^18*b^10 + 224*a^19*b^9 - 416*a^20*b^8 + 32*a^22*b^6 + (a^3*tan(c/2 + (d*x)/2)*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^28 - 64*a*b^29 + 576*a^3*b^27 - 1280*a^4*b^26 - 2240*a^5*b^25 + 5760*a^6*b^24 + 4800*a^7*b^23 - 15360*a^8*b^22 - 5760*a^9*b^21 + 26880*a^10*b^20 + 2688*a^11*b^19 - 32256*a^12*b^18 + 2688*a^13*b^17 + 26880*a^14*b^16 - 5760*a^15*b^15 - 15360*a^16*b^14 + 4800*a^17*b^13 + 5760*a^18*b^12 - 2240*a^19*b^11 - 1280*a^20*b^10 + 576*a^21*b^9 + 128*a^22*b^8 - 64*a^23*b^7))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))/(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2)))*(a - 2*b)*(a + 2*b)*((a + b)^5*(a - b)^5)^(1/2)*2i)/(d*(b^12 - 5*a^2*b^10 + 10*a^4*b^8 - 10*a^6*b^6 + 5*a^8*b^4 - a^10*b^2))","B"
264,1,527,248,2.048687,"\text{Not used}","int(cos(c + d*x)^3/(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^7+5\,a^6\,b-10\,a^5\,b^2+10\,a^4\,b^3-5\,a^3\,b^4+97\,a^2\,b^5+16\,a\,b^6-16\,b^7\right)}{2\,a^2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}-\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^7-5\,a^6\,b+10\,a^5\,b^2-10\,a^4\,b^3+5\,a^3\,b^4-49\,a^2\,b^5+8\,b^7\right)}{a^2\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a+5\,b\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}-\frac{b^4\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(15\,a^4-4\,a^2\,b^2+b^4\right)}{a^3\,d\,{\left(a^2-b^2\right)}^4}","Not used",1,"((tan(c/2 + (d*x)/2)^4*(16*a*b^6 + 5*a^6*b - a^7 - 16*b^7 + 97*a^2*b^5 - 5*a^3*b^4 + 10*a^4*b^3 - 10*a^5*b^2))/(2*a^2*(a + b)*(2*a*b + a^2 + b^2)) - (3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) + (tan(c/2 + (d*x)/2)^2*(a^7 - 5*a^6*b + 8*b^7 - 49*a^2*b^5 + 5*a^3*b^4 - 10*a^4*b^3 + 10*a^5*b^2))/(a^2*(a + b)^2*(a - b)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) - tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a^3*d) - (log(tan(c/2 + (d*x)/2))*(2*a + 5*b))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2)) - (b^4*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(15*a^4 + b^4 - 4*a^2*b^2))/(a^3*d*(a^2 - b^2)^4)","B"
265,1,491,232,1.212011,"\text{Not used}","int(cos(c + d*x)^2/(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}-\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+85\,a\,b^4+15\,b^5\right)}{2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-5\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+45\,a\,b^4-b^5\right)}{\left(a-b\right)\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a+4\,b\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}+\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(10\,a^2\,b^3+2\,b^5\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) - ((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) + (tan(c/2 + (d*x)/2)^4*(85*a*b^4 - 5*a^4*b + a^5 + 15*b^5 - 10*a^2*b^3 + 10*a^3*b^2))/(2*(a + b)*(2*a*b + a^2 + b^2)) - (tan(c/2 + (d*x)/2)^2*(45*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))/((a - b)*(2*a*b + a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) - (log(tan(c/2 + (d*x)/2))*(a + 4*b))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2)) + (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(2*b^5 + 10*a^2*b^3))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
266,1,490,211,1.108596,"\text{Not used}","int(cos(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-5\,a^4\,b+10\,a^3\,b^2-42\,a^2\,b^3+5\,a\,b^4-9\,b^5\right)}{\left(a-b\right)\,\left(a^2+2\,a\,b+b^2\right)}-\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^5+5\,a^4\,b-10\,a^3\,b^2+74\,a^2\,b^3+11\,a\,b^4+17\,b^5\right)}{2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(6\,a^3\,b^2+6\,a\,b^4\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^2*(5*a*b^4 - 5*a^4*b + a^5 - 9*b^5 - 42*a^2*b^3 + 10*a^3*b^2))/((a - b)*(2*a*b + a^2 + b^2)) - (3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) + (tan(c/2 + (d*x)/2)^4*(11*a*b^4 + 5*a^4*b - a^5 + 17*b^5 + 74*a^2*b^3 - 10*a^3*b^2))/(2*(a + b)*(2*a*b + a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) - tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(6*a*b^4 + 6*a^3*b^2))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (3*b*log(tan(c/2 + (d*x)/2)))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2))","B"
267,1,494,229,1.129804,"\text{Not used}","int(1/(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}-\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^5-5\,a^4\,b+58\,a^3\,b^2+6\,a^2\,b^3+37\,a\,b^4-b^5\right)}{2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-5\,a^4\,b+34\,a^3\,b^2-10\,a^2\,b^3+21\,a\,b^4-b^5\right)}{\left(a-b\right)\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a-2\,b\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}+\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(3\,a^4\,b+8\,a^2\,b^3+b^5\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) - ((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) + (tan(c/2 + (d*x)/2)^4*(37*a*b^4 - 5*a^4*b + a^5 - b^5 + 6*a^2*b^3 + 58*a^3*b^2))/(2*(a + b)*(2*a*b + a^2 + b^2)) - (tan(c/2 + (d*x)/2)^2*(21*a*b^4 - 5*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 34*a^3*b^2))/((a - b)*(2*a*b + a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) + (log(tan(c/2 + (d*x)/2))*(a - 2*b))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2)) + (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(3*a^4*b + b^5 + 8*a^2*b^3))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
268,1,496,231,1.122226,"\text{Not used}","int(1/(cos(c + d*x)*(a*sin(c + d*x) + b*tan(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^5+37\,a^4\,b+6\,a^3\,b^2+58\,a^2\,b^3-5\,a\,b^4+b^5\right)}{2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}-\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-21\,a^4\,b+10\,a^3\,b^2-34\,a^2\,b^3+5\,a\,b^4-b^5\right)}{\left(a-b\right)\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a-b\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(a^5+8\,a^3\,b^2+3\,a\,b^4\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^4*(37*a^4*b - 5*a*b^4 - a^5 + b^5 + 58*a^2*b^3 + 6*a^3*b^2))/(2*(a + b)*(2*a*b + a^2 + b^2)) - (3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) + (tan(c/2 + (d*x)/2)^2*(5*a*b^4 - 21*a^4*b + a^5 - b^5 - 34*a^2*b^3 + 10*a^3*b^2))/((a - b)*(2*a*b + a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) - tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) + (log(tan(c/2 + (d*x)/2))*(2*a - b))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2)) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(3*a*b^4 + a^5 + 8*a^3*b^2))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
269,1,492,212,1.128559,"\text{Not used}","int(1/(cos(c + d*x)^2*(a*sin(c + d*x) + b*tan(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}-\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(9\,a^5-5\,a^4\,b+42\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5\right)}{\left(a-b\right)\,\left(a^2+2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(17\,a^5+11\,a^4\,b+74\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5\right)}{2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(6\,a^4\,b+6\,a^2\,b^3\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) - ((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) - (tan(c/2 + (d*x)/2)^2*(5*a*b^4 - 5*a^4*b + 9*a^5 - b^5 - 10*a^2*b^3 + 42*a^3*b^2))/((a - b)*(2*a*b + a^2 + b^2)) + (tan(c/2 + (d*x)/2)^4*(5*a*b^4 + 11*a^4*b + 17*a^5 - b^5 - 10*a^2*b^3 + 74*a^3*b^2))/(2*(a + b)*(2*a*b + a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) + (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(6*a^4*b + 6*a^2*b^3))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (3*a*log(tan(c/2 + (d*x)/2)))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2))","B"
270,1,490,228,1.132651,"\text{Not used}","int(1/(cos(c + d*x)^3*(a*sin(c + d*x) + b*tan(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(15\,a^5+85\,a^4\,b-10\,a^3\,b^2+10\,a^2\,b^3-5\,a\,b^4+b^5\right)}{2\,\left(a+b\right)\,\left(a^2+2\,a\,b+b^2\right)}-\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-45\,a^4\,b+10\,a^3\,b^2-10\,a^2\,b^3+5\,a\,b^4-b^5\right)}{\left(a-b\right)\,\left(a^2+2\,a\,b+b^2\right)}}{d\,\left(\left(4\,a^5-20\,a^4\,b+40\,a^3\,b^2-40\,a^2\,b^3+20\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(-8\,a^5+24\,a^4\,b-16\,a^3\,b^2-16\,a^2\,b^3+24\,a\,b^4-8\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a^5-4\,a^4\,b-8\,a^3\,b^2+8\,a^2\,b^3+4\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^3}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,a+b\right)}{d\,\left(2\,a^4+8\,a^3\,b+12\,a^2\,b^2+8\,a\,b^3+2\,b^4\right)}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(2\,a^5+10\,a^3\,b^2\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^4*(85*a^4*b - 5*a*b^4 + 15*a^5 + b^5 + 10*a^2*b^3 - 10*a^3*b^2))/(2*(a + b)*(2*a*b + a^2 + b^2)) - (3*a*b^2 - 3*a^2*b + a^3 - b^3)/(2*(a + b)) + (tan(c/2 + (d*x)/2)^2*(5*a*b^4 - 45*a^4*b + a^5 - b^5 - 10*a^2*b^3 + 10*a^3*b^2))/((a - b)*(2*a*b + a^2 + b^2)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^4 - 4*a^4*b + 4*a^5 - 4*b^5 + 8*a^2*b^3 - 8*a^3*b^2) - tan(c/2 + (d*x)/2)^4*(8*a^5 - 24*a^4*b - 24*a*b^4 + 8*b^5 + 16*a^2*b^3 + 16*a^3*b^2) + tan(c/2 + (d*x)/2)^6*(20*a*b^4 - 20*a^4*b + 4*a^5 - 4*b^5 - 40*a^2*b^3 + 40*a^3*b^2))) - tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^3) + (log(tan(c/2 + (d*x)/2))*(4*a + b))/(d*(8*a*b^3 + 8*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2)) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(2*a^5 + 10*a^3*b^2))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
271,1,861,155,7.512348,"\text{Not used}","int(cos(c + d*x)^m*(a*sin(c + d*x) + b*tan(c + d*x))^3,x)","\frac{{\left(\frac{1}{2}\right)}^m\,{\left({\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\right)}^m\,\left(\frac{a^3\,\left(\frac{m^4}{8}-\frac{5\,m^2}{8}+\frac{1}{2}\right)}{d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}+\frac{a^3\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\left(m^4-5\,m^2+4\right)}{8\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}-\frac{a\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(-m^3+m^2+4\,m-4\right)\,\left(a^2\,m+12\,b^2\,m-7\,a^2+36\,b^2\right)}{8\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}-\frac{a\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\left(-m^3+m^2+4\,m-4\right)\,\left(a^2\,m+12\,b^2\,m-7\,a^2+36\,b^2\right)}{8\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}+\frac{3\,a^2\,b\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\left(m^4+m^3-7\,m^2-m+6\right)}{4\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}+\frac{3\,a^2\,b\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(m^4+m^3-7\,m^2-m+6\right)}{4\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}-\frac{a\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(m^2-4\right)\,\left(a^2\,m^2+12\,a^2\,m-13\,a^2+6\,b^2\,m^2+60\,b^2\,m+126\,b^2\right)}{4\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}-\frac{a\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(m^2-4\right)\,\left(a^2\,m^2+12\,a^2\,m-13\,a^2+6\,b^2\,m^2+60\,b^2\,m+126\,b^2\right)}{4\,d\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}+\frac{b\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(b^2\,m-6\,a^2+2\,b^2\right)\,\left(m^4+m^3-7\,m^2-m+6\right)}{d\,m\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}+\frac{b\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(b^2\,m-6\,a^2+2\,b^2\right)\,\left(m^4+m^3-7\,m^2-m+6\right)}{d\,m\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}+\frac{b\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(-m^3-3\,m^2+m+3\right)\,\left(3\,a^2\,m^2+18\,a^2\,m-48\,a^2+4\,b^2\,m^2+16\,b^2\,m+16\,b^2\right)}{2\,d\,m\,\left(m^5+3\,m^4-5\,m^3-15\,m^2+4\,m+12\right)}\right)}{{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}}","Not used",1,"((1/2)^m*(exp(- c*1i - d*x*1i) + exp(c*1i + d*x*1i))^m*((a^3*(m^4/8 - (5*m^2)/8 + 1/2))/(d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) + (a^3*exp(c*10i + d*x*10i)*(m^4 - 5*m^2 + 4))/(8*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) - (a*exp(c*2i + d*x*2i)*(4*m + m^2 - m^3 - 4)*(a^2*m + 12*b^2*m - 7*a^2 + 36*b^2))/(8*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) - (a*exp(c*8i + d*x*8i)*(4*m + m^2 - m^3 - 4)*(a^2*m + 12*b^2*m - 7*a^2 + 36*b^2))/(8*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) + (3*a^2*b*exp(c*1i + d*x*1i)*(m^3 - 7*m^2 - m + m^4 + 6))/(4*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) + (3*a^2*b*exp(c*9i + d*x*9i)*(m^3 - 7*m^2 - m + m^4 + 6))/(4*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) - (a*exp(c*4i + d*x*4i)*(m^2 - 4)*(12*a^2*m + 60*b^2*m - 13*a^2 + 126*b^2 + a^2*m^2 + 6*b^2*m^2))/(4*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) - (a*exp(c*6i + d*x*6i)*(m^2 - 4)*(12*a^2*m + 60*b^2*m - 13*a^2 + 126*b^2 + a^2*m^2 + 6*b^2*m^2))/(4*d*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) + (b*exp(c*3i + d*x*3i)*(b^2*m - 6*a^2 + 2*b^2)*(m^3 - 7*m^2 - m + m^4 + 6))/(d*m*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) + (b*exp(c*7i + d*x*7i)*(b^2*m - 6*a^2 + 2*b^2)*(m^3 - 7*m^2 - m + m^4 + 6))/(d*m*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12)) + (b*exp(c*5i + d*x*5i)*(m - 3*m^2 - m^3 + 3)*(18*a^2*m + 16*b^2*m - 48*a^2 + 16*b^2 + 3*a^2*m^2 + 4*b^2*m^2))/(2*d*m*(4*m - 15*m^2 - 5*m^3 + 3*m^4 + m^5 + 12))))/(exp(c*3i + d*x*3i) + 2*exp(c*5i + d*x*5i) + exp(c*7i + d*x*7i))","B"
272,0,-1,264,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a*sin(c + d*x) + b*tan(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a\,\sin\left(c+d\,x\right)+b\,\mathrm{tan}\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^m*(a*sin(c + d*x) + b*tan(c + d*x))^2, x)","F"
273,1,35,39,0.978559,"\text{Not used}","int(cos(c + d*x)^m*(a*sin(c + d*x) + b*tan(c + d*x)),x)","-\frac{{\cos\left(c+d\,x\right)}^m\,\left(b+b\,m+a\,m\,\cos\left(c+d\,x\right)\right)}{d\,m\,\left(m+1\right)}","Not used",1,"-(cos(c + d*x)^m*(b + b*m + a*m*cos(c + d*x)))/(d*m*(m + 1))","B"
274,0,-1,144,0.000000,"\text{Not used}","int(cos(c + d*x)^m/(a*sin(c + d*x) + b*tan(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\cos\left(c+d\,x\right)}^m}{\sin\left(c+d\,x\right)\,\left(b+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((cos(c + d*x)*cos(c + d*x)^m)/(sin(c + d*x)*(b + a*cos(c + d*x))), x)","F"
275,1,93,65,1.380914,"\text{Not used}","int((cos(x)*sin(x))/(a*cos(x) + b*sin(x)),x)","\frac{2\,a\,b\,\mathrm{atanh}\left(\frac{2\,a^2\,b+2\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+b^2\right)}{2\,{\left(a^2+b^2\right)}^{3/2}}\right)}{{\left(a^2+b^2\right)}^{3/2}}-\frac{\frac{2\,a}{a^2+b^2}-\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"(2*a*b*atanh((2*a^2*b + 2*b^3 - 2*a*tan(x/2)*(a^2 + b^2))/(2*(a^2 + b^2)^(3/2))))/(a^2 + b^2)^(3/2) - ((2*a)/(a^2 + b^2) - (2*b*tan(x/2))/(a^2 + b^2))/(tan(x/2)^2 + 1)","B"
276,1,3401,92,6.232507,"\text{Not used}","int((cos(x)*sin(x)^2)/(a*cos(x) + b*sin(x)),x)","\frac{\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^2+b^2}-\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2+b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{a^2\,b\,\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{4\,a^2\,b\,\left(\frac{a\,\left(a+b\right)\,\left(\frac{8\,\left(12\,a^9\,b+24\,a^7\,b^3+12\,a^5\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^2\,b\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a^3\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{a\,\left(\frac{8\,\left(a^9-8\,a^7\,b^2-7\,a^5\,b^4+2\,a^3\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a^2\,b\,\left(\frac{8\,\left(12\,a^9\,b+24\,a^7\,b^3+12\,a^5\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^2\,b\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)\,\left(a+b\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{a^3\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^6-35\,a^4\,b^2+35\,a^2\,b^4-b^6\right)}{{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}-\frac{2\,a\,b\,\left(5\,a^4-26\,a^2\,b^2+5\,b^4\right)\,\left(\frac{8\,\left(a^7\,b+2\,a^5\,b^3\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a^2\,b\,\left(\frac{8\,\left(a^9-8\,a^7\,b^2-7\,a^5\,b^4+2\,a^3\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a^2\,b\,\left(\frac{8\,\left(12\,a^9\,b+24\,a^7\,b^3+12\,a^5\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^2\,b\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{a\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{a\,\left(a+b\right)\,\left(\frac{8\,\left(12\,a^9\,b+24\,a^7\,b^3+12\,a^5\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^2\,b\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a^3\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{8\,a^4\,b\,{\left(a+b\right)}^2\,{\left(a-b\right)}^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{4\,a^6-4\,a^4\,b^2}+\frac{\left(\frac{a\,\left(a+b\right)\,\left(\frac{8\,\left(3\,a^8\,b+6\,a^6\,b^3+3\,a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a^2\,b\,\left(\frac{8\,\left(-2\,a^{10}+4\,a^8\,b^2+12\,a^6\,b^4+4\,a^4\,b^6-2\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^2\,b\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{4\,a^2\,b\,\left(\frac{a\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(-2\,a^{10}+4\,a^8\,b^2+12\,a^6\,b^4+4\,a^4\,b^6-2\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^2\,b\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{16\,a^3\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{a^3\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^6-35\,a^4\,b^2+35\,a^2\,b^4-b^6\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(4\,a^6-4\,a^4\,b^2\right)\,{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}+\frac{2\,a\,b\,\left(5\,a^4-26\,a^2\,b^2+5\,b^4\right)\,\left(\frac{8\,a^6\,b^2}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a^2\,b\,\left(\frac{8\,\left(3\,a^8\,b+6\,a^6\,b^3+3\,a^4\,b^5\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a^2\,b\,\left(\frac{8\,\left(-2\,a^{10}+4\,a^8\,b^2+12\,a^6\,b^4+4\,a^4\,b^6-2\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^2\,b\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{a\,\left(\frac{a\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(-2\,a^{10}+4\,a^8\,b^2+12\,a^6\,b^4+4\,a^4\,b^6-2\,a^2\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^2\,b\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{16\,a^3\,b\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{8\,a^4\,b\,{\left(a+b\right)}^2\,{\left(a-b\right)}^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(4\,a^6-4\,a^4\,b^2\right)\,{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}\right)\,\left(a+b\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}","Not used",1,"((a*tan(x/2)^3)/(a^2 + b^2) - (a*tan(x/2))/(a^2 + b^2) + (2*b*tan(x/2)^2)/(a^2 + b^2))/(2*tan(x/2)^2 + tan(x/2)^4 + 1) + (a^2*b*log(a + 2*b*tan(x/2) - a*tan(x/2)^2))/(a^4 + b^4 + 2*a^2*b^2) - (4*a^2*b*log(1/(cos(x) + 1)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (a*atan((tan(x/2)*((((4*a^2*b*((a*(a + b)*((8*(12*a^9*b + 12*a^5*b^5 + 24*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^2*b*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a^3*b*(a + b)*(a - b)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (a*((8*(a^9 + 2*a^3*b^6 - 7*a^5*b^4 - 8*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a^2*b*((8*(12*a^9*b + 12*a^5*b^5 + 24*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^2*b*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2))*(a + b)*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (a^3*(a + b)^3*(a - b)^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^6 - b^6 + 35*a^2*b^4 - 35*a^4*b^2))/(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2 - (2*a*b*(5*a^4 + 5*b^4 - 26*a^2*b^2)*((8*(a^7*b + 2*a^5*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a^2*b*((8*(a^9 + 2*a^3*b^6 - 7*a^5*b^4 - 8*a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a^2*b*((8*(12*a^9*b + 12*a^5*b^5 + 24*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^2*b*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (a*(a + b)*(a - b)*((a*(a + b)*((8*(12*a^9*b + 12*a^5*b^5 + 24*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^2*b*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a^3*b*(a + b)*(a - b)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (8*a^4*b*(a + b)^2*(a - b)^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/(4*a^6 - 4*a^4*b^2) + (((a*(a + b)*((8*(3*a^8*b + 3*a^4*b^5 + 6*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a^2*b*((8*(4*a^4*b^6 - 2*a^2*b^8 - 2*a^10 + 12*a^6*b^4 + 4*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^2*b*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2))*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (4*a^2*b*((a*(a + b)*(a - b)*((8*(4*a^4*b^6 - 2*a^2*b^8 - 2*a^10 + 12*a^6*b^4 + 4*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^2*b*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (16*a^3*b*(a + b)*(a - b)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (a^3*(a + b)^3*(a - b)^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^6 - b^6 + 35*a^2*b^4 - 35*a^4*b^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a^6 - 4*a^4*b^2)*(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2) + (2*a*b*(5*a^4 + 5*b^4 - 26*a^2*b^2)*((8*a^6*b^2)/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a^2*b*((8*(3*a^8*b + 3*a^4*b^5 + 6*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a^2*b*((8*(4*a^4*b^6 - 2*a^2*b^8 - 2*a^10 + 12*a^6*b^4 + 4*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^2*b*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (a*((a*(a + b)*(a - b)*((8*(4*a^4*b^6 - 2*a^2*b^8 - 2*a^10 + 12*a^6*b^4 + 4*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^2*b*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (16*a^3*b*(a + b)*(a - b)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (8*a^4*b*(a + b)^2*(a - b)^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a^6 - 4*a^4*b^2)*(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2))*(a + b)*(a - b))/(a^4 + b^4 + 2*a^2*b^2)","B"
277,1,286,122,1.195252,"\text{Not used}","int((cos(x)*sin(x)^3)/(a*cos(x) + b*sin(x)),x)","\frac{\frac{2\,\left(a\,b^2-2\,a^3\right)}{3\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(5\,a^2\,b+2\,b^3\right)}{3\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{4\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4+2\,a^2\,b^2+b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{2\,a^3\,b\,\mathrm{atanh}\left(\frac{2\,a^4\,b+2\,b^5+4\,a^2\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{2\,{\left(a^2+b^2\right)}^{5/2}}\right)}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"((2*(a*b^2 - 2*a^3))/(3*(a^4 + b^4 + 2*a^2*b^2)) + (4*tan(x/2)^3*(5*a^2*b + 2*b^3))/(3*(a^4 + b^4 + 2*a^2*b^2)) - (4*a^3*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b^2*tan(x/2)^4)/(a^4 + b^4 + 2*a^2*b^2) + (2*a^2*b*tan(x/2)^5)/(a^4 + b^4 + 2*a^2*b^2) + (2*a^2*b*tan(x/2))/(a^4 + b^4 + 2*a^2*b^2))/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1) + (2*a^3*b*atanh((2*a^4*b + 2*b^5 + 4*a^2*b^3 - 2*a*tan(x/2)*(a^4 + b^4 + 2*a^2*b^2))/(2*(a^2 + b^2)^(5/2))))/(a^2 + b^2)^(5/2)","B"
278,1,3419,93,6.186761,"\text{Not used}","int((cos(x)^2*sin(x))/(a*cos(x) + b*sin(x)),x)","\frac{\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2+b^2}-\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^2+b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{a\,b^2\,\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{4\,a\,b^2\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{4\,a\,b^2\,\left(\frac{b\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(12\,a^8\,b^2+24\,a^6\,b^4+12\,a^4\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a\,b^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a\,b^3\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}-\frac{b\,\left(a+b\right)\,\left(\frac{8\,\left(a^7\,b^2-8\,a^5\,b^4-7\,a^3\,b^6+2\,a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a\,b^2\,\left(\frac{8\,\left(12\,a^8\,b^2+24\,a^6\,b^4+12\,a^4\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a\,b^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{b^3\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^6-35\,a^4\,b^2+35\,a^2\,b^4-b^6\right)}{{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}-\frac{2\,a\,b\,\left(5\,a^4-26\,a^2\,b^2+5\,b^4\right)\,\left(\frac{8\,\left(a^4\,b^4+2\,a^2\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a\,b^2\,\left(\frac{8\,\left(a^7\,b^2-8\,a^5\,b^4-7\,a^3\,b^6+2\,a\,b^8\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a\,b^2\,\left(\frac{8\,\left(12\,a^8\,b^2+24\,a^6\,b^4+12\,a^4\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a\,b^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{b\,\left(\frac{b\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(12\,a^8\,b^2+24\,a^6\,b^4+12\,a^4\,b^6\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a\,b^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{16\,a\,b^3\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{8\,a\,b^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^2\,\left(12\,a^9\,b^2+48\,a^7\,b^4+72\,a^5\,b^6+48\,a^3\,b^8+12\,a\,b^{10}\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{4\,a\,b^5-4\,a^3\,b^3}+\frac{\left(\frac{b\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(3\,a^6\,b^3+6\,a^4\,b^5+3\,a^2\,b^7\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a\,b^2\,\left(\frac{8\,\left(-2\,a^9\,b+4\,a^7\,b^3+12\,a^5\,b^5+4\,a^3\,b^7-2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a\,b^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{4\,a\,b^2\,\left(\frac{b\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(-2\,a^9\,b+4\,a^7\,b^3+12\,a^5\,b^5+4\,a^3\,b^7-2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a\,b^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{16\,a\,b^3\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{b^3\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^6-35\,a^4\,b^2+35\,a^2\,b^4-b^6\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(4\,a\,b^5-4\,a^3\,b^3\right)\,{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}+\frac{2\,a\,b\,\left(5\,a^4-26\,a^2\,b^2+5\,b^4\right)\,\left(\frac{8\,a^3\,b^5}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{4\,a\,b^2\,\left(\frac{8\,\left(3\,a^6\,b^3+6\,a^4\,b^5+3\,a^2\,b^7\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,a\,b^2\,\left(\frac{8\,\left(-2\,a^9\,b+4\,a^7\,b^3+12\,a^5\,b^5+4\,a^3\,b^7-2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a\,b^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}\right)}{4\,a^4+8\,a^2\,b^2+4\,b^4}+\frac{b\,\left(\frac{b\,\left(a+b\right)\,\left(a-b\right)\,\left(\frac{8\,\left(-2\,a^9\,b+4\,a^7\,b^3+12\,a^5\,b^5+4\,a^3\,b^7-2\,a\,b^9\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a\,b^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{16\,a\,b^3\,\left(a+b\right)\,\left(a-b\right)\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a+b\right)\,\left(a-b\right)}{2\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{8\,a\,b^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^2\,\left(12\,a^{10}\,b+48\,a^8\,b^3+72\,a^6\,b^5+48\,a^4\,b^7+12\,a^2\,b^9\right)}{\left(4\,a^4+8\,a^2\,b^2+4\,b^4\right)\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(a^{10}+5\,a^8\,b^2+10\,a^6\,b^4+10\,a^4\,b^6+5\,a^2\,b^8+b^{10}\right)}{\left(4\,a\,b^5-4\,a^3\,b^3\right)\,{\left(a^6+15\,a^4\,b^2+15\,a^2\,b^4+b^6\right)}^2}\right)\,\left(a+b\right)\,\left(a-b\right)}{a^4+2\,a^2\,b^2+b^4}","Not used",1,"((b*tan(x/2))/(a^2 + b^2) + (2*a*tan(x/2)^2)/(a^2 + b^2) - (b*tan(x/2)^3)/(a^2 + b^2))/(2*tan(x/2)^2 + tan(x/2)^4 + 1) - (a*b^2*log(a + 2*b*tan(x/2) - a*tan(x/2)^2))/(a^4 + b^4 + 2*a^2*b^2) + (4*a*b^2*log(1/(cos(x) + 1)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (b*atan((tan(x/2)*((((4*a*b^2*((b*(a + b)*(a - b)*((8*(12*a^4*b^6 + 24*a^6*b^4 + 12*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a*b^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a*b^3*(a + b)*(a - b)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) - (b*(a + b)*((8*(2*a*b^8 - 7*a^3*b^6 - 8*a^5*b^4 + a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a*b^2*((8*(12*a^4*b^6 + 24*a^6*b^4 + 12*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a*b^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2))*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (b^3*(a + b)^3*(a - b)^3*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^6 - b^6 + 35*a^2*b^4 - 35*a^4*b^2))/(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2 - (2*a*b*(5*a^4 + 5*b^4 - 26*a^2*b^2)*((8*(2*a^2*b^6 + a^4*b^4))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a*b^2*((8*(2*a*b^8 - 7*a^3*b^6 - 8*a^5*b^4 + a^7*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a*b^2*((8*(12*a^4*b^6 + 24*a^6*b^4 + 12*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a*b^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (b*((b*(a + b)*(a - b)*((8*(12*a^4*b^6 + 24*a^6*b^4 + 12*a^8*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a*b^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (16*a*b^3*(a + b)*(a - b)*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (8*a*b^4*(a + b)^2*(a - b)^2*(12*a*b^10 + 48*a^3*b^8 + 72*a^5*b^6 + 48*a^7*b^4 + 12*a^9*b^2))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/(4*a*b^5 - 4*a^3*b^3) + (((b*(a + b)*(a - b)*((8*(3*a^2*b^7 + 6*a^4*b^5 + 3*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a*b^2*((8*(4*a^3*b^7 - 2*a^9*b - 2*a*b^9 + 12*a^5*b^5 + 4*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a*b^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(2*(a^4 + b^4 + 2*a^2*b^2)) - (4*a*b^2*((b*(a + b)*(a - b)*((8*(4*a^3*b^7 - 2*a^9*b - 2*a*b^9 + 12*a^5*b^5 + 4*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a*b^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (16*a*b^3*(a + b)*(a - b)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (b^3*(a + b)^3*(a - b)^3*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((a^4 + b^4 + 2*a^2*b^2)^3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^6 - b^6 + 35*a^2*b^4 - 35*a^4*b^2)*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a*b^5 - 4*a^3*b^3)*(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2) + (2*a*b*(5*a^4 + 5*b^4 - 26*a^2*b^2)*((8*a^3*b^5)/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (4*a*b^2*((8*(3*a^2*b^7 + 6*a^4*b^5 + 3*a^6*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*a*b^2*((8*(4*a^3*b^7 - 2*a^9*b - 2*a*b^9 + 12*a^5*b^5 + 4*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a*b^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(4*a^4 + 4*b^4 + 8*a^2*b^2)))/(4*a^4 + 4*b^4 + 8*a^2*b^2) + (b*((b*(a + b)*(a - b)*((8*(4*a^3*b^7 - 2*a^9*b - 2*a*b^9 + 12*a^5*b^5 + 4*a^7*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a*b^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (16*a*b^3*(a + b)*(a - b)*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a + b)*(a - b))/(2*(a^4 + b^4 + 2*a^2*b^2)) + (8*a*b^4*(a + b)^2*(a - b)^2*(12*a^10*b + 12*a^2*b^9 + 48*a^4*b^7 + 72*a^6*b^5 + 48*a^8*b^3))/((4*a^4 + 4*b^4 + 8*a^2*b^2)*(a^4 + b^4 + 2*a^2*b^2)^2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(a^10 + b^10 + 5*a^2*b^8 + 10*a^4*b^6 + 10*a^6*b^4 + 5*a^8*b^2))/((4*a*b^5 - 4*a^3*b^3)*(a^6 + b^6 + 15*a^2*b^4 + 15*a^4*b^2)^2))*(a + b)*(a - b))/(a^4 + b^4 + 2*a^2*b^2)","B"
279,1,277,112,1.001406,"\text{Not used}","int((cos(x)^2*sin(x)^2)/(a*cos(x) + b*sin(x)),x)","-\frac{\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a\,b^2-2\,a^3\right)}{3\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,b\,\left(2\,a^2-b^2\right)}{3\,{\left(a^2+b^2\right)}^2}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^4+2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4+2\,a^2\,b^2+b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{2\,a^2\,b^2\,\mathrm{atanh}\left(\frac{2\,a^4\,b+2\,b^5+4\,a^2\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{2\,{\left(a^2+b^2\right)}^{5/2}}\right)}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"- ((4*tan(x/2)^3*(a*b^2 - 2*a^3))/(3*(a^4 + b^4 + 2*a^2*b^2)) - (2*b*(2*a^2 - b^2))/(3*(a^2 + b^2)^2) + (2*b^3*tan(x/2)^4)/(a^4 + b^4 + 2*a^2*b^2) - (4*a^2*b*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b^2*tan(x/2)^5)/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b^2*tan(x/2))/(a^4 + b^4 + 2*a^2*b^2))/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1) - (2*a^2*b^2*atanh((2*a^4*b + 2*b^5 + 4*a^2*b^3 - 2*a*tan(x/2)*(a^4 + b^4 + 2*a^2*b^2))/(2*(a^2 + b^2)^(5/2))))/(a^2 + b^2)^(5/2)","B"
280,1,5902,176,11.949078,"\text{Not used}","int((cos(x)^2*sin(x)^3)/(a*cos(x) + b*sin(x)),x)","\frac{64\,a^3\,b^2\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{64\,a^3\,b^2\,\left(\frac{b\,\left(\frac{176\,a^{14}\,b^2+672\,a^{12}\,b^4+912\,a^{10}\,b^6+448\,a^8\,b^8-48\,a^6\,b^{10}-96\,a^4\,b^{12}-16\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{b\,\left(\frac{9\,a^{13}\,b^2-105\,a^{11}\,b^4-156\,a^9\,b^6+62\,a^7\,b^8+129\,a^5\,b^{10}+27\,a^3\,b^{12}+2\,a\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,a^3\,b^2\,\left(\frac{176\,a^{14}\,b^2+672\,a^{12}\,b^4+912\,a^{10}\,b^6+448\,a^8\,b^8-48\,a^6\,b^{10}-96\,a^4\,b^{12}-16\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{b^3\,{\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{1024\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(9\,a^{10}-493\,a^8\,b^2+706\,a^6\,b^4+46\,a^4\,b^6-11\,a^2\,b^8-b^{10}\right)}{{\left(9\,a^{10}+229\,a^8\,b^2+250\,a^6\,b^4+42\,a^4\,b^6+13\,a^2\,b^8+b^{10}\right)}^2}+\frac{2\,a\,b\,\left(\frac{9\,a^{10}\,b^4+44\,a^8\,b^6+21\,a^6\,b^8+2\,a^4\,b^{10}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,a^3\,b^2\,\left(\frac{9\,a^{13}\,b^2-105\,a^{11}\,b^4-156\,a^9\,b^6+62\,a^7\,b^8+129\,a^5\,b^{10}+27\,a^3\,b^{12}+2\,a\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,a^3\,b^2\,\left(\frac{176\,a^{14}\,b^2+672\,a^{12}\,b^4+912\,a^{10}\,b^6+448\,a^8\,b^8-48\,a^6\,b^{10}-96\,a^4\,b^{12}-16\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}+\frac{b\,\left(\frac{b\,\left(\frac{176\,a^{14}\,b^2+672\,a^{12}\,b^4+912\,a^{10}\,b^6+448\,a^8\,b^8-48\,a^6\,b^{10}-96\,a^4\,b^{12}-16\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{a^3\,b^4\,{\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{2\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(57\,a^8-436\,a^6\,b^2+110\,a^4\,b^4+28\,a^2\,b^6+b^8\right)}{{\left(9\,a^{10}+229\,a^8\,b^2+250\,a^6\,b^4+42\,a^4\,b^6+13\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{-3\,a^5\,b^3+6\,a^3\,b^5+a\,b^7}+\frac{\left(\frac{64\,a^3\,b^2\,\left(\frac{b\,\left(\frac{24\,a^{15}\,b-40\,a^{13}\,b^3-360\,a^{11}\,b^5-552\,a^9\,b^7-248\,a^7\,b^9+72\,a^5\,b^{11}+72\,a^3\,b^{13}+8\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}+\frac{b\,\left(\frac{39\,a^{12}\,b^3+123\,a^{10}\,b^5+134\,a^8\,b^7+54\,a^6\,b^9+3\,a^4\,b^{11}-a^2\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,a^3\,b^2\,\left(\frac{24\,a^{15}\,b-40\,a^{13}\,b^3-360\,a^{11}\,b^5-552\,a^9\,b^7-248\,a^7\,b^9+72\,a^5\,b^{11}+72\,a^3\,b^{13}+8\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{b^3\,{\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{1024\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(9\,a^{10}-493\,a^8\,b^2+706\,a^6\,b^4+46\,a^4\,b^6-11\,a^2\,b^8-b^{10}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{\left(-3\,a^5\,b^3+6\,a^3\,b^5+a\,b^7\right)\,{\left(9\,a^{10}+229\,a^8\,b^2+250\,a^6\,b^4+42\,a^4\,b^6+13\,a^2\,b^8+b^{10}\right)}^2}+\frac{2\,a\,b\,\left(\frac{-15\,a^9\,b^5+2\,a^7\,b^7+a^5\,b^9}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{b\,\left(\frac{b\,\left(\frac{24\,a^{15}\,b-40\,a^{13}\,b^3-360\,a^{11}\,b^5-552\,a^9\,b^7-248\,a^7\,b^9+72\,a^5\,b^{11}+72\,a^3\,b^{13}+8\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,a^3\,b^2\,\left(\frac{39\,a^{12}\,b^3+123\,a^{10}\,b^5+134\,a^8\,b^7+54\,a^6\,b^9+3\,a^4\,b^{11}-a^2\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,a^3\,b^2\,\left(\frac{24\,a^{15}\,b-40\,a^{13}\,b^3-360\,a^{11}\,b^5-552\,a^9\,b^7-248\,a^7\,b^9+72\,a^5\,b^{11}+72\,a^3\,b^{13}+8\,a\,b^{15}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^3\,b^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{a^3\,b^4\,{\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{2\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(57\,a^8-436\,a^6\,b^2+110\,a^4\,b^4+28\,a^2\,b^6+b^8\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{\left(-3\,a^5\,b^3+6\,a^3\,b^5+a\,b^7\right)\,{\left(9\,a^{10}+229\,a^8\,b^2+250\,a^6\,b^4+42\,a^4\,b^6+13\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(-3\,a^4+6\,a^2\,b^2+b^4\right)}{4\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{a^3\,b^2\,\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(3\,a^2\,b-b^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(11\,a^2\,b+7\,b^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(11\,a^2\,b+7\,b^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2\,b-b^3\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{4\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{a^4+2\,a^2\,b^2+b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"(64*a^3*b^2*log(1/(cos(x) + 1)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (b*atan((tan(x/2)*((((64*a^3*b^2*((b*((448*a^8*b^8 - 96*a^4*b^12 - 48*a^6*b^10 - 16*a^2*b^14 + 912*a^10*b^6 + 672*a^12*b^4 + 176*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(b^4 - 3*a^4 + 6*a^2*b^2)*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (b*((2*a*b^14 + 27*a^3*b^12 + 129*a^5*b^10 + 62*a^7*b^8 - 156*a^9*b^6 - 105*a^11*b^4 + 9*a^13*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*a^3*b^2*((448*a^8*b^8 - 96*a^4*b^12 - 48*a^6*b^10 - 16*a^2*b^14 + 912*a^10*b^6 + 672*a^12*b^4 + 176*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (b^3*(b^4 - 3*a^4 + 6*a^2*b^2)^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/(1024*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(9*a^10 - b^10 - 11*a^2*b^8 + 46*a^4*b^6 + 706*a^6*b^4 - 493*a^8*b^2))/(9*a^10 + b^10 + 13*a^2*b^8 + 42*a^4*b^6 + 250*a^6*b^4 + 229*a^8*b^2)^2 + (2*a*b*((2*a^4*b^10 + 21*a^6*b^8 + 44*a^8*b^6 + 9*a^10*b^4)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*a^3*b^2*((2*a*b^14 + 27*a^3*b^12 + 129*a^5*b^10 + 62*a^7*b^8 - 156*a^9*b^6 - 105*a^11*b^4 + 9*a^13*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*a^3*b^2*((448*a^8*b^8 - 96*a^4*b^12 - 48*a^6*b^10 - 16*a^2*b^14 + 912*a^10*b^6 + 672*a^12*b^4 + 176*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) + (b*((b*((448*a^8*b^8 - 96*a^4*b^12 - 48*a^6*b^10 - 16*a^2*b^14 + 912*a^10*b^6 + 672*a^12*b^4 + 176*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(b^4 - 3*a^4 + 6*a^2*b^2)*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (a^3*b^4*(b^4 - 3*a^4 + 6*a^2*b^2)^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/(2*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(57*a^8 + b^8 + 28*a^2*b^6 + 110*a^4*b^4 - 436*a^6*b^2))/(9*a^10 + b^10 + 13*a^2*b^8 + 42*a^4*b^6 + 250*a^6*b^4 + 229*a^8*b^2)^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/(a*b^7 + 6*a^3*b^5 - 3*a^5*b^3) + (((64*a^3*b^2*((b*((8*a*b^15 + 24*a^15*b + 72*a^3*b^13 + 72*a^5*b^11 - 248*a^7*b^9 - 552*a^9*b^7 - 360*a^11*b^5 - 40*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(b^4 - 3*a^4 + 6*a^2*b^2)*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) + (b*((3*a^4*b^11 - a^2*b^13 + 54*a^6*b^9 + 134*a^8*b^7 + 123*a^10*b^5 + 39*a^12*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*a^3*b^2*((8*a*b^15 + 24*a^15*b + 72*a^3*b^13 + 72*a^5*b^11 - 248*a^7*b^9 - 552*a^9*b^7 - 360*a^11*b^5 - 40*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (b^3*(b^4 - 3*a^4 + 6*a^2*b^2)^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/(1024*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(9*a^10 - b^10 - 11*a^2*b^8 + 46*a^4*b^6 + 706*a^6*b^4 - 493*a^8*b^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/((a*b^7 + 6*a^3*b^5 - 3*a^5*b^3)*(9*a^10 + b^10 + 13*a^2*b^8 + 42*a^4*b^6 + 250*a^6*b^4 + 229*a^8*b^2)^2) + (2*a*b*((a^5*b^9 + 2*a^7*b^7 - 15*a^9*b^5)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (b*((b*((8*a*b^15 + 24*a^15*b + 72*a^3*b^13 + 72*a^5*b^11 - 248*a^7*b^9 - 552*a^9*b^7 - 360*a^11*b^5 - 40*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(b^4 - 3*a^4 + 6*a^2*b^2)*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(b^4 - 3*a^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*a^3*b^2*((3*a^4*b^11 - a^2*b^13 + 54*a^6*b^9 + 134*a^8*b^7 + 123*a^10*b^5 + 39*a^12*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*a^3*b^2*((8*a*b^15 + 24*a^15*b + 72*a^3*b^13 + 72*a^5*b^11 - 248*a^7*b^9 - 552*a^9*b^7 - 360*a^11*b^5 - 40*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^3*b^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (a^3*b^4*(b^4 - 3*a^4 + 6*a^2*b^2)^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/(2*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(57*a^8 + b^8 + 28*a^2*b^6 + 110*a^4*b^4 - 436*a^6*b^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/((a*b^7 + 6*a^3*b^5 - 3*a^5*b^3)*(9*a^10 + b^10 + 13*a^2*b^8 + 42*a^4*b^6 + 250*a^6*b^4 + 229*a^8*b^2)^2))*(b^4 - 3*a^4 + 6*a^2*b^2))/(4*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (a^3*b^2*log(a + 2*b*tan(x/2) - a*tan(x/2)^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - ((tan(x/2)^7*(3*a^2*b - b^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - (tan(x/2)^3*(11*a^2*b + 7*b^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (tan(x/2)^5*(11*a^2*b + 7*b^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - (tan(x/2)*(3*a^2*b - b^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - (4*a^3*tan(x/2)^4)/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b^2*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b^2*tan(x/2)^6)/(a^4 + b^4 + 2*a^2*b^2))/(4*tan(x/2)^2 + 6*tan(x/2)^4 + 4*tan(x/2)^6 + tan(x/2)^8 + 1)","B"
281,1,291,123,1.264598,"\text{Not used}","int((cos(x)^3*sin(x))/(a*cos(x) + b*sin(x)),x)","\frac{2\,a\,b^3\,\mathrm{atanh}\left(\frac{2\,a^4\,b+2\,b^5+4\,a^2\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{2\,{\left(a^2+b^2\right)}^{5/2}}\right)}{{\left(a^2+b^2\right)}^{5/2}}-\frac{\frac{2\,\left(a^3+4\,a\,b^2\right)}{3\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(2\,a^2\,b-b^3\right)}{3\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^3+2\,a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^4+2\,a^2\,b^2+b^4}+\frac{4\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}","Not used",1,"(2*a*b^3*atanh((2*a^4*b + 2*b^5 + 4*a^2*b^3 - 2*a*tan(x/2)*(a^4 + b^4 + 2*a^2*b^2))/(2*(a^2 + b^2)^(5/2))))/(a^2 + b^2)^(5/2) - ((2*(4*a*b^2 + a^3))/(3*(a^4 + b^4 + 2*a^2*b^2)) + (4*tan(x/2)^3*(2*a^2*b - b^3))/(3*(a^4 + b^4 + 2*a^2*b^2)) - (2*b^3*tan(x/2))/(a^4 + b^4 + 2*a^2*b^2) + (2*tan(x/2)^4*(2*a*b^2 + a^3))/(a^4 + b^4 + 2*a^2*b^2) - (2*b^3*tan(x/2)^5)/(a^4 + b^4 + 2*a^2*b^2) + (4*a*b^2*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2))/(3*tan(x/2)^2 + 3*tan(x/2)^4 + tan(x/2)^6 + 1)","B"
282,1,5870,175,11.143698,"\text{Not used}","int((cos(x)^3*sin(x)^2)/(a*cos(x) + b*sin(x)),x)","\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(7\,a^3+3\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(7\,a^3+3\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^3+5\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(a^3+5\,a\,b^2\right)}{4\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6}{a^4+2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^4+2\,a^2\,b^2+b^4}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{64\,a^2\,b^3\,\left(\frac{a\,\left(\frac{16\,a^{15}\,b+288\,a^{13}\,b^3+1008\,a^{11}\,b^5+1472\,a^9\,b^7+1008\,a^7\,b^9+288\,a^5\,b^{11}+16\,a^3\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{a\,\left(\frac{a^{15}+15\,a^{13}\,b^2+36\,a^{11}\,b^4-146\,a^9\,b^6-327\,a^7\,b^8-141\,a^5\,b^{10}+18\,a^3\,b^{12}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,a^2\,b^3\,\left(\frac{16\,a^{15}\,b+288\,a^{13}\,b^3+1008\,a^{11}\,b^5+1472\,a^9\,b^7+1008\,a^7\,b^9+288\,a^5\,b^{11}+16\,a^3\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a^3\,{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{1024\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^{10}+11\,a^8\,b^2-46\,a^6\,b^4-706\,a^4\,b^6+493\,a^2\,b^8-9\,b^{10}\right)}{{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}-\frac{2\,a\,b\,\left(\frac{a^{11}\,b^3+12\,a^9\,b^5+13\,a^7\,b^7+18\,a^5\,b^9}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{a\,\left(\frac{a\,\left(\frac{16\,a^{15}\,b+288\,a^{13}\,b^3+1008\,a^{11}\,b^5+1472\,a^9\,b^7+1008\,a^7\,b^9+288\,a^5\,b^{11}+16\,a^3\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{64\,a^2\,b^3\,\left(\frac{a^{15}+15\,a^{13}\,b^2+36\,a^{11}\,b^4-146\,a^9\,b^6-327\,a^7\,b^8-141\,a^5\,b^{10}+18\,a^3\,b^{12}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{64\,a^2\,b^3\,\left(\frac{16\,a^{15}\,b+288\,a^{13}\,b^3+1008\,a^{11}\,b^5+1472\,a^9\,b^7+1008\,a^7\,b^9+288\,a^5\,b^{11}+16\,a^3\,b^{13}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{a^4\,b^3\,{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2\,\left(192\,a^{15}\,b^2+1344\,a^{13}\,b^4+4032\,a^{11}\,b^6+6720\,a^9\,b^8+6720\,a^7\,b^{10}+4032\,a^5\,b^{12}+1344\,a^3\,b^{14}+192\,a\,b^{16}\right)}{2\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8+28\,a^6\,b^2+110\,a^4\,b^4-436\,a^2\,b^6+57\,b^8\right)}{{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{a^8+6\,a^6\,b^2-3\,a^4\,b^4}+\frac{\left(\frac{a\,\left(\frac{-a^{14}\,b+3\,a^{12}\,b^3+54\,a^{10}\,b^5+134\,a^8\,b^7+123\,a^6\,b^9+39\,a^4\,b^{11}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,a^2\,b^3\,\left(\frac{8\,a^{16}+72\,a^{14}\,b^2+72\,a^{12}\,b^4-248\,a^{10}\,b^6-552\,a^8\,b^8-360\,a^6\,b^{10}-40\,a^4\,b^{12}+24\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{64\,a^2\,b^3\,\left(\frac{a\,\left(\frac{8\,a^{16}+72\,a^{14}\,b^2+72\,a^{12}\,b^4-248\,a^{10}\,b^6-552\,a^8\,b^8-360\,a^6\,b^{10}-40\,a^4\,b^{12}+24\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}+\frac{a^3\,{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{1024\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^{10}+11\,a^8\,b^2-46\,a^6\,b^4-706\,a^4\,b^6+493\,a^2\,b^8-9\,b^{10}\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{\left(a^8+6\,a^6\,b^2-3\,a^4\,b^4\right)\,{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}-\frac{2\,a\,b\,\left(\frac{a^{10}\,b^4+2\,a^8\,b^6-15\,a^6\,b^8}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{a\,\left(\frac{a\,\left(\frac{8\,a^{16}+72\,a^{14}\,b^2+72\,a^{12}\,b^4-248\,a^{10}\,b^6-552\,a^8\,b^8-360\,a^6\,b^{10}-40\,a^4\,b^{12}+24\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,a^3\,b^3\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{8\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{64\,a^2\,b^3\,\left(\frac{-a^{14}\,b+3\,a^{12}\,b^3+54\,a^{10}\,b^5+134\,a^8\,b^7+123\,a^6\,b^9+39\,a^4\,b^{11}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}+\frac{64\,a^2\,b^3\,\left(\frac{8\,a^{16}+72\,a^{14}\,b^2+72\,a^{12}\,b^4-248\,a^{10}\,b^6-552\,a^8\,b^8-360\,a^6\,b^{10}-40\,a^4\,b^{12}+24\,a^2\,b^{14}}{2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}-\frac{32\,a^2\,b^3\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}-\frac{a^4\,b^3\,{\left(a^4+6\,a^2\,b^2-3\,b^4\right)}^2\,\left(192\,a^{16}\,b+1344\,a^{14}\,b^3+4032\,a^{12}\,b^5+6720\,a^{10}\,b^7+6720\,a^8\,b^9+4032\,a^6\,b^{11}+1344\,a^4\,b^{13}+192\,a^2\,b^{15}\right)}{2\,\left(64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6\right)\,{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8+28\,a^6\,b^2+110\,a^4\,b^4-436\,a^2\,b^6+57\,b^8\right)\,\left(16\,a^{16}+128\,a^{14}\,b^2+448\,a^{12}\,b^4+896\,a^{10}\,b^6+1120\,a^8\,b^8+896\,a^6\,b^{10}+448\,a^4\,b^{12}+128\,a^2\,b^{14}+16\,b^{16}\right)}{\left(a^8+6\,a^6\,b^2-3\,a^4\,b^4\right)\,{\left(a^{10}+13\,a^8\,b^2+42\,a^6\,b^4+250\,a^4\,b^6+229\,a^2\,b^8+9\,b^{10}\right)}^2}\right)\,\left(a^4+6\,a^2\,b^2-3\,b^4\right)}{4\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a^2\,b^3\,\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{64\,a^2\,b^3\,\ln\left(\frac{1}{\cos\left(x\right)+1}\right)}{64\,a^6+192\,a^4\,b^2+192\,a^2\,b^4+64\,b^6}","Not used",1,"((tan(x/2)^3*(3*a*b^2 + 7*a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - (tan(x/2)^5*(3*a*b^2 + 7*a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) - (tan(x/2)*(5*a*b^2 + a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (tan(x/2)^7*(5*a*b^2 + a^3))/(4*(a^4 + b^4 + 2*a^2*b^2)) + (2*b^3*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (2*b^3*tan(x/2)^6)/(a^4 + b^4 + 2*a^2*b^2) - (4*a^2*b*tan(x/2)^4)/(a^4 + b^4 + 2*a^2*b^2))/(4*tan(x/2)^2 + 6*tan(x/2)^4 + 4*tan(x/2)^6 + tan(x/2)^8 + 1) - (a*atan((tan(x/2)*((((64*a^2*b^3*((a*((16*a^15*b + 16*a^3*b^13 + 288*a^5*b^11 + 1008*a^7*b^9 + 1472*a^9*b^7 + 1008*a^11*b^5 + 288*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (a*((a^15 + 18*a^3*b^12 - 141*a^5*b^10 - 327*a^7*b^8 - 146*a^9*b^6 + 36*a^11*b^4 + 15*a^13*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*a^2*b^3*((16*a^15*b + 16*a^3*b^13 + 288*a^5*b^11 + 1008*a^7*b^9 + 1472*a^9*b^7 + 1008*a^11*b^5 + 288*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a^3*(a^4 - 3*b^4 + 6*a^2*b^2)^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/(1024*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^10 - 9*b^10 + 493*a^2*b^8 - 706*a^4*b^6 - 46*a^6*b^4 + 11*a^8*b^2))/(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2 - (2*a*b*((18*a^5*b^9 + 13*a^7*b^7 + 12*a^9*b^5 + a^11*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (a*((a*((16*a^15*b + 16*a^3*b^13 + 288*a^5*b^11 + 1008*a^7*b^9 + 1472*a^9*b^7 + 1008*a^11*b^5 + 288*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (64*a^2*b^3*((a^15 + 18*a^3*b^12 - 141*a^5*b^10 - 327*a^7*b^8 - 146*a^9*b^6 + 36*a^11*b^4 + 15*a^13*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (64*a^2*b^3*((16*a^15*b + 16*a^3*b^13 + 288*a^5*b^11 + 1008*a^7*b^9 + 1472*a^9*b^7 + 1008*a^11*b^5 + 288*a^13*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (a^4*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)^2*(192*a*b^16 + 1344*a^3*b^14 + 4032*a^5*b^12 + 6720*a^7*b^10 + 6720*a^9*b^8 + 4032*a^11*b^6 + 1344*a^13*b^4 + 192*a^15*b^2))/(2*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 57*b^8 - 436*a^2*b^6 + 110*a^4*b^4 + 28*a^6*b^2))/(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/(a^8 - 3*a^4*b^4 + 6*a^6*b^2) + (((a*((39*a^4*b^11 - a^14*b + 123*a^6*b^9 + 134*a^8*b^7 + 54*a^10*b^5 + 3*a^12*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*a^2*b^3*((8*a^16 + 24*a^2*b^14 - 40*a^4*b^12 - 360*a^6*b^10 - 552*a^8*b^8 - 248*a^10*b^6 + 72*a^12*b^4 + 72*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (64*a^2*b^3*((a*((8*a^16 + 24*a^2*b^14 - 40*a^4*b^12 - 360*a^6*b^10 - 552*a^8*b^8 - 248*a^10*b^6 + 72*a^12*b^4 + 72*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) + (a^3*(a^4 - 3*b^4 + 6*a^2*b^2)^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/(1024*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^10 - 9*b^10 + 493*a^2*b^8 - 706*a^4*b^6 - 46*a^6*b^4 + 11*a^8*b^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/((a^8 - 3*a^4*b^4 + 6*a^6*b^2)*(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2) - (2*a*b*((2*a^8*b^6 - 15*a^6*b^8 + a^10*b^4)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (a*((a*((8*a^16 + 24*a^2*b^14 - 40*a^4*b^12 - 360*a^6*b^10 - 552*a^8*b^8 - 248*a^10*b^6 + 72*a^12*b^4 + 72*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*a^3*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^4 - 3*b^4 + 6*a^2*b^2))/(8*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (64*a^2*b^3*((39*a^4*b^11 - a^14*b + 123*a^6*b^9 + 134*a^8*b^7 + 54*a^10*b^5 + 3*a^12*b^3)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) + (64*a^2*b^3*((8*a^16 + 24*a^2*b^14 - 40*a^4*b^12 - 360*a^6*b^10 - 552*a^8*b^8 - 248*a^10*b^6 + 72*a^12*b^4 + 72*a^14*b^2)/(2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)) - (32*a^2*b^3*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/((64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2) - (a^4*b^3*(a^4 - 3*b^4 + 6*a^2*b^2)^2*(192*a^16*b + 192*a^2*b^15 + 1344*a^4*b^13 + 4032*a^6*b^11 + 6720*a^8*b^9 + 6720*a^10*b^7 + 4032*a^12*b^5 + 1344*a^14*b^3))/(2*(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 57*b^8 - 436*a^2*b^6 + 110*a^4*b^4 + 28*a^6*b^2)*(16*a^16 + 16*b^16 + 128*a^2*b^14 + 448*a^4*b^12 + 896*a^6*b^10 + 1120*a^8*b^8 + 896*a^10*b^6 + 448*a^12*b^4 + 128*a^14*b^2))/((a^8 - 3*a^4*b^4 + 6*a^6*b^2)*(a^10 + 9*b^10 + 229*a^2*b^8 + 250*a^4*b^6 + 42*a^6*b^4 + 13*a^8*b^2)^2))*(a^4 - 3*b^4 + 6*a^2*b^2))/(4*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a^2*b^3*log(a + 2*b*tan(x/2) - a*tan(x/2)^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (64*a^2*b^3*log(1/(cos(x) + 1)))/(64*a^6 + 64*b^6 + 192*a^2*b^4 + 192*a^4*b^2)","B"
283,1,600,193,1.643285,"\text{Not used}","int((cos(x)^3*sin(x)^3)/(a*cos(x) + b*sin(x)),x)","\frac{\frac{8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a^2\,b^3+b^5\right)}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^5+7\,a^3\,b^2\right)}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(a^5+3\,a^3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,\left(2\,a^5+14\,a^3\,b^2-3\,a\,b^4\right)}{15\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(a^5-5\,a^3\,b^2+3\,a\,b^4\right)}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{8\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(4\,a^2+b^2\right)}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{2\,a^2\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{2\,a\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{2\,a^2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(24\,a^4-17\,a^2\,b^2+4\,b^4\right)}{15\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}+\frac{2\,a^3\,b^3\,\mathrm{atanh}\left(\frac{2\,a^6\,b+2\,b^7+6\,a^2\,b^5+6\,a^4\,b^3-2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}{2\,{\left(a^2+b^2\right)}^{7/2}}\right)}{{\left(a^2+b^2\right)}^{7/2}}","Not used",1,"((8*tan(x/2)^3*(b^5 + 4*a^2*b^3))/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*tan(x/2)^2*(a^5 + 7*a^3*b^2))/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (4*tan(x/2)^6*(a^5 + 3*a^3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*(2*a^5 - 3*a*b^4 + 14*a^3*b^2))/(15*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (4*tan(x/2)^4*(3*a*b^4 + a^5 - 5*a^3*b^2))/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (8*b^3*tan(x/2)^7*(4*a^2 + b^2))/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (2*a^2*b^3*tan(x/2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (2*a*b^4*tan(x/2)^8)/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (2*a^2*b^3*tan(x/2)^9)/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (4*b*tan(x/2)^5*(24*a^4 + 4*b^4 - 17*a^2*b^2))/(15*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))/(5*tan(x/2)^2 + 10*tan(x/2)^4 + 10*tan(x/2)^6 + 5*tan(x/2)^8 + tan(x/2)^10 + 1) + (2*a^3*b^3*atanh((2*a^6*b + 2*b^7 + 6*a^2*b^5 + 6*a^4*b^3 - 2*a*tan(x/2)*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))/(2*(a^2 + b^2)^(7/2))))/(a^2 + b^2)^(7/2)","B"
284,1,1017,70,5.160597,"\text{Not used}","int((cos(x)*sin(x))/(a*cos(x) + b*sin(x))^2,x)","-\frac{b^3\,\sin\left(x\right)+a^3\,\ln\left(\frac{a\,\cos\left(x\right)+b\,\sin\left(x\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)\,\cos\left(x\right)-b^3\,\ln\left(\frac{a\,\cos\left(x\right)+b\,\sin\left(x\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)\,\sin\left(x\right)+a^2\,b\,\sin\left(x\right)-a^3\,\ln\left(-\frac{65536\,a^{12}\,b^2-131072\,a^{10}\,b^4+196608\,a^8\,b^6-131072\,a^6\,b^8+65536\,a^4\,b^{10}}{\frac{a^{16}}{2}+\frac{b^{16}}{2}+4\,a^2\,b^{14}+14\,a^4\,b^{12}+28\,a^6\,b^{10}+35\,a^8\,b^8+28\,a^{10}\,b^6+14\,a^{12}\,b^4+4\,a^{14}\,b^2+\frac{a^{16}\,\cos\left(x\right)}{2}+\frac{b^{16}\,\cos\left(x\right)}{2}+4\,a^2\,b^{14}\,\cos\left(x\right)+14\,a^4\,b^{12}\,\cos\left(x\right)+28\,a^6\,b^{10}\,\cos\left(x\right)+35\,a^8\,b^8\,\cos\left(x\right)+28\,a^{10}\,b^6\,\cos\left(x\right)+14\,a^{12}\,b^4\,\cos\left(x\right)+4\,a^{14}\,b^2\,\cos\left(x\right)}\right)\,\cos\left(x\right)+b^3\,\ln\left(-\frac{65536\,a^{12}\,b^2-131072\,a^{10}\,b^4+196608\,a^8\,b^6-131072\,a^6\,b^8+65536\,a^4\,b^{10}}{\frac{a^{16}}{2}+\frac{b^{16}}{2}+4\,a^2\,b^{14}+14\,a^4\,b^{12}+28\,a^6\,b^{10}+35\,a^8\,b^8+28\,a^{10}\,b^6+14\,a^{12}\,b^4+4\,a^{14}\,b^2+\frac{a^{16}\,\cos\left(x\right)}{2}+\frac{b^{16}\,\cos\left(x\right)}{2}+4\,a^2\,b^{14}\,\cos\left(x\right)+14\,a^4\,b^{12}\,\cos\left(x\right)+28\,a^6\,b^{10}\,\cos\left(x\right)+35\,a^8\,b^8\,\cos\left(x\right)+28\,a^{10}\,b^6\,\cos\left(x\right)+14\,a^{12}\,b^4\,\cos\left(x\right)+4\,a^{14}\,b^2\,\cos\left(x\right)}\right)\,\sin\left(x\right)-4\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\cos\left(x\right)-4\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)\,\sin\left(x\right)+a\,b^2\,\ln\left(-\frac{65536\,a^{12}\,b^2-131072\,a^{10}\,b^4+196608\,a^8\,b^6-131072\,a^6\,b^8+65536\,a^4\,b^{10}}{\frac{a^{16}}{2}+\frac{b^{16}}{2}+4\,a^2\,b^{14}+14\,a^4\,b^{12}+28\,a^6\,b^{10}+35\,a^8\,b^8+28\,a^{10}\,b^6+14\,a^{12}\,b^4+4\,a^{14}\,b^2+\frac{a^{16}\,\cos\left(x\right)}{2}+\frac{b^{16}\,\cos\left(x\right)}{2}+4\,a^2\,b^{14}\,\cos\left(x\right)+14\,a^4\,b^{12}\,\cos\left(x\right)+28\,a^6\,b^{10}\,\cos\left(x\right)+35\,a^8\,b^8\,\cos\left(x\right)+28\,a^{10}\,b^6\,\cos\left(x\right)+14\,a^{12}\,b^4\,\cos\left(x\right)+4\,a^{14}\,b^2\,\cos\left(x\right)}\right)\,\cos\left(x\right)-a^2\,b\,\ln\left(-\frac{65536\,a^{12}\,b^2-131072\,a^{10}\,b^4+196608\,a^8\,b^6-131072\,a^6\,b^8+65536\,a^4\,b^{10}}{\frac{a^{16}}{2}+\frac{b^{16}}{2}+4\,a^2\,b^{14}+14\,a^4\,b^{12}+28\,a^6\,b^{10}+35\,a^8\,b^8+28\,a^{10}\,b^6+14\,a^{12}\,b^4+4\,a^{14}\,b^2+\frac{a^{16}\,\cos\left(x\right)}{2}+\frac{b^{16}\,\cos\left(x\right)}{2}+4\,a^2\,b^{14}\,\cos\left(x\right)+14\,a^4\,b^{12}\,\cos\left(x\right)+28\,a^6\,b^{10}\,\cos\left(x\right)+35\,a^8\,b^8\,\cos\left(x\right)+28\,a^{10}\,b^6\,\cos\left(x\right)+14\,a^{12}\,b^4\,\cos\left(x\right)+4\,a^{14}\,b^2\,\cos\left(x\right)}\right)\,\sin\left(x\right)-a\,b^2\,\ln\left(\frac{a\,\cos\left(x\right)+b\,\sin\left(x\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)\,\cos\left(x\right)+a^2\,b\,\ln\left(\frac{a\,\cos\left(x\right)+b\,\sin\left(x\right)}{{\cos\left(\frac{x}{2}\right)}^2}\right)\,\sin\left(x\right)}{\cos\left(x\right)\,a^5+\sin\left(x\right)\,a^4\,b+2\,\cos\left(x\right)\,a^3\,b^2+2\,\sin\left(x\right)\,a^2\,b^3+\cos\left(x\right)\,a\,b^4+\sin\left(x\right)\,b^5}","Not used",1,"-(b^3*sin(x) + a^3*log((a*cos(x) + b*sin(x))/cos(x/2)^2)*cos(x) - b^3*log((a*cos(x) + b*sin(x))/cos(x/2)^2)*sin(x) + a^2*b*sin(x) - a^3*log(-(65536*a^4*b^10 - 131072*a^6*b^8 + 196608*a^8*b^6 - 131072*a^10*b^4 + 65536*a^12*b^2)/(a^16/2 + b^16/2 + 4*a^2*b^14 + 14*a^4*b^12 + 28*a^6*b^10 + 35*a^8*b^8 + 28*a^10*b^6 + 14*a^12*b^4 + 4*a^14*b^2 + (a^16*cos(x))/2 + (b^16*cos(x))/2 + 4*a^2*b^14*cos(x) + 14*a^4*b^12*cos(x) + 28*a^6*b^10*cos(x) + 35*a^8*b^8*cos(x) + 28*a^10*b^6*cos(x) + 14*a^12*b^4*cos(x) + 4*a^14*b^2*cos(x)))*cos(x) + b^3*log(-(65536*a^4*b^10 - 131072*a^6*b^8 + 196608*a^8*b^6 - 131072*a^10*b^4 + 65536*a^12*b^2)/(a^16/2 + b^16/2 + 4*a^2*b^14 + 14*a^4*b^12 + 28*a^6*b^10 + 35*a^8*b^8 + 28*a^10*b^6 + 14*a^12*b^4 + 4*a^14*b^2 + (a^16*cos(x))/2 + (b^16*cos(x))/2 + 4*a^2*b^14*cos(x) + 14*a^4*b^12*cos(x) + 28*a^6*b^10*cos(x) + 35*a^8*b^8*cos(x) + 28*a^10*b^6*cos(x) + 14*a^12*b^4*cos(x) + 4*a^14*b^2*cos(x)))*sin(x) - 4*a^2*b*atan(sin(x/2)/cos(x/2))*cos(x) - 4*a*b^2*atan(sin(x/2)/cos(x/2))*sin(x) + a*b^2*log(-(65536*a^4*b^10 - 131072*a^6*b^8 + 196608*a^8*b^6 - 131072*a^10*b^4 + 65536*a^12*b^2)/(a^16/2 + b^16/2 + 4*a^2*b^14 + 14*a^4*b^12 + 28*a^6*b^10 + 35*a^8*b^8 + 28*a^10*b^6 + 14*a^12*b^4 + 4*a^14*b^2 + (a^16*cos(x))/2 + (b^16*cos(x))/2 + 4*a^2*b^14*cos(x) + 14*a^4*b^12*cos(x) + 28*a^6*b^10*cos(x) + 35*a^8*b^8*cos(x) + 28*a^10*b^6*cos(x) + 14*a^12*b^4*cos(x) + 4*a^14*b^2*cos(x)))*cos(x) - a^2*b*log(-(65536*a^4*b^10 - 131072*a^6*b^8 + 196608*a^8*b^6 - 131072*a^10*b^4 + 65536*a^12*b^2)/(a^16/2 + b^16/2 + 4*a^2*b^14 + 14*a^4*b^12 + 28*a^6*b^10 + 35*a^8*b^8 + 28*a^10*b^6 + 14*a^12*b^4 + 4*a^14*b^2 + (a^16*cos(x))/2 + (b^16*cos(x))/2 + 4*a^2*b^14*cos(x) + 14*a^4*b^12*cos(x) + 28*a^6*b^10*cos(x) + 35*a^8*b^8*cos(x) + 28*a^10*b^6*cos(x) + 14*a^12*b^4*cos(x) + 4*a^14*b^2*cos(x)))*sin(x) - a*b^2*log((a*cos(x) + b*sin(x))/cos(x/2)^2)*cos(x) + a^2*b*log((a*cos(x) + b*sin(x))/cos(x/2)^2)*sin(x))/(b^5*sin(x) + a^5*cos(x) + a*b^4*cos(x) + a^4*b*sin(x) + 2*a^3*b^2*cos(x) + 2*a^2*b^3*sin(x))","B"
285,1,249,110,1.232105,"\text{Not used}","int((cos(x)*sin(x)^2)/(a*cos(x) + b*sin(x))^2,x)","-\frac{\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^3+4\,a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{6\,a^2\,b}{a^4+2\,a^2\,b^2+b^4}-\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2-2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2-2\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{a\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^5-a^4\,b\,1{}\mathrm{i}+2{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,b^2-a^2\,b^3\,2{}\mathrm{i}+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^4-b^5\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{5/2}}\right)\,\left(a^2-2\,b^2\right)\,2{}\mathrm{i}}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"- ((2*tan(x/2)*(4*a*b^2 + a^3))/(a^4 + b^4 + 2*a^2*b^2) + (6*a^2*b)/(a^4 + b^4 + 2*a^2*b^2) - (2*a*tan(x/2)^3*(a^2 - 2*b^2))/(a^4 + b^4 + 2*a^2*b^2) + (2*b*tan(x/2)^2*(a^2 - 2*b^2))/(a^4 + b^4 + 2*a^2*b^2))/(a + 2*b*tan(x/2) - a*tan(x/2)^4 + 2*b*tan(x/2)^3) - (a*atan((a^5*tan(x/2)*1i - a^4*b*1i - b^5*1i - a^2*b^3*2i + a^3*b^2*tan(x/2)*2i + a*b^4*tan(x/2)*1i)/(a^2 + b^2)^(5/2))*(a^2 - 2*b^2)*2i)/(a^2 + b^2)^(5/2)","B"
286,1,5431,129,7.681878,"\text{Not used}","int((cos(x)*sin(x)^3)/(a*cos(x) + b*sin(x))^2,x)","\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(2\,a^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(a^4-3\,a^2\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2+b^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^2+b^2}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left(a^2+b^2\right)}^2}+\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^4+2\,a^2\,b^2+b^4}+\frac{4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^2}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{2\,a\,b\,\mathrm{atan}\left(\frac{\left(\frac{\left(\frac{a\,b\,\left(\frac{32\,\left(-4\,a^{14}\,b-9\,a^{12}\,b^3+3\,a^{10}\,b^5+22\,a^8\,b^7+18\,a^6\,b^9+3\,a^4\,b^{11}-a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a\,b\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,a^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(\frac{32\,\left(-3\,a^{12}\,b-4\,a^{10}\,b^3+6\,a^8\,b^5+12\,a^6\,b^7+5\,a^4\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{32\,\left(-4\,a^{14}\,b-9\,a^{12}\,b^3+3\,a^{10}\,b^5+22\,a^8\,b^7+18\,a^6\,b^9+3\,a^4\,b^{11}-a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,a^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,b^3\,{\left(3\,a^2-b^2\right)}^3\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(4\,a^8-61\,a^6\,b^2+155\,a^4\,b^4-67\,a^2\,b^6+b^8\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(96\,a^6\,b-32\,a^4\,b^3\right)\,{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{\left(2\,a^4-6\,a^2\,b^2\right)\,\left(\frac{a\,b\,\left(3\,a^2-b^2\right)\,\left(\frac{32\,\left(-2\,a^{15}+3\,a^{13}\,b^2+33\,a^{11}\,b^4+62\,a^9\,b^6+48\,a^7\,b^8+15\,a^5\,b^{10}+a^3\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a\,b\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(\frac{32\,\left(18\,a^{11}\,b^2+8\,a^9\,b^4-36\,a^7\,b^6-24\,a^5\,b^8+2\,a^3\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(2\,a^4-6\,a^2\,b^2\right)\,\left(\frac{32\,\left(-2\,a^{15}+3\,a^{13}\,b^2+33\,a^{11}\,b^4+62\,a^9\,b^6+48\,a^7\,b^8+15\,a^5\,b^{10}+a^3\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{32\,a^3\,b^3\,{\left(3\,a^2-b^2\right)}^3\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(4\,a^8-61\,a^6\,b^2+155\,a^4\,b^4-67\,a^2\,b^6+b^8\right)}{{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}-\frac{2\,a\,b\,\left(\frac{32\,\left(2\,a^{11}-6\,a^9\,b^2+2\,a^7\,b^4-6\,a^5\,b^6\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(2\,a^4-6\,a^2\,b^2\right)\,\left(\frac{32\,\left(18\,a^{11}\,b^2+8\,a^9\,b^4-36\,a^7\,b^6-24\,a^5\,b^8+2\,a^3\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(2\,a^4-6\,a^2\,b^2\right)\,\left(\frac{32\,\left(-2\,a^{15}+3\,a^{13}\,b^2+33\,a^{11}\,b^4+62\,a^9\,b^6+48\,a^7\,b^8+15\,a^5\,b^{10}+a^3\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{a\,b\,\left(\frac{a\,b\,\left(3\,a^2-b^2\right)\,\left(\frac{32\,\left(-2\,a^{15}+3\,a^{13}\,b^2+33\,a^{11}\,b^4+62\,a^9\,b^6+48\,a^7\,b^8+15\,a^5\,b^{10}+a^3\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{16\,a\,b\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a^2\,b^2\,\left(2\,a^4-6\,a^2\,b^2\right)\,{\left(3\,a^2-b^2\right)}^2\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(10\,a^6-59\,a^4\,b^2+68\,a^2\,b^4-7\,b^6\right)}{{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{96\,a^6\,b-32\,a^4\,b^3}+\frac{2\,a\,b\,\left(\frac{32\,\left(2\,a^{10}\,b-8\,a^8\,b^3+6\,a^6\,b^5\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(2\,a^4-6\,a^2\,b^2\right)\,\left(\frac{32\,\left(-3\,a^{12}\,b-4\,a^{10}\,b^3+6\,a^8\,b^5+12\,a^6\,b^7+5\,a^4\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{32\,\left(-4\,a^{14}\,b-9\,a^{12}\,b^3+3\,a^{10}\,b^5+22\,a^8\,b^7+18\,a^6\,b^9+3\,a^4\,b^{11}-a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,a^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(\frac{a\,b\,\left(\frac{32\,\left(-4\,a^{14}\,b-9\,a^{12}\,b^3+3\,a^{10}\,b^5+22\,a^8\,b^7+18\,a^6\,b^9+3\,a^4\,b^{11}-a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a\,b\,\left(2\,a^4-6\,a^2\,b^2\right)\,\left(3\,a^2-b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a^2\,b^2\,\left(2\,a^4-6\,a^2\,b^2\right)\,{\left(3\,a^2-b^2\right)}^2\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(10\,a^6-59\,a^4\,b^2+68\,a^2\,b^4-7\,b^6\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(96\,a^6\,b-32\,a^4\,b^3\right)\,{\left(4\,a^8-11\,a^6\,b^2+15\,a^4\,b^4+31\,a^2\,b^6+b^8\right)}^2}\right)\,\left(3\,a^2-b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}","Not used",1,"(log(1/(cos(x) + 1))*(2*a^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(a^4 - 3*a^2*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - ((2*a*tan(x/2)^2)/(a^2 + b^2) - (2*a*tan(x/2)^4)/(a^2 + b^2) + (4*a^2*b*tan(x/2))/(a^2 + b^2)^2 + (4*a^2*b*tan(x/2)^5)/(a^4 + b^4 + 2*a^2*b^2) + (4*b*tan(x/2)^3*(a^2 - b^2))/(a^2 + b^2)^2)/(a + 2*b*tan(x/2) + a*tan(x/2)^2 - a*tan(x/2)^4 - a*tan(x/2)^6 + 4*b*tan(x/2)^3 + 2*b*tan(x/2)^5) + (2*a*b*atan((((((a*b*((32*(3*a^4*b^11 - a^2*b^13 - 4*a^14*b + 18*a^6*b^9 + 22*a^8*b^7 + 3*a^10*b^5 - 9*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*a^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a*b*(2*a^4 - 6*a^2*b^2)*(3*a^2 - b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*((32*(5*a^4*b^9 - 3*a^12*b + 12*a^6*b^7 + 6*a^8*b^5 - 4*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((32*(3*a^4*b^11 - a^2*b^13 - 4*a^14*b + 18*a^6*b^9 + 22*a^8*b^7 + 3*a^10*b^5 - 9*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*a^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*b^3*(3*a^2 - b^2)^3*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(4*a^8 + b^8 - 67*a^2*b^6 + 155*a^4*b^4 - 61*a^6*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((96*a^6*b - 32*a^4*b^3)*(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2) - (tan(x/2)*(((((2*a^4 - 6*a^2*b^2)*((a*b*(3*a^2 - b^2)*((32*(a^3*b^12 - 2*a^15 + 15*a^5*b^10 + 48*a^7*b^8 + 62*a^9*b^6 + 33*a^11*b^4 + 3*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(2*a^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a*b*(2*a^4 - 6*a^2*b^2)*(3*a^2 - b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*((32*(2*a^3*b^10 - 24*a^5*b^8 - 36*a^7*b^6 + 8*a^9*b^4 + 18*a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((2*a^4 - 6*a^2*b^2)*((32*(a^3*b^12 - 2*a^15 + 15*a^5*b^10 + 48*a^7*b^8 + 62*a^9*b^6 + 33*a^11*b^4 + 3*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(2*a^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (32*a^3*b^3*(3*a^2 - b^2)^3*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(4*a^8 + b^8 - 67*a^2*b^6 + 155*a^4*b^4 - 61*a^6*b^2))/(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2 - (2*a*b*((32*(2*a^11 - 6*a^5*b^6 + 2*a^7*b^4 - 6*a^9*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((2*a^4 - 6*a^2*b^2)*((32*(2*a^3*b^10 - 24*a^5*b^8 - 36*a^7*b^6 + 8*a^9*b^4 + 18*a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((2*a^4 - 6*a^2*b^2)*((32*(a^3*b^12 - 2*a^15 + 15*a^5*b^10 + 48*a^7*b^8 + 62*a^9*b^6 + 33*a^11*b^4 + 3*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(2*a^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (a*b*((a*b*(3*a^2 - b^2)*((32*(a^3*b^12 - 2*a^15 + 15*a^5*b^10 + 48*a^7*b^8 + 62*a^9*b^6 + 33*a^11*b^4 + 3*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (16*(2*a^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (16*a*b*(2*a^4 - 6*a^2*b^2)*(3*a^2 - b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a^2*b^2*(2*a^4 - 6*a^2*b^2)*(3*a^2 - b^2)^2*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(10*a^6 - 7*b^6 + 68*a^2*b^4 - 59*a^4*b^2))/(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/(96*a^6*b - 32*a^4*b^3) + (2*a*b*((32*(2*a^10*b + 6*a^6*b^5 - 8*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((2*a^4 - 6*a^2*b^2)*((32*(5*a^4*b^9 - 3*a^12*b + 12*a^6*b^7 + 6*a^8*b^5 - 4*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((32*(3*a^4*b^11 - a^2*b^13 - 4*a^14*b + 18*a^6*b^9 + 22*a^8*b^7 + 3*a^10*b^5 - 9*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*a^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*((a*b*((32*(3*a^4*b^11 - a^2*b^13 - 4*a^14*b + 18*a^6*b^9 + 22*a^8*b^7 + 3*a^10*b^5 - 9*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*a^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a*b*(2*a^4 - 6*a^2*b^2)*(3*a^2 - b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a^2*b^2*(2*a^4 - 6*a^2*b^2)*(3*a^2 - b^2)^2*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(10*a^6 - 7*b^6 + 68*a^2*b^4 - 59*a^4*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((96*a^6*b - 32*a^4*b^3)*(4*a^8 + b^8 + 31*a^2*b^6 + 15*a^4*b^4 - 11*a^6*b^2)^2))*(3*a^2 - b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)","B"
287,1,253,109,1.157907,"\text{Not used}","int((cos(x)^2*sin(x))/(a*cos(x) + b*sin(x))^2,x)","\frac{\frac{2\,\left(2\,a\,b^2-a^3\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{6\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^3+4\,a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(2\,a^2-b^2\right)}{a^4+2\,a^2\,b^2+b^4}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^5-a^4\,b\,1{}\mathrm{i}+2{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,b^2-a^2\,b^3\,2{}\mathrm{i}+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^4-b^5\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{5/2}}\right)\,\left(2\,a^2-b^2\right)\,2{}\mathrm{i}}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"((2*(2*a*b^2 - a^3))/(a^4 + b^4 + 2*a^2*b^2) + (6*b^3*tan(x/2))/(a^4 + b^4 + 2*a^2*b^2) + (2*tan(x/2)^2*(4*a*b^2 + a^3))/(a^4 + b^4 + 2*a^2*b^2) - (2*b*tan(x/2)^3*(2*a^2 - b^2))/(a^4 + b^4 + 2*a^2*b^2))/(a + 2*b*tan(x/2) - a*tan(x/2)^4 + 2*b*tan(x/2)^3) + (b*atan((a^5*tan(x/2)*1i - a^4*b*1i - b^5*1i - a^2*b^3*2i + a^3*b^2*tan(x/2)*2i + a*b^4*tan(x/2)*1i)/(a^2 + b^2)^(5/2))*(2*a^2 - b^2)*2i)/(a^2 + b^2)^(5/2)","B"
288,1,6012,131,12.130687,"\text{Not used}","int((cos(x)^2*sin(x)^2)/(a*cos(x) + b*sin(x))^2,x)","\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(3\,a\,b^2-a^3\right)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2+b^2}-\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^2+b^2}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a\,b^2-a^3\right)}{{\left(a^2+b^2\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^3+5\,a\,b^2\right)}{{\left(a^2+b^2\right)}^2}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(2\,a\,b^3-2\,a^3\,b\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(16\,a\,b^3-16\,a^3\,b\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}-\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{\left(\frac{\left(\frac{8\,\left(-20\,a^{14}\,b-48\,a^{12}\,b^3+12\,a^{10}\,b^5+128\,a^8\,b^7+132\,a^6\,b^9+48\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(16\,a\,b^3-16\,a^3\,b\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}-\frac{\left(\frac{8\,\left(a^{13}-25\,a^{11}\,b^2+52\,a^9\,b^4+126\,a^7\,b^6-7\,a^5\,b^8-53\,a^3\,b^{10}+2\,a\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(\frac{8\,\left(-20\,a^{14}\,b-48\,a^{12}\,b^3+12\,a^{10}\,b^5+128\,a^8\,b^7+132\,a^6\,b^9+48\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\left(-a^2+2\,a\,b+b^2\right)}^3\,{\left(a^2+2\,a\,b-b^2\right)}^3\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{{\left(a^2+b^2\right)}^3\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^{10}-109\,a^8\,b^2+466\,a^6\,b^4-466\,a^4\,b^6+109\,a^2\,b^8-b^{10}\right)}{{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}+\frac{\left(\frac{8\,\left(2\,a^{10}\,b+22\,a^8\,b^3-30\,a^6\,b^5+10\,a^4\,b^7-4\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(\frac{8\,\left(a^{13}-25\,a^{11}\,b^2+52\,a^9\,b^4+126\,a^7\,b^6-7\,a^5\,b^8-53\,a^3\,b^{10}+2\,a\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(\frac{8\,\left(-20\,a^{14}\,b-48\,a^{12}\,b^3+12\,a^{10}\,b^5+128\,a^8\,b^7+132\,a^6\,b^9+48\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}-\frac{\left(\frac{\left(\frac{8\,\left(-20\,a^{14}\,b-48\,a^{12}\,b^3+12\,a^{10}\,b^5+128\,a^8\,b^7+132\,a^6\,b^9+48\,a^4\,b^{11}+4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,{\left(-a^2+2\,a\,b+b^2\right)}^2\,{\left(a^2+2\,a\,b-b^2\right)}^2\,\left(12\,a^{15}\,b^2+84\,a^{13}\,b^4+252\,a^{11}\,b^6+420\,a^9\,b^8+420\,a^7\,b^{10}+252\,a^5\,b^{12}+84\,a^3\,b^{14}+12\,a\,b^{16}\right)}{{\left(a^2+b^2\right)}^2\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(18\,a^9\,b-280\,a^7\,b^3+556\,a^5\,b^5-280\,a^3\,b^7+18\,a\,b^9\right)}{{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{4\,a^5-24\,a^3\,b^2+4\,a\,b^4}+\frac{\left(\frac{8\,\left(-6\,a^9\,b^2+26\,a^7\,b^4-26\,a^5\,b^6+6\,a^3\,b^8\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{8\,\left(7\,a^{12}\,b+3\,a^{10}\,b^3-26\,a^8\,b^5-26\,a^6\,b^7+3\,a^4\,b^9+7\,a^2\,b^{11}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(\frac{8\,\left(-2\,a^{15}+14\,a^{13}\,b^2+54\,a^{11}\,b^4+38\,a^9\,b^6-38\,a^7\,b^8-54\,a^5\,b^{10}-14\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}\right)\,\left(16\,a\,b^3-16\,a^3\,b\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}-\frac{\left(\frac{\left(\frac{8\,\left(-2\,a^{15}+14\,a^{13}\,b^2+54\,a^{11}\,b^4+38\,a^9\,b^6-38\,a^7\,b^8-54\,a^5\,b^{10}-14\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,{\left(-a^2+2\,a\,b+b^2\right)}^2\,{\left(a^2+2\,a\,b-b^2\right)}^2\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{{\left(a^2+b^2\right)}^2\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(18\,a^9\,b-280\,a^7\,b^3+556\,a^5\,b^5-280\,a^3\,b^7+18\,a\,b^9\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(4\,a^5-24\,a^3\,b^2+4\,a\,b^4\right)\,{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}+\frac{\left(\frac{\left(\frac{\left(\frac{8\,\left(-2\,a^{15}+14\,a^{13}\,b^2+54\,a^{11}\,b^4+38\,a^9\,b^6-38\,a^7\,b^8-54\,a^5\,b^{10}-14\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(16\,a\,b^3-16\,a^3\,b\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}+\frac{\left(\frac{8\,\left(7\,a^{12}\,b+3\,a^{10}\,b^3-26\,a^8\,b^5-26\,a^6\,b^7+3\,a^4\,b^9+7\,a^2\,b^{11}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(\frac{8\,\left(-2\,a^{15}+14\,a^{13}\,b^2+54\,a^{11}\,b^4+38\,a^9\,b^6-38\,a^7\,b^8-54\,a^5\,b^{10}-14\,a^3\,b^{12}+2\,a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{4\,\left(16\,a\,b^3-16\,a^3\,b\right)\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{2\,\left(4\,a^6+12\,a^4\,b^2+12\,a^2\,b^4+4\,b^6\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\left(-a^2+2\,a\,b+b^2\right)}^3\,{\left(a^2+2\,a\,b-b^2\right)}^3\,\left(12\,a^{16}\,b+84\,a^{14}\,b^3+252\,a^{12}\,b^5+420\,a^{10}\,b^7+420\,a^8\,b^9+252\,a^6\,b^{11}+84\,a^4\,b^{13}+12\,a^2\,b^{15}\right)}{{\left(a^2+b^2\right)}^3\,{\left(a^4+2\,a^2\,b^2+b^4\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^{10}-109\,a^8\,b^2+466\,a^6\,b^4-466\,a^4\,b^6+109\,a^2\,b^8-b^{10}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(4\,a^5-24\,a^3\,b^2+4\,a\,b^4\right)\,{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}","Not used",1,"((tan(x/2)^5*(3*a*b^2 - a^3))/(a^4 + b^4 + 2*a^2*b^2) + (2*b*tan(x/2)^2)/(a^2 + b^2) - (2*b*tan(x/2)^4)/(a^2 + b^2) + (tan(x/2)*(3*a*b^2 - a^3))/(a^2 + b^2)^2 + (2*tan(x/2)^3*(5*a*b^2 + a^3))/(a^2 + b^2)^2)/(a + 2*b*tan(x/2) + a*tan(x/2)^2 - a*tan(x/2)^4 - a*tan(x/2)^6 + 4*b*tan(x/2)^3 + 2*b*tan(x/2)^5) - (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(2*a*b^3 - 2*a^3*b))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (log(1/(cos(x) + 1))*(16*a*b^3 - 16*a^3*b))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)) - (atan((tan(x/2)*((((((((8*(4*a^2*b^13 - 20*a^14*b + 48*a^4*b^11 + 132*a^6*b^9 + 128*a^8*b^7 + 12*a^10*b^5 - 48*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (2*(16*a*b^3 - 16*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(16*a*b^3 - 16*a^3*b))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)) - (((8*(2*a*b^12 + a^13 - 53*a^3*b^10 - 7*a^5*b^8 + 126*a^7*b^6 + 52*a^9*b^4 - 25*a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((16*a*b^3 - 16*a^3*b)*((8*(4*a^2*b^13 - 20*a^14*b + 48*a^4*b^11 + 132*a^6*b^9 + 128*a^8*b^7 + 12*a^10*b^5 - 48*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + ((2*a*b - a^2 + b^2)^3*(2*a*b + a^2 - b^2)^3*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((a^2 + b^2)^3*(a^4 + b^4 + 2*a^2*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^10 - b^10 + 109*a^2*b^8 - 466*a^4*b^6 + 466*a^6*b^4 - 109*a^8*b^2))/(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2 + (((8*(2*a^10*b - 4*a^2*b^9 + 10*a^4*b^7 - 30*a^6*b^5 + 22*a^8*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((16*a*b^3 - 16*a^3*b)*((8*(2*a*b^12 + a^13 - 53*a^3*b^10 - 7*a^5*b^8 + 126*a^7*b^6 + 52*a^9*b^4 - 25*a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((16*a*b^3 - 16*a^3*b)*((8*(4*a^2*b^13 - 20*a^14*b + 48*a^4*b^11 + 132*a^6*b^9 + 128*a^8*b^7 + 12*a^10*b^5 - 48*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2))))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)) - (((((8*(4*a^2*b^13 - 20*a^14*b + 48*a^4*b^11 + 132*a^6*b^9 + 128*a^8*b^7 + 12*a^10*b^5 - 48*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (2*(16*a*b^3 - 16*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + ((16*a*b^3 - 16*a^3*b)*(2*a*b - a^2 + b^2)^2*(2*a*b + a^2 - b^2)^2*(12*a*b^16 + 84*a^3*b^14 + 252*a^5*b^12 + 420*a^7*b^10 + 420*a^9*b^8 + 252*a^11*b^6 + 84*a^13*b^4 + 12*a^15*b^2))/((a^2 + b^2)^2*(a^4 + b^4 + 2*a^2*b^2)^2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(18*a*b^9 + 18*a^9*b - 280*a^3*b^7 + 556*a^5*b^5 - 280*a^7*b^3))/(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/(4*a*b^4 + 4*a^5 - 24*a^3*b^2) + (((8*(6*a^3*b^8 - 26*a^5*b^6 + 26*a^7*b^4 - 6*a^9*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((8*(7*a^12*b + 7*a^2*b^11 + 3*a^4*b^9 - 26*a^6*b^7 - 26*a^8*b^5 + 3*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((16*a*b^3 - 16*a^3*b)*((8*(2*a*b^14 - 2*a^15 - 14*a^3*b^12 - 54*a^5*b^10 - 38*a^7*b^8 + 38*a^9*b^6 + 54*a^11*b^4 + 14*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)))*(16*a*b^3 - 16*a^3*b))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)) - (((((8*(2*a*b^14 - 2*a^15 - 14*a^3*b^12 - 54*a^5*b^10 - 38*a^7*b^8 + 38*a^9*b^6 + 54*a^11*b^4 + 14*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (2*(16*a*b^3 - 16*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + ((16*a*b^3 - 16*a^3*b)*(2*a*b - a^2 + b^2)^2*(2*a*b + a^2 - b^2)^2*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((a^2 + b^2)^2*(a^4 + b^4 + 2*a^2*b^2)^2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(18*a*b^9 + 18*a^9*b - 280*a^3*b^7 + 556*a^5*b^5 - 280*a^7*b^3)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((4*a*b^4 + 4*a^5 - 24*a^3*b^2)*(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2) + (((((((8*(2*a*b^14 - 2*a^15 - 14*a^3*b^12 - 54*a^5*b^10 - 38*a^7*b^8 + 38*a^9*b^6 + 54*a^11*b^4 + 14*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (2*(16*a*b^3 - 16*a^3*b)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(16*a*b^3 - 16*a^3*b))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)) + (((8*(7*a^12*b + 7*a^2*b^11 + 3*a^4*b^9 - 26*a^6*b^7 - 26*a^8*b^5 + 3*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + ((16*a*b^3 - 16*a^3*b)*((8*(2*a*b^14 - 2*a^15 - 14*a^3*b^12 - 54*a^5*b^10 - 38*a^7*b^8 + 38*a^9*b^6 + 54*a^11*b^4 + 14*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (4*(16*a*b^3 - 16*a^3*b)*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(2*(4*a^6 + 4*b^6 + 12*a^2*b^4 + 12*a^4*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + ((2*a*b - a^2 + b^2)^3*(2*a*b + a^2 - b^2)^3*(12*a^16*b + 12*a^2*b^15 + 84*a^4*b^13 + 252*a^6*b^11 + 420*a^8*b^9 + 420*a^10*b^7 + 252*a^12*b^5 + 84*a^14*b^3))/((a^2 + b^2)^3*(a^4 + b^4 + 2*a^2*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^10 - b^10 + 109*a^2*b^8 - 466*a^4*b^6 + 466*a^6*b^4 - 109*a^8*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((4*a*b^4 + 4*a^5 - 24*a^3*b^2)*(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2))","B"
289,1,594,172,2.923941,"\text{Not used}","int((cos(x)^2*sin(x)^3)/(a*cos(x) + b*sin(x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(3\,a\,b^4-2\,a^3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(6\,a^5+40\,a^3\,b^2-11\,a\,b^4\right)}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(2\,a^4\,b+47\,a^2\,b^3\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,\left(2\,a^4-12\,a^2\,b^2+b^4\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(4\,a^4-30\,a^2\,b^2+11\,b^4\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(14\,a^4-25\,a^2\,b^2+6\,b^4\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(2\,a^2-3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^4+15\,a^2\,b^2-2\,b^4\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7-2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+6\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{a^2\,b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^7-a^6\,b\,1{}\mathrm{i}+3{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^5\,b^2-a^4\,b^3\,3{}\mathrm{i}+3{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,b^4-a^2\,b^5\,3{}\mathrm{i}+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^6-b^7\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{7/2}}\right)\,\left(2\,a^2-3\,b^2\right)\,2{}\mathrm{i}}{{\left(a^2+b^2\right)}^{7/2}}","Not used",1,"(a^2*b*atan((a^7*tan(x/2)*1i - a^6*b*1i - b^7*1i - a^2*b^5*3i - a^4*b^3*3i + a^3*b^4*tan(x/2)*3i + a^5*b^2*tan(x/2)*3i + a*b^6*tan(x/2)*1i)/(a^2 + b^2)^(7/2))*(2*a^2 - 3*b^2)*2i)/(a^2 + b^2)^(7/2) - ((2*tan(x/2)^6*(3*a*b^4 - 2*a^3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*tan(x/2)^4*(6*a^5 - 11*a*b^4 + 40*a^3*b^2))/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (2*tan(x/2)^3*(2*a^4*b + 47*a^2*b^3))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (2*a*(2*a^4 + b^4 - 12*a^2*b^2))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (2*a*tan(x/2)^2*(4*a^4 + 11*b^4 - 30*a^2*b^2))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (2*b*tan(x/2)^5*(14*a^4 + 6*b^4 - 25*a^2*b^2))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (2*a^2*b*tan(x/2)^7*(2*a^2 - 3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (2*b*tan(x/2)*(2*a^4 - 2*b^4 + 15*a^2*b^2))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)))/(a + 2*b*tan(x/2) + 2*a*tan(x/2)^2 - 2*a*tan(x/2)^6 - a*tan(x/2)^8 + 6*b*tan(x/2)^3 + 6*b*tan(x/2)^5 + 2*b*tan(x/2)^7)","B"
290,1,5428,128,8.157689,"\text{Not used}","int((cos(x)^3*sin(x))/(a*cos(x) + b*sin(x))^2,x)","\frac{\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2+b^2}-\frac{8\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{{\left(a^2+b^2\right)}^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^2+b^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-b^2\right)}{{\left(a^2+b^2\right)}^2}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(a^2-b^2\right)}{a^4+2\,a^2\,b^2+b^4}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(b^4-3\,a^2\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{2\,a\,b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{\left(\frac{a\,b\,\left(\frac{32\,\left(-8\,a^{13}\,b^2-27\,a^{11}\,b^4-27\,a^9\,b^6+2\,a^7\,b^8+18\,a^5\,b^{10}+9\,a^3\,b^{12}+a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^2-3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a\,b\,\left(a^2-3\,b^2\right)\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(-a^{11}\,b^2+15\,a^9\,b^4+6\,a^7\,b^6-34\,a^5\,b^8-21\,a^3\,b^{10}+3\,a\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{32\,\left(-8\,a^{13}\,b^2-27\,a^{11}\,b^4-27\,a^9\,b^6+2\,a^7\,b^8+18\,a^5\,b^{10}+9\,a^3\,b^{12}+a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,b^3\,{\left(a^2-3\,b^2\right)}^3\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8-67\,a^6\,b^2+155\,a^4\,b^4-61\,a^2\,b^6+4\,b^8\right)}{{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}+\frac{2\,a\,b\,\left(7\,a^6-68\,a^4\,b^2+59\,a^2\,b^4-10\,b^6\right)\,\left(\frac{32\,\left(-3\,a^7\,b^4-17\,a^5\,b^6+3\,a^3\,b^8+a\,b^{10}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(2\,b^4-6\,a^2\,b^2\right)\,\left(\frac{32\,\left(-a^{11}\,b^2+15\,a^9\,b^4+6\,a^7\,b^6-34\,a^5\,b^8-21\,a^3\,b^{10}+3\,a\,b^{12}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{32\,\left(-8\,a^{13}\,b^2-27\,a^{11}\,b^4-27\,a^9\,b^6+2\,a^7\,b^8+18\,a^5\,b^{10}+9\,a^3\,b^{12}+a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(a^2-3\,b^2\right)\,\left(\frac{a\,b\,\left(\frac{32\,\left(-8\,a^{13}\,b^2-27\,a^{11}\,b^4-27\,a^9\,b^6+2\,a^7\,b^8+18\,a^5\,b^{10}+9\,a^3\,b^{12}+a\,b^{14}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^2-3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a\,b\,\left(a^2-3\,b^2\right)\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a^2\,b^2\,{\left(a^2-3\,b^2\right)}^2\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{15}\,b^2+21\,a^{13}\,b^4+63\,a^{11}\,b^6+105\,a^9\,b^8+105\,a^7\,b^{10}+63\,a^5\,b^{12}+21\,a^3\,b^{14}+3\,a\,b^{16}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{96\,a^2\,b^5-32\,a^4\,b^3}+\frac{\left(\frac{\left(\frac{a\,b\,\left(\frac{32\,\left(-a^{14}\,b+3\,a^{12}\,b^3+18\,a^{10}\,b^5+22\,a^8\,b^7+3\,a^6\,b^9-9\,a^4\,b^{11}-4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^2-3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a\,b\,\left(a^2-3\,b^2\right)\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(a^2-3\,b^2\right)\,\left(\frac{32\,\left(5\,a^{10}\,b^3+12\,a^8\,b^5+6\,a^6\,b^7-4\,a^4\,b^9-3\,a^2\,b^{11}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{32\,\left(-a^{14}\,b+3\,a^{12}\,b^3+18\,a^{10}\,b^5+22\,a^8\,b^7+3\,a^6\,b^9-9\,a^4\,b^{11}-4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{32\,a^3\,b^3\,{\left(a^2-3\,b^2\right)}^3\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^8-67\,a^6\,b^2+155\,a^4\,b^4-61\,a^2\,b^6+4\,b^8\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(96\,a^2\,b^5-32\,a^4\,b^3\right)\,{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}+\frac{2\,a\,b\,\left(7\,a^6-68\,a^4\,b^2+59\,a^2\,b^4-10\,b^6\right)\,\left(\frac{32\,\left(6\,a^6\,b^5-8\,a^4\,b^7+2\,a^2\,b^9\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{\left(2\,b^4-6\,a^2\,b^2\right)\,\left(\frac{32\,\left(5\,a^{10}\,b^3+12\,a^8\,b^5+6\,a^6\,b^7-4\,a^4\,b^9-3\,a^2\,b^{11}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}+\frac{\left(\frac{32\,\left(-a^{14}\,b+3\,a^{12}\,b^3+18\,a^{10}\,b^5+22\,a^8\,b^7+3\,a^6\,b^9-9\,a^4\,b^{11}-4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(2\,b^4-6\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{a\,b\,\left(a^2-3\,b^2\right)\,\left(\frac{a\,b\,\left(\frac{32\,\left(-a^{14}\,b+3\,a^{12}\,b^3+18\,a^{10}\,b^5+22\,a^8\,b^7+3\,a^6\,b^9-9\,a^4\,b^{11}-4\,a^2\,b^{13}\right)}{a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}}-\frac{16\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^2-3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a\,b\,\left(a^2-3\,b^2\right)\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^2\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}-\frac{16\,a^2\,b^2\,{\left(a^2-3\,b^2\right)}^2\,\left(2\,b^4-6\,a^2\,b^2\right)\,\left(3\,a^{16}\,b+21\,a^{14}\,b^3+63\,a^{12}\,b^5+105\,a^{10}\,b^7+105\,a^8\,b^9+63\,a^6\,b^{11}+21\,a^4\,b^{13}+3\,a^2\,b^{15}\right)}{{\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}^3\,\left(a^{12}+6\,a^{10}\,b^2+15\,a^8\,b^4+20\,a^6\,b^6+15\,a^4\,b^8+6\,a^2\,b^{10}+b^{12}\right)}\right)\,\left(a^{16}+8\,a^{14}\,b^2+28\,a^{12}\,b^4+56\,a^{10}\,b^6+70\,a^8\,b^8+56\,a^6\,b^{10}+28\,a^4\,b^{12}+8\,a^2\,b^{14}+b^{16}\right)}{\left(96\,a^2\,b^5-32\,a^4\,b^3\right)\,{\left(a^8+31\,a^6\,b^2+15\,a^4\,b^4-11\,a^2\,b^6+4\,b^8\right)}^2}\right)\,\left(a^2-3\,b^2\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}","Not used",1,"((2*a*tan(x/2)^2)/(a^2 + b^2) - (8*b^3*tan(x/2)^3)/(a^2 + b^2)^2 - (2*a*tan(x/2)^4)/(a^2 + b^2) + (2*b*tan(x/2)*(a^2 - b^2))/(a^2 + b^2)^2 + (2*b*tan(x/2)^5*(a^2 - b^2))/(a^4 + b^4 + 2*a^2*b^2))/(a + 2*b*tan(x/2) + a*tan(x/2)^2 - a*tan(x/2)^4 - a*tan(x/2)^6 + 4*b*tan(x/2)^3 + 2*b*tan(x/2)^5) + (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(b^4 - 3*a^2*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (log(1/(cos(x) + 1))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (2*a*b*atan((tan(x/2)*((((((a*b*((32*(a*b^14 + 9*a^3*b^12 + 18*a^5*b^10 + 2*a^7*b^8 - 27*a^9*b^6 - 27*a^11*b^4 - 8*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^2 - 3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a*b*(a^2 - 3*b^2)*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*(a^2 - 3*b^2)*((32*(3*a*b^12 - 21*a^3*b^10 - 34*a^5*b^8 + 6*a^7*b^6 + 15*a^9*b^4 - a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((32*(a*b^14 + 9*a^3*b^12 + 18*a^5*b^10 + 2*a^7*b^8 - 27*a^9*b^6 - 27*a^11*b^4 - 8*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*b^3*(a^2 - 3*b^2)^3*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 4*b^8 - 61*a^2*b^6 + 155*a^4*b^4 - 67*a^6*b^2))/(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2 + (2*a*b*(7*a^6 - 10*b^6 + 59*a^2*b^4 - 68*a^4*b^2)*((32*(a*b^10 + 3*a^3*b^8 - 17*a^5*b^6 - 3*a^7*b^4))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((2*b^4 - 6*a^2*b^2)*((32*(3*a*b^12 - 21*a^3*b^10 - 34*a^5*b^8 + 6*a^7*b^6 + 15*a^9*b^4 - a^11*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((32*(a*b^14 + 9*a^3*b^12 + 18*a^5*b^10 + 2*a^7*b^8 - 27*a^9*b^6 - 27*a^11*b^4 - 8*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*(a^2 - 3*b^2)*((a*b*((32*(a*b^14 + 9*a^3*b^12 + 18*a^5*b^10 + 2*a^7*b^8 - 27*a^9*b^6 - 27*a^11*b^4 - 8*a^13*b^2))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^2 - 3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a*b*(a^2 - 3*b^2)*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a^2*b^2*(a^2 - 3*b^2)^2*(2*b^4 - 6*a^2*b^2)*(3*a*b^16 + 21*a^3*b^14 + 63*a^5*b^12 + 105*a^7*b^10 + 105*a^9*b^8 + 63*a^11*b^6 + 21*a^13*b^4 + 3*a^15*b^2))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/(96*a^2*b^5 - 32*a^4*b^3) + (((((a*b*((32*(3*a^6*b^9 - 4*a^2*b^13 - 9*a^4*b^11 - a^14*b + 22*a^8*b^7 + 18*a^10*b^5 + 3*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^2 - 3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a*b*(a^2 - 3*b^2)*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*(a^2 - 3*b^2)*((32*(6*a^6*b^7 - 4*a^4*b^9 - 3*a^2*b^11 + 12*a^8*b^5 + 5*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((32*(3*a^6*b^9 - 4*a^2*b^13 - 9*a^4*b^11 - a^14*b + 22*a^8*b^7 + 18*a^10*b^5 + 3*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (32*a^3*b^3*(a^2 - 3*b^2)^3*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^8 + 4*b^8 - 61*a^2*b^6 + 155*a^4*b^4 - 67*a^6*b^2)*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((96*a^2*b^5 - 32*a^4*b^3)*(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2) + (2*a*b*(7*a^6 - 10*b^6 + 59*a^2*b^4 - 68*a^4*b^2)*((32*(2*a^2*b^9 - 8*a^4*b^7 + 6*a^6*b^5))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - ((2*b^4 - 6*a^2*b^2)*((32*(6*a^6*b^7 - 4*a^4*b^9 - 3*a^2*b^11 + 12*a^8*b^5 + 5*a^10*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) + (((32*(3*a^6*b^9 - 4*a^2*b^13 - 9*a^4*b^11 - a^14*b + 22*a^8*b^7 + 18*a^10*b^5 + 3*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(2*b^4 - 6*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2))))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (a*b*(a^2 - 3*b^2)*((a*b*((32*(3*a^6*b^9 - 4*a^2*b^13 - 9*a^4*b^11 - a^14*b + 22*a^8*b^7 + 18*a^10*b^5 + 3*a^12*b^3))/(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2) - (16*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^2 - 3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a*b*(a^2 - 3*b^2)*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^2*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2))))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) - (16*a^2*b^2*(a^2 - 3*b^2)^2*(2*b^4 - 6*a^2*b^2)*(3*a^16*b + 3*a^2*b^15 + 21*a^4*b^13 + 63*a^6*b^11 + 105*a^8*b^9 + 105*a^10*b^7 + 63*a^12*b^5 + 21*a^14*b^3))/((a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)^3*(a^12 + b^12 + 6*a^2*b^10 + 15*a^4*b^8 + 20*a^6*b^6 + 15*a^8*b^4 + 6*a^10*b^2)))*(a^16 + b^16 + 8*a^2*b^14 + 28*a^4*b^12 + 56*a^6*b^10 + 70*a^8*b^8 + 56*a^10*b^6 + 28*a^12*b^4 + 8*a^14*b^2))/((96*a^2*b^5 - 32*a^4*b^3)*(a^8 + 4*b^8 - 11*a^2*b^6 + 15*a^4*b^4 + 31*a^6*b^2)^2))*(a^2 - 3*b^2))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)","B"
291,1,586,176,2.874562,"\text{Not used}","int((cos(x)^3*sin(x)^2)/(a*cos(x) + b*sin(x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(4\,a^4\,b+45\,a^2\,b^3-4\,b^5\right)}{3\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(2\,b^5-3\,a^2\,b^3\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(4\,a^5-9\,a^3\,b^2+32\,a\,b^4\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(4\,a^5+15\,a^3\,b^2-34\,a\,b^4\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(8\,a^4\,b-31\,a^2\,b^3+6\,b^5\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,\left(11\,a\,b^3-4\,a^3\,b\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(2\,a\,b^3-3\,a^3\,b\right)}{a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^3\,b+16\,a\,b^3\right)}{3\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7-2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+6\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{a\,b^2\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^7-a^6\,b\,1{}\mathrm{i}+3{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^5\,b^2-a^4\,b^3\,3{}\mathrm{i}+3{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^3\,b^4-a^2\,b^5\,3{}\mathrm{i}+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{x}{2}\right)\,a\,b^6-b^7\,1{}\mathrm{i}}{{\left(a^2+b^2\right)}^{7/2}}\right)\,\left(3\,a^2-2\,b^2\right)\,2{}\mathrm{i}}{{\left(a^2+b^2\right)}^{7/2}}","Not used",1,"- ((2*tan(x/2)^4*(4*a^4*b - 4*b^5 + 45*a^2*b^3))/(3*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) - (2*tan(x/2)^6*(2*b^5 - 3*a^2*b^3))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (2*tan(x/2)^5*(32*a*b^4 + 4*a^5 - 9*a^3*b^2))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (2*tan(x/2)^3*(4*a^5 - 34*a*b^4 + 15*a^3*b^2))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (2*tan(x/2)^2*(8*a^4*b + 6*b^5 - 31*a^2*b^3))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (2*a*(11*a*b^3 - 4*a^3*b))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (2*b*tan(x/2)^7*(2*a*b^3 - 3*a^3*b))/(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2) + (2*b*tan(x/2)*(16*a*b^3 + a^3*b))/(3*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)))/(a + 2*b*tan(x/2) + 2*a*tan(x/2)^2 - 2*a*tan(x/2)^6 - a*tan(x/2)^8 + 6*b*tan(x/2)^3 + 6*b*tan(x/2)^5 + 2*b*tan(x/2)^7) - (a*b^2*atan((a^7*tan(x/2)*1i - a^6*b*1i - b^7*1i - a^2*b^5*3i - a^4*b^3*3i + a^3*b^4*tan(x/2)*3i + a^5*b^2*tan(x/2)*3i + a*b^6*tan(x/2)*1i)/(a^2 + b^2)^(7/2))*(3*a^2 - 2*b^2)*2i)/(a^2 + b^2)^(7/2)","B"
292,1,8198,210,13.919656,"\text{Not used}","int((cos(x)^3*sin(x)^3)/(a*cos(x) + b*sin(x))^2,x)","\frac{\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(4\,a^3+a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(4\,a^3+a\,b^2\right)}{a^4+2\,a^2\,b^2+b^4}-\frac{3\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^4+2\,a^2\,b^2+b^4}+\frac{3\,a\,b^2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8}{a^4+2\,a^2\,b^2+b^4}+\frac{3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9\,\left(a^4-3\,a^2\,b^2\right)}{2\,\left(a^6+3\,a^4\,b^2+3\,a^2\,b^4+b^6\right)}+\frac{3\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4-3\,a^2\,b^2\right)}{2\,\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(a^4-4\,a^2\,b^2+b^4\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{4\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(a^4-4\,a^2\,b^2+b^4\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}-\frac{3\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(a^4+13\,a^2\,b^2\right)}{\left(a^2+b^2\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{10}+2\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9-3\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8+8\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7-2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+12\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5+2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+8\,b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+3\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a}+\frac{\ln\left(-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)+a\right)\,\left(3\,a^2\,b^4-3\,a^4\,b^2\right)}{a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8}-\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}+\frac{3\,a\,b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{6\,\left(9\,a^{13}\,b^4+99\,a^{11}\,b^6-135\,a^9\,b^8+45\,a^7\,b^{10}-18\,a^5\,b^{12}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(\frac{6\,\left(3\,a^{17}\,b^2-72\,a^{15}\,b^4+81\,a^{13}\,b^6+534\,a^{11}\,b^8+357\,a^9\,b^{10}-180\,a^7\,b^{12}-153\,a^5\,b^{14}+6\,a^3\,b^{16}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{6\,\left(-40\,a^{19}\,b^2-176\,a^{17}\,b^4-208\,a^{15}\,b^6+208\,a^{13}\,b^8+800\,a^{11}\,b^{10}+880\,a^9\,b^{12}+464\,a^7\,b^{14}+112\,a^5\,b^{16}+8\,a^3\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}\right)\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}-\frac{3\,a\,b\,\left(\frac{3\,a\,b\,\left(\frac{6\,\left(-40\,a^{19}\,b^2-176\,a^{17}\,b^4-208\,a^{15}\,b^6+208\,a^{13}\,b^8+800\,a^{11}\,b^{10}+880\,a^9\,b^{12}+464\,a^7\,b^{14}+112\,a^5\,b^{16}+8\,a^3\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{9\,a\,b\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{4\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{27\,a^2\,b^2\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,{\left(-a^2+2\,a\,b+b^2\right)}^2\,{\left(a^2+2\,a\,b-b^2\right)}^2\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{16\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^2\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(18\,a^9\,b-280\,a^7\,b^3+556\,a^5\,b^5-280\,a^3\,b^7+18\,a\,b^9\right)}{{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}+\frac{\left(\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{3\,a\,b\,\left(\frac{6\,\left(-40\,a^{19}\,b^2-176\,a^{17}\,b^4-208\,a^{15}\,b^6+208\,a^{13}\,b^8+800\,a^{11}\,b^{10}+880\,a^9\,b^{12}+464\,a^7\,b^{14}+112\,a^5\,b^{16}+8\,a^3\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{9\,a\,b\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{4\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}-\frac{3\,a\,b\,\left(\frac{6\,\left(3\,a^{17}\,b^2-72\,a^{15}\,b^4+81\,a^{13}\,b^6+534\,a^{11}\,b^8+357\,a^9\,b^{10}-180\,a^7\,b^{12}-153\,a^5\,b^{14}+6\,a^3\,b^{16}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{6\,\left(-40\,a^{19}\,b^2-176\,a^{17}\,b^4-208\,a^{15}\,b^6+208\,a^{13}\,b^8+800\,a^{11}\,b^{10}+880\,a^9\,b^{12}+464\,a^7\,b^{14}+112\,a^5\,b^{16}+8\,a^3\,b^{18}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{81\,a^3\,b^3\,{\left(-a^2+2\,a\,b+b^2\right)}^3\,{\left(a^2+2\,a\,b-b^2\right)}^3\,\left(16\,a^{21}\,b^2+160\,a^{19}\,b^4+720\,a^{17}\,b^6+1920\,a^{15}\,b^8+3360\,a^{13}\,b^{10}+4032\,a^{11}\,b^{12}+3360\,a^9\,b^{14}+1920\,a^7\,b^{16}+720\,a^5\,b^{18}+160\,a^3\,b^{20}+16\,a\,b^{22}\right)}{32\,{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^3\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(a^{10}-109\,a^8\,b^2+466\,a^6\,b^4-466\,a^4\,b^6+109\,a^2\,b^8-b^{10}\right)}{{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(2\,a^{22}+22\,a^{20}\,b^2+110\,a^{18}\,b^4+330\,a^{16}\,b^6+660\,a^{14}\,b^8+924\,a^{12}\,b^{10}+924\,a^{10}\,b^{12}+660\,a^8\,b^{14}+330\,a^6\,b^{16}+110\,a^4\,b^{18}+22\,a^2\,b^{20}+2\,b^{22}\right)}{27\,a^8\,b^3-162\,a^6\,b^5+27\,a^4\,b^7}+\frac{\left(\frac{6\,\left(-27\,a^{12}\,b^5+117\,a^{10}\,b^7-117\,a^8\,b^9+27\,a^6\,b^{11}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{6\,\left(21\,a^{16}\,b^3+30\,a^{14}\,b^5-69\,a^{12}\,b^7-156\,a^{10}\,b^9-69\,a^8\,b^{11}+30\,a^6\,b^{13}+21\,a^4\,b^{15}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{6\,\left(4\,a^{20}\,b-20\,a^{18}\,b^3-160\,a^{16}\,b^5-320\,a^{14}\,b^7-184\,a^{12}\,b^9+184\,a^{10}\,b^{11}+320\,a^8\,b^{13}+160\,a^6\,b^{15}+20\,a^4\,b^{17}-4\,a^2\,b^{19}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}+\frac{3\,a\,b\,\left(\frac{3\,a\,b\,\left(\frac{6\,\left(4\,a^{20}\,b-20\,a^{18}\,b^3-160\,a^{16}\,b^5-320\,a^{14}\,b^7-184\,a^{12}\,b^9+184\,a^{10}\,b^{11}+320\,a^8\,b^{13}+160\,a^6\,b^{15}+20\,a^4\,b^{17}-4\,a^2\,b^{19}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{9\,a\,b\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{4\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{27\,a^2\,b^2\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,{\left(-a^2+2\,a\,b+b^2\right)}^2\,{\left(a^2+2\,a\,b-b^2\right)}^2\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{16\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^2\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(18\,a^9\,b-280\,a^7\,b^3+556\,a^5\,b^5-280\,a^3\,b^7+18\,a\,b^9\right)\,\left(2\,a^{22}+22\,a^{20}\,b^2+110\,a^{18}\,b^4+330\,a^{16}\,b^6+660\,a^{14}\,b^8+924\,a^{12}\,b^{10}+924\,a^{10}\,b^{12}+660\,a^8\,b^{14}+330\,a^6\,b^{16}+110\,a^4\,b^{18}+22\,a^2\,b^{20}+2\,b^{22}\right)}{\left(27\,a^8\,b^3-162\,a^6\,b^5+27\,a^4\,b^7\right)\,{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}+\frac{\left(\frac{3\,a\,b\,\left(\frac{6\,\left(21\,a^{16}\,b^3+30\,a^{14}\,b^5-69\,a^{12}\,b^7-156\,a^{10}\,b^9-69\,a^8\,b^{11}+30\,a^6\,b^{13}+21\,a^4\,b^{15}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}-\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{6\,\left(4\,a^{20}\,b-20\,a^{18}\,b^3-160\,a^{16}\,b^5-320\,a^{14}\,b^7-184\,a^{12}\,b^9+184\,a^{10}\,b^{11}+320\,a^8\,b^{13}+160\,a^6\,b^{15}+20\,a^4\,b^{17}-4\,a^2\,b^{19}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}-\frac{\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(\frac{3\,a\,b\,\left(\frac{6\,\left(4\,a^{20}\,b-20\,a^{18}\,b^3-160\,a^{16}\,b^5-320\,a^{14}\,b^7-184\,a^{12}\,b^9+184\,a^{10}\,b^{11}+320\,a^8\,b^{13}+160\,a^6\,b^{15}+20\,a^4\,b^{17}-4\,a^2\,b^{19}\right)}{a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}}+\frac{3\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{4\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}+\frac{9\,a\,b\,\left(96\,a^2\,b^4-96\,a^4\,b^2\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{4\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)}{2\,\left(16\,a^8+64\,a^6\,b^2+96\,a^4\,b^4+64\,a^2\,b^6+16\,b^8\right)}+\frac{81\,a^3\,b^3\,{\left(-a^2+2\,a\,b+b^2\right)}^3\,{\left(a^2+2\,a\,b-b^2\right)}^3\,\left(16\,a^{22}\,b+160\,a^{20}\,b^3+720\,a^{18}\,b^5+1920\,a^{16}\,b^7+3360\,a^{14}\,b^9+4032\,a^{12}\,b^{11}+3360\,a^{10}\,b^{13}+1920\,a^8\,b^{15}+720\,a^6\,b^{17}+160\,a^4\,b^{19}+16\,a^2\,b^{21}\right)}{32\,{\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}^3\,\left(a^{18}+9\,a^{16}\,b^2+36\,a^{14}\,b^4+84\,a^{12}\,b^6+126\,a^{10}\,b^8+126\,a^8\,b^{10}+84\,a^6\,b^{12}+36\,a^4\,b^{14}+9\,a^2\,b^{16}+b^{18}\right)}\right)\,\left(a^{10}-109\,a^8\,b^2+466\,a^6\,b^4-466\,a^4\,b^6+109\,a^2\,b^8-b^{10}\right)\,\left(2\,a^{22}+22\,a^{20}\,b^2+110\,a^{18}\,b^4+330\,a^{16}\,b^6+660\,a^{14}\,b^8+924\,a^{12}\,b^{10}+924\,a^{10}\,b^{12}+660\,a^8\,b^{14}+330\,a^6\,b^{16}+110\,a^4\,b^{18}+22\,a^2\,b^{20}+2\,b^{22}\right)}{\left(27\,a^8\,b^3-162\,a^6\,b^5+27\,a^4\,b^7\right)\,{\left(a^{10}+53\,a^8\,b^2-38\,a^6\,b^4-38\,a^4\,b^6+53\,a^2\,b^8+b^{10}\right)}^2}\right)\,\left(-a^2+2\,a\,b+b^2\right)\,\left(a^2+2\,a\,b-b^2\right)}{2\,\left(a^8+4\,a^6\,b^2+6\,a^4\,b^4+4\,a^2\,b^6+b^8\right)}","Not used",1,"((tan(x/2)^4*(a*b^2 + 4*a^3))/(a^4 + b^4 + 2*a^2*b^2) - (tan(x/2)^6*(a*b^2 + 4*a^3))/(a^4 + b^4 + 2*a^2*b^2) - (3*a*b^2*tan(x/2)^2)/(a^4 + b^4 + 2*a^2*b^2) + (3*a*b^2*tan(x/2)^8)/(a^4 + b^4 + 2*a^2*b^2) + (3*b*tan(x/2)^9*(a^4 - 3*a^2*b^2))/(2*(a^6 + b^6 + 3*a^2*b^4 + 3*a^4*b^2)) + (3*b*tan(x/2)*(a^4 - 3*a^2*b^2))/(2*(a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (4*b*tan(x/2)^3*(a^4 + b^4 - 4*a^2*b^2))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) + (4*b*tan(x/2)^7*(a^4 + b^4 - 4*a^2*b^2))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)) - (3*b*tan(x/2)^5*(a^4 + 13*a^2*b^2))/((a^2 + b^2)*(a^4 + b^4 + 2*a^2*b^2)))/(a + 2*b*tan(x/2) + 3*a*tan(x/2)^2 + 2*a*tan(x/2)^4 - 2*a*tan(x/2)^6 - 3*a*tan(x/2)^8 - a*tan(x/2)^10 + 8*b*tan(x/2)^3 + 12*b*tan(x/2)^5 + 8*b*tan(x/2)^7 + 2*b*tan(x/2)^9) + (log(a + 2*b*tan(x/2) - a*tan(x/2)^2)*(3*a^2*b^4 - 3*a^4*b^2))/(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2) - (log(1/(cos(x) + 1))*(96*a^2*b^4 - 96*a^4*b^2))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)) + (3*a*b*atan((tan(x/2)*((((6*(45*a^7*b^10 - 18*a^5*b^12 - 135*a^9*b^8 + 99*a^11*b^6 + 9*a^13*b^4))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (((6*(6*a^3*b^16 - 153*a^5*b^14 - 180*a^7*b^12 + 357*a^9*b^10 + 534*a^11*b^8 + 81*a^13*b^6 - 72*a^15*b^4 + 3*a^17*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - ((96*a^2*b^4 - 96*a^4*b^2)*((6*(8*a^3*b^18 + 112*a^5*b^16 + 464*a^7*b^14 + 880*a^9*b^12 + 800*a^11*b^10 + 208*a^13*b^8 - 208*a^15*b^6 - 176*a^17*b^4 - 40*a^19*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)))*(96*a^2*b^4 - 96*a^4*b^2))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)) - (3*a*b*((3*a*b*((6*(8*a^3*b^18 + 112*a^5*b^16 + 464*a^7*b^14 + 880*a^9*b^12 + 800*a^11*b^10 + 208*a^13*b^8 - 208*a^15*b^6 - 176*a^17*b^4 - 40*a^19*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - (9*a*b*(96*a^2*b^4 - 96*a^4*b^2)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/(4*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (27*a^2*b^2*(96*a^2*b^4 - 96*a^4*b^2)*(2*a*b - a^2 + b^2)^2*(2*a*b + a^2 - b^2)^2*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/(16*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^2*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(18*a*b^9 + 18*a^9*b - 280*a^3*b^7 + 556*a^5*b^5 - 280*a^7*b^3))/(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2 + ((((96*a^2*b^4 - 96*a^4*b^2)*((3*a*b*((6*(8*a^3*b^18 + 112*a^5*b^16 + 464*a^7*b^14 + 880*a^9*b^12 + 800*a^11*b^10 + 208*a^13*b^8 - 208*a^15*b^6 - 176*a^17*b^4 - 40*a^19*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - (9*a*b*(96*a^2*b^4 - 96*a^4*b^2)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/(4*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)) - (3*a*b*((6*(6*a^3*b^16 - 153*a^5*b^14 - 180*a^7*b^12 + 357*a^9*b^10 + 534*a^11*b^8 + 81*a^13*b^6 - 72*a^15*b^4 + 3*a^17*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - ((96*a^2*b^4 - 96*a^4*b^2)*((6*(8*a^3*b^18 + 112*a^5*b^16 + 464*a^7*b^14 + 880*a^9*b^12 + 800*a^11*b^10 + 208*a^13*b^8 - 208*a^15*b^6 - 176*a^17*b^4 - 40*a^19*b^2))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (81*a^3*b^3*(2*a*b - a^2 + b^2)^3*(2*a*b + a^2 - b^2)^3*(16*a*b^22 + 160*a^3*b^20 + 720*a^5*b^18 + 1920*a^7*b^16 + 3360*a^9*b^14 + 4032*a^11*b^12 + 3360*a^13*b^10 + 1920*a^15*b^8 + 720*a^17*b^6 + 160*a^19*b^4 + 16*a^21*b^2))/(32*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^3*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(a^10 - b^10 + 109*a^2*b^8 - 466*a^4*b^6 + 466*a^6*b^4 - 109*a^8*b^2))/(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2)*(2*a^22 + 2*b^22 + 22*a^2*b^20 + 110*a^4*b^18 + 330*a^6*b^16 + 660*a^8*b^14 + 924*a^10*b^12 + 924*a^12*b^10 + 660*a^14*b^8 + 330*a^16*b^6 + 110*a^18*b^4 + 22*a^20*b^2))/(27*a^4*b^7 - 162*a^6*b^5 + 27*a^8*b^3) + (((6*(27*a^6*b^11 - 117*a^8*b^9 + 117*a^10*b^7 - 27*a^12*b^5))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + ((96*a^2*b^4 - 96*a^4*b^2)*((6*(21*a^4*b^15 + 30*a^6*b^13 - 69*a^8*b^11 - 156*a^10*b^9 - 69*a^12*b^7 + 30*a^14*b^5 + 21*a^16*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - ((96*a^2*b^4 - 96*a^4*b^2)*((6*(4*a^20*b - 4*a^2*b^19 + 20*a^4*b^17 + 160*a^6*b^15 + 320*a^8*b^13 + 184*a^10*b^11 - 184*a^12*b^9 - 320*a^14*b^7 - 160*a^16*b^5 - 20*a^18*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)) + (3*a*b*((3*a*b*((6*(4*a^20*b - 4*a^2*b^19 + 20*a^4*b^17 + 160*a^6*b^15 + 320*a^8*b^13 + 184*a^10*b^11 - 184*a^12*b^9 - 320*a^14*b^7 - 160*a^16*b^5 - 20*a^18*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (9*a*b*(96*a^2*b^4 - 96*a^4*b^2)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/(4*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (27*a^2*b^2*(96*a^2*b^4 - 96*a^4*b^2)*(2*a*b - a^2 + b^2)^2*(2*a*b + a^2 - b^2)^2*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/(16*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^2*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(18*a*b^9 + 18*a^9*b - 280*a^3*b^7 + 556*a^5*b^5 - 280*a^7*b^3)*(2*a^22 + 2*b^22 + 22*a^2*b^20 + 110*a^4*b^18 + 330*a^6*b^16 + 660*a^8*b^14 + 924*a^10*b^12 + 924*a^12*b^10 + 660*a^14*b^8 + 330*a^16*b^6 + 110*a^18*b^4 + 22*a^20*b^2))/((27*a^4*b^7 - 162*a^6*b^5 + 27*a^8*b^3)*(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2) + (((3*a*b*((6*(21*a^4*b^15 + 30*a^6*b^13 - 69*a^8*b^11 - 156*a^10*b^9 - 69*a^12*b^7 + 30*a^14*b^5 + 21*a^16*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) - ((96*a^2*b^4 - 96*a^4*b^2)*((6*(4*a^20*b - 4*a^2*b^19 + 20*a^4*b^17 + 160*a^6*b^15 + 320*a^8*b^13 + 184*a^10*b^11 - 184*a^12*b^9 - 320*a^14*b^7 - 160*a^16*b^5 - 20*a^18*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) - ((96*a^2*b^4 - 96*a^4*b^2)*((3*a*b*((6*(4*a^20*b - 4*a^2*b^19 + 20*a^4*b^17 + 160*a^6*b^15 + 320*a^8*b^13 + 184*a^10*b^11 - 184*a^12*b^9 - 320*a^14*b^7 - 160*a^16*b^5 - 20*a^18*b^3))/(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2) + (3*(96*a^2*b^4 - 96*a^4*b^2)*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/((16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(4*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)) + (9*a*b*(96*a^2*b^4 - 96*a^4*b^2)*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2)*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/(4*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2))))/(2*(16*a^8 + 16*b^8 + 64*a^2*b^6 + 96*a^4*b^4 + 64*a^6*b^2)) + (81*a^3*b^3*(2*a*b - a^2 + b^2)^3*(2*a*b + a^2 - b^2)^3*(16*a^22*b + 16*a^2*b^21 + 160*a^4*b^19 + 720*a^6*b^17 + 1920*a^8*b^15 + 3360*a^10*b^13 + 4032*a^12*b^11 + 3360*a^14*b^9 + 1920*a^16*b^7 + 720*a^18*b^5 + 160*a^20*b^3))/(32*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2)^3*(a^18 + b^18 + 9*a^2*b^16 + 36*a^4*b^14 + 84*a^6*b^12 + 126*a^8*b^10 + 126*a^10*b^8 + 84*a^12*b^6 + 36*a^14*b^4 + 9*a^16*b^2)))*(a^10 - b^10 + 109*a^2*b^8 - 466*a^4*b^6 + 466*a^6*b^4 - 109*a^8*b^2)*(2*a^22 + 2*b^22 + 22*a^2*b^20 + 110*a^4*b^18 + 330*a^6*b^16 + 660*a^8*b^14 + 924*a^10*b^12 + 924*a^12*b^10 + 660*a^14*b^8 + 330*a^16*b^6 + 110*a^18*b^4 + 22*a^20*b^2))/((27*a^4*b^7 - 162*a^6*b^5 + 27*a^8*b^3)*(a^10 + b^10 + 53*a^2*b^8 - 38*a^4*b^6 - 38*a^6*b^4 + 53*a^8*b^2)^2))*(2*a*b - a^2 + b^2)*(2*a*b + a^2 - b^2))/(2*(a^8 + b^8 + 4*a^2*b^6 + 6*a^4*b^4 + 4*a^6*b^2))","B"
293,1,408,47,1.475705,"\text{Not used}","int(tan(x)/(b*cos(x) + a*sin(x)),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}-\frac{2\,b\,\mathrm{atanh}\left(\frac{64\,b^3}{\sqrt{a^2+b^2}\,\left(128\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{128\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{64\,a\,b^3}{a^2+b^2}\right)}-\frac{64\,b^5}{{\left(a^2+b^2\right)}^{3/2}\,\left(128\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{128\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{64\,a\,b^3}{a^2+b^2}\right)}+\frac{128\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}\,\left(\frac{64\,a^2\,b^3}{a^2+b^2}+128\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{128\,a\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}\right)}-\frac{128\,b^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left(a^2+b^2\right)}^{3/2}\,\left(\frac{64\,a^2\,b^3}{a^2+b^2}+128\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{128\,a\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}\right)}+\frac{128\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}\,\left(128\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{128\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{64\,a\,b^3}{a^2+b^2}\right)}-\frac{192\,a\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{{\left(a^2+b^2\right)}^{3/2}\,\left(128\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{128\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}+\frac{64\,a\,b^3}{a^2+b^2}\right)}\right)}{a\,\sqrt{a^2+b^2}}","Not used",1,"(2*atanh(tan(x/2)))/a - (2*b*atanh((64*b^3)/((a^2 + b^2)^(1/2)*(128*b^2*tan(x/2) - (128*b^4*tan(x/2))/(a^2 + b^2) + (64*a*b^3)/(a^2 + b^2))) - (64*b^5)/((a^2 + b^2)^(3/2)*(128*b^2*tan(x/2) - (128*b^4*tan(x/2))/(a^2 + b^2) + (64*a*b^3)/(a^2 + b^2))) + (128*b^4*tan(x/2))/((a^2 + b^2)^(1/2)*((64*a^2*b^3)/(a^2 + b^2) + 128*a*b^2*tan(x/2) - (128*a*b^4*tan(x/2))/(a^2 + b^2))) - (128*b^6*tan(x/2))/((a^2 + b^2)^(3/2)*((64*a^2*b^3)/(a^2 + b^2) + 128*a*b^2*tan(x/2) - (128*a*b^4*tan(x/2))/(a^2 + b^2))) + (128*a*b^2*tan(x/2))/((a^2 + b^2)^(1/2)*(128*b^2*tan(x/2) - (128*b^4*tan(x/2))/(a^2 + b^2) + (64*a*b^3)/(a^2 + b^2))) - (192*a*b^4*tan(x/2))/((a^2 + b^2)^(3/2)*(128*b^2*tan(x/2) - (128*b^4*tan(x/2))/(a^2 + b^2) + (64*a*b^3)/(a^2 + b^2)))))/(a*(a^2 + b^2)^(1/2))","B"
294,1,123,48,0.983745,"\text{Not used}","int(cot(x)/(b*cos(x) + a*sin(x)),x)","\frac{\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{b}-\frac{2\,a\,\mathrm{atanh}\left(\frac{\sqrt{a^2+b^2}\,\left(4{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^2+2{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a\,b+1{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,b^2\right)}{a^3\,\sin\left(\frac{x}{2}\right)\,4{}\mathrm{i}+a^2\,b\,\cos\left(\frac{x}{2}\right)\,1{}\mathrm{i}+a\,b^2\,\sin\left(\frac{x}{2}\right)\,3{}\mathrm{i}+b\,\cos\left(\frac{x}{2}\right)\,\left(a^2+b^2\right)\,1{}\mathrm{i}}\right)}{b\,\sqrt{a^2+b^2}}","Not used",1,"log(sin(x/2)/cos(x/2))/b - (2*a*atanh(((a^2 + b^2)^(1/2)*(a^2*sin(x/2)*4i + b^2*sin(x/2)*1i + a*b*cos(x/2)*2i))/(a^3*sin(x/2)*4i + a^2*b*cos(x/2)*1i + a*b^2*sin(x/2)*3i + b*cos(x/2)*(a^2 + b^2)*1i)))/(b*(a^2 + b^2)^(1/2))","B"