1,1,32,0,0.262831," ","integrate(2/(3-cos(4+6*x)),x)","\frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(3 x + 2 \right)} \right)} + \pi \left\lfloor{\frac{3 x - \frac{\pi}{2} + 2}{\pi}}\right\rfloor\right)}{6}"," ",0,"sqrt(2)*(atan(sqrt(2)*tan(3*x + 2)) + pi*floor((3*x - pi/2 + 2)/pi))/6","A",0
2,0,0,0,0.000000," ","integrate(2*csc(4+6*x)/(-cot(4+6*x)+3*csc(4+6*x)),x)","- 2 \int \frac{\csc{\left(6 x + 4 \right)}}{\cot{\left(6 x + 4 \right)} - 3 \csc{\left(6 x + 4 \right)}}\, dx"," ",0,"-2*Integral(csc(6*x + 4)/(cot(6*x + 4) - 3*csc(6*x + 4)), x)","F",0
3,1,246,0,6.818232," ","integrate(1/(1+sin(2+3*x)**2),x)","\frac{47321 \sqrt{2} \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{66922 \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{8119 \sqrt{2} \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{11482 \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606}"," ",0,"47321*sqrt(2)*sqrt(3 - 2*sqrt(2))*(atan(tan(3*x/2 + 1)/sqrt(3 - 2*sqrt(2))) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 66922*sqrt(3 - 2*sqrt(2))*(atan(tan(3*x/2 + 1)/sqrt(3 - 2*sqrt(2))) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 8119*sqrt(2)*sqrt(2*sqrt(2) + 3)*(atan(tan(3*x/2 + 1)/sqrt(2*sqrt(2) + 3)) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 11482*sqrt(2*sqrt(2) + 3)*(atan(tan(3*x/2 + 1)/sqrt(2*sqrt(2) + 3)) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606)","B",0
4,1,246,0,7.115178," ","integrate(1/(2-cos(2+3*x)**2),x)","\frac{47321 \sqrt{2} \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{66922 \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{8119 \sqrt{2} \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{11482 \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606}"," ",0,"47321*sqrt(2)*sqrt(3 - 2*sqrt(2))*(atan(tan(3*x/2 + 1)/sqrt(3 - 2*sqrt(2))) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 66922*sqrt(3 - 2*sqrt(2))*(atan(tan(3*x/2 + 1)/sqrt(3 - 2*sqrt(2))) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 8119*sqrt(2)*sqrt(2*sqrt(2) + 3)*(atan(tan(3*x/2 + 1)/sqrt(2*sqrt(2) + 3)) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 11482*sqrt(2*sqrt(2) + 3)*(atan(tan(3*x/2 + 1)/sqrt(2*sqrt(2) + 3)) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606)","B",0
5,1,246,0,6.994711," ","integrate(1/(cos(2+3*x)**2+2*sin(2+3*x)**2),x)","\frac{47321 \sqrt{2} \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{66922 \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{8119 \sqrt{2} \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606} + \frac{11482 \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} + 1 \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{83160 \sqrt{2} + 117606}"," ",0,"47321*sqrt(2)*sqrt(3 - 2*sqrt(2))*(atan(tan(3*x/2 + 1)/sqrt(3 - 2*sqrt(2))) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 66922*sqrt(3 - 2*sqrt(2))*(atan(tan(3*x/2 + 1)/sqrt(3 - 2*sqrt(2))) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 8119*sqrt(2)*sqrt(2*sqrt(2) + 3)*(atan(tan(3*x/2 + 1)/sqrt(2*sqrt(2) + 3)) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606) + 11482*sqrt(2*sqrt(2) + 3)*(atan(tan(3*x/2 + 1)/sqrt(2*sqrt(2) + 3)) + pi*floor((3*x/2 - pi/2 + 1)/pi))/(83160*sqrt(2) + 117606)","B",0
6,0,0,0,0.000000," ","integrate(sec(2+3*x)**2/(1+2*tan(2+3*x)**2),x)","\int \frac{\sec^{2}{\left(3 x + 2 \right)}}{2 \tan^{2}{\left(3 x + 2 \right)} + 1}\, dx"," ",0,"Integral(sec(3*x + 2)**2/(2*tan(3*x + 2)**2 + 1), x)","F",0
7,0,0,0,0.000000," ","integrate(csc(2+3*x)**2/(2+cot(2+3*x)**2),x)","\int \frac{\csc^{2}{\left(3 x + 2 \right)}}{\cot^{2}{\left(3 x + 2 \right)} + 2}\, dx"," ",0,"Integral(csc(3*x + 2)**2/(cot(3*x + 2)**2 + 2), x)","F",0
8,1,42,0,0.311873," ","integrate(2/(1-3*cos(4+6*x)),x)","\frac{\sqrt{2} \log{\left(\tan{\left(3 x + 2 \right)} - \frac{\sqrt{2}}{2} \right)}}{12} - \frac{\sqrt{2} \log{\left(\tan{\left(3 x + 2 \right)} + \frac{\sqrt{2}}{2} \right)}}{12}"," ",0,"sqrt(2)*log(tan(3*x + 2) - sqrt(2)/2)/12 - sqrt(2)*log(tan(3*x + 2) + sqrt(2)/2)/12","A",0
9,0,0,0,0.000000," ","integrate(2*csc(4+6*x)/(-3*cot(4+6*x)+csc(4+6*x)),x)","- 2 \int \frac{\csc{\left(6 x + 4 \right)}}{3 \cot{\left(6 x + 4 \right)} - \csc{\left(6 x + 4 \right)}}\, dx"," ",0,"-2*Integral(csc(6*x + 4)/(3*cot(6*x + 4) - csc(6*x + 4)), x)","F",0
10,1,1644,0,18.470890," ","integrate(1/(-1+3*sin(2+3*x)**2),x)","- \frac{1387702511766624 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{566527178101133 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{1376499295618884 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{561953484261121 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{1247944371758796 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{509471156364528 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{47005690897992 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{115139957707068 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{12353375735168316 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{5043244525340232 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{4748539075824 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{11631497759436 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{140186421619524 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{57230866972417 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{13625938289227872 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{5562766012543373 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}}"," ",0,"-1387702511766624*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 566527178101133*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 1376499295618884*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 561953484261121*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 1247944371758796*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 509471156364528*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 47005690897992*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 115139957707068*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 12353375735168316*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 5043244525340232*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 4748539075824*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 11631497759436*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 140186421619524*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 57230866972417*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 13625938289227872*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 5562766012543373*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5))","B",0
11,1,1644,0,14.403245," ","integrate(1/(2-3*cos(2+3*x)**2),x)","- \frac{1387702511766624 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{566527178101133 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{1376499295618884 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{561953484261121 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{1247944371758796 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{509471156364528 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{47005690897992 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{115139957707068 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{12353375735168316 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{5043244525340232 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{4748539075824 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{11631497759436 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{140186421619524 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{57230866972417 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{13625938289227872 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{5562766012543373 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}}"," ",0,"-1387702511766624*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 566527178101133*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 1376499295618884*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 561953484261121*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 1247944371758796*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 509471156364528*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 47005690897992*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 115139957707068*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 12353375735168316*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 5043244525340232*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 4748539075824*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 11631497759436*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 140186421619524*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 57230866972417*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 13625938289227872*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 5562766012543373*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5))","B",0
12,1,1644,0,17.089666," ","integrate(1/(-cos(2+3*x)**2+2*sin(2+3*x)**2),x)","- \frac{1387702511766624 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{566527178101133 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{1376499295618884 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{561953484261121 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{1247944371758796 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{509471156364528 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{47005690897992 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{115139957707068 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{12353375735168316 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{5043244525340232 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{4748539075824 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{11631497759436 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{140186421619524 \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} - \frac{57230866972417 \sqrt{6} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{13625938289227872 \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}} + \frac{5562766012543373 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{-467972363532675 - 191048917396548 \sqrt{6} + 13665597568857156 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} + 33473741073918339 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5}}"," ",0,"-1387702511766624*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 566527178101133*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 1376499295618884*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 561953484261121*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 1247944371758796*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 509471156364528*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 47005690897992*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 115139957707068*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(5 - 2*sqrt(6)))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 12353375735168316*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 5043244525340232*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 4748539075824*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 11631497759436*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) - sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 140186421619524*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) - 57230866972417*sqrt(6)*sqrt(2*sqrt(6) + 5)*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 13625938289227872*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5)) + 5562766012543373*sqrt(6)*sqrt(5 - 2*sqrt(6))*log(tan(3*x/2 + 1) + sqrt(2*sqrt(6) + 5))/(-467972363532675 - 191048917396548*sqrt(6) + 13665597568857156*sqrt(6)*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5) + 33473741073918339*sqrt(5 - 2*sqrt(6))*sqrt(2*sqrt(6) + 5))","B",0
13,0,0,0,0.000000," ","integrate(sec(2+3*x)**2/(-1+2*tan(2+3*x)**2),x)","\int \frac{\sec^{2}{\left(3 x + 2 \right)}}{2 \tan^{2}{\left(3 x + 2 \right)} - 1}\, dx"," ",0,"Integral(sec(3*x + 2)**2/(2*tan(3*x + 2)**2 - 1), x)","F",0
14,0,0,0,0.000000," ","integrate(csc(2+3*x)**2/(2-cot(2+3*x)**2),x)","- \int \frac{\csc^{2}{\left(3 x + 2 \right)}}{\cot^{2}{\left(3 x + 2 \right)} - 2}\, dx"," ",0,"-Integral(csc(3*x + 2)**2/(cot(3*x + 2)**2 - 2), x)","F",0
15,1,34,0,0.255187," ","integrate(2/(3+cos(4+6*x)),x)","\frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(3 x + 2 \right)}}{2} \right)} + \pi \left\lfloor{\frac{3 x - \frac{\pi}{2} + 2}{\pi}}\right\rfloor\right)}{6}"," ",0,"sqrt(2)*(atan(sqrt(2)*tan(3*x + 2)/2) + pi*floor((3*x - pi/2 + 2)/pi))/6","A",0
16,0,0,0,0.000000," ","integrate(2*csc(4+6*x)/(cot(4+6*x)+3*csc(4+6*x)),x)","2 \int \frac{\csc{\left(6 x + 4 \right)}}{\cot{\left(6 x + 4 \right)} + 3 \csc{\left(6 x + 4 \right)}}\, dx"," ",0,"2*Integral(csc(6*x + 4)/(cot(6*x + 4) + 3*csc(6*x + 4)), x)","F",0
17,1,76,0,0.750306," ","integrate(1/(2-sin(2+3*x)**2),x)","\frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{3 x}{2} + 1 \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{6} + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{3 x}{2} + 1 \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{6}"," ",0,"sqrt(2)*(atan(sqrt(2)*tan(3*x/2 + 1) - 1) + pi*floor((3*x/2 - pi/2 + 1)/pi))/6 + sqrt(2)*(atan(sqrt(2)*tan(3*x/2 + 1) + 1) + pi*floor((3*x/2 - pi/2 + 1)/pi))/6","A",0
18,1,76,0,0.647899," ","integrate(1/(1+cos(2+3*x)**2),x)","\frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{3 x}{2} + 1 \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{6} + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{3 x}{2} + 1 \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{6}"," ",0,"sqrt(2)*(atan(sqrt(2)*tan(3*x/2 + 1) - 1) + pi*floor((3*x/2 - pi/2 + 1)/pi))/6 + sqrt(2)*(atan(sqrt(2)*tan(3*x/2 + 1) + 1) + pi*floor((3*x/2 - pi/2 + 1)/pi))/6","A",0
19,1,76,0,0.797528," ","integrate(1/(2*cos(2+3*x)**2+sin(2+3*x)**2),x)","\frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{3 x}{2} + 1 \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{6} + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{3 x}{2} + 1 \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2} + 1}{\pi}}\right\rfloor\right)}{6}"," ",0,"sqrt(2)*(atan(sqrt(2)*tan(3*x/2 + 1) - 1) + pi*floor((3*x/2 - pi/2 + 1)/pi))/6 + sqrt(2)*(atan(sqrt(2)*tan(3*x/2 + 1) + 1) + pi*floor((3*x/2 - pi/2 + 1)/pi))/6","A",0
20,0,0,0,0.000000," ","integrate(sec(2+3*x)**2/(2+tan(2+3*x)**2),x)","\int \frac{\sec^{2}{\left(3 x + 2 \right)}}{\tan^{2}{\left(3 x + 2 \right)} + 2}\, dx"," ",0,"Integral(sec(3*x + 2)**2/(tan(3*x + 2)**2 + 2), x)","F",0
21,0,0,0,0.000000," ","integrate(csc(2+3*x)**2/(1+2*cot(2+3*x)**2),x)","\int \frac{\csc^{2}{\left(3 x + 2 \right)}}{2 \cot^{2}{\left(3 x + 2 \right)} + 1}\, dx"," ",0,"Integral(csc(3*x + 2)**2/(2*cot(3*x + 2)**2 + 1), x)","F",0
22,1,39,0,0.308194," ","integrate(-2/(1+3*cos(4+6*x)),x)","\frac{\sqrt{2} \log{\left(\tan{\left(3 x + 2 \right)} - \sqrt{2} \right)}}{12} - \frac{\sqrt{2} \log{\left(\tan{\left(3 x + 2 \right)} + \sqrt{2} \right)}}{12}"," ",0,"sqrt(2)*log(tan(3*x + 2) - sqrt(2))/12 - sqrt(2)*log(tan(3*x + 2) + sqrt(2))/12","A",0
23,0,0,0,0.000000," ","integrate(-2*csc(4+6*x)/(3*cot(4+6*x)+csc(4+6*x)),x)","- 2 \int \frac{\csc{\left(6 x + 4 \right)}}{3 \cot{\left(6 x + 4 \right)} + \csc{\left(6 x + 4 \right)}}\, dx"," ",0,"-2*Integral(csc(6*x + 4)/(3*cot(6*x + 4) + csc(6*x + 4)), x)","F",0
24,1,1481,0,14.067034," ","integrate(1/(-2+3*sin(2+3*x)**2),x)","- \frac{4988289 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{136929 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{79056 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{8639970 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{11281635 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{487723 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{844761 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{6513455 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{1820207 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{3022905 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{1745275 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{3152691 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{1336608 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{511026 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{295041 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{2315073 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}}"," ",0,"-4988289*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 136929*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 79056*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 8639970*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 11281635*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 487723*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 844761*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 6513455*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 1820207*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 3022905*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 1745275*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 3152691*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 1336608*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 511026*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 295041*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 2315073*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2))","B",0
25,1,1481,0,12.826981," ","integrate(1/(1-3*cos(2+3*x)**2),x)","- \frac{4988289 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{136929 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{79056 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{8639970 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{11281635 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{487723 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{844761 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{6513455 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{1820207 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{3022905 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{1745275 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{3152691 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{1336608 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{511026 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{295041 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{2315073 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}}"," ",0,"-4988289*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 136929*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 79056*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 8639970*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 11281635*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 487723*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 844761*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 6513455*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 1820207*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 3022905*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 1745275*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 3152691*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 1336608*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 511026*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 295041*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 2315073*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2))","B",0
26,1,1481,0,16.477622," ","integrate(1/(-2*cos(2+3*x)**2+sin(2+3*x)**2),x)","- \frac{4988289 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{136929 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{79056 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{8639970 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{11281635 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{487723 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{844761 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{6513455 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{2 - \sqrt{3}} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{1820207 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{3022905 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{1745275 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{3152691 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} - \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{1336608 \sqrt{3} \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} - \frac{511026 \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{295041 \sqrt{3} \sqrt{\sqrt{3} + 2} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}} + \frac{2315073 \sqrt{2 - \sqrt{3}} \log{\left(\tan{\left(\frac{3 x}{2} + 1 \right)} + \sqrt{\sqrt{3} + 2} \right)}}{- 39175383 \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2} - 2003742 \sqrt{3} + 3470583 + 22617918 \sqrt{3} \sqrt{2 - \sqrt{3}} \sqrt{\sqrt{3} + 2}}"," ",0,"-4988289*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 136929*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 79056*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 8639970*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 11281635*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 487723*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 844761*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 6513455*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(2 - sqrt(3)))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 1820207*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 3022905*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 1745275*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 3152691*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) - sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 1336608*sqrt(3)*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) - 511026*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 295041*sqrt(3)*sqrt(sqrt(3) + 2)*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2)) + 2315073*sqrt(2 - sqrt(3))*log(tan(3*x/2 + 1) + sqrt(sqrt(3) + 2))/(-39175383*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2) - 2003742*sqrt(3) + 3470583 + 22617918*sqrt(3)*sqrt(2 - sqrt(3))*sqrt(sqrt(3) + 2))","B",0
27,0,0,0,0.000000," ","integrate(sec(2+3*x)**2/(-2+tan(2+3*x)**2),x)","\int \frac{\sec^{2}{\left(3 x + 2 \right)}}{\tan^{2}{\left(3 x + 2 \right)} - 2}\, dx"," ",0,"Integral(sec(3*x + 2)**2/(tan(3*x + 2)**2 - 2), x)","F",0
28,0,0,0,0.000000," ","integrate(csc(2+3*x)**2/(1-2*cot(2+3*x)**2),x)","- \int \frac{\csc^{2}{\left(3 x + 2 \right)}}{2 \cot^{2}{\left(3 x + 2 \right)} - 1}\, dx"," ",0,"-Integral(csc(3*x + 2)**2/(2*cot(3*x + 2)**2 - 1), x)","F",0
29,1,41,0,0.162859," ","integrate((x+sin(x))**2,x)","\frac{x^{3}}{3} + \frac{x \sin^{2}{\left(x \right)}}{2} + \frac{x \cos^{2}{\left(x \right)}}{2} - 2 x \cos{\left(x \right)} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + 2 \sin{\left(x \right)}"," ",0,"x**3/3 + x*sin(x)**2/2 + x*cos(x)**2/2 - 2*x*cos(x) - sin(x)*cos(x)/2 + 2*sin(x)","A",0
30,1,85,0,0.303513," ","integrate((x+sin(x))**3,x)","\frac{x^{4}}{4} + \frac{3 x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{3 x^{2} \cos^{2}{\left(x \right)}}{4} - 3 x^{2} \cos{\left(x \right)} - \frac{3 x \sin{\left(x \right)} \cos{\left(x \right)}}{2} + 6 x \sin{\left(x \right)} - \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin^{2}{\left(x \right)}}{4} - \frac{2 \cos^{3}{\left(x \right)}}{3} + 6 \cos{\left(x \right)}"," ",0,"x**4/4 + 3*x**2*sin(x)**2/4 + 3*x**2*cos(x)**2/4 - 3*x**2*cos(x) - 3*x*sin(x)*cos(x)/2 + 6*x*sin(x) - sin(x)**2*cos(x) + 3*sin(x)**2/4 - 2*cos(x)**3/3 + 6*cos(x)","A",0
31,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x**2+c),x)","\int \frac{\sin{\left(a + b x \right)}}{c + d x^{2}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x**2), x)","F",0
32,0,0,0,0.000000," ","integrate(sin(b*x+a)/(e*x**2+d*x+c),x)","\int \frac{\sin{\left(a + b x \right)}}{c + d x + e x^{2}}\, dx"," ",0,"Integral(sin(a + b*x)/(c + d*x + e*x**2), x)","F",0
33,1,10,0,0.258339," ","integrate(sin((-7+x)**(1/2))/(-7+x)**(1/2),x)","- 2 \cos{\left(\sqrt{x - 7} \right)}"," ",0,"-2*cos(sqrt(x - 7))","A",0
34,0,0,0,0.000000," ","integrate(sin(x)*(b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- \frac{a}{x^{2}} + b} \sin{\left(x \right)}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-a/x**2 + b)*sin(x)/sqrt(a - b*x**2), x)","F",0
35,1,10,0,1.362535," ","integrate(1/x/(1+sin(ln(x))),x)","- \frac{2}{\tan{\left(\frac{\log{\left(x \right)}}{2} \right)} + 1}"," ",0,"-2/(tan(log(x)/2) + 1)","A",0
36,0,0,0,0.000000," ","integrate(sin((b*x+a)/(d*x+c)),x)","\int \sin{\left(\frac{a + b x}{c + d x} \right)}\, dx"," ",0,"Integral(sin((a + b*x)/(c + d*x)), x)","F",0
37,-1,0,0,0.000000," ","integrate(sin((b*x+a)/(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(sin((b*x+a)/(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,0,0,0,0.000000," ","integrate(sin((-a*x+1)**(1/2)/(a*x+1)**(1/2))**3/(-a**2*x**2+1),x)","- \int \frac{\sin^{3}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(sin(sqrt(-a*x + 1)/sqrt(a*x + 1))**3/(a**2*x**2 - 1), x)","F",0
40,0,0,0,0.000000," ","integrate(sin((-a*x+1)**(1/2)/(a*x+1)**(1/2))**2/(-a**2*x**2+1),x)","- \int \frac{\sin^{2}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(sin(sqrt(-a*x + 1)/sqrt(a*x + 1))**2/(a**2*x**2 - 1), x)","F",0
41,0,0,0,0.000000," ","integrate(sin((-a*x+1)**(1/2)/(a*x+1)**(1/2))/(-a**2*x**2+1),x)","- \int \frac{\sin{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(sin(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a**2*x**2 - 1), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)/sin((-a*x+1)**(1/2)/(a*x+1)**(1/2)),x)","- \int \frac{1}{a^{2} x^{2} \sin{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)} - \sin{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**2*sin(sqrt(-a*x + 1)/sqrt(a*x + 1)) - sin(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)/sin((-a*x+1)**(1/2)/(a*x+1)**(1/2))**2,x)","- \int \frac{1}{a^{2} x^{2} \sin^{2}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)} - \sin^{2}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**2*sin(sqrt(-a*x + 1)/sqrt(a*x + 1))**2 - sin(sqrt(-a*x + 1)/sqrt(a*x + 1))**2), x)","F",0
44,1,41,0,0.164355," ","integrate((x+cos(x))**2,x)","\frac{x^{3}}{3} + \frac{x \sin^{2}{\left(x \right)}}{2} + 2 x \sin{\left(x \right)} + \frac{x \cos^{2}{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + 2 \cos{\left(x \right)}"," ",0,"x**3/3 + x*sin(x)**2/2 + 2*x*sin(x) + x*cos(x)**2/2 + sin(x)*cos(x)/2 + 2*cos(x)","A",0
45,1,85,0,0.306721," ","integrate((x+cos(x))**3,x)","\frac{x^{4}}{4} + \frac{3 x^{2} \sin^{2}{\left(x \right)}}{4} + 3 x^{2} \sin{\left(x \right)} + \frac{3 x^{2} \cos^{2}{\left(x \right)}}{4} + \frac{3 x \sin{\left(x \right)} \cos{\left(x \right)}}{2} + 6 x \cos{\left(x \right)} + \frac{2 \sin^{3}{\left(x \right)}}{3} - \frac{3 \sin^{2}{\left(x \right)}}{4} + \sin{\left(x \right)} \cos^{2}{\left(x \right)} - 6 \sin{\left(x \right)}"," ",0,"x**4/4 + 3*x**2*sin(x)**2/4 + 3*x**2*sin(x) + 3*x**2*cos(x)**2/4 + 3*x*sin(x)*cos(x)/2 + 6*x*cos(x) + 2*sin(x)**3/3 - 3*sin(x)**2/4 + sin(x)*cos(x)**2 - 6*sin(x)","A",0
46,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x**2+c),x)","\int \frac{\cos{\left(a + b x \right)}}{c + d x^{2}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x**2), x)","F",0
47,0,0,0,0.000000," ","integrate(cos(b*x+a)/(e*x**2+d*x+c),x)","\int \frac{\cos{\left(a + b x \right)}}{c + d x + e x^{2}}\, dx"," ",0,"Integral(cos(a + b*x)/(c + d*x + e*x**2), x)","F",0
48,1,8,0,0.432411," ","integrate(x*cos((x**2+1)**(1/2))/(x**2+1)**(1/2),x)","\sin{\left(\sqrt{x^{2} + 1} \right)}"," ",0,"sin(sqrt(x**2 + 1))","A",0
49,1,20,0,0.684474," ","integrate(x*cos(3**(1/2)*(x**2+2)**(1/2))/(x**2+2)**(1/2),x)","\frac{\sqrt{3} \sin{\left(\sqrt{3} \sqrt{x^{2} + 2} \right)}}{3}"," ",0,"sqrt(3)*sin(sqrt(3)*sqrt(x**2 + 2))/3","A",0
50,1,15,0,5.493535," ","integrate((-1+2*x)*cos((6+3*(-1+2*x)**2)**(1/2))/(6+3*(-1+2*x)**2)**(1/2),x)","\frac{\sin{\left(\sqrt{3 \left(2 x - 1\right)^{2} + 6} \right)}}{6}"," ",0,"sin(sqrt(3*(2*x - 1)**2 + 6))/6","A",0
51,0,0,0,0.000000," ","integrate(cos((b*x+a)/(d*x+c)),x)","\int \cos{\left(\frac{a + b x}{c + d x} \right)}\, dx"," ",0,"Integral(cos((a + b*x)/(c + d*x)), x)","F",0
52,-1,0,0,0.000000," ","integrate(cos((b*x+a)/(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate(cos((-a*x+1)**(1/2)/(a*x+1)**(1/2))**3/(-a**2*x**2+1),x)","- \int \frac{\cos^{3}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(cos(sqrt(-a*x + 1)/sqrt(a*x + 1))**3/(a**2*x**2 - 1), x)","F",0
54,0,0,0,0.000000," ","integrate(cos((-a*x+1)**(1/2)/(a*x+1)**(1/2))**2/(-a**2*x**2+1),x)","- \int \frac{\cos^{2}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(cos(sqrt(-a*x + 1)/sqrt(a*x + 1))**2/(a**2*x**2 - 1), x)","F",0
55,0,0,0,0.000000," ","integrate(cos((-a*x+1)**(1/2)/(a*x+1)**(1/2))/(-a**2*x**2+1),x)","- \int \frac{\cos{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(cos(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a**2*x**2 - 1), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)/cos((-a*x+1)**(1/2)/(a*x+1)**(1/2)),x)","- \int \frac{1}{a^{2} x^{2} \cos{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)} - \cos{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**2*cos(sqrt(-a*x + 1)/sqrt(a*x + 1)) - cos(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)/cos((-a*x+1)**(1/2)/(a*x+1)**(1/2))**2,x)","- \int \frac{1}{a^{2} x^{2} \cos^{2}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)} - \cos^{2}{\left(\frac{\sqrt{- a x + 1}}{\sqrt{a x + 1}} \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**2*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))**2 - cos(sqrt(-a*x + 1)/sqrt(a*x + 1))**2), x)","F",0
58,1,10,0,0.170826," ","integrate(tan(x**(1/2))/x**(1/2),x)","\log{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1 \right)}"," ",0,"log(tan(sqrt(x))**2 + 1)","A",0
59,1,14,0,0.178196," ","integrate(tan(x**(1/2))**2/x**(1/2),x)","- 2 \sqrt{x} + 2 \tan{\left(\sqrt{x} \right)}"," ",0,"-2*sqrt(x) + 2*tan(sqrt(x))","A",0
60,0,0,0,0.000000," ","integrate(x**(1/2)*tan(x**(1/2)),x)","\int \sqrt{x} \tan{\left(\sqrt{x} \right)}\, dx"," ",0,"Integral(sqrt(x)*tan(sqrt(x)), x)","F",0
61,0,0,0,0.000000," ","integrate(1/2*b*tan(c*x**2+b*x+a)/c+x*tan(c*x**2+b*x+a),x)","\frac{\int b \tan{\left(a + b x + c x^{2} \right)}\, dx + \int 2 c x \tan{\left(a + b x + c x^{2} \right)}\, dx}{2 c}"," ",0,"(Integral(b*tan(a + b*x + c*x**2), x) + Integral(2*c*x*tan(a + b*x + c*x**2), x))/(2*c)","F",0
62,1,15,0,0.169030," ","integrate(cot(x**(1/2))**2/x**(1/2),x)","- 2 \sqrt{x} - 2 \cot{\left(\sqrt{x} \right)}"," ",0,"-2*sqrt(x) - 2*cot(sqrt(x))","A",0
63,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))**(1/2)/(1+cos(d*x+c)),x)","\int \frac{\sqrt{a + b \sec{\left(c + d x \right)}}}{\cos{\left(c + d x \right)} + 1}\, dx"," ",0,"Integral(sqrt(a + b*sec(c + d*x))/(cos(c + d*x) + 1), x)","F",0
64,0,0,0,0.000000," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x)","\int \sec{\left(a + b x \right)} \sec{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(sec(a + b*x)*sec(2*a + 2*b*x), x)","F",0
65,0,0,0,0.000000," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x)","\int \sec{\left(a + b x \right)} \sec{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(sec(a + b*x)*sec(2*a + 2*b*x), x)","F",0
66,1,20,0,0.452104," ","integrate(sin(x)*sin(2*x),x)","- \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)}}{3} + \frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{3}"," ",0,"-2*sin(x)*cos(2*x)/3 + sin(2*x)*cos(x)/3","A",0
67,1,20,0,0.415671," ","integrate(sin(x)*sin(3*x),x)","- \frac{3 \sin{\left(x \right)} \cos{\left(3 x \right)}}{8} + \frac{\sin{\left(3 x \right)} \cos{\left(x \right)}}{8}"," ",0,"-3*sin(x)*cos(3*x)/8 + sin(3*x)*cos(x)/8","A",0
68,1,20,0,0.410387," ","integrate(sin(x)*sin(4*x),x)","- \frac{4 \sin{\left(x \right)} \cos{\left(4 x \right)}}{15} + \frac{\sin{\left(4 x \right)} \cos{\left(x \right)}}{15}"," ",0,"-4*sin(x)*cos(4*x)/15 + sin(4*x)*cos(x)/15","A",0
69,1,78,0,0.794989," ","integrate(sin(x)*sin(m*x),x)","\begin{cases} - \frac{x \sin^{2}{\left(x \right)}}{2} - \frac{x \cos^{2}{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} & \text{for}\: m = -1 \\\frac{x \sin^{2}{\left(x \right)}}{2} + \frac{x \cos^{2}{\left(x \right)}}{2} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} & \text{for}\: m = 1 \\- \frac{m \sin{\left(x \right)} \cos{\left(m x \right)}}{m^{2} - 1} + \frac{\sin{\left(m x \right)} \cos{\left(x \right)}}{m^{2} - 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x*sin(x)**2/2 - x*cos(x)**2/2 + sin(x)*cos(x)/2, Eq(m, -1)), (x*sin(x)**2/2 + x*cos(x)**2/2 - sin(x)*cos(x)/2, Eq(m, 1)), (-m*sin(x)*cos(m*x)/(m**2 - 1) + sin(m*x)*cos(x)/(m**2 - 1), True))","A",0
70,1,20,0,0.449654," ","integrate(cos(2*x)*sin(x),x)","\frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{3} + \frac{\cos{\left(x \right)} \cos{\left(2 x \right)}}{3}"," ",0,"2*sin(x)*sin(2*x)/3 + cos(x)*cos(2*x)/3","A",0
71,1,20,0,0.414878," ","integrate(cos(3*x)*sin(x),x)","\frac{3 \sin{\left(x \right)} \sin{\left(3 x \right)}}{8} + \frac{\cos{\left(x \right)} \cos{\left(3 x \right)}}{8}"," ",0,"3*sin(x)*sin(3*x)/8 + cos(x)*cos(3*x)/8","A",0
72,1,20,0,0.410325," ","integrate(cos(4*x)*sin(x),x)","\frac{4 \sin{\left(x \right)} \sin{\left(4 x \right)}}{15} + \frac{\cos{\left(x \right)} \cos{\left(4 x \right)}}{15}"," ",0,"4*sin(x)*sin(4*x)/15 + cos(x)*cos(4*x)/15","A",0
73,1,37,0,0.930255," ","integrate(cos(m*x)*sin(x),x)","\begin{cases} \frac{\sin^{2}{\left(x \right)}}{2} & \text{for}\: m = -1 \vee m = 1 \\\frac{m \sin{\left(x \right)} \sin{\left(m x \right)}}{m^{2} - 1} + \frac{\cos{\left(x \right)} \cos{\left(m x \right)}}{m^{2} - 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(x)**2/2, Eq(m, -1) | Eq(m, 1)), (m*sin(x)*sin(m*x)/(m**2 - 1) + cos(x)*cos(m*x)/(m**2 - 1), True))","A",0
74,0,0,0,0.000000," ","integrate(sin(x)*tan(2*x),x)","\int \sin{\left(x \right)} \tan{\left(2 x \right)}\, dx"," ",0,"Integral(sin(x)*tan(2*x), x)","F",0
75,0,0,0,0.000000," ","integrate(sin(x)*tan(3*x),x)","\int \sin{\left(x \right)} \tan{\left(3 x \right)}\, dx"," ",0,"Integral(sin(x)*tan(3*x), x)","F",0
76,0,0,0,0.000000," ","integrate(sin(x)*tan(4*x),x)","\int \sin{\left(x \right)} \tan{\left(4 x \right)}\, dx"," ",0,"Integral(sin(x)*tan(4*x), x)","F",0
77,0,0,0,0.000000," ","integrate(sin(x)*tan(5*x),x)","\int \sin{\left(x \right)} \tan{\left(5 x \right)}\, dx"," ",0,"Integral(sin(x)*tan(5*x), x)","F",0
78,0,0,0,0.000000," ","integrate(sin(x)*tan(6*x),x)","\int \sin{\left(x \right)} \tan{\left(6 x \right)}\, dx"," ",0,"Integral(sin(x)*tan(6*x), x)","F",0
79,0,0,0,0.000000," ","integrate(sin(x)*tan(n*x),x)","\int \sin{\left(x \right)} \tan{\left(n x \right)}\, dx"," ",0,"Integral(sin(x)*tan(n*x), x)","F",0
80,1,19,0,0.815347," ","integrate(cot(2*x)*sin(x),x)","\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + \sin{\left(x \right)}"," ",0,"log(sin(x) - 1)/4 - log(sin(x) + 1)/4 + sin(x)","B",0
81,0,0,0,0.000000," ","integrate(cot(3*x)*sin(x),x)","\int \sin{\left(x \right)} \cot{\left(3 x \right)}\, dx"," ",0,"Integral(sin(x)*cot(3*x), x)","F",0
82,0,0,0,0.000000," ","integrate(cot(4*x)*sin(x),x)","\int \sin{\left(x \right)} \cot{\left(4 x \right)}\, dx"," ",0,"Integral(sin(x)*cot(4*x), x)","F",0
83,0,0,0,0.000000," ","integrate(cot(5*x)*sin(x),x)","\int \sin{\left(x \right)} \cot{\left(5 x \right)}\, dx"," ",0,"Integral(sin(x)*cot(5*x), x)","F",0
84,0,0,0,0.000000," ","integrate(cot(6*x)*sin(x),x)","\int \sin{\left(x \right)} \cot{\left(6 x \right)}\, dx"," ",0,"Integral(sin(x)*cot(6*x), x)","F",0
85,0,0,0,0.000000," ","integrate(sec(2*x)*sin(x),x)","\int \sin{\left(x \right)} \sec{\left(2 x \right)}\, dx"," ",0,"Integral(sin(x)*sec(2*x), x)","F",0
86,0,0,0,0.000000," ","integrate(sec(3*x)*sin(x),x)","\int \sin{\left(x \right)} \sec{\left(3 x \right)}\, dx"," ",0,"Integral(sin(x)*sec(3*x), x)","F",0
87,0,0,0,0.000000," ","integrate(sec(4*x)*sin(x),x)","\int \sin{\left(x \right)} \sec{\left(4 x \right)}\, dx"," ",0,"Integral(sin(x)*sec(4*x), x)","F",0
88,0,0,0,0.000000," ","integrate(sec(5*x)*sin(x),x)","\int \sin{\left(x \right)} \sec{\left(5 x \right)}\, dx"," ",0,"Integral(sin(x)*sec(5*x), x)","F",0
89,0,0,0,0.000000," ","integrate(sec(6*x)*sin(x),x)","\int \sin{\left(x \right)} \sec{\left(6 x \right)}\, dx"," ",0,"Integral(sin(x)*sec(6*x), x)","F",0
90,1,15,0,0.850554," ","integrate(csc(2*x)*sin(x),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4}"," ",0,"-log(sin(x) - 1)/4 + log(sin(x) + 1)/4","B",0
91,1,76,0,1.868723," ","integrate(csc(3*x)*sin(x),x)","\frac{\sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{3} \right)}}{6} - \frac{\sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3}}{3} \right)}}{6} + \frac{\sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3}}{3} \right)}}{6} - \frac{\sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{3} \right)}}{6}"," ",0,"sqrt(3)*log(tan(x/2) - sqrt(3))/6 - sqrt(3)*log(tan(x/2) - sqrt(3)/3)/6 + sqrt(3)*log(tan(x/2) + sqrt(3)/3)/6 - sqrt(3)*log(tan(x/2) + sqrt(3))/6","A",0
92,1,294,0,7.363975," ","integrate(csc(4*x)*sin(x),x)","\frac{27720 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{110880 \sqrt{2} + 156808} + \frac{39202 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{39202 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} - \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{110880 \sqrt{2} + 156808}"," ",0,"27720*sqrt(2)*log(tan(x/2) - 1)/(110880*sqrt(2) + 156808) + 39202*log(tan(x/2) - 1)/(110880*sqrt(2) + 156808) - 39202*log(tan(x/2) + 1)/(110880*sqrt(2) + 156808) - 27720*sqrt(2)*log(tan(x/2) + 1)/(110880*sqrt(2) + 156808) + 27720*log(tan(x/2) - 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 19601*sqrt(2)*log(tan(x/2) - 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 27720*log(tan(x/2) + 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 19601*sqrt(2)*log(tan(x/2) + 1 + sqrt(2))/(110880*sqrt(2) + 156808) - 19601*sqrt(2)*log(tan(x/2) - sqrt(2) - 1)/(110880*sqrt(2) + 156808) - 27720*log(tan(x/2) - sqrt(2) - 1)/(110880*sqrt(2) + 156808) - 19601*sqrt(2)*log(tan(x/2) - sqrt(2) + 1)/(110880*sqrt(2) + 156808) - 27720*log(tan(x/2) - sqrt(2) + 1)/(110880*sqrt(2) + 156808)","B",0
93,0,0,0,0.000000," ","integrate(csc(5*x)*sin(x),x)","\int \sin{\left(x \right)} \csc{\left(5 x \right)}\, dx"," ",0,"Integral(sin(x)*csc(5*x), x)","F",0
94,0,0,0,0.000000," ","integrate(csc(6*x)*sin(x),x)","\int \sin{\left(x \right)} \csc{\left(6 x \right)}\, dx"," ",0,"Integral(sin(x)*csc(6*x), x)","F",0
95,1,5,0,0.980612," ","integrate(csc(x)*sin(3*x),x)","x + \sin{\left(2 x \right)}"," ",0,"x + sin(2*x)","A",0
96,1,7,0,3.255599," ","integrate(csc(3*x)*sin(6*x),x)","\frac{2 \sin{\left(3 x \right)}}{3}"," ",0,"2*sin(3*x)/3","A",0
97,1,22,0,0.445882," ","integrate(cos(x)*sin(2*x),x)","- \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{3} - \frac{2 \cos{\left(x \right)} \cos{\left(2 x \right)}}{3}"," ",0,"-sin(x)*sin(2*x)/3 - 2*cos(x)*cos(2*x)/3","A",0
98,1,22,0,0.415697," ","integrate(cos(x)*sin(3*x),x)","- \frac{\sin{\left(x \right)} \sin{\left(3 x \right)}}{8} - \frac{3 \cos{\left(x \right)} \cos{\left(3 x \right)}}{8}"," ",0,"-sin(x)*sin(3*x)/8 - 3*cos(x)*cos(3*x)/8","A",0
99,1,22,0,0.409135," ","integrate(cos(x)*sin(4*x),x)","- \frac{\sin{\left(x \right)} \sin{\left(4 x \right)}}{15} - \frac{4 \cos{\left(x \right)} \cos{\left(4 x \right)}}{15}"," ",0,"-sin(x)*sin(4*x)/15 - 4*cos(x)*cos(4*x)/15","A",0
100,1,44,0,0.777388," ","integrate(cos(x)*sin(m*x),x)","\begin{cases} - \frac{\sin^{2}{\left(x \right)}}{2} & \text{for}\: m = -1 \\\frac{\sin^{2}{\left(x \right)}}{2} & \text{for}\: m = 1 \\- \frac{m \cos{\left(x \right)} \cos{\left(m x \right)}}{m^{2} - 1} - \frac{\sin{\left(x \right)} \sin{\left(m x \right)}}{m^{2} - 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(x)**2/2, Eq(m, -1)), (sin(x)**2/2, Eq(m, 1)), (-m*cos(x)*cos(m*x)/(m**2 - 1) - sin(x)*sin(m*x)/(m**2 - 1), True))","A",0
101,1,20,0,0.447609," ","integrate(cos(x)*cos(2*x),x)","- \frac{\sin{\left(x \right)} \cos{\left(2 x \right)}}{3} + \frac{2 \sin{\left(2 x \right)} \cos{\left(x \right)}}{3}"," ",0,"-sin(x)*cos(2*x)/3 + 2*sin(2*x)*cos(x)/3","A",0
102,1,20,0,0.412278," ","integrate(cos(x)*cos(3*x),x)","- \frac{\sin{\left(x \right)} \cos{\left(3 x \right)}}{8} + \frac{3 \sin{\left(3 x \right)} \cos{\left(x \right)}}{8}"," ",0,"-sin(x)*cos(3*x)/8 + 3*sin(3*x)*cos(x)/8","A",0
103,1,20,0,0.408846," ","integrate(cos(x)*cos(4*x),x)","- \frac{\sin{\left(x \right)} \cos{\left(4 x \right)}}{15} + \frac{4 \sin{\left(4 x \right)} \cos{\left(x \right)}}{15}"," ",0,"-sin(x)*cos(4*x)/15 + 4*sin(4*x)*cos(x)/15","A",0
104,1,56,0,0.935011," ","integrate(cos(x)*cos(m*x),x)","\begin{cases} \frac{x \sin^{2}{\left(x \right)}}{2} + \frac{x \cos^{2}{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} & \text{for}\: m = -1 \vee m = 1 \\\frac{m \sin{\left(m x \right)} \cos{\left(x \right)}}{m^{2} - 1} - \frac{\sin{\left(x \right)} \cos{\left(m x \right)}}{m^{2} - 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(x)**2/2 + x*cos(x)**2/2 + sin(x)*cos(x)/2, Eq(m, -1) | Eq(m, 1)), (m*sin(m*x)*cos(x)/(m**2 - 1) - sin(x)*cos(m*x)/(m**2 - 1), True))","A",0
105,0,0,0,0.000000," ","integrate(cos(x)*tan(2*x),x)","\int \cos{\left(x \right)} \tan{\left(2 x \right)}\, dx"," ",0,"Integral(cos(x)*tan(2*x), x)","F",0
106,0,0,0,0.000000," ","integrate(cos(x)*tan(3*x),x)","\int \cos{\left(x \right)} \tan{\left(3 x \right)}\, dx"," ",0,"Integral(cos(x)*tan(3*x), x)","F",0
107,0,0,0,0.000000," ","integrate(cos(x)*tan(4*x),x)","\int \cos{\left(x \right)} \tan{\left(4 x \right)}\, dx"," ",0,"Integral(cos(x)*tan(4*x), x)","F",0
108,0,0,0,0.000000," ","integrate(cos(x)*tan(5*x),x)","\int \cos{\left(x \right)} \tan{\left(5 x \right)}\, dx"," ",0,"Integral(cos(x)*tan(5*x), x)","F",0
109,0,0,0,0.000000," ","integrate(cos(x)*tan(6*x),x)","\int \cos{\left(x \right)} \tan{\left(6 x \right)}\, dx"," ",0,"Integral(cos(x)*tan(6*x), x)","F",0
110,1,19,0,0.832313," ","integrate(cos(x)*cot(2*x),x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{4} + \cos{\left(x \right)}"," ",0,"log(cos(x) - 1)/4 - log(cos(x) + 1)/4 + cos(x)","B",0
111,0,0,0,0.000000," ","integrate(cos(x)*cot(3*x),x)","\int \cos{\left(x \right)} \cot{\left(3 x \right)}\, dx"," ",0,"Integral(cos(x)*cot(3*x), x)","F",0
112,0,0,0,0.000000," ","integrate(cos(x)*cot(4*x),x)","\int \cos{\left(x \right)} \cot{\left(4 x \right)}\, dx"," ",0,"Integral(cos(x)*cot(4*x), x)","F",0
113,0,0,0,0.000000," ","integrate(cos(x)*cot(5*x),x)","\int \cos{\left(x \right)} \cot{\left(5 x \right)}\, dx"," ",0,"Integral(cos(x)*cot(5*x), x)","F",0
114,0,0,0,0.000000," ","integrate(cos(x)*cot(6*x),x)","\int \cos{\left(x \right)} \cot{\left(6 x \right)}\, dx"," ",0,"Integral(cos(x)*cot(6*x), x)","F",0
115,0,0,0,0.000000," ","integrate(cos(x)*cot(n*x),x)","\int \cos{\left(x \right)} \cot{\left(n x \right)}\, dx"," ",0,"Integral(cos(x)*cot(n*x), x)","F",0
116,0,0,0,0.000000," ","integrate(cos(x)*sec(2*x),x)","\int \cos{\left(x \right)} \sec{\left(2 x \right)}\, dx"," ",0,"Integral(cos(x)*sec(2*x), x)","F",0
117,0,0,0,0.000000," ","integrate(cos(x)*sec(3*x),x)","\int \cos{\left(x \right)} \sec{\left(3 x \right)}\, dx"," ",0,"Integral(cos(x)*sec(3*x), x)","F",0
118,0,0,0,0.000000," ","integrate(cos(x)*sec(4*x),x)","\int \cos{\left(x \right)} \sec{\left(4 x \right)}\, dx"," ",0,"Integral(cos(x)*sec(4*x), x)","F",0
119,0,0,0,0.000000," ","integrate(cos(x)*sec(5*x),x)","\int \cos{\left(x \right)} \sec{\left(5 x \right)}\, dx"," ",0,"Integral(cos(x)*sec(5*x), x)","F",0
120,0,0,0,0.000000," ","integrate(cos(x)*sec(6*x),x)","\int \cos{\left(x \right)} \sec{\left(6 x \right)}\, dx"," ",0,"Integral(cos(x)*sec(6*x), x)","F",0
121,1,20,0,1.053424," ","integrate(cos(2*x)*sec(x),x)","\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} + 2 \sin{\left(x \right)}"," ",0,"log(sin(x) - 1)/2 - log(sin(x) + 1)/2 + 2*sin(x)","B",0
122,1,427,0,5.350202," ","integrate(cos(4*x)*sec(2*x),x)","- 4 x + \frac{32 x \tan^{4}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} + \frac{64 x \tan^{2}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} + \frac{32 x}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} - \frac{3 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{2} + \frac{3 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{2} + \frac{8 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} + \frac{16 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} + \frac{8 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} - \frac{8 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} - \frac{16 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} - \frac{8 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} - \frac{32 \tan^{3}{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8} + \frac{32 \tan{\left(\frac{x}{2} \right)}}{8 \tan^{4}{\left(\frac{x}{2} \right)} + 16 \tan^{2}{\left(\frac{x}{2} \right)} + 8}"," ",0,"-4*x + 32*x*tan(x/2)**4/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) + 64*x*tan(x/2)**2/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) + 32*x/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) - 3*log(tan(x/2)**2 - 2*tan(x/2) - 1)/2 + 3*log(tan(x/2)**2 + 2*tan(x/2) - 1)/2 + 8*log(tan(x/2)**2 - 2*tan(x/2) - 1)*tan(x/2)**4/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) + 16*log(tan(x/2)**2 - 2*tan(x/2) - 1)*tan(x/2)**2/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) + 8*log(tan(x/2)**2 - 2*tan(x/2) - 1)/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) - 8*log(tan(x/2)**2 + 2*tan(x/2) - 1)*tan(x/2)**4/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) - 16*log(tan(x/2)**2 + 2*tan(x/2) - 1)*tan(x/2)**2/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) - 8*log(tan(x/2)**2 + 2*tan(x/2) - 1)/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) - 32*tan(x/2)**3/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8) + 32*tan(x/2)/(8*tan(x/2)**4 + 16*tan(x/2)**2 + 8)","B",0
123,1,15,0,0.874753," ","integrate(cos(x)*csc(2*x),x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{4}"," ",0,"log(cos(x) - 1)/4 - log(cos(x) + 1)/4","B",0
124,1,17,0,1.331774," ","integrate(cos(x)*csc(3*x),x)","- \frac{\log{\left(4 \sin^{2}{\left(x \right)} - 3 \right)}}{6} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{3}"," ",0,"-log(4*sin(x)**2 - 3)/6 + log(sin(x))/3","A",0
125,1,248,0,6.138647," ","integrate(cos(x)*csc(4*x),x)","- \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 + \sqrt{2} \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{110880 \sqrt{2} + 156808} + \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{19601 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{110880 \sqrt{2} + 156808} - \frac{27720 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} + 1 \right)}}{110880 \sqrt{2} + 156808} + \frac{27720 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{110880 \sqrt{2} + 156808} + \frac{39202 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{110880 \sqrt{2} + 156808}"," ",0,"-19601*sqrt(2)*log(tan(x/2) - 1 + sqrt(2))/(110880*sqrt(2) + 156808) - 27720*log(tan(x/2) - 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 27720*log(tan(x/2) + 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 19601*sqrt(2)*log(tan(x/2) + 1 + sqrt(2))/(110880*sqrt(2) + 156808) + 27720*log(tan(x/2) - sqrt(2) - 1)/(110880*sqrt(2) + 156808) + 19601*sqrt(2)*log(tan(x/2) - sqrt(2) - 1)/(110880*sqrt(2) + 156808) - 19601*sqrt(2)*log(tan(x/2) - sqrt(2) + 1)/(110880*sqrt(2) + 156808) - 27720*log(tan(x/2) - sqrt(2) + 1)/(110880*sqrt(2) + 156808) + 27720*sqrt(2)*log(tan(x/2))/(110880*sqrt(2) + 156808) + 39202*log(tan(x/2))/(110880*sqrt(2) + 156808)","B",0
126,0,0,0,0.000000," ","integrate(cos(x)*csc(5*x),x)","\int \cos{\left(x \right)} \csc{\left(5 x \right)}\, dx"," ",0,"Integral(cos(x)*csc(5*x), x)","F",0
127,0,0,0,0.000000," ","integrate(cos(x)*csc(6*x),x)","\int \cos{\left(x \right)} \csc{\left(6 x \right)}\, dx"," ",0,"Integral(cos(x)*csc(6*x), x)","F",0
128,1,63,0,5.211035," ","integrate(cos(6*x)**3*sin(x),x)","\frac{1296 \sin{\left(x \right)} \sin^{3}{\left(6 x \right)}}{11305} + \frac{1926 \sin{\left(x \right)} \sin{\left(6 x \right)} \cos^{2}{\left(6 x \right)}}{11305} + \frac{216 \sin^{2}{\left(6 x \right)} \cos{\left(x \right)} \cos{\left(6 x \right)}}{11305} + \frac{251 \cos{\left(x \right)} \cos^{3}{\left(6 x \right)}}{11305}"," ",0,"1296*sin(x)*sin(6*x)**3/11305 + 1926*sin(x)*sin(6*x)*cos(6*x)**2/11305 + 216*sin(6*x)**2*cos(x)*cos(6*x)/11305 + 251*cos(x)*cos(6*x)**3/11305","B",0
129,1,71,0,5.727995," ","integrate(cos(6*x)**3*sin(9*x),x)","- \frac{16 \sin^{3}{\left(6 x \right)} \sin{\left(9 x \right)}}{135} - \frac{8 \sin^{2}{\left(6 x \right)} \cos{\left(6 x \right)} \cos{\left(9 x \right)}}{45} - \frac{2 \sin{\left(6 x \right)} \sin{\left(9 x \right)} \cos^{2}{\left(6 x \right)}}{45} - \frac{19 \cos^{3}{\left(6 x \right)} \cos{\left(9 x \right)}}{135}"," ",0,"-16*sin(6*x)**3*sin(9*x)/135 - 8*sin(6*x)**2*cos(6*x)*cos(9*x)/45 - 2*sin(6*x)*sin(9*x)*cos(6*x)**2/45 - 19*cos(6*x)**3*cos(9*x)/135","B",0
130,1,48,0,1.728168," ","integrate(cos(2*x)*sin(6*x)**2,x)","\frac{17 \sin{\left(2 x \right)} \sin^{2}{\left(6 x \right)}}{70} + \frac{9 \sin{\left(2 x \right)} \cos^{2}{\left(6 x \right)}}{35} - \frac{3 \sin{\left(6 x \right)} \cos{\left(2 x \right)} \cos{\left(6 x \right)}}{35}"," ",0,"17*sin(2*x)*sin(6*x)**2/70 + 9*sin(2*x)*cos(6*x)**2/35 - 3*sin(6*x)*cos(2*x)*cos(6*x)/35","B",0
131,1,42,0,1.637431," ","integrate(cos(x)*sin(6*x)**2,x)","\frac{71 \sin{\left(x \right)} \sin^{2}{\left(6 x \right)}}{143} + \frac{72 \sin{\left(x \right)} \cos^{2}{\left(6 x \right)}}{143} - \frac{12 \sin{\left(6 x \right)} \cos{\left(x \right)} \cos{\left(6 x \right)}}{143}"," ",0,"71*sin(x)*sin(6*x)**2/143 + 72*sin(x)*cos(6*x)**2/143 - 12*sin(6*x)*cos(x)*cos(6*x)/143","B",0
132,1,65,0,5.187222," ","integrate(cos(x)*sin(6*x)**3,x)","- \frac{251 \sin{\left(x \right)} \sin^{3}{\left(6 x \right)}}{11305} - \frac{216 \sin{\left(x \right)} \sin{\left(6 x \right)} \cos^{2}{\left(6 x \right)}}{11305} - \frac{1926 \sin^{2}{\left(6 x \right)} \cos{\left(x \right)} \cos{\left(6 x \right)}}{11305} - \frac{1296 \cos{\left(x \right)} \cos^{3}{\left(6 x \right)}}{11305}"," ",0,"-251*sin(x)*sin(6*x)**3/11305 - 216*sin(x)*sin(6*x)*cos(6*x)**2/11305 - 1926*sin(6*x)**2*cos(x)*cos(6*x)/11305 - 1296*cos(x)*cos(6*x)**3/11305","B",0
133,1,70,0,5.271519," ","integrate(cos(7*x)*sin(6*x)**3,x)","\frac{1421 \sin^{3}{\left(6 x \right)} \sin{\left(7 x \right)}}{3575} + \frac{1062 \sin^{2}{\left(6 x \right)} \cos{\left(6 x \right)} \cos{\left(7 x \right)}}{3575} + \frac{1512 \sin{\left(6 x \right)} \sin{\left(7 x \right)} \cos^{2}{\left(6 x \right)}}{3575} + \frac{1296 \cos^{3}{\left(6 x \right)} \cos{\left(7 x \right)}}{3575}"," ",0,"1421*sin(6*x)**3*sin(7*x)/3575 + 1062*sin(6*x)**2*cos(6*x)*cos(7*x)/3575 + 1512*sin(6*x)*sin(7*x)*cos(6*x)**2/3575 + 1296*cos(6*x)**3*cos(7*x)/3575","B",0
134,1,228,0,18.541517," ","integrate(cos(3*x)**2*sin(2*x)**3,x)","- \frac{x \sin^{3}{\left(2 x \right)} \sin^{2}{\left(3 x \right)}}{16} + \frac{x \sin^{3}{\left(2 x \right)} \cos^{2}{\left(3 x \right)}}{16} - \frac{3 x \sin^{2}{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{8} + \frac{3 x \sin{\left(2 x \right)} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(2 x \right)}}{16} - \frac{3 x \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)}}{16} + \frac{x \sin{\left(3 x \right)} \cos^{3}{\left(2 x \right)} \cos{\left(3 x \right)}}{8} + \frac{5 \sin^{3}{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{16} - \frac{\sin^{2}{\left(2 x \right)} \sin^{2}{\left(3 x \right)} \cos{\left(2 x \right)}}{2} - \frac{3 \sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos^{2}{\left(2 x \right)} \cos{\left(3 x \right)}}{8} - \frac{11 \sin^{2}{\left(3 x \right)} \cos^{3}{\left(2 x \right)}}{96} - \frac{7 \cos^{3}{\left(2 x \right)} \cos^{2}{\left(3 x \right)}}{32}"," ",0,"-x*sin(2*x)**3*sin(3*x)**2/16 + x*sin(2*x)**3*cos(3*x)**2/16 - 3*x*sin(2*x)**2*sin(3*x)*cos(2*x)*cos(3*x)/8 + 3*x*sin(2*x)*sin(3*x)**2*cos(2*x)**2/16 - 3*x*sin(2*x)*cos(2*x)**2*cos(3*x)**2/16 + x*sin(3*x)*cos(2*x)**3*cos(3*x)/8 + 5*sin(2*x)**3*sin(3*x)*cos(3*x)/16 - sin(2*x)**2*sin(3*x)**2*cos(2*x)/2 - 3*sin(2*x)*sin(3*x)*cos(2*x)**2*cos(3*x)/8 - 11*sin(3*x)**2*cos(2*x)**3/96 - 7*cos(2*x)**3*cos(3*x)**2/32","B",0
135,1,58,0,0.741571," ","integrate(sin(b*x+a)*sin(b*x+c),x)","\begin{cases} \frac{x \sin{\left(a + b x \right)} \sin{\left(b x + c \right)}}{2} + \frac{x \cos{\left(a + b x \right)} \cos{\left(b x + c \right)}}{2} - \frac{\sin{\left(b x + c \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)*sin(b*x + c)/2 + x*cos(a + b*x)*cos(b*x + c)/2 - sin(b*x + c)*cos(a + b*x)/(2*b), Ne(b, 0)), (x*sin(a)*sin(c), True))","A",0
136,1,61,0,0.734366," ","integrate(-sin(b*x-c)*sin(b*x+a),x)","- \begin{cases} \frac{x \sin{\left(a + b x \right)} \sin{\left(b x - c \right)}}{2} + \frac{x \cos{\left(a + b x \right)} \cos{\left(b x - c \right)}}{2} - \frac{\sin{\left(b x - c \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\- x \sin{\left(a \right)} \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((x*sin(a + b*x)*sin(b*x - c)/2 + x*cos(a + b*x)*cos(b*x - c)/2 - sin(b*x - c)*cos(a + b*x)/(2*b), Ne(b, 0)), (-x*sin(a)*sin(c), True))","A",0
137,1,58,0,0.723897," ","integrate(cos(b*x+a)*cos(b*x+c),x)","\begin{cases} \frac{x \sin{\left(a + b x \right)} \sin{\left(b x + c \right)}}{2} + \frac{x \cos{\left(a + b x \right)} \cos{\left(b x + c \right)}}{2} + \frac{\sin{\left(a + b x \right)} \cos{\left(b x + c \right)}}{2 b} & \text{for}\: b \neq 0 \\x \cos{\left(a \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)*sin(b*x + c)/2 + x*cos(a + b*x)*cos(b*x + c)/2 + sin(a + b*x)*cos(b*x + c)/(2*b), Ne(b, 0)), (x*cos(a)*cos(c), True))","A",0
138,1,58,0,0.730576," ","integrate(cos(b*x-c)*cos(b*x+a),x)","\begin{cases} \frac{x \sin{\left(a + b x \right)} \sin{\left(b x - c \right)}}{2} + \frac{x \cos{\left(a + b x \right)} \cos{\left(b x - c \right)}}{2} + \frac{\sin{\left(b x - c \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \cos{\left(a \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)*sin(b*x - c)/2 + x*cos(a + b*x)*cos(b*x - c)/2 + sin(b*x - c)*cos(a + b*x)/(2*b), Ne(b, 0)), (x*cos(a)*cos(c), True))","A",0
139,1,7713,0,6.575758," ","integrate(tan(b*x+a)*tan(b*x+c),x)","\begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\\frac{b x \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} - \frac{b x \tan^{3}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} - \frac{b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} + \frac{b x \tan{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} - \frac{\tan^{2}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} - \frac{1}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} + 2 b \tan{\left(a \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{3}{\left(a \right)} + 2 b \tan{\left(a \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} + 2 b \tan{\left(a \right)}} & \text{for}\: c = 0 \\- \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{for}\: a = 0 \\\frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases} + \left(\begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\- \frac{4 b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{4 b x \tan{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2 \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} & \text{for}\: c = 0 \\- \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} & \text{for}\: a = 0 \\- \frac{2 b x \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(a \right)} + \left(\begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\- \frac{4 b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{4 b x \tan{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2 \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} - \frac{2}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} - 2 b} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} & \text{for}\: c = 0 \\- \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} & \text{for}\: a = 0 \\- \frac{2 b x \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(c \right)} + \left(\begin{cases} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\- \frac{b x \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} + \frac{b x \tan^{2}{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} + \frac{b x \tan{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} - \frac{b x}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} - \frac{\tan^{3}{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} - \frac{\tan{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} - b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} - b} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\x & \text{for}\: b = 0 \\\frac{2 b x}{2 b \tan^{2}{\left(a \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} & \text{for}\: c = 0 \\\frac{2 b x}{2 b \tan^{2}{\left(c \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} & \text{for}\: a = 0 \\- \frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan^{2}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(a \right)} \tan{\left(c \right)}"," ",0,"Piecewise((0, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (b*x*tan(c)**4*tan(b*x)/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) - b*x*tan(c)**3/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) - b*x*tan(c)**2*tan(b*x)/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) + b*x*tan(c)/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(c)**3*tan(b*x)/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) - 2*log(tan(b*x) - 1/tan(c))*tan(c)**2/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) + log(tan(b*x)**2 + 1)*tan(c)**2/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) - tan(c)**2/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)) - 1/(b*tan(c)**6*tan(b*x) - b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) - b*tan(c)), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (0, Eq(b, 0)), (-2*b*x*tan(a)/(2*b*tan(a)**3 + 2*b*tan(a)) - 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**3 + 2*b*tan(a)) - log(tan(b*x)**2 + 1)*tan(a)**2/(2*b*tan(a)**3 + 2*b*tan(a)), Eq(c, 0)), (-2*b*x*tan(c)/(2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(c))/(2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(c)**3 + 2*b*tan(c)), Eq(a, 0)), (2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True)) + Piecewise((0, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (-4*b*x*tan(c)**2*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + 4*b*x*tan(c)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + 2*log(tan(b*x) - 1/tan(c))*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2*log(tan(b*x) - 1/tan(c))*tan(c)**2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2*log(tan(b*x) - 1/tan(c))*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + 2*log(tan(b*x) - 1/tan(c))/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + log(tan(b*x)**2 + 1)*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2*tan(c)**2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (0, Eq(b, 0)), (-2*b*x*tan(a)/(2*b*tan(a)**2 + 2*b) - 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**2 + 2*b) + log(tan(b*x)**2 + 1)/(2*b*tan(a)**2 + 2*b), Eq(c, 0)), (-2*b*x*tan(c)/(2*b*tan(c)**2 + 2*b) - 2*log(tan(b*x) - 1/tan(c))/(2*b*tan(c)**2 + 2*b) + log(tan(b*x)**2 + 1)/(2*b*tan(c)**2 + 2*b), Eq(a, 0)), (-2*b*x*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True))*tan(a) + Piecewise((0, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (-4*b*x*tan(c)**2*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + 4*b*x*tan(c)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + 2*log(tan(b*x) - 1/tan(c))*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2*log(tan(b*x) - 1/tan(c))*tan(c)**2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2*log(tan(b*x) - 1/tan(c))*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + 2*log(tan(b*x) - 1/tan(c))/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) + log(tan(b*x)**2 + 1)*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2*tan(c)**2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b) - 2/(2*b*tan(c)**5*tan(b*x) - 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) - 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) - 2*b), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (0, Eq(b, 0)), (-2*b*x*tan(a)/(2*b*tan(a)**2 + 2*b) - 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**2 + 2*b) + log(tan(b*x)**2 + 1)/(2*b*tan(a)**2 + 2*b), Eq(c, 0)), (-2*b*x*tan(c)/(2*b*tan(c)**2 + 2*b) - 2*log(tan(b*x) - 1/tan(c))/(2*b*tan(c)**2 + 2*b) + log(tan(b*x)**2 + 1)/(2*b*tan(c)**2 + 2*b), Eq(a, 0)), (-2*b*x*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True))*tan(c) + Piecewise((x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (-b*x*tan(c)**3*tan(b*x)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) + b*x*tan(c)**2/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) + b*x*tan(c)*tan(b*x)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) - b*x/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) - 2*log(tan(b*x) - 1/tan(c))*tan(c)**2*tan(b*x)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) + 2*log(tan(b*x) - 1/tan(c))*tan(c)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) + log(tan(b*x)**2 + 1)*tan(c)**2*tan(b*x)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) - log(tan(b*x)**2 + 1)*tan(c)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) - tan(c)**3/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b) - tan(c)/(b*tan(c)**5*tan(b*x) - b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) - 2*b*tan(c)**2 + b*tan(c)*tan(b*x) - b), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (x, Eq(b, 0)), (2*b*x/(2*b*tan(a)**2 + 2*b) - 2*log(tan(b*x) - 1/tan(a))*tan(a)/(2*b*tan(a)**2 + 2*b) + log(tan(b*x)**2 + 1)*tan(a)/(2*b*tan(a)**2 + 2*b), Eq(c, 0)), (2*b*x/(2*b*tan(c)**2 + 2*b) - 2*log(tan(b*x) - 1/tan(c))*tan(c)/(2*b*tan(c)**2 + 2*b) + log(tan(b*x)**2 + 1)*tan(c)/(2*b*tan(c)**2 + 2*b), Eq(a, 0)), (-2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(a)**2*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(b*x) - 1/tan(a))*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(a)**2*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(c))*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True))*tan(a)*tan(c)","B",0
140,1,7720,0,8.524966," ","integrate(-tan(b*x-c)*tan(b*x+a),x)","\left(\begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\\frac{2 b x \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} & \text{for}\: c = 0 \\- \frac{4 b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{4 b x \tan{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2 \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} & \text{for}\: a = 0 \\\frac{2 b x \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(a \right)} - \left(\begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\\frac{2 b x \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} & \text{for}\: c = 0 \\- \frac{4 b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{4 b x \tan{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2 \tan^{2}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} - \frac{2}{2 b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{4}{\left(c \right)} + 4 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{2}{\left(c \right)} + 2 b \tan{\left(c \right)} \tan{\left(b x \right)} + 2 b} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} & \text{for}\: a = 0 \\\frac{2 b x \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(c \right)} + \begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\\frac{2 b x \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} + 2 b \tan{\left(a \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{3}{\left(a \right)} + 2 b \tan{\left(a \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} + 2 b \tan{\left(a \right)}} & \text{for}\: c = 0 \\- \frac{b x \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} - \frac{b x \tan^{3}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} + \frac{b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} + \frac{b x \tan{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} + \frac{\tan^{2}{\left(c \right)}}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} + \frac{1}{b \tan^{6}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\0 & \text{for}\: b = 0 \\\frac{2 b x \tan{\left(c \right)}}{2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{for}\: a = 0 \\\frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases} - \left(\begin{cases} - x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \\- \frac{2 b x}{2 b \tan^{2}{\left(a \right)} + 2 b} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)}}{2 b \tan^{2}{\left(a \right)} + 2 b} & \text{for}\: c = 0 \\\frac{b x \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} + \frac{b x \tan^{2}{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} - \frac{b x \tan{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} - \frac{b x}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} + \frac{\tan^{3}{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} + \frac{\tan{\left(c \right)}}{b \tan^{5}{\left(c \right)} \tan{\left(b x \right)} + b \tan^{4}{\left(c \right)} + 2 b \tan^{3}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{2}{\left(c \right)} + b \tan{\left(c \right)} \tan{\left(b x \right)} + b} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\- x & \text{for}\: b = 0 \\- \frac{2 b x}{2 b \tan^{2}{\left(c \right)} + 2 b} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(c \right)}}{2 b \tan^{2}{\left(c \right)} + 2 b} & \text{for}\: a = 0 \\- \frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan^{2}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(b x \right)} - \frac{1}{\tan{\left(a \right)}} \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(b x \right)} + \frac{1}{\tan{\left(c \right)}} \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(a \right)} \tan{\left(c \right)}"," ",0,"Piecewise((0, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (2*b*x*tan(a)/(2*b*tan(a)**2 + 2*b) + 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**2 + 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(a)**2 + 2*b), Eq(c, 0)), (-4*b*x*tan(c)**2*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 4*b*x*tan(c)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)**2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + 2*log(tan(b*x) + 1/tan(c))*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + 2*log(tan(b*x) + 1/tan(c))/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - log(tan(b*x)**2 + 1)*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2*tan(c)**2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (0, Eq(b, 0)), (-2*b*x*tan(c)/(2*b*tan(c)**2 + 2*b) + 2*log(tan(b*x) + 1/tan(c))/(2*b*tan(c)**2 + 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(c)**2 + 2*b), Eq(a, 0)), (2*b*x*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) + 1/tan(c))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) + 1/tan(c))*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True))*tan(a) - Piecewise((0, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (2*b*x*tan(a)/(2*b*tan(a)**2 + 2*b) + 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**2 + 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(a)**2 + 2*b), Eq(c, 0)), (-4*b*x*tan(c)**2*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 4*b*x*tan(c)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)**2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + 2*log(tan(b*x) + 1/tan(c))*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + 2*log(tan(b*x) + 1/tan(c))/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) + log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - log(tan(b*x)**2 + 1)*tan(c)*tan(b*x)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2*tan(c)**2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b) - 2/(2*b*tan(c)**5*tan(b*x) + 2*b*tan(c)**4 + 4*b*tan(c)**3*tan(b*x) + 4*b*tan(c)**2 + 2*b*tan(c)*tan(b*x) + 2*b), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (0, Eq(b, 0)), (-2*b*x*tan(c)/(2*b*tan(c)**2 + 2*b) + 2*log(tan(b*x) + 1/tan(c))/(2*b*tan(c)**2 + 2*b) - log(tan(b*x)**2 + 1)/(2*b*tan(c)**2 + 2*b), Eq(a, 0)), (2*b*x*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) + 1/tan(c))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) + 1/tan(c))*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True))*tan(c) + Piecewise((0, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (2*b*x*tan(a)/(2*b*tan(a)**3 + 2*b*tan(a)) + 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**3 + 2*b*tan(a)) + log(tan(b*x)**2 + 1)*tan(a)**2/(2*b*tan(a)**3 + 2*b*tan(a)), Eq(c, 0)), (-b*x*tan(c)**4*tan(b*x)/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) - b*x*tan(c)**3/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) + b*x*tan(c)**2*tan(b*x)/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) + b*x*tan(c)/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) + 2*log(tan(b*x) + 1/tan(c))*tan(c)**3*tan(b*x)/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) + 2*log(tan(b*x) + 1/tan(c))*tan(c)**2/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**2/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) + tan(c)**2/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)) + 1/(b*tan(c)**6*tan(b*x) + b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + b*tan(c)**2*tan(b*x) + b*tan(c)), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (0, Eq(b, 0)), (2*b*x*tan(c)/(2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(b*x) + 1/tan(c))/(2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(c)**3 + 2*b*tan(c)), Eq(a, 0)), (2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(b*x) + 1/tan(c))*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(b*x) + 1/tan(c))/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True)) - Piecewise((-x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0)), (-2*b*x/(2*b*tan(a)**2 + 2*b) + 2*log(tan(b*x) - 1/tan(a))*tan(a)/(2*b*tan(a)**2 + 2*b) - log(tan(b*x)**2 + 1)*tan(a)/(2*b*tan(a)**2 + 2*b), Eq(c, 0)), (b*x*tan(c)**3*tan(b*x)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) + b*x*tan(c)**2/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) - b*x*tan(c)*tan(b*x)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) - b*x/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)**2*tan(b*x)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) + log(tan(b*x)**2 + 1)*tan(c)**2*tan(b*x)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) + log(tan(b*x)**2 + 1)*tan(c)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) + tan(c)**3/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b) + tan(c)/(b*tan(c)**5*tan(b*x) + b*tan(c)**4 + 2*b*tan(c)**3*tan(b*x) + 2*b*tan(c)**2 + b*tan(c)*tan(b*x) + b), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (-x, Eq(b, 0)), (-2*b*x/(2*b*tan(c)**2 + 2*b) - 2*log(tan(b*x) + 1/tan(c))*tan(c)/(2*b*tan(c)**2 + 2*b) + log(tan(b*x)**2 + 1)*tan(c)/(2*b*tan(c)**2 + 2*b), Eq(a, 0)), (-2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(a)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(a)**2*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(b*x) - 1/tan(a))*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(b*x) + 1/tan(c))*tan(a)**2*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(b*x) + 1/tan(c))*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True))*tan(a)*tan(c)","B",0
141,1,7485,0,24.276824," ","integrate(cot(b*x+a)*cot(b*x+c),x)","\begin{cases} \frac{x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\- \frac{b x \tan^{5}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{b x \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{b x \tan^{3}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{6}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{4}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{x}{\cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\- \frac{2 b x \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases} + \left(\begin{cases} \frac{\tilde{\infty} x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\\frac{b x \tan^{5}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{b x \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{b x \tan^{3}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{4}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{2}{\left(c \right)}}{b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + b \tan{\left(c \right)} + b \tan{\left(b x \right)}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{\tilde{\infty} x}{\cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\\frac{2 b x \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)} \cot{\left(c \right)} - \left(\begin{cases} \frac{\tilde{\infty} x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\\frac{4 b x \tan^{4}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{4 b x \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{5}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{5}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \tan^{5}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \tan^{3}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{\tilde{\infty} x}{\cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\\frac{2 b x \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)} - \left(\begin{cases} \frac{\tilde{\infty} x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\\frac{4 b x \tan^{4}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{4 b x \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{5}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{5}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \tan^{5}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \tan^{3}{\left(c \right)}}{2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} + 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} + 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} & \text{for}\: a = \operatorname{atan}{\left(\tan{\left(c \right)} \right)} + \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor + \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{\tilde{\infty} x}{\cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\\frac{2 b x \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} - 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} - 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} - 2 b \tan^{3}{\left(c \right)} - 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \cot{\left(c \right)}"," ",0,"Piecewise((x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (-b*x*tan(c)**5/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - b*x*tan(c)**4*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + b*x*tan(c)**3/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + b*x*tan(c)**2*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - 2*log(tan(c) + tan(b*x))*tan(c)**4/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - 2*log(tan(c) + tan(b*x))*tan(c)**3*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**4/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - tan(c)**6/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - tan(c)**4/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (x/(cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (-2*b*x*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)**3*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(c) + tan(b*x))*tan(a)**3*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(c) + tan(b*x))*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True)) + Piecewise((zoo*x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (b*x*tan(c)**5/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + b*x*tan(c)**4*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - b*x*tan(c)**3/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - b*x*tan(c)**2*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + 2*log(tan(c) + tan(b*x))*tan(c)**4/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) + 2*log(tan(c) + tan(b*x))*tan(c)**3*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**4/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - tan(c)**4/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)) - tan(c)**2/(b*tan(c)**5 + b*tan(c)**4*tan(b*x) + 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) + b*tan(c) + b*tan(b*x)), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (zoo*x/(cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (2*b*x*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(c) + tan(b*x))*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(c) + tan(b*x))*tan(a)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True))*cot(a)*cot(c) - Piecewise((zoo*x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (4*b*x*tan(c)**4/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 4*b*x*tan(c)**3*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(tan(c) + tan(b*x))*tan(c)**5/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(tan(c) + tan(b*x))*tan(c)**4*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(tan(c) + tan(b*x))*tan(c)**3/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(tan(c) + tan(b*x))*tan(c)**2*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**5/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**4*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**3/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**2*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*tan(c)**5/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*tan(c)**3/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (zoo*x/(cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (2*b*x*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(c) + tan(b*x))*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(c) + tan(b*x))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True))*cot(a) - Piecewise((zoo*x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (4*b*x*tan(c)**4/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 4*b*x*tan(c)**3*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(tan(c) + tan(b*x))*tan(c)**5/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(tan(c) + tan(b*x))*tan(c)**4*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(tan(c) + tan(b*x))*tan(c)**3/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(tan(c) + tan(b*x))*tan(c)**2*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**5/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**4*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**3/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**2*tan(b*x)/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*tan(c)**5/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)) + 2*tan(c)**3/(2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) + 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) + 2*b*tan(c) + 2*b*tan(b*x)), Eq(a, atan(tan(c)) + pi*floor((c - pi/2)/pi) + pi*floor(c/pi - 1/2))), (zoo*x/(cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (2*b*x*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*b*x*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(c) + tan(b*x))*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - 2*log(tan(c) + tan(b*x))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 - 2*b*tan(a)**2*tan(c)**3 - 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) - 2*b*tan(c)**3 - 2*b*tan(c)), True))*cot(c)","B",0
142,1,7499,0,24.888943," ","integrate(-cot(b*x-c)*cot(b*x+a),x)","- \begin{cases} \frac{x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\\frac{b x \tan^{5}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{b x \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{b x \tan^{3}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{6}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{4}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{x}{- \cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\- \frac{2 b x \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases} + \left(\begin{cases} \frac{\tilde{\infty} x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\- \frac{b x \tan^{5}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{b x \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{b x \tan^{3}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{b x \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{4}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} - \frac{\tan^{2}{\left(c \right)}}{- b \tan^{5}{\left(c \right)} + b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - b \tan{\left(c \right)} + b \tan{\left(b x \right)}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{\tilde{\infty} x}{- \cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\\frac{2 b x \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)} \cot{\left(c \right)} + \left(\begin{cases} \frac{\tilde{\infty} x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\\frac{4 b x \tan^{4}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{4 b x \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{5}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{5}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \tan^{5}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \tan^{3}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{\tilde{\infty} x}{- \cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\- \frac{2 b x \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)} - \left(\begin{cases} \frac{\tilde{\infty} x}{\tilde{\infty} \cot{\left(c \right)} + \tilde{\infty} + \frac{\cot{\left(c \right)}}{\tan{\left(c \right)}} + \frac{\tilde{\infty}}{\tan{\left(c \right)}}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \wedge b = 0 \\\frac{4 b x \tan^{4}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{4 b x \tan^{3}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{5}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{5}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{4}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(c \right)} \tan{\left(b x \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \tan^{5}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} - \frac{2 \tan^{3}{\left(c \right)}}{- 2 b \tan^{5}{\left(c \right)} + 2 b \tan^{4}{\left(c \right)} \tan{\left(b x \right)} - 4 b \tan^{3}{\left(c \right)} + 4 b \tan^{2}{\left(c \right)} \tan{\left(b x \right)} - 2 b \tan{\left(c \right)} + 2 b \tan{\left(b x \right)}} & \text{for}\: a = - \operatorname{atan}{\left(\tan{\left(c \right)} \right)} - \pi \left\lfloor{\frac{c - \frac{\pi}{2}}{\pi}}\right\rfloor - \pi \left\lfloor{\frac{c}{\pi} - \frac{1}{2}}\right\rfloor \\\frac{\tilde{\infty} x}{- \cot{\left(a \right)} \cot{\left(c \right)} + \tilde{\infty} \cot{\left(a \right)} + \tilde{\infty} \cot{\left(c \right)} + \tilde{\infty}} & \text{for}\: b = 0 \\- \frac{2 b x \tan^{3}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{2 b x \tan{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(\tan{\left(a \right)} + \tan{\left(b x \right)} \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} - \frac{2 \log{\left(- \tan{\left(c \right)} + \tan{\left(b x \right)} \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan^{2}{\left(a \right)} \tan{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} + \frac{\log{\left(\tan^{2}{\left(b x \right)} + 1 \right)} \tan{\left(a \right)} \tan^{2}{\left(c \right)}}{2 b \tan^{3}{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan^{3}{\left(a \right)} + 2 b \tan^{2}{\left(a \right)} \tan^{3}{\left(c \right)} + 2 b \tan^{2}{\left(a \right)} \tan{\left(c \right)} + 2 b \tan{\left(a \right)} \tan^{2}{\left(c \right)} + 2 b \tan{\left(a \right)} + 2 b \tan^{3}{\left(c \right)} + 2 b \tan{\left(c \right)}} & \text{otherwise} \end{cases}\right) \cot{\left(c \right)}"," ",0,"-Piecewise((x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (b*x*tan(c)**5/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - b*x*tan(c)**4*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - b*x*tan(c)**3/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + b*x*tan(c)**2*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - 2*log(-tan(c) + tan(b*x))*tan(c)**4/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + 2*log(-tan(c) + tan(b*x))*tan(c)**3*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**4/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - tan(c)**6/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - tan(c)**4/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (x/(-cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (-2*b*x*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)**3*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)**3*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True)) + Piecewise((zoo*x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (-b*x*tan(c)**5/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + b*x*tan(c)**4*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + b*x*tan(c)**3/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - b*x*tan(c)**2*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + 2*log(-tan(c) + tan(b*x))*tan(c)**4/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - 2*log(-tan(c) + tan(b*x))*tan(c)**3*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**4/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**3*tan(b*x)/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - tan(c)**4/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)) - tan(c)**2/(-b*tan(c)**5 + b*tan(c)**4*tan(b*x) - 2*b*tan(c)**3 + 2*b*tan(c)**2*tan(b*x) - b*tan(c) + b*tan(b*x)), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (zoo*x/(-cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (2*b*x*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*log(tan(a) + tan(b*x))*tan(a)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - log(tan(b*x)**2 + 1)*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True))*cot(a)*cot(c) + Piecewise((zoo*x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (4*b*x*tan(c)**4/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 4*b*x*tan(c)**3*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(-tan(c) + tan(b*x))*tan(c)**5/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(-tan(c) + tan(b*x))*tan(c)**4*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(-tan(c) + tan(b*x))*tan(c)**3/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(-tan(c) + tan(b*x))*tan(c)**2*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**5/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**4*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**3/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**2*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*tan(c)**5/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*tan(c)**3/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (zoo*x/(-cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (-2*b*x*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True))*cot(a) - Piecewise((zoo*x/(zoo*cot(c) + zoo + cot(c)/tan(c) + zoo/tan(c)), Eq(b, 0) & Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (4*b*x*tan(c)**4/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 4*b*x*tan(c)**3*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(-tan(c) + tan(b*x))*tan(c)**5/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(-tan(c) + tan(b*x))*tan(c)**4*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*log(-tan(c) + tan(b*x))*tan(c)**3/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + 2*log(-tan(c) + tan(b*x))*tan(c)**2*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**5/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**4*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) + log(tan(b*x)**2 + 1)*tan(c)**3/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - log(tan(b*x)**2 + 1)*tan(c)**2*tan(b*x)/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*tan(c)**5/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)) - 2*tan(c)**3/(-2*b*tan(c)**5 + 2*b*tan(c)**4*tan(b*x) - 4*b*tan(c)**3 + 4*b*tan(c)**2*tan(b*x) - 2*b*tan(c) + 2*b*tan(b*x)), Eq(a, -atan(tan(c)) - pi*floor((c - pi/2)/pi) - pi*floor(c/pi - 1/2))), (zoo*x/(-cot(a)*cot(c) + zoo*cot(a) + zoo*cot(c) + zoo), Eq(b, 0)), (-2*b*x*tan(a)**3*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + 2*b*x*tan(a)*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(tan(a) + tan(b*x))*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) - 2*log(-tan(c) + tan(b*x))*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**3*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)**3/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)**2*tan(c)/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)) + log(tan(b*x)**2 + 1)*tan(a)*tan(c)**2/(2*b*tan(a)**3*tan(c)**2 + 2*b*tan(a)**3 + 2*b*tan(a)**2*tan(c)**3 + 2*b*tan(a)**2*tan(c) + 2*b*tan(a)*tan(c)**2 + 2*b*tan(a) + 2*b*tan(c)**3 + 2*b*tan(c)), True))*cot(c)","B",0
143,0,0,0,0.000000," ","integrate(sec(b*x+a)*sec(b*x+c),x)","\int \sec{\left(a + b x \right)} \sec{\left(b x + c \right)}\, dx"," ",0,"Integral(sec(a + b*x)*sec(b*x + c), x)","F",0
144,0,0,0,0.000000," ","integrate(sec(b*x-c)*sec(b*x+a),x)","\int \sec{\left(a + b x \right)} \sec{\left(b x - c \right)}\, dx"," ",0,"Integral(sec(a + b*x)*sec(b*x - c), x)","F",0
145,0,0,0,0.000000," ","integrate(csc(b*x+a)*csc(b*x+c),x)","\int \csc{\left(a + b x \right)} \csc{\left(b x + c \right)}\, dx"," ",0,"Integral(csc(a + b*x)*csc(b*x + c), x)","F",0
146,1,1838,0,129.080927," ","integrate(-csc(b*x-c)*csc(b*x+a),x)","\begin{cases} - \frac{\tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{- 2 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{- 2 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan{\left(\frac{b x}{2} \right)}}{- 2 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} & \text{for}\: a = 2 \operatorname{atan}{\left(\frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \\\frac{\tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{- 2 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{2 \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{- 2 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan{\left(\frac{b x}{2} \right)}}{- 2 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} & \text{for}\: a = - 2 \operatorname{atan}{\left(\tan{\left(\frac{c}{2} \right)} \right)} - 2 \pi \left\lfloor{\frac{\frac{c}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor - 2 \pi \left\lfloor{\frac{c}{2 \pi} - \frac{1}{2}}\right\rfloor \\\frac{x}{\sin{\left(a \right)} \sin{\left(c \right)}} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{a}{2} \right)}}{2 b} + \frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{2 b \tan{\left(\frac{a}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)} \tan{\left(\frac{a}{2} \right)}}{2 b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)}}{2 b \tan{\left(\frac{a}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{a}{2} \right)}}{2 b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{2 b \tan{\left(\frac{a}{2} \right)}} & \text{for}\: c = 0 \\- \frac{\log{\left(- \tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)}}{2 b} - \frac{\log{\left(- \tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)}}{2 b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)}}{2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)}}{2 b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{2 b \tan{\left(\frac{c}{2} \right)}} & \text{for}\: a = 0 \\- \frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(- \tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(- \tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(- \tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(- \tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)}}{2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{c}{2} \right)} + 2 b \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{a}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-tan(c/2)**4*tan(b*x/2)/(-2*b*tan(c/2)**3*tan(b*x/2) + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 + 2*b*tan(c/2)*tan(b*x/2)) - 2*tan(c/2)**2*tan(b*x/2)/(-2*b*tan(c/2)**3*tan(b*x/2) + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 + 2*b*tan(c/2)*tan(b*x/2)) - tan(b*x/2)/(-2*b*tan(c/2)**3*tan(b*x/2) + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 + 2*b*tan(c/2)*tan(b*x/2)), Eq(a, 2*atan(1/tan(c/2)))), (tan(c/2)**4*tan(b*x/2)/(-2*b*tan(c/2)**3*tan(b*x/2) + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 + 2*b*tan(c/2)*tan(b*x/2)) + 2*tan(c/2)**2*tan(b*x/2)/(-2*b*tan(c/2)**3*tan(b*x/2) + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 + 2*b*tan(c/2)*tan(b*x/2)) + tan(b*x/2)/(-2*b*tan(c/2)**3*tan(b*x/2) + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 + 2*b*tan(c/2)*tan(b*x/2)), Eq(a, -2*atan(tan(c/2)) - 2*pi*floor((c/2 - pi/2)/pi) - 2*pi*floor(c/(2*pi) - 1/2))), (x/(sin(a)*sin(c)), Eq(b, 0)), (log(tan(a/2) + tan(b*x/2))*tan(a/2)/(2*b) + log(tan(a/2) + tan(b*x/2))/(2*b*tan(a/2)) + log(tan(b*x/2) - 1/tan(a/2))*tan(a/2)/(2*b) + log(tan(b*x/2) - 1/tan(a/2))/(2*b*tan(a/2)) - log(tan(b*x/2))*tan(a/2)/(2*b) - log(tan(b*x/2))/(2*b*tan(a/2)), Eq(c, 0)), (-log(-tan(c/2) + tan(b*x/2))*tan(c/2)/(2*b) - log(-tan(c/2) + tan(b*x/2))/(2*b*tan(c/2)) - log(tan(b*x/2) + 1/tan(c/2))*tan(c/2)/(2*b) - log(tan(b*x/2) + 1/tan(c/2))/(2*b*tan(c/2)) + log(tan(b*x/2))*tan(c/2)/(2*b) + log(tan(b*x/2))/(2*b*tan(c/2)), Eq(a, 0)), (-log(tan(a/2) + tan(b*x/2))*tan(a/2)**2*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(a/2) + tan(b*x/2))*tan(a/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(a/2) + tan(b*x/2))*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(a/2) + tan(b*x/2))/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(-tan(c/2) + tan(b*x/2))*tan(a/2)**2*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(-tan(c/2) + tan(b*x/2))*tan(a/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(-tan(c/2) + tan(b*x/2))*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(-tan(c/2) + tan(b*x/2))/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(b*x/2) - 1/tan(a/2))*tan(a/2)**2*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(b*x/2) - 1/tan(a/2))*tan(a/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(b*x/2) - 1/tan(a/2))*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) - log(tan(b*x/2) - 1/tan(a/2))/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(tan(b*x/2) + 1/tan(c/2))*tan(a/2)**2*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(tan(b*x/2) + 1/tan(c/2))*tan(a/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(tan(b*x/2) + 1/tan(c/2))*tan(c/2)**2/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)) + log(tan(b*x/2) + 1/tan(c/2))/(2*b*tan(a/2)**2*tan(c/2) + 2*b*tan(a/2)*tan(c/2)**2 - 2*b*tan(a/2) - 2*b*tan(c/2)), True))","A",0
147,0,0,0,0.000000," ","integrate((sin(x)*tan(x))**(1/2),x)","\int \sqrt{\sin{\left(x \right)} \tan{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(sin(x)*tan(x)), x)","F",0
148,0,0,0,0.000000," ","integrate((sin(x)*tan(x))**(3/2),x)","\int \left(\sin{\left(x \right)} \tan{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((sin(x)*tan(x))**(3/2), x)","F",0
149,-1,0,0,0.000000," ","integrate((sin(x)*tan(x))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,0,0,0,0.000000," ","integrate((cos(x)*cot(x))**(1/2),x)","\int \sqrt{\cos{\left(x \right)} \cot{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(cos(x)*cot(x)), x)","F",0
151,0,0,0,0.000000," ","integrate((cos(x)*cot(x))**(3/2),x)","\int \left(\cos{\left(x \right)} \cot{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((cos(x)*cot(x))**(3/2), x)","F",0
152,-1,0,0,0.000000," ","integrate((cos(x)*cot(x))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(x*cos(x)/(a+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(x*cos(x)/(a+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,0,0,0,0.000000," ","integrate(x*sin(x)/(a+b*cos(x))**2,x)","\int \frac{x \sin{\left(x \right)}}{\left(a + b \cos{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*sin(x)/(a + b*cos(x))**2, x)","F",0
156,-1,0,0,0.000000," ","integrate(x*sin(x)/(a+b*cos(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,0,0,0,0.000000," ","integrate(x*sec(x)**2/(a+b*tan(x))**2,x)","\int \frac{x \sec^{2}{\left(x \right)}}{\left(a + b \tan{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*sec(x)**2/(a + b*tan(x))**2, x)","F",0
158,0,0,0,0.000000," ","integrate(x*csc(x)**2/(a+b*cot(x))**2,x)","\int \frac{x \csc^{2}{\left(x \right)}}{\left(a + b \cot{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*csc(x)**2/(a + b*cot(x))**2, x)","F",0
159,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*tan(c + d*x)**2), x)","F",0
160,0,0,0,0.000000," ","integrate(x*sec(d*x+c)**2/(a+b*tan(d*x+c)**2),x)","\int \frac{x \sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x*sec(c + d*x)**2/(a + b*tan(c + d*x)**2), x)","F",0
161,0,0,0,0.000000," ","integrate(x**2*sec(d*x+c)**2/(a+b*tan(d*x+c)**2),x)","\int \frac{x^{2} \sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x**2*sec(c + d*x)**2/(a + b*tan(c + d*x)**2), x)","F",0
162,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+c*sec(d*x+c)**2+b*tan(d*x+c)**2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)} + c \sec^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*tan(c + d*x)**2 + c*sec(c + d*x)**2), x)","F",0
163,0,0,0,0.000000," ","integrate(x*sec(d*x+c)**2/(a+c*sec(d*x+c)**2+b*tan(d*x+c)**2),x)","\int \frac{x \sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)} + c \sec^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x*sec(c + d*x)**2/(a + b*tan(c + d*x)**2 + c*sec(c + d*x)**2), x)","F",0
164,0,0,0,0.000000," ","integrate(x**2*sec(d*x+c)**2/(a+c*sec(d*x+c)**2+b*tan(d*x+c)**2),x)","\int \frac{x^{2} \sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)} + c \sec^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x**2*sec(c + d*x)**2/(a + b*tan(c + d*x)**2 + c*sec(c + d*x)**2), x)","F",0
165,0,0,0,0.000000," ","integrate(x**3*(a-a*sin(f*x+e))**(1/2)*(c+c*sin(f*x+e))**(1/2),x)","\int x^{3} \sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}\, dx"," ",0,"Integral(x**3*sqrt(c*(sin(e + f*x) + 1))*sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
166,0,0,0,0.000000," ","integrate(x**2*(a-a*sin(f*x+e))**(1/2)*(c+c*sin(f*x+e))**(1/2),x)","\int x^{2} \sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}\, dx"," ",0,"Integral(x**2*sqrt(c*(sin(e + f*x) + 1))*sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
167,0,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))**(1/2)*(c+c*sin(f*x+e))**(1/2),x)","\int x \sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}\, dx"," ",0,"Integral(x*sqrt(c*(sin(e + f*x) + 1))*sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
168,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**(1/2)*(c+c*sin(f*x+e))**(1/2)/x,x)","\int \frac{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{x}\, dx"," ",0,"Integral(sqrt(c*(sin(e + f*x) + 1))*sqrt(-a*(sin(e + f*x) - 1))/x, x)","F",0
169,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**(1/2)*(c+c*sin(f*x+e))**(1/2)/x**2,x)","\int \frac{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*(sin(e + f*x) + 1))*sqrt(-a*(sin(e + f*x) - 1))/x**2, x)","F",0
170,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**(1/2)*(c+c*sin(f*x+e))**(1/2)/x**3,x)","\int \frac{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*(sin(e + f*x) + 1))*sqrt(-a*(sin(e + f*x) - 1))/x**3, x)","F",0
171,-1,0,0,0.000000," ","integrate(x**3*(c+c*sin(f*x+e))**(3/2)*(a-a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,0,0,0,0.000000," ","integrate(x**2*(c+c*sin(f*x+e))**(3/2)*(a-a*sin(f*x+e))**(1/2),x)","\int x^{2} \left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}\, dx"," ",0,"Integral(x**2*(c*(sin(e + f*x) + 1))**(3/2)*sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
173,0,0,0,0.000000," ","integrate(x*(c+c*sin(f*x+e))**(3/2)*(a-a*sin(f*x+e))**(1/2),x)","\int x \left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}\, dx"," ",0,"Integral(x*(c*(sin(e + f*x) + 1))**(3/2)*sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
174,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))**(3/2)*(a-a*sin(f*x+e))**(1/2)/x,x)","\int \frac{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{x}\, dx"," ",0,"Integral((c*(sin(e + f*x) + 1))**(3/2)*sqrt(-a*(sin(e + f*x) - 1))/x, x)","F",0
175,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))**(3/2)*(a-a*sin(f*x+e))**(1/2)/x**2,x)","\int \frac{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{x^{2}}\, dx"," ",0,"Integral((c*(sin(e + f*x) + 1))**(3/2)*sqrt(-a*(sin(e + f*x) - 1))/x**2, x)","F",0
176,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))**(3/2)*(a-a*sin(f*x+e))**(1/2)/x**3,x)","\int \frac{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{x^{3}}\, dx"," ",0,"Integral((c*(sin(e + f*x) + 1))**(3/2)*sqrt(-a*(sin(e + f*x) - 1))/x**3, x)","F",0
177,0,0,0,0.000000," ","integrate((h*x+g)**3*(a-a*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)} \left(g + h x\right)^{3}}{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1))*(g + h*x)**3/sqrt(c*(sin(e + f*x) + 1)), x)","F",0
178,0,0,0,0.000000," ","integrate((h*x+g)**2*(a-a*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)} \left(g + h x\right)^{2}}{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1))*(g + h*x)**2/sqrt(c*(sin(e + f*x) + 1)), x)","F",0
179,0,0,0,0.000000," ","integrate((h*x+g)*(a-a*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)} \left(g + h x\right)}{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1))*(g + h*x)/sqrt(c*(sin(e + f*x) + 1)), x)","F",0
180,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))**(1/2)/(h*x+g)/(c+c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{\sqrt{c \left(\sin{\left(e + f x \right)} + 1\right)} \left(g + h x\right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1))/(sqrt(c*(sin(e + f*x) + 1))*(g + h*x)), x)","F",0
181,0,0,0,0.000000," ","integrate(x**3*(a-a*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))**(3/2),x)","\int \frac{x^{3} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*sqrt(-a*(sin(e + f*x) - 1))/(c*(sin(e + f*x) + 1))**(3/2), x)","F",0
182,0,0,0,0.000000," ","integrate(x**2*(a-a*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))**(3/2),x)","\int \frac{x^{2} \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*sqrt(-a*(sin(e + f*x) - 1))/(c*(sin(e + f*x) + 1))**(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))**(3/2),x)","\int \frac{x \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*sqrt(-a*(sin(e + f*x) - 1))/(c*(sin(e + f*x) + 1))**(3/2), x)","F",0
184,0,0,0,0.000000," ","integrate(z**2*(1+cos(z))**(1/2)/(1-cos(z))**(1/2),z)","\int \frac{z^{2} \sqrt{\cos{\left(z \right)} + 1}}{\sqrt{1 - \cos{\left(z \right)}}}\, dz"," ",0,"Integral(z**2*sqrt(cos(z) + 1)/sqrt(1 - cos(z)), z)","F",0
185,1,27,0,2.167516," ","integrate((a+a*cos(x))*(A+B*sec(x)),x)","A a x + A a \sin{\left(x \right)} + B a x + B a \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)}"," ",0,"A*a*x + A*a*sin(x) + B*a*x + B*a*log(tan(x) + sec(x))","A",0
186,1,61,0,3.541960," ","integrate((a+a*cos(x))**2*(A+B*sec(x)),x)","\frac{3 A a^{2} x}{2} + 2 A a^{2} \sin{\left(x \right)} + \frac{A a^{2} \sin{\left(2 x \right)}}{4} + 2 B a^{2} x + B a^{2} \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} + B a^{2} \sin{\left(x \right)}"," ",0,"3*A*a**2*x/2 + 2*A*a**2*sin(x) + A*a**2*sin(2*x)/4 + 2*B*a**2*x + B*a**2*log(tan(x) + sec(x)) + B*a**2*sin(x)","A",0
187,1,92,0,7.627901," ","integrate((a+a*cos(x))**3*(A+B*sec(x)),x)","\frac{5 A a^{3} x}{2} - \frac{A a^{3} \sin^{3}{\left(x \right)}}{3} + 4 A a^{3} \sin{\left(x \right)} + \frac{3 A a^{3} \sin{\left(2 x \right)}}{4} + \frac{7 B a^{3} x}{2} + B a^{3} \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} + \frac{B a^{3} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + 3 B a^{3} \sin{\left(x \right)}"," ",0,"5*A*a**3*x/2 - A*a**3*sin(x)**3/3 + 4*A*a**3*sin(x) + 3*A*a**3*sin(2*x)/4 + 7*B*a**3*x/2 + B*a**3*log(tan(x) + sec(x)) + B*a**3*sin(x)*cos(x)/2 + 3*B*a**3*sin(x)","A",0
188,1,116,0,15.257685," ","integrate((a+a*cos(x))**4*(A+B*sec(x)),x)","\frac{35 A a^{4} x}{8} - \frac{4 A a^{4} \sin^{3}{\left(x \right)}}{3} + 8 A a^{4} \sin{\left(x \right)} + \frac{7 A a^{4} \sin{\left(2 x \right)}}{4} + \frac{A a^{4} \sin{\left(4 x \right)}}{32} + 6 B a^{4} x + B a^{4} \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} - \frac{B a^{4} \sin^{3}{\left(x \right)}}{3} + 2 B a^{4} \sin{\left(x \right)} \cos{\left(x \right)} + 7 B a^{4} \sin{\left(x \right)}"," ",0,"35*A*a**4*x/8 - 4*A*a**4*sin(x)**3/3 + 8*A*a**4*sin(x) + 7*A*a**4*sin(2*x)/4 + A*a**4*sin(4*x)/32 + 6*B*a**4*x + B*a**4*log(tan(x) + sec(x)) - B*a**4*sin(x)**3/3 + 2*B*a**4*sin(x)*cos(x) + 7*B*a**4*sin(x)","A",0
189,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x)),x)","\frac{\int \frac{A}{\cos{\left(x \right)} + 1}\, dx + \int \frac{B \sec{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A/(cos(x) + 1), x) + Integral(B*sec(x)/(cos(x) + 1), x))/a","F",0
190,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))**2,x)","\frac{\int \frac{A}{\cos^{2}{\left(x \right)} + 2 \cos{\left(x \right)} + 1}\, dx + \int \frac{B \sec{\left(x \right)}}{\cos^{2}{\left(x \right)} + 2 \cos{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A/(cos(x)**2 + 2*cos(x) + 1), x) + Integral(B*sec(x)/(cos(x)**2 + 2*cos(x) + 1), x))/a**2","F",0
191,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))**3,x)","\frac{\int \frac{A}{\cos^{3}{\left(x \right)} + 3 \cos^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 1}\, dx + \int \frac{B \sec{\left(x \right)}}{\cos^{3}{\left(x \right)} + 3 \cos^{2}{\left(x \right)} + 3 \cos{\left(x \right)} + 1}\, dx}{a^{3}}"," ",0,"(Integral(A/(cos(x)**3 + 3*cos(x)**2 + 3*cos(x) + 1), x) + Integral(B*sec(x)/(cos(x)**3 + 3*cos(x)**2 + 3*cos(x) + 1), x))/a**3","F",0
192,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))**4,x)","\frac{\int \frac{A}{\cos^{4}{\left(x \right)} + 4 \cos^{3}{\left(x \right)} + 6 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 1}\, dx + \int \frac{B \sec{\left(x \right)}}{\cos^{4}{\left(x \right)} + 4 \cos^{3}{\left(x \right)} + 6 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 1}\, dx}{a^{4}}"," ",0,"(Integral(A/(cos(x)**4 + 4*cos(x)**3 + 6*cos(x)**2 + 4*cos(x) + 1), x) + Integral(B*sec(x)/(cos(x)**4 + 4*cos(x)**3 + 6*cos(x)**2 + 4*cos(x) + 1), x))/a**4","F",0
193,-1,0,0,0.000000," ","integrate((a+a*cos(x))**(5/2)*(A+B*sec(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate((a+a*cos(x))**(3/2)*(A+B*sec(x)),x)","\int \left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}} \left(A + B \sec{\left(x \right)}\right)\, dx"," ",0,"Integral((a*(cos(x) + 1))**(3/2)*(A + B*sec(x)), x)","F",0
195,0,0,0,0.000000," ","integrate((a+a*cos(x))**(1/2)*(A+B*sec(x)),x)","\int \sqrt{a \left(\cos{\left(x \right)} + 1\right)} \left(A + B \sec{\left(x \right)}\right)\, dx"," ",0,"Integral(sqrt(a*(cos(x) + 1))*(A + B*sec(x)), x)","F",0
196,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))**(1/2),x)","\int \frac{A + B \sec{\left(x \right)}}{\sqrt{a \left(\cos{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral((A + B*sec(x))/sqrt(a*(cos(x) + 1)), x)","F",0
197,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))**(3/2),x)","\int \frac{A + B \sec{\left(x \right)}}{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*sec(x))/(a*(cos(x) + 1))**(3/2), x)","F",0
198,0,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))**(5/2),x)","\int \frac{A + B \sec{\left(x \right)}}{\left(a \left(\cos{\left(x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*sec(x))/(a*(cos(x) + 1))**(5/2), x)","F",0
199,-1,0,0,0.000000," ","integrate(x*(b+a*sin(x))/(a+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate(x*(b+a*cos(x))/(a+b*cos(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,1,41,0,0.970333," ","integrate((1+sin(x)**2)/(1-sin(x)**2),x)","- \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{x}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{4 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}"," ",0,"-x*tan(x/2)**2/(tan(x/2)**2 - 1) + x/(tan(x/2)**2 - 1) - 4*tan(x/2)/(tan(x/2)**2 - 1)","B",0
202,1,248,0,48.461447," ","integrate((1-sin(x)**2)/(1+sin(x)**2),x)","- \frac{22619537 x}{15994428 \sqrt{2} + 22619537} - \frac{15994428 \sqrt{2} x}{15994428 \sqrt{2} + 22619537} + \frac{54608393 \sqrt{2} \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{15994428 \sqrt{2} + 22619537} + \frac{77227930 \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{15994428 \sqrt{2} + 22619537} + \frac{9369319 \sqrt{2} \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{15994428 \sqrt{2} + 22619537} + \frac{13250218 \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{15994428 \sqrt{2} + 22619537}"," ",0,"-22619537*x/(15994428*sqrt(2) + 22619537) - 15994428*sqrt(2)*x/(15994428*sqrt(2) + 22619537) + 54608393*sqrt(2)*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(15994428*sqrt(2) + 22619537) + 77227930*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(15994428*sqrt(2) + 22619537) + 9369319*sqrt(2)*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(15994428*sqrt(2) + 22619537) + 13250218*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(15994428*sqrt(2) + 22619537)","B",0
203,1,12,0,0.859457," ","integrate((1+cos(x)**2)/(1-cos(x)**2),x)","- x + \tan{\left(\frac{x}{2} \right)} - \frac{1}{\tan{\left(\frac{x}{2} \right)}}"," ",0,"-x + tan(x/2) - 1/tan(x/2)","A",0
204,1,61,0,2.659614," ","integrate((1-cos(x)**2)/(1+cos(x)**2),x)","- x + \sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) + \sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)"," ",0,"-x + sqrt(2)*(atan(sqrt(2)*tan(x/2) - 1) + pi*floor((x/2 - pi/2)/pi)) + sqrt(2)*(atan(sqrt(2)*tan(x/2) + 1) + pi*floor((x/2 - pi/2)/pi))","A",0
205,1,61,0,56.758466," ","integrate((-1+c**2/d**2+sin(x)**2)/(c+d*cos(x)),x)","\frac{c x \tan^{2}{\left(\frac{x}{2} \right)}}{d^{2} \tan^{2}{\left(\frac{x}{2} \right)} + d^{2}} + \frac{c x}{d^{2} \tan^{2}{\left(\frac{x}{2} \right)} + d^{2}} - \frac{2 d \tan{\left(\frac{x}{2} \right)}}{d^{2} \tan^{2}{\left(\frac{x}{2} \right)} + d^{2}}"," ",0,"c*x*tan(x/2)**2/(d**2*tan(x/2)**2 + d**2) + c*x/(d**2*tan(x/2)**2 + d**2) - 2*d*tan(x/2)/(d**2*tan(x/2)**2 + d**2)","B",0
206,1,2608,0,111.367008," ","integrate((a+b*sin(x)**2)/(c+d*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- \frac{a \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{a \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{a \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{a \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{b \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{b \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{b \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{b \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 b \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) & \text{for}\: c = 0 \wedge d = 0 \\\frac{a \tan^{3}{\left(\frac{x}{2} \right)}}{d \tan^{2}{\left(\frac{x}{2} \right)} + d} + \frac{a \tan{\left(\frac{x}{2} \right)}}{d \tan^{2}{\left(\frac{x}{2} \right)} + d} + \frac{b x \tan^{2}{\left(\frac{x}{2} \right)}}{d \tan^{2}{\left(\frac{x}{2} \right)} + d} + \frac{b x}{d \tan^{2}{\left(\frac{x}{2} \right)} + d} - \frac{2 b \tan{\left(\frac{x}{2} \right)}}{d \tan^{2}{\left(\frac{x}{2} \right)} + d} & \text{for}\: c = d \\\frac{a \tan^{2}{\left(\frac{x}{2} \right)}}{d \tan^{3}{\left(\frac{x}{2} \right)} + d \tan{\left(\frac{x}{2} \right)}} + \frac{a}{d \tan^{3}{\left(\frac{x}{2} \right)} + d \tan{\left(\frac{x}{2} \right)}} - \frac{b x \tan^{3}{\left(\frac{x}{2} \right)}}{d \tan^{3}{\left(\frac{x}{2} \right)} + d \tan{\left(\frac{x}{2} \right)}} - \frac{b x \tan{\left(\frac{x}{2} \right)}}{d \tan^{3}{\left(\frac{x}{2} \right)} + d \tan{\left(\frac{x}{2} \right)}} - \frac{2 b \tan^{2}{\left(\frac{x}{2} \right)}}{d \tan^{3}{\left(\frac{x}{2} \right)} + d \tan{\left(\frac{x}{2} \right)}} & \text{for}\: c = - d \\\frac{a x + \frac{b x \sin^{2}{\left(x \right)}}{2} + \frac{b x \cos^{2}{\left(x \right)}}{2} - \frac{b \sin{\left(x \right)} \cos{\left(x \right)}}{2}}{c} & \text{for}\: d = 0 \\\frac{a d^{2} \log{\left(- \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{a d^{2} \log{\left(- \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{a d^{2} \log{\left(\sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{a d^{2} \log{\left(\sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{b c^{2} x \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{b c^{2} x \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{b c^{2} \log{\left(- \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{b c^{2} \log{\left(- \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{b c^{2} \log{\left(\sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{b c^{2} \log{\left(\sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{b c d x \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{b c d x \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{2 b c d \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{2 b d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{b d^{2} \log{\left(- \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} + \frac{b d^{2} \log{\left(- \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{b d^{2} \log{\left(\sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} - \frac{b d^{2} \log{\left(\sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} + \tan{\left(\frac{x}{2} \right)} \right)}}{c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} + c d^{2} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}} \tan^{2}{\left(\frac{x}{2} \right)} - d^{3} \sqrt{- \frac{c}{c - d} - \frac{d}{c - d}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a*log(tan(x/2) - 1)*tan(x/2)**2/(tan(x/2)**2 + 1) - a*log(tan(x/2) - 1)/(tan(x/2)**2 + 1) + a*log(tan(x/2) + 1)*tan(x/2)**2/(tan(x/2)**2 + 1) + a*log(tan(x/2) + 1)/(tan(x/2)**2 + 1) - b*log(tan(x/2) - 1)*tan(x/2)**2/(tan(x/2)**2 + 1) - b*log(tan(x/2) - 1)/(tan(x/2)**2 + 1) + b*log(tan(x/2) + 1)*tan(x/2)**2/(tan(x/2)**2 + 1) + b*log(tan(x/2) + 1)/(tan(x/2)**2 + 1) - 2*b*tan(x/2)/(tan(x/2)**2 + 1)), Eq(c, 0) & Eq(d, 0)), (a*tan(x/2)**3/(d*tan(x/2)**2 + d) + a*tan(x/2)/(d*tan(x/2)**2 + d) + b*x*tan(x/2)**2/(d*tan(x/2)**2 + d) + b*x/(d*tan(x/2)**2 + d) - 2*b*tan(x/2)/(d*tan(x/2)**2 + d), Eq(c, d)), (a*tan(x/2)**2/(d*tan(x/2)**3 + d*tan(x/2)) + a/(d*tan(x/2)**3 + d*tan(x/2)) - b*x*tan(x/2)**3/(d*tan(x/2)**3 + d*tan(x/2)) - b*x*tan(x/2)/(d*tan(x/2)**3 + d*tan(x/2)) - 2*b*tan(x/2)**2/(d*tan(x/2)**3 + d*tan(x/2)), Eq(c, -d)), ((a*x + b*x*sin(x)**2/2 + b*x*cos(x)**2/2 - b*sin(x)*cos(x)/2)/c, Eq(d, 0)), (a*d**2*log(-sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + a*d**2*log(-sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - a*d**2*log(sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - a*d**2*log(sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + b*c**2*x*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + b*c**2*x*sqrt(-c/(c - d) - d/(c - d))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - b*c**2*log(-sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - b*c**2*log(-sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + b*c**2*log(sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + b*c**2*log(sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - b*c*d*x*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - b*c*d*x*sqrt(-c/(c - d) - d/(c - d))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - 2*b*c*d*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + 2*b*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + b*d**2*log(-sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) + b*d**2*log(-sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - b*d**2*log(sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))*tan(x/2)**2/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))) - b*d**2*log(sqrt(-c/(c - d) - d/(c - d)) + tan(x/2))/(c*d**2*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 + c*d**2*sqrt(-c/(c - d) - d/(c - d)) - d**3*sqrt(-c/(c - d) - d/(c - d))*tan(x/2)**2 - d**3*sqrt(-c/(c - d) - d/(c - d))), True))","A",0
207,1,143,0,10.667166," ","integrate((a+b*sin(x)**2)/(c+c*cos(x)**2),x)","\frac{\sqrt{2} a \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2 c} + \frac{\sqrt{2} a \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2 c} - \frac{b x}{c} + \frac{\sqrt{2} b \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{c} + \frac{\sqrt{2} b \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{c}"," ",0,"sqrt(2)*a*(atan(sqrt(2)*tan(x/2) - 1) + pi*floor((x/2 - pi/2)/pi))/(2*c) + sqrt(2)*a*(atan(sqrt(2)*tan(x/2) + 1) + pi*floor((x/2 - pi/2)/pi))/(2*c) - b*x/c + sqrt(2)*b*(atan(sqrt(2)*tan(x/2) - 1) + pi*floor((x/2 - pi/2)/pi))/c + sqrt(2)*b*(atan(sqrt(2)*tan(x/2) + 1) + pi*floor((x/2 - pi/2)/pi))/c","B",0
208,1,24,0,1.178032," ","integrate((a+b*sin(x)**2)/(c-c*cos(x)**2),x)","\frac{a \tan{\left(\frac{x}{2} \right)}}{2 c} - \frac{a}{2 c \tan{\left(\frac{x}{2} \right)}} + \frac{b x}{c}"," ",0,"a*tan(x/2)/(2*c) - a/(2*c*tan(x/2)) + b*x/c","B",0
209,-1,0,0,0.000000," ","integrate((a+b*sin(x)**2)/(c+d*cos(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,1,56,0,103.318025," ","integrate((-1+c**2/d**2+cos(x)**2)/(c+d*sin(x)),x)","\frac{c x \tan^{2}{\left(\frac{x}{2} \right)}}{d^{2} \tan^{2}{\left(\frac{x}{2} \right)} + d^{2}} + \frac{c x}{d^{2} \tan^{2}{\left(\frac{x}{2} \right)} + d^{2}} + \frac{2 d}{d^{2} \tan^{2}{\left(\frac{x}{2} \right)} + d^{2}}"," ",0,"c*x*tan(x/2)**2/(d**2*tan(x/2)**2 + d**2) + c*x/(d**2*tan(x/2)**2 + d**2) + 2*d/(d**2*tan(x/2)**2 + d**2)","B",0
211,-1,0,0,0.000000," ","integrate((a+b*cos(x)**2)/(c+d*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,1,520,0,55.653551," ","integrate((a+b*cos(x)**2)/(c+c*sin(x)**2),x)","\frac{54608393 \sqrt{2} a \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} + \frac{77227930 a \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} + \frac{9369319 \sqrt{2} a \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} + \frac{13250218 a \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} - \frac{45239074 b x}{31988856 \sqrt{2} c + 45239074 c} - \frac{31988856 \sqrt{2} b x}{31988856 \sqrt{2} c + 45239074 c} + \frac{109216786 \sqrt{2} b \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} + \frac{154455860 b \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} + \frac{18738638 \sqrt{2} b \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c} + \frac{26500436 b \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{31988856 \sqrt{2} c + 45239074 c}"," ",0,"54608393*sqrt(2)*a*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) + 77227930*a*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) + 9369319*sqrt(2)*a*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) + 13250218*a*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) - 45239074*b*x/(31988856*sqrt(2)*c + 45239074*c) - 31988856*sqrt(2)*b*x/(31988856*sqrt(2)*c + 45239074*c) + 109216786*sqrt(2)*b*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) + 154455860*b*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) + 18738638*sqrt(2)*b*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c) + 26500436*b*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(31988856*sqrt(2)*c + 45239074*c)","B",0
213,1,51,0,1.331331," ","integrate((a+b*cos(x)**2)/(c-c*sin(x)**2),x)","- \frac{2 a \tan{\left(\frac{x}{2} \right)}}{c \tan^{2}{\left(\frac{x}{2} \right)} - c} + \frac{b x \tan^{2}{\left(\frac{x}{2} \right)}}{c \tan^{2}{\left(\frac{x}{2} \right)} - c} - \frac{b x}{c \tan^{2}{\left(\frac{x}{2} \right)} - c}"," ",0,"-2*a*tan(x/2)/(c*tan(x/2)**2 - c) + b*x*tan(x/2)**2/(c*tan(x/2)**2 - c) - b*x/(c*tan(x/2)**2 - c)","B",0
214,-1,0,0,0.000000," ","integrate((a+b*cos(x)**2)/(c+d*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,0,0,0,0.000000," ","integrate((a+b*sec(x)**2)/(c+d*cos(x)),x)","\int \frac{a + b \sec^{2}{\left(x \right)}}{c + d \cos{\left(x \right)}}\, dx"," ",0,"Integral((a + b*sec(x)**2)/(c + d*cos(x)), x)","F",0
216,0,0,0,0.000000," ","integrate((a+b*csc(x)**2)/(c+d*sin(x)),x)","\int \frac{a + b \csc^{2}{\left(x \right)}}{c + d \sin{\left(x \right)}}\, dx"," ",0,"Integral((a + b*csc(x)**2)/(c + d*sin(x)), x)","F",0
217,-1,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))**n,x)","\int \left(3 \sin{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((3*sin(c + d*x) + 2*cos(c + d*x))**n, x)","F",0
219,1,461,0,6.555557," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**7,x)","\begin{cases} \frac{16 a^{7} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a^{7} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a^{7} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a^{7} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{a^{6} b \cos^{7}{\left(c + d x \right)}}{d} + \frac{8 a^{5} b^{2} \sin^{7}{\left(c + d x \right)}}{5 d} + \frac{28 a^{5} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{7 a^{5} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{7 a^{4} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{d} - \frac{2 a^{4} b^{3} \cos^{7}{\left(c + d x \right)}}{d} + \frac{2 a^{3} b^{4} \sin^{7}{\left(c + d x \right)}}{d} + \frac{7 a^{3} b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{7 a^{2} b^{5} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{28 a^{2} b^{5} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{8 a^{2} b^{5} \cos^{7}{\left(c + d x \right)}}{5 d} + \frac{a b^{6} \sin^{7}{\left(c + d x \right)}}{d} - \frac{b^{7} \sin^{6}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 b^{7} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{8 b^{7} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{16 b^{7} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{7} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**7*sin(c + d*x)**7/(35*d) + 8*a**7*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a**7*sin(c + d*x)**3*cos(c + d*x)**4/d + a**7*sin(c + d*x)*cos(c + d*x)**6/d - a**6*b*cos(c + d*x)**7/d + 8*a**5*b**2*sin(c + d*x)**7/(5*d) + 28*a**5*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 7*a**5*b**2*sin(c + d*x)**3*cos(c + d*x)**4/d - 7*a**4*b**3*sin(c + d*x)**2*cos(c + d*x)**5/d - 2*a**4*b**3*cos(c + d*x)**7/d + 2*a**3*b**4*sin(c + d*x)**7/d + 7*a**3*b**4*sin(c + d*x)**5*cos(c + d*x)**2/d - 7*a**2*b**5*sin(c + d*x)**4*cos(c + d*x)**3/d - 28*a**2*b**5*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 8*a**2*b**5*cos(c + d*x)**7/(5*d) + a*b**6*sin(c + d*x)**7/d - b**7*sin(c + d*x)**6*cos(c + d*x)/d - 2*b**7*sin(c + d*x)**4*cos(c + d*x)**3/d - 8*b**7*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 16*b**7*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**7, True))","A",0
220,1,770,0,4.623471," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**6,x)","\begin{cases} \frac{5 a^{6} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{6} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{6} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{6} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{6} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{6} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a^{6} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a^{5} b \cos^{6}{\left(c + d x \right)}}{d} + \frac{15 a^{4} b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{45 a^{4} b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{45 a^{4} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{15 a^{4} b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{4} b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{4} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{15 a^{4} b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{5 a^{3} b^{3} \sin^{6}{\left(c + d x \right)}}{3 d} + \frac{5 a^{3} b^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{15 a^{2} b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{45 a^{2} b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{45 a^{2} b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{15 a^{2} b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{2} b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{5 a^{2} b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{15 a^{2} b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{a b^{5} \sin^{6}{\left(c + d x \right)}}{d} + \frac{5 b^{6} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 b^{6} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 b^{6} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 b^{6} x \cos^{6}{\left(c + d x \right)}}{16} - \frac{11 b^{6} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{5 b^{6} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{5 b^{6} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**6*x*sin(c + d*x)**6/16 + 15*a**6*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**6*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**6*x*cos(c + d*x)**6/16 + 5*a**6*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**6*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a**6*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a**5*b*cos(c + d*x)**6/d + 15*a**4*b**2*x*sin(c + d*x)**6/16 + 45*a**4*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 45*a**4*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 15*a**4*b**2*x*cos(c + d*x)**6/16 + 15*a**4*b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**4*b**2*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 15*a**4*b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 5*a**3*b**3*sin(c + d*x)**6/(3*d) + 5*a**3*b**3*sin(c + d*x)**4*cos(c + d*x)**2/d + 15*a**2*b**4*x*sin(c + d*x)**6/16 + 45*a**2*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 45*a**2*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 15*a**2*b**4*x*cos(c + d*x)**6/16 + 15*a**2*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 5*a**2*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 15*a**2*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + a*b**5*sin(c + d*x)**6/d + 5*b**6*x*sin(c + d*x)**6/16 + 15*b**6*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*b**6*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*b**6*x*cos(c + d*x)**6/16 - 11*b**6*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 5*b**6*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 5*b**6*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**6, True))","A",0
221,1,267,0,2.216661," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{8 a^{5} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{5} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{4} b \cos^{5}{\left(c + d x \right)}}{d} + \frac{4 a^{3} b^{2} \sin^{5}{\left(c + d x \right)}}{3 d} + \frac{10 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{10 a^{2} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 a^{2} b^{3} \cos^{5}{\left(c + d x \right)}}{3 d} + \frac{a b^{4} \sin^{5}{\left(c + d x \right)}}{d} - \frac{b^{5} \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{4 b^{5} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{8 b^{5} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**5*sin(c + d*x)**5/(15*d) + 4*a**5*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**5*sin(c + d*x)*cos(c + d*x)**4/d - a**4*b*cos(c + d*x)**5/d + 4*a**3*b**2*sin(c + d*x)**5/(3*d) + 10*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - 10*a**2*b**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 4*a**2*b**3*cos(c + d*x)**5/(3*d) + a*b**4*sin(c + d*x)**5/d - b**5*sin(c + d*x)**4*cos(c + d*x)/d - 4*b**5*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 8*b**5*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5, True))","A",0
222,1,381,0,1.271328," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{3 a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a^{3} b \cos^{4}{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{3 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{a b^{3} \sin^{4}{\left(c + d x \right)}}{d} + \frac{3 b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} x \cos^{4}{\left(c + d x \right)}}{8} - \frac{5 b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x*sin(c + d*x)**4/8 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**4*x*cos(c + d*x)**4/8 + 3*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a**3*b*cos(c + d*x)**4/d + 3*a**2*b**2*x*sin(c + d*x)**4/4 + 3*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*a**2*b**2*x*cos(c + d*x)**4/4 + 3*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) - 3*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + a*b**3*sin(c + d*x)**4/d + 3*b**4*x*sin(c + d*x)**4/8 + 3*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b**4*x*cos(c + d*x)**4/8 - 5*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4, True))","A",0
223,1,117,0,0.519837," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{2 a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a^{2} b \cos^{3}{\left(c + d x \right)}}{d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)}}{d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 b^{3} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*sin(c + d*x)**3/(3*d) + a**3*sin(c + d*x)*cos(c + d*x)**2/d - a**2*b*cos(c + d*x)**3/d + a*b**2*sin(c + d*x)**3/d - b**3*sin(c + d*x)**2*cos(c + d*x)/d - 2*b**3*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3, True))","A",0
224,1,128,0,0.276573," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{a b \cos^{2}{\left(c + d x \right)}}{d} + \frac{b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(c + d x \right)}}{2} - \frac{b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**2/2 + a**2*x*cos(c + d*x)**2/2 + a**2*sin(c + d*x)*cos(c + d*x)/(2*d) - a*b*cos(c + d*x)**2/d + b**2*x*sin(c + d*x)**2/2 + b**2*x*cos(c + d*x)**2/2 - b**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2, True))","A",0
225,1,31,0,0.145123," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x)","a \left(\begin{cases} \frac{\sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cos{\left(c \right)} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} - \frac{\cos{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \sin{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*Piecewise((sin(c + d*x)/d, Ne(d, 0)), (x*cos(c), True)) + b*Piecewise((-cos(c + d*x)/d, Ne(d, 0)), (x*sin(c), True))","A",0
226,-2,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
227,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \frac{1}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**(-2), x)","F",0
228,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**(3/2),x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**(3/2), x)","F",0
235,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**(-3/2), x)","F",0
238,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))**(1/2),x)","\int \sqrt{3 \sin{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(3*sin(c + d*x) + 2*cos(c + d*x)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{3 \sin{\left(c + d x \right)} + 2 \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(3*sin(c + d*x) + 2*cos(c + d*x)), x)","F",0
245,-1,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,1,44,0,0.253949," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**n,x)","\begin{cases} x & \text{for}\: n = 0 \wedge \left(d = 0 \vee n = 0\right) \\x \left(i a \sin{\left(c \right)} + a \cos{\left(c \right)}\right)^{n} & \text{for}\: d = 0 \\- \frac{i \left(i a \sin{\left(c + d x \right)} + a \cos{\left(c + d x \right)}\right)^{n}}{d n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x, Eq(n, 0) & (Eq(d, 0) | Eq(n, 0))), (x*(I*a*sin(c) + a*cos(c))**n, Eq(d, 0)), (-I*(I*a*sin(c + d*x) + a*cos(c + d*x))**n/(d*n), True))","A",0
249,1,37,0,0.140517," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**4,x)","\begin{cases} - \frac{i a^{4} e^{4 i c} e^{4 i d x}}{4 d} & \text{for}\: 4 d \neq 0 \\a^{4} x e^{4 i c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**4*exp(4*I*c)*exp(4*I*d*x)/(4*d), Ne(4*d, 0)), (a**4*x*exp(4*I*c), True))","A",0
250,1,37,0,0.137980," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} - \frac{i a^{3} e^{3 i c} e^{3 i d x}}{3 d} & \text{for}\: 3 d \neq 0 \\a^{3} x e^{3 i c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**3*exp(3*I*c)*exp(3*I*d*x)/(3*d), Ne(3*d, 0)), (a**3*x*exp(3*I*c), True))","A",0
251,1,37,0,0.133540," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} - \frac{i a^{2} e^{2 i c} e^{2 i d x}}{2 d} & \text{for}\: 2 d \neq 0 \\a^{2} x e^{2 i c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**2*exp(2*I*c)*exp(2*I*d*x)/(2*d), Ne(2*d, 0)), (a**2*x*exp(2*I*c), True))","A",0
252,1,26,0,0.123366," ","integrate(a*cos(d*x+c)+I*a*sin(d*x+c),x)","\begin{cases} - \frac{i a e^{i c} e^{i d x}}{d} & \text{for}\: d \neq 0 \\a x e^{i c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a*exp(I*c)*exp(I*d*x)/d, Ne(d, 0)), (a*x*exp(I*c), True))","A",0
253,1,31,0,0.141819," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} \frac{i e^{- i c} e^{- i d x}}{a d} & \text{for}\: a d e^{i c} \neq 0 \\\frac{x e^{- i c}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-I*c)*exp(-I*d*x)/(a*d), Ne(a*d*exp(I*c), 0)), (x*exp(-I*c)/a, True))","A",0
254,1,46,0,0.144010," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{i e^{- 2 i c} e^{- 2 i d x}}{2 a^{2} d} & \text{for}\: 2 a^{2} d e^{2 i c} \neq 0 \\\frac{x e^{- 2 i c}}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-2*I*c)*exp(-2*I*d*x)/(2*a**2*d), Ne(2*a**2*d*exp(2*I*c), 0)), (x*exp(-2*I*c)/a**2, True))","A",0
255,1,46,0,0.144999," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} \frac{i e^{- 3 i c} e^{- 3 i d x}}{3 a^{3} d} & \text{for}\: 3 a^{3} d e^{3 i c} \neq 0 \\\frac{x e^{- 3 i c}}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-3*I*c)*exp(-3*I*d*x)/(3*a**3*d), Ne(3*a**3*d*exp(3*I*c), 0)), (x*exp(-3*I*c)/a**3, True))","A",0
256,1,46,0,0.150018," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**4,x)","\begin{cases} \frac{i e^{- 4 i c} e^{- 4 i d x}}{4 a^{4} d} & \text{for}\: 4 a^{4} d e^{4 i c} \neq 0 \\\frac{x e^{- 4 i c}}{a^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-4*I*c)*exp(-4*I*d*x)/(4*a**4*d), Ne(4*a**4*d*exp(4*I*c), 0)), (x*exp(-4*I*c)/a**4, True))","A",0
257,-1,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**(3/2),x)","\int \left(i a \sin{\left(c + d x \right)} + a \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((I*a*sin(c + d*x) + a*cos(c + d*x))**(3/2), x)","F",0
259,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**(1/2),x)","\int \sqrt{i a \sin{\left(c + d x \right)} + a \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*sin(c + d*x) + a*cos(c + d*x)), x)","F",0
260,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{i a \sin{\left(c + d x \right)} + a \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(I*a*sin(c + d*x) + a*cos(c + d*x)), x)","F",0
261,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \sin{\left(c + d x \right)} + a \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*sin(c + d*x) + a*cos(c + d*x))**(-3/2), x)","F",0
262,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**(5/2),x)","\int \frac{1}{\left(i a \sin{\left(c + d x \right)} + a \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*sin(c + d*x) + a*cos(c + d*x))**(-5/2), x)","F",0
263,1,308,0,7.121193," ","integrate((a*sec(x)+b*tan(x))**5,x)","- \frac{3 a^{5} \log{\left(\sin{\left(x \right)} - 1 \right)}}{16} + \frac{3 a^{5} \log{\left(\sin{\left(x \right)} + 1 \right)}}{16} - \frac{3 a^{5} \sin^{3}{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{5 a^{5} \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{5 a^{4} b \sec^{4}{\left(x \right)}}{4} + \frac{5 a^{3} b^{2} \log{\left(\sin{\left(x \right)} - 1 \right)}}{8} - \frac{5 a^{3} b^{2} \log{\left(\sin{\left(x \right)} + 1 \right)}}{8} + \frac{10 a^{3} b^{2} \sin^{3}{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{10 a^{3} b^{2} \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{5 a^{2} b^{3} \tan^{4}{\left(x \right)}}{2} - \frac{15 a b^{4} \log{\left(\sin{\left(x \right)} - 1 \right)}}{16} + \frac{15 a b^{4} \log{\left(\sin{\left(x \right)} + 1 \right)}}{16} + \frac{25 a b^{4} \sin^{3}{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} - \frac{15 a b^{4} \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{b^{5} \log{\left(\sec^{2}{\left(x \right)} \right)}}{2} + \frac{b^{5} \sec^{4}{\left(x \right)}}{4} - b^{5} \sec^{2}{\left(x \right)}"," ",0,"-3*a**5*log(sin(x) - 1)/16 + 3*a**5*log(sin(x) + 1)/16 - 3*a**5*sin(x)**3/(8*sin(x)**4 - 16*sin(x)**2 + 8) + 5*a**5*sin(x)/(8*sin(x)**4 - 16*sin(x)**2 + 8) + 5*a**4*b*sec(x)**4/4 + 5*a**3*b**2*log(sin(x) - 1)/8 - 5*a**3*b**2*log(sin(x) + 1)/8 + 10*a**3*b**2*sin(x)**3/(8*sin(x)**4 - 16*sin(x)**2 + 8) + 10*a**3*b**2*sin(x)/(8*sin(x)**4 - 16*sin(x)**2 + 8) + 5*a**2*b**3*tan(x)**4/2 - 15*a*b**4*log(sin(x) - 1)/16 + 15*a*b**4*log(sin(x) + 1)/16 + 25*a*b**4*sin(x)**3/(8*sin(x)**4 - 16*sin(x)**2 + 8) - 15*a*b**4*sin(x)/(8*sin(x)**4 - 16*sin(x)**2 + 8) + b**5*log(sec(x)**2)/2 + b**5*sec(x)**4/4 - b**5*sec(x)**2","B",0
264,1,97,0,4.223930," ","integrate((a*sec(x)+b*tan(x))**4,x)","\frac{a^{4} \tan^{3}{\left(x \right)}}{3} + a^{4} \tan{\left(x \right)} + \frac{4 a^{3} b \sec^{3}{\left(x \right)}}{3} + 2 a^{2} b^{2} \tan^{3}{\left(x \right)} + \frac{4 a b^{3} \sec^{3}{\left(x \right)}}{3} - 4 a b^{3} \sec{\left(x \right)} + b^{4} x + \frac{b^{4} \sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} - \frac{b^{4} \sin{\left(x \right)}}{\cos{\left(x \right)}}"," ",0,"a**4*tan(x)**3/3 + a**4*tan(x) + 4*a**3*b*sec(x)**3/3 + 2*a**2*b**2*tan(x)**3 + 4*a*b**3*sec(x)**3/3 - 4*a*b**3*sec(x) + b**4*x + b**4*sin(x)**3/(3*cos(x)**3) - b**4*sin(x)/cos(x)","A",0
265,1,122,0,4.935583," ","integrate((a*sec(x)+b*tan(x))**3,x)","- \frac{a^{3} \log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{a^{3} \log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{a^{3} \sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2} + \frac{3 a^{2} b \sec^{2}{\left(x \right)}}{2} + \frac{3 a b^{2} \log{\left(\sin{\left(x \right)} - 1 \right)}}{4} - \frac{3 a b^{2} \log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{3 a b^{2} \sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2} - \frac{b^{3} \log{\left(\sec^{2}{\left(x \right)} \right)}}{2} + \frac{b^{3} \sec^{2}{\left(x \right)}}{2}"," ",0,"-a**3*log(sin(x) - 1)/4 + a**3*log(sin(x) + 1)/4 - a**3*sin(x)/(2*sin(x)**2 - 2) + 3*a**2*b*sec(x)**2/2 + 3*a*b**2*log(sin(x) - 1)/4 - 3*a*b**2*log(sin(x) + 1)/4 - 3*a*b**2*sin(x)/(2*sin(x)**2 - 2) - b**3*log(sec(x)**2)/2 + b**3*sec(x)**2/2","A",0
266,1,22,0,1.253573," ","integrate((a*sec(x)+b*tan(x))**2,x)","a^{2} \tan{\left(x \right)} + 2 a b \sec{\left(x \right)} + b^{2} \left(- x + \tan{\left(x \right)}\right)"," ",0,"a**2*tan(x) + 2*a*b*sec(x) + b**2*(-x + tan(x))","A",0
267,1,24,0,0.091102," ","integrate(a*sec(x)+b*tan(x),x)","a \left(- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}\right) - b \log{\left(\cos{\left(x \right)} \right)}"," ",0,"a*(-log(sin(x) - 1)/2 + log(sin(x) + 1)/2) - b*log(cos(x))","A",0
268,1,32,0,0.418356," ","integrate(1/(a*sec(x)+b*tan(x)),x)","\begin{cases} \frac{\log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)}}{b} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2 b} & \text{for}\: b \neq 0 \\\frac{\tan{\left(x \right)}}{a \sec{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(a*sec(x)/b + tan(x))/b - log(tan(x)**2 + 1)/(2*b), Ne(b, 0)), (tan(x)/(a*sec(x)), True))","A",0
269,0,0,0,0.000000," ","integrate(1/(a*sec(x)+b*tan(x))**2,x)","\int \frac{1}{\left(a \sec{\left(x \right)} + b \tan{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((a*sec(x) + b*tan(x))**(-2), x)","F",0
270,1,503,0,2.758833," ","integrate(1/(a*sec(x)+b*tan(x))**3,x)","\begin{cases} - \frac{2 a^{2} \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \sec^{2}{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} + \frac{a^{2} \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \sec^{2}{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} - \frac{a^{2} \sec^{2}{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} - \frac{4 a b \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \tan{\left(x \right)} \sec{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} + \frac{2 a b \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} - \frac{2 b^{2} \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} + \frac{b^{2} \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} + \frac{b^{2} \tan^{2}{\left(x \right)}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} - \frac{b^{2}}{2 a^{2} b^{3} \sec^{2}{\left(x \right)} + 4 a b^{4} \tan{\left(x \right)} \sec{\left(x \right)} + 2 b^{5} \tan^{2}{\left(x \right)}} & \text{for}\: b \neq 0 \\\frac{\frac{2 \tan^{3}{\left(x \right)}}{3 \sec^{3}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{\sec^{3}{\left(x \right)}}}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*log(a*sec(x)/b + tan(x))*sec(x)**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) + a**2*log(tan(x)**2 + 1)*sec(x)**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) - a**2*sec(x)**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) - 4*a*b*log(a*sec(x)/b + tan(x))*tan(x)*sec(x)/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) + 2*a*b*log(tan(x)**2 + 1)*tan(x)*sec(x)/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) - 2*b**2*log(a*sec(x)/b + tan(x))*tan(x)**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) + b**2*log(tan(x)**2 + 1)*tan(x)**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) + b**2*tan(x)**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2) - b**2/(2*a**2*b**3*sec(x)**2 + 4*a*b**4*tan(x)*sec(x) + 2*b**5*tan(x)**2), Ne(b, 0)), ((2*tan(x)**3/(3*sec(x)**3) + tan(x)/sec(x)**3)/a**3, True))","A",0
271,0,0,0,0.000000," ","integrate(1/(a*sec(x)+b*tan(x))**4,x)","\int \frac{1}{\left(a \sec{\left(x \right)} + b \tan{\left(x \right)}\right)^{4}}\, dx"," ",0,"Integral((a*sec(x) + b*tan(x))**(-4), x)","F",0
272,1,1719,0,15.190002," ","integrate(1/(a*sec(x)+b*tan(x))**5,x)","\begin{cases} \frac{36 a^{4} \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \sec^{4}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{18 a^{4} \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \sec^{4}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{20 a^{4} \sec^{4}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{144 a^{3} b \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \tan{\left(x \right)} \sec^{3}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{72 a^{3} b \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)} \sec^{3}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{44 a^{3} b \tan{\left(x \right)} \sec^{3}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{216 a^{2} b^{2} \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{108 a^{2} b^{2} \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{6 a^{2} b^{2} \sec^{2}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{144 a b^{3} \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \tan^{3}{\left(x \right)} \sec{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{72 a b^{3} \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{3}{\left(x \right)} \sec{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{52 a b^{3} \tan^{3}{\left(x \right)} \sec{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{24 a b^{3} \tan{\left(x \right)} \sec{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{36 b^{4} \log{\left(\frac{a \sec{\left(x \right)}}{b} + \tan{\left(x \right)} \right)} \tan^{4}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{18 b^{4} \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{4}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{28 b^{4} \tan^{4}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} + \frac{18 b^{4} \tan^{2}{\left(x \right)}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} - \frac{9 b^{4}}{36 a^{4} b^{5} \sec^{4}{\left(x \right)} + 144 a^{3} b^{6} \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 216 a^{2} b^{7} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 a b^{8} \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 36 b^{9} \tan^{4}{\left(x \right)}} & \text{for}\: b \neq 0 \\\frac{\frac{8 \tan^{5}{\left(x \right)}}{15 \sec^{5}{\left(x \right)}} + \frac{4 \tan^{3}{\left(x \right)}}{3 \sec^{5}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{\sec^{5}{\left(x \right)}}}{a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((36*a**4*log(a*sec(x)/b + tan(x))*sec(x)**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 18*a**4*log(tan(x)**2 + 1)*sec(x)**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 20*a**4*sec(x)**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 144*a**3*b*log(a*sec(x)/b + tan(x))*tan(x)*sec(x)**3/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 72*a**3*b*log(tan(x)**2 + 1)*tan(x)*sec(x)**3/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 44*a**3*b*tan(x)*sec(x)**3/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 216*a**2*b**2*log(a*sec(x)/b + tan(x))*tan(x)**2*sec(x)**2/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 108*a**2*b**2*log(tan(x)**2 + 1)*tan(x)**2*sec(x)**2/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 6*a**2*b**2*sec(x)**2/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 144*a*b**3*log(a*sec(x)/b + tan(x))*tan(x)**3*sec(x)/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 72*a*b**3*log(tan(x)**2 + 1)*tan(x)**3*sec(x)/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 52*a*b**3*tan(x)**3*sec(x)/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 24*a*b**3*tan(x)*sec(x)/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 36*b**4*log(a*sec(x)/b + tan(x))*tan(x)**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 18*b**4*log(tan(x)**2 + 1)*tan(x)**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 28*b**4*tan(x)**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) + 18*b**4*tan(x)**2/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4) - 9*b**4/(36*a**4*b**5*sec(x)**4 + 144*a**3*b**6*tan(x)*sec(x)**3 + 216*a**2*b**7*tan(x)**2*sec(x)**2 + 144*a*b**8*tan(x)**3*sec(x) + 36*b**9*tan(x)**4), Ne(b, 0)), ((8*tan(x)**5/(15*sec(x)**5) + 4*tan(x)**3/(3*sec(x)**5) + tan(x)/sec(x)**5)/a**5, True))","A",0
273,1,68,0,7.127450," ","integrate((sec(x)+tan(x))**5,x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} + \frac{\log{\left(\sec^{2}{\left(x \right)} \right)}}{2} + \frac{5 \tan^{4}{\left(x \right)}}{2} + \frac{3 \sec^{4}{\left(x \right)}}{2} - \sec^{2}{\left(x \right)} + \frac{32 \sin^{3}{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8}"," ",0,"-log(sin(x) - 1)/2 + log(sin(x) + 1)/2 + log(sec(x)**2)/2 + 5*tan(x)**4/2 + 3*sec(x)**4/2 - sec(x)**2 + 32*sin(x)**3/(8*sin(x)**4 - 16*sin(x)**2 + 8)","B",0
274,1,44,0,4.096054," ","integrate((sec(x)+tan(x))**4,x)","x + \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{7 \tan^{3}{\left(x \right)}}{3} + \tan{\left(x \right)} + \frac{8 \sec^{3}{\left(x \right)}}{3} - 4 \sec{\left(x \right)}"," ",0,"x + sin(x)**3/(3*cos(x)**3) - sin(x)/cos(x) + 7*tan(x)**3/3 + tan(x) + 8*sec(x)**3/3 - 4*sec(x)","A",0
275,1,44,0,4.807475," ","integrate((sec(x)+tan(x))**3,x)","\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \frac{\log{\left(\sec^{2}{\left(x \right)} \right)}}{2} + 2 \sec^{2}{\left(x \right)} - \frac{4 \sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}"," ",0,"log(sin(x) - 1)/2 - log(sin(x) + 1)/2 - log(sec(x)**2)/2 + 2*sec(x)**2 - 4*sin(x)/(2*sin(x)**2 - 2)","B",0
276,1,10,0,1.108204," ","integrate((sec(x)+tan(x))**2,x)","- x + 2 \tan{\left(x \right)} + 2 \sec{\left(x \right)}"," ",0,"-x + 2*tan(x) + 2*sec(x)","A",0
277,1,20,0,0.090968," ","integrate(sec(x)+tan(x),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \log{\left(\cos{\left(x \right)} \right)}"," ",0,"-log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - log(cos(x))","A",0
278,1,17,0,0.137617," ","integrate(1/(sec(x)+tan(x)),x)","\log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2}"," ",0,"log(tan(x) + sec(x)) - log(tan(x)**2 + 1)/2","B",0
279,0,0,0,0.000000," ","integrate(1/(sec(x)+tan(x))**2,x)","\int \frac{1}{\left(\tan{\left(x \right)} + \sec{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((tan(x) + sec(x))**(-2), x)","F",0
280,1,301,0,0.830494," ","integrate(1/(sec(x)+tan(x))**3,x)","- \frac{2 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \tan{\left(x \right)} \sec{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} - \frac{2 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \sec^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} + \frac{2 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \sec^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} - \frac{\sec^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}} - \frac{1}{2 \tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)} \sec{\left(x \right)} + 2 \sec^{2}{\left(x \right)}}"," ",0,"-2*log(tan(x) + sec(x))*tan(x)**2/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) - 4*log(tan(x) + sec(x))*tan(x)*sec(x)/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) - 2*log(tan(x) + sec(x))*sec(x)**2/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) + log(tan(x)**2 + 1)*tan(x)**2/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) + 2*log(tan(x)**2 + 1)*tan(x)*sec(x)/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) + log(tan(x)**2 + 1)*sec(x)**2/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) + tan(x)**2/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) - sec(x)**2/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2) - 1/(2*tan(x)**2 + 4*tan(x)*sec(x) + 2*sec(x)**2)","B",0
281,0,0,0,0.000000," ","integrate(1/(sec(x)+tan(x))**4,x)","\int \frac{1}{\left(\tan{\left(x \right)} + \sec{\left(x \right)}\right)^{4}}\, dx"," ",0,"Integral((tan(x) + sec(x))**(-4), x)","F",0
282,1,1059,0,2.761700," ","integrate(1/(sec(x)+tan(x))**5,x)","\frac{36 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \tan^{4}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{144 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \tan^{3}{\left(x \right)} \sec{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{216 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{144 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \tan{\left(x \right)} \sec^{3}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{36 \log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} \sec^{4}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{18 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{4}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{72 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{3}{\left(x \right)} \sec{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{108 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{72 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)} \sec^{3}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{18 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \sec^{4}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{28 \tan^{4}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{52 \tan^{3}{\left(x \right)} \sec{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{18 \tan^{2}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{44 \tan{\left(x \right)} \sec^{3}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{24 \tan{\left(x \right)} \sec{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{20 \sec^{4}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} + \frac{6 \sec^{2}{\left(x \right)}}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}} - \frac{9}{36 \tan^{4}{\left(x \right)} + 144 \tan^{3}{\left(x \right)} \sec{\left(x \right)} + 216 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 144 \tan{\left(x \right)} \sec^{3}{\left(x \right)} + 36 \sec^{4}{\left(x \right)}}"," ",0,"36*log(tan(x) + sec(x))*tan(x)**4/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 144*log(tan(x) + sec(x))*tan(x)**3*sec(x)/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 216*log(tan(x) + sec(x))*tan(x)**2*sec(x)**2/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 144*log(tan(x) + sec(x))*tan(x)*sec(x)**3/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 36*log(tan(x) + sec(x))*sec(x)**4/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 18*log(tan(x)**2 + 1)*tan(x)**4/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 72*log(tan(x)**2 + 1)*tan(x)**3*sec(x)/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 108*log(tan(x)**2 + 1)*tan(x)**2*sec(x)**2/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 72*log(tan(x)**2 + 1)*tan(x)*sec(x)**3/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 18*log(tan(x)**2 + 1)*sec(x)**4/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 28*tan(x)**4/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 52*tan(x)**3*sec(x)/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 18*tan(x)**2/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 44*tan(x)*sec(x)**3/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 24*tan(x)*sec(x)/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 20*sec(x)**4/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) + 6*sec(x)**2/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4) - 9/(36*tan(x)**4 + 144*tan(x)**3*sec(x) + 216*tan(x)**2*sec(x)**2 + 144*tan(x)*sec(x)**3 + 36*sec(x)**4)","B",0
283,1,308,0,102.278480," ","integrate((a*cot(x)+b*csc(x))**5,x)","- \frac{a^{5} \log{\left(\csc^{2}{\left(x \right)} \right)}}{2} - \frac{a^{5} \csc^{4}{\left(x \right)}}{4} + a^{5} \csc^{2}{\left(x \right)} + \frac{15 a^{4} b \log{\left(\cos{\left(x \right)} - 1 \right)}}{16} - \frac{15 a^{4} b \log{\left(\cos{\left(x \right)} + 1 \right)}}{16} - \frac{25 a^{4} b \cos^{3}{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} + \frac{15 a^{4} b \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} - \frac{5 a^{3} b^{2} \cot^{4}{\left(x \right)}}{2} - \frac{5 a^{2} b^{3} \log{\left(\cos{\left(x \right)} - 1 \right)}}{8} + \frac{5 a^{2} b^{3} \log{\left(\cos{\left(x \right)} + 1 \right)}}{8} - \frac{10 a^{2} b^{3} \cos^{3}{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} - \frac{10 a^{2} b^{3} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} - \frac{5 a b^{4} \csc^{4}{\left(x \right)}}{4} + \frac{3 b^{5} \log{\left(\cos{\left(x \right)} - 1 \right)}}{16} - \frac{3 b^{5} \log{\left(\cos{\left(x \right)} + 1 \right)}}{16} + \frac{3 b^{5} \cos^{3}{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8} - \frac{5 b^{5} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8}"," ",0,"-a**5*log(csc(x)**2)/2 - a**5*csc(x)**4/4 + a**5*csc(x)**2 + 15*a**4*b*log(cos(x) - 1)/16 - 15*a**4*b*log(cos(x) + 1)/16 - 25*a**4*b*cos(x)**3/(8*cos(x)**4 - 16*cos(x)**2 + 8) + 15*a**4*b*cos(x)/(8*cos(x)**4 - 16*cos(x)**2 + 8) - 5*a**3*b**2*cot(x)**4/2 - 5*a**2*b**3*log(cos(x) - 1)/8 + 5*a**2*b**3*log(cos(x) + 1)/8 - 10*a**2*b**3*cos(x)**3/(8*cos(x)**4 - 16*cos(x)**2 + 8) - 10*a**2*b**3*cos(x)/(8*cos(x)**4 - 16*cos(x)**2 + 8) - 5*a*b**4*csc(x)**4/4 + 3*b**5*log(cos(x) - 1)/16 - 3*b**5*log(cos(x) + 1)/16 + 3*b**5*cos(x)**3/(8*cos(x)**4 - 16*cos(x)**2 + 8) - 5*b**5*cos(x)/(8*cos(x)**4 - 16*cos(x)**2 + 8)","B",0
284,1,97,0,33.024686," ","integrate((a*cot(x)+b*csc(x))**4,x)","a^{4} x + \frac{a^{4} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{a^{4} \cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} - \frac{4 a^{3} b \csc^{3}{\left(x \right)}}{3} + 4 a^{3} b \csc{\left(x \right)} - 2 a^{2} b^{2} \cot^{3}{\left(x \right)} - \frac{4 a b^{3} \csc^{3}{\left(x \right)}}{3} - \frac{b^{4} \cot^{3}{\left(x \right)}}{3} - b^{4} \cot{\left(x \right)}"," ",0,"a**4*x + a**4*cos(x)/sin(x) - a**4*cos(x)**3/(3*sin(x)**3) - 4*a**3*b*csc(x)**3/3 + 4*a**3*b*csc(x) - 2*a**2*b**2*cot(x)**3 - 4*a*b**3*csc(x)**3/3 - b**4*cot(x)**3/3 - b**4*cot(x)","A",0
285,1,124,0,14.105686," ","integrate((a*cot(x)+b*csc(x))**3,x)","\frac{a^{3} \log{\left(- \csc^{2}{\left(x \right)} \right)}}{2} - \frac{a^{3} \csc^{2}{\left(x \right)}}{2} - \frac{3 a^{2} b \log{\left(\cos{\left(x \right)} - 1 \right)}}{4} + \frac{3 a^{2} b \log{\left(\cos{\left(x \right)} + 1 \right)}}{4} + \frac{3 a^{2} b \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 2} - \frac{3 a b^{2} \csc^{2}{\left(x \right)}}{2} + \frac{b^{3} \log{\left(\cos{\left(x \right)} - 1 \right)}}{4} - \frac{b^{3} \log{\left(\cos{\left(x \right)} + 1 \right)}}{4} + \frac{b^{3} \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 2}"," ",0,"a**3*log(-csc(x)**2)/2 - a**3*csc(x)**2/2 - 3*a**2*b*log(cos(x) - 1)/4 + 3*a**2*b*log(cos(x) + 1)/4 + 3*a**2*b*cos(x)/(2*cos(x)**2 - 2) - 3*a*b**2*csc(x)**2/2 + b**3*log(cos(x) - 1)/4 - b**3*log(cos(x) + 1)/4 + b**3*cos(x)/(2*cos(x)**2 - 2)","A",0
286,1,31,0,2.785939," ","integrate((a*cot(x)+b*csc(x))**2,x)","- a^{2} x - \frac{a^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} - 2 a b \csc{\left(x \right)} - b^{2} \cot{\left(x \right)}"," ",0,"-a**2*x - a**2*cos(x)/sin(x) - 2*a*b*csc(x) - b**2*cot(x)","A",0
287,1,24,0,0.095284," ","integrate(a*cot(x)+b*csc(x),x)","a \log{\left(\sin{\left(x \right)} \right)} + b \left(\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2}\right)"," ",0,"a*log(sin(x)) + b*(log(cos(x) - 1)/2 - log(cos(x) + 1)/2)","A",0
288,0,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x)),x)","\int \frac{1}{a \cot{\left(x \right)} + b \csc{\left(x \right)}}\, dx"," ",0,"Integral(1/(a*cot(x) + b*csc(x)), x)","F",0
289,0,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x))**2,x)","\int \frac{1}{\left(a \cot{\left(x \right)} + b \csc{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((a*cot(x) + b*csc(x))**(-2), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x))**3,x)","\int \frac{1}{\left(a \cot{\left(x \right)} + b \csc{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral((a*cot(x) + b*csc(x))**(-3), x)","F",0
291,-1,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,1,68,0,107.209888," ","integrate((cot(x)+csc(x))**5,x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} - \frac{\log{\left(\csc^{2}{\left(x \right)} \right)}}{2} - \frac{5 \cot^{4}{\left(x \right)}}{2} - \frac{3 \csc^{4}{\left(x \right)}}{2} + \csc^{2}{\left(x \right)} - \frac{32 \cos^{3}{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 8}"," ",0,"log(cos(x) - 1)/2 - log(cos(x) + 1)/2 - log(csc(x)**2)/2 - 5*cot(x)**4/2 - 3*csc(x)**4/2 + csc(x)**2 - 32*cos(x)**3/(8*cos(x)**4 - 16*cos(x)**2 + 8)","B",0
294,1,44,0,35.042358," ","integrate((cot(x)+csc(x))**4,x)","x - \frac{7 \cot^{3}{\left(x \right)}}{3} - \cot{\left(x \right)} - \frac{8 \csc^{3}{\left(x \right)}}{3} + 4 \csc{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}}"," ",0,"x - 7*cot(x)**3/3 - cot(x) - 8*csc(x)**3/3 + 4*csc(x) + cos(x)/sin(x) - cos(x)**3/(3*sin(x)**3)","A",0
295,1,46,0,14.638047," ","integrate((cot(x)+csc(x))**3,x)","- \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} + \frac{\log{\left(- \csc^{2}{\left(x \right)} \right)}}{2} - 2 \csc^{2}{\left(x \right)} + \frac{4 \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 2}"," ",0,"-log(cos(x) - 1)/2 + log(cos(x) + 1)/2 + log(-csc(x)**2)/2 - 2*csc(x)**2 + 4*cos(x)/(2*cos(x)**2 - 2)","B",0
296,1,17,0,2.702792," ","integrate((cot(x)+csc(x))**2,x)","- x - \cot{\left(x \right)} - 2 \csc{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}"," ",0,"-x - cot(x) - 2*csc(x) - cos(x)/sin(x)","A",0
297,1,20,0,0.095842," ","integrate(cot(x)+csc(x),x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} + \log{\left(\sin{\left(x \right)} \right)}"," ",0,"log(cos(x) - 1)/2 - log(cos(x) + 1)/2 + log(sin(x))","B",0
298,0,0,0,0.000000," ","integrate(1/(cot(x)+csc(x)),x)","\int \frac{1}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(1/(cot(x) + csc(x)), x)","F",0
299,0,0,0,0.000000," ","integrate(1/(cot(x)+csc(x))**2,x)","\int \frac{1}{\left(\cot{\left(x \right)} + \csc{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((cot(x) + csc(x))**(-2), x)","F",0
300,0,0,0,0.000000," ","integrate(1/(cot(x)+csc(x))**3,x)","\int \frac{1}{\left(\cot{\left(x \right)} + \csc{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral((cot(x) + csc(x))**(-3), x)","F",0
301,-1,0,0,0.000000," ","integrate(1/(cot(x)+csc(x))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate(1/(cot(x)+csc(x))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,1,44,0,8.780682," ","integrate((csc(x)-sin(x))**4,x)","\frac{35 x}{8} + 2 \sin{\left(x \right)} \cos{\left(x \right)} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} - \frac{\cot^{3}{\left(x \right)}}{3} - \cot{\left(x \right)} + \frac{4 \cos{\left(x \right)}}{\sin{\left(x \right)}}"," ",0,"35*x/8 + 2*sin(x)*cos(x) - sin(2*x)/4 + sin(4*x)/32 - cot(x)**3/3 - cot(x) + 4*cos(x)/sin(x)","A",0
304,1,42,0,3.468980," ","integrate((csc(x)-sin(x))**3,x)","- \frac{5 \log{\left(\cos{\left(x \right)} - 1 \right)}}{4} + \frac{5 \log{\left(\cos{\left(x \right)} + 1 \right)}}{4} - \frac{\cos^{3}{\left(x \right)}}{3} - 2 \cos{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 2}"," ",0,"-5*log(cos(x) - 1)/4 + 5*log(cos(x) + 1)/4 - cos(x)**3/3 - 2*cos(x) + cos(x)/(2*cos(x)**2 - 2)","A",0
305,1,15,0,1.569400," ","integrate((csc(x)-sin(x))**2,x)","- \frac{3 x}{2} - \frac{\sin{\left(2 x \right)}}{4} - \cot{\left(x \right)}"," ",0,"-3*x/2 - sin(2*x)/4 - cot(x)","A",0
306,1,19,0,0.088588," ","integrate(csc(x)-sin(x),x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} + \cos{\left(x \right)}"," ",0,"log(cos(x) - 1)/2 - log(cos(x) + 1)/2 + cos(x)","B",0
307,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x)),x)","\int \frac{1}{- \sin{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(1/(-sin(x) + csc(x)), x)","F",0
308,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**2,x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-2), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**3,x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-3), x)","F",0
310,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**4,x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{4}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-4), x)","F",0
311,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**5,x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{5}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-5), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**6,x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{6}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-6), x)","F",0
313,-1,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((csc(x)-sin(x))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((csc(x)-sin(x))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,0,0,0,0.000000," ","integrate((csc(x)-sin(x))**(3/2),x)","\int \left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(3/2), x)","F",0
317,0,0,0,0.000000," ","integrate((csc(x)-sin(x))**(1/2),x)","\int \sqrt{- \sin{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(-sin(x) + csc(x)), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**(1/2),x)","\int \frac{1}{\sqrt{- \sin{\left(x \right)} + \csc{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(-sin(x) + csc(x)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**(3/2),x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-3/2), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**(5/2),x)","\int \frac{1}{\left(- \sin{\left(x \right)} + \csc{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-sin(x) + csc(x))**(-5/2), x)","F",0
321,-1,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,1,44,0,8.967973," ","integrate((-cos(x)+sec(x))**4,x)","\frac{35 x}{8} - 2 \sin{\left(x \right)} \cos{\left(x \right)} - \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} + \frac{\tan^{3}{\left(x \right)}}{3} + \tan{\left(x \right)}"," ",0,"35*x/8 - 2*sin(x)*cos(x) - 4*sin(x)/cos(x) + sin(2*x)/4 + sin(4*x)/32 + tan(x)**3/3 + tan(x)","A",0
323,1,42,0,3.737590," ","integrate((-cos(x)+sec(x))**3,x)","\frac{5 \log{\left(\sin{\left(x \right)} - 1 \right)}}{4} - \frac{5 \log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + \frac{\sin^{3}{\left(x \right)}}{3} + 2 \sin{\left(x \right)} - \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}"," ",0,"5*log(sin(x) - 1)/4 - 5*log(sin(x) + 1)/4 + sin(x)**3/3 + 2*sin(x) - sin(x)/(2*sin(x)**2 - 2)","A",0
324,1,14,0,1.622046," ","integrate((-cos(x)+sec(x))**2,x)","- \frac{3 x}{2} + \frac{\sin{\left(2 x \right)}}{4} + \tan{\left(x \right)}"," ",0,"-3*x/2 + sin(2*x)/4 + tan(x)","A",0
325,1,19,0,0.087027," ","integrate(-cos(x)+sec(x),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \sin{\left(x \right)}"," ",0,"-log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - sin(x)","B",0
326,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x)),x)","- \int \frac{1}{\cos{\left(x \right)} - \sec{\left(x \right)}}\, dx"," ",0,"-Integral(1/(cos(x) - sec(x)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**2,x)","\int \frac{1}{\left(- \cos{\left(x \right)} + \sec{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((-cos(x) + sec(x))**(-2), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**3,x)","- \int \frac{1}{\cos^{3}{\left(x \right)} - 3 \cos^{2}{\left(x \right)} \sec{\left(x \right)} + 3 \cos{\left(x \right)} \sec^{2}{\left(x \right)} - \sec^{3}{\left(x \right)}}\, dx"," ",0,"-Integral(1/(cos(x)**3 - 3*cos(x)**2*sec(x) + 3*cos(x)*sec(x)**2 - sec(x)**3), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**4,x)","\int \frac{1}{\left(- \cos{\left(x \right)} + \sec{\left(x \right)}\right)^{4}}\, dx"," ",0,"Integral((-cos(x) + sec(x))**(-4), x)","F",0
330,-1,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate((-cos(x)+sec(x))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate((-cos(x)+sec(x))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,0,0,0,0.000000," ","integrate((-cos(x)+sec(x))**(3/2),x)","\int \left(- \cos{\left(x \right)} + \sec{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-cos(x) + sec(x))**(3/2), x)","F",0
336,0,0,0,0.000000," ","integrate((-cos(x)+sec(x))**(1/2),x)","\int \sqrt{- \cos{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(-cos(x) + sec(x)), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**(1/2),x)","\int \frac{1}{\sqrt{- \cos{\left(x \right)} + \sec{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(-cos(x) + sec(x)), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**(3/2),x)","\int \frac{1}{\left(- \cos{\left(x \right)} + \sec{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-cos(x) + sec(x))**(-3/2), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**(5/2),x)","\int \frac{1}{\left(- \cos{\left(x \right)} + \sec{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-cos(x) + sec(x))**(-5/2), x)","F",0
340,-1,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,1,90,0,4.626722," ","integrate((sin(x)+tan(x))**4,x)","- \frac{61 x}{8} + \log{\left(\sin{\left(x \right)} - 1 \right)} - \log{\left(\sin{\left(x \right)} + 1 \right)} - \frac{4 \sin^{3}{\left(x \right)}}{3} + \frac{6 \sin^{3}{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\sin^{3}{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} + 9 \sin{\left(x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32} - \frac{4 \sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}"," ",0,"-61*x/8 + log(sin(x) - 1) - log(sin(x) + 1) - 4*sin(x)**3/3 + 6*sin(x)**3/cos(x) + sin(x)**3/(3*cos(x)**3) + 9*sin(x)*cos(x) - sin(x)/cos(x) - sin(2*x)/4 + sin(4*x)/32 - 4*sin(x)/(2*sin(x)**2 - 2)","A",0
342,1,46,0,5.985073," ","integrate((sin(x)+tan(x))**3,x)","- 3 \log{\left(\cos{\left(x \right)} \right)} - \frac{\log{\left(\sec^{2}{\left(x \right)} \right)}}{2} + \frac{\cos^{3}{\left(x \right)}}{3} + \frac{3 \cos^{2}{\left(x \right)}}{2} + 2 \cos{\left(x \right)} + \frac{\sec^{2}{\left(x \right)}}{2} + \frac{3}{\cos{\left(x \right)}}"," ",0,"-3*log(cos(x)) - log(sec(x)**2)/2 + cos(x)**3/3 + 3*cos(x)**2/2 + 2*cos(x) + sec(x)**2/2 + 3/cos(x)","A",0
343,1,31,0,1.663013," ","integrate((sin(x)+tan(x))**2,x)","- \frac{x}{2} - \log{\left(\sin{\left(x \right)} - 1 \right)} + \log{\left(\sin{\left(x \right)} + 1 \right)} - 2 \sin{\left(x \right)} - \frac{\sin{\left(2 x \right)}}{4} + \tan{\left(x \right)}"," ",0,"-x/2 - log(sin(x) - 1) + log(sin(x) + 1) - 2*sin(x) - sin(2*x)/4 + tan(x)","A",0
344,1,8,0,0.051187," ","integrate(sin(x)+tan(x),x)","- \log{\left(\cos{\left(x \right)} \right)} - \cos{\left(x \right)}"," ",0,"-log(cos(x)) - cos(x)","A",0
345,0,0,0,0.000000," ","integrate(1/(sin(x)+tan(x)),x)","\int \frac{1}{\sin{\left(x \right)} + \tan{\left(x \right)}}\, dx"," ",0,"Integral(1/(sin(x) + tan(x)), x)","F",0
346,0,0,0,0.000000," ","integrate(1/(sin(x)+tan(x))**2,x)","\int \frac{1}{\left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((sin(x) + tan(x))**(-2), x)","F",0
347,0,0,0,0.000000," ","integrate(1/(sin(x)+tan(x))**3,x)","\int \frac{1}{\left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral((sin(x) + tan(x))**(-3), x)","F",0
348,0,0,0,0.000000," ","integrate(1/(sin(x)+tan(x))**4,x)","\int \frac{1}{\left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)^{4}}\, dx"," ",0,"Integral((sin(x) + tan(x))**(-4), x)","F",0
349,1,641,0,36.722957," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x)),x)","\begin{cases} \tilde{\infty} \left(A \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + C x\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{A \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + C x}{c} & \text{for}\: b = 0 \\\frac{2 A}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i C x \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{C x \cos{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{C \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = - i c \\\frac{2 A}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i C x \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{C x \cos{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{C \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = i c \\- \frac{A b^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{A b^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{A c^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{A c^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{C b \sqrt{b^{2} + c^{2}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{C b \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{C b \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{C c x \sqrt{b^{2} + c^{2}}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(A*log(tan(x/2)) + C*x), Eq(b, 0) & Eq(c, 0)), ((A*log(tan(x/2)) + C*x)/c, Eq(b, 0)), (2*A/(-2*I*c*sin(x) - 2*c*cos(x)) - I*C*x*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - C*x*cos(x)/(-2*I*c*sin(x) - 2*c*cos(x)) + C*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)), Eq(b, -I*c)), (2*A/(2*I*c*sin(x) - 2*c*cos(x)) + I*C*x*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) - C*x*cos(x)/(2*I*c*sin(x) - 2*c*cos(x)) + C*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)), Eq(b, I*c)), (-A*b**2*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + A*b**2*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - A*c**2*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + A*c**2*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + C*b*sqrt(b**2 + c**2)*log(tan(x/2)**2 + 1)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - C*b*sqrt(b**2 + c**2)*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - C*b*sqrt(b**2 + c**2)*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + C*c*x*sqrt(b**2 + c**2)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)), True))","A",0
350,-1,0,0,0.000000," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,1,678,0,37.029805," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x)),x)","\begin{cases} \tilde{\infty} \left(A \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + B \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{A \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + B \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{c} & \text{for}\: b = 0 \\\frac{2 A}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{B x \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i B x \cos{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i B \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = - i c \\\frac{2 A}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{B x \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i B x \cos{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i B \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = i c \\- \frac{A b^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{A b^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{A c^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{A c^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{B b x \sqrt{b^{2} + c^{2}}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{B c \sqrt{b^{2} + c^{2}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{B c \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{B c \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(A*log(tan(x/2)) - B*log(tan(x/2)**2 + 1) + B*log(tan(x/2))), Eq(b, 0) & Eq(c, 0)), ((A*log(tan(x/2)) - B*log(tan(x/2)**2 + 1) + B*log(tan(x/2)))/c, Eq(b, 0)), (2*A/(-2*I*c*sin(x) - 2*c*cos(x)) + B*x*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*B*x*cos(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*B*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)), Eq(b, -I*c)), (2*A/(2*I*c*sin(x) - 2*c*cos(x)) + B*x*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*B*x*cos(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*B*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)), Eq(b, I*c)), (-A*b**2*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + A*b**2*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - A*c**2*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + A*c**2*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + B*b*x*sqrt(b**2 + c**2)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - B*c*sqrt(b**2 + c**2)*log(tan(x/2)**2 + 1)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + B*c*sqrt(b**2 + c**2)*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + B*c*sqrt(b**2 + c**2)*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)), True))","A",0
353,-1,0,0,0.000000," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,1,857,0,3.038092," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**4,x)","\begin{cases} \frac{3 b^{4} x \sin^{4}{\left(d + e x \right)}}{8} + \frac{3 b^{4} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{4} + 3 b^{4} x \sin^{2}{\left(d + e x \right)} + \frac{3 b^{4} x \cos^{4}{\left(d + e x \right)}}{8} + 3 b^{4} x \cos^{2}{\left(d + e x \right)} + b^{4} x + \frac{3 b^{4} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{8 e} + \frac{5 b^{4} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{8 e} + \frac{3 b^{4} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{b^{3} c \cos^{4}{\left(d + e x \right)}}{e} - \frac{6 b^{3} c \cos^{2}{\left(d + e x \right)}}{e} + \frac{8 b^{3} \sqrt{b^{2} + c^{2}} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{4 b^{3} \sqrt{b^{2} + c^{2}} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} + \frac{4 b^{3} \sqrt{b^{2} + c^{2}} \sin{\left(d + e x \right)}}{e} + \frac{3 b^{2} c^{2} x \sin^{4}{\left(d + e x \right)}}{4} + \frac{3 b^{2} c^{2} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{2} + 6 b^{2} c^{2} x \sin^{2}{\left(d + e x \right)} + \frac{3 b^{2} c^{2} x \cos^{4}{\left(d + e x \right)}}{4} + 6 b^{2} c^{2} x \cos^{2}{\left(d + e x \right)} + 2 b^{2} c^{2} x + \frac{3 b^{2} c^{2} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{4 e} - \frac{3 b^{2} c^{2} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{4 e} - \frac{4 b^{2} c \sqrt{b^{2} + c^{2}} \cos^{3}{\left(d + e x \right)}}{e} - \frac{4 b^{2} c \sqrt{b^{2} + c^{2}} \cos{\left(d + e x \right)}}{e} + \frac{b c^{3} \sin^{4}{\left(d + e x \right)}}{e} - \frac{6 b c^{3} \cos^{2}{\left(d + e x \right)}}{e} + \frac{4 b c^{2} \sqrt{b^{2} + c^{2}} \sin^{3}{\left(d + e x \right)}}{e} + \frac{4 b c^{2} \sqrt{b^{2} + c^{2}} \sin{\left(d + e x \right)}}{e} + \frac{3 c^{4} x \sin^{4}{\left(d + e x \right)}}{8} + \frac{3 c^{4} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{4} + 3 c^{4} x \sin^{2}{\left(d + e x \right)} + \frac{3 c^{4} x \cos^{4}{\left(d + e x \right)}}{8} + 3 c^{4} x \cos^{2}{\left(d + e x \right)} + c^{4} x - \frac{5 c^{4} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{8 e} - \frac{3 c^{4} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{8 e} - \frac{3 c^{4} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{4 c^{3} \sqrt{b^{2} + c^{2}} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 c^{3} \sqrt{b^{2} + c^{2}} \cos^{3}{\left(d + e x \right)}}{3 e} - \frac{4 c^{3} \sqrt{b^{2} + c^{2}} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(b \cos{\left(d \right)} + c \sin{\left(d \right)} + \sqrt{b^{2} + c^{2}}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*b**4*x*sin(d + e*x)**4/8 + 3*b**4*x*sin(d + e*x)**2*cos(d + e*x)**2/4 + 3*b**4*x*sin(d + e*x)**2 + 3*b**4*x*cos(d + e*x)**4/8 + 3*b**4*x*cos(d + e*x)**2 + b**4*x + 3*b**4*sin(d + e*x)**3*cos(d + e*x)/(8*e) + 5*b**4*sin(d + e*x)*cos(d + e*x)**3/(8*e) + 3*b**4*sin(d + e*x)*cos(d + e*x)/e - b**3*c*cos(d + e*x)**4/e - 6*b**3*c*cos(d + e*x)**2/e + 8*b**3*sqrt(b**2 + c**2)*sin(d + e*x)**3/(3*e) + 4*b**3*sqrt(b**2 + c**2)*sin(d + e*x)*cos(d + e*x)**2/e + 4*b**3*sqrt(b**2 + c**2)*sin(d + e*x)/e + 3*b**2*c**2*x*sin(d + e*x)**4/4 + 3*b**2*c**2*x*sin(d + e*x)**2*cos(d + e*x)**2/2 + 6*b**2*c**2*x*sin(d + e*x)**2 + 3*b**2*c**2*x*cos(d + e*x)**4/4 + 6*b**2*c**2*x*cos(d + e*x)**2 + 2*b**2*c**2*x + 3*b**2*c**2*sin(d + e*x)**3*cos(d + e*x)/(4*e) - 3*b**2*c**2*sin(d + e*x)*cos(d + e*x)**3/(4*e) - 4*b**2*c*sqrt(b**2 + c**2)*cos(d + e*x)**3/e - 4*b**2*c*sqrt(b**2 + c**2)*cos(d + e*x)/e + b*c**3*sin(d + e*x)**4/e - 6*b*c**3*cos(d + e*x)**2/e + 4*b*c**2*sqrt(b**2 + c**2)*sin(d + e*x)**3/e + 4*b*c**2*sqrt(b**2 + c**2)*sin(d + e*x)/e + 3*c**4*x*sin(d + e*x)**4/8 + 3*c**4*x*sin(d + e*x)**2*cos(d + e*x)**2/4 + 3*c**4*x*sin(d + e*x)**2 + 3*c**4*x*cos(d + e*x)**4/8 + 3*c**4*x*cos(d + e*x)**2 + c**4*x - 5*c**4*sin(d + e*x)**3*cos(d + e*x)/(8*e) - 3*c**4*sin(d + e*x)*cos(d + e*x)**3/(8*e) - 3*c**4*sin(d + e*x)*cos(d + e*x)/e - 4*c**3*sqrt(b**2 + c**2)*sin(d + e*x)**2*cos(d + e*x)/e - 8*c**3*sqrt(b**2 + c**2)*cos(d + e*x)**3/(3*e) - 4*c**3*sqrt(b**2 + c**2)*cos(d + e*x)/e, Ne(e, 0)), (x*(b*cos(d) + c*sin(d) + sqrt(b**2 + c**2))**4, True))","A",0
356,1,415,0,1.374581," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**3,x)","\begin{cases} \frac{2 b^{3} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{b^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} + \frac{3 b^{3} \sin{\left(d + e x \right)}}{e} - \frac{b^{2} c \cos^{3}{\left(d + e x \right)}}{e} - \frac{3 b^{2} c \cos{\left(d + e x \right)}}{e} + \frac{3 b^{2} x \sqrt{b^{2} + c^{2}} \sin^{2}{\left(d + e x \right)}}{2} + \frac{3 b^{2} x \sqrt{b^{2} + c^{2}} \cos^{2}{\left(d + e x \right)}}{2} + b^{2} x \sqrt{b^{2} + c^{2}} + \frac{3 b^{2} \sqrt{b^{2} + c^{2}} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} + \frac{b c^{2} \sin^{3}{\left(d + e x \right)}}{e} + \frac{3 b c^{2} \sin{\left(d + e x \right)}}{e} - \frac{3 b c \sqrt{b^{2} + c^{2}} \cos^{2}{\left(d + e x \right)}}{e} - \frac{c^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{2 c^{3} \cos^{3}{\left(d + e x \right)}}{3 e} - \frac{3 c^{3} \cos{\left(d + e x \right)}}{e} + \frac{3 c^{2} x \sqrt{b^{2} + c^{2}} \sin^{2}{\left(d + e x \right)}}{2} + \frac{3 c^{2} x \sqrt{b^{2} + c^{2}} \cos^{2}{\left(d + e x \right)}}{2} + c^{2} x \sqrt{b^{2} + c^{2}} - \frac{3 c^{2} \sqrt{b^{2} + c^{2}} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: e \neq 0 \\x \left(b \cos{\left(d \right)} + c \sin{\left(d \right)} + \sqrt{b^{2} + c^{2}}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**3*sin(d + e*x)**3/(3*e) + b**3*sin(d + e*x)*cos(d + e*x)**2/e + 3*b**3*sin(d + e*x)/e - b**2*c*cos(d + e*x)**3/e - 3*b**2*c*cos(d + e*x)/e + 3*b**2*x*sqrt(b**2 + c**2)*sin(d + e*x)**2/2 + 3*b**2*x*sqrt(b**2 + c**2)*cos(d + e*x)**2/2 + b**2*x*sqrt(b**2 + c**2) + 3*b**2*sqrt(b**2 + c**2)*sin(d + e*x)*cos(d + e*x)/(2*e) + b*c**2*sin(d + e*x)**3/e + 3*b*c**2*sin(d + e*x)/e - 3*b*c*sqrt(b**2 + c**2)*cos(d + e*x)**2/e - c**3*sin(d + e*x)**2*cos(d + e*x)/e - 2*c**3*cos(d + e*x)**3/(3*e) - 3*c**3*cos(d + e*x)/e + 3*c**2*x*sqrt(b**2 + c**2)*sin(d + e*x)**2/2 + 3*c**2*x*sqrt(b**2 + c**2)*cos(d + e*x)**2/2 + c**2*x*sqrt(b**2 + c**2) - 3*c**2*sqrt(b**2 + c**2)*sin(d + e*x)*cos(d + e*x)/(2*e), Ne(e, 0)), (x*(b*cos(d) + c*sin(d) + sqrt(b**2 + c**2))**3, True))","A",0
357,1,192,0,0.454361," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**2,x)","\begin{cases} \frac{b^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(d + e x \right)}}{2} + b^{2} x + \frac{b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{b c \cos^{2}{\left(d + e x \right)}}{e} + \frac{2 b \sqrt{b^{2} + c^{2}} \sin{\left(d + e x \right)}}{e} + \frac{c^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{c^{2} x \cos^{2}{\left(d + e x \right)}}{2} + c^{2} x - \frac{c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{2 c \sqrt{b^{2} + c^{2}} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(b \cos{\left(d \right)} + c \sin{\left(d \right)} + \sqrt{b^{2} + c^{2}}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**2*x*sin(d + e*x)**2/2 + b**2*x*cos(d + e*x)**2/2 + b**2*x + b**2*sin(d + e*x)*cos(d + e*x)/(2*e) - b*c*cos(d + e*x)**2/e + 2*b*sqrt(b**2 + c**2)*sin(d + e*x)/e + c**2*x*sin(d + e*x)**2/2 + c**2*x*cos(d + e*x)**2/2 + c**2*x - c**2*sin(d + e*x)*cos(d + e*x)/(2*e) - 2*c*sqrt(b**2 + c**2)*cos(d + e*x)/e, Ne(e, 0)), (x*(b*cos(d) + c*sin(d) + sqrt(b**2 + c**2))**2, True))","A",0
358,1,42,0,0.141749," ","integrate(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2),x)","b \left(\begin{cases} \frac{\sin{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \cos{\left(d \right)} & \text{otherwise} \end{cases}\right) + c \left(\begin{cases} - \frac{\cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \sin{\left(d \right)} & \text{otherwise} \end{cases}\right) + x \sqrt{b^{2} + c^{2}}"," ",0,"b*Piecewise((sin(d + e*x)/e, Ne(e, 0)), (x*cos(d), True)) + c*Piecewise((-cos(d + e*x)/e, Ne(e, 0)), (x*sin(d), True)) + x*sqrt(b**2 + c**2)","A",0
359,-1,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,1,291,0,0.755632," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))**3,x)","\begin{cases} 12 a^{3} x \sin^{2}{\left(d + e x \right)} + 12 a^{3} x \cos^{2}{\left(d + e x \right)} + 8 a^{3} x + \frac{16 a^{3} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{8 a^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} + \frac{12 a^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} + \frac{24 a^{3} \sin{\left(d + e x \right)}}{e} - \frac{8 a^{2} c \cos^{3}{\left(d + e x \right)}}{e} - \frac{24 a^{2} c \cos^{2}{\left(d + e x \right)}}{e} - \frac{24 a^{2} c \cos{\left(d + e x \right)}}{e} + 12 a c^{2} x \sin^{2}{\left(d + e x \right)} + 12 a c^{2} x \cos^{2}{\left(d + e x \right)} + \frac{8 a c^{2} \sin^{3}{\left(d + e x \right)}}{e} - \frac{12 a c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 c^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{16 c^{3} \cos^{3}{\left(d + e x \right)}}{3 e} & \text{for}\: e \neq 0 \\x \left(2 a \cos{\left(d \right)} + 2 a + 2 c \sin{\left(d \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*a**3*x*sin(d + e*x)**2 + 12*a**3*x*cos(d + e*x)**2 + 8*a**3*x + 16*a**3*sin(d + e*x)**3/(3*e) + 8*a**3*sin(d + e*x)*cos(d + e*x)**2/e + 12*a**3*sin(d + e*x)*cos(d + e*x)/e + 24*a**3*sin(d + e*x)/e - 8*a**2*c*cos(d + e*x)**3/e - 24*a**2*c*cos(d + e*x)**2/e - 24*a**2*c*cos(d + e*x)/e + 12*a*c**2*x*sin(d + e*x)**2 + 12*a*c**2*x*cos(d + e*x)**2 + 8*a*c**2*sin(d + e*x)**3/e - 12*a*c**2*sin(d + e*x)*cos(d + e*x)/e - 8*c**3*sin(d + e*x)**2*cos(d + e*x)/e - 16*c**3*cos(d + e*x)**3/(3*e), Ne(e, 0)), (x*(2*a*cos(d) + 2*a + 2*c*sin(d))**3, True))","A",0
364,1,170,0,0.313593," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))**2,x)","\begin{cases} 2 a^{2} x \sin^{2}{\left(d + e x \right)} + 2 a^{2} x \cos^{2}{\left(d + e x \right)} + 4 a^{2} x + \frac{2 a^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} + \frac{8 a^{2} \sin{\left(d + e x \right)}}{e} - \frac{4 a c \cos^{2}{\left(d + e x \right)}}{e} - \frac{8 a c \cos{\left(d + e x \right)}}{e} + 2 c^{2} x \sin^{2}{\left(d + e x \right)} + 2 c^{2} x \cos^{2}{\left(d + e x \right)} - \frac{2 c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(2 a \cos{\left(d \right)} + 2 a + 2 c \sin{\left(d \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*x*sin(d + e*x)**2 + 2*a**2*x*cos(d + e*x)**2 + 4*a**2*x + 2*a**2*sin(d + e*x)*cos(d + e*x)/e + 8*a**2*sin(d + e*x)/e - 4*a*c*cos(d + e*x)**2/e - 8*a*c*cos(d + e*x)/e + 2*c**2*x*sin(d + e*x)**2 + 2*c**2*x*cos(d + e*x)**2 - 2*c**2*sin(d + e*x)*cos(d + e*x)/e, Ne(e, 0)), (x*(2*a*cos(d) + 2*a + 2*c*sin(d))**2, True))","A",0
365,1,39,0,0.140187," ","integrate(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d),x)","2 a x + 2 a \left(\begin{cases} \frac{\sin{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \cos{\left(d \right)} & \text{otherwise} \end{cases}\right) + 2 c \left(\begin{cases} - \frac{\cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \sin{\left(d \right)} & \text{otherwise} \end{cases}\right)"," ",0,"2*a*x + 2*a*Piecewise((sin(d + e*x)/e, Ne(e, 0)), (x*cos(d), True)) + 2*c*Piecewise((-cos(d + e*x)/e, Ne(e, 0)), (x*sin(d), True))","A",0
366,1,63,0,1.098722," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d)),x)","\begin{cases} \frac{x}{2 a \cos{\left(d \right)} + 2 a} & \text{for}\: c = 0 \wedge e = 0 \\\frac{\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{2 a e} & \text{for}\: c = 0 \\\frac{x}{2 a \cos{\left(d \right)} + 2 a + 2 c \sin{\left(d \right)}} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{a}{c} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{2 c e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(2*a*cos(d) + 2*a), Eq(c, 0) & Eq(e, 0)), (tan(d/2 + e*x/2)/(2*a*e), Eq(c, 0)), (x/(2*a*cos(d) + 2*a + 2*c*sin(d)), Eq(e, 0)), (log(a/c + tan(d/2 + e*x/2))/(2*c*e), True))","A",0
367,-1,0,0,0.000000," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,1,36,0,0.609272," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d)),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{2 a e} & \text{for}\: e \neq 0 \\\frac{x}{2 a \sin{\left(d \right)} + 2 a \cos{\left(d \right)} + 2 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(d/2 + e*x/2) + 1)/(2*a*e), Ne(e, 0)), (x/(2*a*sin(d) + 2*a*cos(d) + 2*a), True))","A",0
371,1,168,0,1.828737," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))**2,x)","\begin{cases} - \frac{2 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{8 a^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 8 a^{2} e} - \frac{2 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{8 a^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 8 a^{2} e} + \frac{\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{8 a^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 8 a^{2} e} - \frac{3}{8 a^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 8 a^{2} e} & \text{for}\: e \neq 0 \\\frac{x}{\left(2 a \sin{\left(d \right)} + 2 a \cos{\left(d \right)} + 2 a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)/(8*a**2*e*tan(d/2 + e*x/2) + 8*a**2*e) - 2*log(tan(d/2 + e*x/2) + 1)/(8*a**2*e*tan(d/2 + e*x/2) + 8*a**2*e) + tan(d/2 + e*x/2)**2/(8*a**2*e*tan(d/2 + e*x/2) + 8*a**2*e) - 3/(8*a**2*e*tan(d/2 + e*x/2) + 8*a**2*e), Ne(e, 0)), (x/(2*a*sin(d) + 2*a*cos(d) + 2*a)**2, True))","A",0
372,1,423,0,6.486440," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))**3,x)","\begin{cases} \frac{16 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} + \frac{32 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} + \frac{16 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} + \frac{\tan^{4}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} - \frac{4 \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} + \frac{32 \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} + \frac{23}{64 a^{3} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 128 a^{3} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 64 a^{3} e} & \text{for}\: e \neq 0 \\\frac{x}{\left(2 a \sin{\left(d \right)} + 2 a \cos{\left(d \right)} + 2 a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)**2/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e) + 32*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e) + 16*log(tan(d/2 + e*x/2) + 1)/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e) + tan(d/2 + e*x/2)**4/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e) - 4*tan(d/2 + e*x/2)**3/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e) + 32*tan(d/2 + e*x/2)/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e) + 23/(64*a**3*e*tan(d/2 + e*x/2)**2 + 128*a**3*e*tan(d/2 + e*x/2) + 64*a**3*e), Ne(e, 0)), (x/(2*a*sin(d) + 2*a*cos(d) + 2*a)**3, True))","A",0
373,1,792,0,23.776995," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))**4,x)","\begin{cases} - \frac{96 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{288 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{288 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{96 \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} + \frac{\tan^{6}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{3 \tan^{5}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} + \frac{24 \tan^{4}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{297 \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{441 \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} - \frac{180}{384 a^{4} e \tan^{3}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1152 a^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 384 a^{4} e} & \text{for}\: e \neq 0 \\\frac{x}{\left(2 a \sin{\left(d \right)} + 2 a \cos{\left(d \right)} + 2 a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-96*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)**3/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 288*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)**2/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 288*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 96*log(tan(d/2 + e*x/2) + 1)/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) + tan(d/2 + e*x/2)**6/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 3*tan(d/2 + e*x/2)**5/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) + 24*tan(d/2 + e*x/2)**4/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 297*tan(d/2 + e*x/2)**2/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 441*tan(d/2 + e*x/2)/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e) - 180/(384*a**4*e*tan(d/2 + e*x/2)**3 + 1152*a**4*e*tan(d/2 + e*x/2)**2 + 1152*a**4*e*tan(d/2 + e*x/2) + 384*a**4*e), Ne(e, 0)), (x/(2*a*sin(d) + 2*a*cos(d) + 2*a)**4, True))","A",0
374,1,291,0,0.764435," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))**3,x)","\begin{cases} 12 a^{3} x \sin^{2}{\left(d + e x \right)} + 12 a^{3} x \cos^{2}{\left(d + e x \right)} + 8 a^{3} x - \frac{16 a^{3} \sin^{3}{\left(d + e x \right)}}{3 e} - \frac{8 a^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} + \frac{12 a^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{24 a^{3} \sin{\left(d + e x \right)}}{e} - \frac{8 a^{2} c \cos^{3}{\left(d + e x \right)}}{e} + \frac{24 a^{2} c \cos^{2}{\left(d + e x \right)}}{e} - \frac{24 a^{2} c \cos{\left(d + e x \right)}}{e} + 12 a c^{2} x \sin^{2}{\left(d + e x \right)} + 12 a c^{2} x \cos^{2}{\left(d + e x \right)} - \frac{8 a c^{2} \sin^{3}{\left(d + e x \right)}}{e} - \frac{12 a c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 c^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{16 c^{3} \cos^{3}{\left(d + e x \right)}}{3 e} & \text{for}\: e \neq 0 \\x \left(- 2 a \cos{\left(d \right)} + 2 a + 2 c \sin{\left(d \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*a**3*x*sin(d + e*x)**2 + 12*a**3*x*cos(d + e*x)**2 + 8*a**3*x - 16*a**3*sin(d + e*x)**3/(3*e) - 8*a**3*sin(d + e*x)*cos(d + e*x)**2/e + 12*a**3*sin(d + e*x)*cos(d + e*x)/e - 24*a**3*sin(d + e*x)/e - 8*a**2*c*cos(d + e*x)**3/e + 24*a**2*c*cos(d + e*x)**2/e - 24*a**2*c*cos(d + e*x)/e + 12*a*c**2*x*sin(d + e*x)**2 + 12*a*c**2*x*cos(d + e*x)**2 - 8*a*c**2*sin(d + e*x)**3/e - 12*a*c**2*sin(d + e*x)*cos(d + e*x)/e - 8*c**3*sin(d + e*x)**2*cos(d + e*x)/e - 16*c**3*cos(d + e*x)**3/(3*e), Ne(e, 0)), (x*(-2*a*cos(d) + 2*a + 2*c*sin(d))**3, True))","A",0
375,1,170,0,0.319686," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))**2,x)","\begin{cases} 2 a^{2} x \sin^{2}{\left(d + e x \right)} + 2 a^{2} x \cos^{2}{\left(d + e x \right)} + 4 a^{2} x + \frac{2 a^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 a^{2} \sin{\left(d + e x \right)}}{e} + \frac{4 a c \cos^{2}{\left(d + e x \right)}}{e} - \frac{8 a c \cos{\left(d + e x \right)}}{e} + 2 c^{2} x \sin^{2}{\left(d + e x \right)} + 2 c^{2} x \cos^{2}{\left(d + e x \right)} - \frac{2 c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(- 2 a \cos{\left(d \right)} + 2 a + 2 c \sin{\left(d \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*x*sin(d + e*x)**2 + 2*a**2*x*cos(d + e*x)**2 + 4*a**2*x + 2*a**2*sin(d + e*x)*cos(d + e*x)/e - 8*a**2*sin(d + e*x)/e + 4*a*c*cos(d + e*x)**2/e - 8*a*c*cos(d + e*x)/e + 2*c**2*x*sin(d + e*x)**2 + 2*c**2*x*cos(d + e*x)**2 - 2*c**2*sin(d + e*x)*cos(d + e*x)/e, Ne(e, 0)), (x*(-2*a*cos(d) + 2*a + 2*c*sin(d))**2, True))","A",0
376,1,39,0,0.145554," ","integrate(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d),x)","2 a x - 2 a \left(\begin{cases} \frac{\sin{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \cos{\left(d \right)} & \text{otherwise} \end{cases}\right) + 2 c \left(\begin{cases} - \frac{\cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \sin{\left(d \right)} & \text{otherwise} \end{cases}\right)"," ",0,"2*a*x - 2*a*Piecewise((sin(d + e*x)/e, Ne(e, 0)), (x*cos(d), True)) + 2*c*Piecewise((-cos(d + e*x)/e, Ne(e, 0)), (x*sin(d), True))","A",0
377,1,95,0,1.300184," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d)),x)","\begin{cases} \frac{\tilde{\infty} x}{\sin{\left(d \right)}} & \text{for}\: a = 0 \wedge c = 0 \wedge e = 0 \\- \frac{1}{2 a e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}} & \text{for}\: c = 0 \\\frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{2 c e} & \text{for}\: a = 0 \\\frac{x}{- 2 a \cos{\left(d \right)} + 2 a + 2 c \sin{\left(d \right)}} & \text{for}\: e = 0 \\- \frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} \right)}}{2 c e} + \frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{2 c e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/sin(d), Eq(a, 0) & Eq(c, 0) & Eq(e, 0)), (-1/(2*a*e*tan(d/2 + e*x/2)), Eq(c, 0)), (log(tan(d/2 + e*x/2))/(2*c*e), Eq(a, 0)), (x/(-2*a*cos(d) + 2*a + 2*c*sin(d)), Eq(e, 0)), (-log(tan(d/2 + e*x/2) + c/a)/(2*c*e) + log(tan(d/2 + e*x/2))/(2*c*e), True))","A",0
378,-1,0,0,0.000000," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,1,291,0,0.753612," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))**3,x)","\begin{cases} 12 a^{3} x \sin^{2}{\left(d + e x \right)} + 12 a^{3} x \cos^{2}{\left(d + e x \right)} + 8 a^{3} x - \frac{8 a^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{12 a^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{16 a^{3} \cos^{3}{\left(d + e x \right)}}{3 e} - \frac{24 a^{3} \cos{\left(d + e x \right)}}{e} + \frac{8 a^{2} b \sin^{3}{\left(d + e x \right)}}{e} + \frac{24 a^{2} b \sin{\left(d + e x \right)}}{e} - \frac{24 a^{2} b \cos^{2}{\left(d + e x \right)}}{e} + 12 a b^{2} x \sin^{2}{\left(d + e x \right)} + 12 a b^{2} x \cos^{2}{\left(d + e x \right)} + \frac{12 a b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 a b^{2} \cos^{3}{\left(d + e x \right)}}{e} + \frac{16 b^{3} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{8 b^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(2 a \sin{\left(d \right)} + 2 a + 2 b \cos{\left(d \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*a**3*x*sin(d + e*x)**2 + 12*a**3*x*cos(d + e*x)**2 + 8*a**3*x - 8*a**3*sin(d + e*x)**2*cos(d + e*x)/e - 12*a**3*sin(d + e*x)*cos(d + e*x)/e - 16*a**3*cos(d + e*x)**3/(3*e) - 24*a**3*cos(d + e*x)/e + 8*a**2*b*sin(d + e*x)**3/e + 24*a**2*b*sin(d + e*x)/e - 24*a**2*b*cos(d + e*x)**2/e + 12*a*b**2*x*sin(d + e*x)**2 + 12*a*b**2*x*cos(d + e*x)**2 + 12*a*b**2*sin(d + e*x)*cos(d + e*x)/e - 8*a*b**2*cos(d + e*x)**3/e + 16*b**3*sin(d + e*x)**3/(3*e) + 8*b**3*sin(d + e*x)*cos(d + e*x)**2/e, Ne(e, 0)), (x*(2*a*sin(d) + 2*a + 2*b*cos(d))**3, True))","A",0
382,1,170,0,0.314099," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))**2,x)","\begin{cases} 2 a^{2} x \sin^{2}{\left(d + e x \right)} + 2 a^{2} x \cos^{2}{\left(d + e x \right)} + 4 a^{2} x - \frac{2 a^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 a^{2} \cos{\left(d + e x \right)}}{e} + \frac{8 a b \sin{\left(d + e x \right)}}{e} - \frac{4 a b \cos^{2}{\left(d + e x \right)}}{e} + 2 b^{2} x \sin^{2}{\left(d + e x \right)} + 2 b^{2} x \cos^{2}{\left(d + e x \right)} + \frac{2 b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(2 a \sin{\left(d \right)} + 2 a + 2 b \cos{\left(d \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*x*sin(d + e*x)**2 + 2*a**2*x*cos(d + e*x)**2 + 4*a**2*x - 2*a**2*sin(d + e*x)*cos(d + e*x)/e - 8*a**2*cos(d + e*x)/e + 8*a*b*sin(d + e*x)/e - 4*a*b*cos(d + e*x)**2/e + 2*b**2*x*sin(d + e*x)**2 + 2*b**2*x*cos(d + e*x)**2 + 2*b**2*sin(d + e*x)*cos(d + e*x)/e, Ne(e, 0)), (x*(2*a*sin(d) + 2*a + 2*b*cos(d))**2, True))","A",0
383,1,39,0,0.138355," ","integrate(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d),x)","2 a x + 2 a \left(\begin{cases} - \frac{\cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \sin{\left(d \right)} & \text{otherwise} \end{cases}\right) + 2 b \left(\begin{cases} \frac{\sin{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \cos{\left(d \right)} & \text{otherwise} \end{cases}\right)"," ",0,"2*a*x + 2*a*Piecewise((-cos(d + e*x)/e, Ne(e, 0)), (x*sin(d), True)) + 2*b*Piecewise((sin(d + e*x)/e, Ne(e, 0)), (x*cos(d), True))","A",0
384,1,107,0,1.691037," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d)),x)","\begin{cases} \frac{\tilde{\infty} x}{\cos{\left(d \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \\- \frac{1}{a e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + a e} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{2 b e} & \text{for}\: a = b \\\frac{x}{2 a \sin{\left(d \right)} + 2 a + 2 b \cos{\left(d \right)}} & \text{for}\: e = 0 \\\frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{2 b e} - \frac{\log{\left(\frac{a}{a - b} + \frac{b}{a - b} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{2 b e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/cos(d), Eq(a, 0) & Eq(b, 0) & Eq(e, 0)), (-1/(a*e*tan(d/2 + e*x/2) + a*e), Eq(b, 0)), (log(tan(d/2 + e*x/2) + 1)/(2*b*e), Eq(a, b)), (x/(2*a*sin(d) + 2*a + 2*b*cos(d)), Eq(e, 0)), (log(tan(d/2 + e*x/2) + 1)/(2*b*e) - log(a/(a - b) + b/(a - b) + tan(d/2 + e*x/2))/(2*b*e), True))","A",0
385,-1,0,0,0.000000," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,1,291,0,0.757893," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))**3,x)","\begin{cases} 12 a^{3} x \sin^{2}{\left(d + e x \right)} + 12 a^{3} x \cos^{2}{\left(d + e x \right)} + 8 a^{3} x + \frac{8 a^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{12 a^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} + \frac{16 a^{3} \cos^{3}{\left(d + e x \right)}}{3 e} + \frac{24 a^{3} \cos{\left(d + e x \right)}}{e} + \frac{8 a^{2} b \sin^{3}{\left(d + e x \right)}}{e} + \frac{24 a^{2} b \sin{\left(d + e x \right)}}{e} + \frac{24 a^{2} b \cos^{2}{\left(d + e x \right)}}{e} + 12 a b^{2} x \sin^{2}{\left(d + e x \right)} + 12 a b^{2} x \cos^{2}{\left(d + e x \right)} + \frac{12 a b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} + \frac{8 a b^{2} \cos^{3}{\left(d + e x \right)}}{e} + \frac{16 b^{3} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{8 b^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(- 2 a \sin{\left(d \right)} + 2 a + 2 b \cos{\left(d \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*a**3*x*sin(d + e*x)**2 + 12*a**3*x*cos(d + e*x)**2 + 8*a**3*x + 8*a**3*sin(d + e*x)**2*cos(d + e*x)/e - 12*a**3*sin(d + e*x)*cos(d + e*x)/e + 16*a**3*cos(d + e*x)**3/(3*e) + 24*a**3*cos(d + e*x)/e + 8*a**2*b*sin(d + e*x)**3/e + 24*a**2*b*sin(d + e*x)/e + 24*a**2*b*cos(d + e*x)**2/e + 12*a*b**2*x*sin(d + e*x)**2 + 12*a*b**2*x*cos(d + e*x)**2 + 12*a*b**2*sin(d + e*x)*cos(d + e*x)/e + 8*a*b**2*cos(d + e*x)**3/e + 16*b**3*sin(d + e*x)**3/(3*e) + 8*b**3*sin(d + e*x)*cos(d + e*x)**2/e, Ne(e, 0)), (x*(-2*a*sin(d) + 2*a + 2*b*cos(d))**3, True))","A",0
389,1,170,0,0.315799," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))**2,x)","\begin{cases} 2 a^{2} x \sin^{2}{\left(d + e x \right)} + 2 a^{2} x \cos^{2}{\left(d + e x \right)} + 4 a^{2} x - \frac{2 a^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} + \frac{8 a^{2} \cos{\left(d + e x \right)}}{e} + \frac{8 a b \sin{\left(d + e x \right)}}{e} + \frac{4 a b \cos^{2}{\left(d + e x \right)}}{e} + 2 b^{2} x \sin^{2}{\left(d + e x \right)} + 2 b^{2} x \cos^{2}{\left(d + e x \right)} + \frac{2 b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(- 2 a \sin{\left(d \right)} + 2 a + 2 b \cos{\left(d \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*x*sin(d + e*x)**2 + 2*a**2*x*cos(d + e*x)**2 + 4*a**2*x - 2*a**2*sin(d + e*x)*cos(d + e*x)/e + 8*a**2*cos(d + e*x)/e + 8*a*b*sin(d + e*x)/e + 4*a*b*cos(d + e*x)**2/e + 2*b**2*x*sin(d + e*x)**2 + 2*b**2*x*cos(d + e*x)**2 + 2*b**2*sin(d + e*x)*cos(d + e*x)/e, Ne(e, 0)), (x*(-2*a*sin(d) + 2*a + 2*b*cos(d))**2, True))","A",0
390,1,39,0,0.142063," ","integrate(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d),x)","2 a x - 2 a \left(\begin{cases} - \frac{\cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \sin{\left(d \right)} & \text{otherwise} \end{cases}\right) + 2 b \left(\begin{cases} \frac{\sin{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \cos{\left(d \right)} & \text{otherwise} \end{cases}\right)"," ",0,"2*a*x - 2*a*Piecewise((-cos(d + e*x)/e, Ne(e, 0)), (x*sin(d), True)) + 2*b*Piecewise((sin(d + e*x)/e, Ne(e, 0)), (x*cos(d), True))","A",0
391,1,109,0,1.720116," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d)),x)","\begin{cases} \frac{\tilde{\infty} x}{\cos{\left(d \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \\- \frac{1}{a e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - a e} & \text{for}\: b = 0 \\- \frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 1 \right)}}{2 b e} & \text{for}\: a = b \\\frac{x}{- 2 a \sin{\left(d \right)} + 2 a + 2 b \cos{\left(d \right)}} & \text{for}\: e = 0 \\- \frac{\log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 1 \right)}}{2 b e} + \frac{\log{\left(- \frac{a}{a - b} - \frac{b}{a - b} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{2 b e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/cos(d), Eq(a, 0) & Eq(b, 0) & Eq(e, 0)), (-1/(a*e*tan(d/2 + e*x/2) - a*e), Eq(b, 0)), (-log(tan(d/2 + e*x/2) - 1)/(2*b*e), Eq(a, b)), (x/(-2*a*sin(d) + 2*a + 2*b*cos(d)), Eq(e, 0)), (-log(tan(d/2 + e*x/2) - 1)/(2*b*e) + log(-a/(a - b) - b/(a - b) + tan(d/2 + e*x/2))/(2*b*e), True))","A",0
392,-1,0,0,0.000000," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,1,682,0,1.855526," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b \sin{\left(d + e x \right)}}{e} - \frac{4 a^{3} c \cos{\left(d + e x \right)}}{e} + 3 a^{2} b^{2} x \sin^{2}{\left(d + e x \right)} + 3 a^{2} b^{2} x \cos^{2}{\left(d + e x \right)} + \frac{3 a^{2} b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{6 a^{2} b c \cos^{2}{\left(d + e x \right)}}{e} + 3 a^{2} c^{2} x \sin^{2}{\left(d + e x \right)} + 3 a^{2} c^{2} x \cos^{2}{\left(d + e x \right)} - \frac{3 a^{2} c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} + \frac{8 a b^{3} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{4 a b^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} - \frac{4 a b^{2} c \cos^{3}{\left(d + e x \right)}}{e} + \frac{4 a b c^{2} \sin^{3}{\left(d + e x \right)}}{e} - \frac{4 a c^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 a c^{3} \cos^{3}{\left(d + e x \right)}}{3 e} + \frac{3 b^{4} x \sin^{4}{\left(d + e x \right)}}{8} + \frac{3 b^{4} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{4} + \frac{3 b^{4} x \cos^{4}{\left(d + e x \right)}}{8} + \frac{3 b^{4} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{8 e} + \frac{5 b^{4} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{8 e} - \frac{b^{3} c \cos^{4}{\left(d + e x \right)}}{e} + \frac{3 b^{2} c^{2} x \sin^{4}{\left(d + e x \right)}}{4} + \frac{3 b^{2} c^{2} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{2} + \frac{3 b^{2} c^{2} x \cos^{4}{\left(d + e x \right)}}{4} + \frac{3 b^{2} c^{2} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{4 e} - \frac{3 b^{2} c^{2} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{4 e} + \frac{b c^{3} \sin^{4}{\left(d + e x \right)}}{e} + \frac{3 c^{4} x \sin^{4}{\left(d + e x \right)}}{8} + \frac{3 c^{4} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{4} + \frac{3 c^{4} x \cos^{4}{\left(d + e x \right)}}{8} - \frac{5 c^{4} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{8 e} - \frac{3 c^{4} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{8 e} & \text{for}\: e \neq 0 \\x \left(a + b \cos{\left(d \right)} + c \sin{\left(d \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*sin(d + e*x)/e - 4*a**3*c*cos(d + e*x)/e + 3*a**2*b**2*x*sin(d + e*x)**2 + 3*a**2*b**2*x*cos(d + e*x)**2 + 3*a**2*b**2*sin(d + e*x)*cos(d + e*x)/e - 6*a**2*b*c*cos(d + e*x)**2/e + 3*a**2*c**2*x*sin(d + e*x)**2 + 3*a**2*c**2*x*cos(d + e*x)**2 - 3*a**2*c**2*sin(d + e*x)*cos(d + e*x)/e + 8*a*b**3*sin(d + e*x)**3/(3*e) + 4*a*b**3*sin(d + e*x)*cos(d + e*x)**2/e - 4*a*b**2*c*cos(d + e*x)**3/e + 4*a*b*c**2*sin(d + e*x)**3/e - 4*a*c**3*sin(d + e*x)**2*cos(d + e*x)/e - 8*a*c**3*cos(d + e*x)**3/(3*e) + 3*b**4*x*sin(d + e*x)**4/8 + 3*b**4*x*sin(d + e*x)**2*cos(d + e*x)**2/4 + 3*b**4*x*cos(d + e*x)**4/8 + 3*b**4*sin(d + e*x)**3*cos(d + e*x)/(8*e) + 5*b**4*sin(d + e*x)*cos(d + e*x)**3/(8*e) - b**3*c*cos(d + e*x)**4/e + 3*b**2*c**2*x*sin(d + e*x)**4/4 + 3*b**2*c**2*x*sin(d + e*x)**2*cos(d + e*x)**2/2 + 3*b**2*c**2*x*cos(d + e*x)**4/4 + 3*b**2*c**2*sin(d + e*x)**3*cos(d + e*x)/(4*e) - 3*b**2*c**2*sin(d + e*x)*cos(d + e*x)**3/(4*e) + b*c**3*sin(d + e*x)**4/e + 3*c**4*x*sin(d + e*x)**4/8 + 3*c**4*x*sin(d + e*x)**2*cos(d + e*x)**2/4 + 3*c**4*x*cos(d + e*x)**4/8 - 5*c**4*sin(d + e*x)**3*cos(d + e*x)/(8*e) - 3*c**4*sin(d + e*x)*cos(d + e*x)**3/(8*e), Ne(e, 0)), (x*(a + b*cos(d) + c*sin(d))**4, True))","A",0
396,1,294,0,0.755298," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b \sin{\left(d + e x \right)}}{e} - \frac{3 a^{2} c \cos{\left(d + e x \right)}}{e} + \frac{3 a b^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{3 a b^{2} x \cos^{2}{\left(d + e x \right)}}{2} + \frac{3 a b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{3 a b c \cos^{2}{\left(d + e x \right)}}{e} + \frac{3 a c^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{3 a c^{2} x \cos^{2}{\left(d + e x \right)}}{2} - \frac{3 a c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} + \frac{2 b^{3} \sin^{3}{\left(d + e x \right)}}{3 e} + \frac{b^{3} \sin{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{e} - \frac{b^{2} c \cos^{3}{\left(d + e x \right)}}{e} + \frac{b c^{2} \sin^{3}{\left(d + e x \right)}}{e} - \frac{c^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{2 c^{3} \cos^{3}{\left(d + e x \right)}}{3 e} & \text{for}\: e \neq 0 \\x \left(a + b \cos{\left(d \right)} + c \sin{\left(d \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*sin(d + e*x)/e - 3*a**2*c*cos(d + e*x)/e + 3*a*b**2*x*sin(d + e*x)**2/2 + 3*a*b**2*x*cos(d + e*x)**2/2 + 3*a*b**2*sin(d + e*x)*cos(d + e*x)/(2*e) - 3*a*b*c*cos(d + e*x)**2/e + 3*a*c**2*x*sin(d + e*x)**2/2 + 3*a*c**2*x*cos(d + e*x)**2/2 - 3*a*c**2*sin(d + e*x)*cos(d + e*x)/(2*e) + 2*b**3*sin(d + e*x)**3/(3*e) + b**3*sin(d + e*x)*cos(d + e*x)**2/e - b**2*c*cos(d + e*x)**3/e + b*c**2*sin(d + e*x)**3/e - c**3*sin(d + e*x)**2*cos(d + e*x)/e - 2*c**3*cos(d + e*x)**3/(3*e), Ne(e, 0)), (x*(a + b*cos(d) + c*sin(d))**3, True))","A",0
397,1,162,0,0.307422," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))**2,x)","\begin{cases} a^{2} x + \frac{2 a b \sin{\left(d + e x \right)}}{e} - \frac{2 a c \cos{\left(d + e x \right)}}{e} + \frac{b^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(d + e x \right)}}{2} + \frac{b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{b c \cos^{2}{\left(d + e x \right)}}{e} + \frac{c^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{c^{2} x \cos^{2}{\left(d + e x \right)}}{2} - \frac{c^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: e \neq 0 \\x \left(a + b \cos{\left(d \right)} + c \sin{\left(d \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*sin(d + e*x)/e - 2*a*c*cos(d + e*x)/e + b**2*x*sin(d + e*x)**2/2 + b**2*x*cos(d + e*x)**2/2 + b**2*sin(d + e*x)*cos(d + e*x)/(2*e) - b*c*cos(d + e*x)**2/e + c**2*x*sin(d + e*x)**2/2 + c**2*x*cos(d + e*x)**2/2 - c**2*sin(d + e*x)*cos(d + e*x)/(2*e), Ne(e, 0)), (x*(a + b*cos(d) + c*sin(d))**2, True))","A",0
398,1,34,0,0.138535," ","integrate(a+b*cos(e*x+d)+c*sin(e*x+d),x)","a x + b \left(\begin{cases} \frac{\sin{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \cos{\left(d \right)} & \text{otherwise} \end{cases}\right) + c \left(\begin{cases} - \frac{\cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \sin{\left(d \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((sin(d + e*x)/e, Ne(e, 0)), (x*cos(d), True)) + c*Piecewise((-cos(d + e*x)/e, Ne(e, 0)), (x*sin(d), True))","A",0
399,1,3179,0,152.526790," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d)),x)","\begin{cases} \frac{32 b^{5}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e + 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e + 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e + 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{32 b^{4} \sqrt{b^{2} + c^{2}}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e + 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e + 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e + 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{40 b^{3} c^{2}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e + 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e + 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e + 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{24 b^{2} c^{2} \sqrt{b^{2} + c^{2}}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e + 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e + 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e + 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{10 b c^{4}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e + 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e + 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e + 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{2 c^{4} \sqrt{b^{2} + c^{2}}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e + 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e + 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e + 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c^{5} e \sqrt{b^{2} + c^{2}}} & \text{for}\: a = - \sqrt{b^{2} + c^{2}} \\\frac{32 b^{5}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e - 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e - 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e - 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{5} e \sqrt{b^{2} + c^{2}}} - \frac{32 b^{4} \sqrt{b^{2} + c^{2}}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e - 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e - 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e - 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{40 b^{3} c^{2}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e - 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e - 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e - 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{5} e \sqrt{b^{2} + c^{2}}} - \frac{24 b^{2} c^{2} \sqrt{b^{2} + c^{2}}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e - 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e - 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e - 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{5} e \sqrt{b^{2} + c^{2}}} + \frac{10 b c^{4}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e - 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e - 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e - 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{5} e \sqrt{b^{2} + c^{2}}} - \frac{2 c^{4} \sqrt{b^{2} + c^{2}}}{32 b^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 16 b^{5} c e - 32 b^{5} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 48 b^{4} c^{2} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 16 b^{4} c e \sqrt{b^{2} + c^{2}} - 20 b^{3} c^{3} e - 32 b^{3} c^{2} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 18 b^{2} c^{4} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 12 b^{2} c^{3} e \sqrt{b^{2} + c^{2}} - 5 b c^{5} e - 6 b c^{4} e \sqrt{b^{2} + c^{2}} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{6} e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c^{5} e \sqrt{b^{2} + c^{2}}} & \text{for}\: a = \sqrt{b^{2} + c^{2}} \\\frac{\log{\left(\frac{b}{c} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{c e} & \text{for}\: a = b \\\frac{x}{a + b \cos{\left(d \right)} + c \sin{\left(d \right)}} & \text{for}\: e = 0 \\\frac{\log{\left(\frac{c}{a - b} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - \frac{\sqrt{- a^{2} + b^{2} + c^{2}}}{a - b} \right)}}{e \sqrt{- a^{2} + b^{2} + c^{2}}} - \frac{\log{\left(\frac{c}{a - b} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{\sqrt{- a^{2} + b^{2} + c^{2}}}{a - b} \right)}}{e \sqrt{- a^{2} + b^{2} + c^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((32*b**5/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e + 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) - 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e + 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) - 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e + 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) - c**5*e*sqrt(b**2 + c**2)) + 32*b**4*sqrt(b**2 + c**2)/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e + 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) - 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e + 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) - 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e + 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) - c**5*e*sqrt(b**2 + c**2)) + 40*b**3*c**2/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e + 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) - 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e + 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) - 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e + 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) - c**5*e*sqrt(b**2 + c**2)) + 24*b**2*c**2*sqrt(b**2 + c**2)/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e + 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) - 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e + 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) - 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e + 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) - c**5*e*sqrt(b**2 + c**2)) + 10*b*c**4/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e + 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) - 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e + 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) - 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e + 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) - c**5*e*sqrt(b**2 + c**2)) + 2*c**4*sqrt(b**2 + c**2)/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e + 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) - 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e + 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) - 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e + 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) - c**5*e*sqrt(b**2 + c**2)), Eq(a, -sqrt(b**2 + c**2))), (32*b**5/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e - 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) + 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e - 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) + 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e - 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) + c**5*e*sqrt(b**2 + c**2)) - 32*b**4*sqrt(b**2 + c**2)/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e - 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) + 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e - 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) + 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e - 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) + c**5*e*sqrt(b**2 + c**2)) + 40*b**3*c**2/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e - 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) + 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e - 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) + 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e - 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) + c**5*e*sqrt(b**2 + c**2)) - 24*b**2*c**2*sqrt(b**2 + c**2)/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e - 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) + 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e - 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) + 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e - 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) + c**5*e*sqrt(b**2 + c**2)) + 10*b*c**4/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e - 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) + 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e - 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) + 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e - 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) + c**5*e*sqrt(b**2 + c**2)) - 2*c**4*sqrt(b**2 + c**2)/(32*b**6*e*tan(d/2 + e*x/2) - 16*b**5*c*e - 32*b**5*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 48*b**4*c**2*e*tan(d/2 + e*x/2) + 16*b**4*c*e*sqrt(b**2 + c**2) - 20*b**3*c**3*e - 32*b**3*c**2*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + 18*b**2*c**4*e*tan(d/2 + e*x/2) + 12*b**2*c**3*e*sqrt(b**2 + c**2) - 5*b*c**5*e - 6*b*c**4*e*sqrt(b**2 + c**2)*tan(d/2 + e*x/2) + c**6*e*tan(d/2 + e*x/2) + c**5*e*sqrt(b**2 + c**2)), Eq(a, sqrt(b**2 + c**2))), (log(b/c + tan(d/2 + e*x/2))/(c*e), Eq(a, b)), (x/(a + b*cos(d) + c*sin(d)), Eq(e, 0)), (log(c/(a - b) + tan(d/2 + e*x/2) - sqrt(-a**2 + b**2 + c**2)/(a - b))/(e*sqrt(-a**2 + b**2 + c**2)) - log(c/(a - b) + tan(d/2 + e*x/2) + sqrt(-a**2 + b**2 + c**2)/(a - b))/(e*sqrt(-a**2 + b**2 + c**2)), True))","A",0
400,-1,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))**(3/2),x)","\int \left(5 \sin{\left(d + e x \right)} + 3 \cos{\left(d + e x \right)} + 2\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((5*sin(d + e*x) + 3*cos(d + e*x) + 2)**(3/2), x)","F",0
405,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))**(1/2),x)","\int \sqrt{5 \sin{\left(d + e x \right)} + 3 \cos{\left(d + e x \right)} + 2}\, dx"," ",0,"Integral(sqrt(5*sin(d + e*x) + 3*cos(d + e*x) + 2), x)","F",0
406,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))**(1/2),x)","\int \frac{1}{\sqrt{5 \sin{\left(d + e x \right)} + 3 \cos{\left(d + e x \right)} + 2}}\, dx"," ",0,"Integral(1/sqrt(5*sin(d + e*x) + 3*cos(d + e*x) + 2), x)","F",0
407,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))**(3/2),x)","\int \frac{1}{\left(5 \sin{\left(d + e x \right)} + 3 \cos{\left(d + e x \right)} + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*sin(d + e*x) + 3*cos(d + e*x) + 2)**(-3/2), x)","F",0
408,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))**(5/2),x)","\int \frac{1}{\left(5 \sin{\left(d + e x \right)} + 3 \cos{\left(d + e x \right)} + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((5*sin(d + e*x) + 3*cos(d + e*x) + 2)**(-5/2), x)","F",0
409,-1,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))**(3/2),x)","\int \left(a + b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*cos(d + e*x) + c*sin(d + e*x))**(3/2), x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))**(1/2),x)","\int \sqrt{a + b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cos(d + e*x) + c*sin(d + e*x)), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**(1/2),x)","\int \frac{1}{\sqrt{a + b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*cos(d + e*x) + c*sin(d + e*x)), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**(3/2),x)","\int \frac{1}{\left(a + b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cos(d + e*x) + c*sin(d + e*x))**(-3/2), x)","F",0
415,-1,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))**(3/2),x)","\int \left(3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} + 5\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((3*sin(d + e*x) + 4*cos(d + e*x) + 5)**(3/2), x)","F",0
419,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))**(1/2),x)","\int \sqrt{3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} + 5}\, dx"," ",0,"Integral(sqrt(3*sin(d + e*x) + 4*cos(d + e*x) + 5), x)","F",0
420,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))**(1/2),x)","\int \frac{1}{\sqrt{3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} + 5}}\, dx"," ",0,"Integral(1/sqrt(3*sin(d + e*x) + 4*cos(d + e*x) + 5), x)","F",0
421,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))**(3/2),x)","\int \frac{1}{\left(3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} + 5\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((3*sin(d + e*x) + 4*cos(d + e*x) + 5)**(-3/2), x)","F",0
422,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))**(5/2),x)","\int \frac{1}{\left(3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} + 5\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((3*sin(d + e*x) + 4*cos(d + e*x) + 5)**(-5/2), x)","F",0
423,-1,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))**(3/2),x)","\int \left(3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} - 5\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((3*sin(d + e*x) + 4*cos(d + e*x) - 5)**(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))**(1/2),x)","\int \sqrt{3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} - 5}\, dx"," ",0,"Integral(sqrt(3*sin(d + e*x) + 4*cos(d + e*x) - 5), x)","F",0
427,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))**(1/2),x)","\int \frac{1}{\sqrt{3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} - 5}}\, dx"," ",0,"Integral(1/sqrt(3*sin(d + e*x) + 4*cos(d + e*x) - 5), x)","F",0
428,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))**(3/2),x)","\int \frac{1}{\left(3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} - 5\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((3*sin(d + e*x) + 4*cos(d + e*x) - 5)**(-3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))**(5/2),x)","\int \frac{1}{\left(3 \sin{\left(d + e x \right)} + 4 \cos{\left(d + e x \right)} - 5\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((3*sin(d + e*x) + 4*cos(d + e*x) - 5)**(-5/2), x)","F",0
430,-1,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,0,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(3/2),x)","\int \left(b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} + \sqrt{b^{2} + c^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*cos(d + e*x) + c*sin(d + e*x) + sqrt(b**2 + c**2))**(3/2), x)","F",0
433,0,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(1/2),x)","\int \sqrt{b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} + \sqrt{b^{2} + c^{2}}}\, dx"," ",0,"Integral(sqrt(b*cos(d + e*x) + c*sin(d + e*x) + sqrt(b**2 + c**2)), x)","F",0
434,0,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} + \sqrt{b^{2} + c^{2}}}}\, dx"," ",0,"Integral(1/sqrt(b*cos(d + e*x) + c*sin(d + e*x) + sqrt(b**2 + c**2)), x)","F",0
435,0,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(3/2),x)","\int \frac{1}{\left(b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} + \sqrt{b^{2} + c^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*cos(d + e*x) + c*sin(d + e*x) + sqrt(b**2 + c**2))**(-3/2), x)","F",0
436,0,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b**2+c**2)**(1/2))**(5/2),x)","\int \frac{1}{\left(b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} + \sqrt{b^{2} + c^{2}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*cos(d + e*x) + c*sin(d + e*x) + sqrt(b**2 + c**2))**(-5/2), x)","F",0
437,-1,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b**2+c**2)**(1/2))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,0,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b**2+c**2)**(1/2))**(3/2),x)","\int \left(b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} - \sqrt{b^{2} + c^{2}}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*cos(d + e*x) + c*sin(d + e*x) - sqrt(b**2 + c**2))**(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b**2+c**2)**(1/2))**(1/2),x)","\int \sqrt{b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} - \sqrt{b^{2} + c^{2}}}\, dx"," ",0,"Integral(sqrt(b*cos(d + e*x) + c*sin(d + e*x) - sqrt(b**2 + c**2)), x)","F",0
440,0,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b**2+c**2)**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} - \sqrt{b^{2} + c^{2}}}}\, dx"," ",0,"Integral(1/sqrt(b*cos(d + e*x) + c*sin(d + e*x) - sqrt(b**2 + c**2)), x)","F",0
441,0,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b**2+c**2)**(1/2))**(3/2),x)","\int \frac{1}{\left(b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} - \sqrt{b^{2} + c^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*cos(d + e*x) + c*sin(d + e*x) - sqrt(b**2 + c**2))**(-3/2), x)","F",0
442,0,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b**2+c**2)**(1/2))**(5/2),x)","\int \frac{1}{\left(b \cos{\left(d + e x \right)} + c \sin{\left(d + e x \right)} - \sqrt{b^{2} + c^{2}}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*cos(d + e*x) + c*sin(d + e*x) - sqrt(b**2 + c**2))**(-5/2), x)","F",0
443,-1,0,0,0.000000," ","integrate(sin(x)/(a+b*cos(x)+c*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,1,22,0,0.255715," ","integrate(sin(x)/(1+cos(x)+sin(x)),x)","\frac{x}{2} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{2}"," ",0,"x/2 - log(tan(x/2) + 1) + log(tan(x/2)**2 + 1)/2","A",0
445,0,0,0,0.000000," ","integrate(1/(a+c*sec(x)+b*tan(x)),x)","\int \frac{1}{a + b \tan{\left(x \right)} + c \sec{\left(x \right)}}\, dx"," ",0,"Integral(1/(a + b*tan(x) + c*sec(x)), x)","F",0
446,0,0,0,0.000000," ","integrate(sec(x)/(a+c*sec(x)+b*tan(x)),x)","\int \frac{\sec{\left(x \right)}}{a + b \tan{\left(x \right)} + c \sec{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)/(a + b*tan(x) + c*sec(x)), x)","F",0
447,0,0,0,0.000000," ","integrate(sec(x)**2/(a+c*sec(x)+b*tan(x)),x)","\int \frac{\sec^{2}{\left(x \right)}}{a + b \tan{\left(x \right)} + c \sec{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**2/(a + b*tan(x) + c*sec(x)), x)","F",0
448,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))**(3/2)/sec(e*x+d)**(3/2),x)","\int \frac{\left(a + b \sec{\left(d + e x \right)} + c \tan{\left(d + e x \right)}\right)^{\frac{3}{2}}}{\sec^{\frac{3}{2}}{\left(d + e x \right)}}\, dx"," ",0,"Integral((a + b*sec(d + e*x) + c*tan(d + e*x))**(3/2)/sec(d + e*x)**(3/2), x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))**(1/2)/sec(e*x+d)**(1/2),x)","\int \frac{\sqrt{a + b \sec{\left(d + e x \right)} + c \tan{\left(d + e x \right)}}}{\sqrt{\sec{\left(d + e x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*sec(d + e*x) + c*tan(d + e*x))/sqrt(sec(d + e*x)), x)","F",0
450,0,0,0,0.000000," ","integrate(sec(e*x+d)**(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))**(1/2),x)","\int \frac{\sqrt{\sec{\left(d + e x \right)}}}{\sqrt{a + b \sec{\left(d + e x \right)} + c \tan{\left(d + e x \right)}}}\, dx"," ",0,"Integral(sqrt(sec(d + e*x))/sqrt(a + b*sec(d + e*x) + c*tan(d + e*x)), x)","F",0
451,0,0,0,0.000000," ","integrate(sec(e*x+d)**(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))**(3/2),x)","\int \frac{\sec^{\frac{3}{2}}{\left(d + e x \right)}}{\left(a + b \sec{\left(d + e x \right)} + c \tan{\left(d + e x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(d + e*x)**(3/2)/(a + b*sec(d + e*x) + c*tan(d + e*x))**(3/2), x)","F",0
452,-1,0,0,0.000000," ","integrate(sec(e*x+d)**(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,-1,0,0,0.000000," ","integrate(cos(e*x+d)**(3/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
454,0,0,0,0.000000," ","integrate(cos(e*x+d)**(1/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))**(1/2),x)","\int \sqrt{a + b \sec{\left(d + e x \right)} + c \tan{\left(d + e x \right)}} \sqrt{\cos{\left(d + e x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sec(d + e*x) + c*tan(d + e*x))*sqrt(cos(d + e*x)), x)","F",0
455,0,0,0,0.000000," ","integrate(1/cos(e*x+d)**(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sec{\left(d + e x \right)} + c \tan{\left(d + e x \right)}} \sqrt{\cos{\left(d + e x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*sec(d + e*x) + c*tan(d + e*x))*sqrt(cos(d + e*x))), x)","F",0
456,-1,0,0,0.000000," ","integrate(1/cos(e*x+d)**(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(1/cos(e*x+d)**(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,0,0,0,0.000000," ","integrate(1/(a+b*cot(x)+c*csc(x)),x)","\int \frac{1}{a + b \cot{\left(x \right)} + c \csc{\left(x \right)}}\, dx"," ",0,"Integral(1/(a + b*cot(x) + c*csc(x)), x)","F",0
459,0,0,0,0.000000," ","integrate(csc(x)/(a+b*cot(x)+c*csc(x)),x)","\int \frac{\csc{\left(x \right)}}{a + b \cot{\left(x \right)} + c \csc{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(a + b*cot(x) + c*csc(x)), x)","F",0
460,0,0,0,0.000000," ","integrate(csc(x)**2/(a+b*cot(x)+c*csc(x)),x)","\int \frac{\csc^{2}{\left(x \right)}}{a + b \cot{\left(x \right)} + c \csc{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**2/(a + b*cot(x) + c*csc(x)), x)","F",0
461,0,0,0,0.000000," ","integrate(csc(x)/(2+2*cot(x)+3*csc(x)),x)","\int \frac{\csc{\left(x \right)}}{2 \cot{\left(x \right)} + 3 \csc{\left(x \right)} + 2}\, dx"," ",0,"Integral(csc(x)/(2*cot(x) + 3*csc(x) + 2), x)","F",0
462,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))**(3/2)/csc(e*x+d)**(3/2),x)","\int \frac{\left(a + b \csc{\left(d + e x \right)} + c \cot{\left(d + e x \right)}\right)^{\frac{3}{2}}}{\csc^{\frac{3}{2}}{\left(d + e x \right)}}\, dx"," ",0,"Integral((a + b*csc(d + e*x) + c*cot(d + e*x))**(3/2)/csc(d + e*x)**(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))**(1/2)/csc(e*x+d)**(1/2),x)","\int \frac{\sqrt{a + b \csc{\left(d + e x \right)} + c \cot{\left(d + e x \right)}}}{\sqrt{\csc{\left(d + e x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*csc(d + e*x) + c*cot(d + e*x))/sqrt(csc(d + e*x)), x)","F",0
464,0,0,0,0.000000," ","integrate(csc(e*x+d)**(1/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))**(1/2),x)","\int \frac{\sqrt{\csc{\left(d + e x \right)}}}{\sqrt{a + b \csc{\left(d + e x \right)} + c \cot{\left(d + e x \right)}}}\, dx"," ",0,"Integral(sqrt(csc(d + e*x))/sqrt(a + b*csc(d + e*x) + c*cot(d + e*x)), x)","F",0
465,0,0,0,0.000000," ","integrate(csc(e*x+d)**(3/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))**(3/2),x)","\int \frac{\csc^{\frac{3}{2}}{\left(d + e x \right)}}{\left(a + b \csc{\left(d + e x \right)} + c \cot{\left(d + e x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(d + e*x)**(3/2)/(a + b*csc(d + e*x) + c*cot(d + e*x))**(3/2), x)","F",0
466,-1,0,0,0.000000," ","integrate(csc(e*x+d)**(5/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))**(3/2)*sin(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))**(1/2)*sin(e*x+d)**(1/2),x)","\int \sqrt{a + b \csc{\left(d + e x \right)} + c \cot{\left(d + e x \right)}} \sqrt{\sin{\left(d + e x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*csc(d + e*x) + c*cot(d + e*x))*sqrt(sin(d + e*x)), x)","F",0
469,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))**(1/2)/sin(e*x+d)**(1/2),x)","\int \frac{1}{\sqrt{a + b \csc{\left(d + e x \right)} + c \cot{\left(d + e x \right)}} \sqrt{\sin{\left(d + e x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*csc(d + e*x) + c*cot(d + e*x))*sqrt(sin(d + e*x))), x)","F",0
470,-1,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))**(3/2)/sin(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))**(5/2)/sin(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,1,10,0,0.356560," ","integrate(1/(cos(x)**2+sin(x)**2),x)","\frac{x}{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}"," ",0,"x/(sin(x)**2 + cos(x)**2)","B",0
473,1,22,0,0.829922," ","integrate(1/(cos(x)**2+sin(x)**2)**2,x)","\frac{x}{\sin^{4}{\left(x \right)} + 2 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{4}{\left(x \right)}}"," ",0,"x/(sin(x)**4 + 2*sin(x)**2*cos(x)**2 + cos(x)**4)","B",0
474,1,34,0,2.096190," ","integrate(1/(cos(x)**2+sin(x)**2)**3,x)","\frac{x}{\sin^{6}{\left(x \right)} + 3 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)} + \cos^{6}{\left(x \right)}}"," ",0,"x/(sin(x)**6 + 3*sin(x)**4*cos(x)**2 + 3*sin(x)**2*cos(x)**4 + cos(x)**6)","B",0
475,1,36,0,0.345413," ","integrate(1/(cos(x)**2-sin(x)**2),x)","\frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{2} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{2}"," ",0,"log(tan(x/2)**2 - 2*tan(x/2) - 1)/2 - log(tan(x/2)**2 + 2*tan(x/2) - 1)/2","B",0
476,1,48,0,1.335717," ","integrate(1/(cos(x)**2-sin(x)**2)**2,x)","- \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{\tan^{4}{\left(\frac{x}{2} \right)} - 6 \tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{4}{\left(\frac{x}{2} \right)} - 6 \tan^{2}{\left(\frac{x}{2} \right)} + 1}"," ",0,"-2*tan(x/2)**3/(tan(x/2)**4 - 6*tan(x/2)**2 + 1) + 2*tan(x/2)/(tan(x/2)**4 - 6*tan(x/2)**2 + 1)","B",0
477,1,765,0,3.475633," ","integrate(1/(cos(x)**2-sin(x)**2)**3,x)","\frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{8}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{12 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{38 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{12 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{8}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{12 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{38 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{12 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{4 \tan^{7}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{4 \tan^{5}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{4 \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{4 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 152 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 4}"," ",0,"log(tan(x/2)**2 - 2*tan(x/2) - 1)*tan(x/2)**8/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - 12*log(tan(x/2)**2 - 2*tan(x/2) - 1)*tan(x/2)**6/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) + 38*log(tan(x/2)**2 - 2*tan(x/2) - 1)*tan(x/2)**4/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - 12*log(tan(x/2)**2 - 2*tan(x/2) - 1)*tan(x/2)**2/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) + log(tan(x/2)**2 - 2*tan(x/2) - 1)/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - log(tan(x/2)**2 + 2*tan(x/2) - 1)*tan(x/2)**8/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) + 12*log(tan(x/2)**2 + 2*tan(x/2) - 1)*tan(x/2)**6/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - 38*log(tan(x/2)**2 + 2*tan(x/2) - 1)*tan(x/2)**4/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) + 12*log(tan(x/2)**2 + 2*tan(x/2) - 1)*tan(x/2)**2/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - log(tan(x/2)**2 + 2*tan(x/2) - 1)/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - 4*tan(x/2)**7/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) - 4*tan(x/2)**5/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) + 4*tan(x/2)**3/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4) + 4*tan(x/2)/(4*tan(x/2)**8 - 48*tan(x/2)**6 + 152*tan(x/2)**4 - 48*tan(x/2)**2 + 4)","B",0
478,1,12007,0,22.401033," ","integrate(1/(cos(x)**2+a**2*sin(x)**2),x)","\begin{cases} \frac{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{112 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{112 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{16 a^{5} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{16 a^{5} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 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2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{7 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{7 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{5 a \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{5 a \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{\sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{\sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} - \frac{\sqrt{a^{2} - 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} \log{\left(- \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} + \frac{\sqrt{a^{2} - 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} \log{\left(\sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} + \tan{\left(\frac{x}{2} \right)} \right)}}{64 a^{7} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 64 a^{6} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 96 a^{5} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 64 a^{4} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} + 36 a^{3} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 12 a^{2} \sqrt{a^{2} - 1} \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1} - 2 a \sqrt{- 2 a^{2} - 2 a \sqrt{a^{2} - 1} + 1} \sqrt{- 2 a^{2} + 2 a \sqrt{a^{2} - 1} + 1}} & \text{for}\: a \neq 0 \\- \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 112*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 112*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 16*a**5*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 16*a**5*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 80*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 80*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 16*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 16*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 56*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 56*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 20*a**3*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 20*a**3*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 24*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 24*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 7*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 7*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 5*a*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 5*a*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)), Ne(a, 0)), (-2*tan(x/2)/(tan(x/2)**2 - 1), True))","B",0
479,-1,0,0,0.000000," ","integrate(1/(b**2*cos(x)**2+sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(1/(b**2*cos(x)**2+a**2*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,1,87,0,0.808456," ","integrate(1/(4*cos(1+2*x)**2+3*sin(1+2*x)**2),x)","\frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(x + \frac{1}{2} \right)}}{3} - \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2} + \frac{1}{2}}{\pi}}\right\rfloor\right)}{12} + \frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(x + \frac{1}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2} + \frac{1}{2}}{\pi}}\right\rfloor\right)}{12}"," ",0,"sqrt(3)*(atan(2*sqrt(3)*tan(x + 1/2)/3 - sqrt(3)/3) + pi*floor((x - pi/2 + 1/2)/pi))/12 + sqrt(3)*(atan(2*sqrt(3)*tan(x + 1/2)/3 + sqrt(3)/3) + pi*floor((x - pi/2 + 1/2)/pi))/12","A",0
482,1,241,0,1.564157," ","integrate(sin(x)**2/(a*cos(x)**2+b*sin(x)**2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{x \sin^{2}{\left(x \right)}}{2 b \sin^{2}{\left(x \right)} + 2 b \cos^{2}{\left(x \right)}} + \frac{x \cos^{2}{\left(x \right)}}{2 b \sin^{2}{\left(x \right)} + 2 b \cos^{2}{\left(x \right)}} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2 b \sin^{2}{\left(x \right)} + 2 b \cos^{2}{\left(x \right)}} & \text{for}\: a = b \\\frac{- x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}}{a} & \text{for}\: b = 0 \\\frac{x}{b} & \text{for}\: a = 0 \\- \frac{2 i \sqrt{b} x \sqrt{\frac{1}{a}}}{2 i a \sqrt{b} \sqrt{\frac{1}{a}} - 2 i b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{\log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} \sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{2 i a \sqrt{b} \sqrt{\frac{1}{a}} - 2 i b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{\log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} \sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{2 i a \sqrt{b} \sqrt{\frac{1}{a}} - 2 i b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (x*sin(x)**2/(2*b*sin(x)**2 + 2*b*cos(x)**2) + x*cos(x)**2/(2*b*sin(x)**2 + 2*b*cos(x)**2) - sin(x)*cos(x)/(2*b*sin(x)**2 + 2*b*cos(x)**2), Eq(a, b)), ((-x + sin(x)/cos(x))/a, Eq(b, 0)), (x/b, Eq(a, 0)), (-2*I*sqrt(b)*x*sqrt(1/a)/(2*I*a*sqrt(b)*sqrt(1/a) - 2*I*b**(3/2)*sqrt(1/a)) - log(-I*sqrt(b)*sqrt(1/a)*sin(x) + cos(x))/(2*I*a*sqrt(b)*sqrt(1/a) - 2*I*b**(3/2)*sqrt(1/a)) + log(I*sqrt(b)*sqrt(1/a)*sin(x) + cos(x))/(2*I*a*sqrt(b)*sqrt(1/a) - 2*I*b**(3/2)*sqrt(1/a)), True))","A",0
483,1,267,0,1.621397," ","integrate(cos(x)**2/(a*cos(x)**2+b*sin(x)**2),x)","\begin{cases} \tilde{\infty} \left(- x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{x \sin^{2}{\left(x \right)}}{2 b \sin^{2}{\left(x \right)} + 2 b \cos^{2}{\left(x \right)}} + \frac{x \cos^{2}{\left(x \right)}}{2 b \sin^{2}{\left(x \right)} + 2 b \cos^{2}{\left(x \right)}} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2 b \sin^{2}{\left(x \right)} + 2 b \cos^{2}{\left(x \right)}} & \text{for}\: a = b \\\frac{x}{a} & \text{for}\: b = 0 \\\frac{- x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}}{b} & \text{for}\: a = 0 \\\frac{2 i a \sqrt{b} x \sqrt{\frac{1}{a}}}{2 i a^{2} \sqrt{b} \sqrt{\frac{1}{a}} - 2 i a b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} + \frac{b \log{\left(- i \sqrt{b} \sqrt{\frac{1}{a}} \sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{2 i a^{2} \sqrt{b} \sqrt{\frac{1}{a}} - 2 i a b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} - \frac{b \log{\left(i \sqrt{b} \sqrt{\frac{1}{a}} \sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{2 i a^{2} \sqrt{b} \sqrt{\frac{1}{a}} - 2 i a b^{\frac{3}{2}} \sqrt{\frac{1}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-x - cos(x)/sin(x)), Eq(a, 0) & Eq(b, 0)), (x*sin(x)**2/(2*b*sin(x)**2 + 2*b*cos(x)**2) + x*cos(x)**2/(2*b*sin(x)**2 + 2*b*cos(x)**2) + sin(x)*cos(x)/(2*b*sin(x)**2 + 2*b*cos(x)**2), Eq(a, b)), (x/a, Eq(b, 0)), ((-x - cos(x)/sin(x))/b, Eq(a, 0)), (2*I*a*sqrt(b)*x*sqrt(1/a)/(2*I*a**2*sqrt(b)*sqrt(1/a) - 2*I*a*b**(3/2)*sqrt(1/a)) + b*log(-I*sqrt(b)*sqrt(1/a)*sin(x) + cos(x))/(2*I*a**2*sqrt(b)*sqrt(1/a) - 2*I*a*b**(3/2)*sqrt(1/a)) - b*log(I*sqrt(b)*sqrt(1/a)*sin(x) + cos(x))/(2*I*a**2*sqrt(b)*sqrt(1/a) - 2*I*a*b**(3/2)*sqrt(1/a)), True))","A",0
484,0,0,0,0.000000," ","integrate(1/(sec(x)**2+tan(x)**2),x)","\int \frac{1}{\tan^{2}{\left(x \right)} + \sec^{2}{\left(x \right)}}\, dx"," ",0,"Integral(1/(tan(x)**2 + sec(x)**2), x)","F",0
485,0,0,0,0.000000," ","integrate(1/(sec(x)**2+tan(x)**2)**2,x)","\int \frac{1}{\left(\tan^{2}{\left(x \right)} + \sec^{2}{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((tan(x)**2 + sec(x)**2)**(-2), x)","F",0
486,0,0,0,0.000000," ","integrate(1/(sec(x)**2+tan(x)**2)**3,x)","\int \frac{1}{\left(\tan^{2}{\left(x \right)} + \sec^{2}{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral((tan(x)**2 + sec(x)**2)**(-3), x)","F",0
487,0,0,0,0.000000," ","integrate(1/(sec(x)**2-tan(x)**2),x)","\int \frac{1}{\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right) \left(\tan{\left(x \right)} + \sec{\left(x \right)}\right)}\, dx"," ",0,"Integral(1/((-tan(x) + sec(x))*(tan(x) + sec(x))), x)","F",0
488,0,0,0,0.000000," ","integrate(1/(sec(x)**2-tan(x)**2)**2,x)","\int \frac{1}{\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right)^{2} \left(\tan{\left(x \right)} + \sec{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/((-tan(x) + sec(x))**2*(tan(x) + sec(x))**2), x)","F",0
489,0,0,0,0.000000," ","integrate(1/(sec(x)**2-tan(x)**2)**3,x)","\int \frac{1}{\left(- \tan{\left(x \right)} + \sec{\left(x \right)}\right)^{3} \left(\tan{\left(x \right)} + \sec{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/((-tan(x) + sec(x))**3*(tan(x) + sec(x))**3), x)","F",0
490,0,0,0,0.000000," ","integrate(1/(cot(x)**2+csc(x)**2),x)","\int \frac{1}{\cot^{2}{\left(x \right)} + \csc^{2}{\left(x \right)}}\, dx"," ",0,"Integral(1/(cot(x)**2 + csc(x)**2), x)","F",0
491,0,0,0,0.000000," ","integrate(1/(cot(x)**2+csc(x)**2)**2,x)","\int \frac{1}{\left(\cot^{2}{\left(x \right)} + \csc^{2}{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral((cot(x)**2 + csc(x)**2)**(-2), x)","F",0
492,-1,0,0,0.000000," ","integrate(1/(cot(x)**2+csc(x)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,0,0,0,0.000000," ","integrate(1/(cot(x)**2-csc(x)**2),x)","\int \frac{1}{\left(\cot{\left(x \right)} - \csc{\left(x \right)}\right) \left(\cot{\left(x \right)} + \csc{\left(x \right)}\right)}\, dx"," ",0,"Integral(1/((cot(x) - csc(x))*(cot(x) + csc(x))), x)","F",0
494,-1,0,0,0.000000," ","integrate(1/(cot(x)**2-csc(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate(1/(cot(x)**2-csc(x)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,0,0,0,0.000000," ","integrate(1/(a+b*cos(x)**2+c*sin(x)**2),x)","\int \frac{1}{a + b \cos^{2}{\left(x \right)} + c \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a + b*cos(x)**2 + c*sin(x)**2), x)","F",0
497,0,0,0,0.000000," ","integrate(x/(a+b*cos(x)**2+c*sin(x)**2),x)","\int \frac{x}{a + b \cos^{2}{\left(x \right)} + c \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(x/(a + b*cos(x)**2 + c*sin(x)**2), x)","F",0
498,0,0,0,0.000000," ","integrate(x**2/(a+b*cos(x)**2+c*sin(x)**2),x)","\int \frac{x^{2}}{a + b \cos^{2}{\left(x \right)} + c \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(x**2/(a + b*cos(x)**2 + c*sin(x)**2), x)","F",0
499,1,566,0,2.997814," ","integrate((a+b*sin(e*x+d))*(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2)**2,x)","\begin{cases} \frac{3 a^{5} x \sin^{4}{\left(d + e x \right)}}{8} + \frac{3 a^{5} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)}}{4} + \frac{3 a^{5} x \cos^{4}{\left(d + e x \right)}}{8} - \frac{5 a^{5} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{8 e} - \frac{3 a^{5} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{8 e} - \frac{a^{4} b \sin^{4}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{4 a^{4} b \sin^{2}{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{3 e} - \frac{4 a^{4} b \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{8 a^{4} b \cos^{5}{\left(d + e x \right)}}{15 e} - \frac{8 a^{4} b \cos^{3}{\left(d + e x \right)}}{3 e} + \frac{3 a^{3} b^{2} x \sin^{4}{\left(d + e x \right)}}{2} + 3 a^{3} b^{2} x \sin^{2}{\left(d + e x \right)} \cos^{2}{\left(d + e x \right)} + 3 a^{3} b^{2} x \sin^{2}{\left(d + e x \right)} + \frac{3 a^{3} b^{2} x \cos^{4}{\left(d + e x \right)}}{2} + 3 a^{3} b^{2} x \cos^{2}{\left(d + e x \right)} - \frac{5 a^{3} b^{2} \sin^{3}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{3 a^{3} b^{2} \sin{\left(d + e x \right)} \cos^{3}{\left(d + e x \right)}}{2 e} - \frac{3 a^{3} b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{6 a^{2} b^{3} \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{4 a^{2} b^{3} \cos^{3}{\left(d + e x \right)}}{e} - \frac{4 a^{2} b^{3} \cos{\left(d + e x \right)}}{e} + 2 a b^{4} x \sin^{2}{\left(d + e x \right)} + 2 a b^{4} x \cos^{2}{\left(d + e x \right)} + a b^{4} x - \frac{2 a b^{4} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{b^{5} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(a + b \sin{\left(d \right)}\right) \left(a^{2} \sin^{2}{\left(d \right)} + 2 a b \sin{\left(d \right)} + b^{2}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**5*x*sin(d + e*x)**4/8 + 3*a**5*x*sin(d + e*x)**2*cos(d + e*x)**2/4 + 3*a**5*x*cos(d + e*x)**4/8 - 5*a**5*sin(d + e*x)**3*cos(d + e*x)/(8*e) - 3*a**5*sin(d + e*x)*cos(d + e*x)**3/(8*e) - a**4*b*sin(d + e*x)**4*cos(d + e*x)/e - 4*a**4*b*sin(d + e*x)**2*cos(d + e*x)**3/(3*e) - 4*a**4*b*sin(d + e*x)**2*cos(d + e*x)/e - 8*a**4*b*cos(d + e*x)**5/(15*e) - 8*a**4*b*cos(d + e*x)**3/(3*e) + 3*a**3*b**2*x*sin(d + e*x)**4/2 + 3*a**3*b**2*x*sin(d + e*x)**2*cos(d + e*x)**2 + 3*a**3*b**2*x*sin(d + e*x)**2 + 3*a**3*b**2*x*cos(d + e*x)**4/2 + 3*a**3*b**2*x*cos(d + e*x)**2 - 5*a**3*b**2*sin(d + e*x)**3*cos(d + e*x)/(2*e) - 3*a**3*b**2*sin(d + e*x)*cos(d + e*x)**3/(2*e) - 3*a**3*b**2*sin(d + e*x)*cos(d + e*x)/e - 6*a**2*b**3*sin(d + e*x)**2*cos(d + e*x)/e - 4*a**2*b**3*cos(d + e*x)**3/e - 4*a**2*b**3*cos(d + e*x)/e + 2*a*b**4*x*sin(d + e*x)**2 + 2*a*b**4*x*cos(d + e*x)**2 + a*b**4*x - 2*a*b**4*sin(d + e*x)*cos(d + e*x)/e - b**5*cos(d + e*x)/e, Ne(e, 0)), (x*(a + b*sin(d))*(a**2*sin(d)**2 + 2*a*b*sin(d) + b**2)**2, True))","A",0
500,1,204,0,0.673583," ","integrate((a+b*sin(e*x+d))*(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2),x)","\begin{cases} \frac{a^{3} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{a^{3} x \cos^{2}{\left(d + e x \right)}}{2} - \frac{a^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{a^{2} b \sin^{2}{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{2 a^{2} b \cos^{3}{\left(d + e x \right)}}{3 e} - \frac{2 a^{2} b \cos{\left(d + e x \right)}}{e} + a b^{2} x \sin^{2}{\left(d + e x \right)} + a b^{2} x \cos^{2}{\left(d + e x \right)} + a b^{2} x - \frac{a b^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{e} - \frac{b^{3} \cos{\left(d + e x \right)}}{e} & \text{for}\: e \neq 0 \\x \left(a + b \sin{\left(d \right)}\right) \left(a^{2} \sin^{2}{\left(d \right)} + 2 a b \sin{\left(d \right)} + b^{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x*sin(d + e*x)**2/2 + a**3*x*cos(d + e*x)**2/2 - a**3*sin(d + e*x)*cos(d + e*x)/(2*e) - a**2*b*sin(d + e*x)**2*cos(d + e*x)/e - 2*a**2*b*cos(d + e*x)**3/(3*e) - 2*a**2*b*cos(d + e*x)/e + a*b**2*x*sin(d + e*x)**2 + a*b**2*x*cos(d + e*x)**2 + a*b**2*x - a*b**2*sin(d + e*x)*cos(d + e*x)/e - b**3*cos(d + e*x)/e, Ne(e, 0)), (x*(a + b*sin(d))*(a**2*sin(d)**2 + 2*a*b*sin(d) + b**2), True))","A",0
501,-1,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate((d+e*sin(x))/(a+b*sin(x)+c*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate((a+b*sin(e*x+d))*(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,0,0,0,0.000000," ","integrate((a+b*sin(e*x+d))*(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2)**(1/2),x)","\int \left(a + b \sin{\left(d + e x \right)}\right) \sqrt{\left(a \sin{\left(d + e x \right)} + b\right)^{2}}\, dx"," ",0,"Integral((a + b*sin(d + e*x))*sqrt((a*sin(d + e*x) + b)**2), x)","F",0
506,0,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2)**(1/2),x)","\int \frac{a + b \sin{\left(d + e x \right)}}{\sqrt{\left(a \sin{\left(d + e x \right)} + b\right)^{2}}}\, dx"," ",0,"Integral((a + b*sin(d + e*x))/sqrt((a*sin(d + e*x) + b)**2), x)","F",0
507,-1,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b**2+2*a*b*sin(e*x+d)+a**2*sin(e*x+d)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate((a+b*cos(x))/(b**2+2*a*b*cos(x)+a**2*cos(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate((d+e*cos(x))/(a+b*cos(x)+c*cos(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,1,248,0,0.625483," ","integrate((a+b*tan(e*x+d))*(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2)**2,x)","\begin{cases} a^{5} x + \frac{a^{5} \tan^{3}{\left(d + e x \right)}}{3 e} - \frac{a^{5} \tan{\left(d + e x \right)}}{e} - \frac{3 a^{4} b \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 e} + \frac{a^{4} b \tan^{4}{\left(d + e x \right)}}{4 e} + \frac{3 a^{4} b \tan^{2}{\left(d + e x \right)}}{2 e} - 2 a^{3} b^{2} x + \frac{4 a^{3} b^{2} \tan^{3}{\left(d + e x \right)}}{3 e} + \frac{2 a^{3} b^{2} \tan{\left(d + e x \right)}}{e} - \frac{a^{2} b^{3} \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{e} + \frac{3 a^{2} b^{3} \tan^{2}{\left(d + e x \right)}}{e} - 3 a b^{4} x + \frac{4 a b^{4} \tan{\left(d + e x \right)}}{e} + \frac{b^{5} \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 e} & \text{for}\: e \neq 0 \\x \left(a + b \tan{\left(d \right)}\right) \left(a^{2} \tan^{2}{\left(d \right)} + 2 a b \tan{\left(d \right)} + b^{2}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x + a**5*tan(d + e*x)**3/(3*e) - a**5*tan(d + e*x)/e - 3*a**4*b*log(tan(d + e*x)**2 + 1)/(2*e) + a**4*b*tan(d + e*x)**4/(4*e) + 3*a**4*b*tan(d + e*x)**2/(2*e) - 2*a**3*b**2*x + 4*a**3*b**2*tan(d + e*x)**3/(3*e) + 2*a**3*b**2*tan(d + e*x)/e - a**2*b**3*log(tan(d + e*x)**2 + 1)/e + 3*a**2*b**3*tan(d + e*x)**2/e - 3*a*b**4*x + 4*a*b**4*tan(d + e*x)/e + b**5*log(tan(d + e*x)**2 + 1)/(2*e), Ne(e, 0)), (x*(a + b*tan(d))*(a**2*tan(d)**2 + 2*a*b*tan(d) + b**2)**2, True))","A",0
511,1,122,0,0.250326," ","integrate((a+b*tan(e*x+d))*(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2),x)","\begin{cases} - a^{3} x + \frac{a^{3} \tan{\left(d + e x \right)}}{e} + \frac{a^{2} b \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 e} + \frac{a^{2} b \tan^{2}{\left(d + e x \right)}}{2 e} - a b^{2} x + \frac{2 a b^{2} \tan{\left(d + e x \right)}}{e} + \frac{b^{3} \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 e} & \text{for}\: e \neq 0 \\x \left(a + b \tan{\left(d \right)}\right) \left(a^{2} \tan^{2}{\left(d \right)} + 2 a b \tan{\left(d \right)} + b^{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*x + a**3*tan(d + e*x)/e + a**2*b*log(tan(d + e*x)**2 + 1)/(2*e) + a**2*b*tan(d + e*x)**2/(2*e) - a*b**2*x + 2*a*b**2*tan(d + e*x)/e + b**3*log(tan(d + e*x)**2 + 1)/(2*e), Ne(e, 0)), (x*(a + b*tan(d))*(a**2*tan(d)**2 + 2*a*b*tan(d) + b**2), True))","A",0
512,1,1358,0,1.622988," ","integrate((a+b*tan(e*x+d))/(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2),x)","\begin{cases} \tilde{\infty} x \tan{\left(d \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \\\frac{\log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 b e} & \text{for}\: a = 0 \\\frac{1}{2 b e \tan^{2}{\left(d + e x \right)} + 4 i b e \tan{\left(d + e x \right)} - 2 b e} & \text{for}\: a = - i b \\\frac{1}{2 b e \tan^{2}{\left(d + e x \right)} - 4 i b e \tan{\left(d + e x \right)} - 2 b e} & \text{for}\: a = i b \\\frac{x \left(a + b \tan{\left(d \right)}\right)}{a^{2} \tan^{2}{\left(d \right)} + 2 a b \tan{\left(d \right)} + b^{2}} & \text{for}\: e = 0 \\- \frac{2 a^{4} e x \tan{\left(d + e x \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} - \frac{2 a^{4}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} - \frac{2 a^{3} b e x}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{6 a^{3} b \log{\left(\tan{\left(d + e x \right)} + \frac{b}{a} \right)} \tan{\left(d + e x \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} - \frac{3 a^{3} b \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)} \tan{\left(d + e x \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{6 a^{2} b^{2} e x \tan{\left(d + e x \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{6 a^{2} b^{2} \log{\left(\tan{\left(d + e x \right)} + \frac{b}{a} \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} - \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{6 a b^{3} e x}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} - \frac{2 a b^{3} \log{\left(\tan{\left(d + e x \right)} + \frac{b}{a} \right)} \tan{\left(d + e x \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{a b^{3} \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)} \tan{\left(d + e x \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} - \frac{2 b^{4} \log{\left(\tan{\left(d + e x \right)} + \frac{b}{a} \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{b^{4} \log{\left(\tan^{2}{\left(d + e x \right)} + 1 \right)}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} + \frac{2 b^{4}}{2 a^{5} e \tan{\left(d + e x \right)} + 2 a^{4} b e + 4 a^{3} b^{2} e \tan{\left(d + e x \right)} + 4 a^{2} b^{3} e + 2 a b^{4} e \tan{\left(d + e x \right)} + 2 b^{5} e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(d), Eq(a, 0) & Eq(b, 0) & Eq(e, 0)), (log(tan(d + e*x)**2 + 1)/(2*b*e), Eq(a, 0)), (1/(2*b*e*tan(d + e*x)**2 + 4*I*b*e*tan(d + e*x) - 2*b*e), Eq(a, -I*b)), (1/(2*b*e*tan(d + e*x)**2 - 4*I*b*e*tan(d + e*x) - 2*b*e), Eq(a, I*b)), (x*(a + b*tan(d))/(a**2*tan(d)**2 + 2*a*b*tan(d) + b**2), Eq(e, 0)), (-2*a**4*e*x*tan(d + e*x)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) - 2*a**4/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) - 2*a**3*b*e*x/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + 6*a**3*b*log(tan(d + e*x) + b/a)*tan(d + e*x)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) - 3*a**3*b*log(tan(d + e*x)**2 + 1)*tan(d + e*x)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + 6*a**2*b**2*e*x*tan(d + e*x)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + 6*a**2*b**2*log(tan(d + e*x) + b/a)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) - 3*a**2*b**2*log(tan(d + e*x)**2 + 1)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + 6*a*b**3*e*x/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) - 2*a*b**3*log(tan(d + e*x) + b/a)*tan(d + e*x)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + a*b**3*log(tan(d + e*x)**2 + 1)*tan(d + e*x)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) - 2*b**4*log(tan(d + e*x) + b/a)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + b**4*log(tan(d + e*x)**2 + 1)/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e) + 2*b**4/(2*a**5*e*tan(d + e*x) + 2*a**4*b*e + 4*a**3*b**2*e*tan(d + e*x) + 4*a**2*b**3*e + 2*a*b**4*e*tan(d + e*x) + 2*b**5*e), True))","A",0
513,-2,0,0,0.000000," ","integrate((a+b*tan(e*x+d))/(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2)**2,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
514,0,0,0,0.000000," ","integrate((a+b*tan(e*x+d))*(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2)**(3/2),x)","\int \left(a + b \tan{\left(d + e x \right)}\right) \left(\left(a \tan{\left(d + e x \right)} + b\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(d + e*x))*((a*tan(d + e*x) + b)**2)**(3/2), x)","F",0
515,0,0,0,0.000000," ","integrate((b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2)**(1/2)*(a+b*tan(e*x+d)),x)","\int \left(a + b \tan{\left(d + e x \right)}\right) \sqrt{\left(a \tan{\left(d + e x \right)} + b\right)^{2}}\, dx"," ",0,"Integral((a + b*tan(d + e*x))*sqrt((a*tan(d + e*x) + b)**2), x)","F",0
516,0,0,0,0.000000," ","integrate((a+b*tan(e*x+d))/(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2)**(1/2),x)","\int \frac{a + b \tan{\left(d + e x \right)}}{\sqrt{\left(a \tan{\left(d + e x \right)} + b\right)^{2}}}\, dx"," ",0,"Integral((a + b*tan(d + e*x))/sqrt((a*tan(d + e*x) + b)**2), x)","F",0
517,0,0,0,0.000000," ","integrate((a+b*tan(e*x+d))/(b**2+2*a*b*tan(e*x+d)+a**2*tan(e*x+d)**2)**(3/2),x)","\int \frac{a + b \tan{\left(d + e x \right)}}{\left(\left(a \tan{\left(d + e x \right)} + b\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(d + e*x))/((a*tan(d + e*x) + b)**2)**(3/2), x)","F",0
518,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))*(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2)**2,x)","\int \left(a + b \sec{\left(d + e x \right)}\right) \left(a \sec{\left(d + e x \right)} + b\right)^{4}\, dx"," ",0,"Integral((a + b*sec(d + e*x))*(a*sec(d + e*x) + b)**4, x)","F",0
519,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))*(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2),x)","\int \left(a + b \sec{\left(d + e x \right)}\right) \left(a \sec{\left(d + e x \right)} + b\right)^{2}\, dx"," ",0,"Integral((a + b*sec(d + e*x))*(a*sec(d + e*x) + b)**2, x)","F",0
520,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2),x)","\int \frac{a + b \sec{\left(d + e x \right)}}{\left(a \sec{\left(d + e x \right)} + b\right)^{2}}\, dx"," ",0,"Integral((a + b*sec(d + e*x))/(a*sec(d + e*x) + b)**2, x)","F",0
521,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2)**2,x)","\int \frac{a + b \sec{\left(d + e x \right)}}{\left(a \sec{\left(d + e x \right)} + b\right)^{4}}\, dx"," ",0,"Integral((a + b*sec(d + e*x))/(a*sec(d + e*x) + b)**4, x)","F",0
522,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))*(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2)**(3/2),x)","\int \left(a + b \sec{\left(d + e x \right)}\right) \left(\left(a \sec{\left(d + e x \right)} + b\right)^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*sec(d + e*x))*((a*sec(d + e*x) + b)**2)**(3/2), x)","F",0
523,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))*(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2)**(1/2),x)","\int \left(a + b \sec{\left(d + e x \right)}\right) \sqrt{\left(a \sec{\left(d + e x \right)} + b\right)^{2}}\, dx"," ",0,"Integral((a + b*sec(d + e*x))*sqrt((a*sec(d + e*x) + b)**2), x)","F",0
524,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2)**(1/2),x)","\int \frac{a + b \sec{\left(d + e x \right)}}{\sqrt{\left(a \sec{\left(d + e x \right)} + b\right)^{2}}}\, dx"," ",0,"Integral((a + b*sec(d + e*x))/sqrt((a*sec(d + e*x) + b)**2), x)","F",0
525,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b**2+2*a*b*sec(e*x+d)+a**2*sec(e*x+d)**2)**(3/2),x)","\int \frac{a + b \sec{\left(d + e x \right)}}{\left(\left(a \sec{\left(d + e x \right)} + b\right)^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sec(d + e*x))/((a*sec(d + e*x) + b)**2)**(3/2), x)","F",0
526,1,8,0,0.076783," ","integrate((cos(x)-I*sin(x))/(cos(x)+I*sin(x)),x)","\frac{i e^{- 2 i x}}{2}"," ",0,"I*exp(-2*I*x)/2","A",0
527,1,10,0,0.075894," ","integrate((cos(x)+I*sin(x))/(cos(x)-I*sin(x)),x)","- \frac{i e^{2 i x}}{2}"," ",0,"-I*exp(2*I*x)/2","A",0
528,1,7,0,0.118549," ","integrate((cos(x)-sin(x))/(cos(x)+sin(x)),x)","\log{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}"," ",0,"log(sin(x) + cos(x))","A",0
529,1,371,0,0.877329," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x)","\begin{cases} \tilde{\infty} \left(B \log{\left(\sin{\left(x \right)} \right)} + C x\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{B \log{\left(\sin{\left(x \right)} \right)} + C x}{c} & \text{for}\: b = 0 \\\frac{B x \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i B x \cos{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i B \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i C x \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{C x \cos{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{C \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = - i c \\\frac{B x \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i B x \cos{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i B \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i C x \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{C x \cos{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{C \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = i c \\\frac{B b x}{b^{2} + c^{2}} + \frac{B c \log{\left(\cos{\left(x \right)} + \frac{c \sin{\left(x \right)}}{b} \right)}}{b^{2} + c^{2}} - \frac{C b \log{\left(\cos{\left(x \right)} + \frac{c \sin{\left(x \right)}}{b} \right)}}{b^{2} + c^{2}} + \frac{C c x}{b^{2} + c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(B*log(sin(x)) + C*x), Eq(b, 0) & Eq(c, 0)), ((B*log(sin(x)) + C*x)/c, Eq(b, 0)), (B*x*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*B*x*cos(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*B*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*C*x*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - C*x*cos(x)/(-2*I*c*sin(x) - 2*c*cos(x)) + C*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)), Eq(b, -I*c)), (B*x*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*B*x*cos(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*B*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*C*x*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) - C*x*cos(x)/(2*I*c*sin(x) - 2*c*cos(x)) + C*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)), Eq(b, I*c)), (B*b*x/(b**2 + c**2) + B*c*log(cos(x) + c*sin(x)/b)/(b**2 + c**2) - C*b*log(cos(x) + c*sin(x)/b)/(b**2 + c**2) + C*c*x/(b**2 + c**2), True))","A",0
530,-1,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,1,1042,0,38.588802," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x)","\begin{cases} \tilde{\infty} \left(A \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + B \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + C x\right) & \text{for}\: b = 0 \wedge c = 0 \\\frac{A \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + B \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + C x}{c} & \text{for}\: b = 0 \\\frac{2 A}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{B x \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i B x \cos{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i B \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{i C x \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{C x \cos{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{C \sin{\left(x \right)}}{- 2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = - i c \\\frac{2 A}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{B x \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i B x \cos{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i B \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{i C x \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} - \frac{C x \cos{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} + \frac{C \sin{\left(x \right)}}{2 i c \sin{\left(x \right)} - 2 c \cos{\left(x \right)}} & \text{for}\: b = i c \\- \frac{A b^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{A b^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{A c^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{A c^{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{B b x \sqrt{b^{2} + c^{2}}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{B c \sqrt{b^{2} + c^{2}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{B c \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{B c \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{C b \sqrt{b^{2} + c^{2}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{C b \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} - \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} - \frac{C b \sqrt{b^{2} + c^{2}} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{c}{b} + \frac{\sqrt{b^{2} + c^{2}}}{b} \right)}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} + \frac{C c x \sqrt{b^{2} + c^{2}}}{b^{2} \sqrt{b^{2} + c^{2}} + c^{2} \sqrt{b^{2} + c^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(A*log(tan(x/2)) - B*log(tan(x/2)**2 + 1) + B*log(tan(x/2)) + C*x), Eq(b, 0) & Eq(c, 0)), ((A*log(tan(x/2)) - B*log(tan(x/2)**2 + 1) + B*log(tan(x/2)) + C*x)/c, Eq(b, 0)), (2*A/(-2*I*c*sin(x) - 2*c*cos(x)) + B*x*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*B*x*cos(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*B*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - I*C*x*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)) - C*x*cos(x)/(-2*I*c*sin(x) - 2*c*cos(x)) + C*sin(x)/(-2*I*c*sin(x) - 2*c*cos(x)), Eq(b, -I*c)), (2*A/(2*I*c*sin(x) - 2*c*cos(x)) + B*x*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*B*x*cos(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*B*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) + I*C*x*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)) - C*x*cos(x)/(2*I*c*sin(x) - 2*c*cos(x)) + C*sin(x)/(2*I*c*sin(x) - 2*c*cos(x)), Eq(b, I*c)), (-A*b**2*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + A*b**2*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - A*c**2*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + A*c**2*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + B*b*x*sqrt(b**2 + c**2)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - B*c*sqrt(b**2 + c**2)*log(tan(x/2)**2 + 1)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + B*c*sqrt(b**2 + c**2)*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + B*c*sqrt(b**2 + c**2)*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + C*b*sqrt(b**2 + c**2)*log(tan(x/2)**2 + 1)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - C*b*sqrt(b**2 + c**2)*log(tan(x/2) - c/b - sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) - C*b*sqrt(b**2 + c**2)*log(tan(x/2) - c/b + sqrt(b**2 + c**2)/b)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)) + C*c*x*sqrt(b**2 + c**2)/(b**2*sqrt(b**2 + c**2) + c**2*sqrt(b**2 + c**2)), True))","A",0
533,-1,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,1,95,0,0.576180," ","integrate((A+B*cos(x))/(a+b*cos(x)+I*b*sin(x)),x)","\begin{cases} \frac{i B e^{- i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{2 A a - B b}{2 a^{2}} + \frac{2 A a + B a - B b}{2 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{x \left(2 A a - B b\right)}{2 a^{2}} - \frac{i \left(- 2 A a b + B a^{2} + B b^{2}\right) \log{\left(\frac{a}{b} + e^{i x} \right)}}{2 a^{2} b}"," ",0,"Piecewise((I*B*exp(-I*x)/(2*a), Ne(2*a, 0)), (x*(-(2*A*a - B*b)/(2*a**2) + (2*A*a + B*a - B*b)/(2*a**2)), True)) + x*(2*A*a - B*b)/(2*a**2) - I*(-2*A*a*b + B*a**2 + B*b**2)*log(a/b + exp(I*x))/(2*a**2*b)","A",0
539,1,75,0,0.577996," ","integrate((A+B*cos(x))/(a+b*cos(x)-I*b*sin(x)),x)","\frac{B x}{2 b} + \begin{cases} - \frac{i B e^{i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{B}{2 b} + \frac{B a + B b}{2 a b}\right) & \text{otherwise} \end{cases} + \frac{i \left(- 2 A a b + B a^{2} + B b^{2}\right) \log{\left(e^{i x} + \frac{b}{a} \right)}}{2 a^{2} b}"," ",0,"B*x/(2*b) + Piecewise((-I*B*exp(I*x)/(2*a), Ne(2*a, 0)), (x*(-B/(2*b) + (B*a + B*b)/(2*a*b)), True)) + I*(-2*A*a*b + B*a**2 + B*b**2)*log(exp(I*x) + b/a)/(2*a**2*b)","A",0
540,-1,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,1,104,0,0.798216," ","integrate((A+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x)","\begin{cases} - \frac{C e^{- i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{2 A a - i C b}{2 a^{2}} - \frac{i \left(2 i A a - C a + C b\right)}{2 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 2 A a + i C b\right)}{2 a^{2}} - \frac{\left(- 2 i A a b + C a^{2} - C b^{2}\right) \log{\left(\frac{a}{b} + e^{i x} \right)}}{2 a^{2} b}"," ",0,"Piecewise((-C*exp(-I*x)/(2*a), Ne(2*a, 0)), (x*(-(2*A*a - I*C*b)/(2*a**2) - I*(2*I*A*a - C*a + C*b)/(2*a**2)), True)) - x*(-2*A*a + I*C*b)/(2*a**2) - (-2*I*A*a*b + C*a**2 - C*b**2)*log(a/b + exp(I*x))/(2*a**2*b)","A",0
544,1,80,0,0.743984," ","integrate((A+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x)","\frac{i C x}{2 b} + \begin{cases} - \frac{C e^{i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{i C}{2 b} + \frac{i C a - i C b}{2 a b}\right) & \text{otherwise} \end{cases} - \frac{\left(2 i A a b + C a^{2} - C b^{2}\right) \log{\left(e^{i x} + \frac{b}{a} \right)}}{2 a^{2} b}"," ",0,"I*C*x/(2*b) + Piecewise((-C*exp(I*x)/(2*a), Ne(2*a, 0)), (x*(-I*C/(2*b) + (I*C*a - I*C*b)/(2*a*b)), True)) - (2*I*A*a*b + C*a**2 - C*b**2)*log(exp(I*x) + b/a)/(2*a**2*b)","A",0
545,-1,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,1,116,0,0.850256," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x)","\begin{cases} - \frac{\left(- i B + C\right) e^{- i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{- B b - i C b}{2 a^{2}} - \frac{i \left(i B a - i B b - C a + C b\right)}{2 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(B b + i C b\right)}{2 a^{2}} - \frac{i \left(B a^{2} + B b^{2} - i C a^{2} + i C b^{2}\right) \log{\left(\frac{a}{b} + e^{i x} \right)}}{2 a^{2} b}"," ",0,"Piecewise((-(-I*B + C)*exp(-I*x)/(2*a), Ne(2*a, 0)), (x*(-(-B*b - I*C*b)/(2*a**2) - I*(I*B*a - I*B*b - C*a + C*b)/(2*a**2)), True)) - x*(B*b + I*C*b)/(2*a**2) - I*(B*a**2 + B*b**2 - I*C*a**2 + I*C*b**2)*log(a/b + exp(I*x))/(2*a**2*b)","A",0
549,1,102,0,0.813090," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x)","\begin{cases} - \frac{\left(i B + C\right) e^{i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{B + i C}{2 b} + \frac{B a + B b + i C a - i C b}{2 a b}\right) & \text{otherwise} \end{cases} - \frac{x \left(- B - i C\right)}{2 b} + \frac{i \left(B a^{2} + B b^{2} + i C a^{2} - i C b^{2}\right) \log{\left(e^{i x} + \frac{b}{a} \right)}}{2 a^{2} b}"," ",0,"Piecewise((-(I*B + C)*exp(I*x)/(2*a), Ne(2*a, 0)), (x*(-(B + I*C)/(2*b) + (B*a + B*b + I*C*a - I*C*b)/(2*a*b)), True)) - x*(-B - I*C)/(2*b) + I*(B*a**2 + B*b**2 + I*C*a**2 - I*C*b**2)*log(exp(I*x) + b/a)/(2*a**2*b)","A",0
550,-1,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,1,138,0,1.373091," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x)","\begin{cases} - \frac{\left(- i B + C\right) e^{- i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{2 A a - B b - i C b}{2 a^{2}} - \frac{i \left(2 i A a + i B a - i B b - C a + C b\right)}{2 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 2 A a + B b + i C b\right)}{2 a^{2}} - \frac{i \left(- 2 A a b + B a^{2} + B b^{2} - i C a^{2} + i C b^{2}\right) \log{\left(\frac{a}{b} + e^{i x} \right)}}{2 a^{2} b}"," ",0,"Piecewise((-(-I*B + C)*exp(-I*x)/(2*a), Ne(2*a, 0)), (x*(-(2*A*a - B*b - I*C*b)/(2*a**2) - I*(2*I*A*a + I*B*a - I*B*b - C*a + C*b)/(2*a**2)), True)) - x*(-2*A*a + B*b + I*C*b)/(2*a**2) - I*(-2*A*a*b + B*a**2 + B*b**2 - I*C*a**2 + I*C*b**2)*log(a/b + exp(I*x))/(2*a**2*b)","A",0
554,1,109,0,1.271122," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x)","\begin{cases} - \frac{\left(i B + C\right) e^{i x}}{2 a} & \text{for}\: 2 a \neq 0 \\x \left(- \frac{B + i C}{2 b} + \frac{B a + B b + i C a - i C b}{2 a b}\right) & \text{otherwise} \end{cases} - \frac{x \left(- B - i C\right)}{2 b} + \frac{i \left(- 2 A a b + B a^{2} + B b^{2} + i C a^{2} - i C b^{2}\right) \log{\left(e^{i x} + \frac{b}{a} \right)}}{2 a^{2} b}"," ",0,"Piecewise((-(I*B + C)*exp(I*x)/(2*a), Ne(2*a, 0)), (x*(-(B + I*C)/(2*b) + (B*a + B*b + I*C*a - I*C*b)/(2*a*b)), True)) - x*(-B - I*C)/(2*b) + I*(-2*A*a*b + B*a**2 + B*b**2 + I*C*a**2 - I*C*b**2)*log(exp(I*x) + b/a)/(2*a**2*b)","A",0
555,-1,0,0,0.000000," ","integrate((b**2+c**2+a*b*cos(x)+a*c*sin(x))/(a+b*cos(x)+c*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))**(5/2)*(d+b*e*cos(x)+c*e*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))**(3/2)*(d+b*e*cos(x)+c*e*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))**(1/2)*(d+b*e*cos(x)+c*e*sin(x)),x)","\int \sqrt{a + b \cos{\left(x \right)} + c \sin{\left(x \right)}} \left(b e \cos{\left(x \right)} + c e \sin{\left(x \right)} + d\right)\, dx"," ",0,"Integral(sqrt(a + b*cos(x) + c*sin(x))*(b*e*cos(x) + c*e*sin(x) + d), x)","F",0
559,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))**(1/2),x)","\int \frac{b e \cos{\left(x \right)} + c e \sin{\left(x \right)} + d}{\sqrt{a + b \cos{\left(x \right)} + c \sin{\left(x \right)}}}\, dx"," ",0,"Integral((b*e*cos(x) + c*e*sin(x) + d)/sqrt(a + b*cos(x) + c*sin(x)), x)","F",0
560,-1,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,1,1110,0,29.516057," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \cos{\left(d \right)} + C \sin{\left(d \right)}\right)}{\sin{\left(d \right)}} & \text{for}\: a = 0 \wedge c = 0 \wedge e = 0 \\\frac{\frac{A \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{e} - \frac{B \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{e} + \frac{B \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{e} + C x}{c} & \text{for}\: a = 0 \\\frac{2 A}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} + \frac{2 B \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} - \frac{2 B \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - 1 \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} - \frac{B \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} + \frac{B \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} + \frac{C e x \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} - \frac{C e x}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} + \frac{2 C}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} - c e} & \text{for}\: a = - c \\- \frac{2 A}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} + \frac{2 B \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} + \frac{2 B \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} - \frac{B \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)} \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} - \frac{B \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} + \frac{C e x \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} + \frac{C e x}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} + \frac{2 C}{c e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + c e} & \text{for}\: a = c \\\frac{A x + \frac{B \sin{\left(d + e x \right)}}{e} - \frac{C \cos{\left(d + e x \right)}}{e}}{a} & \text{for}\: c = 0 \\\frac{x \left(A + B \cos{\left(d \right)} + C \sin{\left(d \right)}\right)}{a + c \sin{\left(d \right)}} & \text{for}\: e = 0 \\- \frac{A c \sqrt{- a^{2} + c^{2}} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} - \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} + \frac{A c \sqrt{- a^{2} + c^{2}} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} + \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} - \frac{B a^{2} \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{a^{2} c e - c^{3} e} + \frac{B a^{2} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} - \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} + \frac{B a^{2} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} + \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} + \frac{B c^{2} \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{a^{2} c e - c^{3} e} - \frac{B c^{2} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} - \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} - \frac{B c^{2} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} + \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} + \frac{C a^{2} e x}{a^{2} c e - c^{3} e} + \frac{C a \sqrt{- a^{2} + c^{2}} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} - \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} - \frac{C a \sqrt{- a^{2} + c^{2}} \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} + \frac{c}{a} + \frac{\sqrt{- a^{2} + c^{2}}}{a} \right)}}{a^{2} c e - c^{3} e} - \frac{C c^{2} e x}{a^{2} c e - c^{3} e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*cos(d) + C*sin(d))/sin(d), Eq(a, 0) & Eq(c, 0) & Eq(e, 0)), ((A*log(tan(d/2 + e*x/2))/e - B*log(tan(d/2 + e*x/2)**2 + 1)/e + B*log(tan(d/2 + e*x/2))/e + C*x)/c, Eq(a, 0)), (2*A/(c*e*tan(d/2 + e*x/2) - c*e) + 2*B*log(tan(d/2 + e*x/2) - 1)*tan(d/2 + e*x/2)/(c*e*tan(d/2 + e*x/2) - c*e) - 2*B*log(tan(d/2 + e*x/2) - 1)/(c*e*tan(d/2 + e*x/2) - c*e) - B*log(tan(d/2 + e*x/2)**2 + 1)*tan(d/2 + e*x/2)/(c*e*tan(d/2 + e*x/2) - c*e) + B*log(tan(d/2 + e*x/2)**2 + 1)/(c*e*tan(d/2 + e*x/2) - c*e) + C*e*x*tan(d/2 + e*x/2)/(c*e*tan(d/2 + e*x/2) - c*e) - C*e*x/(c*e*tan(d/2 + e*x/2) - c*e) + 2*C/(c*e*tan(d/2 + e*x/2) - c*e), Eq(a, -c)), (-2*A/(c*e*tan(d/2 + e*x/2) + c*e) + 2*B*log(tan(d/2 + e*x/2) + 1)*tan(d/2 + e*x/2)/(c*e*tan(d/2 + e*x/2) + c*e) + 2*B*log(tan(d/2 + e*x/2) + 1)/(c*e*tan(d/2 + e*x/2) + c*e) - B*log(tan(d/2 + e*x/2)**2 + 1)*tan(d/2 + e*x/2)/(c*e*tan(d/2 + e*x/2) + c*e) - B*log(tan(d/2 + e*x/2)**2 + 1)/(c*e*tan(d/2 + e*x/2) + c*e) + C*e*x*tan(d/2 + e*x/2)/(c*e*tan(d/2 + e*x/2) + c*e) + C*e*x/(c*e*tan(d/2 + e*x/2) + c*e) + 2*C/(c*e*tan(d/2 + e*x/2) + c*e), Eq(a, c)), ((A*x + B*sin(d + e*x)/e - C*cos(d + e*x)/e)/a, Eq(c, 0)), (x*(A + B*cos(d) + C*sin(d))/(a + c*sin(d)), Eq(e, 0)), (-A*c*sqrt(-a**2 + c**2)*log(tan(d/2 + e*x/2) + c/a - sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) + A*c*sqrt(-a**2 + c**2)*log(tan(d/2 + e*x/2) + c/a + sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) - B*a**2*log(tan(d/2 + e*x/2)**2 + 1)/(a**2*c*e - c**3*e) + B*a**2*log(tan(d/2 + e*x/2) + c/a - sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) + B*a**2*log(tan(d/2 + e*x/2) + c/a + sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) + B*c**2*log(tan(d/2 + e*x/2)**2 + 1)/(a**2*c*e - c**3*e) - B*c**2*log(tan(d/2 + e*x/2) + c/a - sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) - B*c**2*log(tan(d/2 + e*x/2) + c/a + sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) + C*a**2*e*x/(a**2*c*e - c**3*e) + C*a*sqrt(-a**2 + c**2)*log(tan(d/2 + e*x/2) + c/a - sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) - C*a*sqrt(-a**2 + c**2)*log(tan(d/2 + e*x/2) + c/a + sqrt(-a**2 + c**2)/a)/(a**2*c*e - c**3*e) - C*c**2*e*x/(a**2*c*e - c**3*e), True))","A",0
563,-1,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,1,190,0,3.355102," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))**3,x)","\begin{cases} a^{3} x - \frac{3 a^{2} b \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{3 a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{b^{3} \sin^{6}{\left(c + d x \right)}}{12 d} + \frac{b^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)} \cos{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x - 3*a**2*b*cos(c + d*x)**2/(2*d) + 3*a*b**2*x*sin(c + d*x)**4/8 + 3*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a*b**2*x*cos(c + d*x)**4/8 + 3*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + b**3*sin(c + d*x)**6/(12*d) + b**3*sin(c + d*x)**4*cos(c + d*x)**2/(4*d), Ne(d, 0)), (x*(a + b*sin(c)*cos(c))**3, True))","A",0
568,1,129,0,0.954776," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))**2,x)","\begin{cases} a^{2} x - \frac{a b \cos^{2}{\left(c + d x \right)}}{d} + \frac{b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)} \cos{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - a*b*cos(c + d*x)**2/d + b**2*x*sin(c + d*x)**4/8 + b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + b**2*x*cos(c + d*x)**4/8 + b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*sin(c)*cos(c))**2, True))","A",0
569,1,26,0,0.177508," ","integrate(a+b*cos(d*x+c)*sin(d*x+c),x)","a x + b \left(\begin{cases} - \frac{\cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \sin{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-cos(c + d*x)**2/(2*d), Ne(d, 0)), (x*sin(c)*cos(c), True))","A",0
570,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))**(3/2),x)","\int \left(a + b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*sin(c + d*x)*cos(c + d*x))**(3/2), x)","F",0
575,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x)*cos(c + d*x)), x)","F",0
576,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(c + d*x)*cos(c + d*x)), x)","F",0
577,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x)*cos(c + d*x))**(-3/2), x)","F",0
578,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate(x**3/(a+b*cos(x)*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate(x**2/(a+b*cos(x)*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,0,0,0,0.000000," ","integrate(x/(a+b*cos(x)*sin(x)),x)","\int \frac{x}{a + b \sin{\left(x \right)} \cos{\left(x \right)}}\, dx"," ",0,"Integral(x/(a + b*sin(x)*cos(x)), x)","F",0
582,0,0,0,0.000000," ","integrate(1/x/(a+b*cos(x)*sin(x)),x)","\int \frac{1}{x \left(a + b \sin{\left(x \right)} \cos{\left(x \right)}\right)}\, dx"," ",0,"Integral(1/(x*(a + b*sin(x)*cos(x))), x)","F",0
583,-1,0,0,0.000000," ","integrate((b*x)**(2-n)*sin(a*x)**n/(a*c*x*cos(a*x)-c*sin(a*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((b*x)**(2-n)*cos(a*x)**n/(c*cos(a*x)+a*c*x*sin(a*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,0,0,0,0.000000," ","integrate(sin(a*x)**6/x**4/(a*x*cos(a*x)-sin(a*x))**2,x)","\int \frac{\sin^{6}{\left(a x \right)}}{x^{4} \left(a x \cos{\left(a x \right)} - \sin{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(a*x)**6/(x**4*(a*x*cos(a*x) - sin(a*x))**2), x)","F",0
586,0,0,0,0.000000," ","integrate(sin(a*x)**5/x**3/(a*x*cos(a*x)-sin(a*x))**2,x)","\int \frac{\sin^{5}{\left(a x \right)}}{x^{3} \left(a x \cos{\left(a x \right)} - \sin{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(a*x)**5/(x**3*(a*x*cos(a*x) - sin(a*x))**2), x)","F",0
587,0,0,0,0.000000," ","integrate(sin(a*x)**4/x**2/(a*x*cos(a*x)-sin(a*x))**2,x)","\int \frac{\sin^{4}{\left(a x \right)}}{x^{2} \left(a x \cos{\left(a x \right)} - \sin{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(a*x)**4/(x**2*(a*x*cos(a*x) - sin(a*x))**2), x)","F",0
588,0,0,0,0.000000," ","integrate(sin(a*x)**3/x/(a*x*cos(a*x)-sin(a*x))**2,x)","\int \frac{\sin^{3}{\left(a x \right)}}{x \left(a x \cos{\left(a x \right)} - \sin{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(a*x)**3/(x*(a*x*cos(a*x) - sin(a*x))**2), x)","F",0
589,1,20,0,3.415277," ","integrate(sin(a*x)**2/(a*x*cos(a*x)-sin(a*x))**2,x)","\frac{\cos{\left(a x \right)}}{a^{2} x \cos{\left(a x \right)} - a \sin{\left(a x \right)}}"," ",0,"cos(a*x)/(a**2*x*cos(a*x) - a*sin(a*x))","A",0
590,1,19,0,3.482369," ","integrate(x*sin(a*x)/(a*x*cos(a*x)-sin(a*x))**2,x)","\frac{1}{a^{3} x \cos{\left(a x \right)} - a^{2} \sin{\left(a x \right)}}"," ",0,"1/(a**3*x*cos(a*x) - a**2*sin(a*x))","A",0
591,1,112,0,5.045546," ","integrate(x**2/(a*x*cos(a*x)-sin(a*x))**2,x)","- \frac{2 a x \tan{\left(\frac{a x}{2} \right)}}{a^{4} x \tan^{2}{\left(\frac{a x}{2} \right)} - a^{4} x + 2 a^{3} \tan{\left(\frac{a x}{2} \right)}} + \frac{\tan^{2}{\left(\frac{a x}{2} \right)}}{a^{4} x \tan^{2}{\left(\frac{a x}{2} \right)} - a^{4} x + 2 a^{3} \tan{\left(\frac{a x}{2} \right)}} - \frac{1}{a^{4} x \tan^{2}{\left(\frac{a x}{2} \right)} - a^{4} x + 2 a^{3} \tan{\left(\frac{a x}{2} \right)}}"," ",0,"-2*a*x*tan(a*x/2)/(a**4*x*tan(a*x/2)**2 - a**4*x + 2*a**3*tan(a*x/2)) + tan(a*x/2)**2/(a**4*x*tan(a*x/2)**2 - a**4*x + 2*a**3*tan(a*x/2)) - 1/(a**4*x*tan(a*x/2)**2 - a**4*x + 2*a**3*tan(a*x/2))","B",0
592,0,0,0,0.000000," ","integrate(x**3*csc(a*x)/(a*x*cos(a*x)-sin(a*x))**2,x)","\int \frac{x^{3} \csc{\left(a x \right)}}{\left(a x \cos{\left(a x \right)} - \sin{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**3*csc(a*x)/(a*x*cos(a*x) - sin(a*x))**2, x)","F",0
593,0,0,0,0.000000," ","integrate(x**4*csc(a*x)**2/(a*x*cos(a*x)-sin(a*x))**2,x)","\int \frac{x^{4} \csc^{2}{\left(a x \right)}}{\left(a x \cos{\left(a x \right)} - \sin{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**4*csc(a*x)**2/(a*x*cos(a*x) - sin(a*x))**2, x)","F",0
594,0,0,0,0.000000," ","integrate(cos(a*x)**6/x**4/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{\cos^{6}{\left(a x \right)}}{x^{4} \left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(a*x)**6/(x**4*(a*x*sin(a*x) + cos(a*x))**2), x)","F",0
595,0,0,0,0.000000," ","integrate(cos(a*x)**5/x**3/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{\cos^{5}{\left(a x \right)}}{x^{3} \left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(a*x)**5/(x**3*(a*x*sin(a*x) + cos(a*x))**2), x)","F",0
596,0,0,0,0.000000," ","integrate(cos(a*x)**4/x**2/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{\cos^{4}{\left(a x \right)}}{x^{2} \left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(a*x)**4/(x**2*(a*x*sin(a*x) + cos(a*x))**2), x)","F",0
597,0,0,0,0.000000," ","integrate(cos(a*x)**3/x/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{\cos^{3}{\left(a x \right)}}{x \left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(a*x)**3/(x*(a*x*sin(a*x) + cos(a*x))**2), x)","F",0
598,1,20,0,3.003053," ","integrate(cos(a*x)**2/(cos(a*x)+a*x*sin(a*x))**2,x)","\frac{\sin{\left(a x \right)}}{a^{2} x \sin{\left(a x \right)} + a \cos{\left(a x \right)}}"," ",0,"sin(a*x)/(a**2*x*sin(a*x) + a*cos(a*x))","A",0
599,1,20,0,3.007061," ","integrate(x*cos(a*x)/(cos(a*x)+a*x*sin(a*x))**2,x)","- \frac{1}{a^{3} x \sin{\left(a x \right)} + a^{2} \cos{\left(a x \right)}}"," ",0,"-1/(a**3*x*sin(a*x) + a**2*cos(a*x))","A",0
600,0,0,0,0.000000," ","integrate(x**2/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{x^{2}}{\left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**2/(a*x*sin(a*x) + cos(a*x))**2, x)","F",0
601,0,0,0,0.000000," ","integrate(x**3*sec(a*x)/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{x^{3} \sec{\left(a x \right)}}{\left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**3*sec(a*x)/(a*x*sin(a*x) + cos(a*x))**2, x)","F",0
602,0,0,0,0.000000," ","integrate(x**4*sec(a*x)**2/(cos(a*x)+a*x*sin(a*x))**2,x)","\int \frac{x^{4} \sec^{2}{\left(a x \right)}}{\left(a x \sin{\left(a x \right)} + \cos{\left(a x \right)}\right)^{2}}\, dx"," ",0,"Integral(x**4*sec(a*x)**2/(a*x*sin(a*x) + cos(a*x))**2, x)","F",0
603,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**4*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**3*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**2*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)**2*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)**3*(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**4*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**3*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**2*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)**2*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)**3*(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**4/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**3/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**2/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)**2/(c*tan(b*x+a)*tan(2*b*x+2*a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**4/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**3/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)**2/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)**2/(c*tan(b*x+a)*tan(2*b*x+2*a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.000000," ","integrate(cot(x)*csc(x)/sin(2*x)**(1/2),x)","\int \frac{\cot{\left(x \right)} \csc{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)}}}\, dx"," ",0,"Integral(cot(x)*csc(x)/sqrt(sin(2*x)), x)","F",0
634,0,0,0,0.000000," ","integrate(csc(x)**2*sec(x)/sin(2*x)**(1/2)/(-2+tan(x)),x)","\int \frac{\csc^{2}{\left(x \right)} \sec{\left(x \right)}}{\left(\tan{\left(x \right)} - 2\right) \sqrt{\sin{\left(2 x \right)}}}\, dx"," ",0,"Integral(csc(x)**2*sec(x)/((tan(x) - 2)*sqrt(sin(2*x))), x)","F",0
635,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)/(sin(x)**2-sin(2*x))/sin(2*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(cos(x)**3*cos(2*x)/(sin(x)**2-sin(2*x))/sin(2*x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,1,138,0,74.067112," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))**n*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\begin{cases} \frac{x \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right)}{a \sin{\left(c \right)} + b \sec{\left(c \right)}} & \text{for}\: d = 0 \wedge n = -1 \\x \left(a \sin{\left(c \right)} + b \sec{\left(c \right)}\right)^{n} \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right) & \text{for}\: d = 0 \\\frac{\log{\left(\sin{\left(c + d x \right)} + \frac{b \sec{\left(c + d x \right)}}{a} \right)}}{d} & \text{for}\: n = -1 \\\frac{a \left(a \sin{\left(c + d x \right)} + b \sec{\left(c + d x \right)}\right)^{n} \sin{\left(c + d x \right)}}{d n + d} + \frac{b \left(a \sin{\left(c + d x \right)} + b \sec{\left(c + d x \right)}\right)^{n} \sec{\left(c + d x \right)}}{d n + d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*cos(c) + b*tan(c)*sec(c))/(a*sin(c) + b*sec(c)), Eq(d, 0) & Eq(n, -1)), (x*(a*sin(c) + b*sec(c))**n*(a*cos(c) + b*tan(c)*sec(c)), Eq(d, 0)), (log(sin(c + d*x) + b*sec(c + d*x)/a)/d, Eq(n, -1)), (a*(a*sin(c + d*x) + b*sec(c + d*x))**n*sin(c + d*x)/(d*n + d) + b*(a*sin(c + d*x) + b*sec(c + d*x))**n*sec(c + d*x)/(d*n + d), True))","A",0
638,1,129,0,35.717851," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))**3*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\begin{cases} \frac{a^{4} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{a^{3} b \sin^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{2 d} + \frac{a b^{3} \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{d} + \frac{b^{4} \sec^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + b \sec{\left(c \right)}\right)^{3} \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sin(c + d*x)**4/(4*d) + a**3*b*sin(c + d*x)**3*sec(c + d*x)/d + 3*a**2*b**2*sin(c + d*x)**2*sec(c + d*x)**2/(2*d) + a*b**3*sin(c + d*x)*sec(c + d*x)**3/d + b**4*sec(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + b*sec(c))**3*(a*cos(c) + b*tan(c)*sec(c)), True))","A",0
639,1,100,0,11.160873," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))**2*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\begin{cases} \frac{a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} b \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{d} + \frac{a b^{2} \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{d} + \frac{b^{3} \sec^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + b \sec{\left(c \right)}\right)^{2} \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sin(c + d*x)**3/(3*d) + a**2*b*sin(c + d*x)**2*sec(c + d*x)/d + a*b**2*sin(c + d*x)*sec(c + d*x)**2/d + b**3*sec(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + b*sec(c))**2*(a*cos(c) + b*tan(c)*sec(c)), True))","A",0
640,1,73,0,3.457046," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x)","\begin{cases} \frac{a^{2} \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{a b \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}}{d} + \frac{b^{2} \sec^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + b \sec{\left(c \right)}\right) \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sin(c + d*x)**2/(2*d) + a*b*sin(c + d*x)*sec(c + d*x)/d + b**2*sec(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a*sin(c) + b*sec(c))*(a*cos(c) + b*tan(c)*sec(c)), True))","A",0
641,1,63,0,7.478663," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c)),x)","\begin{cases} x \tan{\left(c \right)} & \text{for}\: a = 0 \wedge d = 0 \\\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: a = 0 \\\frac{x \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right)}{a \sin{\left(c \right)} + b \sec{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\log{\left(\sin{\left(c + d x \right)} + \frac{b \sec{\left(c + d x \right)}}{a} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*tan(c), Eq(a, 0) & Eq(d, 0)), (log(tan(c + d*x)**2 + 1)/(2*d), Eq(a, 0)), (x*(a*cos(c) + b*tan(c)*sec(c))/(a*sin(c) + b*sec(c)), Eq(d, 0)), (log(sin(c + d*x) + b*sec(c + d*x)/a)/d, True))","A",0
642,1,49,0,21.182749," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{1}{a d \sin{\left(c + d x \right)} + b d \sec{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right)}{\left(a \sin{\left(c \right)} + b \sec{\left(c \right)}\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(a*d*sin(c + d*x) + b*d*sec(c + d*x)), Ne(d, 0)), (x*(a*cos(c) + b*tan(c)*sec(c))/(a*sin(c) + b*sec(c))**2, True))","A",0
643,1,80,0,44.089038," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{1}{2 a^{2} d \sin^{2}{\left(c + d x \right)} + 4 a b d \sin{\left(c + d x \right)} \sec{\left(c + d x \right)} + 2 b^{2} d \sec^{2}{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x \left(a \cos{\left(c \right)} + b \tan{\left(c \right)} \sec{\left(c \right)}\right)}{\left(a \sin{\left(c \right)} + b \sec{\left(c \right)}\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*a**2*d*sin(c + d*x)**2 + 4*a*b*d*sin(c + d*x)*sec(c + d*x) + 2*b**2*d*sec(c + d*x)**2), Ne(d, 0)), (x*(a*cos(c) + b*tan(c)*sec(c))/(a*sin(c) + b*sec(c))**3, True))","A",0
644,0,0,0,0.000000," ","integrate(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)","\int F{\left(c,d,\cos{\left(a + b x \right)},r,s \right)} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(F(c, d, cos(a + b*x), r, s)*sin(a + b*x), x)","F",0
645,0,0,0,0.000000," ","integrate(cos(b*x+a)*F(c,d,sin(b*x+a),r,s),x)","\int F{\left(c,d,\sin{\left(a + b x \right)},r,s \right)} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(F(c, d, sin(a + b*x), r, s)*cos(a + b*x), x)","F",0
646,0,0,0,0.000000," ","integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)**2,x)","\int F{\left(c,d,\tan{\left(a + b x \right)},r,s \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(F(c, d, tan(a + b*x), r, s)*sec(a + b*x)**2, x)","F",0
647,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*F(c,d,cot(b*x+a),r,s),x)","\int F{\left(c,d,\cot{\left(a + b x \right)},r,s \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(F(c, d, cot(a + b*x), r, s)*csc(a + b*x)**2, x)","F",0
648,1,17,0,0.326549," ","integrate(sin(x)/(a+b*cos(x)),x)","\begin{cases} - \frac{\log{\left(\frac{a}{b} + \cos{\left(x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\- \frac{\cos{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(a/b + cos(x))/b, Ne(b, 0)), (-cos(x)/a, True))","A",0
649,1,63,0,2.018240," ","integrate((a+b*cos(x))**n*sin(x),x)","\begin{cases} - \frac{\cos{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = -1 \\- a^{n} \cos{\left(x \right)} & \text{for}\: b = 0 \\- \frac{\log{\left(\frac{a}{b} + \cos{\left(x \right)} \right)}}{b} & \text{for}\: n = -1 \\- \frac{a \left(a + b \cos{\left(x \right)}\right)^{n}}{b n + b} - \frac{b \left(a + b \cos{\left(x \right)}\right)^{n} \cos{\left(x \right)}}{b n + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-cos(x)/a, Eq(b, 0) & Eq(n, -1)), (-a**n*cos(x), Eq(b, 0)), (-log(a/b + cos(x))/b, Eq(n, -1)), (-a*(a + b*cos(x))**n/(b*n + b) - b*(a + b*cos(x))**n*cos(x)/(b*n + b), True))","A",0
650,0,0,0,0.000000," ","integrate(sin(x)/(1+cos(x)**2)**(1/2),x)","\int \frac{\sin{\left(x \right)}}{\sqrt{\cos^{2}{\left(x \right)} + 1}}\, dx"," ",0,"Integral(sin(x)/sqrt(cos(x)**2 + 1), x)","F",0
651,1,5,0,0.436059," ","integrate(cos(cos(x))*sin(x),x)","- \sin{\left(\cos{\left(x \right)} \right)}"," ",0,"-sin(cos(x))","A",0
652,1,34,0,5.566828," ","integrate(cos(x)*cos(cos(x))*sin(x)*sin(cos(x)),x)","- \frac{\sin^{2}{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{4} - \frac{\sin{\left(\cos{\left(x \right)} \right)} \cos{\left(\cos{\left(x \right)} \right)}}{4} + \frac{\cos{\left(x \right)} \cos^{2}{\left(\cos{\left(x \right)} \right)}}{4}"," ",0,"-sin(cos(x))**2*cos(x)/4 - sin(cos(x))*cos(cos(x))/4 + cos(x)*cos(cos(x))**2/4","A",0
653,1,54,0,47.646106," ","integrate(cos(cos(x))*sin(x)*sin(6*cos(x))**2,x)","- \frac{71 \sin{\left(\cos{\left(x \right)} \right)} \sin^{2}{\left(6 \cos{\left(x \right)} \right)}}{143} - \frac{72 \sin{\left(\cos{\left(x \right)} \right)} \cos^{2}{\left(6 \cos{\left(x \right)} \right)}}{143} + \frac{12 \sin{\left(6 \cos{\left(x \right)} \right)} \cos{\left(\cos{\left(x \right)} \right)} \cos{\left(6 \cos{\left(x \right)} \right)}}{143}"," ",0,"-71*sin(cos(x))*sin(6*cos(x))**2/143 - 72*sin(cos(x))*cos(6*cos(x))**2/143 + 12*sin(6*cos(x))*cos(cos(x))*cos(6*cos(x))/143","B",0
654,1,46,0,11.654453," ","integrate(cos(x)**3*(a+b*cos(x)**2)**3*sin(x),x)","- \frac{a^{3} \cos^{4}{\left(x \right)}}{4} - \frac{a^{2} b \cos^{6}{\left(x \right)}}{2} - \frac{3 a b^{2} \cos^{8}{\left(x \right)}}{8} - \frac{b^{3} \cos^{10}{\left(x \right)}}{10}"," ",0,"-a**3*cos(x)**4/4 - a**2*b*cos(x)**6/2 - 3*a*b**2*cos(x)**8/8 - b**3*cos(x)**10/10","A",0
655,1,7,0,0.421956," ","integrate(sin(3*x)*sin(cos(3*x)),x)","\frac{\cos{\left(\cos{\left(3 x \right)} \right)}}{3}"," ",0,"cos(cos(3*x))/3","A",0
656,1,26,0,0.673526," ","integrate(exp(cos(1+3*x))*cos(1+3*x)*sin(1+3*x),x)","- \frac{e^{\cos{\left(3 x + 1 \right)}} \cos{\left(3 x + 1 \right)}}{3} + \frac{e^{\cos{\left(3 x + 1 \right)}}}{3}"," ",0,"-exp(cos(3*x + 1))*cos(3*x + 1)/3 + exp(cos(3*x + 1))/3","A",0
657,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)/(1-cos(x)**6)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
658,-1,0,0,0.000000," ","integrate(sin(x)**5/(1-5*cos(x))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
659,1,39,0,0.643493," ","integrate(exp(n*cos(b*x+a))*sin(b*x+a),x)","\begin{cases} x \sin{\left(a \right)} & \text{for}\: b = 0 \wedge n = 0 \\x e^{n \cos{\left(a \right)}} \sin{\left(a \right)} & \text{for}\: b = 0 \\- \frac{\cos{\left(a + b x \right)}}{b} & \text{for}\: n = 0 \\- \frac{e^{n \cos{\left(a + b x \right)}}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a), Eq(b, 0) & Eq(n, 0)), (x*exp(n*cos(a))*sin(a), Eq(b, 0)), (-cos(a + b*x)/b, Eq(n, 0)), (-exp(n*cos(a + b*x))/(b*n), True))","A",0
660,1,54,0,9.835605," ","integrate(exp(n*cos(b*c*x+a*c))*sin(c*(b*x+a)),x)","\begin{cases} x e^{n \cos{\left(a c \right)}} \sin{\left(a c \right)} & \text{for}\: b = 0 \\0 & \text{for}\: c = 0 \\\begin{cases} x \sin{\left(a c \right)} & \text{for}\: b = 0 \\0 & \text{for}\: c = 0 \\- \frac{\cos{\left(a c + b c x \right)}}{b c} & \text{otherwise} \end{cases} & \text{for}\: n = 0 \\- \frac{e^{n \cos{\left(a c + b c x \right)}}}{b c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(n*cos(a*c))*sin(a*c), Eq(b, 0)), (0, Eq(c, 0)), (Piecewise((x*sin(a*c), Eq(b, 0)), (0, Eq(c, 0)), (-cos(a*c + b*c*x)/(b*c), True)), Eq(n, 0)), (-exp(n*cos(a*c + b*c*x))/(b*c*n), True))","A",0
661,1,54,0,2.225592," ","integrate(exp(n*cos(c*(b*x+a)))*sin(b*c*x+a*c),x)","\begin{cases} 0 & \text{for}\: c = 0 \wedge \left(b = 0 \vee c = 0\right) \wedge \left(c = 0 \vee n = 0\right) \\x e^{n \cos{\left(a c \right)}} \sin{\left(a c \right)} & \text{for}\: b = 0 \\- \frac{\cos{\left(a c + b c x \right)}}{b c} & \text{for}\: n = 0 \\- \frac{e^{n \cos{\left(a c + b c x \right)}}}{b c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0, Eq(c, 0) & (Eq(b, 0) | Eq(c, 0)) & (Eq(c, 0) | Eq(n, 0))), (x*exp(n*cos(a*c))*sin(a*c), Eq(b, 0)), (-cos(a*c + b*c*x)/(b*c), Eq(n, 0)), (-exp(n*cos(a*c + b*c*x))/(b*c*n), True))","A",0
662,0,0,0,0.000000," ","integrate(exp(n*cos(b*x+a))*tan(b*x+a),x)","\int e^{n \cos{\left(a + b x \right)}} \tan{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(n*cos(a + b*x))*tan(a + b*x), x)","F",0
663,0,0,0,0.000000," ","integrate(exp(n*cos(b*c*x+a*c))*tan(c*(b*x+a)),x)","\int e^{n \cos{\left(a c + b c x \right)}} \tan{\left(a c + b c x \right)}\, dx"," ",0,"Integral(exp(n*cos(a*c + b*c*x))*tan(a*c + b*c*x), x)","F",0
664,0,0,0,0.000000," ","integrate(exp(n*cos(c*(b*x+a)))*tan(b*c*x+a*c),x)","\int e^{n \cos{\left(a c + b c x \right)}} \tan{\left(a c + b c x \right)}\, dx"," ",0,"Integral(exp(n*cos(a*c + b*c*x))*tan(a*c + b*c*x), x)","F",0
665,1,14,0,0.318272," ","integrate(cos(x)/(a+b*sin(x)),x)","\begin{cases} \frac{\log{\left(\frac{a}{b} + \sin{\left(x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{\sin{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(a/b + sin(x))/b, Ne(b, 0)), (sin(x)/a, True))","A",0
666,1,56,0,1.876573," ","integrate(cos(x)*(a+b*sin(x))**n,x)","\begin{cases} \frac{\sin{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = -1 \\a^{n} \sin{\left(x \right)} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + \sin{\left(x \right)} \right)}}{b} & \text{for}\: n = -1 \\\frac{a \left(a + b \sin{\left(x \right)}\right)^{n}}{b n + b} + \frac{b \left(a + b \sin{\left(x \right)}\right)^{n} \sin{\left(x \right)}}{b n + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(x)/a, Eq(b, 0) & Eq(n, -1)), (a**n*sin(x), Eq(b, 0)), (log(a/b + sin(x))/b, Eq(n, -1)), (a*(a + b*sin(x))**n/(b*n + b) + b*(a + b*sin(x))**n*sin(x)/(b*n + b), True))","A",0
667,0,0,0,0.000000," ","integrate(cos(x)/(1+sin(x)**2)**(1/2),x)","\int \frac{\cos{\left(x \right)}}{\sqrt{\sin^{2}{\left(x \right)} + 1}}\, dx"," ",0,"Integral(cos(x)/sqrt(sin(x)**2 + 1), x)","F",0
668,0,0,0,0.000000," ","integrate(cos(x)/(4-sin(x)**2)**(1/2),x)","\int \frac{\cos{\left(x \right)}}{\sqrt{- \left(\sin{\left(x \right)} - 2\right) \left(\sin{\left(x \right)} + 2\right)}}\, dx"," ",0,"Integral(cos(x)/sqrt(-(sin(x) - 2)*(sin(x) + 2)), x)","F",0
669,0,0,0,0.000000," ","integrate(cos(3*x)/(4-sin(3*x)**2)**(1/2),x)","\int \frac{\cos{\left(3 x \right)}}{\sqrt{- \left(\sin{\left(3 x \right)} - 2\right) \left(\sin{\left(3 x \right)} + 2\right)}}\, dx"," ",0,"Integral(cos(3*x)/sqrt(-(sin(3*x) - 2)*(sin(3*x) + 2)), x)","F",0
670,0,0,0,0.000000," ","integrate(cos(x)*(1+csc(x))**(1/2),x)","\int \sqrt{\csc{\left(x \right)} + 1} \cos{\left(x \right)}\, dx"," ",0,"Integral(sqrt(csc(x) + 1)*cos(x), x)","F",0
671,0,0,0,0.000000," ","integrate(cos(x)*(4-sin(x)**2)**(1/2),x)","\int \sqrt{- \left(\sin{\left(x \right)} - 2\right) \left(\sin{\left(x \right)} + 2\right)} \cos{\left(x \right)}\, dx"," ",0,"Integral(sqrt(-(sin(x) - 2)*(sin(x) + 2))*cos(x), x)","F",0
672,1,27,0,0.728652," ","integrate(cos(x)*sin(x)*(1+sin(x)**2)**(1/2),x)","\frac{\sqrt{\sin^{2}{\left(x \right)} + 1} \sin^{2}{\left(x \right)}}{3} + \frac{\sqrt{\sin^{2}{\left(x \right)} + 1}}{3}"," ",0,"sqrt(sin(x)**2 + 1)*sin(x)**2/3 + sqrt(sin(x)**2 + 1)/3","B",0
673,0,0,0,0.000000," ","integrate(cos(x)/(2*sin(x)+sin(x)**2)**(1/2),x)","\int \frac{\cos{\left(x \right)}}{\sqrt{\left(\sin{\left(x \right)} + 2\right) \sin{\left(x \right)}}}\, dx"," ",0,"Integral(cos(x)/sqrt((sin(x) + 2)*sin(x)), x)","F",0
674,1,3,0,0.411531," ","integrate(cos(x)*cos(sin(x)),x)","\sin{\left(\sin{\left(x \right)} \right)}"," ",0,"sin(sin(x))","A",0
675,1,5,0,8.851658," ","integrate(cos(x)*cos(sin(x))*cos(sin(sin(x))),x)","\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}"," ",0,"sin(sin(sin(x)))","A",0
676,1,10,0,1.330207," ","integrate(cos(x)*sec(sin(x)),x)","\log{\left(\tan{\left(\sin{\left(x \right)} \right)} + \sec{\left(\sin{\left(x \right)} \right)} \right)}"," ",0,"log(tan(sin(x)) + sec(sin(x)))","A",0
677,1,44,0,11.378811," ","integrate(cos(x)*sin(x)**3*(a+b*sin(x)**2)**3,x)","\frac{a^{3} \sin^{4}{\left(x \right)}}{4} + \frac{a^{2} b \sin^{6}{\left(x \right)}}{2} + \frac{3 a b^{2} \sin^{8}{\left(x \right)}}{8} + \frac{b^{3} \sin^{10}{\left(x \right)}}{10}"," ",0,"a**3*sin(x)**4/4 + a**2*b*sin(x)**6/2 + 3*a*b**2*sin(x)**8/8 + b**3*sin(x)**10/10","A",0
678,1,12,0,0.636355," ","integrate(exp(sin(x))*cos(x)*sin(x),x)","e^{\sin{\left(x \right)}} \sin{\left(x \right)} - e^{\sin{\left(x \right)}}"," ",0,"exp(sin(x))*sin(x) - exp(sin(x))","A",0
679,1,36,0,2.068726," ","integrate(cos(x)**3/(sin(x)**3)**(1/2),x)","- \frac{8 \sin^{3}{\left(x \right)}}{3 \sqrt{\sin^{3}{\left(x \right)}}} - \frac{2 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\sqrt{\sin^{3}{\left(x \right)}}}"," ",0,"-8*sin(x)**3/(3*sqrt(sin(x)**3)) - 2*sin(x)*cos(x)**2/sqrt(sin(x)**3)","A",0
680,1,8,0,0.461083," ","integrate(exp(sin(x)**(1/2))*cos(x)/sin(x)**(1/2),x)","2 e^{\sqrt{\sin{\left(x \right)}}}"," ",0,"2*exp(sqrt(sin(x)))","A",0
681,1,7,0,0.539617," ","integrate(exp(4+sin(x))*cos(x),x)","e^{4} e^{\sin{\left(x \right)}}"," ",0,"exp(4)*exp(sin(x))","A",0
682,-1,0,0,0.000000," ","integrate(exp(cos(x)*sin(x))*cos(2*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
683,0,0,0,0.000000," ","integrate(exp(cos(1/2*x)*sin(1/2*x))*cos(x),x)","\int e^{\sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)}} \cos{\left(x \right)}\, dx"," ",0,"Integral(exp(sin(x/2)*cos(x/2))*cos(x), x)","F",0
684,1,36,0,0.425036," ","integrate(exp(n*sin(b*x+a))*cos(b*x+a),x)","\begin{cases} x \cos{\left(a \right)} & \text{for}\: b = 0 \wedge n = 0 \\x e^{n \sin{\left(a \right)}} \cos{\left(a \right)} & \text{for}\: b = 0 \\\frac{\sin{\left(a + b x \right)}}{b} & \text{for}\: n = 0 \\\frac{e^{n \sin{\left(a + b x \right)}}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a), Eq(b, 0) & Eq(n, 0)), (x*exp(n*sin(a))*cos(a), Eq(b, 0)), (sin(a + b*x)/b, Eq(n, 0)), (exp(n*sin(a + b*x))/(b*n), True))","A",0
685,1,51,0,9.316363," ","integrate(exp(n*sin(b*c*x+a*c))*cos(c*(b*x+a)),x)","\begin{cases} x e^{n \sin{\left(a c \right)}} \cos{\left(a c \right)} & \text{for}\: b = 0 \\x & \text{for}\: c = 0 \\\begin{cases} x \cos{\left(a c \right)} & \text{for}\: b = 0 \\x & \text{for}\: c = 0 \\\frac{\sin{\left(a c + b c x \right)}}{b c} & \text{otherwise} \end{cases} & \text{for}\: n = 0 \\\frac{e^{n \sin{\left(a c + b c x \right)}}}{b c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(n*sin(a*c))*cos(a*c), Eq(b, 0)), (x, Eq(c, 0)), (Piecewise((x*cos(a*c), Eq(b, 0)), (x, Eq(c, 0)), (sin(a*c + b*c*x)/(b*c), True)), Eq(n, 0)), (exp(n*sin(a*c + b*c*x))/(b*c*n), True))","A",0
686,1,51,0,2.273970," ","integrate(exp(n*sin(c*(b*x+a)))*cos(b*c*x+a*c),x)","\begin{cases} x & \text{for}\: c = 0 \wedge \left(b = 0 \vee c = 0\right) \wedge \left(c = 0 \vee n = 0\right) \\x e^{n \sin{\left(a c \right)}} \cos{\left(a c \right)} & \text{for}\: b = 0 \\\frac{\sin{\left(a c + b c x \right)}}{b c} & \text{for}\: n = 0 \\\frac{e^{n \sin{\left(a c + b c x \right)}}}{b c n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x, Eq(c, 0) & (Eq(b, 0) | Eq(c, 0)) & (Eq(c, 0) | Eq(n, 0))), (x*exp(n*sin(a*c))*cos(a*c), Eq(b, 0)), (sin(a*c + b*c*x)/(b*c), Eq(n, 0)), (exp(n*sin(a*c + b*c*x))/(b*c*n), True))","A",0
687,0,0,0,0.000000," ","integrate(exp(n*sin(b*x+a))*cot(b*x+a),x)","\int e^{n \sin{\left(a + b x \right)}} \cot{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(n*sin(a + b*x))*cot(a + b*x), x)","F",0
688,0,0,0,0.000000," ","integrate(exp(n*sin(b*c*x+a*c))*cot(c*(b*x+a)),x)","\int e^{n \sin{\left(a c + b c x \right)}} \cot{\left(a c + b c x \right)}\, dx"," ",0,"Integral(exp(n*sin(a*c + b*c*x))*cot(a*c + b*c*x), x)","F",0
689,0,0,0,0.000000," ","integrate(exp(n*sin(c*(b*x+a)))*cot(b*c*x+a*c),x)","\int e^{n \sin{\left(a c + b c x \right)}} \cot{\left(a c + b c x \right)}\, dx"," ",0,"Integral(exp(n*sin(a*c + b*c*x))*cot(a*c + b*c*x), x)","F",0
690,0,0,0,0.000000," ","integrate(sec(x)**2/(a+b*tan(x)),x)","\int \frac{\sec^{2}{\left(x \right)}}{a + b \tan{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**2/(a + b*tan(x)), x)","F",0
691,0,0,0,0.000000," ","integrate(sec(x)**2/(1-tan(x)**2),x)","- \int \frac{\sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} - 1}\, dx"," ",0,"-Integral(sec(x)**2/(tan(x)**2 - 1), x)","F",0
692,0,0,0,0.000000," ","integrate(sec(x)**2/(9+tan(x)**2),x)","\int \frac{\sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 9}\, dx"," ",0,"Integral(sec(x)**2/(tan(x)**2 + 9), x)","F",0
693,0,0,0,0.000000," ","integrate(sec(x)**2*(a+b*tan(x))**n,x)","\int \left(a + b \tan{\left(x \right)}\right)^{n} \sec^{2}{\left(x \right)}\, dx"," ",0,"Integral((a + b*tan(x))**n*sec(x)**2, x)","F",0
694,1,27,0,0.742766," ","integrate(sec(x)**2*(1+1/(1+tan(x)**2)),x)","\frac{x \sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{\tan{\left(x \right)} \sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}"," ",0,"x*sec(x)**2/(tan(x)**2 + 1) + tan(x)*sec(x)**2/(tan(x)**2 + 1)","B",0
695,1,27,0,0.736457," ","integrate(sec(x)**2*(2+tan(x)**2)/(1+tan(x)**2),x)","\frac{x \sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + \frac{\tan{\left(x \right)} \sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}"," ",0,"x*sec(x)**2/(tan(x)**2 + 1) + tan(x)*sec(x)**2/(tan(x)**2 + 1)","B",0
696,0,0,0,0.000000," ","integrate(sec(x)**2/(2+2*tan(x)+tan(x)**2),x)","\int \frac{\sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 2 \tan{\left(x \right)} + 2}\, dx"," ",0,"Integral(sec(x)**2/(tan(x)**2 + 2*tan(x) + 2), x)","F",0
697,0,0,0,0.000000," ","integrate(sec(x)**2/(tan(x)**2+tan(x)**3),x)","\int \frac{\sec^{2}{\left(x \right)}}{\left(\tan{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**2/((tan(x) + 1)*tan(x)**2), x)","F",0
698,0,0,0,0.000000," ","integrate(sec(x)**2/(-tan(x)**2+tan(x)**3),x)","\int \frac{\sec^{2}{\left(x \right)}}{\left(\tan{\left(x \right)} - 1\right) \tan^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**2/((tan(x) - 1)*tan(x)**2), x)","F",0
699,0,0,0,0.000000," ","integrate(sec(x)**2/(3-4*tan(x)**3),x)","- \int \frac{\sec^{2}{\left(x \right)}}{4 \tan^{3}{\left(x \right)} - 3}\, dx"," ",0,"-Integral(sec(x)**2/(4*tan(x)**3 - 3), x)","F",0
700,0,0,0,0.000000," ","integrate(sec(x)**2/(11-5*tan(x)+5*tan(x)**2),x)","\int \frac{\sec^{2}{\left(x \right)}}{5 \tan^{2}{\left(x \right)} - 5 \tan{\left(x \right)} + 11}\, dx"," ",0,"Integral(sec(x)**2/(5*tan(x)**2 - 5*tan(x) + 11), x)","F",0
701,1,29,0,4.907111," ","integrate(sec(x)**2*(a+b*tan(x))/(c+d*tan(x)),x)","\frac{b \tan{\left(x \right)}}{d} + \frac{\left(a d - b c\right) \left(\begin{cases} \frac{\tan{\left(x \right)}}{c} & \text{for}\: d = 0 \\\frac{\log{\left(c + d \tan{\left(x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)}{d}"," ",0,"b*tan(x)/d + (a*d - b*c)*Piecewise((tan(x)/c, Eq(d, 0)), (log(c + d*tan(x))/d, True))/d","A",0
702,1,56,0,7.627782," ","integrate(sec(x)**2*(a+b*tan(x))**2/(c+d*tan(x)),x)","\frac{b^{2} \tan^{2}{\left(x \right)}}{2 d} + \frac{\left(a d - b c\right)^{2} \left(\begin{cases} \frac{\tan{\left(x \right)}}{c} & \text{for}\: d = 0 \\\frac{\log{\left(c + d \tan{\left(x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{\left(2 a b d - b^{2} c\right) \tan{\left(x \right)}}{d^{2}}"," ",0,"b**2*tan(x)**2/(2*d) + (a*d - b*c)**2*Piecewise((tan(x)/c, Eq(d, 0)), (log(c + d*tan(x))/d, True))/d**2 + (2*a*b*d - b**2*c)*tan(x)/d**2","A",0
703,1,95,0,10.567462," ","integrate(sec(x)**2*(a+b*tan(x))**3/(c+d*tan(x)),x)","\frac{b^{3} \tan^{3}{\left(x \right)}}{3 d} + \frac{\left(3 a b^{2} d - b^{3} c\right) \tan^{2}{\left(x \right)}}{2 d^{2}} + \frac{\left(a d - b c\right)^{3} \left(\begin{cases} \frac{\tan{\left(x \right)}}{c} & \text{for}\: d = 0 \\\frac{\log{\left(c + d \tan{\left(x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{\left(3 a^{2} b d^{2} - 3 a b^{2} c d + b^{3} c^{2}\right) \tan{\left(x \right)}}{d^{3}}"," ",0,"b**3*tan(x)**3/(3*d) + (3*a*b**2*d - b**3*c)*tan(x)**2/(2*d**2) + (a*d - b*c)**3*Piecewise((tan(x)/c, Eq(d, 0)), (log(c + d*tan(x))/d, True))/d**3 + (3*a**2*b*d**2 - 3*a*b**2*c*d + b**3*c**2)*tan(x)/d**3","A",0
704,-1,0,0,0.000000," ","integrate(sec(x)**2*tan(x)**2/(2+tan(x)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,1,27,0,19.284267," ","integrate(sec(x)**2*tan(x)**6*(1+tan(x)**2)**3,x)","\frac{\tan^{13}{\left(x \right)}}{13} + \frac{3 \tan^{11}{\left(x \right)}}{11} + \frac{\tan^{9}{\left(x \right)}}{3} + \frac{\tan^{7}{\left(x \right)}}{7}"," ",0,"tan(x)**13/13 + 3*tan(x)**11/11 + tan(x)**9/3 + tan(x)**7/7","A",0
706,1,41,0,9.251922," ","integrate(sec(x)**2*(2+tan(x)**2)/(1+tan(x)**3),x)","\frac{2 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\tan{\left(x \right)} - \frac{1}{2}\right)}{3} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3} + \log{\left(\tan{\left(x \right)} + 1 \right)}"," ",0,"2*sqrt(3)*(atan(2*sqrt(3)*(tan(x) - 1/2)/3) + pi*floor((x - pi/2)/pi))/3 + log(tan(x) + 1)","A",0
707,1,3,0,5.384194," ","integrate((1+cos(x)**2)*sec(x)**2,x)","x + \tan{\left(x \right)}"," ",0,"x + tan(x)","A",0
708,0,0,0,0.000000," ","integrate(sec(x)**2/(1+sec(x)**2-3*tan(x)),x)","\int \frac{\sec^{2}{\left(x \right)}}{- 3 \tan{\left(x \right)} + \sec^{2}{\left(x \right)} + 1}\, dx"," ",0,"Integral(sec(x)**2/(-3*tan(x) + sec(x)**2 + 1), x)","F",0
709,0,0,0,0.000000," ","integrate(sec(x)**2/(4-sec(x)**2)**(1/2),x)","\int \frac{\sec^{2}{\left(x \right)}}{\sqrt{- \left(\sec{\left(x \right)} - 2\right) \left(\sec{\left(x \right)} + 2\right)}}\, dx"," ",0,"Integral(sec(x)**2/sqrt(-(sec(x) - 2)*(sec(x) + 2)), x)","F",0
710,0,0,0,0.000000," ","integrate(sec(x)**2/(1-4*tan(x)**2)**(1/2),x)","\int \frac{\sec^{2}{\left(x \right)}}{\sqrt{- \left(2 \tan{\left(x \right)} - 1\right) \left(2 \tan{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(x)**2/sqrt(-(2*tan(x) - 1)*(2*tan(x) + 1)), x)","F",0
711,0,0,0,0.000000," ","integrate(sec(x)**2/(-4+tan(x)**2)**(1/2),x)","\int \frac{\sec^{2}{\left(x \right)}}{\sqrt{\left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} + 2\right)}}\, dx"," ",0,"Integral(sec(x)**2/sqrt((tan(x) - 2)*(tan(x) + 2)), x)","F",0
712,0,0,0,0.000000," ","integrate(sec(x)**2*(1-cot(x)**2)**(1/2),x)","\int \sqrt{- \left(\cot{\left(x \right)} - 1\right) \left(\cot{\left(x \right)} + 1\right)} \sec^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(-(cot(x) - 1)*(cot(x) + 1))*sec(x)**2, x)","F",0
713,0,0,0,0.000000," ","integrate(sec(x)**2*(1-tan(x)**2)**(1/2),x)","\int \sqrt{- \left(\tan{\left(x \right)} - 1\right) \left(\tan{\left(x \right)} + 1\right)} \sec^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(-(tan(x) - 1)*(tan(x) + 1))*sec(x)**2, x)","F",0
714,1,3,0,0.951845," ","integrate(exp(tan(x))*sec(x)**2,x)","e^{\tan{\left(x \right)}}"," ",0,"exp(tan(x))","A",0
715,1,19,0,6.969234," ","integrate(sec(x)**4*(-1+sec(x)**2)**2*tan(x),x)","\frac{\sec^{8}{\left(x \right)}}{8} - \frac{\sec^{6}{\left(x \right)}}{3} + \frac{\sec^{4}{\left(x \right)}}{4}"," ",0,"sec(x)**8/8 - sec(x)**6/3 + sec(x)**4/4","A",0
716,0,0,0,0.000000," ","integrate(csc(x)**2/(a+b*cot(x)),x)","\int \frac{\csc^{2}{\left(x \right)}}{a + b \cot{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**2/(a + b*cot(x)), x)","F",0
717,0,0,0,0.000000," ","integrate((a+b*cot(x))**n*csc(x)**2,x)","\int \left(a + b \cot{\left(x \right)}\right)^{n} \csc^{2}{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x))**n*csc(x)**2, x)","F",0
718,1,3,0,4.214137," ","integrate(csc(x)**2*(1+sin(x)**2),x)","x - \cot{\left(x \right)}"," ",0,"x - cot(x)","A",0
719,1,27,0,0.698511," ","integrate((1+1/(1+cot(x)**2))*csc(x)**2,x)","\frac{x \csc^{2}{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} - \frac{\cot{\left(x \right)} \csc^{2}{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}"," ",0,"x*csc(x)**2/(cot(x)**2 + 1) - cot(x)*csc(x)**2/(cot(x)**2 + 1)","B",0
720,1,31,0,26.515227," ","integrate((a+b*cot(x))*csc(x)**2/(c+d*cot(x)),x)","- \frac{b \cot{\left(x \right)}}{d} - \frac{\left(a d - b c\right) \left(\begin{cases} \frac{\cot{\left(x \right)}}{c} & \text{for}\: d = 0 \\\frac{\log{\left(c + d \cot{\left(x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)}{d}"," ",0,"-b*cot(x)/d - (a*d - b*c)*Piecewise((cot(x)/c, Eq(d, 0)), (log(c + d*cot(x))/d, True))/d","A",0
721,1,58,0,55.638904," ","integrate((a+b*cot(x))**2*csc(x)**2/(c+d*cot(x)),x)","- \frac{b^{2} \cot^{2}{\left(x \right)}}{2 d} - \frac{\left(a d - b c\right)^{2} \left(\begin{cases} \frac{\cot{\left(x \right)}}{c} & \text{for}\: d = 0 \\\frac{\log{\left(c + d \cot{\left(x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{\left(2 a b d - b^{2} c\right) \cot{\left(x \right)}}{d^{2}}"," ",0,"-b**2*cot(x)**2/(2*d) - (a*d - b*c)**2*Piecewise((cot(x)/c, Eq(d, 0)), (log(c + d*cot(x))/d, True))/d**2 - (2*a*b*d - b**2*c)*cot(x)/d**2","A",0
722,1,97,0,69.993322," ","integrate((a+b*cot(x))**3*csc(x)**2/(c+d*cot(x)),x)","- \frac{b^{3} \cot^{3}{\left(x \right)}}{3 d} - \frac{\left(3 a b^{2} d - b^{3} c\right) \cot^{2}{\left(x \right)}}{2 d^{2}} - \frac{\left(a d - b c\right)^{3} \left(\begin{cases} \frac{\cot{\left(x \right)}}{c} & \text{for}\: d = 0 \\\frac{\log{\left(c + d \cot{\left(x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{\left(3 a^{2} b d^{2} - 3 a b^{2} c d + b^{3} c^{2}\right) \cot{\left(x \right)}}{d^{3}}"," ",0,"-b**3*cot(x)**3/(3*d) - (3*a*b**2*d - b**3*c)*cot(x)**2/(2*d**2) - (a*d - b*c)**3*Piecewise((cot(x)/c, Eq(d, 0)), (log(c + d*cot(x))/d, True))/d**3 - (3*a**2*b*d**2 - 3*a*b**2*c*d + b**3*c**2)*cot(x)/d**3","A",0
723,1,5,0,18.865222," ","integrate(csc(x)**2/exp(cot(x)),x)","e^{- \cot{\left(x \right)}}"," ",0,"exp(-cot(x))","A",0
724,1,14,0,0.463179," ","integrate(sec(x)*tan(x)/(a+b*sec(x)),x)","\begin{cases} \frac{\log{\left(\frac{a}{b} + \sec{\left(x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{\sec{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(a/b + sec(x))/b, Ne(b, 0)), (sec(x)/a, True))","A",0
725,1,3,0,0.208893," ","integrate(sec(x)*tan(x)/(1+sec(x)**2),x)","\operatorname{atan}{\left(\sec{\left(x \right)} \right)}"," ",0,"atan(sec(x))","A",0
726,1,8,0,0.232526," ","integrate(sec(x)*tan(x)/(9+4*sec(x)**2),x)","\frac{\operatorname{atan}{\left(\frac{2 \sec{\left(x \right)}}{3} \right)}}{6}"," ",0,"atan(2*sec(x)/3)/6","A",0
727,1,15,0,0.216097," ","integrate(sec(x)*tan(x)/(sec(x)+sec(x)**2),x)","\frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2} - \log{\left(\sec{\left(x \right)} + 1 \right)}"," ",0,"log(tan(x)**2 + 1)/2 - log(sec(x) + 1)","B",0
728,1,5,0,0.726577," ","integrate(sec(x)*tan(x)/(4+sec(x)**2)**(1/2),x)","\operatorname{asinh}{\left(\frac{\sec{\left(x \right)}}{2} \right)}"," ",0,"asinh(sec(x)/2)","A",0
729,0,0,0,0.000000," ","integrate(sec(x)*tan(x)/(1+cos(x)**2)**(1/2),x)","\int \frac{\tan{\left(x \right)} \sec{\left(x \right)}}{\sqrt{\cos^{2}{\left(x \right)} + 1}}\, dx"," ",0,"Integral(tan(x)*sec(x)/sqrt(cos(x)**2 + 1), x)","F",0
730,1,3,0,0.613817," ","integrate(exp(sec(x))*sec(x)*tan(x),x)","e^{\sec{\left(x \right)}}"," ",0,"exp(sec(x))","A",0
731,1,7,0,0.651233," ","integrate(2**sec(x)*sec(x)*tan(x),x)","\frac{2^{\sec{\left(x \right)}}}{\log{\left(2 \right)}}"," ",0,"2**sec(x)/log(2)","A",0
732,1,12,0,1.015396," ","integrate(sec(2*x)*tan(2*x)/(1+sec(2*x))**(3/2),x)","- \frac{1}{\sqrt{\sec{\left(2 x \right)} + 1}}"," ",0,"-1/sqrt(sec(2*x) + 1)","A",0
733,0,0,0,0.000000," ","integrate(sec(3*x)*(1+5*cos(3*x)**2)**(1/2)*tan(3*x),x)","\int \sqrt{5 \cos^{2}{\left(3 x \right)} + 1} \tan{\left(3 x \right)} \sec{\left(3 x \right)}\, dx"," ",0,"Integral(sqrt(5*cos(3*x)**2 + 1)*tan(3*x)*sec(3*x), x)","F",0
734,0,0,0,0.000000," ","integrate(sec(3*x)*tan(3*x)/(1+5*cos(3*x)**2)**(1/2),x)","\int \frac{\tan{\left(3 x \right)} \sec{\left(3 x \right)}}{\sqrt{5 \cos^{2}{\left(3 x \right)} + 1}}\, dx"," ",0,"Integral(tan(3*x)*sec(3*x)/sqrt(5*cos(3*x)**2 + 1), x)","F",0
735,1,17,0,0.386673," ","integrate(cot(x)*csc(x)/(a+b*csc(x)),x)","\begin{cases} - \frac{\log{\left(\frac{a}{b} + \csc{\left(x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\- \frac{\csc{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(a/b + csc(x))/b, Ne(b, 0)), (-csc(x)/a, True))","A",0
736,1,12,0,0.612240," ","integrate(5**csc(3*x)*cot(3*x)*csc(3*x),x)","- \frac{5^{\csc{\left(3 x \right)}}}{3 \log{\left(5 \right)}}"," ",0,"-5**csc(3*x)/(3*log(5))","A",0
737,1,5,0,0.191743," ","integrate(cot(x)*csc(x)/(1+csc(x)**2),x)","- \operatorname{atan}{\left(\csc{\left(x \right)} \right)}"," ",0,"-atan(csc(x))","A",0
738,1,151,0,1.715006," ","integrate(cot(6*x)*csc(6*x)/(5-11*csc(6*x)**2)**2,x)","\frac{11 \sqrt{55} \log{\left(\csc{\left(6 x \right)} - \frac{\sqrt{55}}{11} \right)} \csc^{2}{\left(6 x \right)}}{72600 \csc^{2}{\left(6 x \right)} - 33000} - \frac{5 \sqrt{55} \log{\left(\csc{\left(6 x \right)} - \frac{\sqrt{55}}{11} \right)}}{72600 \csc^{2}{\left(6 x \right)} - 33000} - \frac{11 \sqrt{55} \log{\left(\csc{\left(6 x \right)} + \frac{\sqrt{55}}{11} \right)} \csc^{2}{\left(6 x \right)}}{72600 \csc^{2}{\left(6 x \right)} - 33000} + \frac{5 \sqrt{55} \log{\left(\csc{\left(6 x \right)} + \frac{\sqrt{55}}{11} \right)}}{72600 \csc^{2}{\left(6 x \right)} - 33000} + \frac{110 \csc{\left(6 x \right)}}{72600 \csc^{2}{\left(6 x \right)} - 33000}"," ",0,"11*sqrt(55)*log(csc(6*x) - sqrt(55)/11)*csc(6*x)**2/(72600*csc(6*x)**2 - 33000) - 5*sqrt(55)*log(csc(6*x) - sqrt(55)/11)/(72600*csc(6*x)**2 - 33000) - 11*sqrt(55)*log(csc(6*x) + sqrt(55)/11)*csc(6*x)**2/(72600*csc(6*x)**2 - 33000) + 5*sqrt(55)*log(csc(6*x) + sqrt(55)/11)/(72600*csc(6*x)**2 - 33000) + 110*csc(6*x)/(72600*csc(6*x)**2 - 33000)","B",0
739,0,0,0,0.000000," ","integrate(cot(x)*csc(x)/(1+sin(x)**2)**(1/2),x)","\int \frac{\cot{\left(x \right)} \csc{\left(x \right)}}{\sqrt{\sin^{2}{\left(x \right)} + 1}}\, dx"," ",0,"Integral(cot(x)*csc(x)/sqrt(sin(x)**2 + 1), x)","F",0
740,0,0,0,0.000000," ","integrate(cot(5*x)*csc(5*x)**3/(1+sin(5*x)**2)**(1/2),x)","\int \frac{\cot{\left(5 x \right)} \csc^{3}{\left(5 x \right)}}{\sqrt{\sin^{2}{\left(5 x \right)} + 1}}\, dx"," ",0,"Integral(cot(5*x)*csc(5*x)**3/sqrt(sin(5*x)**2 + 1), x)","F",0
741,0,0,0,0.000000," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x)","\int e^{n \sin{\left(a + b x \right)}} \sin{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(exp(n*sin(a + b*x))*sin(2*a + 2*b*x), x)","F",0
742,0,0,0,0.000000," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x)","\int e^{n \sin{\left(a + b x \right)}} \sin{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(exp(n*sin(a + b*x))*sin(2*a + 2*b*x), x)","F",0
743,0,0,0,0.000000," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x)","\int e^{n \sin{\left(\frac{a}{2} + \frac{b x}{2} \right)}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(n*sin(a/2 + b*x/2))*sin(a + b*x), x)","F",0
744,0,0,0,0.000000," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x)","\int e^{n \sin{\left(\frac{a}{2} + \frac{b x}{2} \right)}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(n*sin(a/2 + b*x/2))*sin(a + b*x), x)","F",0
745,0,0,0,0.000000," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x)","\int e^{n \cos{\left(a + b x \right)}} \sin{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(exp(n*cos(a + b*x))*sin(2*a + 2*b*x), x)","F",0
746,0,0,0,0.000000," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x)","\int e^{n \cos{\left(a + b x \right)}} \sin{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(exp(n*cos(a + b*x))*sin(2*a + 2*b*x), x)","F",0
747,0,0,0,0.000000," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x)","\int e^{n \cos{\left(\frac{a}{2} + \frac{b x}{2} \right)}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(n*cos(a/2 + b*x/2))*sin(a + b*x), x)","F",0
748,0,0,0,0.000000," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x)","\int e^{n \cos{\left(\frac{a}{2} + \frac{b x}{2} \right)}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(n*cos(a/2 + b*x/2))*sin(a + b*x), x)","F",0
749,0,0,0,0.000000," ","integrate(csc(x)*ln(tan(x))*sec(x),x)","\int \log{\left(\tan{\left(x \right)} \right)} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(log(tan(x))*csc(x)*sec(x), x)","F",0
750,-1,0,0,0.000000," ","integrate(csc(2*x)*ln(tan(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,1,14,0,0.142148," ","integrate(exp(cos(x)**2+sin(x)**2),x)","x e^{\sin^{2}{\left(x \right)}} e^{\cos^{2}{\left(x \right)}}"," ",0,"x*exp(sin(x)**2)*exp(cos(x)**2)","B",0
752,0,0,0,0.000000," ","integrate(x*sec(x)**2,x)","\int x \sec^{2}{\left(x \right)}\, dx"," ",0,"Integral(x*sec(x)**2, x)","F",0
753,1,76,0,0.955536," ","integrate(x*cos(x**2)**4,x)","\frac{3 x^{2} \sin^{4}{\left(x^{2} \right)}}{16} + \frac{3 x^{2} \sin^{2}{\left(x^{2} \right)} \cos^{2}{\left(x^{2} \right)}}{8} + \frac{3 x^{2} \cos^{4}{\left(x^{2} \right)}}{16} + \frac{3 \sin^{3}{\left(x^{2} \right)} \cos{\left(x^{2} \right)}}{16} + \frac{5 \sin{\left(x^{2} \right)} \cos^{3}{\left(x^{2} \right)}}{16}"," ",0,"3*x**2*sin(x**2)**4/16 + 3*x**2*sin(x**2)**2*cos(x**2)**2/8 + 3*x**2*cos(x**2)**4/16 + 3*sin(x**2)**3*cos(x**2)/16 + 5*sin(x**2)*cos(x**2)**3/16","B",0
754,1,10,0,0.249610," ","integrate(sin(x)*cos(x)**(1/2),x)","- \frac{2 \cos^{\frac{3}{2}}{\left(x \right)}}{3}"," ",0,"-2*cos(x)**(3/2)/3","A",0
755,1,15,0,0.312234," ","integrate(tan(exp(-2*x))/exp(2*x),x)","- \frac{\log{\left(\tan^{2}{\left(e^{- 2 x} \right)} + 1 \right)}}{4}"," ",0,"-log(tan(exp(-2*x))**2 + 1)/4","A",0
756,1,8,0,2.166050," ","integrate(sec(x)*sin(2*x)/(1+cos(x)),x)","- 2 \log{\left(\cos{\left(x \right)} + 1 \right)}"," ",0,"-2*log(cos(x) + 1)","A",0
757,0,0,0,0.000000," ","integrate(x*sec(3*x)**2,x)","\int x \sec^{2}{\left(3 x \right)}\, dx"," ",0,"Integral(x*sec(3*x)**2, x)","F",0
758,1,32,0,0.422951," ","integrate(cos(2*pi*x)/exp(2*pi*x),x)","\frac{e^{- 2 \pi x} \sin{\left(2 \pi x \right)}}{4 \pi} - \frac{e^{- 2 \pi x} \cos{\left(2 \pi x \right)}}{4 \pi}"," ",0,"exp(-2*pi*x)*sin(2*pi*x)/(4*pi) - exp(-2*pi*x)*cos(2*pi*x)/(4*pi)","A",0
759,1,236,0,0.079629," ","integrate(cos(x)**12*sin(x)**10-cos(x)**10*sin(x)**12,x)","- \frac{\sin^{21}{\left(x \right)} \cos{\left(x \right)}}{22} + \frac{89 \sin^{19}{\left(x \right)} \cos{\left(x \right)}}{440} - \frac{301 \sin^{17}{\left(x \right)} \cos{\left(x \right)}}{880} + \frac{3683 \sin^{15}{\left(x \right)} \cos{\left(x \right)}}{14080} - \frac{433 \sin^{13}{\left(x \right)} \cos{\left(x \right)}}{5632} + \frac{\sin^{11}{\left(x \right)} \cos{\left(x \right)}}{22528} + \frac{\sin^{9}{\left(x \right)} \cos{\left(x \right)}}{20480} + \frac{9 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{163840} + \frac{21 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{327680} + \frac{21 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{262144} - \frac{\sin{\left(x \right)} \cos^{21}{\left(x \right)}}{22} + \frac{89 \sin{\left(x \right)} \cos^{19}{\left(x \right)}}{440} - \frac{301 \sin{\left(x \right)} \cos^{17}{\left(x \right)}}{880} + \frac{3683 \sin{\left(x \right)} \cos^{15}{\left(x \right)}}{14080} - \frac{433 \sin{\left(x \right)} \cos^{13}{\left(x \right)}}{5632} + \frac{\sin{\left(x \right)} \cos^{11}{\left(x \right)}}{22528} + \frac{\sin{\left(x \right)} \cos^{9}{\left(x \right)}}{20480} + \frac{9 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{163840} + \frac{21 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{327680} + \frac{21 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{262144} + \frac{63 \sin{\left(x \right)} \cos{\left(x \right)}}{262144}"," ",0,"-sin(x)**21*cos(x)/22 + 89*sin(x)**19*cos(x)/440 - 301*sin(x)**17*cos(x)/880 + 3683*sin(x)**15*cos(x)/14080 - 433*sin(x)**13*cos(x)/5632 + sin(x)**11*cos(x)/22528 + sin(x)**9*cos(x)/20480 + 9*sin(x)**7*cos(x)/163840 + 21*sin(x)**5*cos(x)/327680 + 21*sin(x)**3*cos(x)/262144 - sin(x)*cos(x)**21/22 + 89*sin(x)*cos(x)**19/440 - 301*sin(x)*cos(x)**17/880 + 3683*sin(x)*cos(x)**15/14080 - 433*sin(x)*cos(x)**13/5632 + sin(x)*cos(x)**11/22528 + sin(x)*cos(x)**9/20480 + 9*sin(x)*cos(x)**7/163840 + 21*sin(x)*cos(x)**5/327680 + 21*sin(x)*cos(x)**3/262144 + 63*sin(x)*cos(x)/262144","B",0
760,1,19,0,0.139086," ","integrate(x*cot(x**2),x)","- \frac{\log{\left(\tan^{2}{\left(x^{2} \right)} + 1 \right)}}{4} + \frac{\log{\left(\tan{\left(x^{2} \right)} \right)}}{2}"," ",0,"-log(tan(x**2)**2 + 1)/4 + log(tan(x**2))/2","B",0
761,0,0,0,0.000000," ","integrate(x*sec(x**2)**2,x)","\int x \sec^{2}{\left(x^{2} \right)}\, dx"," ",0,"Integral(x*sec(x**2)**2, x)","F",0
762,-1,0,0,0.000000," ","integrate(sin(8*x)/(9+sin(4*x)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,1,19,0,0.265752," ","integrate(cos(2*x)/(8+sin(2*x)**2),x)","\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \sin{\left(2 x \right)}}{4} \right)}}{8}"," ",0,"sqrt(2)*atan(sqrt(2)*sin(2*x)/4)/8","A",0
764,1,42,0,0.515526," ","integrate(x*(cos(x**2)**3-sin(x**2)**3),x)","\frac{\sin^{3}{\left(x^{2} \right)}}{3} + \frac{\sin^{2}{\left(x^{2} \right)} \cos{\left(x^{2} \right)}}{2} + \frac{\sin{\left(x^{2} \right)} \cos^{2}{\left(x^{2} \right)}}{2} + \frac{\cos^{3}{\left(x^{2} \right)}}{3}"," ",0,"sin(x**2)**3/3 + sin(x**2)**2*cos(x**2)/2 + sin(x**2)*cos(x**2)**2/2 + cos(x**2)**3/3","A",0
765,1,8,0,0.168440," ","integrate(cos(x)*sin(x)/(1-cos(x)),x)","\log{\left(\cos{\left(x \right)} - 1 \right)} + \cos{\left(x \right)}"," ",0,"log(cos(x) - 1) + cos(x)","A",0
766,1,5,0,0.149587," ","integrate(x*cos(x**2),x)","\frac{\sin{\left(x^{2} \right)}}{2}"," ",0,"sin(x**2)/2","A",0
767,1,7,0,0.279182," ","integrate(x**2*cos(4*x**3),x)","\frac{\sin{\left(4 x^{3} \right)}}{12}"," ",0,"sin(4*x**3)/12","A",0
768,1,5,0,0.477307," ","integrate(x**3*cos(x**4),x)","\frac{\sin{\left(x^{4} \right)}}{4}"," ",0,"sin(x**4)/4","A",0
769,1,7,0,0.149300," ","integrate(x*sin(1/2*x**2),x)","- \cos{\left(\frac{x^{2}}{2} \right)}"," ",0,"-cos(x**2/2)","A",0
770,1,5,0,0.284606," ","integrate(x*sec(x**2)*tan(x**2),x)","\frac{\sec{\left(x^{2} \right)}}{2}"," ",0,"sec(x**2)/2","A",0
771,1,7,0,0.221637," ","integrate(tan(1/x)**2/x**2,x)","- \tan{\left(\frac{1}{x} \right)} + \frac{1}{x}"," ",0,"-tan(1/x) + 1/x","A",0
772,1,12,0,0.118761," ","integrate(x*tan(x**2+1),x)","\frac{\log{\left(\tan^{2}{\left(x^{2} + 1 \right)} + 1 \right)}}{4}"," ",0,"log(tan(x**2 + 1)**2 + 1)/4","A",0
773,1,12,0,0.789760," ","integrate(sin(pi*(1+2*x)),x)","- \frac{\cos{\left(\pi \left(2 x + 1\right) \right)}}{2 \pi}"," ",0,"-cos(pi*(2*x + 1))/(2*pi)","A",0
774,0,0,0,0.000000," ","integrate((cot(x)+csc(x)**2)/(1-cos(x)**2),x)","- \int \frac{\cot{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}\, dx - \int \frac{\csc^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}\, dx"," ",0,"-Integral(cot(x)/(cos(x)**2 - 1), x) - Integral(csc(x)**2/(cos(x)**2 - 1), x)","F",0
775,1,32,0,5.250930," ","integrate(x**2*cos(4*x**3)*cos(5*x**3),x)","- \frac{4 \sin{\left(4 x^{3} \right)} \cos{\left(5 x^{3} \right)}}{27} + \frac{5 \sin{\left(5 x^{3} \right)} \cos{\left(4 x^{3} \right)}}{27}"," ",0,"-4*sin(4*x**3)*cos(5*x**3)/27 + 5*sin(5*x**3)*cos(4*x**3)/27","B",0
776,1,48,0,71.974801," ","integrate(x**14*sin(x**3),x)","- \frac{x^{12} \cos{\left(x^{3} \right)}}{3} + \frac{4 x^{9} \sin{\left(x^{3} \right)}}{3} + 4 x^{6} \cos{\left(x^{3} \right)} - 8 x^{3} \sin{\left(x^{3} \right)} - 8 \cos{\left(x^{3} \right)}"," ",0,"-x**12*cos(x**3)/3 + 4*x**9*sin(x**3)/3 + 4*x**6*cos(x**3) - 8*x**3*sin(x**3) - 8*cos(x**3)","A",0
777,1,32,0,1.817360," ","integrate(x**2*sin(2*x**3)/exp(3*x**3),x)","- \frac{e^{- 3 x^{3}} \sin{\left(2 x^{3} \right)}}{13} - \frac{2 e^{- 3 x^{3}} \cos{\left(2 x^{3} \right)}}{39}"," ",0,"-exp(-3*x**3)*sin(2*x**3)/13 - 2*exp(-3*x**3)*cos(2*x**3)/39","A",0
778,1,3,0,0.152268," ","integrate(2*x*cos(x**2),x)","\sin{\left(x^{2} \right)}"," ",0,"sin(x**2)","A",0
779,1,5,0,0.266954," ","integrate(3*x**2*cos(x**3+7),x)","\sin{\left(x^{3} + 7 \right)}"," ",0,"sin(x**3 + 7)","A",0
780,1,5,0,0.079524," ","integrate(1/(x**2+1)+sin(x),x)","- \cos{\left(x \right)} + \operatorname{atan}{\left(x \right)}"," ",0,"-cos(x) + atan(x)","A",0
781,1,8,0,0.152776," ","integrate(x*sin(x**2+1),x)","- \frac{\cos{\left(x^{2} + 1 \right)}}{2}"," ",0,"-cos(x**2 + 1)/2","A",0
782,1,7,0,0.149316," ","integrate(x*cos(x**2+1),x)","\frac{\sin{\left(x^{2} + 1 \right)}}{2}"," ",0,"sin(x**2 + 1)/2","A",0
783,1,7,0,0.264406," ","integrate(1+x**2*cos(x**3),x)","x + \frac{\sin{\left(x^{3} \right)}}{3}"," ",0,"x + sin(x**3)/3","A",0
784,1,8,0,0.261294," ","integrate(x**2*sin(x**3+1),x)","- \frac{\cos{\left(x^{3} + 1 \right)}}{3}"," ",0,"-cos(x**3 + 1)/3","A",0
785,1,5,0,0.267116," ","integrate(12*x**2*cos(x**3),x)","4 \sin{\left(x^{3} \right)}"," ",0,"4*sin(x**3)","A",0
786,1,15,0,0.153931," ","integrate((1+x)*sin(1+x),x)","- x \cos{\left(x + 1 \right)} + \sin{\left(x + 1 \right)} - \cos{\left(x + 1 \right)}"," ",0,"-x*cos(x + 1) + sin(x + 1) - cos(x + 1)","A",0
787,1,15,0,1.514761," ","integrate(x**5*cos(x**3),x)","\frac{x^{3} \sin{\left(x^{3} \right)}}{3} + \frac{\cos{\left(x^{3} \right)}}{3}"," ",0,"x**3*sin(x**3)/3 + cos(x**3)/3","A",0
788,1,20,0,0.401883," ","integrate(cos(x)/exp(3*x),x)","\frac{e^{- 3 x} \sin{\left(x \right)}}{10} - \frac{3 e^{- 3 x} \cos{\left(x \right)}}{10}"," ",0,"exp(-3*x)*sin(x)/10 - 3*exp(-3*x)*cos(x)/10","A",0
789,1,15,0,0.482548," ","integrate(x**3*sin(x**2),x)","- \frac{x^{2} \cos{\left(x^{2} \right)}}{2} + \frac{\sin{\left(x^{2} \right)}}{2}"," ",0,"-x**2*cos(x**2)/2 + sin(x**2)/2","A",0
790,1,15,0,0.480494," ","integrate(x**3*cos(x**2),x)","\frac{x^{2} \sin{\left(x^{2} \right)}}{2} + \frac{\cos{\left(x^{2} \right)}}{2}"," ",0,"x**2*sin(x**2)/2 + cos(x**2)/2","A",0
791,1,7,0,0.419448," ","integrate(cos(x)*cos(2*sin(x)),x)","\frac{\sin{\left(2 \sin{\left(x \right)} \right)}}{2}"," ",0,"sin(2*sin(x))/2","A",0
792,1,10,0,0.170881," ","integrate(cos(x)*sin(x)/(1+cos(x)**2),x)","- \frac{\log{\left(\cos^{2}{\left(x \right)} + 1 \right)}}{2}"," ",0,"-log(cos(x)**2 + 1)/2","A",0
793,1,36,0,0.522005," ","integrate((1+cos(x))*(x+sin(x))**3,x)","\frac{x^{4}}{4} + x^{3} \sin{\left(x \right)} + \frac{3 x^{2} \sin^{2}{\left(x \right)}}{2} + x \sin^{3}{\left(x \right)} + \frac{\sin^{4}{\left(x \right)}}{4}"," ",0,"x**4/4 + x**3*sin(x) + 3*x**2*sin(x)**2/2 + x*sin(x)**3 + sin(x)**4/4","B",0
794,1,8,0,1.795059," ","integrate((1+cos(x))*csc(x)**2,x)","- \cot{\left(x \right)} - \frac{1}{\sin{\left(x \right)}}"," ",0,"-cot(x) - 1/sin(x)","A",0
795,1,7,0,0.066662," ","integrate(sin(x)*tan(x)**2,x)","\cos{\left(x \right)} + \frac{1}{\cos{\left(x \right)}}"," ",0,"cos(x) + 1/cos(x)","A",0
796,-1,0,0,0.000000," ","integrate(exp(sin(x))*sec(x)**2*(x*cos(x)**3-sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,0,0,0,0.000000," ","integrate(x*csc(x)**2,x)","\int x \csc^{2}{\left(x \right)}\, dx"," ",0,"Integral(x*csc(x)**2, x)","F",0
798,1,37,0,0.460377," ","integrate(cos(x)*sin(1/6*pi+x),x)","- \frac{x \sin{\left(x \right)} \cos{\left(x + \frac{\pi}{6} \right)}}{2} + \frac{x \sin{\left(x + \frac{\pi}{6} \right)} \cos{\left(x \right)}}{2} + \frac{\sin{\left(x \right)} \sin{\left(x + \frac{\pi}{6} \right)}}{2}"," ",0,"-x*sin(x)*cos(x + pi/6)/2 + x*sin(x + pi/6)*cos(x)/2 + sin(x)*sin(x + pi/6)/2","B",0
799,1,22,0,0.479878," ","integrate(x*sin(x**2)**3,x)","- \frac{\sin^{2}{\left(x^{2} \right)} \cos{\left(x^{2} \right)}}{2} - \frac{\cos^{3}{\left(x^{2} \right)}}{3}"," ",0,"-sin(x**2)**2*cos(x**2)/2 - cos(x**2)**3/3","A",0
800,1,10,0,0.071572," ","integrate(sin(x)**2*tan(x),x)","- \log{\left(\cos{\left(x \right)} \right)} + \frac{\cos^{2}{\left(x \right)}}{2}"," ",0,"-log(cos(x)) + cos(x)**2/2","A",0
801,1,20,0,0.083184," ","integrate(cos(x)**2*cot(x)**3,x)","- 2 \log{\left(\sin{\left(x \right)} \right)} + \frac{\sin^{2}{\left(x \right)}}{2} - \frac{1}{2 \sin^{2}{\left(x \right)}}"," ",0,"-2*log(sin(x)) + sin(x)**2/2 - 1/(2*sin(x)**2)","A",0
802,1,12,0,2.043809," ","integrate(sec(x)*(1-sin(x)),x)","\log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} + \log{\left(\cos{\left(x \right)} \right)}"," ",0,"log(tan(x) + sec(x)) + log(cos(x))","B",0
803,1,12,0,1.887924," ","integrate((1+cos(x))*csc(x),x)","- \log{\left(\cot{\left(x \right)} + \csc{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)}"," ",0,"-log(cot(x) + csc(x)) + log(sin(x))","B",0
804,1,14,0,3.113402," ","integrate(cos(x)**2*(1-tan(x)**2),x)","\frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\sin{\left(2 x \right)}}{4}"," ",0,"sin(x)*cos(x)/2 + sin(2*x)/4","B",0
805,1,32,0,1.864522," ","integrate(csc(2*x)*(cos(x)+sin(x)),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{4}"," ",0,"-log(sin(x) - 1)/4 + log(sin(x) + 1)/4 + log(cos(x) - 1)/4 - log(cos(x) + 1)/4","B",0
806,1,12,0,0.189664," ","integrate(cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)**2),x)","\log{\left(\sin{\left(x \right)} - 2 \right)} + \log{\left(\sin{\left(x \right)} - 1 \right)}"," ",0,"log(sin(x) - 2) + log(sin(x) - 1)","A",0
807,1,19,0,0.425756," ","integrate(cos(x)**2*sin(x)/(5+cos(x)**2),x)","- \cos{\left(x \right)} + \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \cos{\left(x \right)}}{5} \right)}"," ",0,"-cos(x) + sqrt(5)*atan(sqrt(5)*cos(x)/5)","A",0
808,1,10,0,0.177748," ","integrate(cos(x)/(sin(x)+sin(x)**2),x)","- \log{\left(\sin{\left(x \right)} + 1 \right)} + \log{\left(\sin{\left(x \right)} \right)}"," ",0,"-log(sin(x) + 1) + log(sin(x))","A",0
809,1,82,0,1.067151," ","integrate(cos(x)/(sin(x)+sin(x)**(2**(1/2))),x)","\frac{\sqrt{2} \log{\left(\sin{\left(x \right)} + \sin^{\sqrt{2}}{\left(x \right)} \right)}}{-3 + 2 \sqrt{2}} - \frac{\log{\left(\sin{\left(x \right)} + \sin^{\sqrt{2}}{\left(x \right)} \right)}}{-3 + 2 \sqrt{2}} + \frac{\sqrt{2} \log{\left(\sin{\left(x \right)} \right)}}{-3 + 2 \sqrt{2}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{-3 + 2 \sqrt{2}}"," ",0,"sqrt(2)*log(sin(x) + sin(x)**(sqrt(2)))/(-3 + 2*sqrt(2)) - log(sin(x) + sin(x)**(sqrt(2)))/(-3 + 2*sqrt(2)) + sqrt(2)*log(sin(x))/(-3 + 2*sqrt(2)) - 2*log(sin(x))/(-3 + 2*sqrt(2))","B",0
810,0,0,0,0.000000," ","integrate(1/(2*sin(x)+sin(2*x)),x)","\int \frac{1}{2 \sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx"," ",0,"Integral(1/(2*sin(x) + sin(2*x)), x)","F",0
811,1,39,0,0.292228," ","integrate((x**2+4*x-3)*sin(2*x),x)","- \frac{x^{2} \cos{\left(2 x \right)}}{2} + \frac{x \sin{\left(2 x \right)}}{2} - 2 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)} + \frac{7 \cos{\left(2 x \right)}}{4}"," ",0,"-x**2*cos(2*x)/2 + x*sin(2*x)/2 - 2*x*cos(2*x) + sin(2*x) + 7*cos(2*x)/4","A",0
812,1,26,0,0.403324," ","integrate(cos(4*x)/exp(3*x),x)","\frac{4 e^{- 3 x} \sin{\left(4 x \right)}}{25} - \frac{3 e^{- 3 x} \cos{\left(4 x \right)}}{25}"," ",0,"4*exp(-3*x)*sin(4*x)/25 - 3*exp(-3*x)*cos(4*x)/25","A",0
813,1,26,0,0.286176," ","integrate(cos(x)*sin(x)/(1+sin(x))**(1/2),x)","\frac{2 \sqrt{\sin{\left(x \right)} + 1} \sin{\left(x \right)}}{3} - \frac{4 \sqrt{\sin{\left(x \right)} + 1}}{3}"," ",0,"2*sqrt(sin(x) + 1)*sin(x)/3 - 4*sqrt(sin(x) + 1)/3","A",0
814,1,27,0,0.059660," ","integrate(x+60*cos(x)**5*sin(x)**4,x)","\frac{x^{2}}{2} + \frac{20 \sin^{9}{\left(x \right)}}{3} - \frac{120 \sin^{7}{\left(x \right)}}{7} + 12 \sin^{5}{\left(x \right)}"," ",0,"x**2/2 + 20*sin(x)**9/3 - 120*sin(x)**7/7 + 12*sin(x)**5","A",0
815,1,3,0,1.132058," ","integrate(cos(x)*(sec(x)+tan(x)),x)","x - \cos{\left(x \right)}"," ",0,"x - cos(x)","A",0
816,1,8,0,4.808569," ","integrate(cos(x)*(sec(x)**3+tan(x)),x)","\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \cos{\left(x \right)}"," ",0,"sin(x)/cos(x) - cos(x)","A",0
817,1,14,0,0.062285," ","integrate(-1/2*cot(x)*csc(x)+1/2*csc(x)**2,x)","- \frac{\cos{\left(x \right)}}{2 \sin{\left(x \right)}} + \frac{1}{2 \sin{\left(x \right)}}"," ",0,"-cos(x)/(2*sin(x)) + 1/(2*sin(x))","A",0
818,1,12,0,0.055899," ","integrate(-csc(x)**2+sin(2*x),x)","- \frac{\cos{\left(2 x \right)}}{2} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}"," ",0,"-cos(2*x)/2 + cos(x)/sin(x)","A",0
819,1,10,0,0.056063," ","integrate(2*cot(2*x)-3*sin(3*x),x)","\log{\left(\sin{\left(2 x \right)} \right)} + \cos{\left(3 x \right)}"," ",0,"log(sin(2*x)) + cos(3*x)","A",0
820,1,8,0,0.154081," ","integrate(x*sin(2*x**2),x)","- \frac{\cos{\left(2 x^{2} \right)}}{4}"," ",0,"-cos(2*x**2)/4","A",0
821,1,32,0,0.746105," ","integrate(cos(-1+x)*sin(-1+x)*(1+sin(-1+x)**2)**(1/2),x)","\frac{\sqrt{\sin^{2}{\left(x - 1 \right)} + 1} \sin^{2}{\left(x - 1 \right)}}{3} + \frac{\sqrt{\sin^{2}{\left(x - 1 \right)} + 1}}{3}"," ",0,"sqrt(sin(x - 1)**2 + 1)*sin(x - 1)**2/3 + sqrt(sin(x - 1)**2 + 1)/3","B",0
822,1,31,0,1.284904," ","integrate(cos(1/x)*sin(1/x)/x**2,x)","- \frac{2 \tan^{2}{\left(\frac{1}{2 x} \right)}}{\tan^{4}{\left(\frac{1}{2 x} \right)} + 2 \tan^{2}{\left(\frac{1}{2 x} \right)} + 1}"," ",0,"-2*tan(1/(2*x))**2/(tan(1/(2*x))**4 + 2*tan(1/(2*x))**2 + 1)","B",0
823,1,12,0,0.463078," ","integrate(cos(1/2+3/2*x)*sin(1/2+3/2*x)**3,x)","\frac{\sin^{4}{\left(\frac{3 x}{2} + \frac{1}{2} \right)}}{6}"," ",0,"sin(3*x/2 + 1/2)**4/6","A",0
824,1,8,0,0.118534," ","integrate(4*x*tan(x**2),x)","\log{\left(\tan^{2}{\left(x^{2} \right)} + 1 \right)}"," ",0,"log(tan(x**2)**2 + 1)","A",0
825,1,15,0,1.032178," ","integrate(x*sec(x**2-5),x)","\frac{\log{\left(\tan{\left(x^{2} - 5 \right)} + \sec{\left(x^{2} - 5 \right)} \right)}}{2}"," ",0,"log(tan(x**2 - 5) + sec(x**2 - 5))/2","A",0
826,1,10,0,1.257302," ","integrate(csc(1/x)/x**2,x)","\log{\left(\cot{\left(\frac{1}{x} \right)} + \csc{\left(\frac{1}{x} \right)} \right)}"," ",0,"log(cot(1/x) + csc(1/x))","A",0
827,1,8,0,2.310544," ","integrate((csc(x)-sec(x))*(cos(x)+sin(x)),x)","\log{\left(\sin{\left(x \right)} \right)} + \log{\left(\cos{\left(x \right)} \right)}"," ",0,"log(sin(x)) + log(cos(x))","A",0
828,1,20,0,0.687429," ","integrate(-cos(3*x)*sin(2*x)+cos(2*x)*sin(3*x),x)","- \sin{\left(2 x \right)} \sin{\left(3 x \right)} - \cos{\left(2 x \right)} \cos{\left(3 x \right)}"," ",0,"-sin(2*x)*sin(3*x) - cos(2*x)*cos(3*x)","B",0
829,0,0,0,0.000000," ","integrate(4*x*sec(2*x)**2,x)","4 \int x \sec^{2}{\left(2 x \right)}\, dx"," ",0,"4*Integral(x*sec(2*x)**2, x)","F",0
830,1,20,0,0.054104," ","integrate(4*sin(x)**2*tan(x)**2,x)","- 6 x + \frac{4 \sin^{3}{\left(x \right)}}{\cos{\left(x \right)}} + 6 \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"-6*x + 4*sin(x)**3/cos(x) + 6*sin(x)*cos(x)","A",0
831,1,36,0,0.055290," ","integrate(cos(x)**4*cot(x)**2,x)","- \frac{15 x}{8} - \frac{5 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{4} - \frac{15 \sin{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{\cos^{5}{\left(x \right)}}{\sin{\left(x \right)}}"," ",0,"-15*x/8 - 5*sin(x)*cos(x)**3/4 - 15*sin(x)*cos(x)/8 - cos(x)**5/sin(x)","A",0
832,1,12,0,0.058234," ","integrate(16*cos(x)**2*sin(x)**2,x)","2 x - \sin{\left(2 x \right)} \cos{\left(2 x \right)}"," ",0,"2*x - sin(2*x)*cos(2*x)","A",0
833,1,32,0,0.053104," ","integrate(8*cos(x)**2*sin(x)**4,x)","\frac{x}{2} + \frac{4 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{3} - \frac{\sin^{3}{\left(x \right)} \cos{\left(x \right)}}{3} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}"," ",0,"x/2 + 4*sin(x)**5*cos(x)/3 - sin(x)**3*cos(x)/3 - sin(x)*cos(x)/2","A",0
834,1,12,0,0.054873," ","integrate(35*cos(x)**3*sin(x)**4,x)","- 5 \sin^{7}{\left(x \right)} + 7 \sin^{5}{\left(x \right)}"," ",0,"-5*sin(x)**7 + 7*sin(x)**5","A",0
835,1,31,0,0.063535," ","integrate(4*cos(x)**4*sin(x)**4,x)","\frac{3 x}{32} - \frac{\sin^{3}{\left(2 x \right)} \cos{\left(2 x \right)}}{32} - \frac{3 \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{64}"," ",0,"3*x/32 - sin(2*x)**3*cos(2*x)/32 - 3*sin(2*x)*cos(2*x)/64","A",0
836,1,20,0,0.323711," ","integrate(cos(x)/(-sin(x)+sin(x)**3),x)","\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \log{\left(\sin{\left(x \right)} \right)}"," ",0,"log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - log(sin(x))","B",0
837,1,12,0,0.054265," ","integrate(-1+2*cos(x)**2+cos(x)*sin(x),x)","\frac{\sin^{2}{\left(x \right)}}{2} + \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"sin(x)**2/2 + sin(x)*cos(x)","A",0
838,1,0,0,0.055488," ","integrate(cos(x)**2+sin(x)**2,x)","x"," ",0,"x","A",0
839,1,7,0,0.056106," ","integrate(-cos(x)**2+sin(x)**2,x)","- \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"-sin(x)*cos(x)","A",0
840,1,7,0,0.248511," ","integrate(2**sin(x)*cos(x),x)","\frac{2^{\sin{\left(x \right)}}}{\log{\left(2 \right)}}"," ",0,"2**sin(x)/log(2)","A",0
841,1,22,0,0.116390," ","integrate(tan(x)**3+tan(x)**5,x)","- \frac{4 \cos^{2}{\left(x \right)} - 1}{4 \cos^{4}{\left(x \right)}} + \frac{1}{2 \cos^{2}{\left(x \right)}}"," ",0,"-(4*cos(x)**2 - 1)/(4*cos(x)**4) + 1/(2*cos(x)**2)","B",0
842,1,5,0,0.481100," ","integrate(x*sec(x)*(2+x*tan(x)),x)","x^{2} \sec{\left(x \right)}"," ",0,"x**2*sec(x)","A",0
843,1,8,0,0.281583," ","integrate(cot(x**(1/2))*csc(x**(1/2))/x**(1/2),x)","- 2 \csc{\left(\sqrt{x} \right)}"," ",0,"-2*csc(sqrt(x))","A",0
844,1,8,0,0.266037," ","integrate(cos(x**(1/2))*sin(x**(1/2))/x**(1/2),x)","- \cos^{2}{\left(\sqrt{x} \right)}"," ",0,"-cos(sqrt(x))**2","A",0
845,1,7,0,0.285686," ","integrate(sec(x**(1/2))*tan(x**(1/2))/x**(1/2),x)","2 \sec{\left(\sqrt{x} \right)}"," ",0,"2*sec(sqrt(x))","A",0
846,1,155,0,9.311972," ","integrate(sin(x)**2/(a+b*sin(2*x)),x)","- \begin{cases} \frac{\log{\left(\frac{a}{b} + \sin{\left(2 x \right)} \right)}}{4 b} & \text{for}\: b \neq 0 \\\frac{\sin{\left(2 x \right)}}{4 a} & \text{otherwise} \end{cases} + \begin{cases} \frac{\sqrt{b^{2}}}{2 b^{2} \tan{\left(x \right)} - 2 b \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\- \frac{\sqrt{b^{2}}}{2 b^{2} \tan{\left(x \right)} + 2 b \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{\log{\left(\tan{\left(x \right)} \right)}}{4 b} & \text{for}\: a = 0 \\\frac{\log{\left(\tan{\left(x \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{4 \sqrt{- a^{2} + b^{2}}} - \frac{\log{\left(\tan{\left(x \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{4 \sqrt{- a^{2} + b^{2}}} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((log(a/b + sin(2*x))/(4*b), Ne(b, 0)), (sin(2*x)/(4*a), True)) + Piecewise((sqrt(b**2)/(2*b**2*tan(x) - 2*b*sqrt(b**2)), Eq(a, -sqrt(b**2))), (-sqrt(b**2)/(2*b**2*tan(x) + 2*b*sqrt(b**2)), Eq(a, sqrt(b**2))), (log(tan(x))/(4*b), Eq(a, 0)), (log(tan(x) + b/a - sqrt(-a**2 + b**2)/a)/(4*sqrt(-a**2 + b**2)) - log(tan(x) + b/a + sqrt(-a**2 + b**2)/a)/(4*sqrt(-a**2 + b**2)), True))","A",0
847,1,155,0,9.453069," ","integrate(cos(x)**2/(a+b*sin(2*x)),x)","\begin{cases} \frac{\log{\left(\frac{a}{b} + \sin{\left(2 x \right)} \right)}}{4 b} & \text{for}\: b \neq 0 \\\frac{\sin{\left(2 x \right)}}{4 a} & \text{otherwise} \end{cases} + \begin{cases} \frac{\sqrt{b^{2}}}{2 b^{2} \tan{\left(x \right)} - 2 b \sqrt{b^{2}}} & \text{for}\: a = - \sqrt{b^{2}} \\- \frac{\sqrt{b^{2}}}{2 b^{2} \tan{\left(x \right)} + 2 b \sqrt{b^{2}}} & \text{for}\: a = \sqrt{b^{2}} \\\frac{\log{\left(\tan{\left(x \right)} \right)}}{4 b} & \text{for}\: a = 0 \\\frac{\log{\left(\tan{\left(x \right)} + \frac{b}{a} - \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{4 \sqrt{- a^{2} + b^{2}}} - \frac{\log{\left(\tan{\left(x \right)} + \frac{b}{a} + \frac{\sqrt{- a^{2} + b^{2}}}{a} \right)}}{4 \sqrt{- a^{2} + b^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(a/b + sin(2*x))/(4*b), Ne(b, 0)), (sin(2*x)/(4*a), True)) + Piecewise((sqrt(b**2)/(2*b**2*tan(x) - 2*b*sqrt(b**2)), Eq(a, -sqrt(b**2))), (-sqrt(b**2)/(2*b**2*tan(x) + 2*b*sqrt(b**2)), Eq(a, sqrt(b**2))), (log(tan(x))/(4*b), Eq(a, 0)), (log(tan(x) + b/a - sqrt(-a**2 + b**2)/a)/(4*sqrt(-a**2 + b**2)) - log(tan(x) + b/a + sqrt(-a**2 + b**2)/a)/(4*sqrt(-a**2 + b**2)), True))","A",0
848,1,432,0,35.267655," ","integrate(sin(x)**2/(a+b*cos(2*x)),x)","\begin{cases} \tilde{\infty} \left(- \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{2}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{1}{4 b \tan{\left(x \right)}} & \text{for}\: a = - b \\\frac{\tan{\left(x \right)}}{4 b} & \text{for}\: a = b \\\frac{\log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{\log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases} - \begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{x}{2 b} - \frac{\tan{\left(x \right)}}{4 b} & \text{for}\: a = b \\\frac{x}{2 b} + \frac{1}{4 b \tan{\left(x \right)}} & \text{for}\: a = - b \\\frac{\sin{\left(2 x \right)}}{4 a} & \text{for}\: b = 0 \\\frac{2 a x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{2 b x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-log(tan(x) - 1)/2 + log(tan(x) + 1)/2), Eq(a, 0) & Eq(b, 0)), (1/(4*b*tan(x)), Eq(a, -b)), (tan(x)/(4*b), Eq(a, b)), (log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*sqrt(-a/(a - b) - b/(a - b)) - 4*b*sqrt(-a/(a - b) - b/(a - b))) - log(sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*sqrt(-a/(a - b) - b/(a - b)) - 4*b*sqrt(-a/(a - b) - b/(a - b))), True)) - Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (x/(2*b) - tan(x)/(4*b), Eq(a, b)), (x/(2*b) + 1/(4*b*tan(x)), Eq(a, -b)), (sin(2*x)/(4*a), Eq(b, 0)), (2*a*x*sqrt(-a/(a - b) - b/(a - b))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))) - 2*b*x*sqrt(-a/(a - b) - b/(a - b))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))), True))","B",0
849,1,432,0,35.326740," ","integrate(cos(x)**2/(a+b*cos(2*x)),x)","\begin{cases} \tilde{\infty} \left(- \frac{\log{\left(\tan{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{2}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{1}{4 b \tan{\left(x \right)}} & \text{for}\: a = - b \\\frac{\tan{\left(x \right)}}{4 b} & \text{for}\: a = b \\\frac{\log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{\log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases} + \begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{x}{2 b} - \frac{\tan{\left(x \right)}}{4 b} & \text{for}\: a = b \\\frac{x}{2 b} + \frac{1}{4 b \tan{\left(x \right)}} & \text{for}\: a = - b \\\frac{\sin{\left(2 x \right)}}{4 a} & \text{for}\: b = 0 \\\frac{2 a x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(x \right)} \right)}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{2 b x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{4 a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - 4 b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-log(tan(x) - 1)/2 + log(tan(x) + 1)/2), Eq(a, 0) & Eq(b, 0)), (1/(4*b*tan(x)), Eq(a, -b)), (tan(x)/(4*b), Eq(a, b)), (log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*sqrt(-a/(a - b) - b/(a - b)) - 4*b*sqrt(-a/(a - b) - b/(a - b))) - log(sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*sqrt(-a/(a - b) - b/(a - b)) - 4*b*sqrt(-a/(a - b) - b/(a - b))), True)) + Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (x/(2*b) - tan(x)/(4*b), Eq(a, b)), (x/(2*b) + 1/(4*b*tan(x)), Eq(a, -b)), (sin(2*x)/(4*a), Eq(b, 0)), (2*a*x*sqrt(-a/(a - b) - b/(a - b))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))) - 2*b*x*sqrt(-a/(a - b) - b/(a - b))/(4*a*b*sqrt(-a/(a - b) - b/(a - b)) - 4*b**2*sqrt(-a/(a - b) - b/(a - b))), True))","B",0
850,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a*sin(d*x+c)**2)**(1/2),x)","\int \frac{\tan{\left(c + d x \right)}}{\sqrt{a \sin^{2}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)/sqrt(a*sin(c + d*x)**2), x)","F",0
851,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a*cos(d*x+c)**2)**(1/2),x)","\int \frac{\cot{\left(c + d x \right)}}{\sqrt{a \cos^{2}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)/sqrt(a*cos(c + d*x)**2), x)","F",0
852,1,7,0,0.291981," ","integrate(x*cos(x**2)/sin(x**2)**(1/2),x)","\sqrt{\sin{\left(x^{2} \right)}}"," ",0,"sqrt(sin(x**2))","A",0
853,0,0,0,0.000000," ","integrate(cos(x)/(1-cos(2*x))**(1/2),x)","\int \frac{\cos{\left(x \right)}}{\sqrt{1 - \cos{\left(2 x \right)}}}\, dx"," ",0,"Integral(cos(x)/sqrt(1 - cos(2*x)), x)","F",0
854,1,476,0,20.215754," ","integrate(cos(ln(x))**2*sin(ln(x))**2/x,x)","\frac{\log{\left(x \right)} \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} + \frac{4 \log{\left(x \right)} \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} + \frac{6 \log{\left(x \right)} \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} + \frac{4 \log{\left(x \right)} \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} + \frac{\log{\left(x \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} + \frac{2 \tan^{7}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} - \frac{14 \tan^{5}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} + \frac{14 \tan^{3}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8} - \frac{2 \tan{\left(\frac{\log{\left(x \right)}}{2} \right)}}{8 \tan^{8}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{6}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 48 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 32 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 8}"," ",0,"log(x)*tan(log(x)/2)**8/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) + 4*log(x)*tan(log(x)/2)**6/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) + 6*log(x)*tan(log(x)/2)**4/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) + 4*log(x)*tan(log(x)/2)**2/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) + log(x)/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) + 2*tan(log(x)/2)**7/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) - 14*tan(log(x)/2)**5/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) + 14*tan(log(x)/2)**3/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8) - 2*tan(log(x)/2)/(8*tan(log(x)/2)**8 + 32*tan(log(x)/2)**6 + 48*tan(log(x)/2)**4 + 32*tan(log(x)/2)**2 + 8)","B",0
855,1,32,0,0.365618," ","integrate(sin(x)**3/(cos(x)**3+sin(x)**3),x)","\frac{x}{2} - \frac{\log{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{6} + \frac{\log{\left(\sin^{2}{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)} \right)}}{3}"," ",0,"x/2 - log(sin(x) + cos(x))/6 + log(sin(x)**2 - sin(x)*cos(x) + cos(x)**2)/3","A",0
856,1,32,0,0.369750," ","integrate(cos(x)**3/(cos(x)**3+sin(x)**3),x)","\frac{x}{2} + \frac{\log{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{6} - \frac{\log{\left(\sin^{2}{\left(x \right)} - \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)} \right)}}{3}"," ",0,"x/2 + log(sin(x) + cos(x))/6 - log(sin(x)**2 - sin(x)*cos(x) + cos(x)**2)/3","A",0
857,0,0,0,0.000000," ","integrate(sec(x)/(-5+cos(x)**2+4*sin(x)),x)","\int \frac{\sec{\left(x \right)}}{4 \sin{\left(x \right)} + \cos^{2}{\left(x \right)} - 5}\, dx"," ",0,"Integral(sec(x)/(4*sin(x) + cos(x)**2 - 5), x)","F",0
858,0,0,0,0.000000," ","integrate(1/cos(x)**(3/2)/(3*cos(x)+sin(x))**(1/2),x)","\int \frac{1}{\sqrt{\sin{\left(x \right)} + 3 \cos{\left(x \right)}} \cos^{\frac{3}{2}}{\left(x \right)}}\, dx"," ",0,"Integral(1/(sqrt(sin(x) + 3*cos(x))*cos(x)**(3/2)), x)","F",0
859,0,0,0,0.000000," ","integrate(csc(x)*(cos(x)+sin(x))**(1/2)/cos(x)**(3/2),x)","\int \frac{\sqrt{\sin{\left(x \right)} + \cos{\left(x \right)}} \csc{\left(x \right)}}{\cos^{\frac{3}{2}}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(sin(x) + cos(x))*csc(x)/cos(x)**(3/2), x)","F",0
860,0,0,0,0.000000," ","integrate((cos(x)+sin(x))/(1+sin(2*x))**(1/2),x)","\int \frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{\sqrt{\sin{\left(2 x \right)} + 1}}\, dx"," ",0,"Integral((sin(x) + cos(x))/sqrt(sin(2*x) + 1), x)","F",0
861,0,0,0,0.000000," ","integrate(sec(x)*(sec(x)+tan(x))**(1/2),x)","\int \sqrt{\tan{\left(x \right)} + \sec{\left(x \right)}} \sec{\left(x \right)}\, dx"," ",0,"Integral(sqrt(tan(x) + sec(x))*sec(x), x)","F",0
862,1,29,0,0.679367," ","integrate(sec(x)*(4+3*sec(x))**(1/2)*tan(x),x)","\frac{2 \sqrt{3 \sec{\left(x \right)} + 4} \sec{\left(x \right)}}{3} + \frac{8 \sqrt{3 \sec{\left(x \right)} + 4}}{9}"," ",0,"2*sqrt(3*sec(x) + 4)*sec(x)/3 + 8*sqrt(3*sec(x) + 4)/9","B",0
863,0,0,0,0.000000," ","integrate(sec(x)*(1+sec(x))**(1/2)*tan(x)**3,x)","\int \sqrt{\sec{\left(x \right)} + 1} \tan^{3}{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(sqrt(sec(x) + 1)*tan(x)**3*sec(x), x)","F",0
864,0,0,0,0.000000," ","integrate(cot(x)**3*csc(x)*(1+csc(x))**(1/2),x)","\int \sqrt{\csc{\left(x \right)} + 1} \cot^{3}{\left(x \right)} \csc{\left(x \right)}\, dx"," ",0,"Integral(sqrt(csc(x) + 1)*cot(x)**3*csc(x), x)","F",0
865,0,0,0,0.000000," ","integrate(csc(x)**(1/2)*(x*cos(x)-4*sec(x)*tan(x)),x)","\int \left(x \cos{\left(x \right)} - 4 \tan{\left(x \right)} \sec{\left(x \right)}\right) \sqrt{\csc{\left(x \right)}}\, dx"," ",0,"Integral((x*cos(x) - 4*tan(x)*sec(x))*sqrt(csc(x)), x)","F",0
866,-1,0,0,0.000000," ","integrate(cot(x)*(1-sin(x)**2)**3*(-1+csc(x)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate(cos(x)*(1-sin(x)**2)**3*(-1+csc(x)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)/(a*sec(x)**2)**(1/2),x)","\int \frac{x \csc{\left(x \right)} \sec{\left(x \right)}}{\sqrt{a \sec^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(x*csc(x)*sec(x)/sqrt(a*sec(x)**2), x)","F",0
869,0,0,0,0.000000," ","integrate(x**2*csc(x)*sec(x)/(a*sec(x)**2)**(1/2),x)","\int \frac{x^{2} \csc{\left(x \right)} \sec{\left(x \right)}}{\sqrt{a \sec^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(x**2*csc(x)*sec(x)/sqrt(a*sec(x)**2), x)","F",0
870,0,0,0,0.000000," ","integrate(x**3*csc(x)*sec(x)/(a*sec(x)**2)**(1/2),x)","\int \frac{x^{3} \csc{\left(x \right)} \sec{\left(x \right)}}{\sqrt{a \sec^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(x**3*csc(x)*sec(x)/sqrt(a*sec(x)**2), x)","F",0
871,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)/(a*sec(x)**4)**(1/2),x)","\int \frac{x \csc{\left(x \right)} \sec{\left(x \right)}}{\sqrt{a \sec^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(x*csc(x)*sec(x)/sqrt(a*sec(x)**4), x)","F",0
872,0,0,0,0.000000," ","integrate(x**2*csc(x)*sec(x)/(a*sec(x)**4)**(1/2),x)","\int \frac{x^{2} \csc{\left(x \right)} \sec{\left(x \right)}}{\sqrt{a \sec^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(x**2*csc(x)*sec(x)/sqrt(a*sec(x)**4), x)","F",0
873,0,0,0,0.000000," ","integrate(x**3*csc(x)*sec(x)/(a*sec(x)**4)**(1/2),x)","\int \frac{x^{3} \csc{\left(x \right)} \sec{\left(x \right)}}{\sqrt{a \sec^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(x**3*csc(x)*sec(x)/sqrt(a*sec(x)**4), x)","F",0
874,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)*(a*sec(x)**2)**(1/2),x)","\int x \sqrt{a \sec^{2}{\left(x \right)}} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x*sqrt(a*sec(x)**2)*csc(x)*sec(x), x)","F",0
875,0,0,0,0.000000," ","integrate(x**2*csc(x)*sec(x)*(a*sec(x)**2)**(1/2),x)","\int x^{2} \sqrt{a \sec^{2}{\left(x \right)}} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x**2*sqrt(a*sec(x)**2)*csc(x)*sec(x), x)","F",0
876,0,0,0,0.000000," ","integrate(x**3*csc(x)*sec(x)*(a*sec(x)**2)**(1/2),x)","\int x^{3} \sqrt{a \sec^{2}{\left(x \right)}} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x**3*sqrt(a*sec(x)**2)*csc(x)*sec(x), x)","F",0
877,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)*(a*sec(x)**4)**(1/2),x)","\int x \sqrt{a \sec^{4}{\left(x \right)}} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x*sqrt(a*sec(x)**4)*csc(x)*sec(x), x)","F",0
878,0,0,0,0.000000," ","integrate(x**2*csc(x)*sec(x)*(a*sec(x)**4)**(1/2),x)","\int x^{2} \sqrt{a \sec^{4}{\left(x \right)}} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x**2*sqrt(a*sec(x)**4)*csc(x)*sec(x), x)","F",0
879,0,0,0,0.000000," ","integrate(x**3*csc(x)*sec(x)*(a*sec(x)**4)**(1/2),x)","\int x^{3} \sqrt{a \sec^{4}{\left(x \right)}} \csc{\left(x \right)} \sec{\left(x \right)}\, dx"," ",0,"Integral(x**3*sqrt(a*sec(x)**4)*csc(x)*sec(x), x)","F",0
880,1,114,0,10.545719," ","integrate(sin(x)*sin(2*x)*sin(3*x),x)","\frac{x \sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{4} + \frac{x \sin{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)}}{4} - \frac{x \sin{\left(3 x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{4} - \frac{3 \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}}{8} + \frac{\sin{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{6} + \frac{\sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(x \right)}}{24}"," ",0,"x*sin(x)*sin(2*x)*sin(3*x)/4 + x*sin(x)*cos(2*x)*cos(3*x)/4 + x*sin(2*x)*cos(x)*cos(3*x)/4 - x*sin(3*x)*cos(x)*cos(2*x)/4 - 3*sin(x)*sin(2*x)*cos(3*x)/8 + sin(x)*sin(3*x)*cos(2*x)/6 + sin(2*x)*sin(3*x)*cos(x)/24","B",0
881,1,116,0,10.538799," ","integrate(cos(x)*cos(2*x)*cos(3*x),x)","- \frac{x \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{x \sin{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(x \right)}}{4} + \frac{x \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{3 \sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{8} + \frac{\sin{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{3} + \frac{5 \sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)}}{24}"," ",0,"-x*sin(x)*sin(2*x)*cos(3*x)/4 + x*sin(x)*sin(3*x)*cos(2*x)/4 + x*sin(2*x)*sin(3*x)*cos(x)/4 + x*cos(x)*cos(2*x)*cos(3*x)/4 + 3*sin(x)*sin(2*x)*sin(3*x)/8 + sin(x)*cos(2*x)*cos(3*x)/3 + 5*sin(2*x)*cos(x)*cos(3*x)/24","B",0
882,1,114,0,10.408518," ","integrate(cos(x)*sin(2*x)*sin(3*x),x)","- \frac{x \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{x \sin{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(x \right)}}{4} + \frac{x \cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{\sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{8} + \frac{\sin{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{6} - \frac{5 \sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)}}{24}"," ",0,"-x*sin(x)*sin(2*x)*cos(3*x)/4 + x*sin(x)*sin(3*x)*cos(2*x)/4 + x*sin(2*x)*sin(3*x)*cos(x)/4 + x*cos(x)*cos(2*x)*cos(3*x)/4 + sin(x)*sin(2*x)*sin(3*x)/8 + sin(x)*cos(2*x)*cos(3*x)/6 - 5*sin(2*x)*cos(x)*cos(3*x)/24","B",0
883,1,112,0,10.451667," ","integrate(cos(2*x)*cos(3*x)*sin(x),x)","\frac{x \sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{4} + \frac{x \sin{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \cos{\left(x \right)} \cos{\left(3 x \right)}}{4} - \frac{x \sin{\left(3 x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{4} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(3 x \right)}}{8} + \frac{\sin{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(2 x \right)}}{3} - \frac{\sin{\left(2 x \right)} \sin{\left(3 x \right)} \cos{\left(x \right)}}{24}"," ",0,"x*sin(x)*sin(2*x)*sin(3*x)/4 + x*sin(x)*cos(2*x)*cos(3*x)/4 + x*sin(2*x)*cos(x)*cos(3*x)/4 - x*sin(3*x)*cos(x)*cos(2*x)/4 - sin(x)*sin(2*x)*cos(3*x)/8 + sin(x)*sin(3*x)*cos(2*x)/3 - sin(2*x)*sin(3*x)*cos(x)/24","B",0
884,1,7,0,0.155237," ","integrate(x*sin(x**2),x)","- \frac{\cos{\left(x^{2} \right)}}{2}"," ",0,"-cos(x**2)/2","A",0
885,1,46,0,1.664340," ","integrate((-cos(x)+sin(x))*(cos(x)+sin(x))**5,x)","\frac{2 \sin^{6}{\left(x \right)}}{3} - \sin^{5}{\left(x \right)} \cos{\left(x \right)} - \frac{10 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \sin{\left(x \right)} \cos^{5}{\left(x \right)} + \frac{2 \cos^{6}{\left(x \right)}}{3}"," ",0,"2*sin(x)**6/3 - sin(x)**5*cos(x) - 10*sin(x)**3*cos(x)**3/3 - sin(x)*cos(x)**5 + 2*cos(x)**6/3","B",0
886,0,0,0,0.000000," ","integrate(2*x*sec(x)**2*tan(x),x)","2 \int x \tan{\left(x \right)} \sec^{2}{\left(x \right)}\, dx"," ",0,"2*Integral(x*tan(x)*sec(x)**2, x)","F",0
887,1,7,0,1.411173," ","integrate((1+cos(x)**2)/(1+cos(2*x)),x)","\frac{x}{2} + \frac{\tan{\left(x \right)}}{2}"," ",0,"x/2 + tan(x)/2","A",0
888,1,29,0,1.491584," ","integrate(sin(x)/(cos(x)**3-cos(x)**5),x)","\frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} - \log{\left(\cos{\left(x \right)} \right)} + \frac{1}{2 \cos^{2}{\left(x \right)}}"," ",0,"log(cos(x) - 1)/2 + log(cos(x) + 1)/2 - log(cos(x)) + 1/(2*cos(x)**2)","B",0
889,1,19,0,24.474347," ","integrate(sec(x)*(5-11*sec(x)**5)**2*tan(x),x)","11 \sec^{11}{\left(x \right)} - \frac{55 \sec^{6}{\left(x \right)}}{3} + 25 \sec{\left(x \right)}"," ",0,"11*sec(x)**11 - 55*sec(x)**6/3 + 25*sec(x)","A",0
890,1,51,0,0.111606," ","integrate(sin(5*x)**3*tan(5*x)**3,x)","\frac{\log{\left(\sin{\left(5 x \right)} - 1 \right)}}{4} - \frac{\log{\left(\sin{\left(5 x \right)} + 1 \right)}}{4} + \frac{\sin^{3}{\left(5 x \right)}}{15} + \frac{2 \sin{\left(5 x \right)}}{5} - \frac{\sin{\left(5 x \right)}}{5 \left(2 \sin^{2}{\left(5 x \right)} - 2\right)}"," ",0,"log(sin(5*x) - 1)/4 - log(sin(5*x) + 1)/4 + sin(5*x)**3/15 + 2*sin(5*x)/5 - sin(5*x)/(5*(2*sin(5*x)**2 - 2))","A",0
891,1,34,0,0.085723," ","integrate(sin(5*x)**3*tan(5*x)**4,x)","\frac{1 - 9 \cos^{2}{\left(5 x \right)}}{15 \cos^{3}{\left(5 x \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{15} - \frac{3 \cos{\left(5 x \right)}}{5}"," ",0,"(1 - 9*cos(5*x)**2)/(15*cos(5*x)**3) + cos(5*x)**3/15 - 3*cos(5*x)/5","A",0
892,1,61,0,0.109189," ","integrate(sin(6*x)**5*tan(6*x)**3,x)","\frac{7 \log{\left(\sin{\left(6 x \right)} - 1 \right)}}{24} - \frac{7 \log{\left(\sin{\left(6 x \right)} + 1 \right)}}{24} + \frac{\sin^{5}{\left(6 x \right)}}{30} + \frac{\sin^{3}{\left(6 x \right)}}{9} + \frac{\sin{\left(6 x \right)}}{2} - \frac{\sin{\left(6 x \right)}}{6 \left(2 \sin^{2}{\left(6 x \right)} - 2\right)}"," ",0,"7*log(sin(6*x) - 1)/24 - 7*log(sin(6*x) + 1)/24 + sin(6*x)**5/30 + sin(6*x)**3/9 + sin(6*x)/2 - sin(6*x)/(6*(2*sin(6*x)**2 - 2))","A",0
893,-1,0,0,0.000000," ","integrate((-1+sec(2*x)**2)**3*sin(2*x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,1,49,0,0.147376," ","integrate(sin(x)*tan(x)**5,x)","- \frac{- 9 \sin^{3}{\left(x \right)} + 7 \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} - \frac{15 \log{\left(\sin{\left(x \right)} - 1 \right)}}{16} + \frac{15 \log{\left(\sin{\left(x \right)} + 1 \right)}}{16} - \sin{\left(x \right)}"," ",0,"-(-9*sin(x)**3 + 7*sin(x))/(8*sin(x)**4 - 16*sin(x)**2 + 8) - 15*log(sin(x) - 1)/16 + 15*log(sin(x) + 1)/16 - sin(x)","A",0
895,1,42,0,0.089282," ","integrate(cos(2*x)**5*cot(2*x)**4,x)","\frac{12 \sin^{2}{\left(2 x \right)} - 1}{6 \sin^{3}{\left(2 x \right)}} + \frac{\sin^{5}{\left(2 x \right)}}{10} - \frac{2 \sin^{3}{\left(2 x \right)}}{3} + 3 \sin{\left(2 x \right)}"," ",0,"(12*sin(2*x)**2 - 1)/(6*sin(2*x)**3) + sin(2*x)**5/10 - 2*sin(2*x)**3/3 + 3*sin(2*x)","A",0
896,-1,0,0,0.000000," ","integrate(cos(3*x)*(-1+csc(3*x)**2)**3*(1-sin(3*x)**2)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate(cot(2*x)*(-1+csc(2*x)**2)**2*(1-sin(2*x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate(cos(2*x)*(-1+csc(2*x)**2)**4*(1-sin(2*x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate(cot(3*x)*(-1+csc(3*x)**2)**3*(1-sin(3*x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,1,44,0,5.196109," ","integrate((1+cot(9*x)**2)**2*(1+tan(9*x)**2)**3,x)","\frac{\tan^{5}{\left(9 x \right)}}{45} + \frac{4 \tan^{3}{\left(9 x \right)}}{27} + \frac{2 \tan{\left(9 x \right)}}{3} - \frac{4}{9 \tan{\left(9 x \right)}} - \frac{1}{27 \tan^{3}{\left(9 x \right)}}"," ",0,"tan(9*x)**5/45 + 4*tan(9*x)**3/27 + 2*tan(9*x)/3 - 4/(9*tan(9*x)) - 1/(27*tan(9*x)**3)","A",0
901,1,44,0,2.945508," ","integrate(cos(x)*(9-7*sin(x)**3)**2/(1-sin(x)**2),x)","- 2 \log{\left(\sin{\left(x \right)} - 1 \right)} + 128 \log{\left(\sin{\left(x \right)} + 1 \right)} - \frac{49 \sin^{5}{\left(x \right)}}{5} - \frac{49 \sin^{3}{\left(x \right)}}{3} + 63 \sin^{2}{\left(x \right)} - 49 \sin{\left(x \right)}"," ",0,"-2*log(sin(x) - 1) + 128*log(sin(x) + 1) - 49*sin(x)**5/5 - 49*sin(x)**3/3 + 63*sin(x)**2 - 49*sin(x)","A",0
902,1,41,0,0.104769," ","integrate(cos(2*x)**4*cot(2*x)**5,x)","\frac{8 \sin^{2}{\left(2 x \right)} - 1}{8 \sin^{4}{\left(2 x \right)}} + 3 \log{\left(\sin{\left(2 x \right)} \right)} + \frac{\sin^{4}{\left(2 x \right)}}{8} - \sin^{2}{\left(2 x \right)}"," ",0,"(8*sin(2*x)**2 - 1)/(8*sin(2*x)**4) + 3*log(sin(2*x)) + sin(2*x)**4/8 - sin(2*x)**2","A",0
903,0,0,0,0.000000," ","integrate(sec(x)*tan(x)**2/(4+3*sec(x)),x)","\int \frac{\tan^{2}{\left(x \right)} \sec{\left(x \right)}}{3 \sec{\left(x \right)} + 4}\, dx"," ",0,"Integral(tan(x)**2*sec(x)/(3*sec(x) + 4), x)","F",0
904,0,0,0,0.000000," ","integrate(x*sec(1+x)*tan(1+x),x)","\int x \tan{\left(x + 1 \right)} \sec{\left(x + 1 \right)}\, dx"," ",0,"Integral(x*tan(x + 1)*sec(x + 1), x)","F",0
905,1,12,0,1.427814," ","integrate(sin(2*x)/(9-sin(x)**2)**(1/2),x)","- 2 \sqrt{9 - \sin^{2}{\left(x \right)}}"," ",0,"-2*sqrt(9 - sin(x)**2)","A",0
906,-1,0,0,0.000000," ","integrate(sin(2*x)/(9-cos(x)**4)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,1,32,0,3.680815," ","integrate(cos(1/x)/x**5,x)","6 \cos{\left(\frac{1}{x} \right)} + \frac{6 \sin{\left(\frac{1}{x} \right)}}{x} - \frac{3 \cos{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\sin{\left(\frac{1}{x} \right)}}{x^{3}}"," ",0,"6*cos(1/x) + 6*sin(1/x)/x - 3*cos(1/x)/x**2 - sin(1/x)/x**3","A",0
908,1,24,0,1.779565," ","integrate(cos(1+x)**3*sin(1+x)**3,x)","- \frac{\sin^{2}{\left(x + 1 \right)} \cos^{4}{\left(x + 1 \right)}}{4} - \frac{\cos^{6}{\left(x + 1 \right)}}{12}"," ",0,"-sin(x + 1)**2*cos(x + 1)**4/4 - cos(x + 1)**6/12","A",0
909,1,189,0,1.298069," ","integrate((1+2*x)**3*sin(1+2*x)**2,x)","x^{4} \sin^{2}{\left(2 x + 1 \right)} + x^{4} \cos^{2}{\left(2 x + 1 \right)} + 2 x^{3} \sin^{2}{\left(2 x + 1 \right)} - 2 x^{3} \sin{\left(2 x + 1 \right)} \cos{\left(2 x + 1 \right)} + 2 x^{3} \cos^{2}{\left(2 x + 1 \right)} + \frac{9 x^{2} \sin^{2}{\left(2 x + 1 \right)}}{4} - 3 x^{2} \sin{\left(2 x + 1 \right)} \cos{\left(2 x + 1 \right)} + \frac{3 x^{2} \cos^{2}{\left(2 x + 1 \right)}}{4} + \frac{5 x \sin^{2}{\left(2 x + 1 \right)}}{4} - \frac{3 x \sin{\left(2 x + 1 \right)} \cos{\left(2 x + 1 \right)}}{4} - \frac{x \cos^{2}{\left(2 x + 1 \right)}}{4} + \frac{3 \sin^{2}{\left(2 x + 1 \right)}}{16} + \frac{\sin{\left(2 x + 1 \right)} \cos{\left(2 x + 1 \right)}}{8}"," ",0,"x**4*sin(2*x + 1)**2 + x**4*cos(2*x + 1)**2 + 2*x**3*sin(2*x + 1)**2 - 2*x**3*sin(2*x + 1)*cos(2*x + 1) + 2*x**3*cos(2*x + 1)**2 + 9*x**2*sin(2*x + 1)**2/4 - 3*x**2*sin(2*x + 1)*cos(2*x + 1) + 3*x**2*cos(2*x + 1)**2/4 + 5*x*sin(2*x + 1)**2/4 - 3*x*sin(2*x + 1)*cos(2*x + 1)/4 - x*cos(2*x + 1)**2/4 + 3*sin(2*x + 1)**2/16 + sin(2*x + 1)*cos(2*x + 1)/8","B",0
910,0,0,0,0.000000," ","integrate((-1+sec(x))/(1-tan(x)),x)","- \int \frac{\sec{\left(x \right)}}{\tan{\left(x \right)} - 1}\, dx - \int \left(- \frac{1}{\tan{\left(x \right)} - 1}\right)\, dx"," ",0,"-Integral(sec(x)/(tan(x) - 1), x) - Integral(-1/(tan(x) - 1), x)","F",0
911,1,90,0,6.018548," ","integrate(x**2*cos(3*x)*cos(5*x),x)","- \frac{3 x^{2} \sin{\left(3 x \right)} \cos{\left(5 x \right)}}{16} + \frac{5 x^{2} \sin{\left(5 x \right)} \cos{\left(3 x \right)}}{16} + \frac{15 x \sin{\left(3 x \right)} \sin{\left(5 x \right)}}{64} + \frac{17 x \cos{\left(3 x \right)} \cos{\left(5 x \right)}}{64} + \frac{63 \sin{\left(3 x \right)} \cos{\left(5 x \right)}}{512} - \frac{65 \sin{\left(5 x \right)} \cos{\left(3 x \right)}}{512}"," ",0,"-3*x**2*sin(3*x)*cos(5*x)/16 + 5*x**2*sin(5*x)*cos(3*x)/16 + 15*x*sin(3*x)*sin(5*x)/64 + 17*x*cos(3*x)*cos(5*x)/64 + 63*sin(3*x)*cos(5*x)/512 - 65*sin(5*x)*cos(3*x)/512","A",0
912,0,0,0,0.000000," ","integrate((cos(x)+sin(x))/cos(x)**(1/2)/sin(x)**(1/2),x)","\int \frac{\sin{\left(x \right)} + \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}} \sqrt{\cos{\left(x \right)}}}\, dx"," ",0,"Integral((sin(x) + cos(x))/(sqrt(sin(x))*sqrt(cos(x))), x)","F",0
913,1,7,0,2.183773," ","integrate(sec(x)**2*(1+sin(x)),x)","\tan{\left(x \right)} + \frac{1}{\cos{\left(x \right)}}"," ",0,"tan(x) + 1/cos(x)","A",0
914,0,0,0,0.000000," ","integrate(10*x**9*cos(x**5*ln(x))-x**10*(x**4+5*x**4*ln(x))*sin(x**5*ln(x)),x)","- \int \left(- 10 x^{9} \cos{\left(x^{5} \log{\left(x \right)} \right)}\right)\, dx - \int x^{14} \sin{\left(x^{5} \log{\left(x \right)} \right)}\, dx - \int 5 x^{14} \log{\left(x \right)} \sin{\left(x^{5} \log{\left(x \right)} \right)}\, dx"," ",0,"-Integral(-10*x**9*cos(x**5*log(x)), x) - Integral(x**14*sin(x**5*log(x)), x) - Integral(5*x**14*log(x)*sin(x**5*log(x)), x)","F",0
915,0,0,0,0.000000," ","integrate(cos(1/2*x)**2*tan(1/4*pi+1/2*x),x)","\int \cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}\, dx"," ",0,"Integral(cos(x/2)**2*tan(x/2 + pi/4), x)","F",0
916,1,100,0,1.217984," ","integrate((2+3*x)**2*sin(x)**3,x)","- 9 x^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 6 x^{2} \cos^{3}{\left(x \right)} + 14 x \sin^{3}{\left(x \right)} - 12 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 12 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} - 8 x \cos^{3}{\left(x \right)} + \frac{28 \sin^{3}{\left(x \right)}}{3} + 10 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 8 \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{32 \cos^{3}{\left(x \right)}}{3}"," ",0,"-9*x**2*sin(x)**2*cos(x) - 6*x**2*cos(x)**3 + 14*x*sin(x)**3 - 12*x*sin(x)**2*cos(x) + 12*x*sin(x)*cos(x)**2 - 8*x*cos(x)**3 + 28*sin(x)**3/3 + 10*sin(x)**2*cos(x) + 8*sin(x)*cos(x)**2 + 32*cos(x)**3/3","A",0
917,0,0,0,0.000000," ","integrate(sec(x)**(1+m)*sin(x),x)","\int \sin{\left(x \right)} \sec^{m + 1}{\left(x \right)}\, dx"," ",0,"Integral(sin(x)*sec(x)**(m + 1), x)","F",0
918,0,0,0,0.000000," ","integrate(cos(b*x+a)**n*sin(b*x+a)**(-2-n),x)","\int \sin^{- n - 2}{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**(-n - 2)*cos(a + b*x)**n, x)","F",0
919,0,0,0,0.000000," ","integrate(1/(sec(x)+sin(x)*tan(x)),x)","\int \frac{1}{\sin{\left(x \right)} \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(1/(sin(x)*tan(x) + sec(x)), x)","F",0
920,1,39,0,0.325361," ","integrate((c*x**2+b*x+a)*sin(x),x)","- a \cos{\left(x \right)} - b x \cos{\left(x \right)} + b \sin{\left(x \right)} - c x^{2} \cos{\left(x \right)} + 2 c x \sin{\left(x \right)} + 2 c \cos{\left(x \right)}"," ",0,"-a*cos(x) - b*x*cos(x) + b*sin(x) - c*x**2*cos(x) + 2*c*x*sin(x) + 2*c*cos(x)","A",0
921,1,5,0,0.638403," ","integrate(sin(x**5)/x,x)","\frac{\operatorname{Si}{\left(x^{5} \right)}}{5}"," ",0,"Si(x**5)/5","A",0
922,0,0,0,0.000000," ","integrate(sin(2**x)/(1+2**x),x)","\int \frac{\sin{\left(2^{x} \right)}}{2^{x} + 1}\, dx"," ",0,"Integral(sin(2**x)/(2**x + 1), x)","F",0
923,1,10,0,84.149098," ","integrate(x*cos(2*x**2)*sin(2*x**2)**(3/4),x)","\frac{\sin^{\frac{7}{4}}{\left(2 x^{2} \right)}}{7}"," ",0,"sin(2*x**2)**(7/4)/7","A",0
924,1,7,0,1.036820," ","integrate(x*sec(x**2)**2*tan(x**2)**2,x)","\frac{\tan^{3}{\left(x^{2} \right)}}{6}"," ",0,"tan(x**2)**3/6","A",0
925,1,27,0,20.859688," ","integrate(x**2*cos(b*x**3+a)**7*sin(b*x**3+a),x)","\begin{cases} - \frac{\cos^{8}{\left(a + b x^{3} \right)}}{24 b} & \text{for}\: b \neq 0 \\\frac{x^{3} \sin{\left(a \right)} \cos^{7}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-cos(a + b*x**3)**8/(24*b), Ne(b, 0)), (x**3*sin(a)*cos(a)**7/3, True))","A",0
926,1,241,0,74.973900," ","integrate(x**5*cos(b*x**3+a)**7*sin(b*x**3+a),x)","\begin{cases} \frac{35 x^{3} \sin^{8}{\left(a + b x^{3} \right)}}{3072 b} + \frac{35 x^{3} \sin^{6}{\left(a + b x^{3} \right)} \cos^{2}{\left(a + b x^{3} \right)}}{768 b} + \frac{35 x^{3} \sin^{4}{\left(a + b x^{3} \right)} \cos^{4}{\left(a + b x^{3} \right)}}{512 b} + \frac{35 x^{3} \sin^{2}{\left(a + b x^{3} \right)} \cos^{6}{\left(a + b x^{3} \right)}}{768 b} - \frac{31 x^{3} \cos^{8}{\left(a + b x^{3} \right)}}{1024 b} + \frac{35 \sin^{7}{\left(a + b x^{3} \right)} \cos{\left(a + b x^{3} \right)}}{3072 b^{2}} + \frac{385 \sin^{5}{\left(a + b x^{3} \right)} \cos^{3}{\left(a + b x^{3} \right)}}{9216 b^{2}} + \frac{511 \sin^{3}{\left(a + b x^{3} \right)} \cos^{5}{\left(a + b x^{3} \right)}}{9216 b^{2}} + \frac{31 \sin{\left(a + b x^{3} \right)} \cos^{7}{\left(a + b x^{3} \right)}}{1024 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{6} \sin{\left(a \right)} \cos^{7}{\left(a \right)}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*x**3*sin(a + b*x**3)**8/(3072*b) + 35*x**3*sin(a + b*x**3)**6*cos(a + b*x**3)**2/(768*b) + 35*x**3*sin(a + b*x**3)**4*cos(a + b*x**3)**4/(512*b) + 35*x**3*sin(a + b*x**3)**2*cos(a + b*x**3)**6/(768*b) - 31*x**3*cos(a + b*x**3)**8/(1024*b) + 35*sin(a + b*x**3)**7*cos(a + b*x**3)/(3072*b**2) + 385*sin(a + b*x**3)**5*cos(a + b*x**3)**3/(9216*b**2) + 511*sin(a + b*x**3)**3*cos(a + b*x**3)**5/(9216*b**2) + 31*sin(a + b*x**3)*cos(a + b*x**3)**7/(1024*b**2), Ne(b, 0)), (x**6*sin(a)*cos(a)**7/6, True))","A",0
927,0,0,0,0.000000," ","integrate(x**5*sec(b*x**3+a)**7*tan(b*x**3+a),x)","\int x^{5} \tan{\left(a + b x^{3} \right)} \sec^{7}{\left(a + b x^{3} \right)}\, dx"," ",0,"Integral(x**5*tan(a + b*x**3)*sec(a + b*x**3)**7, x)","F",0
928,0,0,0,0.000000," ","integrate(sec(1/x)**2/x**2,x)","\int \frac{\sec^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\, dx"," ",0,"Integral(sec(1/x)**2/x**2, x)","F",0
929,1,3,0,0.266598," ","integrate(3*x**2*cos(x**3),x)","\sin{\left(x^{3} \right)}"," ",0,"sin(x**3)","A",0
930,0,0,0,0.000000," ","integrate((1+2*x)*sec(1+2*x)**2,x)","\int \left(2 x + 1\right) \sec^{2}{\left(2 x + 1 \right)}\, dx"," ",0,"Integral((2*x + 1)*sec(2*x + 1)**2, x)","F",0
931,0,0,0,0.000000," ","integrate(x**4/b/(x**3+3*sin(b*x+a))**(1/2)+x**2*cos(b*x+a)/(x**3+3*sin(b*x+a))**(1/2)+4/3*x*(x**3+3*sin(b*x+a))**(1/2)/b,x)","\frac{\int \frac{7 x^{4}}{\sqrt{x^{3} + 3 \sin{\left(a + b x \right)}}}\, dx + \int \frac{12 x \sin{\left(a + b x \right)}}{\sqrt{x^{3} + 3 \sin{\left(a + b x \right)}}}\, dx + \int \frac{3 b x^{2} \cos{\left(a + b x \right)}}{\sqrt{x^{3} + 3 \sin{\left(a + b x \right)}}}\, dx}{3 b}"," ",0,"(Integral(7*x**4/sqrt(x**3 + 3*sin(a + b*x)), x) + Integral(12*x*sin(a + b*x)/sqrt(x**3 + 3*sin(a + b*x)), x) + Integral(3*b*x**2*cos(a + b*x)/sqrt(x**3 + 3*sin(a + b*x)), x))/(3*b)","F",0
932,0,0,0,0.000000," ","integrate(x**2*cos(b*x+a)/(x**3+3*sin(b*x+a))**(1/2),x)","\int \frac{x^{2} \cos{\left(a + b x \right)}}{\sqrt{x^{3} + 3 \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(x**2*cos(a + b*x)/sqrt(x**3 + 3*sin(a + b*x)), x)","F",0
933,1,10,0,0.292226," ","integrate((cos(x)+sin(x))/(exp(-x)+sin(x)),x)","x + \log{\left(\sin{\left(x \right)} + e^{- x} \right)}"," ",0,"x + log(sin(x) + exp(-x))","A",0
934,1,150,0,0.970268," ","integrate(sin(d*x+c)*(a*sin(d*x+c)**2+b*sin(d*x+c)**3),x)","\begin{cases} - \frac{a \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 a \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{3 b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b x \cos^{4}{\left(c + d x \right)}}{8} - \frac{5 b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \sin^{2}{\left(c \right)} + b \sin^{3}{\left(c \right)}\right) \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sin(c + d*x)**2*cos(c + d*x)/d - 2*a*cos(c + d*x)**3/(3*d) + 3*b*x*sin(c + d*x)**4/8 + 3*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b*x*cos(c + d*x)**4/8 - 5*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*sin(c)**2 + b*sin(c)**3)*sin(c), True))","A",0
935,1,326,0,6.008342," ","integrate(sin(d*x+c)*(a*sin(d*x+c)**2+b*sin(d*x+c)**3)**2,x)","\begin{cases} - \frac{a^{2} \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{4 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{8 a^{2} \cos^{5}{\left(c + d x \right)}}{15 d} + \frac{5 a b x \sin^{6}{\left(c + d x \right)}}{8} + \frac{15 a b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{15 a b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 a b x \cos^{6}{\left(c + d x \right)}}{8} - \frac{11 a b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{5 a b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{5 a b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{b^{2} \sin^{6}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 b^{2} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{8 b^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{16 b^{2} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin^{2}{\left(c \right)} + b \sin^{3}{\left(c \right)}\right)^{2} \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(c + d*x)**4*cos(c + d*x)/d - 4*a**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 8*a**2*cos(c + d*x)**5/(15*d) + 5*a*b*x*sin(c + d*x)**6/8 + 15*a*b*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 15*a*b*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 5*a*b*x*cos(c + d*x)**6/8 - 11*a*b*sin(c + d*x)**5*cos(c + d*x)/(8*d) - 5*a*b*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - 5*a*b*sin(c + d*x)*cos(c + d*x)**5/(8*d) - b**2*sin(c + d*x)**6*cos(c + d*x)/d - 2*b**2*sin(c + d*x)**4*cos(c + d*x)**3/d - 8*b**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 16*b**2*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c)**2 + b*sin(c)**3)**2*sin(c), True))","A",0
936,1,201,0,1.033528," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)**2+c*sin(d*x+c)**3),x)","\begin{cases} \frac{a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a x \cos^{2}{\left(c + d x \right)}}{2} - \frac{a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{b \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 b \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{3 c x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 c x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 c x \cos^{4}{\left(c + d x \right)}}{8} - \frac{5 c \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 c \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + b \sin^{2}{\left(c \right)} + c \sin^{3}{\left(c \right)}\right) \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**2/2 + a*x*cos(c + d*x)**2/2 - a*sin(c + d*x)*cos(c + d*x)/(2*d) - b*sin(c + d*x)**2*cos(c + d*x)/d - 2*b*cos(c + d*x)**3/(3*d) + 3*c*x*sin(c + d*x)**4/8 + 3*c*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*c*x*cos(c + d*x)**4/8 - 5*c*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*c*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*sin(c) + b*sin(c)**2 + c*sin(c)**3)*sin(c), True))","A",0
937,1,541,0,6.813271," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)**2+c*sin(d*x+c)**3)**2,x)","\begin{cases} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 a^{2} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{3 a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a b x \cos^{4}{\left(c + d x \right)}}{4} - \frac{5 a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{3 a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} - \frac{2 a c \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{8 a c \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{16 a c \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{b^{2} \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{4 b^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{8 b^{2} \cos^{5}{\left(c + d x \right)}}{15 d} + \frac{5 b c x \sin^{6}{\left(c + d x \right)}}{8} + \frac{15 b c x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{15 b c x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 b c x \cos^{6}{\left(c + d x \right)}}{8} - \frac{11 b c \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{5 b c \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{5 b c \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{c^{2} \sin^{6}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 c^{2} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{8 c^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{16 c^{2} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + b \sin^{2}{\left(c \right)} + c \sin^{3}{\left(c \right)}\right)^{2} \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(c + d*x)**2*cos(c + d*x)/d - 2*a**2*cos(c + d*x)**3/(3*d) + 3*a*b*x*sin(c + d*x)**4/4 + 3*a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*a*b*x*cos(c + d*x)**4/4 - 5*a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) - 3*a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) - 2*a*c*sin(c + d*x)**4*cos(c + d*x)/d - 8*a*c*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 16*a*c*cos(c + d*x)**5/(15*d) - b**2*sin(c + d*x)**4*cos(c + d*x)/d - 4*b**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 8*b**2*cos(c + d*x)**5/(15*d) + 5*b*c*x*sin(c + d*x)**6/8 + 15*b*c*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 15*b*c*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 5*b*c*x*cos(c + d*x)**6/8 - 11*b*c*sin(c + d*x)**5*cos(c + d*x)/(8*d) - 5*b*c*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - 5*b*c*sin(c + d*x)*cos(c + d*x)**5/(8*d) - c**2*sin(c + d*x)**6*cos(c + d*x)/d - 2*c**2*sin(c + d*x)**4*cos(c + d*x)**3/d - 8*c**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 16*c**2*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + b*sin(c)**2 + c*sin(c)**3)**2*sin(c), True))","A",0
938,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)**(1/2)),x)","\int \left(a \sqrt{\sin{\left(c + d x \right)}} + b + c \sin^{\frac{3}{2}}{\left(c + d x \right)}\right) \sqrt{\sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*sqrt(sin(c + d*x)) + b + c*sin(c + d*x)**(3/2))*sqrt(sin(c + d*x)), x)","F",0
939,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)**(1/2))**2,x)","\int \left(a + \frac{b}{\sqrt{\sin{\left(c + d x \right)}}} + c \sin{\left(c + d x \right)}\right)^{2} \sin{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b/sqrt(sin(c + d*x)) + c*sin(c + d*x))**2*sin(c + d*x), x)","F",0
940,1,107,0,6.707625," ","integrate(f**(b*x+a)*(cos(d*x+c)+I*sin(d*x+c))**n,x)","\begin{cases} \frac{f^{a} f^{b x} \left(i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)^{n}}{b \log{\left(f \right)} + i d n} & \text{for}\: b \neq - \frac{i d n}{\log{\left(f \right)}} \\f^{a} x \left(i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)^{n} e^{- i d n x} - \frac{i f^{a} \left(i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)^{n} e^{- i d n x}}{d n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f**a*f**(b*x)*(I*sin(c + d*x) + cos(c + d*x))**n/(b*log(f) + I*d*n), Ne(b, -I*d*n/log(f))), (f**a*x*(I*sin(c + d*x) + cos(c + d*x))**n*exp(-I*d*n*x) - I*f**a*(I*sin(c + d*x) + cos(c + d*x))**n*exp(-I*d*n*x)/(d*n), True))","A",0
941,1,107,0,6.664774," ","integrate(f**(b*x+a)*(cos(d*x+c)-I*sin(d*x+c))**n,x)","\begin{cases} - \frac{f^{a} f^{b x} \left(- i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)^{n}}{- b \log{\left(f \right)} + i d n} & \text{for}\: b \neq \frac{i d n}{\log{\left(f \right)}} \\f^{a} x \left(- i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)^{n} e^{i d n x} + \frac{i f^{a} \left(- i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)^{n} e^{i d n x}}{d n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-f**a*f**(b*x)*(-I*sin(c + d*x) + cos(c + d*x))**n/(-b*log(f) + I*d*n), Ne(b, I*d*n/log(f))), (f**a*x*(-I*sin(c + d*x) + cos(c + d*x))**n*exp(I*d*n*x) + I*f**a*(-I*sin(c + d*x) + cos(c + d*x))**n*exp(I*d*n*x)/(d*n), True))","A",0
942,-1,0,0,0.000000," ","integrate((cos(b*x+a)**5-sin(b*x+a)**5)/(cos(b*x+a)**5+sin(b*x+a)**5),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
943,1,122,0,5.594284," ","integrate((cos(b*x+a)**4-sin(b*x+a)**4)/(cos(b*x+a)**4+sin(b*x+a)**4),x)","\begin{cases} - \frac{\sqrt{2} \log{\left(4 \sin^{2}{\left(a + b x \right)} - 4 \sqrt{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} + 4 \cos^{2}{\left(a + b x \right)} \right)}}{4 b} + \frac{\sqrt{2} \log{\left(4 \sin^{2}{\left(a + b x \right)} + 4 \sqrt{2} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} + 4 \cos^{2}{\left(a + b x \right)} \right)}}{4 b} & \text{for}\: b \neq 0 \\\frac{x \left(- \sin^{4}{\left(a \right)} + \cos^{4}{\left(a \right)}\right)}{\sin^{4}{\left(a \right)} + \cos^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(2)*log(4*sin(a + b*x)**2 - 4*sqrt(2)*sin(a + b*x)*cos(a + b*x) + 4*cos(a + b*x)**2)/(4*b) + sqrt(2)*log(4*sin(a + b*x)**2 + 4*sqrt(2)*sin(a + b*x)*cos(a + b*x) + 4*cos(a + b*x)**2)/(4*b), Ne(b, 0)), (x*(-sin(a)**4 + cos(a)**4)/(sin(a)**4 + cos(a)**4), True))","A",0
944,1,76,0,1.023059," ","integrate((cos(b*x+a)**3-sin(b*x+a)**3)/(cos(b*x+a)**3+sin(b*x+a)**3),x)","\begin{cases} \frac{\log{\left(\sin{\left(a + b x \right)} + \cos{\left(a + b x \right)} \right)}}{3 b} - \frac{2 \log{\left(\sin^{2}{\left(a + b x \right)} - \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} + \cos^{2}{\left(a + b x \right)} \right)}}{3 b} & \text{for}\: b \neq 0 \\\frac{x \left(- \sin^{3}{\left(a \right)} + \cos^{3}{\left(a \right)}\right)}{\sin^{3}{\left(a \right)} + \cos^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(a + b*x) + cos(a + b*x))/(3*b) - 2*log(sin(a + b*x)**2 - sin(a + b*x)*cos(a + b*x) + cos(a + b*x)**2)/(3*b), Ne(b, 0)), (x*(-sin(a)**3 + cos(a)**3)/(sin(a)**3 + cos(a)**3), True))","A",0
945,1,32,0,0.254975," ","integrate((cos(b*x+a)**2-sin(b*x+a)**2)/(cos(b*x+a)**2+sin(b*x+a)**2),x)","\frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b \sin^{2}{\left(a + b x \right)} + b \cos^{2}{\left(a + b x \right)}}"," ",0,"sin(a + b*x)*cos(a + b*x)/(b*sin(a + b*x)**2 + b*cos(a + b*x)**2)","B",0
946,1,31,0,0.390794," ","integrate((cos(b*x+a)-sin(b*x+a))/(cos(b*x+a)+sin(b*x+a)),x)","\begin{cases} \frac{\log{\left(\sin{\left(a + b x \right)} + \cos{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x \left(- \sin{\left(a \right)} + \cos{\left(a \right)}\right)}{\sin{\left(a \right)} + \cos{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(a + b*x) + cos(a + b*x))/b, Ne(b, 0)), (x*(-sin(a) + cos(a))/(sin(a) + cos(a)), True))","A",0
947,0,0,0,0.000000," ","integrate((-csc(b*x+a)+sec(b*x+a))/(csc(b*x+a)+sec(b*x+a)),x)","- \int \frac{\csc{\left(a + b x \right)}}{\csc{\left(a + b x \right)} + \sec{\left(a + b x \right)}}\, dx - \int \left(- \frac{\sec{\left(a + b x \right)}}{\csc{\left(a + b x \right)} + \sec{\left(a + b x \right)}}\right)\, dx"," ",0,"-Integral(csc(a + b*x)/(csc(a + b*x) + sec(a + b*x)), x) - Integral(-sec(a + b*x)/(csc(a + b*x) + sec(a + b*x)), x)","F",0
948,0,0,0,0.000000," ","integrate((-csc(b*x+a)**2+sec(b*x+a)**2)/(csc(b*x+a)**2+sec(b*x+a)**2),x)","- \int \frac{\csc^{2}{\left(a + b x \right)}}{\csc^{2}{\left(a + b x \right)} + \sec^{2}{\left(a + b x \right)}}\, dx - \int \left(- \frac{\sec^{2}{\left(a + b x \right)}}{\csc^{2}{\left(a + b x \right)} + \sec^{2}{\left(a + b x \right)}}\right)\, dx"," ",0,"-Integral(csc(a + b*x)**2/(csc(a + b*x)**2 + sec(a + b*x)**2), x) - Integral(-sec(a + b*x)**2/(csc(a + b*x)**2 + sec(a + b*x)**2), x)","F",0
949,-1,0,0,0.000000," ","integrate((-csc(b*x+a)**3+sec(b*x+a)**3)/(csc(b*x+a)**3+sec(b*x+a)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
950,-1,0,0,0.000000," ","integrate((-csc(b*x+a)**4+sec(b*x+a)**4)/(csc(b*x+a)**4+sec(b*x+a)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
